Prediction of thermophysical and thermodynamic properties of trichlorofluoromethane and chlorotrifluoromethane in the single- and two-phase region using the BACK equation of state

1988 ◽  
Vol 27 (3) ◽  
pp. 536-540 ◽  
Author(s):  
Naila M. Gadalla ◽  
Kenneth N. Marsh
Keyword(s):  
Equation Of State ◽  
Thermodynamic Properties ◽  
Phase Region ◽  
Two Phase

scholarly journals Modification of the Redlich-Kwong-Aungier Equation of State to Determine the Degree of Dryness in the CO2 Two-phase Region

2021 ◽  
Vol 24 (4) ◽  
pp. 17-27
Author(s):  
Hanna S. Vorobieva ◽  
Keyword(s):  
Experimental Data ◽  
Equation Of State ◽  
Gas Phase ◽  
Saturated Vapor ◽  
Phase Region ◽  
Working Fluid ◽  
Two Phase ◽  
Real Gas ◽  
Liquid Phases ◽  
Good Agreement

The degree of dryness is the most important parameter that determines the state of a real gas and the thermodynamic properties of the working fluid in a two-phase region. This article presents a modified Redlich-Kwong-Aungier equation of state to determine the degree of dryness in the two-phase region of a real gas. Selected as the working fluid under study was CO2. The results were validated using the Span-Wanger equation presented in the mini-REFPROP program, the equation being closest to the experimental data in the CO2 two-phase region. For the proposed method, the initial data are temperature and density, critical properties of the working fluid, its eccentricity coefficient, and molar mass. In the process of its solution, determined are the pressure, which for a two-phase region becomes the pressure of saturated vapor, the volumes of the gas and liquid phases of a two-phase region, the densities of the gas and liquid phases, and the degree of dryness. The saturated vapor pressure was found using the Lee-Kesler and Pitzer method, the results being in good agreement with the experimental data. The volume of the gas phase of a two-phase region is determined by the modified Redlich-Kwong-Aungier equation of state. The paper proposes a correlation equation for the scale correction used in the Redlich-Kwongda-Aungier equation of state for the gas phase of a two-phase region. The volume of the liquid phase was found by the Yamada-Gann method. The volumes of both phases were validated against the basic data, and are in good agreement. The results obtained for the degree of dryness also showed good agreement with the basic values, which ensures the applicability of the proposed method in the entire two-phase region, limited by the temperature range from 220 to 300 K. The results also open up the possibility to develop the method in the triple point region (216.59K-220 K) and in the near-critical region (300 K-304.13 K), as well as to determine, with greater accuracy, the basic CO2 thermodynamic parameters in the two-phase region, such as enthalpy, entropy, viscosity, compressibility coefficient, specific heat capacity and thermal conductivity coefficient for the gas and liquid phases. Due to the simplicity of the form of the equation of state and a small number of empirical coefficients, the obtained technique can be used for practical problems of computational fluid dynamics without spending a lot of computation time.

A Simplified Presentation of Equations for the Thermodynamic Properties of Dichlorodifluoromethane, CCl2F2 (Refrigerant-12)

1969 ◽  
Vol 11 (4) ◽  
pp. 376-383
Author(s):  
R. W. Haywood
Keyword(s):  
Equation Of State ◽  
Thermodynamic Properties ◽  
Characteristic Equation ◽  
Single Phase ◽  
Saturation Pressure ◽  
Phase Region ◽  
Pure Substance ◽  
Coherent System ◽  
Saturated Liquid ◽  
System Of Units

The paper commences with a general treatment illustrating the advantages of writing the equation of state of a pure substance in characteristic (canonical or fundamental) form, from which expressions for all other thermodynamic properties can be written down in terms only of the characteristic function and its partial derivatives. In this way, thermodynamic consistency between the equations for the different properties is automatically ensured. The initial difficulties in constructing an equation of state in characteristic form are briefly discussed, and it is shown how the characteristic equation may be built up from an existing p-v-T equation of state and an equation for the specific heat capacity at zero pressure. An existing set of equations for the single-phase region of Refrigerant-12 is transformed in this way into a single characteristic equation of state from which, through given simple expressions, all other thermodynamic properties may be computed. The equation of state is expressed dimensionlessly in reduced co-ordinates so that it may be used with equal facility in any coherent system of units. For the sake of completeness, other existing equations for the saturation pressure and for the saturated liquid have been put into dimensionless form and are given in the paper.

Supplementary Backward Equations p(h,s) for the Critical and Supercritical Regions (Region 3), and Equations for the Two-Phase Region and Region Boundaries of the IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam

2007 ◽  
Vol 129 (4) ◽  
pp. 1125-1137 ◽  
Author(s):  
H.-J. Kretzschmar ◽  
J. R. Cooper ◽  
J. S. Gallagher ◽  
A. H. Harvey ◽  
K. Knobloch ◽  
...  
Keyword(s):  
Thermodynamic Properties ◽  
Steam Turbine ◽  
International Association ◽  
Computing Time ◽  
Phase Region ◽  
Specific Enthalpy ◽  
Two Phase ◽  
Steam Power ◽  
Power Cycles ◽  
Backward Equation

When steam power cycles are modeled, thermodynamic properties as functions of enthalpy and entropy are required in the critical and supercritical regions (region 3 of IAPWS-IF97). With IAPWS-IF97, these calculations require cumbersome two-dimensional iteration of temperature T and specific volume v from specific enthalpy h and specific entropy s. While these calculations are not frequently required, the computing time can be significant. Therefore, the International Association for the Properties of Water and Steam (IAPWS) adopted backward equations for p(h,s) in region 3. For calculating properties as a function of h and s in the part of the two-phase region that is important for steam-turbine calculations, a backward equation Tsat(h,s) is provided. In order to avoid time-consuming iteration in determining the region for given values of h and s, equations for the region boundaries were developed. The numerical consistency of the equations documented here is sufficient for most applications in heat-cycle, boiler, and steam-turbine calculations.

Surface Melting, Spallation, and Stresses Induced in Metals by Pulsed Electron Beam Heating

1971 ◽  
Vol 38 (2) ◽  
pp. 363-370 ◽  
Author(s):  
L. W. Woodruff ◽  
W. H. Giedt ◽  
J. L. Hesse
Keyword(s):  
Electron Beam ◽  
Equation Of State ◽  
Target Surface ◽  
Surface Melting ◽  
Phase Region ◽  
Internal Stresses ◽  
Two Phase ◽  
One Dimensional ◽  
Pulsed Electron Beam ◽  
Specific Objective

The present study was undertaken to investigate the applicability of one-dimensional computer programs for predicting the response of materials exposed to rapid surface heating produced by a pulsed electron beam. A specific objective was to determine modifications necessary to account for surface melting and spall. Measured values of mass loss, impulse, and internal stresses in lead and gold were satisfactorily predicted using a one-dimensional finite-difference program which simultaneously solved the conservation equations and a hydrodynamic equation of state. Required program modifications included: (a) specifying spall to occur to the depth below the target surface at which the energy deposited was sufficient to initiate melting, and (b) revising the equation of state for the material in the two-phase region.

scholarly journals Calculation of thermodynamic properties of mixtures in two-phase equilibrium

2021 ◽  
Vol 2039 (1) ◽  
pp. 012016
Author(s):  
Taiming Luo ◽  
A Yu Chirkov
Keyword(s):  
Free Energy ◽  
Phase Equilibrium ◽  
Equation Of State ◽  
Thermodynamic Properties ◽  
Energy Equation ◽  
Helmholtz Free Energy ◽  
High Accuracy ◽  
Liquid Equilibrium ◽  
Two Phase ◽  
Vapor Liquid Equilibrium

Abstract Thermodynamic properties of mixtures in vapor-liquid equilibrium (VLE) were studied. Thermodynamic properties of the methane-ethane mixtures in VLE were calculated with highly accurate Helmholtz free energy equation of state GERG-2008, simplified GERG-2008 and common cubic PR equation of state (EOS). Results show that GERG-2008 has high accuracy in VLE calculations. However, simplified GERG-2008 and PR-EOS both work unsatisfactorily in VLE calculations.

Calculation of Thermodynamic Properties in Solid-Liquid, Solid-Gas and Liquid-Gas Region

2015 ◽  
Vol 1126 ◽  
pp. 1-8
Author(s):  
Jurij Avsec ◽  
Igor Medveď
Keyword(s):  
Thermal Conductivity ◽  
Thermodynamic Properties ◽  
Heat Transport ◽  
Analytical Calculation ◽  
Phase Region ◽  
Acentric Factor ◽  
Two Phase ◽  
Fluid Theory ◽  
Model Equations ◽  
Pressure Transport

The paper features the mathematical model of analytical calculation of thermodynamic properties like viscosity, speed of sound and thermal conductivity for fluids in one and two-phase region (fluid-solid, fluid-gas) on the basis of statistical mechanics. For the calculation of thermal conductivity and viscosity for fluids will be presented Chung-Lee-Starling model Equations for the thermal conductivity are developed based on kinetic gas theories and correlated with the experimental data. The low-pressure transport properties are extended to fluids at high densities by introducing empirically correlated density dependent functions. These correlations use acentric factor, dimensionless dipole moment and an empirically determined association parameters to characterize molecular structure effect of polyatomic molecules. The calculation of thermodynamic properties for fluids was developed under the theory of statistical thermodynamics and statistical associated fluid theory. For the calculation of thermal conductivity of solids are the most important two contributions: the heat transport by electrons (el) and by phonons (ph). In our model we have made the assumption that heat transport by electrons and by phonons is independent and the thermal conductivity is than a sum of both terms.

Supplementary Backward Equations for the Industrial Formulation IAPWS-IF97 of Water and Steam for Fast Calculations of Heat Cycles, Boilers, and Steam Turbines

2007 ◽  
Author(s):  
H.-J. Kretzschmar ◽  
K. Knobloch ◽  
K. Miyagawa ◽  
A. H. Harvey ◽  
W. Wagner
Keyword(s):  
High Temperature ◽  
Thermodynamic Properties ◽  
Temperature Region ◽  
Process Modeling ◽  
Saturation Temperature ◽  
Phase Region ◽  
High Temperature Region ◽  
Two Phase ◽  
Fundamental Equations ◽  
Boundary Equations

In 1997, the International Association for the Properties of Water and Steam (IAPWS) adopted the “IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam” (IAPWS-IF97) [1, 2]. The IAPWS-IF97 contains fundamental equations g(p, T) for liquid region 1, vapor region 2 and high-temperature region 5, a fundamental equation f(v, T) for the critical and supercritical regions (region 3) and an equation pair for saturation pressure psat(T) and for saturation temperature Tsat(p); see Fig. 1. Using the fundamental equations, all thermodynamic properties can be calculated from a given pressure and temperature in regions 1, 2, 5, or from a given specific volume and temperature in region 3. In addition, the IAPWS-IF97 contains “backward” equations for the most used implicit functions T(p, h) and T(p, s) in regions 1 and 2 for fast calculations in thermodynamic process modeling. Further dependencies must be calculated iteratively from the fundamental equations. Thus, one- and two-dimensional iterations are necessary for determining certain thermodynamic properties in process modeling. Over the past 6 years, IAPWS has established a task group and developed further backward equations for water and steam supplementing the IAPWS Industrial Formulation 1997. First, backward equations p(h, s) for the liquid and vapor regions were developed and adopted as a supplementary release by IAPWS in 2001 (IAPWS-IF97-S01) [3, 4]; see Fig. 1. An international survey of the power industry revealed that backward equations in the critical and supercritical regions were also required in process modeling. Thus the backward equations T(p, h), v(p, h), T(p, s), and v(p, s) were developed for region 3 and adopted as a supplementary release in 2003 and revised in 2004 (IAPWS-IF97-S03rev) [5, 6]. Backward equations p(h, s) developed for the critical and supercritical regions were then adopted by IAPWS in 2004 (IAPWS-IF97-S04) [7, 8]. This supplementary release also contains a backward equation for the saturation temperature Tsat(h, s) in the part of the two-phase region important for steam-turbine calculations. Finally, backward equations v(p, T) for the critical and supercritical regions (region 3) were published in a supplementary release in 2005 (IAPWS-IF97-S05) [9, 10]; see Fig. 1. In order to determine whether a given state point is located in one of the single-phase regions or in the two-phase region, iterations are necessary for the backward functions of the given properties (p, h), (p, s) or (h, s). To avoid these iterations, special region-boundary equations were developed and adopted as a part of the supplementary releases IAPWS-IF97-03rev and IAPWS-IF97-S04. In conclusion, using the equations of IAPWS-IF97, the supplementary backward equations, and the region-boundary equations, all thermodynamic properties can be calculated without iteration from the input variables (p, t), (p, h), (p, s) and (h, s) in the entire range of validity of IAPWS-IF97, including determination of the region (except for the high-temperature region 5). The numerical consistencies of the backward and region-boundary equations are sufficient for most heat-cycle, boiler, and steam-turbine calculations. For users not satisfied with the numerical consistency, the equations are still recommended for generating good starting points for an iterative process. The supplementary backward equations and the region-boundary equations presented will significantly reduce the computing time for calculating the properties of water and steam [11]. All new backward equations and their use are described comprehensively in [12].

scholarly journals Computation of Thermodynamic Properties of Carbon Dioxide in the Range 0–150 Deg C

1969 ◽  
Author(s):  
E. Macchi ◽  
G. Angelino
Keyword(s):  
Carbon Dioxide ◽  
Thermal Properties ◽  
Thermodynamic Properties ◽  
Error Analysis ◽  
Thermodynamic Functions ◽  
Phase Region ◽  
Accurate Information ◽  
Two Phase ◽  
Density Measurements ◽  
Volumetric Measurements

Methods for the computation of thermodynamic properties from volumetric measurements are presented and discussed. Their accuracy is evluated by means of an error analysis based on the generation of a set of pseudo-experimental points through an appropriate comptuer technique. A set of very accurate density measurements is employed for the computation of thermodynamic functions of CO2 between 0 and 150 deg C including the two phase region. The results of the calculations are reported on a series of tables. The comparison of the computed functions with values reported by others suggests the conclusion that the tabulated data give reasonably accurate information about the thermal properties of CO2 as can be evaluated from the best density measurements available in the range 0–150 deg C.

Solution Properties and Phase Behavior of Ammonium Hexylene Octyl Succinate in Water and Water-Oil System

1970 ◽  
Vol 3 (1) ◽  
Author(s):  
Md. Hamidul Kabir ◽  
Ravshan Makhkamov ◽  
Shaila Kabir
Keyword(s):  
Critical Micelle Concentration ◽  
Phase Behavior ◽  
Liquid Crystalline ◽  
Carbon Number ◽  
Phase Region ◽  
Solution Properties ◽  
Middle Phase ◽  
Two Phase ◽  
Lamellar Liquid Crystal ◽  
Drug Ingredient

The solution properties and phase behavior of ammonium hexylene octyl succinate (HOS) was investigated in water and water-oil system. The critical micelle concentration (CMC) of HOS is lower than that of anionic surfactants having same carbon number in the lipophilic part. The phase diagrams of a water/ HOS system and water/ HOS/ C10EO8/ dodecane system were also constructed. Above critical micelle concentration, the surfactant forms a normal micellar solution (Wm) at a low surfactant concentration whereas a lamellar liquid crystalline phase (La) dominates over a wide region through the formation of a two-phase region (La+W) in the binary system. The lamellar phase is arranged in the form of a biocompatible vesicle which is very significant for the drug delivery system. The surfactant tends to be hydrophilic when it is mixed with C10EO8 and a middle-phase microemulsion (D) is appeared in the water-surfactant-dodecane system where both the water and oil soluble drug ingredient can be incorporated in the form of a dispersion. Hence, mixing can tune the hydrophile-lipophile properties of the surfactant. Key words: Ammonium hexylene octyl succinate, mixed surfactant, lamellar liquid crystal, middle-phase microemulsion. Dhaka Univ. J. Pharm. Sci. Vol.3(1-2) 2004 The full text is of this article is available at the Dhaka Univ. J. Pharm. Sci. website

Sign in / Sign up

Export Citation Format

Share Document