Article pubs.acs.org/jced
Accurate Density Measurements on Ternary Mixtures (Carbon Dioxide + Nitrogen + Argon) at Temperatures from (323.15 to 423.15) K with Pressures from (3 to 31) MPa using a Single-Sinker Densimeter Xiaoxian Yang, Zhe Wang,* and Zheng Li State Key Laboratory of Power Systems, Department of Thermal Engineering, Tsinghua University, Beijing, 100084, P.R. China ABSTRACT: The densities of two ternary mixtures (0.900 carbon dioxide + 0.050 nitrogen + 0.050 argon and 0.950 carbon dioxide + 0.040 nitrogen + 0.010 argon in mole fraction) were measured at temperatures from (323.15 to 423.15) K with pressures from (3 to 31) MPa using a singlesinker magnetic suspension densimeter. The expanded measurement uncertainties (k = 2) were 35 mK for temperature, 3.4 kPa for pressure, and 0.033 % for density. Mixture samples were prepared gravimetrically with the expanded uncertainty (k = 2) in composition 0.001 mole fraction. With all of the measurement and composition effects considered, the expanded combined uncertainty (k = 2) in the density determination was generally within 0.2 % except at thermal states at the vicinity of the critical point near the Widom line. Relative deviations of the experimental data from the GERG-2008 equation of state (EOS), a Helmholtz energy model for natural gas mixtures, and from the EOS-CG, another new Helmholtz energy model for humid gases and fluid mixtures relevant for carbon capture and storage, were within 0.6 % for both mixtures. The relative deviation reached a maximum along the isotherm at the thermal state at the vicinity of the critical point near the Widom line.
1. INTRODUCTION The physical science basis of climate change was comprehensively investigated by IPCC1 in 2013. The increase in the atmospheric concentration of carbon dioxide was regarded as the largest contribution to global climate change. Among all of the strategies in reducing global carbon emissions, carbon capture and storage (CCS) was considered as a most efficient and currently practical one.2 Fluid mixtures involved in the pipeline transportation in CCS were mainly composed of carbon dioxide, argon, nitrogen, oxygen, water, sulfur oxide, and nitric oxide.3 Process design for CCS required knowledge of the volumetric properties of carbon dioxide-rich mixtures. However, to the best of our knowledge, there were limited accurate experimental data for the corresponding mixtures; especially, no experimental data were available for the (carbon dioxide + nitrogen + argon) system. To fill this data gap, comprehensive pressure, density, and temperature (p, ρ, T) measurements on two ternary mixtures (0.900 carbon dioxide +0.050 nitrogen + 0.050 argon and 0.950 carbon dioxide + 0.040 nitrogen + 0.010 argon in mole fraction) at temperatures from T = (323.15 to 423.15) K with pressures from p = (3 to 31) MPa were conducted by a single-sinker magnetic suspension densimeter. Besides, the GERG-2008 equation of state (EOS),4 a currently internationally accepted standard for the prediction of the thermodynamic properties of natural gases as implemented in the NIST REFPROP database of Lemmon et al.,5 was built © 2015 American Chemical Society
mainly based on experimental data of pure materials and binary mixtures; thus, the measurement results on ternary mixtures could be significant in evaluating the reliability of the GERG2008 EOS in predicting multicomponent mixtures.
2. EXPERIMENTAL SECTION 2.1. Apparatus Description. The single-sinker magnetic suspension densimeter is a state-of-the-art instrument for accurate density measurements of fluids over large ranges of temperature and pressure. This technique was developed by Brachthäuser et al.6,7 in the early 1990s. An overview of this general type of instrument was published by Wagner and Kleinrahm.8 Our apparatus (FluiDENS, Rubotherm, Germany) was specifically designed to investigate the (p, ρ, T) behavior of fluid mixtures relevant for CCS over the temperature range from (273.15 to 423.15) K with pressures up to 35 MPa. Detailed descriptions of the apparatus, the measuring system, the general experimental procedure, and the data analysis method were given by Yang et al.9 Only a brief introduction of the measurement techniques concerning measurement uncertainty is given here. The temperature measurement was conducted with a calibrated 25 Ω platinum resistance Received: July 20, 2015 Accepted: September 28, 2015 Published: October 12, 2015 3353
DOI: 10.1021/acs.jced.5b00625 J. Chem. Eng. Data 2015, 60, 3353−3357
Journal of Chemical & Engineering Data
Article
Table 1. Sample Information chemical name
source
initial mole fraction purity
purification method
final mole fraction purity
analysis method
carbon dioxide nitrogen argon
Beijing Beiwen Gas Beijing Beiwen Gas Beijing Beiwen Gas
0.999995 0.999999 0.999999
none none none
0.999995 0.999999 0.999999
gas chromatography gas chromatography gas chromatography
thermometer. The resistance of the thermometer was measured by a precision AC resistance thermometry bridge (F700, ASL, U.K.) in reference to a calibrated bridge internal resistor. Pressures were measured with a calibrated Digiquartz intelligent pressure transmitter (9000-6k-101, Paroscientific, U.S.A.). To measure the density of fluid samples, a sinker made of monocrystalline silicon (V ≈ 17.3 cm3, m ≈ 40.0 g, ρ ≈ 2.31 g/ cm3) was weighed inside the high-pressure measuring cell through a magnetic suspension coupling with an analytical balance (XP205, Mettler Toledo, Switzerland). The density was determined according to the Archimedes buoyance principle. Detailed uncertainty analysis for this apparatus were given in a previous paper.9 The expanded measurement uncertainties (k = 2) for temperature U(T), pressure U(p), and density Ur,M(ρ) are 35 mK, 3.4 kPa, and 0.033 %, respectively. The uncertainty guidance we followed is the Guide to the Expression of Uncertainty in Measurement.10 2.2. Fluid Samples. The fluid samples, including the two mixtures to be measured and the pure nitrogen (0.999999 mole fraction) used as a calibration fluid, were all provided by Beijing Beiwen Gas, China. The reason and the method that pure nitrogen was used as a calibration fluid were explained in detail in a previous paper.9 The pure substances are described in Table 1. The mixtures were prepared gravimetrically by the supplier, and the expanded uncertainty (k = 2) in composition was 0.001 mole fraction. The uncertainty in the density determination attributed to the composition uncertainty Ux(ρ) was roughly estimated by Ux(ρ) = ρGERG (T , p , x + Δx) − ρGERG (T , p , x)
where (∂ρ/∂T)p and (∂ρ/∂p)T were estimated by the GERG2008 EOS. The values of Ur,C(ρ) at all the measuring points are listed in Table 2. Generally, Ur,C(ρ) was less than 0.2 %. At the vicinity of the critical point in the supercritical state and near the Widom line, Ur,C(ρ) could be as high as 0.4 %. The definition adopted for the Widom line in this paper is the maximum locus of the isobaric heart capacity in the supercritical state.
3. RESULTS AND DISCUSSION Experimental (p, ρ, T) data for the (0.900 carbon dioxide + 0.050 nitrogen + 0.050 argon) and (0.950 carbon dioxide + 0.040 nitrogen + 0.010 argon) mixtures from T = (323.15 to 423.15) K and from p = (3 to 31) MPa are listed in Table 2. The p−T phase diagrams for both mixtures, the Widom line, and the maximum locus of (∂ρ/∂p)T in the supercritical region for the first mixture estimated by the GERG-2008 EOS, and the measuring points are shown in Figure 1. Relative deviations of the experimental data from the GERG-2008 EOS and the EOSCG,12,13 another Helmholtz energy model for CCS mixtures as implemented in the TREND software package of RuhrUniversity Bochum,14 are shown in Figure 2 and Figure 3 for the two mixtures, respectively. At pressures lower than 10 MPa, the relative deviations decrease with decreasing pressure and are expected to converge to zero at the ideal gas limit. This, to a certain extent, verified the reliability of the experimental results. The experimental densities of the (0.900 carbon dioxide + 0.050 nitrogen + 0.050 argon) mixture agree with values calculated by the GERG-2008 EOS within 0.2 % across the whole measuring range except at pressures from (12 to 24) MPa with temperature 323.15 K. At T = 323.15 K, an obvious maximal negative deviation of −0.59 % was discovered around 13.6 MPa. In the p−T phase diagram, this maximal negative deviation point (323.15 K, 13.6 MPa) is very close to the Widom line, as shown in Figure 1. Similar agreement between the maximal negative deviation points and the Widom line was observed at T = (348.15 and 373.15) K. The density of a fluid changes significantly with a tiny variation in the pressure where (∂ρ/∂p)T reaches a maximum along an isotherm; Therefore, it was difficult for the EOS to predict density accurately at this place. However, as shown in Figure 1, the maximal negative relative deviation points agree better with the Widom line than with the maximum locus of (∂ρ/∂p)T. Further experimental investigation is required to clearly reveal and explain this result. Relative deviations of the experimental data of this mixture from the EOS-CG were generally within 0.5 %, and anomalous behaviors were observed at the vicinity of the critical point near the Widom line as well. At pressures higher than 15 MPa, the relative deviations of the experimental data from values calculated by the EOS-CG were positive, while those from values calculated by the GERG-2008 EOS were negative. Except for pressures from (3 to 14) MPa at temperature 323.15 K, the experimental data of the (0.950 carbon dioxide + 0.040 nitrogen + 0.010 argon) mixture agree well with values calculated by the GERG-2008 EOS within 0.1 %, half of that for the former mixture. In the GERG-2008 EOS, the coefficients of
(1)
where ρGERG(T, p, x) is the density calculated by the GERG2008 EOS4 at temperature T, pressure p, and composition x. The element of the array x is the mole fraction of each component in the mixtures under study. A possible maximal error in the composition was assigned to the value of Δx, i.e., Δx = (0.001, −0.0005, −0.0005) mole fraction. Mixture compositions could vary due to the unequal absorption of components on the walls of the measuring cell and the tubes. The composition distortion would lead to a change of the measured fluid density. However, theoretical or numerical analysis on the sorption effect is not yet available, and the experimental estimation using the flushing-themeasuring-cell method suggested by Richter and Kleinrahm11 was not possible for our densimeter. Therefore, the contribution from sorption effects to the relative expanded uncertainty (k = 2) in the density determination Ur,S(ρ) was roughly estimated to be 0.1 %, as suggested by Richter and Kleinrahm.11 With all of the measurement and composition effects considered, the expanded combined uncertainty (k = 2) in the density determination UC(ρ) was calculated by ⎤2 ⎡⎛ ⎞ ⎤ 2 ⎡⎛ ⎞ ∂ρ ∂ρ ⎢ ⎢ ⎥ ⎜ ⎟ UC(ρ) = ·U (T ) + ⎜ ⎟ ·U (p)⎥ + UM(ρ)2 ⎝ ⎠ ⎢⎣⎝ ∂p ⎠ ⎥⎦ ⎢⎣ ∂T p ⎥⎦ T 2
+ Ux(ρ)2 + US(ρ)2
(2) 3354
DOI: 10.1021/acs.jced.5b00625 J. Chem. Eng. Data 2015, 60, 3353−3357
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Table 2. Experimental Values of Density ρ at Temperature T and Pressure pa T/K 323.194 323.192 323.187 323.211 323.178 323.156 323.186 323.210 323.208 323.188 323.210 323.195 323.203 323.189 323.140 348.158 348.178 348.195 348.185 348.189 348.223 348.222 348.191 348.188 348.166 348.124 348.172 348.169 348.182 348.211 373.192 373.206 373.153 373.164 373.166 373.145 373.165 373.210 373.144 373.206 373.171 373.156 373.141 373.192 373.160 398.217 398.211 398.193 398.186 398.167 398.167 398.178 398.197 398.191 398.176 398.205 398.196 398.211 398.190 398.178
p/MPa
ρ/kg·m−3
0.900 CO2 + 0.050 N2 + 0.050 Ar 2.9817 53.258 4.9827 97.439 6.9790 152.258 8.9732 224.124 10.9686 321.525 12.9658 435.991 14.9639 532.421 16.9615 600.950 18.9611 650.492 20.9625 688.379 22.9606 718.489 24.9594 743.731 26.9575 765.242 28.9557 784.142 30.9507 801.107 2.9838 48.116 4.9819 85.470 6.9806 128.168 8.9746 177.446 10.9696 234.503 12.9669 298.981 14.9641 367.686 16.9638 434.488 18.9619 493.689 20.9715 544.109 22.9607 585.877 24.9611 620.769 26.9653 650.730 28.9549 676.399 30.9516 698.964 2.9845 44.033 4.9813 76.841 6.9769 112.757 8.9749 152.135 10.9697 195.039 12.9681 241.384 14.9645 290.096 16.9629 339.657 18.9627 388.502 20.9640 434.148 22.9600 476.123 24.9631 513.914 26.9563 547.435 28.9639 577.252 30.9503 603.883 2.9867 40.711 4.9845 70.238 6.9803 101.687 8.9761 135.145 10.9719 170.580 12.9706 207.803 14.9682 246.325 16.9673 285.568 18.9659 324.752 20.9690 363.178 22.9665 399.808 24.9627 434.409 26.9601 466.609 28.9575 496.469 30.9530 523.915
Ur,C(ρ)
T/K
0.0016 0.0014 0.0015 0.0020 0.0029 0.0035 0.0030 0.0025 0.0021 0.0019 0.0017 0.0016 0.0015 0.0015 0.0014 0.0016 0.0014 0.0014 0.0015 0.0017 0.0019 0.0021 0.0022 0.0021 0.0020 0.0018 0.0017 0.0016 0.0016 0.0015 0.0016 0.0013 0.0013 0.0013 0.0014 0.0015 0.0016 0.0017 0.0017 0.0017 0.0017 0.0016 0.0016 0.0015 0.0015 0.0016 0.0013 0.0012 0.0012 0.0013 0.0013 0.0014 0.0014 0.0015 0.0015 0.0015 0.0015 0.0015 0.0015 0.0014
323.185 323.182 323.183 323.175 323.167 323.188 323.184 323.190 323.198 323.199 323.181 323.187 323.183 323.175 323.120 348.217 348.195 348.196 348.160 348.156 348.196 348.195 348.190 348.187 348.177 348.189 348.227 348.173 348.165 348.170 373.160 373.165 373.200 373.166 373.151 373.156 373.166 373.167 373.106 373.157 373.187 373.179 373.185 373.159 373.164 398.221 398.197 398.188 398.174 398.133 398.185 398.188 398.179 398.209 398.169 398.171 398.167 398.174 398.198 398.204 3355
p/MPa
ρ/kg·m−3
0.950 CO2 + 0.040 N2 + 0.010 Ar 2.9796 54.080 4.9828 100.144 6.9789 159.616 8.9720 244.568 10.9688 375.296 12.9657 516.776 14.9643 607.677 16.9669 664.847 18.9630 705.140 20.9641 736.284 22.9633 761.704 24.9616 783.039 26.9589 801.570 28.9555 817.986 30.9506 832.920 2.9849 48.816 4.9855 87.381 6.9802 132.201 8.9738 185.567 10.9698 249.680 12.9669 324.501 14.9651 404.366 16.9623 478.045 18.9626 539.173 20.9628 588.100 22.9645 627.462 24.9606 659.694 26.9582 687.343 28.9556 710.990 30.9510 731.660 2.9813 44.555 4.9838 78.266 6.9810 115.488 8.9727 156.839 10.9691 202.791 12.9670 253.145 14.9652 306.812 16.9640 361.550 18.9621 414.690 20.9645 463.318 22.9611 506.593 24.9594 544.704 26.9590 577.986 28.9543 607.237 29.9268 620.187 2.9858 41.170 4.9815 71.260 6.9817 103.674 8.9762 138.405 10.9707 175.543 12.9685 214.869 14.9672 255.989 16.9676 298.124 18.9648 340.028 20.9662 381.054 22.9625 419.843 24.9601 456.021 26.9629 489.349 28.9553 519.572 30.9504 547.177
Ur,C(ρ) 0.0016 0.0014 0.0017 0.0025 0.0042 0.0040 0.0029 0.0023 0.0020 0.0018 0.0016 0.0015 0.0015 0.0014 0.0014 0.0016 0.0014 0.0014 0.0015 0.0018 0.0022 0.0025 0.0024 0.0022 0.0020 0.0018 0.0017 0.0016 0.0015 0.0015 0.0016 0.0013 0.0013 0.0013 0.0014 0.0016 0.0017 0.0018 0.0018 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 0.0016 0.0013 0.0013 0.0013 0.0013 0.0014 0.0014 0.0015 0.0015 0.0015 0.0016 0.0015 0.0015 0.0015 0.0015
DOI: 10.1021/acs.jced.5b00625 J. Chem. Eng. Data 2015, 60, 3353−3357
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Table 2. continued T/K 423.117 423.119 423.128 423.117 423.107 423.123 423.116 423.139 423.176 423.183 423.186 423.184 423.198 423.186 423.195
p/MPa
ρ/kg·m−3
0.900 CO2 + 0.050 N2 + 0.050 Ar 2.9943 38.004 4.9828 64.842 6.9808 93.086 8.9750 122.541 10.9717 153.214 12.9689 184.877 14.9673 217.328 16.9670 250.186 18.9681 283.056 20.9662 315.541 22.9668 347.300 24.9632 377.891 26.9624 407.150 28.9560 434.872 30.9536 461.033
Ur,C(ρ)
T/K
0.0016 0.0013 0.0012 0.0012 0.0012 0.0012 0.0013 0.0013 0.0013 0.0013 0.0014 0.0014 0.0014 0.0014 0.0014
423.151 423.144 423.134 423.129 423.208 423.258 423.188 423.195 423.214 423.264 423.220 423.201 423.198 423.195 423.139
p/MPa
ρ/kg·m−3
0.950 CO2 + 0.040 N2 + 0.010 Ar 2.9870 38.329 4.9839 65.754 6.9774 94.602 8.9730 124.971 10.9698 156.723 12.9701 189.756 14.9662 223.792 16.9621 258.339 18.9656 293.083 20.9649 327.295 22.9609 360.723 24.9588 392.827 26.9593 423.342 28.9556 452.019 30.9508 478.983
Ur,C(ρ) 0.0016 0.0013 0.0012 0.0012 0.0012 0.0013 0.0013 0.0013 0.0014 0.0014 0.0014 0.0014 0.0014 0.0014 0.0014
a The expanded measurement uncertainties (k = 2) are 35 mK for temperature, 3.4 kPa for pressure, and 0.033 % for density. Mixture samples were prepared gravimetrically with the expanded uncertainties (k = 2) in composition 0.001 mole fraction. Ur,C(ρ) is the relative expanded combined uncertainty (k = 2) in the density determination with all the measurement and composition effects considered.
Figure 2. Relative deviations of the experimental densities ρexp for the (0.900 carbon dioxide + 0.050 nitrogen + 0.050 argon) mixture from densities ρEOS calculated by EOS. ●, ■, ◆, ▲, and ▼ refer to the relative deviations of ρexp at T ≈ (323.15, 348.15, 373.15, 398.15, and 423.15) K, respectively, from values calculated by the GERG-2008 EOS4 (zero line); ○, □, ◊, △, and ▽ refer to the relative deviations of ρexp at T ≈ (323.15, 348.15, 373.15, 398.15, and 423.15) K, respectively, from values calculated by the EOS-CG14 (zero line). Error bars for the combined standard uncertainties of the density determination at T ≈ 323.15 K were plotted, while those at other isotherms, which were approximately 0.1 %, were not plotted for simplicity and clarity.
Figure 1. Pressure−temperature phase diagrams of the ternary mixtures. •, critical point, and , liquid−vapor phase boundary for the (0.900 carbon dioxide + 0.050 nitrogen + 0.050 argon) mixture with higher bubble-line and for the (0.950 carbon dioxide + 0.040 nitrogen + 0.010 argon) mixture with lower bubble-line estimated by the GERG-2008 EOS;4 ●, ■, ◆, ▲, and ▼ refer to measuring points at T ≈ (323.15, 348.15, 373.15, 398.15, and 423.15) K, respectively; -, Widom line, and -•-•, maximum locus of (∂ρ/∂p)T for the (0.900 carbon dioxide + 0.050 nitrogen + 0.050 argon) mixture estimated by the GERG-2008 EOS; ×, pressure at which the relative deviation of the experimental data from the GERG-2008 EOS for the (0.900 carbon dioxide + 0.050 nitrogen + 0.050 argon) mixture reaches a maximum along each isotherm.
to the Widom line in the p−T phase diagram as well. The agreement between the experimental data and the EOS-CG was generally within 0.25 %, half of that for the former mixture as well. Similar peculiar behavior at pressures from (3 to 14) MPa with temperature 323.15 K was observed for the EOS-CG. Although the EOS-CG was built based on the GERG-2008 EOS and was specially designed for the CCS mixtures, it did not yield obviously better agreement with the experimental data for these two ternary mixtures than the GERG-2008 EOS did at pressures lower than 9 MPa. Slightly worse performance of the EOS-CG than of the GERG-2008 EOS was found at pressures higher than 15 MPa. Nonetheless, excellent agreement was achieved between the experimental data and both EOSs. These
the equation for the (carbon dioxide + nitrogen) mixture were fitted with a large amount of accurate experimental data, and a characteristic departure function was built, while those for the (carbon dioxide + argon) mixture were fitted without sufficient accurate experimental data, and no departure function was built. Therefore, it was reasonable to expect that, the GERG2008 EOS yielded a lower relative deviation from the experimental data in predicting the (carbon dioxide + nitrogen + argon) mixture with a lower concentration of argon. Obvious maximal negative deviation of the experimental data from the GERG-2008 EOS was found at pressure 10.8 MPa along the isotherm 323.15 K. This point (323.15 K, 10.8 MPa) was close 3356
DOI: 10.1021/acs.jced.5b00625 J. Chem. Eng. Data 2015, 60, 3353−3357
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Article
AUTHOR INFORMATION
Corresponding Author
* E-mail:
[email protected]. Tel.: +86-13811902238. Funding
The research leading to these results has received funding from the European Community’s Seventh Framework Programme (FP7-ENERGY-20121-1-2STAGE) under grant agreement no. 308809 (The IMPACTS project). The authors acknowledge the project partners and the following funding partners for their contributions: Statoil Petroleum AS, Lundin Norway AS, Gas Natural Fenosa, MAN Diesel & Turbo SE and Vattenfall AB. Notes
The authors declare no competing financial interest.
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Figure 3. Relative deviations of the experimental densities ρexp for the (0.950 carbon dioxide + 0.040 nitrogen + 0.010 argon) mixture from densities ρEOS calculated by EOS. ●, ■, ◆, ▲, and ▼ refer to the relative deviations of ρexp at T ≈ (323.15, 348.15, 373.15, 398.15, and 423.15) K, respectively, from values calculated by the GERG-2008 EOS4 (zero line); ○, □, ◊, △, and ▽ refer to the relative deviations of ρexp at T ≈ (323.15, 348.15, 373.15, 398.15, and 423.15) K, respectively, from values calculated by the EOS-CG14 (zero line). Error bars for the combined standard uncertainties of the density determination at T ≈ 323.15 K were plotted, while those at other isotherms, which were approximately 0.1 %, were not plotted for simplicity and clarity.
REFERENCES
(1) Stocker, T. F.; Qin, D.; Plattner, G. K.; Tignor, M.; Allen, S. K.; Boschung, J.; Nauels, A.; Xia, Y.; Bex, V.; Midgley, P. M. Climate Change 2013 - The Physical Science Basis; Cambridge University Press: Cambridge, UK, 2013. (2) Metz, B.; Davidson, O.; De Coninck, H.; Loos, M.; Meyer, L. Carbon dioxide capture and storage; IPCC: Geneva, 2005. (3) De Visser, E.; Hendriks, C.; Barrio, M.; Mølnvik, M. J.; de Koeijer, G.; Liljemark, S.; Le Gallo, Y. Dynamis CO2 quality recommendations. Int. J. Greenhouse Gas Control 2008, 2, 478−484. (4) Kunz, O.; Wagner, W. The GERG-2008 wide-range equation of state for natural gases and other mixtures: an expansion of GERG2004. J. Chem. Eng. Data 2012, 57, 3032−3091. (5) Lemmon, E. W.; Huber, M. L.; McLinden, M. O. NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties-REFPROP, Version 9.1, National Institute of Standards and Technology: Boulder, 2013. (6) Wagner, W.; Brachthäuser, K.; Kleinrahm, R.; Lösch, H. W. A new, accurate single-sinker densitometer for temperatures from 233 to 523 K at pressures up to 30 MPa. Int. J. Thermophys. 1995, 16, 399− 411. (7) Brachthäuser, K.; Kleinrahm, R.; Lösch, H. W.; Wagner, W. Entwicklung eines neuen Dichtemeßverfahrens und Aufbau einer Hochtemperatur-Hochdruck-Dichtemeßanlage; Fortschr.-Ber. VDI, Reihe 8, Nr. 371, VDI-Verlag: Düsseldorf, 1993. (8) Wagner, W.; Kleinrahm, R. Densimeters for very accurate density measurements of fluids over large ranges of temperature, pressure, and density. Metrologia 2004, 41, S24−S39. (9) Yang, X.; Richter, M.; Wang, Z.; Li, Z. Density measurements on binary mixtures (nitrogen + carbon dioxide and argon + carbon dioxide) at temperatures from (298.15 to 423.15) K with pressures from (11 to 31) MPa using a single-sinker densimeter. J. Chem. Thermodyn. 2015, 91, 17−29. (10) JCGM. Evaluation of measurement data - Guide to the expression of uncertainty in measurement; BIPM: Sèvres, 2008. (11) Richter, M.; Kleinrahm, R. Influence of adsorption and desorption on accurate density measurements of gas mixtures. J. Chem. Thermodyn. 2014, 74, 58−66. (12) Gernert, J. A new helmholtz energy model for humid gases and CCS mixtures. Dissertation, Ruhr University Bochum, Bochum, 2013. (13) Gernert, J.; Span, R. EOS-CG: A Helmholtz energy mixture model for humid gases and CCS mixtures. J. Chem. Thermodyn. 2015, 10.1016/j.jct.2015.05.015 (14) Span, R.; Eckermann, T.; Herrig, S.; Hielscher, S.; Jäger, A.; Thol, M. TREND. Thermodynamic Reference and Engineering Data 2.0; Lehrstuhl für Thermodynamik, Ruhr-Universität: Bochum, 2015.
two EOSs were both suitable for estimating the density of the (carbon dioxide + nitrogen + argon) mixture with carbon dioxide mole fractions higher than 0.900 at temperatures from (323.15 to 423.15) K with pressures from (3 to 31) MPa.
4. CONCLUSIONS No experimental data were available for the (carbon dioxide + nitrogen + argon) mixture. To fill this data gap, comprehensive (p, ρ, T) measurements on ternary mixtures (0.900 carbon dioxide + 0.050 nitrogen + 0.050 argon and 0.950 carbon dioxide + 0.040 nitrogen + 0.010 argon in mole fraction) were carried out at temperatures from (323.15 to 423.15) K with pressures from (3 to 31) MPa using a single-sinker magnetic suspension densimeter. With all of the measurement and composition effects considered, the expanded combined uncertainty (k = 2) in the density determination was generally within 0.2 % except at the thermal states at the vicinity of the critical point near the Widom line. Relative deviations of the experimental data from the GERG-2008 EOS were generally within 0.2 % and 0.1 % for the two mixtures, respectively. The relative deviation reached a maximum, as high as approximately 0.6 %, along an isotherm at the thermal state at the vicinity of the critical point near the Widom line. Further experimental investigation is required to clearly reveal and explain this phenomenon. Relative deviations of the experimental data from the EOS-CG were generally within 0.5 % and 0.25 % for the two mixtures, respectively. Generally, the EOS-CG yielded higher deviation from the experimental data than the GERG2008 EOS did at pressures higher than 15 MPa. The experimental results confirmed the suitability of the GERG2008 EOS and the EOS-CG for the density estimation of the (carbon dioxide + nitrogen + argon) mixtures with carbon dioxide mole fractions higher than 0.900 at temperatures from (323.15 to 423.15) K with pressures from (3 to 31) MPa. 3357
DOI: 10.1021/acs.jced.5b00625 J. Chem. Eng. Data 2015, 60, 3353−3357
