Aspen Physical Property System - Physical Property Models

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account for the repulsive interactions. The attractive forces are further divided into different contributions, including dispersion, polar, and association. Using a generated function, �, the copolymer PC-SAFT model in general can be written as follows: where � hc , � disp , � assoc , and � polar are contributions due to hard-chain fluids, dispersion, association, and polarity, respectively. The generated function � is defined as follows: where a res is the molar residual Helmholtz energy of mixtures, R is the gas constant, T is the temperature, � is the molar density, and Zm is the compressibility factor; a res is defined as: where a is the Helmholtz energy of a mixture and a ig is the Helmholtz energy of a mixture of ideal gases at the same temperature, density and composition xi. Once � is known, any other thermodynamic function of interest can be easily derived. For instance, the fugacity coefficient �i is calculated as follows: with where is a partial derivative that is always done to the mole fraction stated in the denominator, while all other mole fractions are considered constant. Applying � to the departure equations, departure functions of enthalpy, entropy, and Gibbs free energy can be obtained as follows: Enthalpy departure: Entropy departure: 36 2 Thermodynamic Property Models
Gibbs free energy departure: The following thermodynamic conditions must be satisfied: Hard-chain Fluids and Chain Connectivity In PC-SAFT model, a molecule is modeled as a chain molecule by a series of freely-jointed tangent spheres. The contribution from hard-chain fluids as a reference system consists of two parts, a nonbonding contribution (i.e., hardsphere mixtures prior to bonding to form chains) and a bonding contribution due to chain formation: where is the mean segment in the mixture, � hs is the contribution from hard-sphere mixtures on a per-segment basis, and � chain is the contribution due to chain formation. Both and � hs are well-defined for mixtures containing polymers, including copolymers; they are given by the following equations: where mi�, �i�, and �i� are the segment number, the segment diameter, and the segment energy parameter of the segment type � in the copolymer 2 Thermodynamic Property Models 37
Page 1 and 2: Aspen Physical Property System Phys
Page 3 and 4: Contents Contents..................
Page 5 and 6: General Pure Component Solid Molar
Page 7 and 8: 1 Introduction This manual describe
Page 9 and 10: Pure Component Temperature- Depende
Page 11 and 12: the Properties Parameters Pure-Comp
Page 13 and 14: 2 Thermodynamic Property Models Thi
Page 15 and 16: Property Model Model Name Phase(s)P
Page 17 and 18: Property Model Model Name 2 Thermod
Page 19 and 20: Where: Parameter Name/Element 2 The
Page 21 and 22: critical temperature, the critical
Page 23 and 24: Where the ideal-gas contribution
Page 25 and 26: , where � For polar, associating
Page 27 and 28: Parameter Name/ Element 2 Thermodyn
Page 29 and 30: The denominator of equation 8 is gi
Page 31 and 32: V. V. De Leeuw and S. Watanasiri, "
Page 33 and 34: References M. Benedict, G. B. Webb,
Page 35 and 36: References L. Haar, J.S. Gallagher,
Page 37: Parameter Name/Element NTHDDH 0 †
Page 41 and 42: For a block copolymer, there is onl
Page 43 and 44: Copolymer PC-SAFT Dispersion Term T
Page 45 and 46: The association-site number of the
Page 47 and 48: Then I2(�) and I3(�) are comput
Page 49 and 50: A databank called PC-SAFT contains
Page 51 and 52: Parameter Name/Element PRKBV/1 k ij
Page 53 and 54: Predictive SRK (PSRK) This model us
Page 55 and 56: ka,ij kb,ij = = For best results, b
Page 57 and 58: J. Schwartzentruber and H. Renon, "
Page 59 and 60: Redlich-Kwong-Soave-MHV2 This equat
Page 61 and 62: ‡ RKUC0, RKUC1, and RKUC2 are tre
Page 63 and 64: Parameter Name/ Element SRKLIJ/3 l
Page 65 and 66: Parameter Name/ Element Symbol Defa
Page 67 and 68: Association Equilibria Every associ
Page 69 and 70: and respectively. For the reactions
Page 71 and 72: R. W. Long, J. H. Hildebrand, and W
Page 73 and 74: Where the L, M, and N are parameter
Page 75 and 76: Alpha function Model name First Opt
Page 77 and 78: mi = Computed by equation 6 Equatio
Page 79 and 80: Parameter Name/Element 2 Thermodyna
Page 81 and 82: standard RKS alpha function, except
Page 83 and 84: These mixing rules are discussed se
Page 85 and 86: Where both Ai* and Am are calculate
Page 87 and 88: Like Huron and Vidal, the limiting
Page 89 and 90:
Model Type Wilson Local composition
Page 91 and 92:
Therefore, the simplified Pitzer eq
Page 93 and 94:
Parameter Name/Element Symbol Defau
Page 95 and 96:
Where: �i 2 Thermodynamic Propert
Page 97 and 98:
The electrolyte NRTL model uses the
Page 99 and 100:
Parameter Symbol No. of Name Elemen
Page 101 and 102:
with Where: xi = Mole fraction of c
Page 103 and 104:
It should be understood that equati
Page 105 and 106:
The reference Gibbs energy is deter
Page 107 and 108:
Where: j and k can be any species (
Page 109 and 110:
The pure component dielectric const
Page 111 and 112:
2 Thermodynamic Property Models 109
Page 113 and 114:
�I *PDH = Pitzer-Debye-Hückel te
Page 115 and 116:
Where: �i Vi = Activity coefficie
Page 117 and 118:
Recommended cij Values for Differen
Page 119 and 120:
Parameter Name/ Element 2 Thermodyn
Page 121 and 122:
NRTL-SAC Reference States The NRTL-
Page 123 and 124:
Page 125 and 126:
For an anionic component, we have M
Page 127 and 128:
For a molecular segment, the activi
Page 129 and 130:
Specifically, The long range intera
Page 131 and 132:
where and are activity coefficients
Page 133 and 134:
and Y+, are used to reflect the wid
Page 135 and 136:
Parameter Name/ Element Symbol Defa
Page 137 and 138:
Reference C.-C. Chen and Y. Song, "
Page 139 and 140:
Parameter Name GMPTPS, GMPTP1, GMPT
Page 141 and 142:
zi = Charge of ion i Subscripts c,
Page 143 and 144:
For option code = 0 (default), the
Page 145 and 146:
and for n-m electrolytes: 2 Thermod
Page 147 and 148:
= 0.00979 Perform the necessary con
Page 149 and 150:
Pitzer, K.S., J.R. Peterson, and L.
Page 151 and 152:
A4,ij = gij / T + hij A5,ij = mij /
Page 153 and 154:
Symmetric and Unsymmetric Electroly
Page 155 and 156:
Parameter Symbol No. of Name Elemen
Page 157 and 158:
Reference state for ionic component
Page 159 and 160:
with 2 Thermodynamic Property Model
Page 161 and 162:
G for these pairs is calculated the
Page 163 and 164:
with 2 Thermodynamic Property Model
Page 165 and 166:
Page 167 and 168:
Activity Coefficient Basis for Henr
Page 169 and 170:
Where is the liquid Gibbs free ener
Page 171 and 172:
Ionic components 2 Thermodynamic Pr
Page 173 and 174:
the pure fused salts. Applying Eq.
Page 175 and 176:
�k is the activity coefficient of
Page 177 and 178:
References U. Weidlich and J. Gmehl
Page 179 and 180:
ti' = �ij 2 Thermodynamic Propert
Page 181 and 182:
Wagner Interaction Parameter The Wa
Page 183 and 184:
References G.M. Wilson, J. Am. Chem
Page 185 and 186:
Extended Antoine Equation Parameter
Page 187 and 188:
IK-CAPE Vapor Pressure Equation The
Page 189 and 190:
Harlacher and Braun, "A Four-Parame
Page 191 and 192:
Parameter Name/Element 2 Thermodyna
Page 193 and 194:
General Pure Component Heat of Vapo
Page 195 and 196:
IK-CAPE Heat of Vaporization Equati
Page 197 and 198:
Where: xp = Mole fraction of pseudo
Page 199 and 200:
Parameter Name/Element VLBROC/1 V i
Page 201 and 202:
Where: Vm l,t = Liquid volume per n
Page 203 and 204:
Debye-Hückel Volume The Debye-Hüc
Page 205 and 206:
DIPPR DIPPR equation 105 is the def
Page 207 and 208:
Rackett The Rackett equation is: Wh
Page 209 and 210:
Rackett/Campbell-Thodos Mixture Liq
Page 211 and 212:
Zm RA Zi *,RA Vcm 2 Thermodynamic P
Page 213 and 214:
General Pure Component Solid Molar
Page 215 and 216:
Liquid Volume Quadratic Mixing Rule
Page 217 and 218:
If THRSWT/6 is This equation is use
Page 219 and 220:
Parameter Symbol Default MDS Lower
Page 221 and 222:
General Pure Component Ideal Gas He
Page 223 and 224:
(Other DIPPR equations may sometime
Page 225 and 226:
General Pure Component Solid Heat C
Page 227 and 228:
Parameter Name/Element 2 Thermodyna
Page 229 and 230:
The expression for the liquid mole
Page 231 and 232:
� Entropy: � Heat capacity: �
Page 233 and 234:
Parameter Name † /Element CPIXPn/
Page 235 and 236:
Option Codes for Electrolyte NRTL E
Page 237 and 238:
Parameter Name Applicable Component
Page 239 and 240:
For subcritical components: Hm l -H
Page 241 and 242:
The vapor enthalpy is calculated fr
Page 243 and 244:
Where: 2 Thermodynamic Property Mod
Page 245 and 246:
Correlation algorithms for ionic sp
Page 247 and 248:
Model Model name Phase(s) Pure Mixt
Page 249 and 250:
Model Type Aspen Liquid Mixture Vis
Page 251 and 252:
(Other DIPPR equations may sometime
Page 253 and 254:
Page 255 and 256:
�i = Viscosity of component i (N-
Page 257 and 258:
Parameter Name/Element 3 Transport
Page 259 and 260:
Where: The Stockmayer or Lennard-Jo
Page 261 and 262:
Where: Vcij = �ij = 0 (in almost
Page 263 and 264:
Where: Vcij = �ij = 0 (in almost
Page 265 and 266:
Jones-Dole Electrolyte Correction T
Page 267 and 268:
Letsou-Stiel The Letsou-Stiel model
Page 269 and 270:
Where: The parameter is the mole fr
Page 271 and 272:
Reference C.H. Twu, "Internally Con
Page 273 and 274:
Vcij 3 Transport Property Models 27
Page 275 and 276:
You must provide parameters for the
Page 277 and 278:
Linear extrapolation of � *,l ver
Page 279 and 280:
If TRNSWT/4 is This equation is use
Page 281 and 282:
Page 283 and 284:
Page 285 and 286:
Page 287 and 288:
Page 289 and 290:
References R.C. Reid, J.M. Prausnit
Page 291 and 292:
The mixture surface tension is then
Page 293 and 294:
Page 295 and 296:
Where: �solv = Dielectric constan
Page 297 and 298:
4 Nonconventional Solid Property Mo
Page 299 and 300:
wij = Mass fraction of the jth cons
Page 301 and 302:
The oxygen and organic sulfur conte
Page 303 and 304:
Page 305 and 306:
The complete oxidation of carbon is
Page 307 and 308:
Page 309 and 310:
The equation for �i dm is good fo
Page 311 and 312:
5 Property Model Option Codes The f
Page 313 and 314:
Model Name Option Code 5 Property M
Page 315 and 316:
Model Name Option Code 5 Property M
Page 317 and 318:
Soave-Redlich-Kwong Option Codes Th
Page 319 and 320:
Model Name Option Code HLRELNRT and
Page 321 and 322:
Model Name Option Code GLRELNRT, GL
Page 323 and 324:
Index A activity coefficient models
Page 325 and 326:
ideal gas/DIPPR heat capacity model
Page 327 and 328:
S Sato-Riedel/DIPPR thermal conduct
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Aspen Physical Property System - Physical Property Models

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