supplementary data - path :.: process and...

Improved prediction of water properties and phase equilibria with a modified CPA EoS

André M. Palma1, António J. Queimada2,* and João A. P. Coutinho1

1CICECO, Chemistry Department, University of Aveiro, Campus de Santiago, 3810-193 Aveiro, Portugal.

2 KBC Advanced Technologies Limited (A Yokogawa Company), 42-50 Hersham Road, Walton-on-Thames, Surrey, United Kingdom, KT12 1RZ.

*Corresponding author. E-mail address: [email protected]

Supplementary Data

1- New parameter set for pure ethanol.

As presented in the main document, the pure parameters for ethanol have been changed. Table A1 presents these new parameters, while figures A1 to A5 present some results using both the new and the old parameters.

Table A1 – Improved set of parameters for ethanol

Parameterac (Pa.m6.mol-2) 1.13b. 105 (m3.mol-1) 6.40c1 1.04c2 -1.46c3 -0.79c4 3.76c5 0.00ε (J.mol-1) 24913β.102 0.162

Figure A1 – Heat capacity results of ethanol using both sets of parameters. Data are from Multiflash. 1

Figure A2 – Liquid density results of ethanol using both sets of parameters. Data are from Multiflash. 1

Figure A3 – LLE for ethanol + hexadecane using both sets of parameters (k ij=-0.026 in both cases). Data are from Matsuda and Ochi. 2

Figure A4 – VLE for ethanol + tert-butanol using both sets of parameters (k ij=-0.023 in both cases). Data are from the TRC database. 3

Figure A5 – VLE for ethanol + 1-octanol using both sets of parameters (no k ij was applied in either case). Data are from Arce et al. 4

2- Results for water + alkanols

Table A2 and A3 present the deviations for pressure, x and y obtained for binary systems of water + alkanols at different temperatures.

Table A2 – Absolute average deviations for pressures of the systems water with methanol, ethanol, 1-propanol and 2-propanol.

water : methanol water : ethanol water : 1-propanol water : 2-propanol%AAD Average %AAD Average %AAD Average %AAD Average

T/K Pbub Pdew T/K Pbub Pdew T/K Pbub Pdew T/K Pbub Pdew323 5 1.00 1.30 298 6 1.42 0.91 273 7 2.42 - 308 8 3.13 1.56328 5 0.93 0.99 313 9 1.86 0.88 279 7 5.25 - 318 8 1.90 1.08333 5 1.08 0.38 363 10 0.74 1.00 313 11 1.40 1.06 338 8 0.80 0.51363 12 3.23 - 381 10 1.09 0.84 403 13 1.41 0.76 348 8 0.92 0.53383 12 2.82 - 403 10 2.44 1.74 413 13 1.59 1.27 423b 14 3.76 3.07403 12 4.55 - 423 10 2.39 1.45 423 13 2.30 0.97 473b 14 2.03 1.61424 12 3.07 - 473 14 3.46 2.36 523a 14 0.52 0.50442 12 5.67 - 473 15 4.36 548a 14 2.19 0.91

523 14 2.68 2.30523 15 5.02548a 14 2.67 1.25548a 15 5.48573a 14 2.52 1.45

a – In these systems the composition of the mixture critical point is slightly underestimated.b – The pure 2-propanol Psat for these systems is not in accordance with more recent data.

Table A2 – Absolute average deviations on mole fractions of the systems water with methanol, ethanol, 1-propanol and 2-propanol.

water : methanol water : ethanol water : 1-propanol water : 2-propanol%AAD Average %AAD Average %AAD

Average%AAD Average

T/K y1 x1 T/K y1 x1 T/K y1 x1 T/K y1 x1

323 5 5.47 4.15 298 6 4.73 6.01 313 11 6.53 13.77 308 8 4.55 6.82328 5 4.54 3.45 313 9 6.15 5.72 403 13 4.28 4.10 318 8 2.80 4.61333 5 3.03 2.17 363 10 2.77 3.97 413 13 8.08 10.43 338 8 2.47 4.34

381 10 3.62 3.39 423 13 6.26 8.79 348 8 1.92 3.58403 10 8.07 5.58 423b 14 5.39 12.89423 10 2.45 1.92 473b 14 1.48 3.98473 14 2.67 2.24 523a 14 3.25 6.15523 14 1.65 1.59 548a 14 5.22 12.47548a 14 2.05 2.30573a 14 2.15 0.85

3- LLE methanol + alkanes and gas solubility on methanol/methanol solubility on gas.

The kij presented in the main document was obtained from the fitting of the systems presented in figures A6 to A9.

Figure A6 – LLE for methanol + pentane and methanol + hexane. Data are from Haarhaus and Schneider 16 and Hradetzky and Lempe. 17

Figure A7 – LLE for methanol + heptane and methanol + octane. Data are from Higashiuchi et al. 18, Katayama and Ichikawa 19 and Ogre et al. 20

Figure A8 – LLE for methanol + nonane and methanol + decane. Data are from Casás et al. 21 and Higashiuchi et al. 18

Figure A9 – LLE for methanol + undecane and methanol + dodecane. Data are from Casás et al. 21

Figure A10 – Solubility of methane in methanol (kij= -0.136 + 7.90x10-4 T)

. Data from Hong et al. 22

0

2000000

4000000

6000000

8000000

10000000

12000000

14000000

16000000

18000000

20000000

22000000

240000001E-05.

1E-04.

1E-03.

1E-02.

1E-01.

1E+00.220 K 250 K273.15 K 290 K310 K 330 K

P/MPa

met

hane

in m

etha

nol/

mol

.mol

-1

Figure A11 – Solubility of methanol in methane (kij= -0.136 + 7.90x10-4 T). Data from Hong et al. 22

Figure A12 – Solubility of ethane in methanol (kij=0.080). Data from Wang et al. 23

Figure A13 – Solubility of N2 in methanol (kij= -0.118 + 4.66x10-4 T). Data from Weber et al. 24

Figure A14 – Solubility of methanol in N2 (kij= -0.118 + 4.66x10-4 T). Data from Schlichting et al. 25

Figure A15 – Solubility of CO2 in methanol (kij=0.060). Data from Naidoo et al. 26

4- MEG + condensate (two condensates not studied on the previous article 27)

Figure A16 – LLE for MEG + Fluid – 2, applying the kij‘s presented in our previous work. 27 Data is from Frost et al. 28

Figure A17 – LLE for MEG + Fluid – 1, applying the kij‘s presented in our previous work. 27 Data is from Frost et al. 28

5- Ternary systems containing water and two polyols/alcohols and LLE of water + MEG/methanol + condensate

Table A3 presents the deviations for the ternary system of water + 1,3-propanediol + glycerol, 29 while table A4 presents the same results for the ternary water + ethanol + MEG. 30 Figure A18 presents some more results for the mixture water + MEG + methane.

Table A3 – Deviations obtained for the description of the system water (1) + 1,3-propanediol (2) + glycerol at 30 kPa (3). 29

Table A4 – Deviations obtained for the description of the system ethanol (1) + water (2) + MEG (3) at 1 atm. 30

Property

%AAD

Tdew 0.2Tbub 0.7x1 20.1x2 5.6y1 2.2y2 4.9

Figure A18 – Results for the system water + MEG + methane at 278.15 K (left) and at 298.15 K (right). Data from Folas et al. 31.

Property

%AAD

Tdew 1.2Tbub 4.1

x1 50.4x2 29.1y1 2.8y2 127.4

Tables A5 to A7 present the deviations obtained for the systems of water + hydrate inhibitor + condensate. Both the deviations obtained with the version of CPA applied in this work and those previously published for s-CPA (when applying correlations for both k ij’s between MEG + hydrocarbons and water + hydrocarbons are presented. 28,32 It is important to note that in some cases our averages cover a smaller range of temperatures than the results with s-CPA. (Cond-1 = condensate 1; L-Oil = Light oil; FL = fluid)

Table A5 – Deviations obtained for the studied LLE of water + MEG + condensate. 33,34,32,35–37,28

%AAD mole fractions

T/K Feed Mixture MEG in HC Water in HC HC in Polar

323.15 Cond-1

1 85.7 32.8 10.8

2 63.5 19.6 1.2

3 36 20.7 9.3

Average this work 61.7 24.4 7.1

303.15 and 323.15 Average s-CPA 55 12 21

303.15

Cond-2

1 18.5 31.5 37.6

2 25.3 27.9 29.8

3 3.6 25.4 1.8

323.151 19.2 18.4 40.4

2 14.9 14.7 44.8

3 0.5 4.9 46.3

303.15 and 323.15Average this work 13.7 20.5 33.5

Average s-CPA 21 28 66

313.15Cond-

3

1 21.8 2.3 27.4

2 16.1 1.4 21.3

3 29.8 3.2 0.4



323.15L.oil-1

1 105.3 98.2 43.7

2 122.9 98.6 24


313.15 and 323.15 Average s-CPA 45 29 54

323.15L.oil-2

1 36 14.7 50

2 47.2 22.9 38.8

3 7.3 15.8 21.4


313.15 and 323.15 Average s-CPA 37 27 28

Table A5 (cont.)

%AAD mole fractionsT/K Feed Mixture MEG in HC Water in HC HC in Polar

303.15

FL-1

1 17.9 19.8 25.2

2 13.3 25.5 19.9

3 33.1 16 40.4

313.151 18.9 71.6 15.5

2 1.5 66.3 13.6

3 21 50.4 34

323.151 8.9 85.4 1.1

2 24.2 78 10.5

3 16.6 43.9 23.3

303.15 to 323.15Average this work 17.3 50.8 20.4


Table A6 – Deviations obtained for a quaternary system containing water, methanol, methane and propane. Data are from Rossihol, 38 s-CPA results are from Yan et al. 39

T=253.15 K ; P=67 bar

Experimental data (mole fraction) %AAD This work %AAD s-CPA

Polar HC phase Vapor Polar HC phase Vapor Polar HC phase Vapormethano

l 0.536 0.0007 0 1.58 75.81 3.17 351.43

water 0.447 0 0 0.96 2.24

methane 0.0105 0.54 0.874 112.79 3.42 3.83 146.67 8.89 3.89

propane 0.0071 0.459 0.126 4.22 3.97 26.76 156.34 10.02 27.46

T=263.15 K ; P=67 bar

Experimental (data mole fraction) %AAD %AAD s-CPA

Polar HC phase Vapor Polar HC phase Vapor Polar HC phase Vapormethano

l 0.545 0.001 0 1.03 122.60 2.39 407.00

water 0.435 0 0 0.92 1.84

methane 0.0105 0.516 0.861 98.52 8.05 2.21 118.10 13.76 2.44

propane 0.0098 0.483 0.139 10.39 8.34 14.06 80.61 4.55 15.11

Table A7 – Deviations obtained for a LLE system of water + methanol + condensate. 40, s-CPA results are from Yan et al. 39

T=276.75 K ; P=60.3 barExperimental data (mol %) %AAD this work %AAD s-CPA

Feed HC liquid HC gas Polar liquid HC liquid HC gas Polar liquid HC liquid

HC gas Polar liquid

HC 84.76 99.799 99.957

- 0.12 0.02 - 0.00 0.02 -

MeOH 2.99 0.201 0.0429

18.68 51.67 7.11 1.93 8.96 5.36 2.70

water 12.25 - - 81.32 - - 1.30 - - 1.36

T=280.85 K ; P=149.9 barExperimental data (mol %) %AAD this work %AAD s-CPA

Feed HC liquid HC gas Polar liquid HC liquid HC gas Polar liquid HC liquid

HC gas Polar liquid

HC 64.04 99.812 99.931

- 0.13 0.01 - 0.03 0.01 -

MeOH 6.72 0.188 0.0687

18.68 57.78 2.14 1.98 5.85 7.13 1.56

water 29.22 - - 81.32 - - 0.46 - - 0.72

6- Pure parameters of hydrocarbons

Table A8 – Pure parameters for the hydrocarbons used in this work.

Compound ac (Pa.m6.mol-

2)b. 105 (m3.mol-1) c1 c2 c3 c4 c5

methane 0.233 2.98 0.594 -1.474 9.02 -27.39 31.55ethane 0.565 4.51 0.710 -1.174 7.00 -20.37 22.42

propane 0.952 6.27 0.819 -1.626 9.36 -24.39 23.68butane 1.407 8.07 0.881 -1.385 7.72 -20.51 21.48

pentane 1.937 10.05 0.998 -2.081 12.24

-32.87 32.84

hexane 2.525 12.12 1.061 -2.009 12.02

-33.14 35.08

heptane 3.161 14.27 1.132 -1.969 11.90

-33.60 36.91

octane 3.836 16.42 1.210 -2.059 12.33

-35.33 40.44

nonane 4.566 18.72 1.320 -2.844 20.14

-72.31 103.53

decane 5.319 20.99 1.413 -3.730 28.05

-102.86 148.30

benzene 1.907 8.27 0.911 -1.938 13.14

-41.13 50.75

toluene 2.522 10.39 1.009 -2.106 14.07

-45.37 57.11

o-xylene 3.147 12.17 1.090 -2.242 15.05

-49.92 64.73

m-xylene 3.183 12.57 1.110 -2.242 15.20

-50.90 66.13

p-xylene 3.196 12.64 1.120 -2.435 16.14

-53.61 69.80

ethylbenzene

3.122 12.33 1.041 -1.365 6.59 -14.49 12.64

7- Fitting of the hydrocarbon phase in water + hydrocarbon LLE

290 340 390 440 490 540 5901E-08.

1E-07.

1E-06.

1E-05.

1E-04.

1E-03.

1E-02.

1E-01.

1E+00.water in hydrocarbon phaseC10 in aqueous phase

T/K

mol

e fr

actio

n

250 300 350 400 450 5001E-04.

1E-03.

1E-02.

1E-01.

1E+00.benzene in aqueous phase

water in hydrocarbon phase

T/K

mol

e fr

actio

n

Figure A19 – Description of the results for water + decane (left) and water + benzene (right), when only the hydrocarbon phase is optimized.

References

(1) MULTIFLASH version 4.4, KBC Process Technology, London, United Kingdom.

(2) Matsuda, H.; Ochi, K. Liquid-liquid equilibrium data for binary alcohol + n-alkane (C 10-C16) systems: Methanol + decane, ethanol + tetradecane, and ethanol + hexadecane. Fluid Phase Equilib. 2004, 224 (1), 31–37.

(3) Thermodynamics Research Center (TRC), ThermoData Engine, version 9.0, National Institute of Standards and Technology, Boulder, Colorado, USA.

(4) Arce, A.; Blanco, A.; Soto, A.; Tojo, J. Isobaric Vapor-Liquid Equilibria of Methanol + 1-Octanol and Ethanol + 1-Octanol Mixtures. J. Chem. Eng. Data 1995, 40 (4), 1011–1014.

(5) Kurihara, K.; Minoura, T.; Takedaj, K. Isothermal Vapor-Liquid Equilibria Isothermal vapor-liquid equilibria for methanol + ethanol + water, methanol + water, and ethanol + water. J. Chem. Eng. Data 1996, 40 (3), 679–684.

(6) Phutela, R. C.; Kooner, Z. S.; Fenby, D. V. Vapour Pressure Study of Deuterium Exchange Reactions in Water-Ethanol Systems : Equilibrium Constant Determination. 1979, No. 2.

(7) Munday, E. B.; Mullins, J. C.; Edie, D. D. Vapor Pressure Data for Toluene, I-Pentanol, I-Butanol, Water, and I-Propanol and for the Water and I-Propanol System from 273.15 to 323.15 K. J. Chem. Eng. Data 1980, 25 (3), 191–194.

(8) Sada, E.; Tetsuo Morisue. Isothermal Vapor-Liquid Equilibrium of Isopropanol-Water System. 1952, 191–195.

(9) Vu, D. T.; Lira, C. T.; Asthana, N. S.; Kolah, A. K.; Miller, D. J. Vapor - Liquid equilibria in the systems ethyl lactate + ethanol and ethyl lactate + water. J. Chem. Eng. Data 2006, 51 (4), 1220–1225.

(10) Cristino, a. F.; Rosa, S.; Morgado, P.; Galindo, A.; Filipe, E. J. M.; Palavra, A. M. F.; Nieto de Castro, C. A. High-temperature vapour-liquid equilibrium for the water-alcohol systems and modeling with SAFT-VR: 1. Water-ethanol. Fluid Phase Equilib. 2013, 341, 48–53.

(11) Raal, J. D.; Motchelaho, A. M.; Perumal, Y.; Courtial, X.; Ramjugernath, D. P–x data for binary systems using a novel static total pressure apparatus. Fluid Phase Equilib. 2011, 310 (1–2), 156–165.

(12) Sentenac, P.; Bur, Y.; Rauzy, E.; Berro, C. Density of Methanol + Water between 250 K and 440 K and up to 40 MPa and Vapor - Liquid Equilibria from 363 K to 440 K. J. Chem. Eng. Data 1998, 9568 (97), 592–600.

(13) Cristino, A. F.; Rosa, S.; Morgado, P.; Galindo, A.; Filipe, E. J. M.; Palavra, A. M. F.; Nieto de Castro, C. A. High-temperature vapour–liquid equilibrium for the (water+alcohol) systems and modelling with SAFT-VR: 2. Water-1-propanol. J. Chem. Thermodyn. 2013, 60, 15–18.

(14) Barr-David, F.; Dodge, B. F. Vapor-Liquid Equilibrium at High Pressures. The Systems Ethanol - Water and 2-Propanol - Water. J. Chem. Eng. Data 1959, 4 (2), 107–121.

(15) Saajanlehto, M.; Uusi-Kyyny, P.; Haimi, P.; Pakkanen, M.; Alopaeus, V. A novel continuous flow apparatus with a video camera system for high pressure phase equilibrium measurements. Fluid Phase Equilib. 2013, 356, 291–300.

(16) Haarhaus, U.; Schneider, G. M. (Liquid + liquid) phase equilibria in (methanol + butane) and (methanol + pentane) at pressures from 0.1 to 140 MPa. J. Chem. Thermodyn. 1988, 20 (10), 1121–1129.

(17) Hradetzky, G.; Lempe, D. a. Phase equilibria in binary and higher systems methanol + hydrocarbon(s). Fluid Phase Equilib. 1991, 69, 285–301.

(18) Higashiuchi, H.; Sakuragi, Y.; Iwai, Y.; Arai, Y.; Nagatani, M. Measurement and correlation of liquid-liquid equilibria of binary and ternary systems containing methanol and hydrocarbons. Fluid Phase Equilib. 1987, 36, 35–47.

(19) Katayama, H.; Ichikawa, M. Liquid-liquid equilibria of three ternary systems: methanol-heptane including 1,3-dioxolane, 1,4-dioxane and tetrahydropyran in the range of 25 3.15 to 303.15K. J.Chem.Eng.Jpn, 1995, 28, 412–418.

(20) Orge, B.; Iglesias, M.; Rodríguez, A.; Canosa, J. M.; Tojo, J. Mixing properties of (methanol, ethanol, or 1-propanol) with (n-pentane, n-hexane, n-heptane and n-octane) at 298.15 K. Fluid Phase Equilib. 1997, 133 (1–2), 213–227.

(21) Casás, L. M.; Touriño, A.; Orge, B.; Marino, G.; Iglesias, M.; Tojo, J. Thermophysical properties of acetone or methanol + n-alkane (C9 to C12) mixtures. J. Chem. Eng. Data 2002, 47 (4), 887–893.

(22) Hong, J. H.; Malone, P. V.; Jett, M. D.; Kobayashi, R. The measurement and interpretation of the fluid-phase equilibria of a normal fluid in a hydrogen bonding

solvent: the methanemethanol system. Fluid Phase Equilib. 1987, 38 (1–2), 83–96.

(23) Wang, L. K.; Chen, G. J.; Han, G. H.; Guo, X. Q.; Guo, T. M. Experimental study on the solubility of natural gas components in water with or without hydrate inhibitor. Fluid Phase Equilib. 2003, 207 (1–2), 143–154.

(24) Weber, W.; Zeck, S.; Knapp, H. Gas solubilities in liquid solvents at high pressures: apparatus and results for binary and ternary systems of N2, CO2 and CH3OH. Fluid Phase Equilib. 1984, 18 (3), 253–278.

(25) Schlichting, H.; Langhorst, R.; Knapp, H. Saturation of high pressure gases with low volatile solvents: experiments and correlation. Fluid Phase Equilib. 1993, 84, 143–163.

(26) Naidoo, P.; Ramjugernath, D.; Raal, J. D. A new high-pressure vapour-liquid equilibrium apparatus. Fluid Phase Equilib. 2008, 269 (1–2), 104–112.

(27) Palma, A. M.; Oliveira, M. B.; Queimada, A. J.; Coutinho, J. A. P. Evaluating Cubic Plus Association Equation of State Predictive Capacities: A Study on the Transferability of the Hydroxyl Group Associative Parameters. Ind. Eng. Chem. Res. 2017, 56 (24), 7086–7099.

(28) Frost, M.; Kontogeorgis, G. M.; von Solms, N.; Haugum, T.; Solbraa, E. Phase equilibrium of North Sea oils with polar chemicals: Experiments and CPA modeling. Fluid Phase Equilib. 2016, 424, 122–136.

(29) Sanz, M. T.; Blanco, B.; Beltrán, S.; Cabezas, J. L. Vapor Liquid Equilibria of Binary and Ternary Systems with Water , 1,3-Propanediol , and Glycerol. J. Chem. Eng. Data 2001, 46, 635–639.

(30) Kamihama, N.; Matsuda, H.; Kurihara, K.; Tochigi, K.; Oba, S. Isobaric Vapor–Liquid Equilibria for Ethanol + Water + Ethylene Glycol and Its Constituent Three Binary Systems. J. Chem. Eng. Data 2012, 57 (2), 339–344.

(31) Folas, G. K.; Berg, O. J.; Solbraa, E.; Fredheim, A. O.; Kontogeorgis, G. M.; Michelsen, M. L.; Stenby, E. H. High-pressure vapor–liquid equilibria of systems containing ethylene glycol, water and methane. Fluid Phase Equilib. 2007, 251 (1), 52–58.

(32) Frost, M.; Kontogeorgis, G. M.; von Solms, N.; Solbraa, E. Modeling of phase equilibrium of North Sea oils with water and MEG. Fluid Phase Equilib. 2016, 424, 79–89.

(33) Riaz, M.; Kontogeorgis, G. M.; Stenby, E. H.; Yan, W.; Haugum, T.; Christensen, K. O.; Lokken, T. V; Solbraa, E. Measurement of Liquid-Liquid Equilibria for Condensate plus Glycol and Condensate plus Glycol plus Water Systems. J. Chem. Eng. Data 2011, 56 (12), 4342–4351.

(34) Riaz, M.; Yussuf, M. a.; Frost, M.; Kontogeorgis, G. M.; Stenby, E. H.; Yan, W.; Solbraa, E. Distribution of gas hydrate inhibitor monoethylene glycol in condensate and water systems: Experimental measurement and thermodynamic modeling using the cubic-plus-association equation of state. Energy and Fuels 2014, 28 (5).

(35) Frost, M.; Kontogeorgis, G. M.; Stenby, E. H.; Yussuf, M. a.; Haugum, T.; Christensen, K. O.; Solbraa, E.; Løkken, T. V. Liquid-liquid equilibria for reservoir fluids+monoethylene glycol and reservoir fluids+monoethylene glycol+water: Experimental measurements and modeling using the CPA EoS. Fluid Phase Equilib. 2013, 340, 1–6.

(36) Riaz, M.; Kontogeorgis, G. M.; Stenby, E. H.; Yan, W.; Haugum, T.; Christensen, K. O.; Solbraa, E.; Løkken, T. V. Mutual solubility of MEG, water and reservoir fluid: Experimental measurements and modeling using the CPA equation of state. Fluid Phase

Equilib. 2011, 300 (1–2), 172–181.

(37) Riaz, M.; Yussuf, M. a.; Kontogeorgis, G. M.; Stenby, E. H.; Yan, W.; Solbraa, E. Distribution of MEG and methanol in well-defined hydrocarbon and water systems: Experimental measurement and modeling using the CPA EoS. Fluid Phase Equilib. 2013, 337, 298–310.

(38) Rossihol, N. Equilibres de phases à basse température de mélanges d’hydrocarbures légers, deméthanol et d’eau: mesure et modélisation,. Thése l’Universite’ Lyon I Claude Bernard, 1995.

(39) Yan, W.; Kontogeorgis, G. M.; Stenby, E. H. Application of the CPA equation of state to reservoir fluids in presence of water and polar chemicals. Fluid Phase Equilib. 2009, 276 (1), 75–85.

(40) Pedersen, K. S.; Michelsen, M. L.; Fredheim, A. O. Phase equilibrium calculations for unprocessed well streams containing hydrate inhibitors. Fluid Phase Equilib. 1996, 126 (1), 13–28.

(41) Miller, D. G. Joule-Thomson Inversion Curve, Corresponding States, and Simpler Equations of State. Ind. Eng. Chem. Fundam. 1970, 9 (4), 585–589.

supplementary data - path :.: process and...

Documents