Compressed Liquid Regions Research Articles

Data-Driven Modeling of General Fluid Density Under Subcritical and Supercritical Conditions

Advanced propulsion and power-generation systems often operate under extreme conditions, where thermophysical properties of the working fluids undergo complex variations in a wide range of fluid states, where empirical cubic equations of state could yield substantial errors in density prediction. The present work develops data-driven models for accurate density estimation of general fluids across all thermodynamic regimes. The model starts with the cubic equation of state, whose alpha function is calibrated in a data-driven manner with statistical correction accounting for inherent correlations among training data samples. The developed models are examined for the representative pure substances in aerospace propulsion systems, including oxygen, nitrogen, carbon dioxide, and hydrocarbon fuels. Results show that the model with pressure and temperature as input variables provides consistently superior accuracy over wide ranges of temperatures and pressures, especially in the compressed-liquid region, where the Peng–Robinson equation of state significantly underperforms. The corresponding absolute average relative deviation for the studied substances is below 0.65% at different pressures, compared to 7.16% by the Peng–Robinson equation of state. The model is also extended to examine the density calculations of the selected binary and ternary mixtures, and the consistent result is obtained. The data-driven approach can be adopted to evaluate other thermodynamic properties of fluids and fluid mixtures and characteristics of vapor–liquid equilibrium, and further incorporated into large-scale multiphysics simulations where nonideal gas behavior occurs in the future.

An apparatus proposed for density measurements in compressed liquid regions at the pressures 0.1-60 MPa and the temperatures 288.15-413.15 K

In this work an apparatus for density measurements in the compressed liquid regions was presented. This installation is based on the use of the DMA HP density measuring cell and the DMA 5000 densimeter (both instruments are products of Anton Paar, Gratz, Austria). Calibration of DMA HP cell was performed by applying the classical method where a vacuum, water and n-decane were recommended to be used as calibration fluids. To test the capabilities of the set-up, the densities of n-hexane, toluene and dichloromethane were measured in the temperature interval 288.15 to 413.15 K and the pressure range 0.1-60 MPa. The obtained results were compared with the corresponding values found in the literature. Depending on the literature selected for comparison (the temperature and pressure ranges available) the average absolute percentage deviations were: for n-hexane 0.03-0.10%; for toluene 0.04-0.08% and for dichloromethane 0.02-0.03%. A deeper insight into the results of this work shows that most of them are in a good agreement with the literature values; higher discrepancies are remarked in the vicinity of the ends of the temperature and pressure ranges.

Density measurements for 2,3,3,3-tetrafluoroprop-1-ene (R1234yf) and trans-1,3,3,3-tetrafluoropropene (R1234ze(E))

2,3,3,3-Tetrafluoroprop-1-ene (R1234yf) and trans-1,3,3,3-tetrafluoropropene (R1234ze(E)) are fluorinated hydrocarbon that has been recently proposed to replace R134a in automotive air-conditioning and other applications. In this work, the densities of 2,3,3,3-tetrafluoroprop-1-ene (R1234yf) and trans-1,3,3,3-tetrafluoropropene (R1234ze(E)) were measured in compressed liquid region, using a vibrating tube densimeter. A total of 128 experimental data for R1234yf and 131 experimental data for R1234ze(E) along nine isotherms between (283 and 363)K with pressures up to 100MPa were obtained. The uncertainty for each measurement was estimated, and the maximum expanded uncertainty with a level of confidence of 0.95 (k=2) of R1234yf and R1234ze(E) are 0.33% and 0.23%, respectively.

An Equation of State for Fluoroethane (R161)

Fluoroethane (R161, C2H5F, 353-36-6) is a potential alternative refrigerant with excellent cycle performance, with zero ozone-depletion potential and low global warming potential. In this study, the thermodynamic property formulation for fluoroethane has been developed with the use of available experimental thermodynamic property data. In determining the equation of state, multiproperty fitting methods were used including single-phase pressure–density–temperature (pρT), vapor pressure, and saturated liquid-density data. The equation of state has been developed to conform to the Maxwell criterion for two-phase liquid–vapor equilibrium states, and is valid for temperatures from 130 K to 450 K, and pressures to 5 MPa. The extrapolation behavior of the equation of state at high temperatures and high pressures is reasonable. As there are very few compressed liquid-density experimental data published, the uncertainties in density of the equation of state are estimated to be 2.0 % in the compressed-liquid region and 0.5 % in the gas and supercritical regions. Uncertainties in vapor pressure are 0.5 % above 200 K and increase at lower temperatures. The uncertainties for all properties are higher in the critical region, except vapor pressure. Detailed comparisons between experimental and calculated data have been performed in this study.

Performance assessment of Tao–Mason equation of state: Results for vapor–liquid equilibrium properties

The present work evaluates the performance of a molecular-based equation of state in predicting thermodynamic properties of several fluids in a very wide range of temperatures encompassing 100 K < T < 1100 K and pressures ranging from zero to 3200 bar. The theoretical equation of state (EOS) is that of Tao–Mason (TM) which is based on statistical mechanical perturbation theory. The 21 fluids including: argon (Ar), krypton (Kr), xenon (Xe), nitrogen (N 2), oxygen (O 2), carbon dioxide (CO 2), methane (CH 4), ethane (C 2H 6), propane (C 3H 8), normal butane (n-C 4H 10), isobutene (i-C 4H 10), ethene (C 2H 4), benzene (C 6H 6), toluene (C 7H 8) as well as refrigerants consisting of 1,1,1,2 tetra fluoroethane (R134a), tetrafluoromethane (R14), chlorodifluromethane (R22), 1,1,1-trifluoroethane (R143a), 1,1,1-trifluoro,2,2-dichloroethane (R123), octafluoropropane (R218), and 1,1-difluoroethane (R152a) are selected and compared with literature data. The calculations cover the ranges from the dilute vapor or gas to the highly compressed liquid and supercritical regions. The thermodynamic properties are the vapor and liquid densities, the vapor pressure, the internal energy, the enthalpy, the entropy, the heat capacity at constant pressure and constant volume, and the speed of sound. It was found that the overall agreement with literature in all phases especially the vapor/gas phase is remarkable. Furthermore, the Zeno line regularity can be well represented by the TM EOS. Finally, the TM EOS is further assessed through comparing with the Ihm–Song–Mason (ISM) equation of state. In general, the TM EOS outperforms the ISM equation of state.

Modification of Tao-Mason equation of state: Application to refrigerant fluids

The present work addresses a simplified procedure for the calculation of certain parameters in the Tao-Mason (TM) equation of state needed to estimate thermodynamic properties of 12 ozone–friendly refrigerants fluids. The calculations cover wide ranges extending from the dilute vapor or gas to highly compressed liquid and supercritical region. The theoretical equation of state (EOS) is that of Tao and Mason which is based on statistical mechanical perturbation theory. The novelty of the present work is that we use two scaling constants, the enthalpy of vaporization and the molar density, both evaluated at the normal boiling temperature. This approach contrasts with the original procedure that employs five scaling constants including the critical temperature, the critical pressure, the Boyle temperature, the Boyle pressure and the acentric factor for calculating three parameters second virial coefficient and temperature-dependent parameters. The modified TM EOS predicts thermodynamic properties with equal or better accuracy than those emerging from the original TM EOS.

Nanoparticles formation for metallocene catalyzed cyclic olefin copolymer via a continuous supercritical anti-solvent process

Nanoparticles of the metallocene catalyzed cyclic olefin copolymer (mCOC) were prepared with a lab scale continuous supercritical anti-solvent (SAS) apparatus. Several experimental parameters were investigated to explore their influences on the morphology and the mean size of the products. These parameters included the character of carbon dioxide injector, precipitation pressure and temperature, anti-solvent density, the polymer concentration, the flow rate of feed, and the nature of organic solvents. The phase states of the mixtures of solvent + anti-solvent in precipitation stage may govern the mean size of the resulting particles. Nanoparticles of mCOC were obtained in the homogeneous compressed liquid or supercritical region, while sub-micrometric particles were formed in the vapor–liquid coexistence region. The morphology of precipitates was also significantly changed, turning from spherical nanoparticles to microfibrils, as the polymer concentration of feed was increased from 2 to 4 wt.%. Under 15 MPa and 306.2 K, the mean size of the resultant primary mCOC particles as small as 39 nm with a standard deviation of about 6 nm could be produced. The residual solvent was about 1.6 wt.% in the sample after SAS processing by analyzing with a thermogravimetric analyzer (TGA), and the particle samples exhibited sub-glass transition behavior according to the thermal histograms of differential scanning calorimeter (DSC).

EQUATION OF STATE FOR 1,1-DIFLUOROETHANE (R152a)

A new equation of state (EOS) for 1,1-difluoroethane (R152a) is developed in the form of the Helmholtz free energy. The EOS is valid for temperatures between 213 and 433 K (0·55<Tr<1·12) and pressures up to 20 MPa (Pr<4·4). It covers the compressed liquid, gas and two-phase regions. R152a, which does not contain any chlorine, is a potentially acceptable alternative refrigerant for chlorofluorocarbons. Chlorofluorocarbon compounds, which are widely used as refrigerants, propellants, foaming agents and cleaning agents, are known to damage the ozone layer that protects the Earth from harmful radiation. The form of the ideal gas Helmholtz free energy is obtained from statistical thermodynamics, and the residual part is determined from experimental data. From a bank of terms that are suggested, an optimum set of terms is selected by a random search method. The results are compared with the experimental data, and tables of the thermodynamic properties of R152a are presented. © 1997 by John Wiley & Sons, Ltd.

Generalized quartic equation of state for pure nonpolar fluids

AbstractA generalized quartic equation of state has been developed for pure nonpolar fluids. The equation of state contains four parameters which depend on three properties of the fluid—critical temperature, critical volume, and acentric factor. A mathematical approximation based on previously reported hard‐sphere molecular dynamics simulations has been used to model repulsive contributions to the pressure. Attractive forces were modeled using an empirical term. While the quartic equation yields four roots, one root is always negative and hence physically meaningless, and three roots behave like three roots of a cubic equation. Thus, the new equation of state has the advantages of a cubic, simplicity and unequivocal identification of the roots, while correctly modeling the attractive and repulsive contributions to the pressure. The new equation of state is more accurate than either the Peng‐Robinson or a previously proposed quartic equation of state. Accuracy in the supercritical and compressed liquid regions is improved substantially.

Study of the equation of state of liquid 2,3-dimethylbutane at high pressures

An expansion apparatus has been used to measure the density of liquid 2,3-dimethylbutane, from 208 to 298 K and pressures up to 110 MPa. The experimcntal results have been used to calculate the isothermal compressibitity and thermal expansion coefficient in the compressed-liquid region. Especially interesting is the behavior shown by the thermal expansion coefficient at high pressures, presenting an intersection of the isotherms at a single point. The results are compared and discussed with others from literature

Thermodynamic properties of unsaturated vapour and liquid states from a cubic equation of state: Supercritical and compressed liquid regions

The applicability of the Lielmezs—Merriman (LM) modification of the Peng—Robinson equation of state has been tested for supercritical and compressed liquid regions. The predicted thermodynamic properties (pressure, volume, temperature, departure functions: Δ H, Δ A, Δ S, Δ G, Δ U) and fugacity of the pure compounds have been compared with experimental data and with results calculated by the Soave—Redlich—Kwong (SRK) and Peng—Robinson (PR) equations of state.

The density and refractive index of carbonyl sulfide

Volumetric measurements on carbonyl sulfide were made using the Burnett method at 273.2 and 323.2 K up to the vapor pressure and at 383.2 K up to a pressure of 50 MPa. Refractive-index measurements were made at temperatures of 273.2, 288.2, 303.2, 323.2, 343.2, 363.2, and 383.2 K up to pressures of about 20 MPa. These measurements were used to calculate the amount-of-substance density of carbonyl sulfide in the compressed-liquid region.

Liquid—Vapor Phase Behavior and Liquid Phase Density in the System Neon—Argon at High Pressures

Liquid—vapor phase compositions for the system neon—argon are reported at five temperatures in the range 95.82°—129.92°K, and at pressures up to 9000 psia. The liquid—vapor critical curve has been determined for mixtures containing up to 60 mole % neon. The density of the liquid phase has been measured in the compressed-liquid region at temperatures of 101.94°, 110.78°, and 121.36°K, at pressures up to 8000 psia.

The PVT Behavior of Methane in the Gaseous and Liquid States

Introduction Considerable time and effort frequently are expended to establish, with a degree of confidence, the PVT behavior of pure substances. In particular, a great deal of experimental information contributed by a number of investigators is available in the literature. The data of each investigator, although significant in themselves, cannot be used with a high degree of confidence until they are compared with the continuum of information presented by others. Current interest in thermodynamic and transport properties, for not only the gaseous state but the condensed state as well, requires that PVT information be presented for both regions. The density dependence on temperature and pressure, when presented as a continuum, is of considerable value in itself, especially since the available equations of state fail to properly account for the PVT behavior in the condensed state. For this reason and to incorporate PVT data recently presented in the literature, this investigation was carried out. In their studies concerned with the thermodynamic properties of methane, Matthews and Hurd in 1946 utilized the data of Kvalnes and Gaddy and Olds, Reamer, Sage and Lacey to establish the PVT behavior of methane in the superheated region and the saturated liquid densities of Keyes, Taylor and Smith in conjunction with the Clapeyron equation to develop the densities for the saturated envelope. Current activity sponsored by API Project No. 44 under the direction of F.D. Rossini has led to a tabular presentation of compressibility factors for gaseous methane in the superheated region. These values were obtained by using smoothed residuals, developed from experimental data and the Benedict-Webb-Rubin equation, to establish internally consistent compressibility factors for the real gas. This approach offers probably the most precise presentation of PVT information for gaseous methane to date. The PVT behavior of methane also can be represented accurately by equations of state such as the Benedict-Webb-Rubin equation or the Martin-Hou equation. These equations, although valuable for analytically representing the PVT behavior, lack precision in the compressed-liquid region.