729 Index a α-function generalized Soave Redlich Kwong 48 Peng Robinson 48 Mathias Copeman 53 Twu 53 57 absorption process 259 261, 606 607 acentric factor 46, 71ff activity and activity coefficient 161 162, 188, 193 197, 675 680 Bromley extension 376 377 Debye Hückel limiting law 374 376 electrolyte-nrtl model 378 387 LIQUAC model 387 395 Mean Spherical Approximation (MSA) model 396 Pitzer model 377 378 pressure dependence 200 201 temperature dependence 200 201 adiabatic compression and expansion 595 600 advanced cubic equations of state 52 58 Aly Lee equation 106 Antoine constants 546 Antoine equation 83 84 apparent permeability constant 444 applications practical adiabatic compression and expansion 595 600 equilibrium thermodynamics limitations 606 608 flash 591 593 Joule Thomson effect 593 595 pressure relief 600 606 special formaldehyde solutions 567 573 vapor phase association 573 587 ARTIST software package 489 ASOG method 293 azeotropic behavior occurrence, conditions for 248 259 azeotropic points 197 investigation in multicomponent systems 257 259, 501 503 temperature dependence of azeotropic composition 243, 251 258, 307, 321, 662 664 b Bancroft point 255 Barker Henderson perturbation theory 464 Berlin form of virial equation 659 Born term 381, 396 Boyle curve 39 Brock Bird Miller equation 134 Bromley extension 376 377 c caloric properties 10 14, 333, 664 665, 681 685 caloric equations of state entropy 336 337 Helmholtz energy and Gibbs energy 337 339 internal energy and enthalpy 333 336 chemical reactions 354 361 enthalpy descriptions in process simulation programs 339 346 G-minimization technique 361 364 Canizzarro reaction 572 Cardano s formula 42, 652 653 Chemical Thermodynamics: for Process Simulation, First Edition. Jürgen Gmehling, Bärbel Kolbe, Michael Kleiber, and Jürgen Rarey. 2012 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2012 by Wiley-VCH Verlag GmbH & Co. KGaA.
730 Index chemical equilibrium 531 551 influence of the real behavior 538 552 multiple 551 552 Gibbs energy minimization 556 563 relaxation method 552 556 chemical potential 154 equivalence of, for pure compounds 654 655 mixtures 658 659 polymer solutions 452 454 Chung equation 130 Clausius Clapeyron equation 26, 27, 56, 75, 99, 100, 216, 236, 347, 572 cloud point curve 450, 479 complex electrolyte systems 400 401 correlation 80 81 corresponding-states principle 46 47 COSTALD method 67, 95 Coulomb s law 368 Cox charts 86 critical condensation point 182 critical locus 183 critical mass flow 603 critical opalescence 8 cross virial coefficients 163 cryoscopic constant 418 cubic equations of state 40 45, 164 174 d Dalton s law 155 Debye Hückel limiting law 374 376 Debye Hückel term 381 degree of freedom 103 departure functions 19 differential relationships 646 653 diffusion coefficients 136 140 dissociation equilibrium 396 398 Dortmund Data Bank (DDB) 615 616 current status of 488 Dortmund Data Bank Software Package (DDBSP) 489, 490, 615 616 e electrolyte-nrtl model 378 387 electrolyte solutions 365 369 activity coefficient models for Bromley extension 376 377 Debye Hückel limiting law 374 376 electrolyte-nrtl model 378 387 LIQUAC model 387 395 Mean Spherical Approximation(MSA) model 396 Pitzer model 377 378 complex electrolyte systems 400 401 dissociation equilibrium 396 398 salt influence on vapor-liquid equilibrium behavior 398 399 solvent activity in 661 662 thermodynamics of 369 374 enantiotropy 406 enthalpy 11, 12, 15, 74 80 descriptions, in process simulation programs 339 340 equation of state 346 354 internal energy 333 336 vaporization 97 102 enthalpy of reaction 525 527 real gas behavior consideration on 529 531 temperature dependence 527 529 entrainer selection for azeotropic and extractive distillation 511 518 entropy 11 equations of state 27 advanced cubic 52 58 application to mixtures 162 163 cubic equations of state 164 174 virial equation 163 164 caloric entropy 336 337 Helmholtz energy and Gibbs energy 337 339 internal energy and enthalpy 333 336 coefficients for high precision 641 644 cubic 40 45 fugacity coefficient for pressure-explicit 665 666 of PSRK 671 675 of Soave Redlich Kwong 669 671 of virial equation (Berlin form) 668 of virial equation (Leiden form) 666 668 generalized 45 52 group contribution 317 326 high precision 32 39 polymer thermodynamics 462 478 predictive Soave Redlich Kwong 312 317 process simulation programs 346 354 solubility of gases in liquids 270 271 van der Waals 40 vapor liquid equilibrium calculation using 235 240 fitted binary parameter of cubic equations of state 240 249 virial equation 27 32
Index 731 VTPR group contribution equation of state 317 326 equilibrium thermodynamics limitations 606 608 Euler theorem 657 658 eutectic systems, and solid liquid equilibrium (SLE) 410 419 f Fenske equation 230 Fick s first law 137 flash 591 593 Flory Huggins equation 207 209, 451 452 ofpsrkg E mixing rule 172 fluid systems, phase equilibrium in 177 186 application of activity coefficient models 193 197 conditions for the occurence of azeotropic behavior 248 259 g E model parameters fitting 216 221 recommended model parameters 231 235 VLE data check for thermodynamic consistency 221 231 liquid liquid equilibrium 273 286 calculation using the K-factor method 282 286 diagrams 274, 276 isoactivity criterion 273, 275 pressure dependence 288 289 temperature dependence of ternary systems 286 288 predictive models 289 290 group contribution methods 292 293 predictive Soave Redlich Kwong equation of state 312 317 regular solution theory 290 291 UNIFAC method 293 312 VTPR group contribution equation of state 317 326 solubility of gases in liquids 259 260 calculation using equations of state 270 271 calculation using Henry constants 261 270 prediction 271 273 thermodynamic fundamentals 186 193 vapor liquid equilibrium calculation, using equation of state 235 240 binary parameter fitting of cubic equations of state 240 249 vapor liquid equlibria using g E models 197 216 formaldehyde solutions 567 573 freezing point depression 417 419 fugacity and fugacity coefficient 19 23, 188 for pressure-explicit equation of state 665 666 of PSRK equation of state 671 675 of Soave Redlich Kwong equation of state 669 671 of virial equation (Berlin form) 668 of virial equation (Leiden form) 666 668 in mixtures 159 ideal 159 160 phase equilibrium 160 161 Fuller method 137 g Gauss Hermitian quadrature 480 481 g E mixing rule 165 172, 241 g E models 197 216, 451 462 fitting of model parameters 216 230 recommended model parameters 231 235 generalized equations of state 45 52 Gibbs Duhem equation 140, 153 154, 162, 372, 709 Gibbs energy 11, 21, 26, 197 198, 213 214, 277 278, 337 339, 357, 360, 362, 372, 377, 409, 452, 453, 531 533, 554, 655 minimization 361 364, 556 563 standard enthalpy and 77 80 Gibbs Helmholtz equation 201, 216, 227, 228, 254, 374 Gibbs phase rule 42 group contribution methods 292 293 group interactions 70 Guldberg rule 66 h Helmholtz energy 11, 114, 337 339, 465 Henry s law 262 Henry constant 261 268 high precision equation of state 32 39, 641 643 Hoffmann Florin equation 86 87 Huron Vidal-g E mixing rule 166, 168
732 Index i ideal gases 14 15, 27 derivation of expressions for the speed of sound 659 660 heat capacity 102 109 polynomial coefficients for selected compounds 711 ideal mixture of 154 156 maximum mass flux 685 687 ideal mixture of ideal gases 154 156 of real fluids 156 157 interaction parameters 380 internal energy, of system 10 inverse gas chromatography 456 inverse reduced viscosity 121 isofugacity condition 187 isothermal compressibility factor 17 j Jamieson equation 126 Joback method 66 67, 87, 88, 108 estimation formula 72 group contributions for 68 Joule Thomson effect 593 595 Joule Thomson inversion curve 39 k Kelvin equation 92 93 derivation of 653 654 Kirchhoff s law 527, 534, 546 Kirchhoff equation 83, 116 Koningsveld Kleintjens model 454 456 Krichevsky Kasarnovsky equation 267 l Lee Kesler approach 162 Lee Kesler Plöcker equation 163 Leiden form of virial equation 659 Lewis Randall rule 160 LIFAC method 317 Li method 128 linear low-density polyethylene (LLDPE) 481 LIQUAC model 387 395, 429, 430 liquid density 94 97 liquid heat capacity 109 113 liquid liquid equilibrium (LLE) 179, 212, 273 286 polymer solutions 449 462, 479 482 pressure dependence 288 temperature dependence of ternary 286 288 liquid thermal conductivity 125 130 liquid viscosity 114 120 local composition 207 lower critical solution temperature (LCST) 275, 462 Lucas equation 118 125 m Mathcad examples 613 615 Mathias Copeman α-function 53 Maurer model 568 572, 608 Maxwell s equal area construction 43 Maxwell relations 13, 18 mean ion activity coefficient 372 Mean Spherical Approximation (MSA) model 396 membrane processes osmosis 439 442 pervaporation 443 444 Microsoft Excel 616 617 Microsoft Office Visual Basic for Application 616 617 Missenard method 128 mixture properties 147 activity and activity coefficient 161 162 application of equation of state to mixtures 162 163 cubic equations of state 164 174 virial equation 163 164 excess properties 157 158 fugacity in mixtures 159 of ideal mixture 159 160 phase equilibrium 160 161 Gibbs Duhem equation 153 154 ideal mixture of ideal gases 154 156 of real fluids 156 157 partial molar properties 149 152 property change of mixing and 148 149 molality 366 monotropy 406 multiple chemical equilibrium 551 552 Gibbs energy minimization 556 563 relaxation method 552 556 n Nernst distribution coefficients 276 NRTL model 213, 378 387, 678 679, 709 recommended model parameters 233 Nußelt number 126
Index 733 o opposite lever arms, law of 180 osmosis 439 442 osmotic coefficient 373ff osmotic pressure 439, 442 p pair parameters 380 partial condensation 606 partial molar Gibbs energy 155, 156, 160 Peng Robinson equation 48, 99, 101, 167 169, 339, 352 generalized α-function 48 permanent gases 8 9 Perturbed-Chain-SAFT (PC-SAFT) model 467 468 Perturbed-Chain-SAFT EOS (PC-SAFT EOS) 463 pervaporation 443 444 phase equilibrium 23 27, 160 161. See also fluid systems, phase equilibrium in for closed system 656 657 for fully closed system 655 656 Pitzer model 377 378 Planck Einstein function 104 polydispersity 450, 479 482 polymer thermodynamics 445 451 g E models 451 462 equation of state 462 478 polydispersity influence 479 482 polymorphism 406 Porter equation 152, 198, 262, 421 Poynting factor (Poy i ) 189, 432, 433 Prandtl number 126 Prausnitz Shair method 271 predictive models 289 290 group contribution methods 292 293 predictive Soave Redlich Kwong equation of state 312 317 regular solution theory 290 291 UNIFAC method 293 312 VTPR group contribution equation of state 317 326 predictive Soave Redlich Kwong (PSRK) 271, 312 317 difference between VTPR and 317 pressure relief 600 606, 685 687 process simulation programs 1 2 enthalpy descriptions in 339 340 equation of state 346 354 model parameter verification 492 g E model parameter verification 493 501 pure component parameter verification 492 493 notation of equations in 678 679 PT-graph 9 PSRK 166, 169 172, 671 675 parameters 721 723 pure component parameters 619 640 pure component properties, correlation and estimation of 65 characteristic physical property constants 65 66 acentric factor 71 72 critical data 66 71 melting point and enthalpy of fusion 74 77 normal boiling point 72 74 standard enthalpy and standard Gibbs energy of formation 77 80 correlation and estimation of transport properties 114 diffusion coefficients 136 140 liquid thermal conductivity 125 130 liquid viscosity 114 120 surface tension 133 136 vapor thermal conductivity 130 133 vapor viscosity 120 125 temperature-dependent properties 80 81 enthalpy of vaporization 97 102 ideal gas heat capacity 102 109 liquid density 94 97 liquid heat capacity 109 113 speed of sound 113 114 vapor pressure 82 94 pure components, PvT behavior of 5 caloric properties 10 14 equations of state 27 advanced cubic 52 58 cubic 40 45 generalized 45 52 high precision 32 39 virial equation 27 32 ideal gases 14 15 real fluids auxiliary functions 16 17 fugacity and fugacity coefficient 19 23 phase equilibrium 23 27 residual functions 17 19 PvT-diagram 6 Pxy-diagram 179 180, 181 182
734 Index r Rackett equation 94 Raoult s law 197, 206 Rarey/Moller method 89 91 Rarey/Nannoolal methods 69 70, 72, 74, 116 reaction kinetics 608 real fluids auxiliary functions 16 17 fugacity and fugacity coefficient 19 23 ideal mixture of 156 157 phase equilibrium 23 27 residual functions 17 19 real gas, expression derivation for speed of sound 660 661 Rectisol process 262 Redlich Kister expansion 198, 199 Redlich Kister test 221 223, 708 709 Redlich Kwong equation 44 refrigeration arrangement, scheme of 599 regression technique for binary parameters 695 709 for pure component data 691 694 Regula Falsi method 458 459 regular solution theory 272 273, 290 291 relaxation method 552 556 residual curves 503 511 boundary residual curves 185 186, 503 511 retrograde condensation 183 reverse osmosis 439 Roy Thodos method 131 s salting out 398 salt solubility 427 432 Sato Riedel equation 127 saturated liquid 23 saturated vapor 23 Schulz Flory distribution 446 Schwarz theorem 13 separation technology, thermodynamic application in 487 492 azeotropic points in multicomponent systems 501 503 entrainer selection for azeotropic and extractive distillation 511 518 extractive distillation applicability examination, for the separation of aliphatics from aromatics 519 522 model parameter verification, prior to process simulation 492 g E model parameter verification 493 501 pure component parameter verification 492 493 residue curves, distillation boundaries, and distillation regions 503 511 solvent selection, for separation processes 518 519 Simon Glatzel equation 75, 77, 427 pressure dependence of melting point description using 76 Simplex Nelder Mead method 218 Soave Redlich Kwong equation 47 48, 101, 165 169, 339, 681 685 generalized α-function 48 solid liquid equilibrium (SLE) 179, 405, 408 410 diagrams 407 with intermolecular compound formation in solid state 424 426 pressure dependence of 427 salt solubility 427 432 of simple eutectic systems 410 419 freezing point depression 417 419 solubility of solids in supercritical fluids 432 434 of systems with solid solutions ideal systems 419 420 nonideal systems 420 423 solubility, of gases in liquids 259 260 calculation using equation of state 270 271 calculation using Henry constants 261 270 prediction 271 273 solution of groups concept 292 293 solvation 368 speed of sound 105, 113 114 expression derivation, for ideal and real gases 659 661 as maximum velocity in adiabatic pipe with constant cross-flow area 685 specific heat capacity 15, 102ff state variable and partial molar property, relationship between 657 658 Statistical Association Fluid Theory (SAFT) 463 Stiel Thodos equation 132 supercritical fluids, solubility of solids in 432 434 surface tension 133 136
Index 735 t Tait equation 96 ternary azeotrope 185 thermal expansion coefficient 17 thermodynamics first Law 10 secondlaw 11 third Law 12 throttle valve 591 Twu-α-function 53 57 Txy-diagram 180 Tyn/Calus equation 139 u UNIFAC 293 300, 515, 521, 568 570 modified 300 310, 412 parameters 715 718 parameters 713 714 weaknesses of group contribution methods 309 312 UNIQUAC equation 207, 213, 233, 279, 283, 294, 496, 500, 678, 709 recommended model parameters 231 upper critical solution temperature (UCST) 275, 462 v van t Hoff equation, application of 200, 269, 428, 533, 572, 651 van der Waals equation of state 40 van Velzen method 116 vapor fraction 24 vapor liquid equilibrium (VLE) 179, 193, 196, 217, 220, 226 calculation, using equation of state 235 240 binary parameter fitting of cubic equations of state 240 249 data check for thermodynamic consistency 221 231 recommended g E model parameters 231 235 diagrams 196 salt influence on 398 399 usingg E models 197 216 vapor liquid separator 591 vapor phase association 343, 573 587 vapor pressure 82 94 vapor thermal conductivity 130 133 vapor viscosity 120 125 Vignes correlation 140 virial equation 27, 163 164 estimation of second virial coefficients Tsonopoulos method 30 Hayden O Connell method 30 Visual Basic for Application 616 617 volume-translated Peng Robinson equation (VTPR) 55, 67, 170 group contribution equation of state 317 326 parameters 725 727 w Wagner equation 81, 84 85 Walden rule 75 Wassiljeva mixing rule 132 Watson equation 98, 133 Wilke mixing rule 124, 132 Wilson equation 209 210, 213, 278, 548, 678, 709 derivation 675 677 inability, to describe miscibility gaps 679 681 recommended model parameters 232 Wood s metal 406 z Zeno line 39