Fundamental Equation

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Ryo Akasaka - One of the best experts on this subject based on the ideXlab platform.

  • a Fundamental Equation of state for 1 1 1 3 3 pentafluoropropane r 245fa
    Journal of Physical and Chemical Reference Data, 2015
    Co-Authors: Ryo Akasaka, Yong Zhou, Eric W Lemmon
    Abstract:

    A new Fundamental Equation of state explicit in the Helmholtz energy is presented for 1,1,1,3,3-pentafluoropropane (R-245fa), based on recent experimental data for vapor pressures, densities, and sound speeds. The functional form uses Gaussian bell-shaped terms, according to recent trends in the development of accurate Equations of state. The independent variables of the Equation of state are temperature and density. The Equation is valid for temperatures between the triple point (170.0 K) and 440 K, and for pressures up to 200 MPa. Estimated uncertainties in this range are 0.1% for vapor pressures, 0.1% for saturated liquid densities, 0.1% for liquid densities below 70 MPa, 0.2% for densities at higher pressures, 0.3% for vapor densities, 0.3% for liquid sound speeds, and 0.1% for vapor sound speeds. The uncertainties in the critical region are higher for all properties except vapor pressures. The Equation shows reasonable extrapolation behavior at extremely low and high temperatures, and at high pressures.

  • A Fundamental Equation of state for cis-1,3,3,3-tetrafluoropropene (R-1234ze(Z))
    International Journal of Refrigeration, 2014
    Co-Authors: Ryo Akasaka, Yukihiro Higashi, Akio Miyara, Shigeru Koyama
    Abstract:

    Abstract A Fundamental Equation of state is presented for cis-1,3,3,3-tetrafluoropropene (R-1234ze(Z)). The Equation of state is expressed explicitly in the Helmholtz energy with independent variables of temperature and density. The Equation of state is based on experimental data for the critical parameters, vapor pressures, densities of the liquid and vapor phases, and sound speeds in the vapor phase. All thermodynamic properties can be derived as derivatives of the Helmholtz energy. The Equation is valid for temperatures from 273 K to 430 K and for pressures up to 6 MPa. The estimated uncertainties of properties calculated from the Equation are 0.15% in vapor pressures, 0.4% in vapor densities, 0.2% in liquid densities, and 0.05% in the vapor phase sound speeds. The Equation exhibits reasonable extrapolation behavior in regions away from the experimental data.

  • a Fundamental Equation of state for trifluoromethyl methyl ether hfe 143m and its application to refrigeration cycle analysis
    International Journal of Refrigeration-revue Internationale Du Froid, 2012
    Co-Authors: Ryo Akasaka, Yohei Kayukawa
    Abstract:

    Abstract A Fundamental Equation of state explicit in the Helmholtz energy is presented for trifluoromethyl methyl ether (HFE-143m). The independent variables of the Equation of state are temperature and density. The Equation of state is based on reliable experimental data for the vapor pressure and densities of the liquid and vapor phases. The Equation covers temperatures between 240 K and 420 K for pressures up to 7.2 MPa. Comparisons to available experimental data are given that establish the accuracy of calculated properties from the Equation of state. The estimated uncertainties are 0.1% in liquid density, 0.3% in pressure of the vapor phase, and 0.1% in vapor pressure. Comparisons of the vapor pressures and heats of vaporization of HFE-143m are made to those of 1,1,1,2-tetrafluoroethane (HFC-134a), 2,3,3,3-tetrafluoropropene (HFO-1234yf), and trans-1,3,3,3-tetrafluoropropene (HFO-1234ze(E)). The performance analysis of refrigeration cycles with these refrigerants is also demonstrated.

Eric W Lemmon - One of the best experts on this subject based on the ideXlab platform.

  • eos lng a Fundamental Equation of state for the calculation of thermodynamic properties of liquefied natural gases
    Journal of Physical and Chemical Reference Data, 2019
    Co-Authors: Monika Thol, Eric W Lemmon, Markus Richter, Eric F May, Roland Span
    Abstract:

    A new mixture model (EOS-LNG) for the accurate representation of thermodynamic property data of multicomponent natural gas mixtures in the liquid state is presented. The mathematical approach of the GERG-2008 Equation of state of Kunz and Wagner is adopted and new binary-specific functions for methane + n-butane, methane + isobutane, methane + n-pentane, and methane + isopentane are developed. The representation of all experimental data available in the literature for the corresponding binary systems is carefully analyzed so that these functions can also be applied at fluid states beyond the liquefied natural gas (LNG) region. The EOS-LNG represents all available binary and multicomponent data in the LNG region within their specified experimental uncertainty, which is significantly more accurate than the GERG-2008 model. The main focus was given to the representation of new density data measured between 100 K and 180 K with a maximum pressure of 10 MPa. Deviations from the EOS-LNG presented here do not exceed 0.02% for binary data and 0.05% for multicomponent systems. Deviations of calculated values of these data from experimental data in other fluid regions are similar to or better than those calculated with the GERG-2008 model.A new mixture model (EOS-LNG) for the accurate representation of thermodynamic property data of multicomponent natural gas mixtures in the liquid state is presented. The mathematical approach of the GERG-2008 Equation of state of Kunz and Wagner is adopted and new binary-specific functions for methane + n-butane, methane + isobutane, methane + n-pentane, and methane + isopentane are developed. The representation of all experimental data available in the literature for the corresponding binary systems is carefully analyzed so that these functions can also be applied at fluid states beyond the liquefied natural gas (LNG) region. The EOS-LNG represents all available binary and multicomponent data in the LNG region within their specified experimental uncertainty, which is significantly more accurate than the GERG-2008 model. The main focus was given to the representation of new density data measured b...

  • speed of sound measurements and a Fundamental Equation of state for cyclopentane
    Journal of Chemical & Engineering Data, 2015
    Co-Authors: Holger Gedanitz, Maria J Davila, Eric W Lemmon
    Abstract:

    The speed of sound in liquid cyclopentane has been measured in the temperature range from (258 to 353) K at pressures up to 30 MPa (42 data points) using a pulse-echo method with a double path type sensor. The expanded overall uncertainty (k = 2) in the speed of sound measurements is estimated to be 0.2 %. A function for the speed of sound with inputs of temperature and pressure has been fitted to the experimental results. The new speed of sound data along with available literature data were used to develop a Fundamental Helmholtz Equation of state for cyclopentane. Typical expanded uncertainties of properties calculated using the new Equations are 0.2 % in density in the liquid phase, 1 % in heat capacity, 0.2 % in liquid-phase sound speed, and 0.5 % in vapor pressure. The Equation of state is valid from the triple-point temperature, 179.7 K, to temperatures of 550 K with pressures to 250 MPa.

  • a Fundamental Equation of state for 1 1 1 3 3 pentafluoropropane r 245fa
    Journal of Physical and Chemical Reference Data, 2015
    Co-Authors: Ryo Akasaka, Yong Zhou, Eric W Lemmon
    Abstract:

    A new Fundamental Equation of state explicit in the Helmholtz energy is presented for 1,1,1,3,3-pentafluoropropane (R-245fa), based on recent experimental data for vapor pressures, densities, and sound speeds. The functional form uses Gaussian bell-shaped terms, according to recent trends in the development of accurate Equations of state. The independent variables of the Equation of state are temperature and density. The Equation is valid for temperatures between the triple point (170.0 K) and 440 K, and for pressures up to 200 MPa. Estimated uncertainties in this range are 0.1% for vapor pressures, 0.1% for saturated liquid densities, 0.1% for liquid densities below 70 MPa, 0.2% for densities at higher pressures, 0.3% for vapor densities, 0.3% for liquid sound speeds, and 0.1% for vapor sound speeds. The uncertainties in the critical region are higher for all properties except vapor pressures. The Equation shows reasonable extrapolation behavior at extremely low and high temperatures, and at high pressures.

  • Fundamental Equation of state for deuterium
    Journal of Physical and Chemical Reference Data, 2014
    Co-Authors: Ian A Richardson, Jacob Leachman, Eric W Lemmon
    Abstract:

    World utilization of deuterium is anticipated to increase with the rise of fusion-energy machines such as ITER and NIF. We present a new Fundamental Equation of state for the thermodynamic properties of fluid deuterium. Differences between thermodynamic properties of orthodeuterium, normal deuterium, and paradeuterium are described. Separate ideal-gas functions were fitted for these separable forms together with a single real-fluid residual function. The Equation of state is valid from the melting line to a maximum pressure of 2000 MPa and an upper temperature limit of 600 K, corresponding to available experimental measurements. The uncertainty in predicted density is 0.5% over the valid temperature range and pressures up to 300 MPa. The uncertainties of vapor pressures and saturated liquid densities are 2% and 3%, respectively, while speed-of-sound values are accurate to within 1% in the liquid phase.

  • an Equation of state for the thermodynamic properties of dimethyl ether
    Journal of Physical and Chemical Reference Data, 2011
    Co-Authors: Yong Zhou, Eric W Lemmon
    Abstract:

    A thermodynamic property formulation for dimethyl ether has been developed based on a selection of experimental thermodynamic property data. The formulation includes a Fundamental Equation, a vapor-pressure Equation, and saturated-density Equations for liquid and vapor states. In determining the coefficients of the Equation of state, multiproperty fitting methods were used that included single-phase pressure-density-temperature (pρT), heat capacity, vapor pressure, and saturated density data. Deviations between experimental and calculated data are generally within the experimental accuracy. 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 the triple-point temperature to 550K, with pressures up to 50MPa and densities up to 19moldm−3. The uncertainties of the Equation of state in density are 0.1% for the liquid phase and 0.3% for the vapor phase. In the extended critical region, the uncertainties in...

Roland Span - One of the best experts on this subject based on the ideXlab platform.

  • eos lng a Fundamental Equation of state for the calculation of thermodynamic properties of liquefied natural gases
    Journal of Physical and Chemical Reference Data, 2019
    Co-Authors: Monika Thol, Eric W Lemmon, Markus Richter, Eric F May, Roland Span
    Abstract:

    A new mixture model (EOS-LNG) for the accurate representation of thermodynamic property data of multicomponent natural gas mixtures in the liquid state is presented. The mathematical approach of the GERG-2008 Equation of state of Kunz and Wagner is adopted and new binary-specific functions for methane + n-butane, methane + isobutane, methane + n-pentane, and methane + isopentane are developed. The representation of all experimental data available in the literature for the corresponding binary systems is carefully analyzed so that these functions can also be applied at fluid states beyond the liquefied natural gas (LNG) region. The EOS-LNG represents all available binary and multicomponent data in the LNG region within their specified experimental uncertainty, which is significantly more accurate than the GERG-2008 model. The main focus was given to the representation of new density data measured between 100 K and 180 K with a maximum pressure of 10 MPa. Deviations from the EOS-LNG presented here do not exceed 0.02% for binary data and 0.05% for multicomponent systems. Deviations of calculated values of these data from experimental data in other fluid regions are similar to or better than those calculated with the GERG-2008 model.A new mixture model (EOS-LNG) for the accurate representation of thermodynamic property data of multicomponent natural gas mixtures in the liquid state is presented. The mathematical approach of the GERG-2008 Equation of state of Kunz and Wagner is adopted and new binary-specific functions for methane + n-butane, methane + isobutane, methane + n-pentane, and methane + isopentane are developed. The representation of all experimental data available in the literature for the corresponding binary systems is carefully analyzed so that these functions can also be applied at fluid states beyond the liquefied natural gas (LNG) region. The EOS-LNG represents all available binary and multicomponent data in the LNG region within their specified experimental uncertainty, which is significantly more accurate than the GERG-2008 model. The main focus was given to the representation of new density data measured b...

  • Equation of state for 1 2 dichloroethane based on a hybrid data set
    Molecular Physics, 2017
    Co-Authors: Monika Thol, Jadran Vrabec, Gábor Rutkai, Andreas Köster, Svetlana Miroshnichenko, Wolfgang Wagner, Roland Span
    Abstract:

    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.

  • Fundamental Equation of state correlation for hexamethyldisiloxane based on experimental and molecular simulation data
    Fluid Phase Equilibria, 2016
    Co-Authors: Monika Thol, Roland Span, Frithjof H. Dubberke, Gábor Rutkai, Andreas Köster, Thorsten Windmann, Jadran Vrabec
    Abstract:

    Abstract An empirical Fundamental Equation of state correlation in terms of the Helmholtz energy is presented for hexamethyldisiloxane. The relatively small amount of thermodynamic data that is available in the literature for this substances is considerably extended by speed of sound measurements and numerical results for Helmholtz energy derivatives from molecular modeling and simulation. The speed of sound apparatus employed in this work is based on the pulse-echo technique and operates up to 150 MPa in the temperature range between 250 K and 600 K. The range of validity of the Equation of state, based on laboratory data from literature and speed of sound data of this work, is from 270 K to 580 K and up to 130 MPa. Molecular simulation data are applied to extend the range of validity up to 1200 K and 600 MPa.

  • Fundamental Equation of state for ethylene oxide based on a hybrid dataset
    Chemical Engineering Science, 2015
    Co-Authors: Monika Thol, Roland Span, Gábor Rutkai, Andreas Köster, Mirco Kortmann, Jadran Vrabec
    Abstract:

    Abstract An empirical Fundamental Equation of state correlation is presented for ethylene oxide. The correlation is explicit in terms of the Helmholtz energy and it can be used to calculate all thermodynamic properties. The underlying dataset consists of experimental and molecular simulation data. The experimental data cover almost exclusively the gaseous phase and are available for temperatures from the triple point up to the critical point. Molecular simulation data are used to extend the validity to the liquid state and up to a maximum temperature of 1000 K and a maximum pressure of 700 MPa.

  • communication Fundamental Equation of state correlation with hybrid data sets
    Journal of Chemical Physics, 2013
    Co-Authors: Gábor Rutkai, Roland Span, Monika Thol, Rolf Lustig, Jadran Vrabec
    Abstract:

    A strategy is proposed for empirical Fundamental Equation of state correlations for pure fluids on the basis of hybrid data sets, composed of experimental and molecular simulation data. Argon and hydrogen chloride are used as examples.

Shigeru Koyama - One of the best experts on this subject based on the ideXlab platform.

  • A Fundamental Equation of state for cis-1,3,3,3-tetrafluoropropene (R-1234ze(Z))
    International Journal of Refrigeration, 2014
    Co-Authors: Ryo Akasaka, Yukihiro Higashi, Akio Miyara, Shigeru Koyama
    Abstract:

    Abstract A Fundamental Equation of state is presented for cis-1,3,3,3-tetrafluoropropene (R-1234ze(Z)). The Equation of state is expressed explicitly in the Helmholtz energy with independent variables of temperature and density. The Equation of state is based on experimental data for the critical parameters, vapor pressures, densities of the liquid and vapor phases, and sound speeds in the vapor phase. All thermodynamic properties can be derived as derivatives of the Helmholtz energy. The Equation is valid for temperatures from 273 K to 430 K and for pressures up to 6 MPa. The estimated uncertainties of properties calculated from the Equation are 0.15% in vapor pressures, 0.4% in vapor densities, 0.2% in liquid densities, and 0.05% in the vapor phase sound speeds. The Equation exhibits reasonable extrapolation behavior in regions away from the experimental data.

Toshihiko Sasaki - One of the best experts on this subject based on the ideXlab platform.

  • a comparison of x ray stress measurement methods based on the Fundamental Equation
    Journal of Applied Crystallography, 2016
    Co-Authors: T Miyazaki, Toshihiko Sasaki
    Abstract:

    Stress measurement methods using X-ray diffraction (XRD) methods are based on so-called Fundamental Equations. The Fundamental Equation is described in the coordinate system that best suits the measurement situation, and so making a comparison between different XRD methods is not straightforward. However, by using the diffraction vector representation, the Fundamental Equations of different methods become identical. Furthermore, the differences between the various XRD methods reside in the choice of diffraction vectors and the way of calculating the stress from the measured data. The stress calculation methods can also be unified using the general least-squares method, which is a common least-squares method of multivariate analysis. Thus, the only difference between these methods turns out to be in the choice of the set of diffraction vectors. In the light of these ideas, three commonly used XRD methods are compared: the sin2ψ method, the XRD2 method and the cosα method, using the estimation of the measurement errors. The XRD2 method with 33 frames (data acquisitions) shows the best accuracy. On the other hand, the accuracy of the cosα method with three frames is comparable to that of the XRD2 method.

  • a comparison of x ray stress measurement methods based on the Fundamental Equation
    arXiv: Materials Science, 2015
    Co-Authors: T Miyazaki, Toshihiko Sasaki
    Abstract:

    Stress measurement methods using X-ray diffraction (XRD methods) are based on so-called Fundamental Equations. The Fundamental Equation is described in the coordinate system that best suites the measurement situation, and, thus, making a comparison between different XRD methods is not straightforward. However, by using the diffraction vector representation, the Fundamental Equations of different methods become identical. Furthermore, the differences between the various XRD methods are in the choice of diffraction vectors and the way of calculating the stress from the measured data. The stress calculation methods can also be unified using the general least-squares method, which is a common least-squares method of multivariate analysis. Thus, the only difference between these methods turns out to be in the choice of the set of diffraction vectors. In light of these ideas, we compare three commonly used XRD methods: the sin^2 psi method, the XRD^2 method, and the cos alpha method using the estimation of the measurement errors.