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III.3.2. soft-SAFT with crossover Modeling The inclusion of the crossover treatment requires the adjust of two additional parameters, the cut-off length L, related to the maximum wavelength fluctuations that are accounted for in the uncorrected free energy, and φ the average gradient of the wavelength function (White 1999 and 2000). In this work the procedure used by Llovell et al. (2004) to apply the soft-SAFT crossover to linear alkanes was followed which implies to treat both L and φ as adjustable parameters. The authors tested the accuracy of the soft-SAFT crossover equation by comparison with molecular simulations of LJ chains and did several studies about the influence of both values φ and L in predicting the phase envelope when compared to simulation data. The model was then applied to experimental systems of chainlike molecules, the n-alkane series, providing a set of transferable parameters equally accurate far from and close to the critical region. As before, n-perfluoroalkanes are described as homonuclear chainlike molecules, modeled as m Lennard-Jones segments of equal diameter σ, and the same dispersive energy ε, bonded tangentially to form the chain. According to the crossover model, these three molecular parameters plus the crossover parameters φ and L, are enough to describe all thermodynamic properties. To minimize the number of adjusted parameters, the parameter L was fixed equal to the one previously adjusted for the n-alkane series (Llovell et al., 2004). A new set of parameters, able to describe simultaneously the vapor-liquid equilibria diagram away and close to the critical region, in contrast to previous correlations accurate for only far from the critical point, was obtained. The correlation comes from optimised parameters for the eight first members of the alkanes series, obtained by fitting experimental saturated liquid densities and vapor pressures, as done before when the model without crossover was applied. The new proposed correlations are given by m = 0.689 + 0.352 CN (III.31) mσ 3 = 43.05 + 34.65 CN (III.32) mε/kB B = 98.29 + 92.55 CN (III.33) mφ = 1.08 + 3.33 CN (III.34) mL = 0.11 + 0.12 CN (III.35) - 119 -
Modeling The correlation coefficients for each of the linear relations is higher than 0.995 in all cases. In the case of the n-alkanes series, Llovell et al. (2004) obtained good results using a fixed m equal to the one adjusted with the original soft-SAFT model. However, in the case of the n-perfluoroalkane series the m parameter was also slightly modified together with σ and ε. The experimental critical temperature, pressure and density and those predicted from the original soft-SAFT and soft-SAFT with crossover for the first eight members of the n-alkanes series are presented in Table III.3. Experimental data was taken from the works of (Smith and Srivastava, 1986) and Vandana et al. (1994). While soft-SAFT overestimates the critical temperature and pressure, as expected, soft-SAFT with crossover is able to predict both critical properties with high accuracy. However, as already observed by other authors using a similar approach, the critical density is slightly overestimated. Table III.3. Critical Constants for Linear (C1-C9) and Aromatic Perfluoroalkanes. Comparison Between Experimental Data and Predictions Given by the soft-SAFT EoS With and Without Crossover. Compound Exp Tc (K) soft SAFT soft SAFT + CV Exp Pc (MPa) soft SAFT soft SAFT + CV Exp Dc (mol/L) soft SAFT soft SAFT + CV CF4 227.6 249.60 227.70 3.74 4.55 3.70 7.17 6.86 8.76 C2F6 293.0 314.00 292.85 3.04 3.72 3.01 4.49 4.44 5.61 C3F8 345.1 370.11 345.17 2.67 3.26 2.60 3.34 3.18 4.04 C4F10 386.5 417.51 386.37 2.31 2.93 2.21 2.65 2.46 3.09 C5F12 421.4 460.67 421.93 2.04 2.67 1.96 2.16 1.99 2.5 C6F14 450.6 498.43 448.78 1.88 2.43 1.81 1.84 1.65 2.2 C7F16 475.3 533.27 474.79 1.62 2.23 1.53 1.60 1.40 1.88 C8F18 498.2 559.70 498.40 1.55 2.05 1.37 1.39 1.21 0.97 C9F20 * 524.0 583.31 517.52 1.56 1.88 1.27 -- 1.06 1.47 C6F6 516.7 555.84 516.22 3.23 4.44 3.03 2.98 2.67 3.36 C7F8 534.5 578.67 534.60 2.71 3.64 2.60 2.34 2.08 2.70 * Critical values extrapolated from the correlations obtained for the linear perfluoroalkane series from C1 to C8. - 120 -
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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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Page 87 and 88: Experimental Methods, Results and D
Page 93 and 94: P / MPa 6 5 4 3 2 1 0 P / MPa 14 12
Page 95 and 96: II.6. Liquid - Liquid Equilibrium I
Page 101 and 102: 0 τ β Δ1 2Δ1 [ 1+ B τ + B τ +
Page 103 and 104: References Experimental Methods, Re
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: Modeling Table III.2. Absolute Aver
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 and 160: P / MPa 14 12 10 8 6 4 2 0 0 0.2 0.
Page 161 and 162: Modeling Figures III.16, III.17 and
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,
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Modeling McCabe, C.; Jackson, SAFT-
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Modeling Poling, B.; Prauznitz, J.;
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Modeling Wertheim, M. S., Fluids wi
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