Fundamental Equation Of State Research Articles

Modeling and simulation of xenon storage and supply system for electric propulsion system based on fundamental equation of state

The electric propulsion system (EPS) xenon storage and supply system (SSS) is a complex pipeline network system, which involves the multi-physics coupled fields of transcritical flow, heat transfer, rigid body motion, electromagnetics, and control. Based on the fundamental equation of state, a one-dimensional finite volume model system is proposed for compressible transcritical transient pipe flow. Six typical components of the SSS are modularization modeled by using an object-oriented programming method in Fortran 2018. To evaluate the performance of the algorithm, a simulation model consisting of 77 components is developed for a proportional controlled EPS xenon SSS, and a system-level simulation is performed. Compared with the standard case constructed on the Amesim platform, the model has a pressure rise time error lower than 6%, and the restrictors mass-flow-rate errors of the anode, cathode, and neutralizer are less than 2.8% of the rated flow rate after stabilization. Moreover, the proposed model yields more accurate results at certain operating points. The model system provides an efficient reference for the design and optimization of EPS SSSs, and offers a new approach to simulate complex cryogenic pipe flow systems.

Generalized Energy-Conserving Dissipative Particle Dynamics with Mass Transfer. Part 2: Applications and Demonstrations.

We present the second part of a two-part paper series intended to address a gap in computational capability for coarse-grain particle modeling and simulation, namely, the simulation of phenomena in which diffusion via mass transfer is a contributing mechanism. In part 1, we presented a formulation of a dissipative particle dynamics method to simulate interparticle mass transfer, termed generalized energy-conserving dissipative particle dynamics with mass transfer (GenDPDE-M). In the GenDPDE-M method, the mass of each mesoparticle remains constant following the interparticle mass exchange. In part 2 of this series, further verification and demonstrations of the GenDPDE-M method are presented for mesoparticles with embedded binary mixtures using the ideal gas (IG) and van der Waals (vdW) equation-of-state (EoS). The targeted readership of part 2 is toward practitioners, where applications and practical considerations for implementing the GenDPDE-M method are presented and discussed, including a numerical discretisztion algorithm for the equations-of-motion. The GenDPDE-M method is verified by reproducing the particle distributions predicted by Monte Carlo simulations for the IG and vdW fluids, along with several demonstrations under both equilibrium and non-equilibrium conditions. GenDPDE-M can be generally applied to multi-component mixtures and to other fundamental EoS, such as the Lennard-Jones or Exponential-6 models, as well as to more advanced EoS models such as Statistical Associating Fluid Theory.

Thermodynamic properties for 1-hexene – Measurements and Modeling

A fundamental equation of state is presented for 1-hexene. It is explicit in the reduced Helmholtz energy and depends on the independent variables temperature and density. It is valid in the fluid region at temperatures from the triple–point temperature Ttr = 133.39 K to Tmax = 535 K with a maximum pressure of pmax = 245 MPa. All thermodynamic properties can be determined from the Helmholtz energy and its derivatives with respect to temperature and density. The equation of state is validated by comparison with experimental data, along with an assessment of correct physical and extrapolation behavior. The available data base is further extended by measurements of the homogeneous density with a vibrating-tube densimeter in the temperature range from 300K to 362K and pressures of up to 92 MPa. Speed of sound measurements are conducted with two independent apparatuses at temperatures of 215 K to 500 K and pressures of up to 151 MPa, applying the double-path-length pulse-echo technique.

A Fundamental Equation of State for Chloroethene for Temperatures from the Triple Point to 430\xa0K and Pressures to 100\xa0MPa

A fundamental equation of state in terms of the Helmholtz energy is presented for chloroethene (vinyl chloride). Due to its fundamental nature, it can be used to consistently calculate all thermodynamic state properties in the fluid region. Based on the underlying experimental database, it is valid from the triple-point temperature 119.31 K to 430 K with a maximum pressure of 100 MPa. In addition to the accurate reproduction of experimental data, correct extrapolation behavior during the development of the equation was attained. This enables the equation to be applied in modern mixture frameworks.

Equation of State for Solid Benzene Valid for Temperatures up to 470 K and Pressures up to 1800 MPa

The thermodynamic property data for solid phase I of benzene are reviewed and utilized to develop a new fundamental equation of state (EOS) based on Helmholtz energy, following the methodology used for solid phase I of CO2 by Trusler [J. Phys. Chem. Ref. Data 40, 043105 (2011)]. With temperature and molar volume as independent variables, the EOS is able to calculate all thermodynamic properties of solid benzene at temperatures up to 470 K and at pressures up to 1800 MPa. The model is constructed using the quasi-harmonic approximation, incorporating a Debye oscillator distribution for the vibrons, four discrete modes for the librons, and a further 30 distinct modes for the internal vibrations of the benzene molecule. An anharmonic term is used to account for inevitable deviations from the quasi-harmonic model, which are particularly important near the triple point. The new EOS is able to describe the available experimental data to a level comparable with the likely experimental uncertainties. The estimated relative standard uncertainties of the EOS are 0.2% and 1.5% for molar volume on the sublimation curve and in the compressed solid region, respectively; 8%–1% for isobaric heat capacity on the sublimation curve between 4 K and 278 K; 4% for thermal expansivity; 1% for isentropic bulk modulus; 1% for enthalpy of sublimation and melting; and 3% and 4% for the computed sublimation and melting pressures, respectively. The EOS behaves in a physically reasonable manner at temperatures approaching absolute zero and also at very high pressures.

Experimental determination of the critical parameters for trans-1-chloro-3,3,3-trifluoroprop-1-ene [R1233zd(E)] and cis-1-chloro-2,3,3,3-tetrafluoroprop-1-ene [R1224yd(Z)

The experimental determination of the critical parameters was performed for R1233zd(E) and R1224yd(Z) by the visual observation of the meniscus. The first measurement was made for R1224yd(Z) to validate the experimental apparatus and procedure used in this work, and the second measurement was carried out for R1233zd(E) to resolve the discrepancy in published critical temperatures of this refrigerant. The critical parameters of both refrigerants were successfully determined; the final values for the critical temperature, density, and pressure of R1224yd(Z) were 428.82±0.03 K, 540.8±7.0 kg·m−3, and 3327±7 kPa, respectively, and those of R1233zd(E) were 438.86±0.03 K, 486.7±5.2 kg·m−3, and 3558±7 kPa, respectively. The critical parameters of R1233zd(E) obtained in this work were adopted in the development of a new fundamental equation of state.

Chrastil revisited for supercritical carbon dioxide

Chrastil’s semi-empirical model has been widely used, since its introduction in 1982, to fit solubility data in supercritical carbon dioxide. However, it has been used with different sources for carbon dioxide’s density, with different objective functions and different numerical algorithms to determine the three Chrastil coefficients. These differences lead to an unnecessary variance in fitting performance and Chrastil coefficient values. The result is a reduction in the perceived quality of Chrastil’s model. Also, calculated solubilities based on published Chrastil coefficients using a different source for carbon dioxide’s density risks introducing considerable incremental error. This work uses Span and Wagner’s Fundamental Equation of State and a two-pass Nelder Mead algorithm to minimize the absolute average relative deviation (AARD) for 701 binary data sets. The median AARD is just 8.8% while just 5.2% of the 701 systems have an AARD greater than 30%.

Speed-of-Sound Measurements and a Fundamental Equation of State for Propylene Glycol

A fundamental equation of state was developed for propylene glycol. It is written in terms of the Helmholtz energy with the independent variables temperature and density. Due to its fundamental nature, it can be used to calculate all thermodynamic state properties from the Helmholtz energy and its derivatives with respect to the independent variables. Special attention was paid not only to accurately reproduce the available experimental data but also to correct extrapolation. Therefore, this equation can be used for application in mixture models. For the development of the present equation of state, the available literature data were supplemented with new experimental speed-of-sound measurements, which were conducted in the temperature range from 293.2 K to 353.2 K with pressures up to 20 MPa. High accuracy was achieved by applying the well-established double-path-length pulse-echo technique and a careful sample preparation.

Speeds of Sound in n-Hexane and n-Heptane at Temperatures from (233.33 to 353.21)\xa0K and Pressures up to 20\xa0MPa

The speed of sound in high-purity n-hexane and n-heptane was experimentally studied utilizing the double-path length pulse-echo technique. Measurements with each alkane were carried out at temperatures from (233 to 353) K with pressures up to 20 MPa. Considering the uncertainty contributions from temperature, pressure, path-length calibration, pulse timing and sample purity, the relative expanded combined uncertainty (k = 2) in the speed of sound in n-hexane ranges from (0.012 to 0.042) % over the investigated ranges of pressure and temperature; for n-heptane, the uncertainty varies from (0.014 to 0.018) %. The sound speed data measured in n-hexane were among the data used for the development of a new fundamental equation of state, which is, however, not described in this work. The experimental data of n-heptane can be considered appropriate for modeling purposes and validation of existing equations of state.

Fundamental equation of state developed on basis of Migdal’s phenomenological theory of critical point

In this work a fundamental equation of state (FEoS) with account taken of requirements of the scale theory of the critical point has been developed. The behavior of the FEOS in the asymptotic vicinity of the critical point is determined by the characteristics of the scaling function a(x) of the Helmholtz scale free energy F. The structure of the function a(x) is calculated on the basis of Migdal’s phenomenological theory and the hypothesis about the identical behavior of the isothermal compressibility coefficient at the critical and near-critical isohors near the critical point (Benedek’s hypothesis). The parameters of the singular component of the FEOS are calculated using the similarity theory. The proposed FEoS has been approved on the example of description of equilibrium properties of the refrigerating agent R1234yf in the range of state parameters: by a temperature from 220 K to 440 K and by pressure up to 40 MPa. The obtained results are discussed.

Thermodynamic properties of trifluoroethene (R1123): (p, ρ, T) behavior and fundamental equation of state

Abstract The (p, ρ, T) behavior of trifluoroethene (R1123) was investigated with the isochoric method. A total of 87 (p, ρ, T) data were measured along nine isochores (42, 98, 151, 197, 296, 493, 691, 790, and 888 kg · m − 3 ) at temperatures from 300 K to 430 K and pressures up to 6.9 MPa. The uncertainties in temperature are estimated to be within 10 mK below 380 K and 20 mK at higher temperatures, and the uncertainties in pressure are estimated to be within 1 kPa below 380 K and 2 kPa at higher temperatures. The estimated relative uncertainties in the density measurements are 0.15 % or less. A new Helmholtz energy equation of state was formulated based on the (p, ρ, T) data and recently published experimental data for the vapor pressure, liquid and vapor densities including those at saturation, vapor-phase sound speed, and ideal-gas isobaric heat capacity. The equation is applicable at temperatures from the triple-point temperature (195.15 K) to 480 K and pressures up to 20 MPa. Typical uncertainties in calculated properties are 0.1 % for vapor pressures, 0.1 % for liquid densities, and 0.2 % for vapor densities, except in the critical region where larger deviations up to about 1.5 % are sometimes observed in densities. The uncertainties in calculated vapor-phase sound speeds and ideal-gas isobaric heat capacities are 0.03 % and 1 %, respectively. The equation shows reasonable extrapolation behavior at extremely low and high temperatures, and at high pressures.

Method for constructing fundamental equation of state based on the relationships of similarity theory and scaling hypothesis

On the basis of the new phenomenological theory of the critical point, the method for constructing fundamental equation of state (FEoS) of liquid and gas has been developed. Within the framework of the method proposed, a number of requirements are met: a) in the region of low densities, the transition of FEoS to the virial equation; b) in a wide vicinity of the critical point, the transition of FEoS to the Berestov equation; c) taking into account asymmetry in the behavior of the isochoric heat capacity, isothermal compressibility coefficient and other thermodynamic functions relative to the critical isochore. To calculate the singular component of FEoS, the Pokrovsky transformations and the similarity relation connecting the parameters of a lattice gas and a real liquid are used. It has been shown that such an approach requires only knowledge of the density data on the saturation line and the values of the critical indices to calculate the singular component of FEoS. This allows us to exclude data on the isochoric heat capacity from the calculation scheme and recommend this method for constructing FEoS of substances little studied in the vicinity of the critical point. The method has been tested on the example of constructing carbon dioxide FEoS. The workspace of FEoS has been set: by temperature 216.592 ≤ T ≤ 1100 K and by pressure up to 200 MPa. The results obtained are discussed.

Method for constructing fundamental equation of state that satisfies the scaling theory and applicable for substances insufficiently explored in the critical point vicinity

Here, the authors discuss the problem of describing the equilibrium properties of a substance in the vicinity of the critical point on the basis of the fundamental equation of state (FEoS) of a liquid and a gas in the absence of experimental information about the calorific properties of a given substance in this field of state parameters. FEoS has the following characteristics: in the region of low densities, FEoS transforms to the virial equation of state; in the asymptotic vicinity of the critical point, FEoS meets the requirements of the scaling theory of critical phenomena. The method is based on a new representation of the scaling hypothesis based on the Scofield–Litster–Ho linear model (LM), the Benedek hypothesis and the Lysenkov–Rykov ratio (LR) which establishes the relationship between LM parameters and the real liquid using the Pokrovsky transformations. Testing of the proposed method for constructing FEoS has been carried out using the example of describing the equilibrium properties of argon. It has been ascertained that the use of the LR ratio has allowed, firstly, reducing the number of individual FEoS parameters and, secondly, excluding the data about isochoric heat capacity CV related to the critical point wide vicinity from the calculation scheme.

EOS-LNG: A Fundamental Equation of State for the Calculation of Thermodynamic Properties of Liquefied Natural Gases (LNG)

EOS-LNG: A Fundamental Equation of State for the Calculation of Thermodynamic Properties of Liquefied Natural Gases (LNG)

A new variant of a scaling hypothesis and a fundamental equation of state based on it

This paper deals with a fundamental equation of state (FEOS) for substances. We have suggested a new method. It allows constructing FEOS that is based on the scaling theory of critical phenomena and describes thermodynamic properties related to liquid and gas phases of a substance in a wide range of the pressures and temperatures. In the framework of the methodological approach, we have provided: (i) a transition of FEOS in a virial equation of state in the low density region; (ii) a transition of FEOS in a Widom equation of state in the critical region. The method has been tested on the example of FEOS of R218. The area of applicability of FEOS is 0 < ρ/ρc < 3.2 in the density and 133 < T < 440 K in the temperature. We have compared FEOS with some equations of state and discussed the results.

Method of constructing a fundamental equation of state based on a scaling hypothesis

The work studies the issues associated with the construction of the equation of state (EOS) taking due account of substance behavior in the critical region and associated with the scaling theory of critical phenomena (ST). The authors have developed a new version of the scaling hypothesis; this approach uses the following: a) substance equation of state having a form of a Schofield-Litster-Ho linear model (LM) and b) the Benedek hypothesis. The Benedek hypothesis has found a similar behavior character for a number of properties (isochoric and isobaric heat capacities, isothermal compressibility coefficient) at critical and near-critical isochors in the vicinity of the critical point. A method is proposed to build the fundamental equation of state (FEOS) which satisfies the ST power laws. The FEOS building method is verified by building the equation of state for argon within the state parameters range: up to 1000 MPa in terms of pressure, and from 83.056 К to 13000 К in terms of temperature. The executed comparison with the fundamental equations of state of Stewart-Jacobsen (1989), of Kozlov at al (1996), of Tegeler-Span-Wagner (1999), of has shown that the FEOS describes the known experimental data with an essentially lower error.

Equation of state for 1,2-dichloroethane based on a hybrid data set

ABSTRACTA fundamental equation of state in terms of the Helmholtz energy is presented for 1,2-dichloroethane. Due to a narrow experimental database, not only laboratory measurements but also molecular simulation data are applied to the fitting procedure. The present equation of state is valid from the triple point up to 560 K for pressures of up to 100 MPa. The accuracy of the equation is assessed in detail. Furthermore, a reasonable extrapolation behaviour is verified.

Thermodynamic theory of equilibrium fluctuations

The postulational basis of classical thermodynamics has been expanded to incorporate equilibrium fluctuations. The main additional elements of the proposed thermodynamic theory are the concept of quasi-equilibrium states, a definition of non-equilibrium entropy, a fundamental equation of state in the entropy representation, and a fluctuation postulate describing the probability distribution of macroscopic parameters of an isolated system. Although these elements introduce a statistical component that does not exist in classical thermodynamics, the logical structure of the theory is different from that of statistical mechanics and represents an expanded version of thermodynamics. Based on this theory, we present a regular procedure for calculations of equilibrium fluctuations of extensive parameters, intensive parameters and densities in systems with any number of fluctuating parameters. The proposed fluctuation formalism is demonstrated by four applications: (1) derivation of the complete set of fluctuation relations for a simple fluid in three different ensembles; (2) fluctuations in finite-reservoir systems interpolating between the canonical and micro-canonical ensembles; (3) derivation of fluctuation relations for excess properties of grain boundaries in binary solid solutions, and (4) derivation of the grain boundary width distribution for pre-melted grain boundaries in alloys. The last two applications offer an efficient fluctuation-based approach to calculations of interface excess properties and extraction of the disjoining potential in pre-melted grain boundaries. Possible future extensions of the theory are outlined.

Measurements of the isobaric heat capacity of R1234yf in liquid phase at temperatures from 305 K to 355 K and pressures up to 5 MPa

2,3,3,3-Tetrafluoropropene (R1234yf) is an environmentally friendly promising alternative to 1,1,1,2-tetrafluoroethane (R134a) in air conditioning applications. The heat capacity of R1234yf in liquid phase was investigated in this study. The measurements were carried out with a modified heat conduction calorimeter. A total of 74 data points were obtained among 305–355K and 1.5–5MPa. The uncertainty of the heat capacity measurements was estimated to be less than 1.7%. An empirical equation was correlated to reproduce the experimental result with its terms chosen by a stepwise method. The maximum deviation between the correlating equation and the experimental data was 1.5%. Furthermore, saturated liquid heat capacity of R1234yf was obtained by extrapolating the correlation to saturated pressures. Finally, a comparison was done between the present data and literature experimental data and calculations from a fundamental equation of state.

Examining the Consistency of Water Content Data in Alkanes Using the Perturbed-Chain Form of the Statistical Associating Fluid Theory Equation of State

Experimental data available in the literature on the water content of alkanes (C5 and higher) is widely scattered. The accurate determination of water content in hydrocarbons is critical for the petroleum and natural gas industries due to corrosion and hydrate formation problems. A molecular theory with a single parameter fit to water content data is shown to accurately correlate water mole fraction in alkanes from C1 to C16 which are in equilibrium with liquid water or ice. Moreover, a list of experimental data is recommended to the reader based on its agreement with the fundamental equation of state used in this work. An empirical equation is proposed to accurately correlate water content in C5–C16 alkanes for temperatures ranging from 293.15 K to 323.15 K and as a function carbon number.