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Modeling The P-x curves for the mixtures CO2/perfluoro-n-octane, CO2/perfluorodecalin, and CO2/perfluoromethylcylohexane were found to be sensitive to the energy binary parameter, ξij, but relatively insensitive to binary size parameter, ηij,. Hence, the procedure followed was to fix the binary size parameter and adjust only the energy parameter to experimental data at 323.15 K for each mixture and use it in a predictive manner for the other temperatures. In this way, the size and energy binary parameters were transferred within the same mixture at different conditions. Additionally, the size parameter was also transferred for different compounds. Table III.8 compares the binary parameters adjusted when the quadrupole moment is considered explicitly and in an effective way. When the polar term is included, the binary energy and size parameters are consistently closer to unity than when the non-polar soft-SAFT EoS is used. This is expected, since the polar equation explicitly considers the quadrupole, with an extra parameter, in this case the binary parameters account only for the unlike van der Waals interactions. On the contrary, when the quadrupole is not included, the binary parameters effectively account for it, showing larger deviations from unity, particularly the energy parameter. Also presented in Table III.8 are the kij parameters adjusted for each mixture to be used in the Peng-Robinson EoS. The kij parameter was adjusted at the same intermediate temperature of 323.15 K and then used to predict the phase diagrams at different temperatures following the procedure used to adjust the binary parameters for the soft-SAFT EoS. Table III.8. Optimised size and energy binary interaction parameters for the soft-SAFT EoS and kij parameter for the Peng-Robinson EoS. Soft-SAFT EoS With polar term Without polar term Peng- Robinson EoS System ηij � ξij ηij � ξij kij CO2 – C8F18 1.04 0.890 1.06 0.790 0.070 CO2 – C10F18 1.04 0.836 1.06 0.732 0.124 CO2 – C7F14 1.04 0.902 1.06 0.806 0.112 - 141 -
Modeling Figures III.16, III.17 and III.18 present P-x diagrams where experimental data for the binary mixtures CO2/perfluoro-n-octane, CO2/perfluoromethylcyclohexane and CO2/perfluorodecalin respectively are compared against the soft-SAFT calculations. It can be observed that the agreement between the experimental data and the description provided by the soft-SAFT model with and without the polar term are both excellent for the three mixtures, at all conditions studied. P / MPa 12 10 8 6 4 2 0 0 0.2 0.4 0.6 0.8 1 x, y CO2 Figure III.16. Vapor-liquid equilibrium of CO2/perfluoro-n-octane system at 293.15K, 323.15K and 353.15K. Symbols represent experimental data measured in this work. Solid lines corresponds to the soft-SAFT model including the polar term and black dashed lines to the original soft-SAFT model at optimised size and the energy binary interaction parameters from Table III.8. The lighter solid lines are predictions given by the Peng Robinson EoS with kij also from Table III.8. Obviously that a more realistic molecular model as is the soft-SAFT EoS can predict the experimental data more accurately, capturing the different curvatures presented by the phase diagrams. However, globally the results obtained with the Peng-Robinson EoS are surprisingly good except in the case of the CO2/perfluorodecalin system, where the equation predicts a LLE region at 293.15 K that was not observed experimentally. These results confirm the idea that the empirical success of the Peng-Robinson equation of state is unique; there is no other simple equation of state of the van der Waals form that has - 142 -
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Ana Maria Antunes Dias Universidade
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o júri presidente Prof. Dr. Joaqui
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palavras-chave resumo perfluoroalca
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Contents Notation List of Tables Li
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Notation Abbreviations AAD EoS LCST
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List of Tables Table I.1 Average Bo
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Table III.6 Adjusted Binary Paramet
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Figure II.9 Comparison between corr
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Figure III.8 Temperature-density di
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Figure III.25 Vapor-phase mole frac
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I.1. Fluorine Properties General In
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Table I.2. Physicochemical Properti
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General Introduction order to compa
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General Introduction the numerous a
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General Introduction carbon dioxide
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General Introduction animals. That
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General Introduction Table I.3. Lit
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References General Introduction Ban
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General Introduction Hildebrand, J.
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General Introduction Rowinsky EK. N
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II. Part EXPERIMENTAL METHODS, RESU
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Experimental Methods, Results and D
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Table II.3. (continued) T K ρexp g
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ρ / g.cm-3 1.750 1.730 1.710 1.690
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I. 3. Vapour pressure I.3.1. Biblio
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I.3.2. Apparatus and Procedure Expe
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I.3.3. Experimental Results and Dis
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Table II.8. (continued) T K Pexp kP
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ΔH vap = TΔS vap 2⎛ d ln P ⎞
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I.4. Solubility at atmospheric pres
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x2 (T,P2) 7.0E-03 6.0E-03 5.0E-03 4
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L 2,1 0.70 0.60 0.50 0.40 0.30 285
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P / MPa 6 5 4 3 2 1 0 P / MPa 14 12
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II.6. Liquid - Liquid Equilibrium I
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0 τ β Δ1 2Δ1 [ 1+ B τ + B τ +
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References Experimental Methods, Re
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Page 109 and 110: Experimental Methods, Results and D
Page 111 and 112: III.1. Introduction Modeling Most c
Page 113 and 114: Modeling The pioneering work of Wer
Page 115 and 116: III.2. Soft-SAFT Model Modeling A S
Page 117 and 118: Modeling The equation of state is w
Page 119 and 120: Chain Term Modeling Originally Wert
Page 121 and 122: Modeling The model is easily extend
Page 123 and 124: ( ) ( ) ∑∑∑ 3 2 2 2 2 qq 32π
Page 125 and 126: Modeling HRT is a promising theory,
Page 127 and 128: ( ρ) ρ , 0 ≤ ρ ( ρ) 2 Modelin
Page 129 and 130: III.3. Application to Pure Compound
Page 131 and 132: Modeling From the optimised paramet
Page 133 and 134: T / K 400 350 300 250 200 150 100 5
Page 135 and 136: ln Pvap 1.0E+01 1.0E+00 1.0E-01 1.0
Page 137 and 138: Modeling Table III.2. Absolute Aver
Page 139 and 140: Modeling The correlation coefficien
Page 141 and 142: Pvap (MPa) 4.00 3.50 3.00 2.50 2.00
Page 143 and 144: Modeling The mixture parameters a a
Page 145 and 146: Modeling the assumptions made by th
Page 147 and 148: Modeling between oxygen and perfluo
Page 149 and 150: xSolute 5.5E-03 5.0E-03 4.5E-03 4.0
Page 151 and 152: Modeling previous work, dealing wit
Page 153 and 154: Modeling These results confirm that
Page 155 and 156: Modeling CO2 binary mixtures using
Page 157 and 158: Modeling average deviation (AAD) be
Page 159: P / MPa 14 12 10 8 6 4 2 0 0 0.2 0.
Page 163 and 164: Modeling calculations from the orig
Page 165 and 166: Table III.9. References for VLE exp
Page 167 and 168: P / MPa 20 18 16 14 12 10 8 6 4 2 0
Page 169 and 170: Modeling Finally, Figure III.24 pre
Page 171 and 172: III.4.4. VLE and LLE of Alkane and
Page 173 and 174: Modeling number of perfluro-n-alkan
Page 175 and 176: y C6F14 1.0 0.8 0.6 0.4 0.2 0.0 0.0
Page 177 and 178: P / MPa 0.08 0.07 0.06 0.05 0.04 0.
Page 179 and 180: P / MPa 0.12 0.10 0.08 0.06 0.04 0.
Page 181 and 182: Modeling approach based on the meth
Page 183 and 184: Modeling Blas, F. J.; Vega, L. F.,
Page 185 and 186: DIPPR, Thermophysical Properties Da
Page 187 and 188: Modeling Hildebrand, J. H.; Fisher,
Page 189 and 190: Modeling McCabe, C.; Jackson, SAFT-
Page 191 and 192: Modeling Poling, B.; Prauznitz, J.;
Page 193 and 194: Modeling Wertheim, M. S., Fluids wi
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