Measurement and correlation of the (pressure, density, temperature) relation of carbon dioxide II. Saturated-liquid and saturated-vapour densities and the vapour pressure along the entire coexistence curve

Duschek, W; Kleinrahm, Reiner; Wagner, Wolfgang

doi:10.1016/0021-9614(90)90173-n

Cited by 155 publications

(92 citation statements)

References 36 publications

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“…This densimeter was developed in order to obtain accurate (p, r, T ) measurements of pure fluids in the homogeneous gas and liquid phase including the critical region and, in particular, the entire (vapour + liquid) coexistence curve. Up to now, comprehensive measurements on methane, (3)(4)(5)(6) carbon dioxide, (7)(8)(9) argon, (10,11) and ethylene (12,13) have been carried out successfully; nitrogen, (14) sulphur hexafluoride, (15) and the refrigerants R12 and R22 (16) have been measured in parts of the fluid region. The design of the densimeter was described in detail in previous papers; (3,6) therefore only the measuring principle is briefly explained here.…”

Section: Methodsmentioning

confidence: 99%

Measurement and correlation of the (p,ρ,T) relation of nitrogen. I. The homogeneous gas and liquid regions in the temperature range from 66 K to 340 K at pressures up to 12 MPa

Nowak

Kleinrahm

Wagner

1997

The Journal of Chemical Thermodynamics

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Section: Methodsmentioning

confidence: 99%

Measurement and correlation of the (p,ρ,T) relation of nitrogen. I. The homogeneous gas and liquid regions in the temperature range from 66 K to 340 K at pressures up to 12 MPa

Nowak

Kleinrahm

Wagner

1997

The Journal of Chemical Thermodynamics

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“…As well as the saturation densities of methane, (3,4) carbon dioxide, (5) argon, (6) and ethylene, (7) the saturated-vapour densities of nitrogen along the largest part of the coexistence curve were determined in the following way. In the lid of the measuring cell (see the schematic drawing in reference 3), an especially designed small reference cell was included which was filled with nitrogen in such a way that the fluid was in the phase equilibrium (vapour + liquid).…”

Section: Methodsmentioning

confidence: 99%

“…Figure 5 shows an enlarged section of figure 4 for the temperature range (T c − 3.7 K) E T E T c . Taking into account the reproducibilities of the measured saturation densities, the probable course of r d in the critical region is plotted; the course of r d turns down significantly for temperatures above 125.7 K. Taking into account our experiences based on the investigations of the critical region of methane, (4) carbon dioxide, (5) argon, (6) and ethylene, (7) the illustrated course of r d is the probable one. But it should be noted that either a straight course or a stronger curvature of r d might also be possible.…”

Section: New Correlation Equations and New Critical Constantsmentioning

confidence: 98%

Measurement and correlation of the (p,ρ,T) relation of nitrogen. II. Saturated-liquid and saturated-vapour densities and vapour pressures along the entire coexistence curve

Nowak

Kleinrahm

Wagner

1997

The Journal of Chemical Thermodynamics

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Comprehensive and accurate measurements of the saturated-liquid and saturated-vapour densities together with the vapour pressure of pure nitrogen were carried out from the temperature T = 64 K (triple-point temperature Tt = 63.151 K) to 0.022 K below the critical temperature. The typical values of the total uncertainties of the measurements are: Q=2·10 −4 ·ps = for the vapour pressures, Q=1.2·10 −4 ·r'= for the saturated-liquid densities, and Q=3·10 −4 ·r0= for the saturated-vapour densities. The critical constants (Tc = 126.192 K, rc = 313.3 kg·m −3 , pc = 3.3958 MPa) and the isothermal compressibilities in the critical region close to the phase boundary have also been determined from these measurements. Comparisons with experimental results of previous workers are presented. Based on the new values of this work, new correlation equations for the vapour pressure, the saturated-liquid density, and the saturated-vapour density have been established. 7

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“…The very accurate data from Duschek et al [51] are 185 used for the saturated liquid density (below 295 K the experimental uncertainty is estimated to less than ±0.015%). For the saturated vapor pressure we employ data from [51][52][53] (experimental uncertainty estimated to ±0.016−0.012%, ±100 Pa and ±0.1% respectively). It is assumed that the standard deviation, σ exp i , of each experimental point can be approximated by the experimental un-…”

Section: Parameter Estimation -Uncertainty and Correlationmentioning

confidence: 99%

Uncertainty analysis of the CPA and a quadrupolar CPA equation of state – With emphasis on CO2

Bjørner

Sin

Kontogeorgis

2016

Fluid Phase Equilibria

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The parameters of thermodynamic models, such as the cubic plus association (CPA) equation of state, are subject to uncertainties due to measurement errors in the experimental data that the models are correlated to. More importantly as the number of adjustable parameters increase, the parameter estimation problem becomes more complicated due to parameter identifiability issues. In this work the uncertainties in the pure compound parameters of CO 2 are investigated using several different CPA approaches, including a new quadrupolar CPA. The uncertainties are estimated using both least squares estimation and the bootstrap method for parameter estimation. The uncertainties in the parameters estimated from the bootstrap method are propagated to physical property and vapor liquid equilibrium predictions using Monte Carlo simulations.The results indicate that both the pure compound parameter uncertainty and the propagated uncertainty is negligible for the modeling approaches which employ three adjustable parameters. For modeling approaches with more than three adjustable parameters, however, there may be significant uncertainties in the pure compound parameters, as well as a high degree of correlation between the adjustable parameters. This results in significant propagated errors * Corresponding author Email address: mgabj@kt.dtu.dk (Martin G. Bjørner)Preprint submitted to Fluid Phase Equilibria December 31, 2015for certain output properties. To reduce the uncertainty in the adjustable model parameters the heat of vaporization was included as additional correlation data.This resulted in parameter distributions which followed a normal distribution more closely, however, the correlation between the adjustable parameters remained high. Overall the results indicate, that it is important to report parameter uncertainties together with their correlation matrix when a model is developed, so that better informed decisions can be made, for instance about which model extension, or association scheme should be employed.

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Measurement and correlation of the (pressure, density, temperature) relation of carbon dioxide II. Saturated-liquid and saturated-vapour densities and the vapour pressure along the entire coexistence curve

Cited by 155 publications

References 36 publications

Measurement and correlation of the (p,ρ,T) relation of nitrogen. I. The homogeneous gas and liquid regions in the temperature range from 66 K to 340 K at pressures up to 12 MPa

Measurement and correlation of the (p,ρ,T) relation of nitrogen. I. The homogeneous gas and liquid regions in the temperature range from 66 K to 340 K at pressures up to 12 MPa

Measurement and correlation of the (p,ρ,T) relation of nitrogen. II. Saturated-liquid and saturated-vapour densities and vapour pressures along the entire coexistence curve

Uncertainty analysis of the CPA and a quadrupolar CPA equation of state – With emphasis on CO2

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