Thermo-physical properties of CO2 mixtures and their impacts on CO2 capture, transport and storage: Progress since 2011

Applied Energy 255 (2019) 113789

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Applied Energy journal homepage: www.elsevier.com/locate/apenergy

Thermo-physical properties of CO2 mixtures and their impacts on CO2 capture, transport and storage: Progress since 2011

T

⁎

Hailong Lia,b, , Beibei Donga, Zhixin Yuc, Jinyue Yanb, Kai Zhua a

Key Laboratory of Refrigeration Technology of Tianjin, Tianjin University of Commerce, Tianjin 300134, China School of Business, Society & Engineering, Mälardalen University, Västerås SE-72123, Sweden c Department of Energy and Petroleum Engineering, University of Stavanger, 4036 Stavanger, Norway b

H I GH L IG H T S

experimental data and theoretical models on thermo-physical properties of CO • The new knowledge gaps regarding measurements are identified. • The performance of different property models are presented. • The • The property impacts on carbon capture and storage are updated.

2

mixtures since 2009 are updated.

A R T I C LE I N FO

A B S T R A C T

Keywords: CO2 capture transport and storage Thermo-physical properties Experimental data Modeling Property impacts

The knowledge of accurate thermo-physical properties is crucial for the development and deployment of CO2 capture, transport and storage (CCS). The progress on the experimental data and theoretical models regarding thermo-physical properties of CO2 mixtures as well as the property impact on the design and operation of different CCS processes has been updated. The newly published experimental data since 2011 have been collected and reviewed based on which the new knowledge gaps regarding measurements have been identified. There have also been some advanced models proposed recently, which have shown good performances. The collected model performances don’t show there exist a model that is superior to others; but they still provide a good guideline regarding model selection. However, developing more-complex models as the complexity may not necessarily improve the accuracy when empirical parameters were included and well-tuned. By comparing the importance of the properties and the accuracy of existing models, suggestions were given regarding the development of property models that should be prioritized.

1. Introduction The latest 2018 Special Report on Global Warming of 1.5 °C by the Intergovernmental Panel on Climate Change (IPCC) indicated that in order to realize net-zero emissions by 2050, it requires to capture at least 4 Gt/year of CO2 in 2040 and 8 Gt/year in 2050 [1–3]. CO2 capture and storage (CCS) is playing a key role, which is the only option capable of decarbonizing major industrial sectors, particularly the power, steel and iron, cement and petrochemical industries [1]. CCS comprises of CO2 capture, which technologies are mainly divided into three categories including post-combustion capture, pre-combustion capture and oxy-fuel combustion capture, CO2 transport and CO2 storage [4]. Significant efforts have been dedicated to the research and development (R&D) of CCS technologies and some commercial

⁎

demonstration projects have been launched globally [1]. Clear progresses have been made in the R&D. For example, from the technical perspective, new solvents have been developed, which can reduce the energy penalty to 1.83 GJ/tCO2 [5]; from the economic perspective, the cost of CCS continues to decrease, which can currently reach 20 USD/ tCO2 [6], as more facilities have been commercialized; and from the policy perspective, a growth in CCS policy confidence across multiple country jurisdictions can be seen, such as the enactment of 45Q (tax credit) legislation in US and the CCUS Cost Challenge Taskforce in UK [1]. In addition, CO2 utilization, which can convert CO2 into valueadded products, has also attracted much attention. International Energy Agency (IEA) findings reported that the potential of CO2 utilization could contribute 14% to Paris climate targets of 2 °C by 2060, up to 32% in the transition between the 2 °C scenario (2DS) to the beyond

Corresponding author. E-mail address: [email protected] (H. Li).

https://doi.org/10.1016/j.apenergy.2019.113789 Received 27 March 2019; Received in revised form 19 August 2019; Accepted 26 August 2019 0306-2619/ © 2019 Elsevier Ltd. All rights reserved.

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CO2 mixtures, more measurements are available, such as VLE of CO2/ Ar/O2, CO2/SO2/O2 [17] and CO2/N2/H2 [20], which are very important for the calibration and validation of theoretical models.

2 °C scenario [1]. The objectives of R&D of CCS are primarily focused on the issues about energy efficiency, cost and safety. It has been well recognized that the design and operation of CCS systems rely on a deeper understanding of the thermo-physical properties of CO2 and CO2 mixtures, which enables the correct estimation of the characteristics of separated streams, the sizing of equipment and the operating conditions of different processes [2,3,7,8]. The key properties include thermodynamic properties such as vapor liquid equilibrium (VLE) and densities; and transport properties such as viscosity, thermal conductivity and diffusivity. In our previous review works published in 2011, the possible impurities from different CCS processes and applications were identified [7], the corresponding operating conditions were collected and the state of the art about the research on thermodynamic properties [7] and transport properties [8] of CO2 and CO2 mixtures was presented respectively. Some important knowledge gaps were identified in both experimental works and modeling studies. Meanwhile, Munkejord et al. [9] investigated the properties needed in CO2 transport, such as phase behavior, density, speed of sound, viscosity, and thermal conductivity. In addition to VLE, vapor-liquid-liquid equilibrium (VLLE) and equilibrium involving solids and hydrates were also included. Furthermore, understanding the impacts of properties on the design and operation of different CCS processes is essential to prioritize the research work about properties. The higher the impact is, the more important the property is. We have also performed a systematic study [10] to review the impacts of thermo-physical properties on different processes and technologies of CCS, including CO2 capture, conditioning, transport and storage. It was concluded that the most important properties are different for different processes. Due to the lack of studies and process complexity, the impacts on some processes still remain unclear. For example, there has been no study about the property impact on physical absorption, physical adsorption and membrane separation; and for the influence of liquid properties on the design of chemical absorption, little information is available. With the advancement of measuring technologies and the increasing attention on the fundamental properties, many new experimental data have been published, which have bridged some of the identified knowledge gaps. Meanwhile, with the development of computer technologies, new models are also emerging. The objective of this review is to update the status regarding the studies on thermo-physical properties of CO2 and CO2 mixtures since 2011 with special attentions paid to the development of property models. In addition, this work will also summarize the progress in assessing the property impacts on CCS processes. The remainder of the paper is organized as follows: Sections 2 and 3 present the latest progresses in the experimental study and modeling work on the thermo-physical properties of CO2 mixtures; the impacts of properties on CCS processes are updated in Section 4; and finally, the knowledge gaps and key findings are concluded in Section 5.

2.1.2. Density Table 3 presents the progress in the experimental data on density. New data have been published for CO2/O2 [21,22], CO2/COS [23], CO2/CO [22,24,25], CO2/N2O4 [19], CO2/H2 [22,26,27], CO2/Ar/N2 [28,29] and CO2/N2/O2/Ar [30]. But some clear gaps still exist. For example, there are no data for CO2/NH3, no vapor density for CO2/O2 and CO2/N2O4, and few data for CO2/H2S, CO2/SO2 and CO2/Ar at temperatures lower than 273 K. More data are also needed for CO2/ N2O. 2.2. Transport properties New data about transport properties published since 2011 are summarized in Table 4 and compared to the previously identified data gaps in Table 5. More data about the viscosity of pure CO2 in the supercritical phase have been published by Heidaryan et al. [31] and Al-Siyabi [22] as a supplement to previous data, which mainly contain gas and liquid phases. More measurements about viscosity have been conducted for liquid mixtures, such as CO2/O2, CO2/H2, CO2/Ar, CO2/CO [22], CO2/ O2/N2/Ar [32], and CO2/O2/N2/Ar/H2/CO/CH4 [22,32] besides aqueous solutions of 4 amines [33] and CO2/H2O [34]. Moreover, data at high pressures become available, such as the viscosity of CO2/O2 and CO2/CO [22] at pressures up to 50 MPa, and the diffusivity of CO2/H2O [35,36] at pressures up to 45 MPa. In general, the study on transport properties is still far behind that on thermodynamic properties. It can be clearly seen in Table 5 that not many data are available; and even though some data exist for a couple of CO2 mixtures, they are in narrow temperature and pressure ranges. For example, the thermal conductivity and diffusivity data are not yet available for most liquid CO2 mixtures, except for CO2/H2O (/NaCl) and CO2/amine solutions. There are no data about any transport property for CO2/H2S, CO2/COS and CO2/NH3. For multi-component CO2 mixtures, only some data are available for CO2/O2/N2/Ar and CO2/O2/N2/Ar/H2/CO/CH4. The slow progress in the experimental study of transport properties is mainly due to the difficulty of measurements caused by the wide ranges of temperature and pressure. New techniques may be needed to have a major breakthrough. 3. Progress on modeling Different from our previous review papers [7,8], a more comprehensive comparison on the performance of models was presented in this work. Regarding different CO2 mixtures, the quantitative accuracy about different properties was provided at given temperatures and pressures. In addition, progress has also been made in the development of advanced models due to the progress in the experimental study and the development of computer technologies. The available models about thermodynamic properties and transport properties are summarized and compared in Tables 6 and 7.

2. Progress in experimental studies about the thermo-physical properties of CO2 mixtures 2.1. Thermodynamic properties New data about thermodynamic properties, including VLE and density, published since 2011 have been collected from the literature and summarized in Table 1. They are also compared with the data gaps identified in our previous review paper [7] in Table 2 and Table 3.

3.1. Thermodynamic property models 3.1.1. Newly developed models

2.1.1. Phase equilibrium As shown in Table 2, it is clear that some gaps about phase equilibrium have been bridged. For example, for CO2/Ar [11–15] and CO2/ CO [16], more data are available and there are no clear gaps; for CO2/ SO2 [2,3,17,18] and CO2/N2O4 [19], even though there are some new data, data at temperatures below 263 K are still missing. For CO2/COS and CO2/NH3, no new data have been published. For multi-component

- GERG-2008 GERG-2008 is an updated version of GERG-2004 [7], which was proposed by Kunz and Wagner (2012) [37]. Compared to GERG-2004, three new components, n-nonane, n-decane and hydrogen sulfide are added. The validity range has extended to temperatures from 60 to 2

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Table 1 New experimental data on VLE and density of CO2 mixtures since 2011. Year

Type

2011 2011 2012 2012 2013 2013 2013 2013 2014 2014 2014 2014 2015 2015 2015 2015 2016 2016 2016 2016 2016 2016 2016 2016 2016 2017 2017 2017 2017 2017 2017 2017 2018 2018 2018 2018 2019

VLE and Density Density Density Density Density Density Density VLE VLE VLE VLE VLE VLE Density Density VLE and VLE VLE VLE Density VLE Density Density Density VLE and VLE and VLE and Density VLE and VLE and Density VLE VLE VLE VLE and Density

density

density

density density density density density

density

Mixture

T (K)

P (MPa)

Uncertainty

Refs.

CO2/NO2, CO2/N2O4 CO2/N2 CO2/N2 CO2/N2, CO2/O2, CO2/Ar CO2/N2/O2/Ar/H2O CO2/N2, CO2/O2, CO2/Ar, CO2/CO, CO2/H2, CO2/CH4 CO2/H2 CO2/CH4, CO2/CO CO2/SO2 CO2/NO CO2/O2/Ar, CO2/SO2/O2 CO2/O2, CO2/N2 CO2/Ar, CO2/CH4 CO2/N2, CO2/H2 CO2/N2, CO2/H2, CO2/N2/H2 CO2/Ar, CO2/N2 CO2/Ar/N2 CO2/H2S CO2/N2 CO2/O2 CO2/Ar CO2/Ar CO2/O2, CO2/N2, CO2/Ar CO2/CH4 CO2/Ar CO2/COS CO2/SO2 CO2/CH4/N2/H2/O2/Ar/CO, CO2/N2/O2/Ar, CO2/CH4/C2H6/C3H8/C4H10 CO2/Ar CO2/H2 CO2/Ar/N2, CO2/Ar/H2 CO2/SO2 CO2/CH4 CO2/CO CO2/Ar CO2/CH4 CO2/SO2 CO2/CO

298.00–328.45 250.00–400.00 250.00–400.00 303.00–383.00 243.15–423.15 283.15–423.15 288.15–333.15 304.21–308.15 263.15–333.21 232.93–273.15 253.00–293.00 277.35–302.15 218.15–303.15 252.00–304.00 298.15–423.15 323.15–423.15 273.00–353.00 223.00–303.00 218.00–298.00 252.95–280.44 273.15–323.15 223.00–293.00 300.15–313.15 273.15–323.15 322.91–393.25 273.00–353.00 273.00–423.00 257.54–291.13 273.15–323.15 268.00–333.00 263.00–473.00 300.00–308.15 253.00–298.00 213.00–299.00 293.13–303.15 263.00–423.00 255.05–313.28

1.000–9.000 1.970–19.990 0.490–19.980 1.000–20.000 1.000–150.000 < 50.000 < 23.000 0.100–20.000 0.100–8.000 1.000–11.500 1.900–7.600 4.100–7.930 0.560–15.440 2.060–10.570 11.000–31.000 3.000–31.000 0.300–41.400 0.680–18.220 0.550–14.410 2.830–6.940 0.480–8.990 0.700–16.530 8.000–10.000 0.500–9.100 2.500–35.000 0.050–41.700 1.000–126.000 2.410–6.010 0.510–5.990 3.100–23.000 0.100–70.000 2.000–18.000 1.970–12.600 2.540–16.000 0.270–8.740 0.100–70.000 2.000–8.000

T: ± 0.1 K; P: ± 0.075 MPa T: 0.0039 K; P: 0.015% T: 0.004 K; P: 0.015% T: ± 0.05 K; P: ± 0.03% T: ± 0.1 K; P: ± 0.05 MPa T: ± 0.01 K T: ± 0.05 K; P: ± 0.0035 MPa T: ± 0.006 K; P: 0.008 MPa T: 0.02 K; P: 0.002 MPa T: 0.02 K; P: 0.002 MPa T: 0.02 K; P: 0.002 MPa – T: 0.006 K; P: 0.003 MPa T: 0.1 K; P: 0.007 MPa T: ± 0.035 K; P: ± 0.00339 MPa T: ± 0.035 K; P: ± 0.0034 MPa T: ± 0.01 K; P: ± 0.02 MPa T: ± 0.006 K; P: ± 0.003 MPa T: ± 0.008 K; P: ± 0.003 MPa T: ± 0.02 K; P: ± 0.01% T: ± 0.0025 K; P: ± 0.0035% T: ± 0.05 K; P: ± 0.008 MPa T: 0.035 K; P: 0.0034 MPa T: ± 0.0025 K; P: ± 0.0035% T: 0.005 K; P: 0.0052% T: ± 0.02 K; P: ± 0.002 MPa T: ± 0.02 K; P: ± 0.02 MPa T: ± 0.02 K; P: ± 0.0001 MPa T: 0.0025 K; P: ± 0.0035% T: 0.02 K; P: 0.007 MPa T: 0.006 K; P: 0.018 MPa T: 0.02 K; P: 0.001 MPa T: ± 0.009 K; P: ± 0.003 MPa T: 0.013 K; P: 0.0032 MPa T: 0.003 K; P: 0.002 MPa T: 0.006 K; P: 0.018 MPa T: 0.02 K; P: 0.138 MPa

[19] [70] [71] [21] [72] [22] [26] [24] [17] [17] [17] [11] [73] [20] [53] [28] [40] [74] [75] [12] [41] [13] [76] [77] [23] [18] [30] [14] [27] [29] [2] [78] [16] [15] [38] [3] [25]

Table 2 Knowledge gaps on VLE. Mixture CO2/Ar CO2/CO CO2/SO2 CO2/NO2 (N2O4) CO2/NO CO2/NH3

Previously identified gaps New data [11–15] Previously identified gaps New data [16] Previously identified gaps New data [2,3,17,18] Previously identified gaps New data [19] Previously identified gaps New data [17] Previously identified gaps New data

[7] [7] [7] [7] [7] [7]

T (K)

P (MPa)

xa

yb

Gaps

218.15–233.15, 288.15–303.15 213.15–300.35 283.15–303.15 253.15–298.16 218.15–295.15 263.15–333.21 218.15–262.15, 293.15–303.15 298.15–328.45 218.15–303.15 232.93–273.15 218.00–413.15 NA

< 4.400 0.689–15.097 < 2.390 1.970–12.540 < 2.120 and > 6.430 0.104–8.785 > 0.670 1.000–8.970 0.500–10.000 1.000–11.500 0.500–4.250

0–0.690 0.492–0.990 0–0.631 0.626–0.999 0–1.000 0.030–0.897 Xc: 0.021–1.000 X: 0.072–0.937 0–1.000 0.527–0.984 X: 0.333–1.000

0–0.266 0.131–0.961 0.827–1.000 0.426–0.999 0–0.750 0.208–0.985

No gaps

0–1.000 0.234–0.849

Previously identified gaps [7] New data

218.15–303.15 NA

0.500–10.000

0–1.000

0–1.000

CO2/Ar/O2

Previously identified New data [17] Previously identified New data [17] Previously identified New data [20] Previously identified New data [29] Previously identified New data [29]

218.15–303.15 253.28–293.21 218.15–303.15 253.28–293.24 218.15–303.15 252.80–301.50 218.15–303.15 267.94–302.50 218.15–303.15 267.97–301.59

0.500–10.000 2.327–7.638 0.500–10.000 1.935–6.473 0.500–10.000 2.140–9.820 0.500–10.000 3.100–8.960 0.500–10.000 3.260–9.080

0–1.000 0.942–0.991 0–1.000 0.002–0.025 0–1.000 X: 0.930–0.950 0–1.000 X: 0.900–0.980 0–1.000 X: 0.950

0–1.000 0.536–0.921 0–1.000 0.035–0.323 0–1.000

CO2/SO2/O2 CO2/N2/H2 CO2/Ar/N2 CO2/Ar/H2

a b c

gaps [7] gaps [7] gaps [7] gaps [7]

: x means liquid mole fraction of carbon dioxide. : y means vapor mole fraction of carbon dioxide. : X means the total mole fraction of carbon dioxide. 3

T: 218.15–263.15 K T: 218.15–262.15 K

CO2/COS

gaps [7]

x: 0–0.631

0–1.000 0–1.000

T: 273.15–303.15 K; x: 0–0.527 T: 218.00–413.15 K; P: 0.500–4.250 MPa; x: 0.333–1.000 T: 218.15–303.15 K; P: 0.500–10.000 MPa; x/y: 0–1.000 T: 218.15–253.28 K; x: 0–0.942 T: 218.15–253.28 K; x: 0.025–1.000 T: 218.15–252.80 K T: 218.15–267.94 K; x: 0–0.900 T: 218.15–267.97 K; x: 0–0.950

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Table 3 Knowledge gaps on density. Mixture CO2/O2 CO2/COS CO2/CO CO2/NO2(N2O4) CO2/H2 CO2/H2S CO2/SO2 CO2/Ar CO2/N2O CO2/NH3

CO2/Ar/N2 CO2/N2/O2/Ar

T (K)

P (MPa)

Phase*

Gaps

Previously identified gaps [7] New data [21,22] Previously identified gaps [7] New data [23] Previously identified gaps [7] New data [22,24,25] Previously identified gaps [7] New data [19] Previously identified gaps [7] New data [22,26,27] Previously identified gaps [7] New data [40] Previously identified gaps [7] New data [2,3,18] Previously identified gaps [7] New data [14,21,22,41,53] Previously identified gaps [7] New data Previously identified gaps [7] New data

218.00–1620.00 283.15–423.15 218.00–1620.00 322.91–393.25 218.00–1620.00 255.05–423.15 218.00–1620.00 298.00–328.45 218.00–278.00, 290.00–1620.00 273.15–423.15 218.00–275.00, 306.00–1620.00 273.15–353.15 218.00–278.00, 347.00–1620.00 263.15–473.15 218.00–288.00, 303.00–1620.00 273.15–423.35 218.00–293.00, 307.00–1620.00 NA 218.00–1620.00 NA

0–50.000 1.003–47.790 0–50.000 2.500–35.000 0–50.000 2.000–48.550 0–50.000 1.000–9.000 0–4.800, 19.200–50.000 0.503–49.240 0–3.500,6.990–50.000 0.300–41.400 10.640–50.000 0.051–70.000 0–7.510, 9.780–50.000 0.455–57.770 0–5.300, 7.100–50.000

L. + G. L. (Sc.) L. + G. L. + G. L. + G. L. + G. (Sc.) L. + G. L. (Sc.) G. L. + G. (Sc.) NA L. NA L. + G. NA L. (Sc.) NA

T: 218.00–283.00 K; Phase: G. T: 218.00–322.00 K

0–50.000

L. + G.

Previously identified gaps [7] New data [28,29] Previously identified gaps [7] New data [30]

218.00–1620.00 268.15–423.15 218.00–1620.00 273.15–423.15

0–50.000 1.510–30.954 0–50.000 1.070–126.000

L. + G. L. + G. (Sc.) L. + G. L. + G. (Sc.)

T: 218.00–255.00 K T: 218.00–298.00 K Phase: G. T: 218.00–278.00 K T: 218.00–275.00 K T: 218.00–278.00 K T: 218.00–273.00 K T: 218.00–293.00 K, 307.00–1620.00 K; P: 0–5.300 MPa, 7.100–50.000 MPa T: 218.00–1620.00 K; P: 0–50.000 MPa; Phase: L. + G. T: 218.00–293.00 K T: 218.00–273.00 K

* G.: gas; L.: liquid; and Sc.: supercritical. Table 4 New experimental data on the transport properties of CO2 and CO2 mixtures since 2011. Year

Phase

Mixture

T/K

P/MPa

Uncertainty

No. of data

Refs.

Viscosity 2011 Sc.a

Pure CO2

313.15–523.15

7.700–81.1 00

102

[31]

2012

G.

Pure CO2

309.82–388.71

27.580–55.160

45

[79]

2015

G.

Pure CO2

253.15–473.15

< 1.200

54

[80]

2013

L. + Sc.

280.00–343.15

L. + G. + Sc.

243.00–423.00

7.150–48.100 8.730–48.260 8.750–48.290 7.750–50.390 8.900–53.790 6.500–50.100 10.680–51.210 1.000–150.000

50 51 60 48 56 54 54 42

[22]

2013

Pure CO2 CO2/H2 CO2/O2 CO2/Ar CO2/CO CO2/CH4 CO2/H2/CH4/N2/CO/Ar/O2 CO2/O2/N2/Ar/H2O

T: ± 0.02 K; P: ± 0.1%; Viscosity: ± 0.2% T: ± 0.556 K; P: ± 0.007 MPa; Viscosity: ± 1% T: 0.109 K; P: 0.001 MPa; Viscosity: 0.20–0.41% T: ± 0.01 K; P: ± 0.05 MPa; Viscosity: ± 1%

2013

G.

CO2/CH4

310.93–455.37

34.500–172.400

168

[81]

2014

L.

CO2/H2O

274.00–449.00

< 100.000

71

[34]

2015

G.

CO2/CH4

229.00–348.00

1.000–32.000

119

[82]

2017 2018

L. L. + G. + Sc.

MDEA, DMEA, DEEA, MAPAb/H2O/CO2 CO2/O2/N2/Ar/H2/CO/CH4, CO2/O2/N2/Ar, CO2/alkane,

293.00–353.00 243.00–423.00

– 1.000–155.000

171 153

[33] [32]

Thermal conductivity 2014 L. + G.

Pure CO2

219.00–751.00

< 69.000

T: 0.005 K; P:0.007 MPa; Thermal conductivity: 0.5% (3%*)

–

[83]

Diffusivity 2013 L. 2014 L.

CO2/H2O CO2/H2O

268.00–473.00 298.15–423.15

0–45.000 15.000–45.000

T: ± 0.2 K; P: ± 0.14% T: 0.01 K; Diffusivity: 2.3%

17 17

[35] [36]

a

T: ± 0.1 K; P: 0.05 MPa; Viscosity: ± 1% T: ± 0.556 K; P: ± 0.007 MPa; Viscosity: ± 1% T: 0.025 K; P: 0.1 MPa; Viscosity: 1.4% T: 0.005 K; P: 0.004 MPa; Viscosity: 0.8% T: ± 0.03 K T: 0.1 K; P: ± 0.02 MPa

: Supercritical phase. : MDEA: N-Methyldiethanolamine; DMEA: N, N-Dimethylethanolamine; DEEA: Diethylethanolamine; MAPA: N-Methyl-1,3-diaminopropane. * : In the supercritical area.

b

4

[72]

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Table 5 Knowledge gaps on the transport properties. Mixture Viscosity Pure CO2 CO2/O2 CO2/CO CO2/CH4 CO2/H2 CO2/Ar

CO2/H2O CO2/O2/N2/Ar /H2O MDEA or DMEA or DEEA or MAPA/H2O/CO2 CO2/O2/N2/Ar CO2/O2/N2/Ar/H2/CO/CH4 Thermal conductivity Pure CO2 Diffusivity CO2/H2O

T (K)

P (MPa)

Phase

Gaps

NA 280.00–523.00 < 297.00, > 673.00 280.00–343.15 < 298.00, > 473.00 280.00–343.15 < 293.00, > 673.00 229.00–455.37 < 291.00 280.00–343.15 < 293.00, > 673.00 280.00–343.15 < 273.00, > 313.00 274.00–449.00 218.00–1620.00 243.00–423.00 not 295.00 293.00–353.00 218.00–1620.00 243.00–423.00 218.00–1620.00 243.00–423.00

NA < 81.100 not 0.100 8.750–48.290 not 0.100 8.900–53.790 NA 1.000–172.400 > 0.300 8.730–48.260 > 2.500

NA L. + G.(Sc.) L. L.(Sc.) L. L.(Sc.) L. L. + G.(Sc.) L. L.(Sc.) L.

No gaps

7.750–50.390 > 30.000 < 100.000 0–50.000 1.000–150.000 – – 0–50.000 1.000–150.000 0–50.000 1.000–150.000

L.(Sc.) NA L. L. + G. L. + G.(Sc.) NA L. L. + G. L. + G.(Sc.) L. + G. L. + G.(Sc.)

Previously identified gaps [8] New data [83]

NA 219.00–751.00

NA < 69.000

L. L. + G.

No gaps

Previously identified gaps [8] New data [35,36]

352.00–1620.00 352.00–473.00

0.400–50.000 0.400–45.000

NA L.

T > 473.00 K

Previously identified gaps New data [22,31,79,80] Previously identified gaps New data [22] Previously identified gaps New data [22] Previously identified gaps New data [22,81,82] Previously identified gaps New data [22] Previously identified gaps New data [22] Previously identified New data [34] Previously identified New data [72] Previously identified New data [33] Previously identified New data [32] Previously identified New data [22,32]

[8] [8] [8] [8] [8] [8]

gaps [8] gaps [8] gaps [8] gaps [8] gaps [8]

T < 280.00 K, and T > 673.00 K T < 280.00 K and T > 473.00 K T < 280.00 K and T > 673.00 K T < 280.00 K T < 280.00 K and T > 673.00 K T < 273.00 K and T > 449.00 K T > 423.00 K T < 293.00 K and T > 353.00 K No gaps No gaps

activity-coefficient models (gE) has shown clear superiority in the critical region, which is particularly suitable for VLE of polar and nonpolar mixtures at low and high pressures. The E-PPR78 (Enhanced Predictive Peng-Robinson, 1978) proposed by Qian [44] for natural gas and petroleum mixtures, using Huron–Vidal excess Gibbs energy mixing rules, can be seen as the combination of PR EOS and a Van Laar type activity coefficient (gE) model under infinite pressure. Its applicability range was further extended by Xu et al. to SO2, O2 and NO [45], and COS, NH3, NO2, N2O4 and N2O [46], which covered the main components of mixtures involved CCS. A group contribution method allowing the estimation of the temperature-dependent binary interaction parameters (kij (T)) for the Soave–Redlich–Kwong equation of state (PR2SRK) [47] was used to deduce kijSRK from a known kijPR estimated from the PPR78 model. It results in a big advantage that is not necessary to re-estimate the parameters for SRK. Generally, PR2SRK and PPR78 are of comparable accuracy. A pressure-explicit EOS was derived by Demetriades et al. from the pure fluid fugacity and mixing rules without further integration, which was obtained to generalize a EOS for pure CO2 to binary mixtures with N2, O2 and H2 [48]. It was found that this EOS had a comparable or superior performance to GERG-2008 for those three CO2 mixtures. Further, an expression for the mixture fugacity for an arbitrary EOS with arbitrary mixing rules could also be deduced. The general and flexible framework will facilitate ongoing development of this customized EOS to respond to new data and computational applications. An improved Helmholtz-energy-explicit mixture model was developed for CO2/Ar by Løvseth et al. based on the new data on VLE, density and speed of sound [15]. A refit is expected when more accurate data become available since the development of EOS-CG was completed. The updated binary correlation is part of the ongoing work to an advanced multi-parameter EOS for CO2-rich mixtures and should be further developed against an extended new database of other mixtures.

700 K and pressures up to 35 MPa. Now GERG-2008 has been adopted as an ISO Standard for natural gases and implemented in the NIST REFPROP database [37,38]. The vapor-liquid equilibrium is described as accurate as density and the speed of sound [7], with the reported uncertainty of bubble/dew point pressures less than 1–2% for binary mixtures, and less than 1–3% for multi-component mixtures. However, the development of a generalized departure function about GERG-2008 is based on several important main and secondary natural gas components, which may not result in a good prediction for key mixtures related to CCS. - Equation of State for Combustion Gases and Combustion Gas like Mixtures Another new Helmholtz energy model, Equation of State (EOS) for Combustion Gases and combustion gas like mixtures (EOS-CG), has been recently developed by Gernert and Span [39] in 2016 specifically for CO2-rich mixtures typical for CCS processes. It has been implemented in TREND software package of Ruhr-University Bochum. EOS-CG uses the mathematical approach of GERG-2008 and obtains new mixing parameters against a significantly wide literature database with a full composition range. It is well proved that the EOS presents a significant improvement for thermodynamic properties of mixtures in CCS compared to Cubic EOS and GERG EOS [29,39–41]. Moreover, its flexible and powerful mathematical structure could be adopted with minor alterations for new models, which could also show great performance. - Other Models An advanced cubic EOS, Peng-Robinson (PR) + residual Helmholtz energy-based model (PR + EOS/a E,Wilson ), was developed based on the res combination of PR and the residual part of the Wilson excess Helmholtz energy model [13,42,43]. This combination of the strengths of EOS and 5

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Table 6 Available models for thermodynamic properties. Mixtures

CO2/N2

Models

PR

BWR PT LK SRK RK Predictive SRK 3P1T GERG 2004 Duan96 PR-Penelousx SRK-Peneloux Improved SRK RKS RKSP BWRS LKP SAFT-VR Mie PC-SAFT EOS-CG GERG-2008

PR + EOS/a E,Wilson res Demetriades and Graham EOS CO2/O2

PR BWR PT SRK RK Predictive SRK 3P1T GERG 2004 Duan96 RKS RKSP BWRS LKP GERG-2008

PR + EOS/a E,Wilson res Demetriades and Graham EOS PC-SAFT E-PPR78

year

T and P

Accuracy (Absolute average relative deviation %) G

v

Refs.

L

T (K)

P (MPa)

VLE

v

1990 2009 2014 2007 1990 2009 1983 1994 2009 2009 2007 2009 2004 2007 1996 2009 2009 2009 2014 2014 2014 2014 2017 2014 2017 2015 2016 2012 2014 2015 2016 2017 2016

220.00–270.00 193.00–363.00 273.00–293.00 216.00–363.00 220.00–270.00 193.00–363.00 220.00–270.00 220.00–273.00 193.00–363.00 193.00–363.00 216.00–363.00 193.00–363.00 90.00–450.00 216.00–363.00 < 2000.00 220.00–347.00 220.00–347.00 220.00–347.00 273.00–293.00 273.00–293.00 273.00–293.00 273.00–293.00 225.00–673.00 273.00–293.00 225.00–673.00 298.15–423.15 223.00–303.00 60.00–700.00 273.00–293.00 298.15–423.15 213.00–473.00 218.00–303.00 273.00–304.00

< 15.800 0.100–14.300 1.000–20.000 0.520–14.500 < 15.800 0.100–14.300 0.600–16.700 2.000–12.000 0.100–14.300 0.100–14.300 0.520–14.500 0.500–14.000 < 35.000 0.520–14.500 < 2500.000 0.100–14.300 0.100–14.300 0.100–14.300 1.000–20.000 1.000–20.000 1.000–20.000 1.000–20.000 4.000–800.000 1.000–20.000 4.000–800.000 11.000–31.000 < 18.000 < 70.000 1.000–20.000 11.000–31.000 1.000–19.900 1.000–16.700 < 16.000

2.1–3.3 1.22–6.04 – 2.7–9.7 1.6–3.2 2.32–10.82 3–3.9 – 1.32–11.28 5.25–14.17 1.4–16.2 3.32–25.75 1.0–3 2.2–10.4 – – – – – – – – 0.99–5.43 – 1.73–7.32 – 0.04–0.63 1.0–3.0 – – 0.76–2.85 0.08–4.22 –

– 1.58–13.02 2.0 0.8–9.2 – 0.98–13.06 – < 5 (10–20 a) 1.5–14 1.47–14.26 0.6–9.2 – 0.2–0.5 0.5–5.7 <2 2.85–11.64 2.59–12.76 5.17–8.83 1.5 1.5 1.7 1.4 1.18b 1.9 3.19b < 0.1 – 0.1 1.3 < 0.1 – – –

– 1.74–9.43 2.0 >9 – 1.77–9.28 – < 5 (10–20 a) 4.18–10.84 4.86–11.96 >9 – 0.1–0.5 3.8–18.4 – 3.79–10.51 4.97–12.15 4.64–13.21 10.7 5.4 2.1 0.7 – 0.5 – < 0.1 – 0.1–0.5 0.1 < 0.1 – – –

[7] [7] [50] [7] [7] [7] [7] [7] [7] [7] [7] [7] [7] [7] [7] [7] [7] [7] [50] [50] [50] [50] [51] [50] [51] [53] [74] [37] [50] [53] [13] [42] [48]

2009 2014 2007 2009 2009 2009 2007 2009 2007 2004 1996 2014 2014 2014 2014 2014 2016 2017 2016 2014 2017 2017

193.00–363.00 273.00–293.00 216.00–363.00 193.00–363.00 193.00–363.00 193.00–363.00 216.00–363.00 193.00–363.00 216.00–363.00 90.00–450.00 < 2000.00 273.00–293.00 273.00–293.00 273.00–293.00 273.00–293.00 273.00–293.00 213.00–473.00 218.00–293.00 273.00–304.00 273.00–293.00 213.10–298.35 213.10–298.35

0.100–14.300 1.000–20.000 0.520–14.500 0.100–14.300 0.100–14.300 0.100–14.300 0.520–14.500 0.500–14.000 0.520–14.500 < 35.000 < 2500.000 1.000–20.000 1.000–20.000 1.000–20.000 1.000–20.000 1.000–20.000 1.000–19.900 0.900–14.200 < 16.000 1.000–20.000 0.555–15.000 0.555–15.000

1.22–6.04 – 2.7–9.7 2.32–10.82 1.32–11.28 5.25–14.17 1.4–16.2 3.32–25.75 2.2–10.4 1.0–3 – – – – – – 0.76–2.85 0.08–4.22 – – 7.60 6.36

1.58–13.02 1.6 0.8–9.2 0.98–13.06 1.5–14 1.47–14.26 0.6–9.2 – 0.5–5.7 0.2–0.5 <2 2.0 2.4 1.6 2.1 2.4 – – – 2.2 – –

1.74–9.43 2.1 >9 1.77–9.28 4.18–10.84 4.86–11.96 >9 – 3.8–18.4 0.1–0.5 – 9.4 5.3 2.1 0.2 0.1 – – – 1.8 – –

[7] [50] [7] [7] [7] [7] [7] [7] [7] [7] [7] [50] [50] [50] [50] [50] [13] [42] [48] [50] [52] [52]

(continued on next page)

6

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Table 6 (continued) Mixtures

CO2/Ar

Models

Accuracy (Absolute average relative deviation %)

Refs.

P (MPa)

VLE

vG

vL

2009 2014 2007 2009 2009 2009 2007 2009 2007 2004 1996 2009 2009 2009 2014 2014 2014 2014 2014 2018

193.00–363.00 273.00–293.00 216.00–363.00 193.00–363.00 193.00–363.00 193.00–363.00 216.00–363.00 193.00–363.00 216.00–363.00 90.00–450.00 < 2000.00 220.00–347.00 220.00–347.00 220.00–347.00 273.00–293.00 273.00–293.00 273.00–293.00 273.00–293.00 273.00–293.00 213.00–299.00

0.100–14.300 1.000–20.000 0.520–14.500 0.100–14.300 0.100–14.300 0.100–14.300 0.520–14.500 0.500–14.000 0.520–14.500 < 35.000 < 2500.000 0.100–14.300 0.100–14.300 0.100–14.300 1.000–20.000 1.000–20.000 1.000–20.000 1.000–20.000 1.000–20.000 0–16.000

1.22–6.04 – 2.7–9.7 2.32–10.82 1.32–11.28 5.25–14.17 1.4–16.2 3.32–25.75 2.2–10.4 1.0–3 – – – – – – – – – 0.042–3.270

1.58–13.02 1.8 0.8–9.2 0.98–13.06 1.5–14 1.47–14.26 0.6–9.2 – 0.5–5.7 0.2–0.5 <2 2.85–11.64 2.59–12.76 5.17–8.83 1.8 1.7 1.6 1.6 2.3 0.016

1.74–9.43 2.2 >9 1.77–9.28 4.18–10.84 4.86–11.96 >9 – 3.8–18.4 0.1–0.5 – 3.79–10.51 4.97–12.15 4.64–13.21 7.4 3.3 2.1 0.6 0.6 1.052–1.570

[7] [50] [7] [7] [7] [7] [7] [7] [7] [7] [7] [7] [7] [7] [50] [50] [50] [50] [50] [15]

2015 2016 2017 2014 2015 2016 2016 2017

298.15–423.15 273.15–323.15 257.00–291.00 273.00–293.00 298.15–423.15 273.15–323.15 213.00–473.00 223.00–299.00

11.000–31.000 < 9.000 2.400–6.000 1.000–20.000 11.000–31.000 < 9.000 1.000–19.900 1.500–14.700

– – 0.35 – – – 0.76–2.85 0.08–4.22

< 0.5 0.18 0.37 1.8 < 0.5 0.95 – –

< 0.5 – – 0.5 < 0.5 – – –

[53] [41] [14] [50] [53] [41] [13] [42]

PR BWR PT SRK RK Predictive SRK 3P1T PR-Penelousx SRK-Peneloux Improved SRK PC-SAFT E-PPR78 An improved Helmholtz-energy-explicit mixture model EOS-CG

2009 2007 2009 2009 2009 2007 2009 2009 2009 2009 2017 2017 2017

193.00–363.00 216.00–363.00 193.00–363.00 193.00–363.00 193.00–363.00 216.00–363.00 193.00–363.00 220.00–347.00 220.00–347.00 220.00–347.00 263.15–333.21 263.15–333.21 273.00–353.00

0.100–14.300 0.520–14.500 0.100–14.300 0.100–14.300 0.100–14.300 0.520–14.500 0.500–14.000 0.100–14.300 0.100–14.300 0.100–14.300 0.200–9.060 0.200–9.060 < 42.000

1.22–6.04 2.7–9.7 2.32–10.82 1.32–11.28 5.25–14.17 1.4–16.2 3.32–25.75 – – – 3.61 3.05 –

1.58–13.02 0.8–9.2 0.98–13.06 1.5–14 1.47–14.26 0.6–9.2 – 2.85–11.64 2.59–12.76 5.17–8.83 – – 1.6

1.74–9.43 >9 1.77–9.28 4.18–10.84 4.86–11.96 >9 – 3.79–10.51 4.97–12.15 4.64–13.21 – – 0.2

[7] [7] [7] [7] [7] [7] [7] [7] [7] [7] [52] [52] [18]

2017 2018

313.15–373.15 263.15–304.21

< 30.000 < 20.000

1.67–6.30 0.88–2.07

8.25 2.91

5.33 0.73

[2] [3]

PR

2002 2009 2007 2002 2009 2002 2009 2009 2007 2009 1996 2002 2009 2002 2009 2009 2017 2017 2012 2016

250.00–450.00 193.00–363.00 216.00–363.00 250.00–450.00 193.00–363.00 250.00–450.00 193.00–363.00 193.00–363.00 216.00–363.00 193.00–363.00 < 2000.00 250.00–450.00 220.00–347.00 250.00–450.00 220.00–347.00 220.00–347.00 249.00–500.00 249.00–500.00 60.00–700.00 273.00–353.00

0–20.000 0.100–14.300 0.520–14.500 0–20.000 0.100–14.300 0–20.000 0.100–14.300 0.100–14.300 0.520–14.500 0.500–14.000 < 2500.000 0–20.000 0.100–14.300 0–20.000 0.100–14.300 0.100–14.300 1.500–60.000 1.500–60.000 < 70.000 < 41.000

– 1.22–6.04 2.7–9.7 – 2.32–10.82 – 1.32–11.28 5.25–14.17 1.4–16.2 3.32–25.75 – – – – – – 0.99–5.43 1.73–7.32 1.0–3.0 –

1.26 (2.76b) 1.58–13.02 0.8–9.2 1.02 (2.26b) 0.98–13.06 0.51 (2.79b) 1.5–14 1.47–14.26 0.6–9.2 – <2 1.39 (3.24b) 2.85–11.64 0.65 (2.89b) 2.59–12.76 5.17–8.83 1.18b 3.19b 0.1 1

2.81 1.74–9.43 >9 2.16 1.77–9.28 9.23 4.18–10.84 4.86–11.96 >9 – – 3.53 3.79–10.51 5 4.97–12.15 4.64–13.21 – – 0.1–0.5 1

[7] [7] [7] [7] [7] [7] [7] [7] [7] [7] [7] [7] [7] [7] [7] [7] [51] [51] [37] [40]

PR

Duan96 PR-Penelousx SRK-Peneloux Improved SRK RKS RKSP BWRS LKP PC-SAFT An improved Helmholtz-energy-explicit mixture model EOS-CG

GERG-2008

PR + EOS/a E,Wilson res

CO2/H2S

T and P T (K)

BWR PT SRK RK Predictive SRK 3P1T GERG 2004

CO2/SO2

year

BWR PT SRK SRK RK Predictive SRK 3P1T Duan96 PR-Penelousx PR-Penelousx SRK-Peneloux Improved SRK SAFT-VR Mie PC-SAFT GERG-2008

(continued on next page)

7

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Table 6 (continued) Mixtures

Models

year

T and P

Accuracy (Absolute average relative deviation %)

Refs.

T (K)

P (MPa)

VLE

vG

vL

1990 2009 2018 1990 2009 1983 1994 2009 2018 2009 2009 2006 2009 2009 2009 2018 2018 2012 2013 2017

220.00–270.00 193.00–363.00 293.13–303.15 220.00–270.00 193.00–363.00 220.00–270.00 220.00–273.00 193.00–363.00 293.13–303.15 193.00–363.00 193.00–363.00 245.00–383.00 220.00–347.00 220.00–347.00 220.00–347.00 293.13–303.15 293.13–303.15 60.00–700.00 304.21 219.00–301.00

< 15.800 0.100–14.300 5.720–7.930 < 15.800 0.100–14.300 0.600–16.700 2.000–12.000 0.100–14.300 5.720–7.930 0.100–14.300 0.500–14.000 0.100–350.000 0.100–14.300 0.100–14.300 0.100–14.300 5.720–7.930 5.720–7.930 < 70.000 0.100–20.000 1.100–8.500

2.1–3.3 1.22–6.04 0.34–0.55 1.6–3.2 2.32–10.82 3–3.9 / 1.32–11.28 0.38–0.58 5.25–14.17 3.32–25.75 3–9.3 – – – 0.18–0.43 0.42–0.52 1.0–3.0 – 0.08–4.22

– 1.58–13.02 – – 0.98–13.06 – < 5 (10–20)a 1.5–14 – 1.47–14.26 – – 2.85–11.64 2.59–12.76 5.17–8.83 – – 0.1 0.4–1.1 –

– 1.74–9.43 – – 1.77–9.28 – < 5 (10–20)a 4.18–10.84 – 4.86–11.96 – – 3.79–10.51 4.97–12.15 4.64–13.21 – – 0.1–0.5 0.4–1.1 –

[7] [7] [38] [7] [7] [7] [7] [7] [38] [7] [7] [7] [7] [7] [7] [38] [38] [37] [24] [42]

2004 1996 2012 2017 2017

90.00–450.00 < 2000.00 60.00–700.00 273.15–323.15 220.00–280.00

< 35.000 < 2500.000 < 70.000 < 6.000 0.900–93.000

1.0–3 – 1.0–3.0 – 0.08–4.22

0.2–0.5 <2 0.1 0.4 –

0.1–0.5 – 0.1–0.5 – –

[7] [7] [37] [27] [42]

2016

273.00–304.00

< 16.000

–

–

–

[48]

PR + EOS/a E,Wilson res

2004 1996 2018 2012 2013 2017

90.00–450.00 < 2000.00 253.00–298.00 60.00–700.00 304.21, 308.15 223.00–283.00

< 35.000 < 2500.000 < 13.000 < 70.000 0.100–20.000 0.800–14.200

1.0–3 – – 1.0–3.0 – 0.08–4.22

0.2–0.5 <2 1.4 0.1 0.4–1.1 –

0.1–0.5 / – 0.1–0.5 0.4–1.1 –

[7] [7] [16] [37] [24] [42]

CO2/n-alkanes

GERG 2004 GERG-2008

2004 2012

90.00–450.00 60.00–700.00

< 35.000 < 70.000

1.0–3 1.0–3.0

0.2–0.5 0.1

0.1–0.5 0.1–0.5

[7] [37]

CO2/H2O

PR-HV EOS-CG

2017 2017

273.00–478.00 273.00–478.00

0.100–60.800 0.100–60.800

4.5 8.0

– –

2.8 0.6

[54] [54]

CO2/NO

PC-SAFT E-PPR78

2017 2017

232.93–273.02 232.93–273.02

1.483–11.486 1.483–11.486

7.82 4.84

– –

– –

[52] [52]

CO2/NO2 (N2O4)

SAFT

2008

298.00–328.00

–

0.003–2.2

–

–

[7]

CO2/Ar/N2

EOS-CG GERG-2008

2017 2017

268.00–303.00 268.00–303.00

< 23.000 < 23.000

0.5–3.5 0.5–3.4

0.5 0.5

0.5 0.5

[29] [29]

CO2/Ar/H2

EOS-CG GERG-2008

2017 2017

268.00–303.00 268.00–303.00

< 23.000 < 23.000

0.5–3.5 0.5–3.4

0.5 0.5

0.5 0.5

[29] [29]

CO2/N2/O2

PR + EOS/a E,Wilson res

2017

233.00,273.00

4.000–15.000

1.0–4.4

–

–

[43]

CO2/CH4/N2

PR + EOS/a E,Wilson res

2017

233.00,273.00

4.000–15.000

1.0–4.4

–

–

[43]

CO2/CH4

PR

PT LK SRK RK 3P1T SRK–HV PR-Penelousx SRK-Peneloux Improved SRK UMR-PRU PC-SAFT GERG-2008

PR + EOS/a E,Wilson res CO2/H2

GERG 2004 Duan96 GERG-2008

PR + EOS/a E,Wilson res Demetriades and Graham EOS CO2/CO

a b

GERG 2004 Duan96 EOS-CG GERG-2008

: In/near the critical area. : In the supercritical area.

SAFT was, on average, more accurate than the others. However, when a binary interaction parameter was fitted, all model correlations were of comparable accuracy. It reveals that it is not necessary that the more complex models, such as PC-SAFT, will have increased accuracy. Therefore, when there is lack of experimental data, PC-SAFT is favorable. On the contrary, when experimental data are available and the binary interaction parameter can be well fitted, the Cubic EOS is the first choice. PR, RKS, RKSP, BWRS, LKP, PC-SAFT and GERG2004/2008 were compared by Mazzoccoli et al. [50] for the density of CO2/N2, CO2/O2 and CO2/Ar under pipeline transport conditions, and new binary interaction parameters were regressed except for GERG. The AARDs of those 7 models about liquid density are 2.2%, 7.4%, 3.3%, 2.1%, 0.6%, 0.6% and 0.5% for CO2/Ar, 2.0%, 10.7%, 5.4%, 2.1%, 0.7%, 0.5% and 0.1% for CO2/N2, 2.1%, 9.4%, 5.3%, 2.1%, 0.2%, 1.8% and 0.1% for

3.1.2. Model evaluation As shown in Table 6, many models have been evaluated for predicting the thermodynamic properties of CO2 mixtures. The work conducted after 2011 has been summarized below. Even though the evaluation results about the performance of different EOSs have not pointed to one particular EOS, which is superior to others, the evaluated accuracy provides a good guideline regarding model selection. Petropoulou et al. [38] compared four EOSs, including SRK, PR, PCSAFT and PR EOS with Universal Mixing Rule (UMR-PRU) for the VLE of CO2/CH4. Results showed that UMR-PRU has the lowest deviation with an absolute average relative deviation (AARD) of 0.18% for the bubble point pressure and 0.43% for CO2 mole fraction of the vapor phase. Diamantonis et al. [49] evaluated RK, SRK, PR, SAFT and PC-SAFT for VLE of CO2 mixtures including CH4, N2, O2, SO2, Ar, and H2S. PC8

Applied Energy 255 (2019) 113789

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Table 7 Available models for transport properties. Mixtures

Viscosity Pure CO2

CO2/N2

Models

T and P T (K)

P (MPa)

AARD (%)

Refs.

[8]

L. + G.

Empirical (Emp.)

200.00–1500.00

0.100–100.000

Fenghour and Wakeham Bahadori and Vuthaluru Heidaryan et al.

1998 2010 2011

L. L. Sc.

Emp. Emp. Emp.

200.00–1500.00 260.00–450.00 310.00–900.00

< 300.000 10.000–70.000 7.500–101.400

G.:5 L.:7 ± 0.3- ± 5.0 1.1 1.7

Hirschfelder Wilkes equation

1948 1950

G. G.

Chapman–Enskog (CE) CE

G.

Emp.

G.

Corresponding State (CS)

G. G.

CS Helmholtz free energy theory (HE)

293.00–303.00 296.00–303.00 293.00 298.00–873.00 – 298.00–873.00 298.00–873.00 298.00–873.00 289.00 298.00–873.00

– – – 0.100–6.000 – 0.100–6.000 – 0.100–6.000 2.000–12.000 0.100–6.000

0.1 0.5 1.7 2.0 1.3–3.6 2.8 1.0 1.3 0–7.8 1.4

[8] [8] [8] [67] [8] [67] [8] [67] [8] [67]

G.

CE

G. G.

CE + CS Emp. CS HE

296.00–303.00 298.00–674.00 298.00–674.00 298.00–674.00

– 0.100 – 0.100

1.9 2.0 0.3 2.8 1.3 1.4

[8] [67] [8] [67]

G. G.

CE CS

G.

CE Emp. HE

293.00–303.00 298.00–873.00 293.00&303.00 293.00&303.00

– – 0.100–2.600 0.100–2.600

0.1 1. 1.3 2.0 2.8 1.4

[8] [8] [67] [67]

298.00–353.00 298.00–353.00 238.00–308.00 298.00–353.00 217.00–500.00 298.00–353.00 289.00

– – – – 1.000–15.000 – 0.100

3.5 2 <1 3.5 2.0 <2 1.8–3.0

[8] [8] [8] [8] [67] [8] [8]

Hanley EH Wilkes equation Boltzmann DS KRW EH Hirschfelder KRW law Wilke DS EH CO2/SO2

Type

1990

KRW law

CO2/Ar

Phase

Vesovic et al.

Dean and Stiel

CO2/O2

Year

Herning-Zipperer Chapman-Enskog Hirschfelder Wilkes equation Brokaw Canonically angle–average pair potential energy function

2017 1965 2017 1972 2017 1976 2017 1950 2017 1977 2017

1948 1972 2017 2017

1936 1939 1948 1950 2017 1965 1971

G. G. G. G.

Emp. CE CE CE

G. G.

CE CE

[8] [55] [31]

CO2/H2O

Runberg and Nissan Arrhenius type function DS KRW EH Wilke

1949 1996 2017

L. L. G.

Emp. Emp. Emp. CS HE CE

273.00–278.00 293.00–333.00 217.00–500.00

0–30.000 – 1.000–15.000

<1 1 2.8 1.3 1.4 2.0

[8] [8] [67]

CO2/CH4

Wilkes equation Dean and Stiel DeWitt and Thodos KRW law

1950 1965 1966 1972

G. G. G. G.

CE Emp. Emp. CS

298.00 – 323.00–473.00 298.00–873.00

– – – –

<1 1.3–3.6 1.8 1

[8] [8] [8] [8]

CO2/H2

Hirschfelder

1948

G.

CE

Wilkes equation

1950

G.

CE

299.00–550.00 288.00 296.00–303.00 500.00–1100.00

– 0.100 – 0.300

2–3 <1 0.6 <8

[8] [8] [8] [8]

CO2/H2O/NaCl

Kumagai and Yokoyama Bando

1999 2004

L. L.

Emp. Emp.

273.00–278.00 303.00–333.00

0.100–30.000 10.000–20.000

1.3 5

[8] [8]

MDEA, DMEA, DEEA, MAPA/ CO2/H2O CO2/O2/H2

NRTL-DVIS correlation

2017

L.

Excess Gibbs energy (GE)

293.00–353.00

–

< 5–6

[33]

Wilkes equation

1950

G.

CE

296.00–303.00

–

1.8

[8]

CO2/O2/N2

Wilkes equation

G.

CE

G.

– – –

G.

298.00–873.00

–

0.8 2.0 1.3 1.4 2.8 1

[8] [67] [67]

1972

CS HE Emp. CS

296.00–303.00 317.00–1161.00 317.00–1161.00

CO2/CH4/N2

KRW EH DS KRW law

1950 2017 2017

[8]

(continued on next page)

9

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H. Li, et al.

Table 7 (continued) Mixtures

CO2/Ar/N2

Models

KRW law

Year

Phase

Type

T and P

AARD (%)

Refs.

T (K)

P (MPa)

298.00–873.00 298.00–873.00 298.00–873.00

– – –

1 1.3 1.4 2.8 2.0

[8] [67] [67]

1972 2017 2017

G.

CS

G.

HE Emp. CE

2018

L. + G. + Sc.

Extended correspondingstates (ECS), CS, CS2, Residual viscosity theory

243.00–423.00

1.000–150.000

3.8, 4.6, 5.3, 9.2

[32]

Thermal conductivity Pure CO2 Jarrahian and Heidaryan Amooey CSA-LSSVM model ANFIS model GP

2012 2014 2015 2016 2017

Sc. Sc. G. + L. G. + L. + Sc. Sc.

Emp. Emp. Emp. Emp. Emp.

310.00–960.00 290.00–800.00 293.50–474.31 293.65–961.50 293.65–961.05

7.400–210.000 – 0.100–93.100 0.100–127.800 0.100–127.800

2.7 2.7 0.8 2.6 2.3

[59] [60] [62] [63] [61]

CO2/N2

Wassiljewa + Lindsay-Bromley Aij

1950

G.

Semi–Emp.

Enskog Hirschfelder

1951 1957

G. G.

Rigorous kinetic theory (RKT) RKT

1958 2017 1964 1983 1988 2017

G.

RKT

G. G. G. G.

RKT CS Emp. Hirschfelder’s equation Wassiljewa’s equation Emp. HE

– 0.100–300.000 0.100 – – – – 0.100–300.000 – 0.900–30.800 0.900–30.800 0.100–300.000

−3~-1 < 30 3.4 10.0 6.4–7.8 4 4.6 5.4 2(≤500 K) 6 5 7.3 5.4 4.9 3.5

[8] [8] [8] [8]

Mason and Saxena

642.00–961.00 348.00 323.00–623.00 294.00–1000.00 323.16 – 323.00–961.00 273.00–2000.00 300.00–1000.00 302.00–470.00 302.00–470.00 273.00–2000.00

273.00–1047.00 369.00–370.00 369.00–370.00

– – –

2.1 4.9 7.3 5.4 3.5 5.4

[8] [67] [67]

EH DS Wilkes equation CO2/O2/N2/Ar CO2/alkane CO2/O2/N2/Ar/ H2/CO/CH4

CO2-SUPERTRAPP, CO2-Pedersen, CO2-CS2, CO2-LBC

Monchick Ely and Hanley Johns WD KM Cheung EH CO2/O2

Cheung WD KM EH MS

1962 2017 2017

G.

Emp.

G.

Hirschfelder’s equation Wassiljewa’s equation HE RKT

[8] [67] [8] [8] [8] [67]

CO2/SO2

Wassiljewa Wassiljewa + Lindsay-Bromley Aij Hirschfelder

1904 1950 1957

G. G. G.

Semi–Emp. Semi–Emp. RKT

323.00–373.00 323.00–373.00 323.00& 373.00

– – –

0.5 −1.2–2.5 0–3

[8] [8] [8]

CO2/H2

Wassiljewa + Lindsay-Bromley Aij Hirschfelder

1950 1957

G. G.

Semi–Emp. RKT

1975 1978 1983

G. G. G.

Emp. RKT Emp.

– – – 0.850–7.500 – – –

−0.2–8.4 2.2–3.5 5–8 > 0.3 1 5 0.4

[8] [8]

Andreev and Mal’ter Mason Kestin

273.00–298.00 273.16 258.00–473.00 300.00 273.00 & 893.00 – 300.00

[8] [8] [8]

Wassiljewa + Lindsay-Bromley Aij Mason and Saxena Tondon and Saxena

1950 1950 1958 1968

G. G. G. L.

Semi–Emp. Semi–Emp. RKT Emp.

338.00 298.00–333.00 298.00–333.00 338.00

– – – –

1.4 10 10 2.2

[8] [8] [8] [8]

CO2/CH4

Wassiljewa + Mason–Saxena Rosenbaum and Thodos Hellmann and Bich

1958 1969 2016

G. G. G.

Semi-Emp. Emp. Improved kinetic theory

298.00–308.00 333.00–433.00 293.00–303.00

0–9.000 3.300–6.900 –

<5 2 < 1.2

[8] [8] [64]

CO2/Ar

Wassiljewa + Mason–Saxena Hirschfelder Kestin WD KM EH MS Cheung

1958 1957 1982 2017

G. G. G. G.

Semi-Emp. RKT Emp. Hirschfelder’s equation Wassiljewa’s equation HE RKT Emp.

298.00–308.00 273.00–473.00 300.00 273.00–473.00

0–9.000 – – 0.100–11.000

<5 3 0.5 7.3 5.4 3.5 5.4 4.9

[8] [8] [8] [67]

CO2/N2O

Kestin Hirschfelder Cheung

1984 1957 1962

G. G. G.

Emp. RKT Emp.

300.00 300.00–750.00 273.00–1047.00

– – –

0.7 −2–9 2.1

[8] [8] [8]

CO2/H2O

CO2/O2N2 Diffusivity

(continued on next page)

10

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H. Li, et al.

Table 7 (continued) Mixtures

CO2/Ar

CO2/O2

Models

Year

Phase

RKT

1954

G.

Fuller–Schettler–Giddings

1964 1966

G.

RKT

1960

G.

Type

T and P

AARD (%)

Refs.

T (K)

P (MPa)

Modified–Buckingham potential Lennard–Jones potential Emp.

276.00–317.00

–

Inconsistent

[8]

194.80–1200.00

0.100

−3.3–14.4

[8] [8]

273.00–293.00

0.100

Within the experimental error

[8] [8] [8] [8]

Fuller–Schettler–Giddings

1966

G.

Lennard–Jones potential Exponential repulsion Point center of repulsion Modified–Buckingham potential Emp.

300.00–1500.00

0.100

−2.4–4.7

[8]

CO2/N2

Fuller–Schettler–Giddings

1966

G.

Emp.

194.80–1200.00 300.00–1500.00

0.100 0.100

−3.3–14.4 −2.4–4.7

[8]

CO2/CO

RKT

G.

–

300.00–1500.00

0.100

1.3 7.3 −2.4–4.7

[8]

G.

Lennard–Jones potential Wilke–Lee Emp.

296.10

Fuller–Schettler–Giddings

1964 1955 1966

[8]

Wilke–Chang

1955

L.

Semi-Emp.

Othmer–Thakar Stokes–Einstein Fuller–Schettler–Giddings

1960 1960 1966

L. L. G.

Semi-Emp. Hydrodynamic theory Emp.

AArrhenius–type

1986 1996 2016

G.

Emp.

279.00–338.00 291.00–348.00 298.00–328.00 279.00–338.00 298.00–328.00 194.80–1200.00 300.00–1500.00 298.00–328.00

– – 0.400 – 0.400 0.100 0.100 0.400

L.

Emp.

323.15–1023.15

200.000–1000.000

< 11 −20 5 < 11 5 −3.3–14.4 20.9 1.7 1.0 2.6

[8] [8] [8] [8] [8] [8] [8] [8] [8] [65]

1966

G.

Emp.

194.80–1200.00 300.00–1500.00 315.20–343.90

0.100 0.100 0.100

−3.3–14.4 −2.4–4.7 < 0.5

[8] [8] [8]

Canonically angle–average pair potential energy function Improved kinetic theory Improved kinetic theory

263.00–473.00

0.100

3

[8]

293.00–303.00 293.00–303.00

– –

< 1.2 < 1.2

[64] [64]

1954

CO2/H2O

A generalized Speedy–Angel correlation Fuller–Schettler–Giddings

CO2/SO2

RKT

1971

G.

CH4/CO2 H2S/CO2

Hellmann and Bich Hellmann and Bich

2016 2016

G. G.

density of CO2/Ar [41]. Results showed that the AARDs were around 0.95% and 0.18% for GERG-2008 and EOS-CG respectively. It was concluded that the improvement of EOS-CG is attributed to the employment of a binary specific departure function. GERG-2008, EOS-CG, PR and gSAFT were evaluated for VLE and density of CO2/Ar/N2 by Ke et al. [29]. Results showed that EOS-CG had the best accuracy on both phase equilibrium and density with an AARD of 0.5%. EOS-CG has also been used to calculate the VLE and density of CO2/SO2 [2,3]. The results showed that the AARD for density, dew point and bubble point were 0.54%, 2.07% and 0.88% in the temperature range of 263–304 K. However, high deviations (25.6% for vapor density and 9.46% for liquid density) were found at 304.21 K, which was due to the close proximity to the critical point of the mixture. Aasen et al. [54] conducted a comprehensive comparison of models for VLE and density of CO2/H2O, including Cubic EOSs (PR and SRK) (with quadratic/Wonge-Sandler/Hurone-Vidal mixing rules), PC-SAFT, Perturbed-chain polar SAFT (PCP-SAFT), Cubic plus association SRK (CPA-SRK), corresponding states models with various reference fluids, GERG-2008 and EOS-CG. Those models were all fitted to the same data and tested outside of the temperature and pressure range used in the fitted interaction parameters. It was found that PR with the Huron–Vidal mixing rule and volume shift and EOS-CG gave the best performance for CO2/H2O, with AARD of 4.5% and 8.0% for phase equilibrium, and 2.8% and 0.6% for density. was compared with the corresponding cubic EOS PR + EOS/a E,Wilson res by Lasala et al. [13] for the VLE of CO2/N2. Results showed that PR highly over-predicted the critical point, while PR + EOS/a E,Wilson can res accurately capture it. Generally speaking, EOS-CG has a better performance on both VLE and density than GERG and Cubic EOSs except for the critical region.

CO2/O2, respectively. Perez et al. [51] investigated SRK, PR, PC-SAFT and SAFT-VR Mie for VLE and density of 108 binary mixtures mainly including CO2, CH4, C2H6, N2, and H2S. Results showed that SAFT-VR Mie had the best performance for both the VLE and density. The work of Diamantonis et al. [49] made similar conclusion that the performances of the four studied EOSs were close for VLE when the regressed binary interaction parameter was used. Xu et al. compared E-PPR78 and PC-SAFT [52] for VLE of 77 binary mixtures containing CO2, SO2, O2, NO, H2O and hydrocarbons. For CO2/SO2, CO2/O2 and CO2/NO, the AARDs of PC-SAFT with one temperature-independent binary interaction parameter and E-PPR78 are 3.61%, 7.60%, 7.82% and 3.05%, 6.36%, 4.84% respectively. GERG-2008 was used to calculate the density of CO2/N2 and CO2/ Ar. The AARD against the data measured by Yang et al. [53] were smaller than 0.1% and 0.5%. It is mainly because no binary specific departure function was available for the (CO2/Ar) system in the GERG2008. GERG-2008 was also tested for the phase equilibrium of CO2/Ar by Løvseth et al. [15]. Results showed that in general, the calculated results agreed well with the measured data at high CO2 mole fractions. However, it predicted a significantly higher critical pressure and lower CO2 mole fraction at and above 243 K. GERG-2008 has been compared with classical Cubic EOSs (PR, SRK and VPT) with volume correction/translation models for the density of CO2/H2S by Nazeri et al. [40]. The results showed that GERG-2008 had the best accuracy with the AARD of 1.1%. High accuracy was also obtained for the derived properties. For instance, the AARDs were 1.1% and 4.8% for compressibility factor and isobaric heat capacities of CO2/ H2S, respectively. GERG-2008 was also compared with EOS-CG by Yang et al. for the 11

Applied Energy 255 (2019) 113789

H. Li, et al. E,Wilson Compared to Cubic EOSs, PR + EOS/ ares shows a significant improvement in the critical region on VLE. When the binary interaction parameters are well-tuned, Cubic EOSs can show accuracy similar to those models with complicated structures, such as PC-SAFT.

for 300 < T/K < 700, 2.5% for 200 < T/K < 300 and 700 < T/ K < 1200, and 3.5% for 150 < T/K < 200.

3.2. Transport property models

The model of Hellmann et al. [64] can also be applied for the calculation of diffusivity of CH4/CO2, CH4/H2S and H2S/CO2. For diffusivity, the deviation reported is 2.0% for 300 < T/K < 700, 2.5% for 200 < T/K < 300 and 700 < T/K < 1200, and 3.5% for 150 < T/ K < 200 too. Moultos et al. [65,66] proposed a new phenomenological equation, a generalized form of the Speedy–Angel relationship, for correlating the diffusivity of CO2/H2O based on atomistic molecular dynamics (MD) simulations. It was a function of pressure and temperature and was found to be in good agreement with experimental data either at 283.15 K < T < 623.15 K (0.1 MPa < P < 100.0 MPa) or at 323.15 K < T < 1023.15 K (200 MPa < P < 1000 MPa) [65] through the combination of specific force fields. The correlation can be useful for engineering calculations by extrapolating experimental data outside the measurement range.

- Diffusivity

3.2.1. Newly developed models - Viscosity Bahadori and Vuthaluru [55] proposed a new empirical correlation for the viscosity of pure CO2, which was an exponential function of pressure and temperature. With simple algebraic equations and few parameters, the AARD was found to be 1.1% against the reported data. The empirical coefficients could be easily tuned when new and more accurate measurements are available, which may serve as a convenient tool for engineers. Lohrenz-Bray-Clark (LBC), originally developed for modeling natural gas and hydrocarbons mixtures [56], was tuned by Nazeri et al. [32] to predict the viscosity of CO2-rich mixtures based on the residual viscosity theory (CO2-LBC). The empirical correlative model was a fourth-order polynomial equation in the reduced density, and PR with the CO2 volume correction (PR-CO2 EOS) was used to calculate the mixture density. It has been concluded that CO2-LBC shows better prediction than original LBC, especially for density correction. Nazeri and Chapoy [32] proposed three predictive models for the viscosity of CO2-rich mixtures based on the corresponding states (CS) theory by using new reference fluids. CO2-Pedersen model (CS model with one reference fluid), originally developed by Pedersen [57], was modified by changing the reference fluid from methane to CO2 [22,32]. Similarly, CO2-CS2 model (CS model with two reference fluids) was modified by changing the reference fluids from methane and n-decane to methane and CO2. Moreover, the SUPERTRAPP model was modified by changing reference fluid from propane to CO2. The NRTL-DVIS correlation was proposed by Pinto and Svendsen [58] to calculate the liquid viscosity of mixtures. The adopted mixing rule was a function of excess Gibbs energy, which was specifically represented using the NRTL model. The adjustable parameters were fitted by the particle swarm optimization (PSO) algorithm and they had a temperature dependency.

3.2.2. Model evaluation Wilke, KRW, DS, and EH were evaluated by Tan et al. for viscosity of binary and multi-component CO2 mixtures with non-condensable gas impurities N2, O2 and Ar in cryogenic process [67], and the AARDs were 2.0%, 1.3%, 2.8% and 1.4% respectively. On average, KRW showed a better performance than the others. However, different models showed different capabilities under different working conditions. EH model was recommended at higher pressures; DS model was recommended at temperature lower than 283 K with an AARD of 1.0%; and for temperature higher than 283 K at atmospheric pressure, KRW model was the first choice. CO2-Pedersen, CO2-SUPERTRAPP, CO2-CS2 and CO2-LBC were compared by Nazeri et al. [32] for the viscosity of CO2/O2/N2/Ar, CO2/ O2/N2/Ar/H2/CO/CH4 and CO2/C2H6/C3H8/C4H10, of which the experiment was conducted at temperatures from 243 to 423 K and pressures from 1 to 155 MPa in gas, liquid and supercritical regions. The AARDs were 3.8%, 4.6%, 5.3% and 9.2% respectively for the three multi-component CO2-rich mixtures. Overall, CO2-Pedesen showed the best accuracy, especially with an AARD of 2.8% for binary CO2 mixtures containing O2, Ar, N2, H2, CO and CH4 [22]. Under the conditions of CO2 cryogenic process, Tan et al. [67] also compared WD, KM, MS, Cheung and EH for thermal conductivity of CO2/N2, CO2/O2 and CO2/Ar and the AARDs were 7.3%, 5.4%, 5.4%, 4.9% and 3.5%, respectively. In general, EH should be recommended for predicting thermal conductivity. Cheung model was recommended for temperature higher than 273 K at atmospheric pressure. For pressures higher than atmospheric pressure, KM model was preferred at pressure lower than 3 MPa, and EH should be employed at pressure higher than 3 MPa. The performances of transport property models are more dependent on the mixtures and T and P conditions, compared to the thermodynamic property models. The newly developed viscosity models, such as CO2-LBC and CO2-Pedersen, are superior to others due to their good accuracy and wide application ranges. The models based on Rigorous kinetic theory have an advantage in extrapolation, particularly for thermal conductivity and diffusivity due to the lack of available data.

- Thermal conductivity Many empirical models are developed for the thermal conductivity of pure CO2. The correlation by Jarrahian and Heidaryan [59] was a function of the pressure and temperature based on the multiple regression analysis technique. Amooey [60] correlated thermal conductivity as a function of density and temperature by minimizing the sum of square of errors. A novel correlation by Rostami et al. [61] served as a powerful equation generator based on genetic programming (GP) mathematical strategy and it provided much flexibility. They are all simple without a large number of parameters. Shams et al. [62] proposed an intelligent modeling approach, Least-Square Support Vector Machine modeling with Coupled Simulated Annealing (CSALSSVM), which set linear equations using support vectors. Another predictive model by Tatar et al. [63] was based on Adaptive NeuroFuzzy Inference System (ANFIS) and trained by the combination of Hybrid and Particle Swarm Optimization (PSO) methods. It was found to be accurate for the prediction of 1042 experimental data from the literature. For CO2 mixtures, the classical trajectory method was used by Hellmann et al. [64] for dilute gas thermal conductivity of CH4/CO2, CH4/H2S and H2S/CO2. The latest intermolecular potential energy surfaces based on highly accurate quantum-chemical were employed in the calculation. The deviation reported on thermal conductivity is 2.0%

4. Impacts of properties on CCS More works have been carried out to investigate the impacts of thermo-physical properties of CO2 mixtures on the design and operation of CCS processes since our previous review carried out in 2016 [10]. The impacts have been updated and summarized in Table 8. 12

Applied Energy 255 (2019) 113789

[69] [69] [67] 217.00–500.00 K 1.000–15.000 MPa 217.00–500.00 K 1.000–15.000 MPa 217.00–500.00 K 1.000–15.000 MPa

Nookuea et al. [68] studied the impact of liquid and gas phase densities on the design parameters of absorber for chemical absorption, including column diameter, packing height and annual capital cost. Results showed that the density of gas had the most significant effect on the column diameter. A 10% underestimation of gas density may result in an increase of about 6% of the column diameter. For the packing height, the density of liquid had the most significant effect. A 10% underestimation of the liquid density may result in an increase of 8% of the packing height. For the annual capital cost (AC), an underestimation of the liquid density of 10% led to a $1.4 million overestimation of the cost for the absorption column. A sensitivity study was conducted by Tan et al. [69] to analyze the impacts of density on the volume and AC of a plate-fin multi-stream heat exchanger. Compared to thermal conductivity, heat capacity and viscosity, density resulted in the smallest impact. - Heat capacity

CO2/CH4, CO2/C2H6, CO2/CH4, CO2/C2H6, CO2/Ar, CO2/O2

[67] 217.00–500.00 K 1.000–15.000 MPa CO2/Ar, CO2/O2, CO2/N2/Ar, CO2/N2/O2, CO2/N2/

The impact of heat capacity on the volume and AC of the heat exchanger in CO2 cryogenic process was also evaluated by Tan et al. [69]. The result showed that overestimating heat capacity would result in the reduction of the dimension and the property impacts underestimated were bigger than those overestimated. It was also found that heat capacity had more significant influence than viscosity. 4.2. Impacts of transport properties

Volume design and annual capital cost of heat exchanger Volume design and annual capital cost of heat exchanger Volume of the plate-fin multi-stream heat exchanger

The viscosity impacts on column diameter, packing height and annual capital cost were also studied by Nookuea et al. for the absorber in chemical absorption [68]. It was found that a 10% underestimation of liquid phase viscosity can result in 0.34%, 7.06% and 5.3% underestimations of the column diameter, packing height and AC respectively. The AC of the absorption tower was affected by the viscosity of liquid phase more obviously than that of the gas phase. The impact of viscosity on the volume and AC of the multi-stream heat exchanger in the cryogenic separation process was evaluated by Tan et al. [67,69]. It was found that the overestimation of viscosity led to the overestimation of the volume. That is because heat transfer coefficient decreases and pressure drop increases when viscosity increases, both resulting in the increase of volume. - Thermal conductivity

CO2 capture in cryogenic process

The impact of thermal conductivity on the volume and AC of the multi-stream heat exchanger in the cryogenic separation process was also studied by Tan et al. [67,69]. Compared to viscosity, the volume and capital cost were more sensitive to thermal conductivity. Overestimating and underestimating the thermal conductivity by 10% would make the volume change from 14.6 m3 to 13.5 m3 and 16.0 m3, respectively. For AC, +20% and −20% deviations of thermal conductivity can correspond to variations of −14.2% and 20.6% [69]. 4.3. Discussions

Thermal conductivity

CO2 capture in cryogenic process

CO2 capture in cryogenic process CO2 capture by chemical absorption Heat capacity Viscosity

- Density

CO2/N2, O2/Ar CO2/N2, CO2/N2, CO2/N2, of the plate-fin multi-stream heat exchanger

[69] [69] [68] 217.00–500.00 K 1.000–15.000 MPa 217.00–500.00 K 1.000–15.000 MPa / CO2/N2, CO2/CH4, CO2/C2/H6, CO2/N2, CO2/CH4, CO2/C2/H6, Aqueous amine solution with CO2 loading design and annual capital cost of heat exchanger design and annual capital cost of heat exchanger diameter, packing height, capital cost of the absorber

[68] / Aqueous amine solution with CO2 loading

Column unit Volume Volume Column unit Volume CO2 capture by chemical absorption

diameter, packing height, capital cost of the absorber

Influenced parameters

Density

4.1. Impacts of thermodynamic properties

- Viscosity

Processes

Working Condition Mixture Impact Property

Table 8 Impacts of thermo-physical property on CCS.

Refs.

H. Li, et al.

According to the property impacts, the key properties have been ranked regarding different CCS processes, as shown in Table 9. It is clear that the importance of properties can be different for different processes. Meanwhile, based on the performance of existing models summarized in Section 3, the possible ranges of AARD are also given in Table 9. By comparing the importance of the properties and the 13

14

219.00–423.00

0–11.000

0.100–20.000

Condensation and liquefaction

Transport

223.00–350.00

219.00–423.00

0–11.000

293.00–343.00

273.00–673.00

Compression and pumping

0.010–5.000

Physical adsorption

217.00–500.00

0.100–3.500

1.000–15.000

Physical absorption

288.00–357.00

T (K)

Membrane separation

0.100–0.110

P (MPa)

Working condition

Chemical absorption

Process

Table 9 Important properties for different processes of CCS.

[68] [68] [68] [68] [68] [68] [68] – –

–

–

[69] [69] [10] [10] [10]

5% variation can change the AC by 1.8% 5% variation can change the AC by 1.3%

viscosity density

[69]

18% variation can change the temperature drop by 20% 5% variation can change the temperature drop by 3% 20% variation results in negligible temperature drop

5% variation can change the AC by 2.2%

heat

[69]

[10] – – – –

5–15% variation can change the compression work by 3.8–6.5% – – – – 5% variation can change the AC by 4.5%

[10]

2% variation can change the pump efficiency by 12%

– – – – – –

annual capital cost (AC) by 5.9% AC by 5.3% AC by 4.2% AC by 2.5% AC by 2.3% AC by 0.1% AC by 0.05%

– – – – – –

the the the the the the the

– – – – – –

change change change change change change change

– – – – – –

can can can can can can can

– – – – – –

variation variation variation variation variation variation variation

Refs.

– – – – – –

10% 10% 10% 10% 10% 10% 10% – –

Property impacts

thermal

1 Liquid density 2 Liquid heat capacity 3 Liquid viscosity and thermal conductivity Phase equilibrium*

1 Gas and liquid conductivity 2 Gas and liquid capacity 3 Gas and liquid 4 Gas and liquid

Liquid heat capacity and liquid density Gas density Gas heat capacity* Gas thermal conductivity* Gas viscosity* Phase equilibrium*

Gas density* Gas viscosity* Gas heat capacity* Phase equilibrium* Gas thermal conductivity* Gas diffusivity*

Gas density* Gas viscosity* Gas heat capacity* Phase equilibrium* Gas thermal conductivity* Gas diffusivity*

Liquid density * Phase equilibrium* Liquid heat capacity* Gas and liquid viscosity* Gas and liquid diffusivity* Gas and liquid thermal conductivity*

1 Liquid density 2 Liquid viscosity 3 Liquid diffusivity 4 Gas density 5 Liquid heat capacity 6 Gas diffusivity 7 Gas viscosity Phase equilibrium* Gas and liquid thermal conductivity*

Property ranking according to the impacts

0.003–25.75

0.1–20 – 1–9.2

0.1–9.2 0.016–20

–

0.2–10

0.016–20 – 0.2–10 0.1–8 0.003–25.75

0.1–20

0.016–20 0.1–8 – 0.003–25.75 0.2–10 0.5–20.91

0.016–20 0.1–8 – 0.003–25.75 0.2–10 0.5–20.91

0.1–20 0.003–25.75 – 0.1–9.2 0.5–20.91 0.2–10

0.1–20 1–9.2 2.6–20 0.016–20 – 0.5–20.91 0.1–8 0.003–25.75 1–9.2

Property model accuracy (AARD %)

(continued on next page)

Models on liquid density and models on phase equilibrium

Models on thermal conductivity of gas and liquid

Models on density of liquid and gas and models on phase equilibrium

Models on phase equilibrium and models on gas diffusivity

Models on phase equilibrium and models on gas diffusivity

Models on phase equilibrium and models on diffusivity of gas and liquid

Models on density of liquid and gas and models on diffusivity of liquid and gas

Priority of model development

H. Li, et al.

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0.003–25.75 –

5. Conclusions

Models on gas density and models on phase equilibrium

– –

Gas and liquid diffusivity* Gas and liquid thermal conductivity* Phase equilibrium* Gas and liquid heat capacity*

– –

0.5–20.91 0.2–10

0.1–9.2 [10]

1 Gas and liquid density

This paper updated the progress in studies on thermodynamic and transport properties of CO2 mixtures, including vapor-liquid equilibrium, density, viscosity, thermal conductivity and diffusion coefficient. The latest experimental data and theoretical models published since 2011 have been collected and reviewed. For experimental data, some knowledge gaps have been bridged. For example, more measurements were conducted for the phase equilibrium of CO2/Ar, CO2/NO2(N2O4) and ternary mixtures, the density of CO2/O2, CO2/COS, CO2/H2 and CO2/CO, and the liquid viscosity of CO2/O2, CO2/Ar, CO2/H2 and CO2/O2/N2/Ar/H2/CO/CH4. There are, nevertheless, still some gaps. For example, no data are available yet about the phase equilibrium of CO2/COS and CO2/NH3, the density of CO2/NH3, gaseous CO2/O2 and CO2/NO2 (N2O4), and transport properties of CO2/H2S, CO2/COS and CO2/NH3. Previous works have mainly focused on the major impurities. However, in order to obtain more accurate properties, more attention needs to be paid to the minor components. Regarding the model development, new models and methods were proposed. The performance of the existing models has been summarized and compared, which provides a good guideline regarding model selection. There have also been some debates that developing morecomplex models to further improve the accuracy may not be necessary since simple models with well-tuned empirical parameters can also show good performance. In addition, the increased number of experimental data has opened a new door for property modeling. Methods of data analysis, such as machine learning and artificial neural network, have been adopted. Such methods, which do not rely on a deep understanding of the fundamental theory, can make the model development easier. Nevertheless, data processing techniques require more experimental data about the properties of CO2 mixtures, especially the multicomponent mixtures. By analyzing thermo-physical property impacts, the important properties were identified and ranked. By comparing the importance of the properties and the accuracy of existing models, suggestions were given regarding the development of property models that should be prioritized. However, clear knowledge gaps still exist, for example, no quantitative results are available yet about the property impacts on physical absorption, physical adsorption and membrane separation, which are important guidelines to experimental measurements and model development.

* No quantitative results are available.

261.00–393.00 10.000–50.000 Storage

T (K) P (MPa)

2 Gas and liquid viscosity

0.016–20 [10]

50% variation can change the normalized storage capacity by 50% (1% variation of gas density can change the enhanced oil recovery rate (EOR) by 9%) 50% variation can change the normalized storage capacity by 50% (1% variation of gas viscosity can change the EOR by 6%) – –

Priority of model development Property model accuracy (AARD %) Refs. Property impacts Property ranking according to the impacts Working condition Process

Table 9 (continued)

accuracy of models, the priority of model development can be determined. For example, for chemical absorption, the liquid density was identified as the most important property and the existing models also show a big range of AARD. Therefore, developing more accurate models for liquid density should be prioritized. In addition, even though the liquid viscosity was also identified as a property that has more impacts than the liquid diffusivity, since the available models of liquid viscosity have a smaller and lower range of AARD, it is more crucial to develop more accurate models for liquid diffusivity than for liquid viscosity. For physical absorption, physical adsorption and membrane separation, even though the properties that can affect those processes have been identified, no quantitative results about the impacts are available yet. Therefore, they cannot be ranked and more works are needed to quantitatively study the impacts. Heat capacity has also been identified as an important property for some processes, such as compression and pumping. Empirical correlations based on polynomial equations are commonly used to calculate heat capacity, which usually show high accuracy.

– –

H. Li, et al.

Acknowledgement The authors gratefully acknowledge the financial supports from 15

Applied Energy 255 (2019) 113789

H. Li, et al.

National Natural Science Foundation of China (No. 51776140).

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