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.

A Robust Iterative Method for Flash Calculations Using the Soave-Redlich-Kwong or the Peng-Robinson Equation of State

1983 ◽  
Vol 23 (03) ◽  
pp. 521-530 ◽  
Author(s):  
L.X. Nghiem ◽  
K. Aziz ◽  
Y.K. Li
Keyword(s):  
Equation Of State ◽  
Iterative Method ◽  
Critical Point ◽  
Newton’S Method ◽  
Newton's Method ◽  
Single Phase ◽  
Saturation Pressure ◽  
Phase Region ◽  
Single Phase Region ◽  
Poor Convergence

Abstract A robust algorithm for flash calculations that uses an equation of state(EOS) is presented. It first uses a special version of the successive substitution(SS) method and switches to Powell's method if poor convergence is observed. Criteria are established for an efficient switch from one method to the other. Experience shows that this method converges near the critical point and also detects the single-phase region without computing the saturation pressure. The Soave-Redlich-Kwong (SRK) and the Peng-Robinson (PR) EOS's are used in this work, but the method is general and applies to any EOS. Introduction The calculation of vapor/liquid equilibrium using an EOS in multicomponent systems yields a system of nonlinear equations that must be solved iteratively. The SS method is commonly used, but it exhibits poor rate of convergence near the critical point. To overcome convergence problems, Newton's method has been used by Fussell and Yanosik to solve the equations. The drawback of Newton's method is the necessity of computing a complicated Jacobian matrix and its inverse at every iteration. Hence, for systems removed from their critical point it involves more work to arrive at the solution than the SS method. Furthermore, the radius of convergence of Newton's method is relatively small when compared to that of the SS method; hence, a good initial guess is required before convergence can be achieved. The single-phase region usually is determined by computing the saturation pressure and comparing it with the pressure of the system. This requires additional work, pressure of the system. This requires additional work, and it is sometimes difficult to decide whether a dewpoint or bubblepoint pressure, which involve different equations, should be computed. This paper presents a robust iterative method for flash calculations using either the SRK or the PR EOS, both of which have received much interest in recent years. The proposed method combines SS with Powell's iteration, proposed method combines SS with Powell's iteration, which is a hybrid algorithm consisting of a quasi-Newton method and a steepest-descent method. The SS method is used initially and is replaced by Powell's method if it demonstrates poor convergence, thus taking advantage of the simplicity of the former method and the robustness of the latter. The SS method has been modified so that the single-phase region can be detected without having to compute the saturation pressure. The nonlinear equations to be solved by an iteration scheme could behave differently, depending on their form and the variables for which they are solved. In this paper three different approaches are considered with paper three different approaches are considered with Powell's method. One of the three approaches is based Powell's method. One of the three approaches is based on the minimization of the Gibbs free energy. The convergence properties of the proposed schemes are demonstrated by three example problems. SPEJ P. 521

A New Approach in Approximating Thermodynamics Properties in Compressed Liquid Region

2008 ◽  
Author(s):  
Amir Karimi ◽  
Isa Tan
Keyword(s):  
Thermodynamic Properties ◽  
Internal Energy ◽  
Saturation Pressure ◽  
Approximation Formula ◽  
Liquid Region ◽  
Saturated Liquid ◽  
Thermodynamics Properties ◽  
Compressed Liquid ◽  
The Right ◽  
Current Approximation

Currently it is a common practice to use saturated liquid properties to approximate thermodynamics properties of fluids in the compressed liquid region. In this practice it is assumed that specific volume, internal energy, and entropy of fluids in the compressed liquid region are functions of temperature only and pressure practically has very little or no effect on these properties. Therefore, these properties at a given temperature and pressure are approximated by the saturated liquid properties at the given temperature. In the current literature the approximation formula given for enthalpy in the compressed liquid region is expressed as h(T, p) = hf (T) + vf (T) [p – psat (T)], where the aim of the second term on the right hand side of the equation is to improve the accuracy of the approximation, when pressure is much greater than the saturation pressure. However, in a recent study of thermodynamic properties of water, Kostic has shown that the second term in the equation improves the accuracy of the approximation of the enthalpy only at temperatures below 100 °C. In fact, he has shown that the second term increases the error when the formula is used to approximate the enthalpy of water in the compressed liquid region at intermediate and high temperatures. Kostic’s investigation is expanded in this paper to include substances other than water. The study shows that in many situations pressure has a bigger influence on the internal energy than it does on enthalpy of fluids in the compressed liquids. This paper demonstrates that the current practice of approximating properties of fluids in the compressed liquid region is not accurate at all range of temperatures and pressures. It establishes the range of pressures and temperatures for which the current approximation method could be used with reasonable accuracies. It also proposes a new scheme for the approximation of thermodynamic properties in the compressed liquid region.

scholarly journals Optimization of the quintic equation of the state based model for the calculations of different thermodynamic properties

2008 ◽  
Vol 10 (1) ◽  
pp. 6-10 ◽  
Author(s):  
Antoni Kozioł ◽  
Radosław Wiśniewski
Keyword(s):  
Experimental Data ◽  
Equation Of State ◽  
Thermodynamic Properties ◽  
Saturation Pressure ◽  
The State ◽  
New Method ◽  
Original Form ◽  
Liquid Density ◽  
Temperature Dependent ◽  
Quintic Equation

Optimization of the quintic equation of the state based model for the calculations of different thermodynamic properties Different thermodynamic properties (the vapour density, the liquid density and the saturation pressure) were calculated by the model based on the Nakamura-Breedveld-Prausnitz equation of state (NBP EOS). Since the original form of the NBP EOS often generates inaccurate results for liquids, it was modified to describe this phase better. The calculations were realized in the subcritical region. So far, the temperature-dependent NBP EOS parameters have been obtained by special correlations. Their constants were fitted to a lot of experimental data. In this paper the equation of state temperature-dependent parameters were obtained by a new method which was based at piecewise cubic Hermite interpolating polynomials (PCHIPs). In the proposed method some experimental data (called the key ones) were used, thus reducing the experimental effort. Seven substances were chosen for the test calculations. Each of them is common in industry. The calculation results were compared with the experimental data. The new method has made an accurate description of vapour-liquid equilibrium for the considered pure substances over a wide temperature range possible.

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

2021 ◽  
Vol 42 (3) ◽  
Author(s):  
Giuseppe Cavuoto ◽  
Nils von Preetzmann ◽  
Philipp Eckmann ◽  
Jianrong Li ◽  
Adriaan M. H. van der Veen ◽  
...  
Keyword(s):  
Carbon Dioxide ◽  
Liquid Phase ◽  
Equation Of State ◽  
Single Phase ◽  
Magnetic Suspension ◽  
Saturated Liquid ◽  
Homogeneous Liquid ◽  
Combined Uncertainty ◽  
Phase Liquid ◽  
Cell Densities

AbstractDensities 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 %.

scholarly journals Density Measurements of (0.99 Methane + 0.01 Butane) and (0.98 Methane + 0.02 Isopentane) over the Temperature Range from (100 to 160) K at Pressures up to 10.8 MPa

2020 ◽  
Vol 41 (11) ◽  
Author(s):  
Philipp Eckmann ◽  
Nils von Preetzmann ◽  
Giuseppe Cavuoto ◽  
Jianrong Li ◽  
Adriaan van der Veen ◽  
...  
Keyword(s):  
Equation Of State ◽  
Binary Mixtures ◽  
Single Phase ◽  
Measurement Procedure ◽  
Magnetic Suspension ◽  
Saturated Liquid ◽  
Time Saving ◽  
Homogeneous Liquid ◽  
Combined Uncertainty ◽  
Phase Liquid

Abstract Densities of two methane-rich binary mixtures were measured in the homogeneous liquid and the supercritical region at temperatures between (100 and 160) K using a low-temperature single-sinker magnetic-suspension densimeter. For each mixture, four isotherms were studied over the pressure range from (0.3 to 10.8) MPa. Molar compositions of the gravimetrically prepared methane-rich binary mixtures were approximately 0.01 butane and 0.02 isopentane, respectively, with the balance being methane. The relative expanded combined uncertainty (k = 2) of the experimental densities was estimated to be in the range of (0.02 to 0.06) %. Due to a supercritical liquefaction procedure and the integration of a special VLE-cell, it was possible to measure densities in the homogeneous liquid phase without changing the composition of the liquefied mixture. Based on the supercritical liquefaction procedure, a new time-saving measurement procedure was developed and applied. Moreover, saturated-liquid densities were determined by extrapolation of the experimental single-phase liquid densities to the vapor pressure calculated with an equation of state (EOS); here, the relative expanded combined uncertainty (k = 2) is less than 0.05 % in most cases. The new experimental results were compared with the GERG-2008 equation of state, the EOS-LNG and the enhanced revised Klosek and McKinley (ERKM) method.

scholarly journals BACKONE equation of state for Cis-1, 3, 3, 3-tetrafluoropropene (R1234ze(Z))

2018 ◽  
Vol 40 (4) ◽  
pp. 387-395
Author(s):  
Phan Thi Thu Huong ◽  
Lai Ngoc Anh
Keyword(s):  
Experimental Data ◽  
Equation Of State ◽  
Thermodynamic Properties ◽  
Vapor Pressure ◽  
Characteristic Temperature ◽  
Liquid Density ◽  
Saturated Liquid ◽  
Density Data ◽  
Factor Α ◽  
Saturated Liquid Density

This paper presents the study on the determination of the thermodynamic properties of Cis-1,3,3,3-tetrafluoropropene (R1234ze(Z)) with the BACKONE equation of state. The BACKONE's characteristic temperature T0, characteristic density ρ0, anisotropy factor α, and reduce quarupole moment Q*2 were found by fitting the BACKONE EOS to experimental data of vapor pressure and saturated liquid density. All thermodynamic properties such as vapor pressure, pressure in gaseous phase, saturated liquid density, and liquid density can be determined easily from the found molecular characteristic properties. Thermodynamic properties of the R1234ze(Z) were evaluated with available experimental data. Average absolute deviations between calculated vapor pressure data and experimental data were 0.43%. Average absolute deviations between calculated saturated liquid density data and experimental data were 0.43%. In the prediction of the thermodynamic properties, average absolute deviations between calculated liquid density data and experimental data were 0.68% and average absolute deviations between calculated gas density data and experimental data were 1.6%.

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