Aspen Physical Property System - Physical Property Models

Aspen Physical
Property System
Physical Property Models

Version Number: V7.2
July 2010
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Contents
Contents..................................................................................................................1
1 Introduction .........................................................................................................5
Units for Temperature-Dependent Parameters .....................................................6
Pure Component Temperature-Dependent Properties............................................7
Extrapolation Methods .................................................................................... 10
2 Thermodynamic Property Models .......................................................................11
Equation-of-State Models ................................................................................ 15
ASME Steam Tables.............................................................................. 16
BWR-Lee-Starling................................................................................. 16
Benedict-Webb-Rubin-Starling ............................................................... 17
GERG2008 Equation of State ................................................................. 20
Hayden-O'Connell ................................................................................ 22
HF Equation-of-State ............................................................................ 25
IAPWS-95 Steam Tables ....................................................................... 29
Ideal Gas ............................................................................................ 29
Lee-Kesler........................................................................................... 29
Lee-Kesler-Plöcker ............................................................................... 31
NBS/NRC Steam Tables ........................................................................ 32
Nothnagel ........................................................................................... 33
Copolymer PC-SAFT EOS Model.............................................................. 35
Peng-Robinson..................................................................................... 47
Standard Peng-Robinson ....................................................................... 49
Peng-Robinson-MHV2 ........................................................................... 50
Predictive SRK (PSRK) .......................................................................... 51
Peng-Robinson-Wong-Sandler................................................................ 51
Redlich-Kwong..................................................................................... 51
Redlich-Kwong-Aspen ........................................................................... 52
Redlich-Kwong-Soave ........................................................................... 53
Redlich-Kwong-Soave-Boston-Mathias .................................................... 55
Redlich-Kwong-Soave-Wong-Sandler ...................................................... 56
Redlich-Kwong-Soave-MHV2.................................................................. 57
Schwartzentruber-Renon....................................................................... 57
Soave-Redlich-Kwong ........................................................................... 59
SRK-Kabadi-Danner.............................................................................. 61
SRK-ML............................................................................................... 63
VPA/IK-CAPE Equation-of-State ............................................................. 64
Peng-Robinson Alpha Functions.............................................................. 69
Huron-Vidal Mixing Rules ...................................................................... 79
MHV2 Mixing Rules ............................................................................... 81
Predictive Soave-Redlich-Kwong-Gmehling Mixing Rules ........................... 82
Contents 1

Wong-Sandler Mixing Rules ................................................................... 84
Activity Coefficient Models ............................................................................... 86
Bromley-Pitzer Activity Coefficient Model................................................. 87
Chien-Null ........................................................................................... 89
Constant Activity Coefficient .................................................................. 91
COSMO-SAC ........................................................................................ 91
Electrolyte NRTL Activity Coefficient Model (GMENRTL) ............................. 94
ENRTL-SAC ....................................................................................... 108
Hansen ............................................................................................. 112
Ideal Liquid ....................................................................................... 114
NRTL (Non-Random Two-Liquid) .......................................................... 114
NRTL-SAC Model ................................................................................ 115
Pitzer Activity Coefficient Model............................................................ 135
Polynomial Activity Coefficient ............................................................. 147
Redlich-Kister .................................................................................... 148
Scatchard-Hildebrand ......................................................................... 149
Three-Suffix Margules......................................................................... 150
Symmetric and Unsymmetric Electrolyte NRTL Activity Coefficient Model... 151
UNIFAC Activity Coefficient Model......................................................... 172
UNIFAC (Dortmund Modified)............................................................... 174
UNIFAC (Lyngby Modified)................................................................... 175
UNIQUAC Activity Coefficient Model ...................................................... 176
Van Laar Activity Coefficient Model ....................................................... 178
Wagner Interaction Parameter ............................................................. 179
Wilson Activity Coefficient Model .......................................................... 179
Wilson Model with Liquid Molar Volume ................................................. 181
Vapor Pressure and Liquid Fugacity Models...................................................... 182
General Pure Component Liquid Vapor Pressure ..................................... 182
API Sour Model .................................................................................. 187
Braun K-10 Model .............................................................................. 187
Chao-Seader Pure Component Liquid Fugacity Model .............................. 188
Grayson-Streed Pure Component Liquid Fugacity Model .......................... 188
Kent-Eisenberg Liquid Fugacity Model ................................................... 189
Maxwell-Bonnell Vapor Pressure Model.................................................. 190
Solid Antoine Vapor Pressure Model...................................................... 190
General Pure Component Heat of Vaporization ................................................. 191
DIPPR Heat of Vaporization Equation .................................................... 191
Watson Heat of Vaporization Equation .................................................. 191
PPDS Heat of Vaporization Equation ..................................................... 192
IK-CAPE Heat of Vaporization Equation ................................................. 193
NIST TDE Watson Heat of Vaporization Equation .................................... 193
Clausius-Clapeyron Equation ............................................................... 194
Molar Volume and Density Models .................................................................. 194
API Liquid Molar Volume ..................................................................... 194
Brelvi-O'Connell ................................................................................. 196
Clarke Aqueous Electrolyte Volume....................................................... 197
COSTALD Liquid Volume ..................................................................... 199
Debye-Hückel Volume......................................................................... 201
Liquid Constant Molar Volume Model..................................................... 202
General Pure Component Liquid Molar Volume ....................................... 202
Rackett/Campbell-Thodos Mixture Liquid Volume ................................... 207
Modified Rackett Liquid Molar Volume ................................................... 208
Rackett Extrapolation Method .............................................................. 209
2 Contents

General Pure Component Solid Molar Volume......................................... 211
Liquid Volume Quadratic Mixing Rule .................................................... 213
Heat Capacity Models ................................................................................... 213
Aqueous Infinite Dilution Heat Capacity................................................. 213
Criss-Cobble Aqueous Infinite Dilution Ionic Heat Capacity ...................... 214
General Pure Component Liquid Heat Capacity....................................... 214
General Pure Component Ideal Gas Heat Capacity.................................. 219
General Pure Component Solid Heat Capacity ........................................ 223
Solubility Correlations................................................................................... 225
Henry's Constant................................................................................ 225
Water Solubility ................................................................................. 226
Hydrocarbon Solubility........................................................................ 227
Other Thermodynamic Property Models........................................................... 228
Cavett .............................................................................................. 228
Barin Equations for Gibbs Energy, Enthalpy, Entropy, and Heat Capacity... 228
Electrolyte NRTL Enthalpy Model (HMXENRTL) ....................................... 231
Electrolyte NRTL Gibbs Free Energy Model (GMXENRTL) .......................... 233
Liquid Enthalpy from Liquid Heat Capacity Correlation............................. 235
Enthalpies Based on Different Reference States ..................................... 236
Helgeson Equations of State ................................................................ 240
Quadratic Mixing Rule ......................................................................... 243
3 Transport Property Models ...............................................................................244
Viscosity Models........................................................................................... 246
Andrade Liquid Mixture Viscosity .......................................................... 247
General Pure Component Liquid Viscosity .............................................. 248
API Liquid Viscosity ............................................................................ 251
API 1997 Liquid Viscosity .................................................................... 251
Aspen Liquid Mixture Viscosity ............................................................. 252
ASTM Liquid Mixture Viscosity.............................................................. 252
General Pure Component Vapor Viscosity .............................................. 253
Chapman-Enskog-Brokaw-Wilke Mixing Rule ......................................... 256
Chung-Lee-Starling Low-Pressure Vapor Viscosity .................................. 258
Chung-Lee-Starling Viscosity ............................................................... 260
Dean-Stiel Pressure Correction ............................................................ 262
IAPS Viscosity for Water...................................................................... 262
Jones-Dole Electrolyte Correction ......................................................... 263
Letsou-Stiel ....................................................................................... 265
Lucas Vapor Viscosity ......................................................................... 265
TRAPP Viscosity Model ........................................................................ 266
Twu Liquid Viscosity ........................................................................... 267
Viscosity Quadratic Mixing Rule............................................................ 269
Thermal Conductivity Models ......................................................................... 269
Chung-Lee-Starling Thermal Conductivity.............................................. 270
IAPS Thermal Conductivity for Water .................................................... 271
Li Mixing Rule .................................................................................... 272
Riedel Electrolyte Correction ................................................................ 272
General Pure Component Liquid Thermal Conductivity ............................ 273
Solid Thermal Conductivity Polynomial.................................................. 276
General Pure Component Vapor Thermal Conductivity............................. 276
Stiel-Thodos Pressure Correction Model................................................. 279
Vredeveld Mixing Rule......................................................................... 279
Contents 3

TRAPP Thermal Conductivity Model....................................................... 280
Wassiljewa-Mason-Saxena Mixing Rule ................................................. 281
Diffusivity Models ......................................................................................... 281
Chapman-Enskog-Wilke-Lee (Binary).................................................... 282
Chapman-Enskog-Wilke-Lee (Mixture) .................................................. 283
Dawson-Khoury-Kobayashi (Binary) ..................................................... 283
Dawson-Khoury-Kobayashi (Mixture).................................................... 284
Nernst-Hartley ................................................................................... 285
Wilke-Chang (Binary) ......................................................................... 286
Wilke-Chang (Mixture) ........................................................................ 287
Surface Tension Models................................................................................. 287
Liquid Mixture Surface Tension ............................................................ 288
API Surface Tension ........................................................................... 288
IAPS Surface Tension for Water ........................................................... 289
General Pure Component Liquid Surface Tension .................................... 289
Onsager-Samaras .............................................................................. 292
Modified MacLeod-Sugden ................................................................... 293
4 Nonconventional Solid Property Models ...........................................................295
General Enthalpy and Density Models ............................................................. 295
General Density Polynomial ................................................................. 295
General Heat Capacity Polynomial ........................................................ 296
Enthalpy and Density Models for Coal and Char................................................ 297
General Coal Enthalpy Model ............................................................... 300
IGT Coal Density Model....................................................................... 306
IGT Char Density Model ...................................................................... 307
5 Property Model Option Codes ...........................................................................309
Option Codes for Transport Property Models .................................................... 309
Option Codes for Activity Coefficient Models .................................................... 310
Option Codes for Equation of State Models ...................................................... 312
Soave-Redlich-Kwong Option Codes ............................................................... 315
Option Codes for K-Value Models.................................................................... 316
Option Codes for Enthalpy Models .................................................................. 316
Option Codes for Gibbs Free Energy Models..................................................... 318
Option Codes for Liquid Volume Models........................................................... 320
Index ..................................................................................................................321
4 Contents

1 Introduction
This manual describes the property models available in the Aspen Physical
Property System and defines the parameters used in each model. The
description for each model lists the parameter names used to enter values on
the Properties Parameters forms.
This manual also lists the pure component temperature-dependent properties
that the Aspen Physical Property System can calculate from a model that
supports several equations or submodels. See Pure Component Temperature-
Dependent Properties (below).
Many parameters have default values indicated in the Default column. A dash
(–) indicates that the parameter has no default value and you must provide a
value. If a parameter is missing, calculations stop. The lower limit and upper
limit for each parameter, when available, indicate the reasonable bounds for
the parameter. The limits are used to detect grossly erroneous parameter
values.
The property models are divided into the following categories:
� Thermodynamic property models
� Transport property models
� Nonconventional solid property models
The property types for each category are discussed in separate sections. The
following table (below) provides an organizational overview of this manual.
The tables labeled Thermodynamic Property Models, Transport Property
Models, and Nonconventional Solid Property Models present detailed lists of
models. These tables also list the Aspen Physical Property System model
names, and their possible use in different phase types, for pure components
and mixtures.
Electrolyte and conventional solid property models are presented in
Thermodynamic Property Models.
1 Introduction 5

Categories of Models
Category Sections
Thermodynamic
Property Models
Transport Property
Models
Nonconventional Solid
Property Models
6 1 Introduction
Equation-of-State Models
Activity Coefficient Models (Including Electrolyte Models)
Vapor Pressure and Liquid Fugacity Models
Heat of Vaporization Models
Molar Volume and Density Models
Heat Capacity Models
Solubility Correlations
Other
Viscosity Models
Thermal Conductivity Models
Diffusivity Models
Surface Tension Models
General Enthalpy and Density Models
Enthalpy and Density Models for Coal and Char
Units for Temperature-
Dependent Parameters
Some temperature-dependent parameters may be based on expressions
which involve logarithmic or reciprocal temperature terms. When the
coefficient of any such term is non-zero, in many cases the entire expression
must be calculated assuming that all the coefficients are in absolute
temperature units. In other cases, terms are independent from one another,
and only certain terms may require calculation using absolute temperature
units. Notes in the models containing such terms explain exactly which
coefficients are affected by this treatment.
When absolute temperature units are forced in this way, this affects the units
for coefficients you have entered as input parameters. If your input
temperature units are Fahrenheit (F), then Rankine (R) is used instead. If
your input units are Celsius (C), then Kelvin (K) is used instead.
If only constant and positive powers of temperature are present in the
expression, then your specified input units are used.
If the parameters include temperature limits, the limits are always interpreted
in user input units even if the expression is forced to absolute units.
Some equations may include a dimensionless parameter, the reduced
temperature Tr = T / Tc. This reduced temperature is calculated using
absolute temperature units. In most cases, input parameters associated with
such equations do not have temperature units.

Pure Component Temperature-
Dependent Properties
The following table lists the pure component temperature-dependent
properties that the Aspen Physical Property System can calculate from a
general model that supports several equations or submodels.
For example, the Aspen Physical Property System can calculate heat of
vaporization using these equations:
� Watson
� DIPPR
� PPDS
� IK-CAPE
� NIST TDE Watson
Pure Component Temperature-Dependent Properties
Property
1 Introduction 7
Submodel-
Selection
Parameter
Element
Number Available Submodels
Solid Volume THRSWT/1 Aspen, DIPPR, IK-CAPE, NIST 100
Liquid Volume THRSWT/2 Aspen (Rackett), DIPPR, PPDS, IK-
CAPE, NIST
Liquid Vapor
Pressure
Heat of
Vaporization
Solid Heat
Capacity
Liquid Heat
Capacity
Ideal Gas Heat
Capacity
Second Virial
Coefficient
THRSWT/3 Aspen (Extended Antoine),
Wagner, BARIN, PPDS, PML, IK-
CAPE, NIST
THRSWT/4 Aspen (Watson), DIPPR, PPDS, IK-
CAPE, NIST
THRSWT/5 Aspen, DIPPR, BARIN, IK-CAPE,
NIST
THRSWT/6 DIPPR, PPDS, BARIN, IK-CAPE,
NIST
THRSWT/7 Aspen, DIPPR, BARIN, PPDS, IK-
CAPE, NIST
DIPPR Equation
Numbers
(† = default)
105 † , 116 for water
only
101
106
THRSWT/8 DIPPR 104
Liquid Viscosity TRNSWT/1 Aspen (Andrade), DIPPR, PPDS,
IK-CAPE, NIST
Vapor Viscosity TRNSWT/2 Aspen (Chapman-Enskog-Brokaw), 102
DIPPR, PPDS, IK-CAPE, NIST
Liquid Thermal
Conductivity
Vapor Thermal
Conductivity
Liquid Surface
Tension
TRNSWT/3 Aspen (Sato-Riedel), DIPPR, PPDS, 100
IK-CAPE, NIST
TRNSWT/4 Aspen (Stiel-Thodos), DIPPR,
PPDS, IK-CAPE, NIST
TRNSWT/5 Aspen (Hakim-Steinberg-Stiel),
DIPPR, PPDS, IK-CAPE, NIST
100 † , 102
100 † , 114
107, 127 †
101 † , 115
102
106

Which equation is actually used to calculate the property for a given
component depends on which parameters are available. If parameters are
available for more than one equation, the Aspen Physical Property System
uses the parameters that were entered or retrieved first from the databanks.
The selection of submodels is driven by the data hierarchy, and controlled by
the submodel-selection parameters.
The thermodynamic properties use the THRSWT (thermo switch) submodelselection
parameter, and the transport properties use the TRNSWT (transport
switch) submodel-selection parameter.
As the previous table shows, a property is associated with an element of the
submodel-selection parameter. For example, THRSWT element 1 controls the
submodel for solid volume.
The following table shows the values for THRSWT or TRNSWT, and the
corresponding submodels.
Parameter Values
(Equation Number) Submodel
0 Aspen
1 to 127 DIPPR
200 to 211 BARIN
301 to 302 PPDS or property-specific methods
400 PML
401 to 404 IK-CAPE
501 to 515 NIST
All built-in databank components have model-selection parameters (THRSWT,
TRNSWT) that are set to use the correct equations that are consistent with
the available parameters. For example, suppose that parameters for the
DIPPR equation 106 are available for liquid surface tension. For that
component, TRNSWT element 5 is set to 106 in the databank. If you are
retrieving data from an in-house or user databank, you should store the
appropriate values for THRSWT and TRNSWT in the databank, using the
appropriate equation number. Otherwise, the Aspen Physical Property System
will search for the parameters needed for the Aspen form of the equations.
If a component is available in more than one databank, the Aspen Physical
Property System uses the data and equations based on the databank list
order on the Components Specifications Selection sheet. For example,
suppose the databank search order is ASPENPCD, then PURE10, and that the
Aspen Physical Property System cannot find the parameters for a particular
submodel (equation) in the ASPENPCD databank. If the PURE10 databank
contains parameters for another equation, the Aspen Physical Property
System will use that equation (most likely the DIPPR equation) to calculate
the property for that component.
If your calculation contains any temperature-dependent property parameters,
(such as CPIGDP for DIPPR ideal gas heat capacity, entered on the Properties
Parameters Pure Component form), the Aspen Physical Property System sets
the corresponding THRSWT and TRNSWT elements for that component to the
default values shown in the table above. This default setting might not always
be correct. If you know the equation number, you should enter it directly on
8 1 Introduction

the Properties Parameters Pure-Components form. For example, suppose you
want to use the:
� DIPPR equation form of heat of vaporization (DHVLDP) for a component
� Aspen equations for the remaining temperature dependent properties
Set the fourth element of the THRSWT parameter to 106, and the 1-3 and 5-8
elements to 0. If you want to set the other temperature-dependent properties
to use what is defined for that component in the databank, leave the element
blank.
The following table lists the available DIPPR equations and the corresponding
equation (submodel) number.
Available DIPPR Equations
Equation
Number Equation Form
100
101
102
103
104
105
106
107
114
115
116
127
For equations 114 and 116, t = 1-Tr.
Note: Reduced temperature Tr is always calculated using absolute
temperature units.
The following sections describe the Aspen, DIPPR, BARIN, IK-CAPE, PPDS, and
NIST equations for each property. For descriptions of the the BARIN equations
for heat capacity and enthalpy, see BARIN Equations for Gibbs Energy,
Enthalpy, Entropy, and Heat Capacity.
1 Introduction 9

Extrapolation Methods
Many temperature dependent property models have upper and lower
temperature limits. The Aspen Physical Property System usually extrapolates
linearly beyond such limits. It calculates the slope of the property-versustemperature
curve, or the ln(property)-versus-temperature curve for models
expressed in logarithmic form, at the upper or lower temperature limit. For
temperatures beyond the limit, it uses a linear model with this slope which
meets the curve from the equation at the temperature limit. Thus the model
is:
For T beyond the upper or lower limit, where Tlim is that limit and Z is the
property or ln(property) as appropriate. Some liquid molar volume models are
actually molar density models which then return the reciprocal of the density
as the liquid molar volume. In these models, the extrapolation occurs for the
density calculation.
There are certain exceptions, detailed below.
Exception 1: Logarithmic Properties Based on Reciprocal
Temperature
This applies to property models expressed in the form (where a(T) includes
any additional dependency on temperature):
For these models, the extrapolation maintains the slope of ln(property) versus
1/T. This applies to the Extended Antoine vapor pressure equation and the
Andrade and DIPPR liquid viscosity equations. Note that the equation for
Henry's Constant is extrapolated by ln(Henry) versus T.
Exception 2: Aspen Ideal Gas Heat Capacity
The Aspen Ideal Gas Heat Capacity model has an explicit equation for
extrapolation at temperatures below the lower limit, which is described in the
model. At high temperatures it follows the usual rule of extrapolating
property-versus-temperature linearly.
Exception 3: No Extrapolation
The equations for certain models are used directly at all temperatures, so that
no extrapolation is performed. These models are the Wagner vapor pressure
equation, the Aly and Lee equation for the DIPPR Ideal Gas Heat Capacity
(using the CPIGDP parameter), and the Water Solubility and Hydrocarbon
Solubility models. The equations for temperature-dependent binary
interaction parameters are also used directly at all temperatures with no
extrapolation.
10 1 Introduction

2 Thermodynamic Property
Models
This section describes the available thermodynamic property models in the
Aspen Physical Property System. The following table provides a list of
available models, with corresponding Aspen Physical Property System model
names. The table provides phase types for which the model can be used and
information on use of the model for pure components and mixtures.
Aspen Physical Property System thermodynamic property models include
classical thermodynamic property models, such as activity coefficient models
and equations of state, as well as solids and electrolyte models. The models
are grouped according to the type of property they describe.
Thermodynamic Property Models
Phases: V = Vapor; L = Liquid; S = Solid. An X indicates applicable to Pure or
Mixture.
Equation-of-State Models
A pure component equation of state model calculates PHIL, PHIV, DHL, DHV,
DGL, DGV, DSL, DSV, VL, and VV. Most mixture equation of state models
calculate PHILMX, PHIVMX, DHLMX, DHVMX, DGLMX, DGVMX, DSLMX,
DSVMX, VLMX, and VVMX. Those marked with * only calculate DHLMX,
DHVMX, DGLMX, DGVMX, DSLMX, DSVMX, VLMX, and VVMX. The alpha
functions and mixing rules are options available in some of the models.
Property Model Model Name(s) Phase(s)Pure Mixture
ASME Steam Tables ESH2O0,ESH2O V L X —
BWR-Lee-Starling ESBWR0, ESCSTBWR V L X X
Benedict-Webb-Rubin-Starling ESBWRS, ESBWRS0 V L X X
Hayden-O'Connell ESHOC0,ESHOC V X X
HF equation-of-state ESHF0, ESHF V X X
Ideal Gas ESIG0, ESIG V X X
Lee-Kesler * ESLK V L — X
Lee-Kesler-Plöcker ESLKP0,ESLKP V L X X
NBS/NRC Steam Tables ESSTEAM0,ESSTEAM V L X —
2 Thermodynamic Property Models 11

Property Model Model Name(s) Phase(s)Pure Mixture
Nothnagel ESNTH0,ESNTH V X X
PC-SAFT ESPSAFT, ESPSAFT0 V L X X
Peng-Robinson ESPR0, ESPR V L X X
Standard Peng-Robinson ESPRSTD0,ESPRSTD V L X X
Peng-Robinson-Wong-Sandler * ESPRWS0,ESPRWS V L X X
Peng-Robinson-MHV2 * ESPRV20,ESPRV2 V L X X
Predictive SRK * ESRKSV10, ESRKSV1 V L X X
Redlich-Kwong ESRK0, ESRK V X X
Redlich-Kwong-Aspen ESRKA0,ESRKA V L X X
Redlich-Kwong-Soave ESRKSTD0,ESRKSTD V L X X
Redlich-Kwong-Soave-Boston-
Mathias
12 2 Thermodynamic Property Models
ESRKS0, ESRKS V L X X
Redlich-Kwong-Soave-MHV2 * ESRKSV20, ESRKSV2 V L X X
Redlich-Kwong-Soave-Wong-
Sandler *
ESRKSWS0, ESRKSWS V L X X
Schwartzentruber-Renon ESRKU0,ESRKU V L X X
Soave-Redlich-Kwong ESSRK0, ESSRK V L X X
SRK-Kabadi-Danner ESSRK0, ESSRK V L X X
SRK-ML ESRKSML0, ESRKSML V L X X
VPA/IK-CAPE equation-of-state ESVPA0, ESVPA V X X
Peng-Robinson Alpha functions — V L X —
RK-Soave Alpha functions — V L X —
Huron-Vidal mixing rules — V L — X
MHV2 mixing rules — V L — X
PSRK mixing rules — V L — X
Wong-Sandler mixing rules — V L — X
Activity Coefficient Models (Including Electrolyte Models)
These models calculate GAMMA.
Property Model Model Name Phase(s)Pure Mixture
Bromley-Pitzer GMPT2 L — X
Chien-Null GMCHNULL L — X
Constant Activity Coefficient GMCONS S — X
COSMO-SAC COSMOSAC L — X
Electrolyte NRTL GMENRTL, GMELC,
GMENRHG
L L1 L2 — X
ENRTL-SAC (patent pending) ENRTLSAC L — X
Hansen HANSEN L — X
Ideal Liquid GMIDL L — X
NRTL (Non-Random-Two-Liquid) GMRENON L L1 L2 — X
NRTL-SAC (patent pending) NRTLSAC L — X
Pitzer GMPT1 L — X
Polynomial Activity Coefficient GMPOLY L S — X

Property Model Model Name Phase(s)Pure Mixture
Redlich-Kister GMREDKIS L S — X
Scatchard-Hildebrand GMXSH L — X
Symmetric Electrolyte NRTL GMENRTLS L — X
Three-Suffix Margules GMMARGUL L S — X
UNIFAC GMUFAC L L1 L2 — X
UNIFAC (Lyngby modified) GMUFLBY L L1 L2 — X
UNIFAC (Dortmund modified) GMUFDMD L L1 L2 — X
UNIQUAC GMUQUAC L L1 L2 — X
Unsymmetric Electrolyte NRTL GMENRTLQ L — X
van Laar GMVLAAR L — X
Wagner interaction parameter GMWIP S — X
Wilson GMWILSON L — X
Wilson model with liquid molar
volume
2 Thermodynamic Property Models 13
GMWSNVOL L — X
Vapor Pressure and Liquid Fugacity Models
Property Model Model
Name
General Pure Component Liquid
Vapor Pressure
Property Phase(s)Pure Mixture
PL0XANT PL L L1 L2 X —
API Sour SWEQ PHILMX L — X
Braun K-10 BK10 PHILMX L — X
Chao-Seader PHL0CS PHIL L X —
Grayson-Streed PHL0GS PHIL L X —
Kent-Eisenberg ESAMINE PHILMX,
GLMX,
HLMX,
SLMX
L — X
Maxwell-Bonnell PL0MXBN PL L L1 L2 X —
Solid Antoine PS0ANT PS S X —
Heat of Vaporization Models
These models calculate DHVL.
Property Model Model Name Phase(s)Pure Mixture
General Pure Component Heat
of Vaporization
DHVLWTSN L X —
Clausius-Clapeyron Equation DHVLCC L X —
Molar Volume and Density Models
These models calculate VL (pure liquid), VLMX (liquid mixture), or VS (pure
solid), except for Brelvi-O'Connell which calculates VLPM.
Property Model Model Name Phase(s)Pure Mixture
API Liquid Volume VL2API L — X
Brelvi-O'Connell VL1BROC L — X

Property Model Model Name Phase(s)Pure Mixture
Clarke Aqueous Electrolyte
Volume
14 2 Thermodynamic Property Models
VAQCLK L — X
COSTALD Liquid Volume VL0CTD,VL2CTD L X X
Debye-Hückel Volume VAQDH L — X
Liquid Constant Molar Volume VL0CONS L X —
General Pure Component Liquid
Molar Volume
Rackett/Campbell-Thodos
Mixture Liquid Volume
VL0RKT,VL2RKT L X —
VL2RKT L X X
Modified Rackett VL2MRK L X X
General Pure Component Solid
Molar Volume
Liquid Volume Quadratic Mixing
Rule
Heat Capacity Models
Property Model Model
Name
Aqueous Infinite Dilution Heat
Capacity Polynomial
Criss-Cobble Aqueous Infinite
Dilution Ionic Heat Capacity
General Pure Component Liquid
Heat Capacity
General Pure Component Ideal
Gas Heat Capacity
General Pure Component Solid
Heat Capacity
Solubility Correlation Models
Property Model Model
Name
Henry's constant HENRY1 HNRY,
WHNRY
VS0POLY S X —
VL2QUAD L — X
Property Phase(s)Pure Mixture
— — L — X
— — L — X
HL0DIP HL, DHL L X —
— CPIG V X X
HS0POLY HS S X —
Property Phase(s)Pure Mixture
L — X
Water solubility — — L — X
Hydrocarbon solubility — — L — X
Other Models
Property Model Model
Name
Cavett Liquid Enthalpy DepartureDHL0CVT,
DHL2CVT
BARIN Equations for Gibbs
Energy, Enthalpy, Entropy and
Heat Capacity
Property Phase(s)Pure Mixture
DHL,
DHLMX
L X X
— — S L V X —
Bromley-Pitzer Enthalpy HAQPT2 HLMX L — X
Bromley-Pitzer Gibbs Energy GAQPT2 GLMX L — X

Property Model Model
Name
2 Thermodynamic Property Models 15
Property Phase(s)Pure Mixture
Electrolyte NRTL Enthalpy HMXENRTL, HLMX
HAQELC,
HMXELC,
HMXENRHG
L — X
Electrolyte NRTL Gibbs Energy GMXENRTL, HLMX
GAQELC,
GMXELC,
GMXENRHG
L — X
Liquid Enthalpy from Liquid Heat
Capacity Correlation
Enthalpies Based on Different
Reference States
DHL0DIP L X X
DHL0HREF DHL L V X X
Helgeson Equations of State — — L — X
Pitzer Enthalpy HAQPT1 HLMX L — X
Pitzer Gibbs Energy GAQPT1 GLMX L — X
Quadratic Mixing Rule — — L V — X
Equation-of-State Models
The Aspen Physical Property System has the following built-in equation-ofstate
property models. This section describes the equation-of-state property
models available.
Model Type
ASME Steam Tables Fundamental
BWR-Lee-Starling Virial
Benedict-Webb-Rubin-Starling Virial
Hayden-O'Connell Virial and association
HF Equation-of-State Ideal and association
Huron-Vidal mixing rules Mixing rules
Ideal Gas Ideal
Lee-Kesler Virial
Lee-Kesler-Plöcker Virial
MHV2 mixing rules Mixing rules
NBS/NRC Steam Tables Fundamental
Nothnagel Ideal
PC-SAFT Association
Peng-Robinson Cubic
Standard Peng-Robinson Cubic
Peng-Robinson Alpha functions Alpha functions
Peng-Robinson-MHV2 Cubic
Peng-Robinson-Wong-Sandler Cubic
Predictive SRK Cubic
PSRK mixing rules Mixing rules
Redlich-Kwong Cubic

Model Type
Redlich-Kwong-Aspen Cubic
Standard Redlich-Kwong-Soave Cubic
Redlich-Kwong-Soave-Boston-Mathias Cubic
Redlich-Kwong-Soave-MHV2 Cubic
Redlich-Kwong-Soave-Wong-Sandler Cubic
RK-Soave Alpha functions Alpha functions
Schwartzentruber-Renon Cubic
Soave-Redlich-Kwong Cubic
SRK-Kabadi-Danner Cubic
SRK-ML Cubic
VPA/IK-CAPE equation-of-state Ideal and association
Wong-Sandler mixing rules Mixing rules
ASME Steam Tables
The ASME steam tables are implemented like any other equation-of-state in
the Aspen Physical Property System. The steam tables can calculate any
thermodynamic property of water or steam and form the basis of the STEAM-
TA property method. There are no parameter requirements. The ASME steam
tables are less accurate than the NBS/NRC steam tables.
References
ASME Steam Tables, Thermodynamic and Transport Properties of Steam,
(1967).
K. V. Moore, Aerojet Nuclear Company, prepared for the U.S. Atomic Energy
Commision, ASTEM - A Collection of FORTRAN Subroutines to Evaluate the
1967 ASME equations of state for water/steam and derivatives of these
equations.
BWR-Lee-Starling
The Benedict-Webb-Rubin-Lee-Starling equation-of-state is the basis of the
BWR-LS property method. It is a generalization by Lee and Starling of the
virial equation-of-state for pure fluids by Benedict, Webb and Rubin. The
equation is used for non-polar components, and can manage hydrogencontaining
systems.
General Form:
Where:
Mixing Rules:
16 2 Thermodynamic Property Models

Where:
Parameter
Name/Element
2 Thermodynamic Property Models 17
Symbol Default MDS Lower
Limit
Upper
Limit
Units
TCBWR T ci TC X 5.0 2000.0 TEMPERATURE
VCBWR V ci *
BWRGMA � i
BWRKV � ij
BWRKT � ij
VC X 0.001 3.5 MOLE-
VOLUME
OMEGA X -0.5 3.0 —
0 X -5.0 1.0 —
0 X -5.0 1.0 —
Binary interaction parameters BWRKV and BWRKT are available in the Aspen
Physical Property System for a large number of components from Brulé et al.
(1982) and from Watanasiri et al. (1982). (See Physical Property Data,
Chapter 1).
References
M.R. Brulé, C.T. Lin, L.L. Lee, and K.E. Starling, AIChE J., Vol. 28, (1982) p.
616.
Brulé et al., Chem. Eng., (Nov., 1979) p. 155.
Watanasiri et al., AIChE J., Vol. 28, (1982) p. 626.
Benedict-Webb-Rubin-Starling
The Benedict-Webb-Rubin-Starling equation-of-state is the basis of the BWRS
property method. It is a modification by Han and Starling of the virial
equation-of-state for pure fluids by Benedict, Webb and Rubin. This equationof-state
can be used for hydrocarbon systems that include the common light
gases, such as H2S, CO2 and N2.
The form of the equation-of-state is:

Where:
kij = kji
In the mixing rules given above, A0i, B0i, C0i, D0i, E0i, ai, bi, ci, di, �i, �i are pure
component constants which can be input by the user. For methane, ethane,
propane, iso-butane, n-butane, iso-pentane, n-pentane, n-hexane, nheptane,
n-octane, ethylene, propylene, nitrogen, carbon dioxide, and
hydrogen sulfide, values of the parameters in the table below are available in
the EOS-LIT databank in the Aspen Properties Enterprise Database.
If the values of these parameters are not given, and not available from the
databank, the Aspen Physical Property System will calculate them using the
18 2 Thermodynamic Property Models

critical temperature, the critical volume (or critical density), the acentric
factor and generalized correlations given by Han and Starling.
When water is present, by default Benedict-Webb-Rubin-Starling uses the
steam table to calculate the enthalpy, entropy, Gibbs energy, and molar
volume of water. The total properties are mole-fraction averages of these
values with the properties calculated by the equation of state for other
components. Fugacity coefficient is not affected. An option code can disable
this use of the steam table.
For best results, the binary parameter kij must be regressed using phaseequilibrium
data such as VLE data.
Parameter SymbolDefault MDS Lower Upper Units
Name/
Element
Limit Limit
BWRSTC T ci TC x 5.0 2000.0 TEMPERATURE
BWRSVC V ci VC x 0.001 3.5 MOLE-VOLUME
BWRSOM � i OMEGA x –0.5 2.0 –
BWRSA/1 B 0i fcn(� i ,V ci , T ci) x – – MOLE-VOLUME
BWRSA/2 A 0i fcn(� i ,V ci , T ci) x – – PRESSURE * MOLE-
VOL^2
BWRSA/3 C 0i fcn(� i ,V ci , T ci) x – – PRESSURE *
TEMPERATURE^2 *
MOLE-VOLUME^2
BWRSA/4 � i
2 Thermodynamic Property Models 19
fcn(� i ,V ci , T ci) x – – MOLE-VOLUME^2
BWRSA/5 b i fcn(� i ,V ci , T ci) x – – MOLE-VOLUME^2
BWRSA/6 a i fcn(� i ,V ci , T ci) x – – PRESSURE * MOLE-
VOL^3
BWRSA/7 � i fcn(� i ,V ci , T ci) x – – MOLE-VOLUME^3
BWRSA/8 c i fcn(� i ,V ci , T ci) x – – PRESSURE *
TEMPERATURE^2 *
MOLE-VOLUME^3
BWRSA/9 D 0i fcn(� i ,V ci , T ci) x – – PRESSURE *
TEMPERATURE^3 *
MOLE-VOLUME^2
BWRSA/10 d i fcn(� i ,V ci , T ci) x – – PRESSURE *
TEMPERATURE * MOLE-
VOLUME^3
BWRSA/11 E 0i fcn(� i ,V ci , T ci) x – – PRESSURE *
TEMPERATURE^4 *
MOLE-VOLUME^2
BWRAIJ k ij – x – – –
Constants Used with the correlations of Han and Starling
Parameter Methane Ethane Propane n-Butane
B 0i 0.723251 0.826059 0.964762 1.56588
A 0i 7520.29 13439.30 18634.70 32544.70
C 0i
2.71092x10 8
2.95195x10 9
7.96178x10 9
1.37436x10 10
D 0i 1.07737x10 10 2.57477x10 11 4.53708x10 11 3.33159x10 11
E 0i 3.01122x10 10 1.46819x10 13 2.56053x10 13 2.30902x10 12

Parameter Methane Ethane Propane n-Butane
b i 0.925404 3.112060 5.462480 9.140660
a i 2574.89 22404.50 40066.40 71181.80
d i 47489.1 702189.0 1.50520x10 7
20 2 Thermodynamic Property Models
3.64238x10 7
� i 0.468828 0.909681 2.014020 4.009850
c i
� i
4.37222x10 8
6.81826x10 9
2.74461x10 10 7.00044x10 10
1.48640 2.99656 4.56182 7.54122
Parameter n-Pentane n-Hexane n-Heptane n-Octane
B 0i 2.44417 2.66233 3.60493 4.86965
A 0i 51108.20 45333.10 77826.90 81690.60
C 0i 2.23931x10 10 5.26067x10 10 6.15662x10 10 9.96546x10 10
D 0i 1.01769x10 12 5.52158x10 12 7.77123x10 12 7.90575x10 12
E 0i 3.90860x10 13 6.26433x10 14 6.36251x10 12 3.46419x10 13
b i 16.607000 29.498300 27.441500 10.590700
a i 162185.00 434517.00 359087.00 131646.00
d i
3.88521x10 7
3.27460x10 7
8351150.0 1.85906x10 8
� i 7.067020 9.702300 21.878200 34.512400
c i 1.35286x10 11 3.18412x10 11 3.74876x10 11 6.42053x10 11
� i
References
11.85930 14.87200 24.76040 21.98880
M. Benedict, G. B. Webb, and L. C. Rubin, J. Chem. Phys., Vol. 8, (1940), p.
334.
M. S. Han, and K. E. Starling, "Thermo Data Refined for LPG. Part 14:
Mixtures", Hydrocarbon Processing, Vol. 51, No. 5, (1972), p. 129.
K. E. Starling, "Fluid Themodynamic Properties for Light Petroleum Systems",
Gulf Publishing Co., Houston, Texas (1973).
References for Parameter Data
K.E. Starling and M.S. Han, "Thermo data refined for LPG, part 14 Mixtures,"
Hydrocarbon Processing, (May 1972), pp. 129-132.
K.E. Starling and M.S. Han, "Thermo data refined for LPG, part 15 Industrial
applications," Hydrocarbon Processing, (June 1972), pp. 107-115.
K.E. Starling, "Fluid Thermodynamic Properties for Light Petroleum Systems,"
Gulf Publishing Co., Houston, Texas (1973).
GERG2008 Equation of State
The GERG2008 equation-of-state model is the basis for the GERG2008
property method.
The equation of state is based on a multi-fluid approximation explicit in the
reduced Helmholtz free energy:

Where the ideal-gas contribution � o and residual contribution � r at a given
mixture density, temperature, and molar composition are:
Where the reduced mixture density � and inverse reduced mixture
temperature � are:
In eq. (2), the ideal-gas contribution of the reduced Helmholtz free energy for
component i is given by:
In eq. (3), the pure substance contribution to the residual part of the reduced
Helmholtz free energy for component i is given by:
In eq. (3), the mixture contribution to the residual part of the reduced
Helmholtz free energy is given by:
The reduced mixture density is given by:
And the reduced mixture temperature is given by:
2 Thermodynamic Property Models 21
(1)
(2)
(3)
(4)
(6)
(5)
(8)
(7)

Where:
R = molar gas constant = 8.314472 J/mol-K.
�c,i and Tc,i = critical density and critical temperature
n o oi,k and � o oi,k = Coefficients and parameters of eq. (5) for pure components
noi,k, doi,k, toi,k, and coi,k = coefficients and exponents of eq. (6) for pure
components
Fij = Composition dependent factor
nij,k = Coefficients and dij,k, tij,k, �ij,k, �ij,k, �ij,k, and �ij,k = the exponents in eq.
(7) for all binary specific and generalized departure functions
�v,ij and �v,ij in eq. (8) and �T,ij and �T,ij in eq. (9) = Binary interaction
parameters
Reference
"The GERG-2004 Wide-Range Equation of State for Natural Gases and Other
Mixtures" O. Kunz, R. Klimeck, W. Wagner, M. Jaeschke; GERG TM15 2007;
ISBN 978-3-18-355706-6; Published for GERG and printed in Germany by
VDI Verlag GmbH (2007).
Kunz, O., Wagner, W., "The new GERG-2004 XT08 wide-range equation of
state for natural gases and other mixtures." To be submitted to Fluid Phase
Equilibria (beginning of 2010).
Hayden-O'Connell
The Hayden-O'Connell equation-of-state calculates thermodynamic properties
for the vapor phase. It is used in property methods NRTL-HOC, UNIF-HOC,
UNIQ-HOC, VANL-HOC, and WILS-HOC, and is recommended for nonpolar,
polar, and associating compounds. Hayden-O'Connell incorporates the
chemical theory of dimerization. This model accounts for strong association
and solvation effects, including those found in systems containing organic
acids, such as acetic acid. The equation-of-state is:
Where:
� For nonpolar, non-associating species:
22 2 Thermodynamic Property Models
, with
(9)

, where
� For polar, associating species:
, where
� For chemically bonding species:
Cross-Interactions
2 Thermodynamic Property Models 23
, with
, and
The previous equations are valid for dimerization and cross-dimerization if
these mixing rules are applied:
� = 0 unless a special solvation contribution can be justified (for example, i
and j are in the same class of compounds). Many � values are present in the
Aspen Physical Property System.
Chemical Theory
When a compound with strong association is present in a mixture,
the entire mixture is treated according to the chemical theory of dimerization.

The chemical reaction for the general case of a mixture of dimerizing
components i and j is:
Where i and j refer to the same component.
The equation-of-state becomes:
with
In this case, molar volume is equal to V/n t .
This represents true total volume over the true number of species n t .
However, the reported molar volume is V/n a .
This represents the true total volume over the apparent number of species n a .
If dimerization does not occur, n a is defined as the number of species. V/n a
reflects the apparently lower molar volume of an associating gas mixture.
The chemical equilibrium constant for the dimerization reaction on pressure
basis Kp, is related to the true mole fractions and fugacity coefficients:
Where:
yi and yj = True mole fractions of monomers
yij = True mole fraction of dimer
�i = True fugacity coefficient of component i
Kij = Equilibrium constant for the dimerization of i and j, on a
pressure basis
24 2 Thermodynamic Property Models
=
�ij = 1 for i=j
= 0 for
Apparent mole fractions yi a are reported, but in the calculation real mole
fractions yi, yj, and yij are used.
The heat of reaction due to each dimerization is calculated according to:
The sum of the contributions of all dimerization reactions, corrected for the
ratio of apparent and true number of moles is added to the molar enthalpy
departure .

Parameter Name/
Element
2 Thermodynamic Property Models 25
Symbol Default MDS Lower
Limit
Upper
Limit
Units
TC T ci — — 5.0 2000.0 TEMPERATURE
PC p ci — — 10 5
RGYR r i gyr
— — 10 -11
10 8
5x10 -9
MUP p i — — 0.0 5x10 -24
HOCETA �� 0.0 X — — —
PRESSURE
LENGTH
DIPOLEMOMENT
The binary parameters HOCETA for many component pairs are available in the
Aspen Physical Property System. These parameters are retrieved
automatically when you specify any of the following property methods: NRTL-
HOC, UNIF-HOC, UNIQ-HOC, VANL-HOC, and WILS-HOC.
References
J.G. Hayden and J.P. O'Connell, "A Generalized Method for Predicting Second
Virial Coefficients," Ind. Eng. Chem., Process Des. Dev., Vol. 14,No. 3,
(1975), pp. 209 – 216.
HF Equation-of-State
HF forms oligomers in the vapor phase. The non-ideality in the vapor phase is
found in important deviations from ideality in all thermodynamic properties.
The HF equation accounts for the vapor phase nonidealities. The model is
based on chemical theory and assumes the formation of hexamers.
Species like HF that associate linearly behave as single species. For example,
they have a vapor pressure curve, like pure components. The component on
which a hypothetical unreacted system is based is often called the apparent
(or parent) component. Apparent components react to the true species.
Electrolyte Calculation in Physical Property Methods discusses apparent and
true species. Abbott and van Ness (1992) provide details and basic
thermodynamics of reactive systems.
The temperature-dependent hexamerization equilibrium constant, can fit the
experimentally determined association factors. The built-in functionality is:
The constants C0 and C1 are from Long et al. (1943), and C2 and C3 are set to
0. The correlation is valid between 270 and 330 K, and can be extrapolated to
about 370 K (cf. sec. 4). Different sets of constants can be determined by
experimental data regression.
Molar Volume Calculation
The non-ideality of HF is often expressed using the association factor, f,
indicating the ratio of apparent number of species to the real number or
species. Assuming the ideal gas law for all true species in terms of (p, V, T)
behavior implies:
(1)

Where the true number of species is given by 1/f. The association factor is
easily determined from (p, V, T) experiments. For a critical evaluation of data
refer to Vanderzee and Rodenburg (1970).
If only one reaction is assumed for a mixture of HF and its associated species,
(refer to Long et al., 1943), then:
If p1 represents the true partial pressure of the HF monomer, and p6
represents the true partial pressure of the hexamer, then the equilibrium
constant is defined as:
The true total pressure is:
p = p1 + p6
If all hexamer were dissociated, the apparent total pressure would be the
hypothetical pressure where:
p a = p1 + 6p6 = p + 5p6
When physical ideality is assumed, partial pressures and mole fractions are
proportional. The total pressure in equation 5 represents the true number of
species. The apparent total pressure from equation 6 represents the apparent
number of species:
Note that the outcome of equation 7 is independent of the assumption of
ideality. Equation 7 can be used to compute the number of true species 1/f
for a mixture containing HF, but the association factor is defined differently.
If p1 and p6 are known, the molar volume or density of a vapor containing HF
can be calculated using equations 2 and 7. The molar volume calculated is the
true molar volume for 1 apparent mole of HF. This is because the volume of 1
mole of ideal gas (the true molar volume per true number of moles) is always
equal to about 0.0224 m3/mol at 298.15 K.
True Mole Fraction (Partial Pressure) Calculation
If you assume the ideal gas law for a mixture containing HF, the apparent HF
mole fraction is:
26 2 Thermodynamic Property Models
(2)
(3)
(4)
(5)
(6)
(7)
(8)

The denominator of equation 8 is given by equation 6. The numerator (the
apparent partial pressure of HF) is the hypothetical partial pressure only if all
of the hexamer was dissociated. If you substitute equation 4, then equation 8
becomes:
K is known from Long et al., or can be regressed from (p,V,T) data. The
apparent mole fraction of HF, y a , is known to the user and the simulator, but
p1, or y = p1/p must also be known in order to calculate the thermodynamic
properties of the mixture. Equation 9 must be solved for p1.
2 Thermodynamic Property Models 27
(9)
Equation 9 can be written as a polynomial in p1 of degree 6:
K(6 - 5y a )(p1) 6 + p1 - py a = 0 (9a)
A second order Newton-Raphson technique is used to determine p1. Then p6
can be calculated by equation 5, and f is known (equation 7).
Gibbs Energy and Fugacity
The apparent fugacity coefficient is related to the true fugacity coefficient and
mole fractions:
(10)
Equation 10 represents a correction to the ideal mixing term of the fugacity.
The ratio of the true number of species to the apparent number of species is
similar to the correction applied in equation 2. Since the ideal gas law is
assumed, the apparent fugacity coefficient is given by the equation. All
variables on the right side are known.
For pure HF, y a = 1:
(11)
From the fugacity coefficient, the Gibbs energy departure of the mixture or
pure apparent components can be calculated:
Enthalpy and Entropy
(12)
(12a)
For the enthalpy departure, the heat of reaction is considered. For an
arbitrary gas phase reaction:

28 2 Thermodynamic Property Models
(13)
(14)
Where �i * is the pure component thermodynamic potential or molar Gibbs
energy of a component. Equation 4 represents the first two terms of the
general equation 14. The second or third equality relates the equilibrium
constant to the Gibbs energy of reaction, which is thus related to the enthalpy
of reaction:
(15)
All components are assumed to be ideal. The enthalpy departure is equal to
the heat of reaction, per apparent number of moles:
(16)
(17)
From the Gibbs energy departure and enthalpy departure, the entropy
departure can be calculated:
(18)
Temperature derivatives for the thermodynamic properties can be obtained
by straightforward differentiation.
Usage
The HF equation-of-state should only be used for vapor phase calculations. It
is not suited for liquid phase calculations.
The HF equation-of-state can be used with any activity coefficient model for
nonelectrolyte VLE. Using the Electrolyte NRTL model and the data package
MHF2 is strongly recommended for aqueous mixtures (de Leeuw and
Watanasiri, 1993).
Parameter Symbol Default MDS Lower
Name/Element
Limit
Upper
Limit
ESHFK/1 C 0 43.65 — — — —
ESHFK/2 C 1 -8910 — — — —
ESHFK/3 C 2 0 — — — —
ESHFK/4 C 3 0 — — — —
References
Units
M. M. Abbott and H. C. van Ness, "Thermodynamics of Solutions Containing
Reactive Species, a Guide to Fundamentals and Applications," Fluid Phase Eq.,
Vol. 77, (1992) pp. 53 – 119.

V. V. De Leeuw and S. Watanasiri, "Modelling Phase Equilibria and Enthalpies
of the System Water and Hydroflouric Acid Using an HF Equation-of-state in
Conjunction with the Electrolyte NRTL Activity Coefficient Model," Paper
presented at the 13th European Seminar on Applied Thermodynamics, June 9
– 12, Carry-le-Rouet, France, 1993.
R. W. Long, J. H. Hildebrand, and W. E. Morrell, "The Polymerization of
Gaseous Hydrogen and Deuterium Flourides," J. Am. Chem. Soc., Vol. 65,
(1943), pp. 182 – 187.
C. E. Vanderzee and W. WM. Rodenburg, "Gas Imperfections and
Thermodynamic Excess Properties of Gaseous Hydrogen Fluoride," J. Chem.
Thermodynamics, Vol. 2, (1970), pp. 461 – 478.
IAPWS-95 Steam Tables
The IAPWS-95 Steam Tables are implemented like any other equation-ofstate
in the Aspen Physical Property System. These steam tables can calculate
any thermodynamic property of water. The tables form the basis of the
IAPWS-95 property method. There are no parameter requirements. They are
the most accurate steam tables in the Aspen Physical Property System.
References
Wanger W. and A. Pruß, ”The IAPWS Formation 1995 for the Thermodynamic
Properties of Ordinary Water Substance for General and Scientific Use,” J.
Phys. Chem. Ref. Data, 31(2), 387- 535, 2002.
Ideal Gas
The ideal gas law (ideal gas equation-of-state) combines the laws of Boyle
and Gay-Lussac. It models a vapor as if it consisted of point masses without
any interactions. The ideal gas law is used as a reference state for equationof-state
calculations, and can be used to model gas mixtures at low pressures
(without specific gas phase interactions).
The equation is:
p = RT / Vm
Lee-Kesler
This equation-of-state model is based on the work of Lee and Kesler (1975).
In this equation, the volumetric and thermodynamic properties of fluids based
on the Curl and Pitzer approach (1958) have been analytically represented by
a modified Benedict-Webb-Rubin equation-of-state (1940). The model
calculates the molar volume, enthalpy departure, Gibbs free energy
departure, and entropy departure of a mixture at a given temperature,
pressure, and composition for either a vapor or a liquid phase. Partial
derivatives of these quantities with respect to temperature can also be
calculated.
Unlike the other equation-of-state models, this model does not calculate
fugacity coefficients.
2 Thermodynamic Property Models 29

The compressibility factor and other derived thermodynamic functions of
nonpolar and slightly polar fluids can be adequately represented, at constant
reduced temperature and pressure, by a linear function of the acentric factor.
In particular, the compressibility factor of a fluid whose acentric factor is �, is
given by the following equation:
Z = Z (0) + �Z (1)
Where:
Z (0)
Z (1)
= Compressibility factor of a simple fluid (� = 0)
= Deviation of the compressibility factor of the real fluid from Z (0)
Z (0) and Z (1) are assumed universal functions of the reduced temperature and
pressure.
Curl and Pitzer (1958) were quite successful in correlating thermodynamic
and volumetric properties using the above approach. Their application
employed tables of properties in terms of reduced temperature and pressure.
A significant weakness of this method is that the various properties (for
example, entropy departure and enthalpy departure) will not be exactly
thermodynamically consistent with each other. Lee and Kesler (1975)
overcame this drawback by an analytic representation of the tables with an
equation-of-state. In addition, the range was extended by including new data.
In the Lee-Kesler implementation, the compressibility factor of any fluid has
been written in terms of a simple fluid and a reference as follows:
In the above equation both Z (0) and Z (1) are represented as generalized
equations of the BWR form in terms of reduced temperature and pressure.
Thus,
Equations for the enthalpy departure, Gibbs free energy departure, and
entropy departure are obtained from the compressibility factor using standard
thermodynamic relationships, thus ensuring thermodynamic consistency.
In the case of mixtures, mixing rules (without any binary parameters) are
used to obtain the mixture values of the critical temperature and pressure,
and the acentric factor.
This equation has been found to provide a good description of the volumetric
and thermodynamic properties of mixtures containing nonpolar and slightly
polar components.
Symbol Parameter Name Default Definition
T c TCLK TC Critical temperature
P c PCLK PC Critical pressure
�� OMGLK OMEGA Acentric factor
30 2 Thermodynamic Property Models

References
M. Benedict, G. B. Webb, and L. C. Rubin, J. Chem. Phys., Vol. 8, (1940), p.
334.
R. F. Curl and K.S. Pitzer, Ind. Eng. Chem., Vol. 50, (1958), p. 265.
B. I. Lee and M.G. Kesler, AIChE J., Vol. 21, (1975), p. 510.
Lee-Kesler-Plöcker
The Lee-Kesler-Plöcker equation-of-state is the basis for the LK-PLOCK
property method. This equation-of-state applies to hydrocarbon systems that
include the common light gases, such as H2S and CO2. It can be used in gasprocessing,
refinery, and petrochemical applications.
The general form of the equation is:
Where:
The fo and fR parameters are functions of the BWR form. The fo parameter is
for a simple fluid, and fR is for reference fluid n-octane.
The mixing rules are:
Vcm
2 Thermodynamic Property Models 31
=
=
�� =
Zm
Where:
Vcij
Tcij
Zci
=
=
=
=
kij = kji

The binary parameter kij is determined from phase-equilibrium data
regression, such as VLE data. The Aspen Physical Property System stores the
binary parameters for a large number of component pairs. These binary
parameters are used automatically with the LK-PLOCK property method. If
binary parameters for certain component pairs are not available, they can be
estimated using built-in correlations. The correlations are designed for binary
interactions among the components CO, CO2, N2, H2, CH4 alcohols and
hydrocarbons. If a component is not CO, CO2, N2, H2, CH4 or an alcohol, it is
assumed to be a hydrocarbon.
Parameter
Name/
Element
32 2 Thermodynamic Property Models
Symbol Default MDS Lower
Limit
Upper
Limit
Units
TCLKP T ci TC x 5.0 2000.0 TEMPERATURE
PCLKP p ci PC x PRESSURE
VCLKP V ci VC x 0.001 3.5 MOLE-
VOLUME
OMGLKP � I OMEGA x -0.5 2.0 —
LKPZC Zci
LKPKIJ kij
fcn(�) (Method 1)
fcn(p ci,V ci,T ci)
(Method 2)
x 0.1 0.5 —
fcn(T ciV ci / T cjV cj) x 5.0 5.0 —
Method 1 is the default for LKPZC; Method 2 can be invoked by setting the
value of LKPZC equal to zero.
Binary interaction parameters LKPKIJ are available for a large number of
components in the Aspen Physical Property System, from Knapp et al.
References
B.I. Lee and M.G. Kesler, AIChE J., Vol. 21, (1975) p. 510; errata: AIChE J.,
Vol. 21, (1975) p. 1040.
V. Plöcker, H. Knapp, and J.M. Prausnitz, Ind. Eng. Chem., Process Des. Dev.,
Vol. 17, (1978), p. 324.
H. Knapp, R. Döring, L. Oellrich, U. Plöcker, and J. M. Prausnitz. "Vapor-Liquid
Equilibria for Mixtures of Low Boiling Substances." Dechema Chemistry Data
Series, Vol. VI.
NBS/NRC Steam Tables
The NBS/NRC Steam Tables are implemented like any other equation-of-state
in the Aspen Physical Property System. These steam tables can calculate any
thermodynamic property of water. The tables form the basis of the
STEAMNBS and STMNBS2 property methods. There are no parameter
requirements. The STMNBS2 model uses the same equations as STEAMNBS
but with different root search method. The STEAMNBS method is
recommended for use with the SRK, BWRS, MXBONNEL and GRAYSON2
property methods.

References
L. Haar, J.S. Gallagher, and J.H. Kell, "NBS/NRC Steam Tables," (Washington:
Hemisphere Publishing Corporation, 1984).
Nothnagel
The Nothnagel equation-of-state calculates thermodynamic properties for the
vapor phase. It is used in property methods NRTL-NTH, UNIQ-NTH, VANL-
NTH, and WILS-NTH. It is recommended for systems that exhibit strong vapor
phase association. The model incorporates the chemical theory of
dimerization to account for strong association and solvation effects, such as
those found in organic acids, like acetic acid. The equation-of-state is:
Where:
b =
bij
=
nc = Number of components in the mixture
The chemical reaction for the general case of a mixture of dimerizing
components i and j is:
The chemical equilibrium constant for the dimerization reaction on pressure
basis Kp is related to the true mole fractions and fugacity coefficients:
Where:
yi and yj = True mole fractions of monomers
yij = True mole fraction of dimer
�i = True fugacity coefficient of component i
Kij = Equilibrium constant for the dimerization of i and j, on a
pressure basis
When accounting for chemical reactions, the number of true species n t in the
mixture changes. The true molar volume V/n t
is calculated from the
equation-of-state. Since both V and n t change in about the same proportion,
this number does not change much. However, the reported molar volume is
the total volume over the apparent number of species: V/n a . Since the
apparent number of species is constant and the total volume decreases with
2 Thermodynamic Property Models 33

association, the quantity V/n a reflects the apparent contraction in an
associating mixture.
The heat of reaction due to each dimerization can be calculated:
The heat of reaction for the mixed dimerization of components i and j is by
default the arithmetic mean of the heats of reaction for the dimerizations of
the individual components. Parameter is a small empirical correction
factor to this value:
The sum of the contributions of all dimerization reactions, corrected for the
ratio of apparent and true number of moles, is added to the molar enthalpy
departure:
The equilibrium constants can be computed using either built-in calculations
or parameters you entered.
� Built-in correlations:
The pure component parameters b, d, and p are stored in the Aspen
Physical Property System for many components.
Parameters you entered:
In this method, you enter Ai, Bi, Ci, and Di on the Properties Parameters
Unary.T-Dependent form. The units for Kii is pressure -1 ; use absolute units for
temperature. If you enter Kii and Kjj, then Kij is computed from
If you enter Ai, Bi, Ci, and Di, the equilibrium constants are computed using
the parameters you entered. Otherwise the equilibrium constants are
computed using built-in correlations.
Parameter
Name/Element
34 2 Thermodynamic Property Models
Symbol Default Lower
Limit
Upper Limit Units
TC T ci — 5.0 2000.0 TEMPERATURE
TB T bi — 4.0 2000.0 TEMPERATURE
PC p ci — 10 5
10 8
PRESSURE
NTHA/1 b i 0.199 RT ci / p ci 0.01 1.0 MOLE-VOLUME
NTHA/2 d i 0.33 0.01 3.0 —
NTHA/3 p i 0 0.0 1.0 —
NTHK/1 A i — — — PRESSURE
NTHK/2 B i 0 — — TEMPERATURE
NTHK/3 C i 0 — — TEMPERATURE
NTHK/4 D i 0 — — TEMPERATURE

Parameter
Name/Element
NTHDDH 0 †
2 Thermodynamic Property Models 35
Symbol Default Lower
Limit
Upper Limit Units
— — MOLE-
ENTHALPY
† For the following systems, the values given in Nothnagel et al., 1973 are
used by default:
� Methyl chloride/acetone
� Acetonitrile/acetaldehyde
� Acetone/chloroform
� Chloroform/diethyl amine
� Acetone/benzene
� Benzene/chloroform
� Chloroform/diethyl ether
� Chloroform/propyl formate
� Chloroform/ethyl acetate
� Chloroform/methyl acetate
� Chloroform/methyl formate
� Acetone/dichloro methane
� n-Butane/n-perfluorobutane
� n-Pentane/n-perfluoropentane
� n-Pentane/n-perfluorohexane
References
K.-H. Nothnagel, D. S. Abrams, and J.M. Prausnitz, "Generalized Correlation
for Fugacity Coefficients in Mixtures at Moderate Pressures," Ind. Eng. Chem.,
Process Des. Dev., Vol. 12, No. 1 (1973), pp. 25 – 35.
Copolymer PC-SAFT EOS Model
This section describes the Copolymer Perturbed-Chain Statistical Associating
Fluid Theory (PC-SAFT). This equation-of-state model is used through the PC-
SAFT property method.
The copolymer PC-SAFT represents the completed PC-SAFT EOS model
developed by Sadowski and co-workers (Gross and Sadowski, 2001, 2002a,
2002b; Gross et al., 2003; Becker et al., 2004; Kleiner et al., 2006). Unlike
the PC-SAFT EOS model (POLYPCSF) in Aspen Plus, the copolymer PC-SAFT
includes the association and polar terms and does not apply mixing rules to
calculate the copolymer parameters from its segments. Its applicability covers
fluid systems from small to large molecules, including normal fluids, water,
alcohols, and ketones, polymers and copolymers and their mixtures.
Copolymer PC-SAFT Fundamental Equations
The copolymer PC-SAFT model is based on the perturbation theory. The
underlying idea is to divide the total intermolecular forces into repulsive and
attractive contributions. The model uses a hard-chain reference system to

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

component i, respectively. The segment number mi� is calculated from the
segment ratio parameter ri�:
where Mi� is the total molecular weight of the segment type � in the
copolymer component i and can be calculated from the segment weight
fraction within the copolymer:
where wi� is the weight fraction of the segment type � in the copolymer
component i, and Mi is the molecular weight of the copolymer component i.
Following Sadowski and co-worker’s work ( Gross et al., 2003; Becker et al.,
2004), the contribution from the chain connectivity can be written as follows:
with
where Bi��i� is defined as the bonding fraction between the segment type �
and the segment type � within the copolymer component i, � is the number of
the segment types within the copolymer component i, and g hs i�,j�(di�,j�) is the
radial distribution function of hard-sphere mixtures at contact.
However, the calculation for Bi��i� depends on the type of copolymers. We
start with a pure copolymer system which consists of only two different types
of segments � and �; this gives:
with
We now apply these equations to three common types of copolymers; a)
alternating, b) block, and c) random.
For an alternating copolymer, m� = m�; there are no �� or �� adjacent
sequences. Therefore:
38 2 Thermodynamic Property Models

For a block copolymer, there is only one �� pair and the number of �� and
�� pairs depend on the length of each block; therefore:
For a random copolymer, the sequence is only known in a statistical sense. If
the sequence is completely random, then the number of �� adjacent pairs is
proportional to the product of the probabilities of finding a segment of type �
and a segment of type � in the copolymer. The probability of finding a
segment of type � is the fraction of segments z� in the copolymer:
The bonding fraction of each pair of types can be written as follows:
where C is a constant and can be determined by the normalization condition
set by Equation 2.70; the value for C is unity. Therefore:
A special case is the Sadowski’s model for random copolymer with two types
of segments only ( Gross et al., 2003; Becker et al., 2004). In this model, the
bonding fractions are calculated as follows:
When z� < z�
When z� < z�
The generalization of three common types of copolymers from two types of
different segments to multi types of different segments � within a copolymer
is straightforward.
For a generalized alternative copolymer, m� = m� = ... = mr = m/� ; there
are no adjacent sequences for the same type of segments. Therefore,
2 Thermodynamic Property Models 39

For a generalized block copolymer, there is only one pair for each adjacent
type of segment pairs (� � �) and the number of pairs for a same type
depends on the length of the block; therefore:
For a generalized random copolymer, the sequence is only known in a
statistical sense. If the sequence is completely random, then the number of
�� adjacent pairs is proportional to the product of the probabilities of finding
a segment of type � and a segment of type � in the copolymer. The
probability of finding a segment of type � is the fraction of � segments z� in
the copolymer:
The bonding fraction of each pair of types can be written as follows:
where C is a constant and can be determined by the normalization condition.
Therefore,
That is,
Put C into the equation above, we obtain:
40 2 Thermodynamic Property Models

Copolymer PC-SAFT Dispersion Term
The equations for the dispersion term are given as follows:
where �i�,j� and �i�,j� are the cross segment diameter and energy parameters,
respectively; only one adjustable binary interaction parameter, �i�,j� is
introduced to calculate them:
2 Thermodynamic Property Models 41

In above equations, the model constants a1i, a2i, a3i, b1i, b2i, and b3i are fitted
to pure-component vapor pressure and liquid density data of n-alkanes (
Gross and Sadowski, 2001).
Association Term for Copolymer Mixtures - 2B
Model
The association term in PC-SAFT model in general needs an iterative
procedure to calculate the fraction of a species (solvent or segment) that are
bounded to each association-site type. Only in pure or binary systems, the
fraction can be derived explicitly for some specific models. We start with
general expressions for the association contribution for copolymer systems as
follows:
where A is the association-site type index, is the association-site
number of the association-site type A on the segment type � in the
copolymer component i, and is the mole fraction of the segment type �
in the copolymer component i that are not bonded with the association-site
type A; it can be estimated as follows:
with
where is the cross effective association volume and is the
cross association energy; they are estimated via simple combination rules:
where and are the effective association volume and the
association energy between the association-site types A and B, of the
segment type � in the copolymer component i, respectively.
42 2 Thermodynamic Property Models

The association-site number of the site type A on the segment type � in the
copolymer component i is equal to the number of the segment type � in the
copolymer component i,
where Ni� is the number of the segment type � in the copolymer component i
and M� is the molecular weight of the segment type �. In other words, the
association-site number for each site type within a segment is the same;
therefore, we can rewrite the equations above as follows:
To calculate , this equation has to be solved iteratively for each
association-site type associated with a species in a component. In practice,
further assumption is needed for efficiency. The commonly used model is the
so-called 2B model ( Huang and Radosz, 1990). It assumes that an
associating species (solvent or segment) has two association sites, one is
designed as the site type A and another as the site type B. Similarly to the
hydrogen bonding, type A treats as a donor site with positive charge and type
B as an acceptor site with negative charge; only the donor-acceptor
association bonding is permitted and this concept applies to both pure
systems (self-association such as water) and mixtures (both self-association
and cross-association such as water-methanol). Therefore, we can rewrite
these equations as follows:
It is easy to show that
Therefore
2 Thermodynamic Property Models 43

Polar Term for Copolymer PC-SAFT
The equations for the polar term are given by Jog et al. (2001) as follows:
In the above equations, I2(�) and I3(�) are the pure fluid integrals and �i�
and (xp)i� are the dipole moment and dipolar fraction of the segment type �
within the copolymer component i, respectively. Both and
44 2 Thermodynamic Property Models
are dimensionless. In terms of them, we can have:
Rushbrooke et al. (1973) have shown that

Then I2(�) and I3(�) are computed in terms of � by the expressions:
Reference
Jog, P. K., Sauer, S. G., Blaesing, J., & Chapman, W. G. (2001), Application
of Dipolar Chain Theory to the Phase Behavior of Polar Fluids and Mixtures.
Ind. Eng. Chem. Res., 40, 4641.
Rushbrooke, G. S., & Stell, G., Hoye, J. S. (1973), Molec. Phys., 26, 1199.
Copolymer PC-SAFT EOS Model Parameters
Pure parameters
Each non-association species (solvent or segment) must have a set of three
pure-component parameter; two of them are the segment diameter � and the
segment energy parameter �. The third parameter for a solvent is the
segment number m and for a segment is the segment ratio parameter r. For
an association species, two additional parameters are the effective association
volume � (AB) and the association energy � (AB) . For a polar species, two
additional parameters are the dipole moment � and the segment dipolar
fraction xp.
Binary parameters
There are three types of binary interactions in copolymer systems: solventsolvent,
solvent-segment, and segment-segment. The binary interaction
parameter �i�,j� allows complex temperature dependence:
with
where Tref is a reference temperature and the default value is 298.15 K.
The following table lists the copolymer PC-SAFT EOS model parameters
implemented in Aspen Plus:
2 Thermodynamic Property Models 45

Parameter
Name/
Element
Symbol Default Lower
Limit
46 2 Thermodynamic Property Models
Upper
Limit
MDS Units Comments
Keyword
PCSFTM m — — — X — Unary
PCSFTV � — — — X — Unary
PCSFTU �/k — — — X TEMP Unary
PCSFTR r — — — X — Unary
PCSFAU � AB /k — — — X TEMP Unary
PCSFAV � AB — — — X — Unary
PCSFMU � — — — X — Unary
PCSFXP x p — — — X — Unary
PCSKIJ/1 ai�,j�
PCSKIJ/2 bi�,j�
PCSKIJ/3 ci�,j�
PCSKIJ/4 di�,j�
PCSKIJ/5 ei�,j�
0.0 — — X — Binary,
Symmetric
0.0 — — X — Binary,
Symmetric
0.0 — — X — Binary,
Symmetric
0.0 — — X — Binary,
Symmetric
0.0 — — X — Binary,
Symmetric
PCSKIJ/6 T ref 298.15 — — X TEMP Binary,
Symmetric
Parameter Input and Regression for Copolymer
PC-SAFT
Since the copolymer PC-SAFT is built based on the segment concept, the
unary (pure) parameters must be specified for a solvent or a segment.
Specifying a unary parameter for a polymer component (homopolymer or
copolymer) will be ignored by the simulation. For a non-association and nonpolar
solvent, three unary parameters PCSFTM, PCSFTU, and PCSFTV must be
specified. For a non-association and non-polar segment, these three unary
parameters PCSFTR, PCSFTU, and PCSFTV must be specified. For an
association species (solvent or segment), two additional unary parameters
PCSFAU and PCSFAV must be specified. For a polar species (solvent or
segment), two additional unary parameters PCSFMU and PCSFXP must be
specified.
Note that the SI units for the segment diameter � (PCSFTV) and dipole
moment � (PCSFMU) are much too large to be practical. The implementation
of PC-SAFT in Aspen Plus has the unit in Angstroms (Å) for the segment
diameter and in Debye (D) for the dipole moment; these units are not allowed
to be changed in PC-SAFT.
The binary parameter PCSKIJ can be specified for each solvent-solvent pair,
or each solvent-segment pair, or each segment-segment pair. By default, the
binary parameter is set to be zero.

A databank called PC-SAFT contains both unary and binary PC-SAFT
parameters available from literature; it must be used with the PC-SAFT
property method. The unary parameters available for segments are stored in
the SEGMENT databank. If unary parameters are not available for a species
(solvent or segment) in a calculation, the user can perform an Aspen Plus
Data Regression Run (DRS) to obtain unary parameters. For non-polymer
components (mainly solvents), the unary parameters are usually obtained by
fitting experimental vapor pressure and liquid molar volume data. To obtain
unary parameters for a segment, experimental data on liquid density of the
homopolymer that is built by the segment should be regressed. Once the
unary parameters are available for a segment, the ideal-gas heat capacity
parameter CPIG may be regressed for the same segment using experimental
liquid heat capacity data for the same homopolymer. In addition to unary
parameters, the binary parameter PCSKIJ for each solvent-solvent pair, or
each solvent-segment pair, or each segment-segment pair, can be regressed
using vapor-liquid equilibrium (VLE) data in the form of TPXY data in Aspen
Plus.
Note: In Data Regression Run, a homopolymer must be defined as an
OLIGOMER type, and the number of the segment that builds the oligomer
must be specified.
Peng-Robinson
The Peng-Robinson equation-of-state is the basis for the PENG-ROB and PR-
BM property methods. The model has been implemented with choices of
different alpha functions (see Peng-Robinson Alpha Functions) and has been
extended to include advanced asymmetric mixing rules.
Note: You can choose any of the available alpha functions, but you cannot
define multiple property methods based on this model using different alpha
functions within the same run.
By default, the PENG-ROB property method uses the literature version of the
alpha function and mixing rules. The PR-BM property method uses the
Boston-Mathias alpha function and standard mixing rules. These default
property methods are recommended for hydrocarbon processing applications
such as gas processing, refinery, and petrochemical processes. Their results
are comparable to those of the property methods that use the standard
Redlich-Kwong-Soave equation-of-state.
When advanced alpha function and asymmetric mixing rules are used with
appropriately obtained parameters, the Peng-Robinson model can be used to
accurately model polar, non-ideal chemical systems. Similar capability is also
available for the Soave-Redlich-Kwong model.
The equation for the Peng-Robinson model is:
Where:
2 Thermodynamic Property Models 47

=
c =
a = a0+a1
a0
kij
a1
lij
ai
bi
ci
48 2 Thermodynamic Property Models
=
=
=
=
=
=
(the standard quadratic mixing term, where kij has
been made temperature-dependent)
kij = kji
(an additional, asymmetric term used to model
highly non-linear systems)
In general, .
For best results, the binary parameters kij and lij must be determined from
regression of phase equilibrium data such as VLE data. The Aspen Physical
Property System also has built-in kij and lij for a large number of component
pairs in the EOS-LIT databank from Knapp et al. These parameters are used
automatically with the PENG-ROB property method. Values in the databank
can be different than those used with other models such as Soave-Redlich-
Kwong or Redlich-Kwong-Soave, and this can produce different results.
The model has option codes which can be used to customize the model, by
selecting a different alpha function and other model options. See Peng-
Robinson Alpha Functions for a description of the alpha functions. See Option
Codes for Equation of State Models (under ESPR) for a list of the option
codes.
Parameter
Name/Element
Symbol Default MDS Lower
Limit
Upper
Limit
Units
PRTC T ci TC x 5.0 2000.0 TEMPERATURE
PRPC p ci PC x 10 5
OMGPR � i
10 8
OMEGA x -0.5 2.0 —
PRZRA z RA RKTZRA x — — —
PRESSURE

Parameter
Name/Element
PRKBV/1 k ij (1)
PRKBV/2 k ij (2)
PRKBV/3 k ij (3)
2 Thermodynamic Property Models 49
Symbol Default MDS Lower
Limit
Upper
Limit
0 x — — —
Units
0 x — — TEMPERATURE
0 x — — TEMPERATURE
PRKBV/4 T lower 0 x — — TEMPERATURE
PRKBV/5 T upper 1000 x — — TEMPERATURE
PRLIJ/1 l ij (1)
PRLIJ/2 l ij (2)
PRLIJ/3 l ij (3)
0 x — — —
0 x — — TEMPERATURE
0 x — — TEMPERATURE
PRLIJ/4 T lower 0 x — — TEMPERATURE
PRLIJ/5 T upper 1000 x — — TEMPERATURE
References
D.-Y. Peng and D. B. Robinson, "A New Two-Constant Equation-of-state," Ind.
Eng. Chem. Fundam., Vol. 15, (1976), pp. 59–64.
P.M. Mathias, H.C. Klotz, and J.M. Prausnitz, "Equation of state mixing rules
for multicomponent mixtures: the problem of invariance," Fluid Phase
Equilibria, Vol 67, (1991), pp. 31-44.
H. Knapp, R. Döring, L. Oellrich, U. Plöcker, and J. M. Prausnitz. "Vapor-Liquid
Equilibria for Mixtures of Low Boiling Substances." Dechema Chemistry Data
Series, Vol. VI.
Standard Peng-Robinson
The Standard Peng-Robinson equation-of-state is the original formulation of
the Peng-Robinson equation of state with the standard alpha function (see
Peng-Robinson Alpha Functions). It is recommended for hydrocarbon
processing applications such as gas processing, refinery, and petrochemical
processes. Its results are comparable to those of the standard Redlich-
Kwong-Soave equation of state.
Note: You can choose any of the available alpha functions, but you cannot
define multiple property methods based on this model using different alpha
functions within the same run.
The equation for this model is:
Where:
b =
a =

ai
bi
kij
50 2 Thermodynamic Property Models
=
=
=
The model has option codes which can be used to customize the model, by
selecting a different alpha function and other model options. See Peng-
Robinson Alpha Functions for a description of the alpha functions. See Option
Codes for Equation of State Models (under ESPRSTD) for a list of the option
codes.
For best results, the binary parameter kij must be determined from regression
of phase equilibrium data such as VLE data. The Aspen Physical Property
System also has built-in kij for a large number of component pairs in the EOS-
LIT databank. These parameters are used automatically with the PENG-ROB
property method. Values in the databank can be different than those used
with other models such as Soave-Redlich-Kwong or Redlich-Kwong-Soave,
and this can produce different results.
Parameter
Name/Element
Symbol Default MDS Lower
Limit
Upper
Limit
Units
TCPRS T ci TC x 5.0 2000.0 TEMPERATURE
PCPRS p ci PC x 10 5
OMGPRS � i
PRKBV/1 k ij (1)
PRKBV/2 k ij (2)
PRKBV/3 k ij (3)
10 8
OMEGA x -0.5 2.0 —
0 x - - -
PRESSURE
0 x - - TEMPERATURE
0 x - - TEMPERATURE
PRKBV/4 T lower 0 x - - TEMPERATURE
PRKBV/5 T upper 1000 x - - TEMPERATURE
References
D.-Y. Peng and D. B. Robinson, "A New Two-Constant Equation-of-state," Ind.
Eng. Chem. Fundam., Vol. 15, (1976), pp. 59–64.
Peng-Robinson-MHV2
This model uses the Peng-Robinson equation-of-state for pure compounds.
The mixing rules are the predictive MHV2 rules. Several alpha functions can
be used in the Peng-Robinson-MHV2 equation-of-state model for a more
accurate description of the pure component behavior. The pure component
behavior and parameter requirements are described in Standard Peng-
Robinson, or in Peng-Robinson Alpha Functions.
The MHV2 mixing rules are an example of modified Huron-Vidal mixing rules.
A brief introduction is provided in Huron-Vidal Mixing Rules. For more details,
see MHV2 Mixing Rules.

Predictive SRK (PSRK)
This model uses the Redlich-Kwong-Soave equation-of-state for pure
compounds. The mixing rules are the predictive Holderbaum rules, or PSRK
method. Several alpha functions can be used in the PSRK equation-of-state
model for a more accurate description of the pure component behavior. The
pure component behavior and parameter requirements are described in
Standard Redlich-Kwong-Soave and in Soave Alpha Functions.
Note: You can choose any of the available alpha functions, but you cannot
define multiple property methods based on this model using different alpha
functions within the same run.
The PSRK method is an example of modified Huron-Vidal mixing rules. A brief
introduction is provided in Huron-Vidal Mixing Rules. For more details, see
Predictive Soave-Redlich-Kwong-Gmehling Mixing Rules.
Peng-Robinson-Wong-Sandler
This model uses the Peng-Robinson equation-of-state for pure compounds.
The mixing rules are the predictive Wong-Sandler rules. Several alpha
functions can be used in the Peng-Robinson-Wong-Sandler equation-of-state
model for a more accurate description of the pure component behavior. The
pure component behavior and parameter requirements are described in Peng-
Robinson, and in Peng-Robinson Alpha Functions.
Note: You can choose any of the available alpha functions, but you cannot
define multiple property methods based on this model using different alpha
functions within the same run.
The Wong-Sandler mixing rules are an example of modified Huron-Vidal
mixing rules. A brief introduction is provided in Huron-Vidal Mixing Rules. For
more details see Wong-Sandler Mixing Rules., this chapter.
Redlich-Kwong
The Redlich-Kwong equation-of-state can calculate vapor phase
thermodynamic properties for the following property methods: NRTL-RK,
UNIFAC, UNIF-LL, UNIQ-RK, VANL-RK, and WILS-RK. It is applicable for
systems at low to moderate pressures (maximum pressure 10 atm) for which
the vapor-phase nonideality is small. The Hayden-O'Connell model is
recommended for a more nonideal vapor phase, such as in systems
containing organic acids. It is not recommended for calculating liquid phase
properties.
The equation for the model is:
p =
Where:
2 Thermodynamic Property Models 51

=
b =
ai
bi
=
=
Parameter
Name/Element
52 2 Thermodynamic Property Models
Symbol Default MDS Lower
Limit
Upper
Limit
Units
TC T ci — — 5.0 2000.0 TEMPERATURE
PC p ci — — 10 5
References
10 8
PRESSURE
O. Redlich and J.N.S. Kwong, "On the Thermodynamics of Solutions V. An
Equation-of-state. Fugacities of Gaseous Solutions," Chem. Rev., Vol. 44,
(1979), pp. 223 – 244.
Redlich-Kwong-Aspen
The Redlich-Kwong-Aspen equation-of-state is the basis for the RK-ASPEN
property method. It can be used for hydrocarbon processing applications. It is
also used for more polar components and mixtures of hydrocarbons, and for
light gases at medium to high pressures.
The equation is the same as Redlich-Kwong-Soave:
p =
A quadratic mixing rule is maintained for:
a =
An interaction parameter is introduced in the mixing rule for:
b =
For ai an extra polar parameter is used:
ai
bi
=
=
The interaction parameters are temperature-dependent:

ka,ij
kb,ij
=
=
For best results, binary parameters kij must be determined from phaseequilibrium
data regression, such as VLE data.
Parameter Symbol Default MDS Lower Upper Units
Name/Element
Limit Limit
TCRKA T ci TC x 5.0 2000.0 TEMPERATURE
PCRKA p ci PC x 10 5
OMGRKA � i
RKAPOL � i
RKAKA0 k a,ij 0
RKAKA1 k a,ij 1
RKAKB0 k b,ij 0
RKAKB1 k b,ij 1
References
2 Thermodynamic Property Models 53
10 8
OMEGA x -0.5 2.0 —
0 x -2.0 2.0 —
0 x -5.0 5.0 —
PRESSURE
0 x -15.0 15.0 TEMPERATURE
0 x -5.0 5.0 —
0 x -15.0 15.0 TEMPERATURE
Mathias, P.M., "A Versatile Phase Equilibrium Equation-of-state", Ind. Eng.
Chem. Process Des. Dev., Vol. 22, (1983), pp. 385 – 391.
Redlich-Kwong-Soave
This is the standard Redlich-Kwong-Soave equation-of-state, and is the basis
for the RK-SOAVE property method. It is recommended for hydrocarbon
processing applications, such as gas-processing, refinery, and petrochemical
processes. Its results are comparable to those of the Peng-Robinson
equation-of-state.
The equation is:
Where:
a0 is the standard quadratic mixing term:
a1 is an additional, asymmetric (polar) term:

=
ai
bi
kij = kji
=
=
; ;
The parameter ai is calculated according to the standard Soave formulation
(see Soave Alpha Functions, equations 1, 2, 3, 5, and 6).
Note: You can choose any of the available alpha functions, but you cannot
define multiple property methods based on this model using different alpha
functions within the same run.
The model uses option codes which are described in Soave-Redlich-Kwong
Option Codes.
For best results, binary parameters kij must be determined from phaseequilibrium
data regression (for example, VLE data). The Aspen Physical
Property System also has built-in kij for a large number of component pairs in
the EOS-LIT databank from Knapp et al. These binary parameters are used
automatically with the RK-SOAVE property method. Values of kij in the
databank can be different than those used with other models such as Soave-
Redlich-Kwong or Standard Peng-Robinson, and this can produce different
results.
Parameter
Name/Element
54 2 Thermodynamic Property Models
Symbol Default MDS Lower
Limit
Upper
Limit
Units
TCRKSS T ci TC x 5.0 2000.0 TEMPERATURE
PCRKSS p ci PC x 10 5
OMRKSS � i
RKSKBV/1 k ij (1)
RKSKBV/2 k ij (2)
RKSKBV/3 k ij (3)
10 8
OMEGA x -0.5 2.0 —
0 x -5.0 5.0 —
PRESSURE
0 x — — TEMPERATURE
0 x — — TEMPERATURE
RKSKBV/4 T k,lower 0 x — — TEMPERATURE
RKSKBV/5 T k,upper 1000 x — — TEMPERATURE
RKSLBV/1 l ij (1)
RKSLBV/2 l ij (2)
RKSLBV/3 l ij (3)
0 x — — —
0 x — — TEMPERATURE
0 x — — TEMPERATURE
RKSLBV/4 T l,lower 0 x — — TEMPERATURE
RKSLBV/5 T l,upper 1000 x — — TEMPERATURE
References
G. Soave, "Equilibrium Constants for Modified Redlich-Kwong Equation-ofstate,"
Chem. Eng. Sci., Vol. 27, (1972), pp. 1196 – 1203.

J. Schwartzentruber and H. Renon, "Extension of UNIFAC to High Pressures
and Temperatures by the Use of a Cubic Equation-of-state," Ind. Eng. Chem.
Res., Vol. 28, (1989), pp. 1049 – 1955.
A. Peneloux, E. Rauzy, and R. Freze, "A Consistent Correction For Redlich-
Kwong-Soave Volumes", Fluid Phase Eq., Vol. 8, (1982), pp. 7–23.
H. Knapp, R. Döring, L. Oellrich, U. Plöcker, and J. M. Prausnitz. "Vapor-Liquid
Equilibria for Mixtures of Low Boiling Substances." Dechema Chemistry Data
Series, Vol. VI.
Redlich-Kwong-Soave-Boston-Mathias
The Redlich-Kwong-Soave-Boston-Mathias equation-of-state is the basis for
the RKS-BM property method. It is the Redlich-Kwong-Soave equation-ofstate
with the Boston-Mathias alpha function (see Soave Alpha Functions). It
is recommended for hydrocarbon processing applications, such as gasprocessing,
refinery, and petrochemical processes. Its results are comparable
to those of the Peng-Robinson-Boston-Mathias equation-of-state.
Note: You can choose any of the available alpha functions, but you cannot
define multiple property methods based on this model using different alpha
functions within the same run.
The equation is:
p =
Where:
a0 is the standard quadratic mixing term:
a1 is an additional, asymmetric (polar) term:
b =
ai
bi
=
=
kij = kji
2 Thermodynamic Property Models 55

; ;
The parameter ai is calculated by the standard Soave formulation at
supercritical temperatures. If the component is supercritical, the Boston-
Mathias extrapolation is used (see Soave Alpha Functions).
The model uses option codes which are described in Soave-Redlich-Kwong
Option Codes.
For best results, binary parameters kij must be determined from phaseequilibrium
data regression (for example, VLE data).
Parameter Symbol Default MDS Lower Upper Units
Name/Element
Limit Limit
TCRKS T ci TC x 5.0 2000.0 TEMPERATURE
PCRKS p ci PC x 10 5
OMGRKS � i
RKSKBV/1 k ij (1)
RKSKBV/2 k ij (2)
RKSKBV/3 k ij (3)
56 2 Thermodynamic Property Models
10 8
OMEGA x -0.5 2.0 —
0 x -5.0 5.0 —
PRESSURE
0 x — — TEMPERATURE
0 x — — TEMPERATURE
RKSKBV/4 T k,lower 0 x — — TEMPERATURE
RKSKBV/5 T k,upper 1000 x — — TEMPERATURE
RKSLBV/1 l ij (1)
RKSLBV/2 l ij (2)
RKSLBV/3 l ij (3)
0 x — — —
0 x — — TEMPERATURE
0 x — — TEMPERATURE
RKSLBV/4 T l,lower 0 x — — TEMPERATURE
RKSLBV/5 T l,upper 1000 x — — TEMPERATURE
References
G. Soave, "Equilibrium Constants for Modified Redlich-Kwong Equation-ofstate,"
Chem. Eng. Sci., Vol. 27, (1972), pp. 1196 – 1203.
Redlich-Kwong-Soave-Wong-Sandler
This equation-of-state model uses the Redlich-Kwong-Soave equation-of-state
for pure compounds. The predictive Wong-Sandler mixing rules are used.
Several alpha functions can be used in the Redlich-Kwong-Soave-Wong-
Sandler equation-of-state model for a more accurate description of the pure
component behavior. The pure component behavior and parameter
requirements are described in Standard Redlich-Kwong-Soave, and in Soave
Alpha Functions.
Note: You can choose any of the available alpha functions, but you cannot
define multiple property methods based on this model using different alpha
functions within the same run.
The Wong-Sandler mixing rules are an example of modified Huron-Vidal
mixing rules. A brief introduction is provided in Huron-Vidal Mixing Rules. For
more details, see Wong-Sandler Mixing Rules.

Redlich-Kwong-Soave-MHV2
This equation-of-state model uses the Redlich-Kwong-Soave equation-of-state
for pure compounds. The predictive MHV2 mixing rules are used. Several
alpha functions can be used in the RK-Soave-MHV2 equation-of-state model
for a more accurate description of the pure component behavior. The pure
component behavior and its parameter requirements are described in
Standard Redlich-Kwong-Soave, and in Soave Alpha Functions.
Note: You can choose any of the available alpha functions, but you cannot
define multiple property methods based on this model using different alpha
functions within the same run.
The MHV2 mixing rules are an example of modified Huron-Vidal mixing rules.
A brief introduction is provided in Huron-Vidal Mixing Rules. For more details,
see MHV2 Mixing Rules.
Schwartzentruber-Renon
The Schwartzentruber-Renon equation-of-state is the basis for the SR-POLAR
property method. It can be used to model chemically nonideal systems with
the same accuracy as activity coefficient property methods, such as the
WILSON property method. This equation-of-state is recommended for highly
non-ideal systems at high temperatures and pressures, such as in methanol
synthesis and supercritical extraction applications.
The equation for the model is:
p =
Where:
a =
b =
c =
ai
bi
ci
ka,ij
lij
=
=
=
=
=
2 Thermodynamic Property Models 57
(for T < Tci)

kb,ij
=
ka,ij = ka,ji
lij = -lji
kb,ij = kb,ji
The binary parameters ka,ij, kb,ij, and lij are temperature-dependent. In most
cases, ka,ij 0 and lij 0 are sufficient to represent the system of interest.
VLE calculations are independent of c. However, c does influence the fugacity
values and can be adjusted to (liquid) molar volumes. For a wide temperature
range, adjust ci0 to the molar volume at 298.15K or at boiling temperature.
The ai are calculated using the Extended Mathias Alpha Function, as described
in Soave Alpha Functions.
Warning: Using c1i and c2i can cause anomalous behavior in enthalpy and
heat capacity. Their use is strongly discouraged.
Parameter
Name/Element
58 2 Thermodynamic Property Models
Symbol Default MDS Lower
Limit
Upper
Limit
Units
TCRKU T ci TC x 5.0 2000.0 TEMPERATURE
PCRKU p ci PC x 105 108 PRESSURE
OMGRKU � i
OMEGA x -0.5 2.0 —
RKUPP0 †† q 0i — x — — —
RKUPP1 †† q 1i 0 x — — —
RKUPP2 †† q 2i 0 x — — —
RKUC0 c 0i 0 x — — ‡
RKUC1 c 1i 0 x — — ‡
RKUC2 c 2i 0 x — — ‡
RKUKA0 ††† k a,ij 0
RKUKA1 ††† k a,ij 1
RKUKA2 ††† k a,ij 2
RKULA0 ††† l ij 0
RKULA1 ††† l ij 1
RKULA2 ††† l ij 2
RKUKB0 ††† k b,ij 0
RKUKB1 ††† k b,ij 1
RKUKB2 ††† k b,ij 2
0 x — — —
0 x — — TEMPERATURE
0 x — — TEMPERATURE †
0 x — — —
0 x — — TEMPERATURE
0 x — — TEMPERATURE †
0 x — — —
0 x — — TEMPERATURE
0 x — — TEMPERATURE †
† Absolute temperature units are assumed for ka,ij 2 , lij 2 , and kb,ij 2 .
†† For polar components (dipole moment >> 0), if you do not enter q0i, the
system estimates q0i, q1i, q2i from vapor pressures using the Antoine vapor
pressure model.
††† If you do not enter at least one of the binary parameters ka,ij 0 , ka,ij 2 , lij 0 ,
lij 2 , kb,ij 0 , or kb,ij 2 the system estimates ka,ij 0 , ka,ij 2 , lij 0 , and lij 2 from the UNIFAC
or Hayden O'Connell models.

‡ RKUC0, RKUC1, and RKUC2 are treated as having units m 3 /kmol. No unit
conversion to other molar volume units is done.
References
G. Soave, "Equilibrium Constants for Modified Redlich-Kwong Equation-ofstate,"
Chem. Eng. Sci., Vol. 27, (1972), pp. 1196 - 1203.
J. Schwartzentruber and H. Renon, "Extension of UNIFAC to High Pressures
and Temperatures by the Use of a Cubic Equation-of-State," Ind. Eng. Chem.
Res., Vol. 28, (1989), pp. 1049 – 1955.
A. Peneloux, E. Rauzy, and R. Freze, "A Consistent Correction For Redlich-
Kwong-Soave Volumes", Fluid Phase Eq., Vol. 8, (1982), pp. 7–23.
Soave-Redlich-Kwong
The Soave-Redlich-Kwong equation-of-state is the basis of the SRK property
method. This model is based on the same equation of state as the Redlich-
Kwong-Soave model. However, this model has several important differences.
� A volume translation concept introduced by Peneloux and Rauzy is used to
improve molar liquid volume calculated from the cubic equation of state.
� Improvement in water properties is achieved by using the NBS Steam
Table.
� Improvement in speed of computation for equation based calculation is
achieved by using composition independent fugacity.
� Optional Kabadi-Danner mixing rules for improved phase equilibrium
calculations in water-hydrocarbon systems (see SRK-Kabadi-Danner)
� Optional Mathias alpha function
Note: You can choose any of the available alpha functions, but you cannot
define multiple property methods based on this model using different alpha
functions within the same run.
This equation-of-state can be used for hydrocarbon systems that include the
common light gases, such as H2S, CO2 and N2.
The form of the equation-of-state is:
Where:
a0 is the standard quadratic mixing term:
Where:
2 Thermodynamic Property Models 59
;

a1 is an additional, asymmetric (polar) term:
Where:
; ;
The enthalpy, entropy, Gibbs energy, and molar volume of water are
calculated from the steam tables. The total properties are mole-fraction
averages of these values with the properties calculated by the equation of
state for other components. Fugacity coefficient is not affected.
For best results, the binary parameter kij must be determined from phase
equilibrium data regression (for example, VLE data). The Aspen Physical
Property System also has built-in kij for a large number of component pairs in
the SRK-ASPEN databank, regressed by AspenTech. These parameters are
used automatically with the SRK property method. Values of kij in the
databank can be different than those used with other models such as
Standard Redlich-Kwong-Soave or Standard Redlich-Kwong-Soave, and this
can produce different results.
The model uses option codes which are described in Soave-Redlich-Kwong
Option Codes.
Parameter Symbol Default MDS Lower
Name/
Element
Limit
60 2 Thermodynamic Property Models
Upper
Limit
Units
SRKTC T ci TC x 5.0 2000.0 TEMPERATURE
SRKPC p ci PC x 10 5
SRKOMG � i
10 8
OMEGA x –0.5 2.0 —
SRKZRA z RA RKTZRA x — — —
SRKKIJ/1 k ij (1)
SRKKIJ/2 k ij (2)
SRKKIJ/3 k ij (3)
0 x — — —
PRESSURE
0 x — — TEMPERATURE
0 x — — TEMPERATURE
SRKKIJ/4 T lower 0 x — — TEMPERATURE
SRKKIJ/5 T upper 1000 x — — TEMPERATURE
SRKLIJ/1 l ij (1)
SRKLIJ/2 l ij (2)
0 x — — —
0 x — — TEMPERATURE

Parameter
Name/
Element
SRKLIJ/3 l ij (3)
Symbol Default MDS Lower
Limit
2 Thermodynamic Property Models 61
Upper
Limit
Units
0 x — — TEMPERATURE
SRKLIJ/4 T lower 0 x — — TEMPERATURE
SRKLIJ/5 T upper 1000 x — — TEMPERATURE
References
G. Soave, "Equilibrium Constants for Modified Redlich-Kwong Equation-ofstate,"
Chem. Eng. Sci., Vol. 27, (1972), pp. 1196 - 1203.
A. Peneloux, E. Rauzy, and R. Freze, "A Consistent Correction For Redlich-
Kwong-Soave Volumes", Fluid Phase Eq., Vol. 8, (1982), pp. 7–23.
P.M. Mathias, H.C. Klotz, and J.M. Prausnitz, "Equation of state mixing rules
for multicomponent mixtures: the problem of invariance," Fluid Phase
Equilibria, Vol 67, (1991), pp. 31-44.
SRK-Kabadi-Danner
The SRK-Kabadi-Danner property model uses the SRK equation-of-state with
improved phase equilibrium calculations for mixtures containing water and
hydrocarbons. These improvements are achieved by using the Kabadi-Danner
mixing rules.
The form of the equation-of-state is:
Where:
a0 is the standard quadratic mixing term:
Where:
;
The best values of kwj (w = water) were obtained from experimental data.
Results are given for seven homologous series.
Best Fit Values of kwj for Different Homologous Series
with Water
Homologous series k wj
Alkanes 0.500
Alkenes 0.393
Dialkenes 0.311

Homologous series k wj
Acetylenes 0.348
Naphthenes 0.445
Cycloalkenes 0.355
Aromatics 0.315
aKD is the Kabadi-Danner term for water:
Where:
Gi is the sum of the group contributions of different groups which make up a
molecule of hydrocarbon i.
gl is the group contribution parameter for groups constituting hydrocarbons.
Groups Constituting Hydrocarbons and Their Group
Contribution Parameters
Group l g l , atm m 6 x 10 5
CH4 1.3580
– CH3 0.9822
– CH2 – 1.0780
> CH – 0.9728
> C < 0.8687
– CH2 – (cyclic) 0.7488
> CH – (cyclic) 0.7352
– CH = CH – (cyclic) † 0.6180
CH2 = CH2 1.7940
CH2 = CH – 1.3450
CH2 = C< 0.9066
CH � CH 1.6870
CH � C – 1.1811
– CH = 0.5117
> C = (aromatic) 0.3902
† This value is obtained from very little data. Might not be reliable.
The model uses option codes which are described in Soave-Redlich-Kwong
Option Codes.
SRK-Kabadi-Danner uses the same parameters as SRK, with added
interaction parameters. Do not specify values for the SRKLIJ parameters
when using SRK-KD.
62 2 Thermodynamic Property Models

Parameter
Name/
Element
Symbol Default MDS Lower
Limit
2 Thermodynamic Property Models 63
Upper
Limit
Units
SRKTC T ci TC x 5.0 2000.0 TEMPERATURE
SRKPC p ci PC x 10 5
10 8
SRKOMG � i OMEGA x –0.5 2.0 —
SRKWF G i 0 x — — —
SRKZRA z RA RKTZRA x — — —
SRKKIJ/1 k ij (1)
SRKKIJ/2 k ij (2)
SRKKIJ/3 k ij (3)
0 x — — —
PRESSURE
0 x — — TEMPERATURE
0 x — — TEMPERATURE
SRKKIJ/4 T lower 0 x — — TEMPERATURE
SRKKIJ/5 T upper 0 x — — TEMPERATURE
References
V. Kabadi and R. P. Danner, "A Modified Soave-Redlich-Kwong Equation of
State for Water-Hydrocarbon Phase Equilibria", Ind. Eng. Chem. Process Des.
Dev., Vol. 24, No. 3, (1985), pp. 537-541.
SRK-ML
The SRK-ML property model is the same as the Soave-Redlich-Kwong model
with two exceptions:
� kij does not equal kji for non-ideal systems; they are unsymmetric, and a
different set of parameters is used, as shown below.
� The lij are calculated from the equation lij = kji - kij
Parameter
Name/
Element
Symbol Default MDS Lower
Limit
Upper
Limit
Units
SMLTC T ci TC x 5.0 2000.0 TEMPERATURE
SMLPC p ci PC x 10 5
SMLOMG � i
10 8
OMEGA x –0.5 2.0 —
SMLZRA z RA RKTZRA x — — —
SMLCMP — 0 x — — —
SRKMLP — † x -2.0 2.0 †
SRKGLP — † x — — †
SMLKIJ/1 k ij (1)
SMLKIJ/2 k ij (2)
SMLKIJ/3 k ij (3)
0 x — — —
PRESSURE
0 x — — TEMPERATURE
0 x — — TEMPERATURE
SMLKIJ/4 T lower 0 x — — TEMPERATURE
SMLKIJ/5 T upper 1000 x — — TEMPERATURE

Additional Parameters
SMLZRA is used in Peneloux-Rauzy volume translation as described in Soave-
Redlich-Kwong. This volume translation feature can be enabled by setting
option code 4 to 1, but is disabled by default (in which case this parameter is
not used).
SMLCMP is the Composition Independent Fugacity Calculation Flag. You can
use this flag to indicate the component for which its fugacity coefficient in the
mixture will be calculated such that it is independent of composition. The
calculated fugacity coefficient of that component is simply the purecomponent
fugacity coefficient. This is a simplification. Enter a value of 1 for
the element i to indicate that the fugacity coefficient of component i is
independent of composition. This parameter defaults to zero.
SRKMLP is a polar parameter for the Mathias alpha function.
SRKGLP is a vector of parameters for the Gibbons-Laughton alpha function.
VPA/IK-CAPE Equation-of-State
The VPA/IK-CAPE equation of state is similar to the HF equation of state but
allows dimerization, tetramerization and hexamerization to occur
simultaneously. The main assumption of the model is that only molecular
association causes the gas phase nonideality. Attractive forces between the
molecules and the complexes are neglected.
There are three kinds of associations, which can be modeled:
� Dimerization (examples: formic acid, acetic acid)
� Tetramerization (example: acetic acid)
� Hexamerization (example: hydrogen fluoride)
To get the largest possible flexibility of the model all these kinds of
association can occur simultaneously, for example, in a mixture containing
acetic acid and HF. Up to five components can associate, and any number of
inert components are allowed. This is the only difference between this model
and the HF equation of state, which account only the hexamerization of HF.
Symbols
In the following description, these symbols are used:
yi = Apparent concentration
zin = True concentration, for component i and degree of
association n=1, 2, 4, 6
zMij = True concentration of cross-dimers of components i
and j, for i,j 1 to 5.
p0 = Reference pressure
k = Number of components
64 2 Thermodynamic Property Models

Association Equilibria
Every association equilibrium reaction
is described by the equilibrium constants
By setting
their temperature dependence can be reproduced.
To evaluate the true concentration of every complex zin, the following
nonlinear systems of equations are to be solved:
Total mass balance:
The sum of true concentrations is unity.
Mass balance for every component i>1:
The ratio of the monomers of each component i>1 and component i=1
occurring in the various complexes must be equal to the ratio of their
apparent concentrations.
Thus, a system of k nonlinear equations for k unknowns zi1 has been
developed. After having solved it, all the zin and zMij can be determined using
2 Thermodynamic Property Models 65
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)

equations (3, 4). This is the main step to evaluate all the properties needed
for a calculation.
Specific Volume of the Gas Phase
The compressibility factor is defined by the ratio between the number of
complexes and the number of monomers in the complexes.
The compressibility factor itself is
Fugacity Coefficient
66 2 Thermodynamic Property Models
(9)
(10)
As is well-known from thermodynamics, the fugacity coefficient can be
calculated by
Isothermal Enthalpy Departure
(11)
According to the ASPEN enthalpy model, an equation of state must supply an
expression to compute the isothermal molar enthalpy departure between zero
pressure and actual pressure. In the following section this enthalpy
contribution per mole monomers is abbreviated by �ha.
Taking this sort of gas phase non-ideality into account, the specific enthalpy
per mole can be written as
with
(12)
(13)
to evaluate �ha, a mixture consisting of N monomers integrated in the
complexes is considered. The quota of monomers i being integrated in a
complex of degree n is given by

and
respectively. For the reactions mentioned above:
the enthalpies of reaction are
as the van't Hoff equation
holds for this case.
2 Thermodynamic Property Models 67
(14)
(16)
(1)
(2)
(17)
(18)
(19)
For each monomer being integrated in a complex of degree n, its contribution
to the enthalpy departure is �hin / n or �hMij / 2, respectively. Hence, �ha can
easily be derived by
(20)
Isothermal entropy and Gibbs energy departure:
A similar expression for �ga should hold as it does for the enthalpy departure
(eq. 20):
(21)

using
and
68 2 Thermodynamic Property Models
(22)
(23)
(24)
Using the association model, more different species occur than can be
distinguished. Thus, the equivalent expression for the entropy of mixing
should be written with the true concentrations. As eq. 24 refers to 1 mole
monomers, the expression should be weighted by the compressibility factor
representing the true number of moles. The new expression is
For �ga we obtain
and, analogously,
Parameter
Name/Element
Symbol Default MDS Lower
Limit
(25)
(26)
(27)
Upper
Limit
DMER/1 A i2 0 X – – –
Units
DMER/2 B i2 0 X – – TEMPERATURE
TMER/1 A i4 0 X – – –
TMER/2 B i4 0 X – – TEMPERATURE
HMER/1 A i6 0 X – – –
HMER/2 B i6 0 X – – TEMPERATURE
References
M. M. Abbott and H. C. van Ness, "Thermodynamics of Solutions Containing
Reactive Species, a Guide to Fundamentals and Applications," Fluid Phase Eq.,
Vol. 77, (1992) pp. 53–119.
V. V. De Leeuw and S. Watanasiri, "Modeling Phase Equilibria and Enthalpies
of the System Water and Hydrofluoric Acid Using an HF Equation-of-state in
Conjunction with the Electrolyte NRTL Activity Coefficient Model," Paper
Presented at the 13th European Seminar on Applied Thermodynamics, June
9–12, Carry-le-Rouet, France, 1993.

R. W. Long, J. H. Hildebrand, and W. E. Morrell, "The Polymerization of
Gaseous Hydrogen and Deuterium Fluorides," J. Am. Chem. Soc., Vol. 65,
(1943), pp. 182–187.
C. E. Vanderzee and W. Wm. Rodenburg, "Gas Imperfections and
Thermodynamic Excess Properties of Gaseous Hydrogen Fluoride," J. Chem.
Thermodynamics, Vol. 2, (1970), pp. 461–478.
Peng-Robinson Alpha Functions
The pure component parameters for the Peng-Robinson equation-of-state are
calculated as follows:
These expressions are derived by applying the critical constraints to the
equation-of-state under these conditions:
The parameter � is a temperature function. It was originally introduced by
Soave in the Redlich-Kwong equation-of-state. This parameter improves the
correlation of the pure component vapor pressure.
Note: You can choose any of the alpha functions described here, but you
cannot define multiple property methods based on this model using different
alpha functions within the same run.
This approach was also adopted by Peng and Robinson:
Equation 3 is still represented. The parameter mi can be correlated with the
acentric factor:
Equations 1 through 5 are the standard Peng-Robinson formulation. The
Peng-Robinson alpha function is adequate for hydrocarbons and other
nonpolar compounds, but is not sufficiently accurate for polar compounds.
Note: Reduced temperature Tr is always calculated using absolute
temperature units.
Parameter Symbol Default MDS Lower Upper Units
Name/Element
Limit Limit
TCPR T ci TC X 5.0 2000.0 TEMPERATURE
PCPR p ci PC X 10 5
OMGPR � i
2 Thermodynamic Property Models 69
10 8
(1)
(2)
(3)
(4)
(5)
OMEGA X -0.5 2.0 —
PRESSURE

Boston-Mathias Extrapolation
For light gases at high reduced temperatures (> 5), equation 4 gives
unrealistic results. The boundary conditions are that attraction between
molecules should vanish for extremely high temperatures, and � reduces
asymptotically to zero. Boston and Mathias derived an alternative function for
temperatures higher than critical:
With
=
=
Where mi is computed by equation 5, and equation 4 is used for subcritical
temperatures. Additional parameters are not needed.
Extended Gibbons-Laughton Alpha Function
The extended Gibbons-Laughton alpha function is suitable for use with both
polar and nonpolar components. It has the flexibility to fit the vapor pressure
of most substances from the triple point to the critical point.
Where Tr is the reduced temperature; Xi, Yi and Zi are substance dependent
parameters.
This function is equivalent to the standard Peng-Robinson alpha function if
Parameter
Name/Element
70 2 Thermodynamic Property Models
Symbol Default MDS Lower
Limit
(6)
Upper
Limit
PRGLP/1 X — X — — —
PRGLP/2 Y 0 X — — —
PRGLP/3 Z 0 X — — —
PRGLP/4 n 2 X — — —
Units
PRGLP/5 T lower 0 X — — TEMPERATURE
PRGLP/6 T upper 1000 X — — TEMPERATURE
Twu Generalized Alpha Function
The Twu generalized alpha function is a theoretically-based function that is
currently recognized as the best available alpha function. It behaves better
than other functions at supercritical conditions (T > Tc) and when the acentric
factor is large. The improved behavior at high values of acentric factor is
important for high molecular weight pseudocomponents. There is no limit on
the minimum value of acentric factor that can be used with this function.

Where the L, M, and N are parameters that vary depending on the equation of
state and whether the temperature is above or below the critical temperature
of the component.
For Peng-Robinson equation of state:
Subcritical T Supercritical T
L (0)
M (0)
N (0)
L (1)
M (1)
N (1)
Twu Alpha Function
0.272838 0.373949
0.924779 4.73020
1.19764 -0.200000
0.625701 0.0239035
0.792014 1.24615
2.46022 -8.000000
The Twu alpha function is a theoretically-based function that is currently
recognized as the best available alpha function. It behaves better than other
functions at supercritical conditions (T > Tc).
Where the L, M, and N are substance-dependent parameters that must be
determined from regression of pure-component vapor pressure data or other
data such as liquid heat capacity.
Parameter
Name/Element
2 Thermodynamic Property Models 71
Symbol Default MDS Lower
Limit
Upper
Limit
PRTWUP/1 L — X — — —
PRTWUP/2 M 0 X — — —
PRTWUP/3 N 0 X — — —
Mathias-Copeman Alpha Function
Units
This is an extension of the Peng-Robinson alpha function which provides a
more accurate fit of vapor pressure for polar compounds.
For c2,i = 0 and c3,i = 0, this expression reduces to the standard Peng-
Robinson formulation if c2,i = mi. You can use vapor pressure data if the
temperature is subcritical to regress the constants. If the temperature is
supercritical, c2,i and c3,i are set to 0.
Parameter
Name/Element
Symbol Default MDS Lower
Limit
(7)
Upper
Limit
Units
TCPR T ci TC X 5.0 2000.0 TEMPERATURE
PCPR p ci PC X 10 5
10 8
PRESSURE

Parameter
Name/Element
72 2 Thermodynamic Property Models
Symbol Default MDS Lower
Limit
Upper
Limit
PRMCP/1 c 1,i — X — — —
PRMCP/2 c 2,i 0 X — — —
PRMCP/3 c 3,i 0 X — — —
Units
Schwartzentruber-Renon-Watanasiri Alpha Function
The Schwartzentruber-Renon-Watanasiri alpha function is:
Where mi is computed by equation 5. The polar parameters p1,i, p2,i and p3,i
are comparable with the c parameters of the Mathias-Copeman expression.
Equation 8 reduces to the standard Peng-Robinson formulation if the polar
parameters are zero. Equation 8 is used only for below-critical temperatures.
For above-critical temperatures, the Boston-Mathias extrapolation is used.
Use equation 6 with:
Parameter
Name/Element
Symbol Default MDS Lower
Limit
(8)
(9)
(10)
Upper
Limit
Units
TCPR T ci TC X 5.0 2000.0 TEMPERATURE
PCPR p ci PC X 10 5
OMGPR � i
10 8
OMEGA X -0.5 2.0 —
PRSRP/1 — X — — —
PRSRP/2 0 X — — —
PRSRP/3 0 X — — —
Use of Alpha Functions
PRESSURE
The alpha functions in Peng-Robinson-based equation-of-state models is
provided in the following table. You can verify and change the value of
possible option codes on the Properties | Property Methods | Model form.
Alpha function Model name First Option code
Standard Peng Robinson ESPRSTD0, ESPRSTD 1
Standard PR/
Boston-Mathias
Extended Gibbons-
Laughton
Twu Generalized alpha
function
ESPR0, ESPR
ESPRWS0, ESPRWS
ESPRV20, ESPRV2
0
0
0
ESPR0, ESPR 2
ESPR0, ESPR 3
Twu alpha function ESPR0, ESPR 4

Alpha function Model name First Option code
Mathias-Copeman ESPRWS0, ESPRWS
ESPRV20, ESPRV2
Schwartzentruber-
Renon-
Watanasiri
References
2 Thermodynamic Property Models 73
ESPRWS0, ESPRWS
ESPRV20, ESPRV2
2
2
3 (default)
3 (default)
J. F. Boston and P.M. Mathias, "Phase Equilibria in a Third-Generation Process
Simulator" in Proceedings of the 2nd International Conference on Phase
Equilibria and Fluid Properties in the Chemical Process Industries, West Berlin,
(17-21 March 1980) pp. 823-849.
D.-Y. Peng and D.B. Robinson, "A New Two-Constant Equation-of-state," Ind.
Eng. Chem. Fundam., Vol. 15, (1976), pp. 59-64.
P.M. Mathias and T.W. Copeman, "Extension of the Peng-Robinson Equationof-state
To Complex Mixtures: Evaluation of the Various Forms of the Local
Composition Concept",Fluid Phase Eq., Vol. 13, (1983), p. 91.
J. Schwartzentruber, H. Renon, and S. Watanasiri, "K-values for Non-Ideal
Systems:An Easier Way," Chem. Eng., March 1990, pp. 118-124.
G. Soave, "Equilibrium Constants for a Modified Redlich-Kwong Equation-ofstate,"
Chem Eng. Sci., Vol. 27, (1972), pp. 1196-1203.
C.H. Twu, J. E. Coon, and J.R. Cunningham, "A New Cubic Equation of State,"
Fluid Phase Equilib., Vol. 75, (1992), pp. 65-79.
C.H. Twu, D. Bluck, J.R. Cunningham, and J.E. Coon, "A Cubic Equation of
State with a New Alpha Function and a New Mixing Rule," Fluid Phase Equilib.,
Vol. 69, (1991), pp. 33-50.
Soave Alpha Functions
The pure component parameters for the Redlich-Kwong equation-of-state are
calculated as:
These expressions are derived by applying the critical constraint to the
equation-of-state under these conditions:
Note: You can choose any of the alpha functions described here, but you
cannot define multiple property methods based on this model using different
alpha functions within the same run.
In the Redlich-Kwong equation-of-state, alpha is:
(1)
(2)
(3)

Note: Reduced temperature Tr is always calculated using absolute
temperature units.
Parameter Symbol Default MDS Lower Upper Units
Name/Element
Limit Limit
TC T ci — — 5.0 2000.0 TEMPERATURE
PC p ci — — 10 5
Soave Modification
74 2 Thermodynamic Property Models
10 8
(4)
PRESSURE
The parameter �i is a temperature function introduced by Soave in the
Redlich-Kwong equation-of-state to improve the correlation of the pure
component vapor pressure:
Equation 3 still holds. The parameter mi can be correlated with the acentric
factor:
Equations 1, 2, 3, 5 and 6 are the standard Redlich-Kwong-Soave
formulation. The Soave alpha function is adequate for hydrocarbons and other
nonpolar compounds, but is not sufficiently accurate for polar compounds.
Parameter
Name/Element
Symbol Default MDS Lower
Limit
(5)
(6)
Upper
Limit
Units
TCRKS T ci TC X 5.0 2000.0 TEMPERATURE
PCRKS p ci PC X 10 5
OMGRKS � i OMEGA X -0.5 2.0 —
Boston-Mathias Extrapolation
10 8
PRESSURE
For light gases at high reduced temperatures (> 5), equation 5 gives
unrealistic results. The boundary conditions are that attraction between
molecules should vanish for extremely high temperatures, and reduces
asymptotically to zero. Boston and Mathias derived an alternative function for
temperatures higher than critical:
With
di
ci
=
=
Where:
(7)

mi = Computed by equation 6
Equation 5 = Used for subcritical temperatures
Additional parameters are not needed.
Mathias Alpha Function
This is an extension of the Soave alpha function which provides a more
accurate fit of vapor pressure for polar compounds.
For �i=0, equation 8 reduces to the standard Redlich-Kwong-Soave
formulation, equations 5 and 6. For temperatures above critical, the Boston-
Mathias extrapolation is used, that is, equation 7 with:
2 Thermodynamic Property Models 75
(8)
(9)
(10)
The Mathias alpha function is used in the Redlich-Kwong-Aspen model, which
is the basis for the RK-ASPEN property method. This alpha function is also
available as an option for SRK, SRKKD, SRK-ML, RK-SOAVE, and RKS-BM.
See Soave-Redlich-Kwong Option Codes for more information.
Parameter
Name/Element
Symbol Default MDS Lower
Limit
Upper
Limit
Units
TCRKA T ci TC X 5.0 2000.0 TEMPERATURE
PCRKA p ci PC X 10 5
OMGRKA � i OMEGA X -0.5 2.0 —
† � i — X -2.0 2.0 —
10 8
PRESSURE
† RKAPOL for Redlich-Kwong-Aspen, SRKPOL for SRK and SRKKD, SRKMLP for
SRK-ML, RKSPOL for RKS-BM, or RKSSPO for RK-SOAVE.
Extended Mathias Alpha Function
An extension of the Mathias approach is:
(11)
Where mi is computed by equation 6. If the polar parameters p1,i, p2,i and p3,i
are zero, equation 11 reduces to the standard Redlich-Kwong-Soave
formulation. You can use vapor pressure data to regress the constants if the
temperature is subcritical. Equation 11 is used only for temperatures below
critical.
The Boston-Mathias extrapolation is used for temperatures above critical, that
is, with:
(12)

76 2 Thermodynamic Property Models
(13)
This alpha function is used in the Redlich-Kwong-UNIFAC model which is the
basis for the SR-POLAR property method.
Parameter Symbol Default MDS Lower Upper Units
Name/Element
Limit Limit
TCRKU T ci TC X 5.0 2000.0 TEMPERATURE
PCRKU p ci PC X 10 5
OMGRKU � i OMEGA X -0.5 2.0 —
RKUPP0 p 1,i — X — — —
RKUPP1 p 2,i 0 X — — —
RKUPP2 p 3,i 0 X — — —
Mathias-Copeman Alpha Function
10 8
PRESSURE
The Mathias-Copeman alpha function is suitable for use with both polar and
nonpolar components. It has the flexibility to fit the vapor pressure of most
substances from the triple point to the critical point.
(14)
For c2,i=0 and c3,i=0 this expression reduces to the standard Redlich-Kwong-
Soave formulation if c1,i=mi. If the temperature is subcritical, use vapor
pressure data to regress the constants. If the temperature is supercritical, set
c2,i and c3,i to 0.
Parameter
Name/Element
Symbol Default MDS Lower
Limit
Upper
Limit
Units
TCRKS T ci TC X 5.0 2000.0 TEMPERATURE
PCRKS p ci PC X 10 5
RKSMCP/1 c 1,i — X — — —
RKSMCP/2 c 2,i 0 X — — —
RKSMCP/3 c 3,i 0 X — — —
10 8
PRESSURE
Schwartzentruber-Renon-Watanasiri Alpha Function
The Schwartzentruber-Renon-Watanasiri alpha function is:
(15)
Where mi is computed by equation 6 and the polar parameters p1,i, p2,i and
p3,i are comparable with the c parameters of the Mathias-Copeman
expression. Equation 15 reduces to the standard Redlich-Kwong-Soave
formulation if the polar parameters are zero. Equation 15 is very similar to
the extended Mathias equation, but it is easier to use in data regression. It is
used only for temperatures below critical. The Boston-Mathias extrapolation is
used for temperatures above critical, that is, use equation 7 with:
(16)

Parameter
Name/Element
2 Thermodynamic Property Models 77
Symbol Default MDS Lower
Limit
(17)
Upper
Limit
Units
TCRKS T ci TC X 5.0 2000.0 TEMPERATURE
PCRKS p ci PC X 10 5
OMGRKS � i OMEGA X -0.5 2.0 —
RKSSRP/1 p 1,i — X — — —
RKSSRP/2 p 2,i 0 X — — —
RKSSRP/3 p 3,i 0 X — — —
10 8
Extended Gibbons-Laughton Alpha Function
PRESSURE
The extended Gibbons-Laughton alpha function is suitable for use with both
polar and nonpolar components. It has the flexibility to fit the vapor pressure
of most substances from the triple point to the critical point.
Where Tr is the reduced temperature; Xi, Yi and Zi are substance dependent
parameters.
This function is equivalent to the standard Soave alpha function if
This function is not intended for use in supercritical conditions. To avoid
predicting negative alpha, when Tri>1 the Boston-Mathias alpha function is
used instead.
Parameter
Name/Element
Symbol Default MDS Lower
Limit
Upper
Limit
SRKGLP/1 X — X — — —
SRKGLP/2 Y 0 X — — —
SRKGLP/3 Z 0 X — — —
SRKGLP/4 n 2 X — — —
Units
SRKGLP/5 T lower 0 X — — TEMPERATURE
SRKGLP/6 T upper 1000 X — — TEMPERATURE
Twu Generalized Alpha Function
The Twu generalized alpha function is a theoretically-based function that is
currently recognized as the best available alpha function. It behaves better
than other functions at supercritical conditions (T > Tc) and when the acentric
factor is large. The improved behavior at high values of acentric factor is
important for high molecular weight pseudocomponents. There is no limit on
the minimum value of acentric factor that can be used with this function.

Where the L, M, and N are parameters that vary depending on the equation of
state and whether the temperature is above or below the critical temperature
of the component.
For Soave-Redlich-Kwong:
Subcritical T Supercritical T
L (0)
M (0)
N (0)
L (1)
M (1)
N (1)
0.544000 0.379919
1.01309 5.67342
0.935995 -0.200000
0.544306 0.0319134
0.802404 1.28756
3.10835 -8.000000
Use of Alpha Functions
The use of alpha functions in Soave-Redlich-Kwong based equation-of-state
models is given in the following table. You can verify and change the value of
possible option codes on the Properties | Property Methods | Models
sheet.
Alpha Function Model Name First Option Code
original RK ESRK0, ESRK —
standard RKS ESRKSTD0, ESRKSTD
*
standard RKS/Boston-Mathias *
ESRKSWS0, ESRKSWS
ESRKSV10, ESRKV1
ESRKSV20, ESRKSV2
Mathias/Boston-Mathias ESRKA0, ESRKA —
Extended Mathias/Boston-
Mathias
78 2 Thermodynamic Property Models
—
1, 2 (default)
0
1
1
1
ESRKU0, ESRKU —
Mathias-Copeman ESRKSV10, ESRKSV1
ESRKSV20, ESRKSV2
Schwartzentruber-Renon-
Watanasiri
ESPRWS0, ESPRWS
ESRKSV10, ESRKSV1
ESRKSV20, ESRKSV2
Twu generalized * 5
Gibbons-Laughton with Patel
extension
Mathias for T < Tc; Boston-
Mathias for T > Tc
2
2
* 3
* 4
3 (default)
3 (default)
3 (default)
* ESRKSTD0, ESRKSTD, ESRKS0, ESRKS, ESSRK, ESSRK0, ESRKSML,
ESRKSML0. The default alpha function (option code 2) for these models is the

standard RKS alpha function, except that the Grabovsky-Daubert alpha
function is used for H2: � = 1.202 exp(-0.30228xTri)
References
J. F. Boston and P.M. Mathias, "Phase Equilibria in a Third-Generation Process
Simulator" in Proceedings of the 2nd International Conference on Phase
Equilibria and Fluid Properties in the Chemical Process Industries, West Berlin,
(17-21 March 1980), pp. 823-849.
P. M. Mathias, "A Versatile Phase Equilibrium Equation-of-state", Ind. Eng.
Chem. Process Des. Dev., Vol. 22, (1983), pp. 385–391.
P.M. Mathias and T.W. Copeman, "Extension of the Peng-Robinson Equationof-state
To Complex Mixtures: Evaluation of the Various Forms of the Local
Composition Concept", Fluid Phase Eq., Vol. 13, (1983), p. 91.
O. Redlich and J. N. S. Kwong, "On the Thermodynamics of Solutions V. An
Equation-of-state. Fugacities of Gaseous Solutions," Chem. Rev., Vol. 44,
(1949), pp. 223–244.
J. Schwartzentruber and H. Renon, "Extension of UNIFAC to High Pressures
and Temperatures by the Use of a Cubic Equation-of-state," Ind. Eng. Chem.
Res., Vol. 28, (1989), pp. 1049–1055.
J. Schwartzentruber, H. Renon, and S. Watanasiri, "K-values for Non-Ideal
Systems:An Easier Way," Chem. Eng., March 1990, pp. 118-124.
G. Soave, "Equilibrium Constants for a Modified Redlich-Kwong Equation-ofstate,"
Chem Eng. Sci., Vol. 27, (1972), pp. 1196-1203.
C.H. Twu, W.D. Sim, and V. Tassone, "Getting a Handle on Advanced Cubic
Equations of State", Chemical Engineering Progress, Vol. 98 #11 (November
2002) pp. 58-65.
Huron-Vidal Mixing Rules
Huron and Vidal (1979) used a simple thermodynamic relationship to equate
the excess Gibbs energy to expressions for the fugacity coefficient as
computed by equations of state:
Equation 1 is valid at any pressure, but cannot be evaluated unless some
assumptions are made. If Equation 1 is evaluated at infinite pressure, the
mixture must be liquid-like and extremely dense. It can be assumed that:
Using equations 2 and 3 in equation 1 results in an expression for a/b that
contains the excess Gibbs energy at an infinite pressure:
2 Thermodynamic Property Models 79
(1)
(2)
(3)
(4)

Where:
The parameters �1and �2depend on the equation-of-state used. In general a
cubic equation-of-state can be written as:
Values for �1and �2 for the Peng-Robinson and the Soave-Redlich-Kwong
equations of state are:
Equation-of-state � 1 � 2
Peng-Robinson
Redlich-Kwong-Soave 1 0
This expression can be used at any pressure as a mixing rule for the
parameter. The mixing rule for b is fixed by equation 3. Even when used at
other pressures, this expression contains the excess Gibbs energy at infinite
pressure. You can use any activity coeffecient model to evaluate the excess
Gibbs energy at infinite pressure. Binary interaction coefficients must be
regressed. The mixing rule used contains as many binary parameters as the
activity coefficient model chosen.
This mixing rule has been used successfully for polar mixtures at high
pressures, such as systems containing light gases. In theory, any activity
coefficient model can be used. But the NRTL equation (as modified by Huron
and Vidal) has demonstrated better performance.
The Huron-Vidal mixing rules combine extreme flexibility with thermodynamic
consistency, unlike many other mole-fraction-dependent equation-of-state
mixing rules. The Huron-Vidal mixing rules do not allow flexibility in the
description of the excess molar volume, but always predict reasonable excess
volumes.
The Huron-Vidal mixing rules are theoretically incorrect for low pressure,
because quadratic mole fraction dependence of the second virial coefficient (if
derived from the equation-of-state) is not preserved. Since equations of state
are primarily used at high pressure, the practical consequences of this
drawback are minimal.
The Gibbs energy at infinite pressure and the Gibbs energy at an arbitrary
high pressure are similar. But the correspondence is not close enough to
make the mixing rule predictive.
There are several methods for modifying the Huron-Vidal mixing rule to make
it more predictive. The following three methods are used in Aspen Physical
Property System equation-of-state models:
� The modified Huron-Vidal mixing rule, second order approximation
(MHV2)
� The Predictive SRK Method (PSRK)
� The Wong-Sandler modified Huron-Vidal mixing rule (WS)
80 2 Thermodynamic Property Models
(5)
(6)

These mixing rules are discussed separately in the following sections. They
have major advantages over other composition-dependent equation-of-state
mixing rules.
References
M.- J. Huron and J. Vidal, "New Mixing Rules in Simple Equations of State for
representing Vapour-liquid equilibria of strongly non-ideal mixtures," Fluid
Phase Eq., Vol. 3, (1979), pp. 255-271.
MHV2 Mixing Rules
Dahl and Michelsen (1990) use a thermodynamic relationship between excess
Gibbs energy and the fugacity computed by equations of state. This
relationship is equivalent to the one used by Huron and Vidal:
The advantage is that the expressions for mixture and pure component
fugacities do not contain the pressure. They are functions of compacity V/b
and �:
Where:
and
With:
The constants �1 and �2, which depend only on the equation-of-state (see
Huron-Vidal Mixing Rules) occur in equations 2 and 4.
Instead of using infinite pressure for simplification of equation 1, the condition
of zero pressure is used. At p = 0 an exact relationship between the
compacity and � can be derived. By substitution the simplified equation q(�)
is obtained, and equation 1 becomes:
2 Thermodynamic Property Models 81
(1)
(2)
(3)
(4)
(5)
(6)

However, q(�) can only be written explicitly for � = 5.8. Only an
approximation is possible below that threshold. Dahl and Michelsen use a
second order polynomial fitted to the analytical solution for 10 < � < 13 that
can be extrapolated to low alpha:
Since q(�)is a universal function (for each equation-of-state), the
combination of equations 6 and 7 form the MHV2 mixing rule. Excess Gibbs
energies, from any activity coefficient model with parameters optimized at
low pressures, can be used to determine �, if �i, bi, and b are known. To
compute b, a linear mixing rule is assumed as in the original Huron-Vidal
mixing rules:
This equation is equivalent to the assumption of zero excess molar volume.
The MHV2 mixing rule was the first successful predictive mixing rule for
equations of state. This mixing rule uses previously determined activity
coefficient parameters for predictions at high pressures. UNIFAC was chosen
as a default for its predictive character. The Lyngby modified UNIFAC
formulation was chosen for optimum performance (see UNIFAC (Lyngby
Modified)). However, any activity coefficient model can be used when its
binary interaction parameters are known.
Like the Huron-Vidal mixing rules, the MHV2 mixing rules are not flexible in
the description of the excess molar volume. The MHV2 mixing rules are
theoretically incorrect at the low pressure limit. But the practical
consequences of this drawback are minimal (see Huron-Vidal Mixing Rules,
this chapter).
Reference: S. Dahl and M.L. Michelsen, "High-Pressure Vapor-Liquid
Equilibrium with a UNIFAC-based Equation-of-state," AIChE J., Vol. 36,
(1990), pp. 1829-1836.
Predictive Soave-Redlich-Kwong-Gmehling
Mixing Rules
These mixing rules by Holderbaum and Gmehling (1991) use a relationship
between the excess Helmholtz energy and equation-of-state. They do not use
a relationship between equation-of-state properties and excess Gibbs energy,
as in the Huron-Vidal mixing rules. The pressure-explicit expression for the
equation-of-state is substituted in the thermodynamic equation:
The Helmholtz energy is calculated by integration. A E is obtained by:
82 2 Thermodynamic Property Models
(7)
(8)
(1)
(2)

Where both Ai* and Am are calculated by using equation 1. Ai* and Am are
written in terms of equation-of-state parameters.
The simplification of constant packing fraction (Vm / b) is used:
With:
Therefore:
The mixing rule is:
Where �' is slightly different from � for the Huron-Vidal mixing rule:
Where �1 and �2, depend on the equation-of-state (see Huron-Vidal Mixing
Rules). If equation 6 is applied at infinite pressure, the packing fraction goes
to 1. The excess Helmholtz energy is equal to the excess Gibbs energy. The
Huron-Vidal mixing rules are recovered.
The goal of these mixing rules is to be able to use binary interaction
parameters for activity coefficient models at any pressure. These parameters
have been optimized at low pressures. UNIFAC is chosen for its predictive
character. Two issues exist: the packing fraction is not equal to one, and the
excess Gibbs and Helmholtz energy are not equal at the low pressure where
the UNIFAC parameters have been derived.
Fischer (1993) determined that boiling point, the average packing fraction for
about 80 different liquids with different chemical natures was 1.1. Adopting
this value, the difference between liquid excess Gibbs energy and liquid
excess Helmholtz energy can be computed as:
The result is a predictive mixing rule for cubic equations of state. But the
original UNIFAC formulation gives the best performance for any binary pair
with interactions available from UNIFAC. Gas-solvent interactions are
unavailable. However, it has poor accuracy for highly asymmetric such as CH4
2 Thermodynamic Property Models 83
(3)
(4)
(5)
(6)
(7)
(8)

– n-C10H22. To address the issue, the Li correction (Li et al., 1998) is
applied.
With the Li correction, the R and Q parameters for groups CH3, CH2, CH, and
C in UNIFAC are modified. R* and Q*, the effective values of R and Q, are
calculated based on the original values and nc, the number of alkyl carbons
(single-bonded carbons in CH3, CH2, CH, and C groups), as follows, for
nc

Like Huron and Vidal, the limiting case of infinite pressure is used. This
simplifies the expressions for Ai* and Am. Equation 2 becomes:
Where � depends on the equation-of-state (see Huron-Vidal Mixing Rules).
Equation 3 is completely analogous to the Huron-Vidal mixing rule for the
excess Gibbs energy at infinite pressure. (See equation 4, Huron-Vidal Mixing
Rules.) The excess Helmholtz energy can be approximated by the excess
Gibbs energy at low pressure from any liquid activity coefficient model. Using
the Helmholtz energy permits another mixing rule for b than the linear mixing
rule. The mixing rule for b is derived as follows. The second virial coefficient
must depend quadratically on the mole fraction:
With:
The relationship between the equation-of-state at low pressure and the virial
coefficient is:
Wong and Sandler discovered the following mixing rule to satisfy equation 4
(using equations 6 and 7):
The excess Helmholtz energy is almost independent of pressure. It can be
approximated by the Gibbs energy at low pressure. The difference between
the two functions is corrected by fitting kij until the excess Gibbs energy from
the equation-of-state (using the mixing rules 3 and 8) is equal to the excess
Gibbs energy computed by an activity coeffecient model. This is done at a
specific mole fraction and temperature.
This mixing rule accurately predicts the VLE of polar mixtures at high
pressures. UNIFAC or other activity coeffecient models and parameters from
the literature are used. Gas solubilities are not predicted. They must be
regressed from experimental data.
Unlike other (modified) Huron-Vidal mixing rules, the Wong and Sandler
mixing rule meets the theoretical limit at low pressure. The use of kij does
2 Thermodynamic Property Models 85
(3)
(4)
(5)
(6)
(7)

influence excess molar volume behavior. For calculations where densities are
important, check whether they are realistic.
References
D. S. Wong and S. I. Sandler, "A Theoretically Correct New Mixing Rule for
Cubic Equations of State for Both Highly and Slightly Non-ideal Mixtures,"
AIChE J., Vol. 38, (1992), pp. 671 – 680.
D. S. Wong, H. Orbey, and S. I. Sandler, "Equation-of-state Mixing Rule for
Non-ideal Mixtures Using Available Activity Coefficient Model Parameters and
That Allows Extrapolation over Large Ranges of Temperature and Pressure",
Ind Eng Chem. Res., Vol. 31, (1992), pp. 2033 – 2039.
H. Orbey, S. I. Sandler and D. S. Wong, "Accurate Equation-of-state
Predictions at High Temperatures and Pressures Using the Existing UNIFAC
Model," Fluid Phase Eq., Vol. 85, (1993), pp. 41 – 54.
Activity Coefficient Models
The Aspen Physical Property System has the following built-in activity
coefficient models. This section describes the activity coefficient models
available.
Model Type
Bromley-Pitzer Electrolyte
Chien-Null Regular solution, local composition
Constant Activity Coefficient Arithmetic
COSMO-SAC Regular solution
Electrolyte NRTL Electrolyte
ENRTL-SAC Segment contribution, electrolyte
Hansen Regular solution
Ideal Liquid Ideal
NRTL (Non-Random-Two-Liquid) Local composition
NRTL-SAC Segment contribution
Pitzer Electrolyte
Polynomial Activity Coefficient Arithmetic
Redlich-Kister Arithmetic
Scatchard-Hildebrand Regular solution
Symmetric Electrolyte NRTL Electrolyte, pure fused salt
reference state for ions
Three-Suffix Margules Arithmetic
UNIFAC Group contribution
UNIFAC (Lyngby modified) Group contribution
UNIFAC (Dortmund modified) Group contribution
UNIQUAC Local composition
Unsymmetric Electrolyte NRTL Electrolyte
Van Laar Regular solution
Wagner interaction parameter Arithmetic
86 2 Thermodynamic Property Models

Model Type
Wilson Local composition
Wilson with Liquid Molar Volume Local composition
Bromley-Pitzer Activity Coefficient Model
The Bromley-Pitzer activity coefficient model is a simplified Pitzer activity
coefficient model with Bromley correlations for the interaction parameters.
See Working Equations for a detailed description. This model has predictive
capabilities. It can be used to compute activity coefficients for aqueous
electrolytes up to 6 molal ionic strength, but is less accurate than the Pitzer
model if the parameter correlations are used. The model should not be used
for mixed-solvent electrolyte systems.
The Bromley-Pitzer model in the Aspen Physical Property System involves
user-supplied parameters, used in the calculation of binary parameters for the
electrolyte system.
Parameters � (0) , � (1) , � (2) , � (3) , and � have five elements to account for
temperature dependencies. Elements P1 through P5 follow the temperature
dependency relation:
Where:
T ref
The user must:
= 298.15K
� Supply these elements using a Properties Parameters Binary T-Dependent
form.
� Specify Comp ID i and Comp ID j on this form, using the same order that
appears on the Components Specifications Selection sheet form.
Parameter Name Symbol No. of Elements Default Units
Ionic Unary Parameters
GMBPB � ion
GMBPD �ion Cation-Anion Parameters
2 Thermodynamic Property Models 87
1 0 —
1 0 —
GMBPB0 � (0) 5 0 —
GMBPB1 � (1) 5 0 —
GMBPB2 � (2) 5 0 —
GMBPB3 � (3) 5 0 —
Cation-Cation Parameters
GMBPTH �cc' Anion-Anion Parameters
5 0 —
GMBPTH �aa' 5 0 —
Molecule-Ion and Molecule-Molecule Parameters
GMBPB0 � (0) 5 0 —

Parameter Name Symbol No. of Elements Default Units
Ionic Unary Parameters
GMBPB1 � (1) 5 0 —
Working Equations
The complete Pitzer equation (Fürst and Renon, 1982) for the excess Gibbs
energy is (see also equation 4):
Where:
G E
88 2 Thermodynamic Property Models
= Excess Gibbs energy
R = Gas constant
T = Temperature
nw = Kilograms of water
zi = Charge number of ion i
Where:
= molality of ion i
xi = Mole fraction of ion i
xw = Mole fraction of water
Mw = Molecular weight of water (g/mol)
ni = Moles of ion i
B, C, � and � are interaction parameters, and f(I) is an electrostatic term as
a function of ionic strength; these terms are discussed in Pitzer Activity
Coefficient Model, which has a detailed discussion of the Pitzer model.
The C term and the � term are dropped from equation 1 to give the
simplified Pitzer equation.
Where:
Bij = f(�ij (0) ,�ij (1) ,�ij (2) ,�ij (3) )
(2)
(1)

Therefore, the simplified Pitzer equation has two types of binary interaction
parameters, � 's and �''s. There are no ternary interaction parameters with
the simplified Pitzer equation.
Note that the Pitzer model parameter databank described in Physical Property
Data, Chapter 1, is not applicable to the simplified Pitzer equation.
A built-in empirical correlation estimates the � (0) and � (1) parameters for
cation-anion pairs from the Bromley ionic parameters, �ion and �ion (Bromley,
1973). The estimated values of � (0) 's and � (1) 's are overridden by the user's
input. For parameter naming and requirements, see Bromley-Pitzer Activity
Coefficient Model.
References
L.A. Bromley, "Thermodynamic Properties of Strong Electrolytes in Aqueous
Solution, " AIChE J., Vol. 19, No. 2, (1973), pp. 313 – 320.
W. Fürst and H. Renon, "Effects of the Various Parameters in the Application
of Pitzer's Model to Solid-Liquid Equilibrium. Preliminary Study for Strong 1-1
Electrolytes," Ind. Eng. Chem. Process Des. Dev., Vol. 21, No. 3, (1982),
pp. 396-400.
Parameter Conversion
For n-m electrolytes, n and m>1 (2-2, 2-3, 3-4, and so on), the parameter
� (3) corresponds to Pitzer's � (1) ; � (2) is the same in both Aspen Physical
Property System and original Pitzer models. Pitzer refers to the n-m
electrolyte parameters as � (1) , � (2) , � (0) . � (0) and � (2) retain their meanings in
both models, but Pitzer's � (1) is Aspen Physical Property System � (3). Be
careful to make this distinction when entering n-m electrolyte parameters.
Chien-Null
The Chien-Null model calculates liquid activity coefficients and it can be used
for highly non-ideal systems. The generalized expression used in its derivation
can be adapted to represent other well known formalisms for the activity
coefficient by properly defining its binary terms. This characteristic allows the
model the use of already available binary parameters regressed for those
other liquid activity models with thermodynamic consistency.
The equation for the Chien-Null liquid activity coeficient is:
Where:
Rji = Aji / Aij
Aii = 0
2 Thermodynamic Property Models 89

Aij = aij + bij / T
Subscripts i and j are component indices.
The choice of model and parameters can be set for each binary pair
constituting the process mixture by assigning the appropriate value to the
ICHNUL parameter.
The Regular Solution and Scatchard-Hamer models are regained by
substituting in the general expression (ICHNUL = 1 or 2).
Vji = Sji = Vj *,l / Vi *,l
Where:
Vj *,l
90 2 Thermodynamic Property Models
= Liquid molar volume of component i
The Chien-Null activity coefficient model collapses to the Margules liquid
activity coefficient expression by setting (ICHNUL = 3):
Vji = Sji = 1
The Van Laar Liquid activity coefficient model is obtained when the V and S
parameters in the Chien-Null models are set to the ratio of the cross terms of
A (ICHNUL = 4:)
Vji = Sji = Aji / Aij
Finally, the Renon or NRTL model is obtained when we make the following
susbstitutions in the Chien-Null expression for the liquid activity (ICHNUL =
5).
Sji = RjiAji / Aij
Aji = 2�jiGji
Vji = Gji
The following are defined for the Non-Random Two-Liquid activity coefficient
model, where:
�ij = aij + bij / T
Cij = cij + dij (T - 273.15 K)
cji = cij
dji = dij
The binary parameters CHNULL/1, CHNULL/2, and CHNULL/3 can be
determined from regression of VLE and/or LLE data. Also, if you have
parameters for many of the mixture pairs for the Margules, Van Laar,
Scatchard-Hildebrand, and NRTL (Non-Random-Two-Liquid) activity models,
you can use them directly with the Chien-Null activity model after selecting
the proper code (ICHNUL) to identify the source model and entering the
appropriate activity model parameters.

Parameter
Name/Element
Symbol Default Lower
Limit
2 Thermodynamic Property Models 91
Upper
Limit
ICHNUL — 3 1 6 —
CHNULL/1 a ij 0 — — —
CHNULL/2 b ij 0 — — —
CHNULL/3 V ij 0 — — —
Units
The parameter ICHNUL is used to identify the activity model parameters
available for each binary pair of interest. The following values are allowed for
ICHNUL:
ICHNUL = 1 or 2, sets the model to the Scatchard-Hamer or regular solution
model for the associated binary;
ICHNUL = 3, sets the model to the Three-Suffix Margules activity model for
the associated binary;
ICHNUL = 4, sets the model to the Van Laar formalism for the activity model
for the associated binary;
ICHNUL = 5, sets the model to the NRTL (Renon) formalism for the activity
model for the associated binary.
ICHNUL = 6, sets the model to the full Chien-Null formalism for the activity
model for the associated binary.
When you specify a value for the ICHNUL parameter that is different than the
default, you must enter the appropriate binary model parameters for the
chosen activity model directly. The routine will automatically convert the
expressions and parameters to conform to the Chien-Null formulation.
Constant Activity Coefficient
This approach is used exclusively in metallurgical applications where multiple
liquid and solid phases can coexist. You can assign any value to the activity
coefficient of component i. Use the Properties Parameters Unary Scalar form.
The equation is:
�i = ai
Parameter
Name/Element
Symbol Default MDS Upper
Limit
Lower
Limit
GMCONS a i 1.0 x — — —
COSMO-SAC
Units
Cosmo-SAC is a solvation model that describes the electric fields on the
molecular surface of species that are polarizable. It requires a fairly
complicated quantum mechanical calculation, but this calculation must be
done only once for a particular molecule; then the results can be stored. In its
final form, it uses individual atoms as the building blocks for predicting phase
equilibria instead of functional groups. This model formulation provides a
considerably larger range of applicability than group-contribution methods.
The calculation for liquid nonideality is only slightly more computationally
intensive than activity-coefficient models such as NRTL or UNIQUAC. Cosmo-

SAC complements the UNIFAC group-contribution method, because it is
applicable to virtually any mixture.
The Cosmo-SAC model calculates liquid activity coefficients. The equation for
the Cosmo-SAC model is:
With
92 2 Thermodynamic Property Models

Where:
�i
2 Thermodynamic Property Models 93
= Activity coefficient of component i
�i SG = Staverman-Guggenheim model for combinatorial
contribution to �i
�i(�m)
�S(�m)
pi(�m)
pi(�m)
�
�W(�m,�n)
�W HB (�m,�n)
= Segment activity coefficient of segment �m in
component i
= Segment activity coefficient of segment �m in
solvent mixture
= Sigma profile of component i
= Sigma profile of solvent mixture
= Surface charge density
= Exchange energy between segments �m and �n
= Hydrogen-bonding contribution to exchange energy
between segments �m and �n
z = Coordination number, 10
Vi
Ai
aeff
Veff
Aeff
�'
= Molecular volume of component i
= Molecular surface area of component i
= Standard segment surface area, 7.50 Å 2
= Standard component volume, 66.69 Å 3
= Standard component surface area, 79.53 Å 2
= Misfit energy constant
The Cosmo-SAC model does not require binary parameters. For each
component, it has six input parameters. CSACVL is the component volume
parameter which is always defined in cubic angstroms, regardless of chosen
units sets. SGPRF1 to SGPRF5 are five component sigma profile parameters;
each can store up to 12 points of sigma profile values. All six input
parameters are obtained from COSMO calculation. The Aspen Physical
Property System includes a database of sigma profiles for over 1400
compounds from Mullins et al. (2006). The parameters were obtained by
permission from the Virginia Tech Sigma Profile Database website
(http://www.design.che.vt.edu/VT-2004.htm). Aspen Technology, Inc. does
not claim proprietary rights to these parameters.
Note: Starting in version V7.2, additional parameters SGPRF6 through
SGPRF9 and SGPR10 through SGPR14 are available in Aspen Plus and
Aspen Properties, as part of a planned expansion to allow larger sigma
profiles to be used. However, the model is not yet updated to use these
parameters and you should not yet try to use sigma profiles larger than 51
elements.

Parameter Symbol Default MDS Lower
Name/Element
Limit
94 2 Thermodynamic Property Models
Upper
Limit
Units
CSACVL V i — x — — VOLUME (Å 3 )
SGPRF1 A i p i(1-12) — x — — —
SGPRF2 A i p i(13-24) — x — — —
SGPRF3 A i p i(25-36) — x — — —
SGPRF4 A i p i(37-48) — x — — —
SGPRF5 A i p i(49-51) — x — — —
Option Codes
The primary version of COSMO-SAC is the model by Lin and Sandler (2002).
Two other versions are available using an option code, as detailed in the table
below:
Option Description
Code
1 COSMO-SAC model by Lin and Sandler (2002)
2 COSMO-RS model by Klamt (1995)
3 Lin and Sandler model with modified exchange energy (Lin
et al., 2002)
References
A. Klamt, "Conductor-like Screening Model for Real Solvents: A New Approach
to the Quantitative Calculation of Solvation Phenomena," J. Phys. Chem. 99,
2224 (1995).
S.-T. Lin, P. M. Mathias, Y. Song, C.-C. Chen, and S. I. Sandler,
"Improvements of Phase-Equilibrium Predictions for Hydrogen-Bonding
Systems from a New Expression for COSMO Solvation Models," presented at
the AIChE Annual Meeting, Indianapolis, IN, 3-8 November (2002).
S.-T. Lin and S. I. Sandler, "A Priori Phase Equilibrium Prediction from a
Segment Contribution Solvation Model," Ind. Eng. Chem. Res. 41, 899
(2002).
E. Mullins, et al. "Sigma-Profile Database for Using COSMO-Based
Thermodynamic Methods," Ind. Eng. Chem. Res. 45, 4389 (2006).
Electrolyte NRTL Activity Coefficient Model
(GMENRTL)
The Electrolyte NRTL activity coefficient model (GMENRTL) is a versatile
model for the calculation of activity coefficients. Using binary and pair
parameters, the model can represent aqueous electrolyte systems as well as
mixed solvent electrolyte systems over the entire range of electrolyte
concentrations. This model can calculate activity coefficients for ionic species
and molecular species in aqueous electrolyte systems as well as in mixed
solvent electrolyte systems. The model reduces to the well-known NRTL
model when electrolyte concentrations become zero (Renon and Prausnitz,
1969).

The electrolyte NRTL model uses the infinite dilution aqueous solution as the
reference state for ions. It adopts the Born equation to account for the
transformation of the reference state of ions from the infinite dilution mixed
solvent solution to the infinite dilution aqueous solution.
Water must be present in the electrolyte system in order to compute the
transformation of the reference state of ions. Thus, it is necessary to
introduce a trace amount of water to use the model for nonaqueous
electrolyte systems.
The Aspen Physical Property System uses the electrolyte NRTL model to
calculate activity coefficients, enthalpies, and Gibbs energies for electrolyte
systems. Model development and working equations are provided in
Theoretical Basis and Working Equations.
The adjustable parameters for the electrolyte NRTL model include the:
� Pure component dielectric constant coefficient of nonaqueous solvents
� Born radius of ionic species
� NRTL parameters for molecule-molecule, molecule-electrolyte, and
electrolyte-electrolyte pairs
The pure component dielectric constant coefficients of nonaqueous solvents
and Born radius of ionic species are required only for mixed-solvent
electrolyte systems. The temperature dependency of the dielectric constant of
solvent B is:
Each type of electrolyte NRTL parameter consists of both the nonrandomness
factor, �, and energy parameters, �. The temperature dependency relations
of the electrolyte NRTL parameters are:
� Molecule-Molecule Binary Parameters:
� Electrolyte-Molecule Pair Parameters:
� Electrolyte-Electrolyte Pair Parameters:
For the electrolyte-electrolyte pair parameters, the two electrolytes must
share either one common cation or one common anion:
2 Thermodynamic Property Models 95

Where:
T ref = 298.15K
Many parameter pairs are included in the electrolyte NRTL model parameter
databank (see Physical Property Data, Chapter 1).
Parameter Symbol No. of Default MDS Units
Name
Elements
Dielectric Constant Unary Parameters
CPDIEC A B 1 — — —
96 2 Thermodynamic Property Models
B B 1 0 — —
C B 1 298.15 — TEMPERATURE †
Ionic Born Radius Unary Parameters
RADIUS r i 1 3x10 -10 — LENGTH
Molecule-Molecule Binary Parameters
NRTL/1 A BB' — 0 x —
A B'B — 0 x —
NRTL/2 B BB' — 0 x TEMPERATURE †
NRTL/3 � BB' = � B'B
B B'B — 0 x TEMPERATURE †
— .3 x —
NRTL/4 — — 0 x TEMPERATURE
NRTL/5 F BB' — 0 x TEMPERATURE
F B'B — 0 x TEMPERATURE
NRTL/6 G BB' — 0 x TEMPERATURE
G B'B — 0 x TEMPERATURE
Electrolyte-Molecule Pair Parameters
GMELCC C ca,B 1 0 x —
C B,ca 1 0 x —
GMELCD D ca,B 1 0 x TEMPERATURE †
D B,ca 1 0 x TEMPERATURE †
GMELCE E ca,B 1 0 x —
GMELCN � ca,B = � B,ca
E B,ca 1 0 x —
Electrolyte-Electrolyte Pair Parameters
1 .2 x —
GMELCC C ca',ca'' 1 0 x —
C ca'',ca' 1 0 x —
C c'a,c''a 1 0 x —
C c''a,c'a 1 0 x —
GMELCD D ca',ca'' 1 0 x TEMPERATURE †
D ca'',ca' 1 0 x TEMPERATURE †
D c'a,c''a 1 0 x TEMPERATURE †
D c''a,c'a 1 0 x TEMPERATURE †
GMELCE E ca',ca'' 1 0 x —

Parameter Symbol No. of
Name
Elements
Dielectric Constant Unary Parameters
2 Thermodynamic Property Models 97
Default MDS Units
E ca'',ca' 1 0 x —
E c'a,c''a 1 0 x —
E c''a,c'a 1 0 x —
GMELCN � ca',ca'' = � ca'',ca' 1 .2 x —
� c'a,c''a = � c''a,c'a 1 .2 x —
† Certain Electrolyte NRTL activity coefficient model parameters are used with
reciprocal temperature terms:
� CPDIEC
� NRTL/2
� GMELCD for electrolyte-electrolyte or electrolyte-molecule pairs
When any of these parameters is specified, absolute temperature units are
used for the calculations in this model.
Reference: H. Renon, and J.M. Prausnitz, "Local Compositions in
Thermodynamic Excess Functions for Liquid Mixtures", AIChE J., Vol. 14, No.
1, (1968), pp. 135-144.
Theoretical Basis and Working Equations
In this section, the theoretical basis of the model is explained and the working
equations are given. The different ways parameters can be obtained are
discussed with references to the databank directories and the Data
Regression System (DRS). The parameter requirements of the model are
given in Electrolyte NRTL Activity Coefficient Model.
Development of the Model
The Electrolyte NRTL model was originally proposed by Chen et al., for
aqueous electrolyte systems. It was later extended to mixed solvent
electrolyte systems (Mock et al., 1984, 1986). The model is based on two
fundamental assumptions:
� The like-ion repulsion assumption: states that the local composition of
cations around cations is zero (and likewise for anions around anions).
This is based on the assumption that the repulsive forces between ions of
like charge are extremely large. This assumption may be justified on the
basis that repulsive forces between ions of the same sign are very strong
for neighboring species. For example, in salt crystal lattices the immediate
neighbors of any central ion are always ions of opposite charge.
� The local electroneutrality assumption: states that the distribution of
cations and anions around a central molecular species is such that the net
local ionic charge is zero. Local electroneutrality has been observed for
interstitial molecules in salt crystals.
Chen proposed an excess Gibbs energy expression which contains two
contributions: one contribution for the long-range ion-ion interactions that
exist beyond the immediate neighborhood of a central ionic species, and the

other related to the local interactions that exist at the immediate
neighborhood of any central species.
The unsymmetric Pitzer-Debye-Hückel model and the Born equation are used
to represent the contribution of the long-range ion-ion interactions, and the
Non-Random Two Liquid (NRTL) theory is used to represent the local
interactions. The local interaction contribution model is developed as a
symmetric model, based on reference states of pure solvent and pure
completely dissociated liquid electrolyte. The model is then normalized by
infinite dilution activity coefficients in order to obtain an unsymmetric model.
This NRTL expression for the local interactions, the Pitzer-Debye-Hückel
expression, and the Born equation are added to give equation 1 for the
excess Gibbs energy (see the following note).
This leads to
Note: The notation using * to denote an unsymmetric reference state is wellaccepted
in electrolyte thermodynamics and will be maintained here. The
reader should be warned not to confuse it with the meaning of * in classical
thermodynamics according to IUPAC/ISO, referring to a pure component
property. In fact in the context of G or �, the asterisk as superscript is never
used to denote pure component property, so the risk of confusion is minimal.
For details on notation, see Chapter 1 of Physical Property Methods.
References
C.-C. Chen, H.I. Britt, J.F. Boston, and L.B. Evans, "Local Compositions Model
for Excess Gibbs Energy of Electrolyte Systems: Part I: Single Solvent, Single
Completely Dissociated Electrolyte Systems:, AIChE J., Vol. 28, No. 4, (1982),
p. 588-596.
C.-C. Chen, and L.B. Evans, "A Local Composition Model for the Excess Gibbs
Energy of Aqueous Electrolyte Systems," AIChE J., Vol. 32, No. 3, (1986), p.
444-459.
B. Mock, L.B. Evans, and C.-C. Chen, "Phase Equilibria in Multiple-Solvent
Electrolyte Systems: A New Thermodynamic Model," Proceedings of the 1984
Summer Computer Simulation Conference, p. 558.
B. Mock, L.B. Evans, and C.-C. Chen, "Thermodynamic Representation of
Phase Equilibria of Mixed-Solvent Electrolyte Systems," AIChE J., Vol. 32, No.
10, (1986), p. 1655-1664.
Long-Range Interaction Contribution
The Pitzer-Debye-Hückel formula, normalized to mole fractions of unity for
solvent and zero for electrolytes, is used to represent the long-range
interaction contribution.
98 2 Thermodynamic Property Models
(1)
(2)

with
Where:
xi = Mole fraction of component i
Ms = Molecular weight of the solvent
A� = Debye-Hückel parameter
NA = Avogadro's number
ds = Mass density of solvent
Qe = Electron charge
�s = Dielectric constant of the solvent
T = Temperature
k = Boltzmann constant
Ix = Ionic strength (mole fraction scale)
xi = Mole fraction of component i
zi = Charge number of ion i
� = "Closest approach" parameter
Taking the appropriate derivative of equation 3, an expression for the activity
coefficient can then be derived.
The Born equation is used to account for the Gibbs energy of transfer of ionic
species from the infinite dilution state in a mixed-solvent to the infinite
dilution state in aqueous phase.
Where:
�w = Dielectric constant of water
ri = Born radius of the ionic species i
2 Thermodynamic Property Models 99
(3)
(4)
(5)
(6)
(7)

The expression for the activity coefficient can be derived from (7):
The Debye-Hückel theory is based on the infinite dilution reference state for
ionic species in the actual solvent media. For systems with water as the only
solvent, the reference state is the infinite dilution aqueous solution. For
mixed-solvent systems, the reference state for which the Debye-Hückel
theory remains valid is the infinite dilution solution with the corresponding
mixed-solvent composition. However, the molecular weight Ms, the mass
density ds, and the dielectric constant �s for the single solvent need to be
extended for mixed solvents; simple composition average mixing rules are
adequate to calculate them as follows:
Where:
100 2 Thermodynamic Property Models
(8)
(6a)
(7a)
(8a)
(8b)
(8c)
(8d)
xm = Mole fraction of the solvent m in the solution
Mm = Molecular weight of the solvent m
Vm l
= Molar volume of the solvent mixture
�m = Dielectric constant of the solvent m
Vw *
= Molar volume of water using the steam table
xnws = Sum of the mole fractions of all non-water
solvents.
Vnws l
= Liquid molar volume for the mixture of all nonwater
solvents. It is calculated using the
Rackett equation.

It should be understood that equations 6a-8a should be used only in
equations 3, 4, and 7. Ms, ds, and �s were already assumed as constants when
deriving equations 6 and 8 for mixed-solvent systems.
Local Interaction Contribution
The local interaction contribution is accounted for by the Non-Random Two
Liquid theory. The basic assumption of the NRTL model is that the nonideal
entropy of mixing is negligible compared to the heat of mixing: this is indeed
the case for electrolyte systems. This model was adopted because of its
algebraic simplicity and its applicability to mixtures that exhibit liquid phase
splitting. The model does not require specific volume or area data.
The effective local mole fractions Xji and Xii of species j and i, respectively, in
the neighborhood of i are related by:
Where:
Xj = xjCj
Gji
�ji
2 Thermodynamic Property Models 101
=
=
(9)
(Cj = zj for ions and Cj = unity for molecules)
�ji = Nonrandomness factor
gji and gii are energies of interaction between species j and i, and i and i,
respectively. Both gij and �ij are inherently symmetric (gij = gji and �ij = �ji).
Similarly,
Where:
Gji,ki
�ji,ki
=
=
�ji,ki = Nonrandomness factor
Apparent Binary Systems
(10)
The derivations that follow are based on a simple system of one completely
dissociated liquid electrolyte ca and one solvent B. They will be later extended

to multicomponent systems. In this simple system, three different
arrangements exist:
In the case of a central solvent molecule with other solvent molecules,
cations, and anions in its immediate neighborhood, the principle of local
electroneutrality is followed: the surrounding cations and anions are such that
the neighborhood of the solvent is electrically neutral. In the case of a central
cation (anion) with solvent molecules and anions (cations) in its immediate
neighborhood, the principle of like-ion repulsion is followed: no ions of like
charge exist anywhere near each other, whereas opposite charged ions are
very close to each other.
The effective local mole fractions are related by the following expressions:
(central solvent cells)
(central cation cells)
(central anion cells)
102 2 Thermodynamic Property Models
(11)
(12)
(13)
Using equation 11 through 13 and the notation introduced in equations 9 and
10 above, expressions for the effective local mole fractions in terms of the
overall mole fractions can be derived.
i = c, a, or B
(14)
(15)
(16)
To obtain an expression for the excess Gibbs energy, let the residual Gibbs
energies, per mole of cells of central cation, anion, or solvent, respectively, be
, , and . These are then related to the
effective local mole fractions:
(17)
(18)
(19)

The reference Gibbs energy is determined for the reference states of
completely dissociated liquid electrolyte and of pure solvent. The reference
Gibbs energies per mole are then:
Where:
zc = Charge number on cations
za = Charge number on anions
2 Thermodynamic Property Models 103
(20)
(21)
(22)
The molar excess Gibbs energy can be found by summing all changes in
residual Gibbs energy per mole that result when the electrolyte and solvent in
their reference state are mixed to form the existing electrolyte system. The
expression is:
(23)
Using the previous relation for the excess Gibbs energy and the expressions
for the residual and reference Gibbs energy (equations 17 to 19 and 20 to
22), the following expression for the excess Gibbs energy is obtained:
(24)
The assumption of local electroneutrality applied to cells with central solvent
molecules may be stated as:
Combining this expression with the expression for the effective local mole
fractions given in equations 9 and 10, the following equality is obtained:
(25)
(26)
The following relationships are further assumed for nonrandomness factors:
and,
It can be inferred from equations 9, 10, and 26 to 29 that:
(27)
(28)
(29)
(30)
(31)

The binary parameters �ca,B , �ca,B and �B,ca are now the adjustable parameters
for an apparent binary system of a single electrolyte and a single solvent.
The excess Gibbs energy expression (equation 24) must now be normalized
to the infinite dilution reference state for ions:
This leads to:
By taking the appropriate derivatives of equation 33, expressions for the
activity coefficients of all three species can be determined.
Multicomponent Systems
The Electrolyte NRTL model can be extended to handle multicomponent
systems.
The excess Gibbs energy expression is:
104 2 Thermodynamic Property Models
(32)
(33)
(34)
(35)
(36)

Where:
j and k can be any species (a, C, or B)
The activity coefficient equation for molecular components is given by:
The activity coefficient equation for cations is given by:
The activity coefficient equation for anions is given by:
Where:
2 Thermodynamic Property Models 105
(39)
(40)
(37)
(38)

106 2 Thermodynamic Property Models
(41)
(42)
(43)
(44)
(45)
(46)
(47)
(48)
It should be understood that and remained constant in
equation 37 when deriving the activity coefficients given by equations 38-40.
Parameters
The model adjustable parameters include:
� Pure component dielectric constant coefficient of nonaqueous solvents
� Born radius of ionic species
� NRTL interaction parameters for molecule-molecule, molecule-electrolyte,
and electrolyte-electrolyte pairs
Note that for the electrolyte-electrolyte pair parameters, the two electrolytes
must share either one common cation or one common anion.
Each type of the electrolyte NRTL parameter consists of both the
nonrandomness factor, �, and energy parameters, �.

The pure component dielectric constant coefficients of nonaqueous solvents
and Born radius of ionic species are required only for mixed-solvent
electrolyte systems.
The temperature dependency relations of these parameters are given in
Electrolyte NRTL Activity Coefficient Model.
Heat of mixing is calculated from temperature derivatives of activity
coefficients. Heat capacity is calculated from secondary temperature
derivative of the activity coefficient. As a result, the temperature dependent
parameters are critical for modeling enthalpy correctly. It is recommended
that enthalpy data and heat capacity data be used to obtain these
temperature dependency parameters. See also Electrolyte NRTL Enthalpy and
Electrolyte NRTL Gibbs Energy.
Obtaining Parameters
In the absence of electrolytes, the electrolyte NRTL model reduces to the
NRTL equation which is widely used for non-electrolyte systems. Therefore,
molecule-molecule binary parameters can be obtained from binary
nonelectrolyte systems.
Electrolyte-molecule pair parameters can be obtained from data regression of
apparent single electrolyte systems.
Electrolyte-electrolyte pair parameters are required only for mixed
electrolytes with a common ion. Electrolyte-electrolyte pair parameters can
affect trace ionic activity precipitation. Electrolyte-electrolyte pair parameters
can be obtained by regressing solubility data of multiple component
electrolyte systems.
When the electrolyte-molecule and electrolyte-electrolyte pair parameters are
zero, the electrolyte NRTL model reduces to the Debye-Hückel limiting law.
Calculation results with electrolyte-molecule and electrolyte-electrolyte pair
parameters fixed to zero should be adequate for very dilute weak electrolyte
systems; however, for concentrated systems, pair parameters are required
for accurate representation.
See Physical Property Data, Chapter 1, for the pair parameters available from
the electrolyte NRTL model databank. The table contains pair parameters for
some electrolytes in aqueous solution at 100�C. These values were obtained
by using the Aspen Physical Property Data Regression System (DRS) to
regress vapor pressure and mole fraction data at T=100�C with SYSOP15S
(Handbook of Chemistry and Physics, 56th Edition, CRC Press, 1975, p. E-1).
In running the DRS, standard deviations for the temperature (�C), vapor
pressure (mmHg), and mole fractions were set at 0.2, 1.0, and 0.001,
respectively. In addition, complete dissociation of the electrolyte was
assumed for all cases.
Option Codes for Electrolyte NRTL Activity
Coefficient Model (GMENRTL)
The electrolyte NRTL activity coefficient model (GMENRTL) has three option
codes and the option codes can affect the performance of this model.
2 Thermodynamic Property Models 107

Option code 1. Use this option code to specify the default values of pair
parameters for water/solute and solvent/solute; the solute represents a
cation/anion pair. The value (1) sets the default values to zero and the value
(3) sets the default values for water/solute to (8,-4) and for solvent/solute to
(10,-2). The value (3) is the default choice of the option code.
Option code 2. Not used.
Option code 3. Always leave this option code set to the value (1) to use the
solvent/solvent binary parameters obtained from NRTL parameters.
ENRTL-SAC
eNRTL-SAC (ENRTLSAC, patent pending) is an extension of the nonrandom
two-liquid segment activity coefficient model (NRTL-SAC, patent pending) by
Chen and Song (Ind. Eng. Chem. Res., 2004, 43, 8354) to include
electrolytes in the solution. It can be used in usable in Aspen Properties and
Aspen Polymers. It is intended for the computation of ionic activity
coefficients and solubilities of electrolytes, organic and inorganic, in common
solvents and solvent mixtures. In addition to the three types of molecular
parameters defined for organic nonelectrolytes in NRTL-SAC (hydrophobicity
X, hydrophilicity Z, and polarity Y- and Y+), an electrolyte parameter, E, is
introduced to characterize both local and long-range ion-ion and ion-molecule
interactions attributed to ionized segments of electrolytes.
In applying the segment contribution concept to electrolytes, a new
conceptual electrolyte segment e corresponding to the electrolyte parameter
E, is introduced. This conceptual segment e would completely dissociate to a
cationic segment (c) and an anionic segment (a), both of unity charge. All
electrolytes, organic or inorganic, symmetric or unsymmetric, univalent or
multivalent, are to be represented with this conceptual uni-univalent
electrolyte segment e together with previously defined hydrophobic segment
x, polar segments y- and y+, and hydrophilic segment z in NRTL-SAC.
A major consideration in the extension of NRTL-SAC for electrolytes is the
treatment of the reference state for activity coefficient calculations. While the
conventional reference state for nonelectrolyte systems is the pure liquid
component, the conventional reference state for electrolytes in solution is the
infinite-dilution aqueous solution and the corresponding activity coefficient is
unsymmetric. The equation for the logarithm of the unsymmetric activity
coefficient of an ionic species is
With
108 2 Thermodynamic Property Models

2 Thermodynamic Property Models 109

Where:
I, J = Component index
i, j, m, c, a = Conceptual segment index
m = Conceptual molecular segment, x, y-, y+, z
c = Conceptual cationic segment
a = Conceptual anionic segment
i, j = m,c,a
�I * = Unsymmetric activity coefficient of an ionic species I
�I *lc = NRTL term
110 2 Thermodynamic Property Models

�I *PDH = Pitzer-Debye-Hückel term
�I *FH = Flory-Huggins term
2 Thermodynamic Property Models 111
= Aqueous-phase infinite-dilution reference state
�i = Activity coefficient of conceptual segment i
rI = Total segment number of component I
xI = Mole fraction of component I
rI,i = Number of conceptual segment i containing in component I
xi = Segment mole fraction of conceptual segment i in mixtures
�ij = NRTL binary non-randomness factor parameter for
conceptual segments
�ij = NRTL binary interaction energy parameter for conceptual
segments
A� = Debye-Hückel parameter
� = Closest approach parameter, 14.9
Ix = Ionic strength (segment mole fraction scale)
= Average solvent molecular weight, g/mol
= Average solvent density, g/cm 3
NA = Avogadro’s number
Qe = Absolute electronic charge
= Average solvent dielectric constant
�w = Water dielectric constant
rc = Born radius of cationic segment
ra = Born radius of anionic segment
NRTL binary parameters for conceptual segments
The NRTL binary parameters between conceptual molecular segments in are
determined by available VLE and LLE data between reference molecules
defined in NRTLSAC.
Segment (1) x x y- y+ x
Segment (2) y- z z z y+
� 12
� 21
� 12 = � 21
1.643 6.547 -2.000 2.000 1.643
1.834 10.949 1.787 1.787 1.834
0.2 0.2 0.3 0.3 0.2
NaCl is used as the reference electrolyte for the conceptual electrolyte
segment e. The NRTL binary parameters between conceptual molecular

segments and the electrolyte segment e are determined from literature data
or preset as follows:
Segment (1) x y- y+ z
Segment (2) e e e e
� 12
� 21
� 12 = � 21
15 12 12 8.885
5 -3 -3 -4.549
0.2 0.2 0.2 0.2
Parameters used in ENRTLSAC
Each component can have up to five parameters, rI,i (i = x, y-, y+, z, e),
although only one or two of these parameters are needed for most solvents
and ionic species in practice. Since conceptual segments apply to all species,
these five parameters are implemented together as a binary parameter,
NRTLXY(I, i) where I represents a component index and i represents a
conceptual segment index.
Option codes
There are three option codes in ENRTLSAC. The first is used to enable or
disable the Flory-Huggins term. The other two are only used internally and
you should not change their values. The Flory-Huggins term is included by
default in eNRTL-SAC model. You can remove this term using the first option
code. The table below lists the values for the first option code.
0 Flory-Huggins term included (default)
Others Flory-Huggins term removed
References
C.-C. Chen and Y. Song, "Solubility Modeling with a Nonrandom Two-Liquid
Segment Activity Coefficient Model," Ind. Eng. Chem. Res. 43, 8354 (2004).
C.-C. Chen and Y. Song, "Extension of Nonrandom Two-Liquid Segment
Activity Coefficient Model for Electrolytes," Ind. Eng. Chem. Res. 44, 8909
(2005).
Hansen
Hansen is a solubility parameter model and is commonly used in the solvent
selection process. It is based on the regular solution theory and Hansen
solubility parameters. This model has no binary parameters and its application
merely follows the empirical guide like dissolves like.
The Hansen model calculates liquid activity coefficients. The equation for the
Hansen model is:
with
112 2 Thermodynamic Property Models

Where:
�i
Vi
= Activity coefficient of component i
= Molar volume of component i
�i d = Hansen solubility parameter of component i for nonpolar
effect
�i p = Hansen solubility parameter of component i for polar effect
�i h = Hansen solubility parameter of component i for hydrogenbonding
effect
�i
xi
= Volume fraction of component i
= Mole fraction of component i
R = Gas constant
T = Temperature
The Hansen model does not require binary parameters. For each component,
it has four input parameters.
Parameter Symbol Default MDS Lower Upper Units
Name/Element
Limit Limit
DELTAD � i d — x — — PRESSURE^0.5
DELTAP � i p — x — — PRESSURE^0.5
DELTAH � i h — x — — PRESSURE^0.5
HANVOL V i — x — — VOLUME
Option codes
The Hansen volume is implemented as an input parameter. If the Hansen
volume is not input by the user it will be calculated by an Aspen Plus internal
method. You can also request the Aspen Plus method using Option Codes in
Aspen Plus Interface. The table below lists the option codes.
First Option Code in Hansen model
0 Hansen volume input by user (default)
2 Thermodynamic Property Models 113

Other values Hansen volume calculated by Aspen Plus
Reference
Frank, T. C.; Downey, J. R.; Gupta, S. K. "Quickly Screen Solvents for
Organic Solids," Chemical Engineering Progress 1999, December, 41.
Hansen, C. M. Hansen Solubility Parameters: A User’s Handbook; CRC Press,
2000.
Ideal Liquid
This model is used in Raoult's law. It represents ideality of the liquid phase.
This model can be used for mixtures of hydrocarbons of similar carbon
number. It can be used as a reference to compare the results of other activity
coefficient models.
The equation is:
ln �i = 0
NRTL (Non-Random Two-Liquid)
The NRTL model calculates liquid activity coefficients for the following
property methods: NRTL, NRTL-2, NRTL-HOC, NRTL-NTH, and NRTL-RK. It is
recommended for highly non-ideal chemical systems, and can be used for VLE
and LLE applications. The model can also be used in the advanced equationof-state
mixing rules, such as Wong-Sandler and MHV2.
The equation for the NRTL model is:
Where:
Gij
�ij
�ij
114 2 Thermodynamic Property Models
=
=
=
�ii = 0
Gii = 1
for Tlower � T � Tupper
aij, bij, eij, and fij are unsymmetrical. That is, aij may not be equal to aji, etc.

Recommended cij Values for Different Types of Mixtures
cij Mixtures
0.30 Nonpolar substances; nonpolar with polar non-associated liquids; small
deviations from ideality
0.20 Saturated hydrocarbons with polar non-associated liquids and systems that
exhibit liquid-liquid immiscibility
0.47 Strongly self-associated substances with nonpolar substances
The binary parameters aij, bij, cij, dij, eij, and fij can be determined from VLE
and/or LLE data regression. The Aspen Physical Property System has a large
number of built-in binary parameters for the NRTL model. The binary
parameters have been regressed using VLE and LLE data from the Dortmund
Databank. The binary parameters for the VLE applications were regressed
using the ideal gas, Redlich-Kwong, and Hayden O'Connell equations of state.
See Physical Property Data, Chapter 1, for details.
Parameter
Name/Element
2 Thermodynamic Property Models 115
Symbol Default MDS Lower
Limit
Upper
Limit
NRTL/1 a ij 0 x -100.0 100.0 —
Units
NRTL/2 b ij 0 x -30000 30000.0 TEMPERATURE
NRTL/3 c ij 0.30 x 0.0 1.0 —
NRTL/4 d ij 0 x -0.02 0.02 TEMPERATURE
NRTL/5 e ij 0 x — — TEMPERATURE
NRTL/6 f ij 0 x — — TEMPERATURE
NRTL/7 T lower 0 x — — TEMPERATURE
NRTL/8 T upper 1000 x — — TEMPERATURE
Note: If any of bij, dij, or eij is non-zero, absolute temperature units are
assumed for bij, dij, eij, and fij. Otherwise, user input units for temperature are
used. The temperature limits are always interpreted in user input units.
The NRTL-2 property method uses data set 2 for NRTL. All other NRTL
methods use data set 1.
References
H. Renon and J.M. Prausnitz, "Local Compositions in Thermodynamic Excess
Functions for Liquid Mixtures," AIChE J., Vol. 14, No. 1, (1968), pp. 135 –
144.
NRTL-SAC Model
NRTL-SAC (patent pending) is a segment contribution activity coefficient
model, derived from the Polymer NRTL model and extended to handle
electrolytes, but usable in Aspen Plus or Aspen Properties without Aspen
Polymers. NRTL-SAC can be used for fast, qualitative estimation of the
solubility of complex organic compounds in common solvents. It can also be
used as a general activity coefficient model in Aspen Plus, Aspen Properties,
and HYSYS.
Conceptually, the model treats the liquid non-ideality of mixtures containing
complex organic molecules (solute) and small molecules (solvent) in terms of
interactions between three pairwise interacting conceptual segments:

hydrophobic segment (x), hydrophilic segment (z), and polar segments (yand
y+). In practice, these conceptual segments become the molecular
descriptors used to represent the molecular surface characteristics of each
solute or solvent molecule. Hexane, water, and acetonitrile are selected as
the reference molecules for the hydrophobic, hydrophilic, and polar segments,
respectively. The molecular parameters for all other solvents can be
determined by regression of available VLE or LLE data for binary systems of
solvent and the reference molecules or their substitutes.
The treatment results in four component-specific molecular parameters:
hydrophobicity X, hydrophilicity Z, and polarity Y- and Y+. The two types of
polar segments, Y- and Y+, are used to reflect the wide variations of
interactions between polar molecules and water.
NRTL-SAC can also be used to model electrolyte systems. In this case, an
electrolyte segment e, corresponding to the electrolyte parameter E, is
introduced. This conceptual segment e completely dissociates to a cationic
segment (c) and an anionic segment (a), both of unit charge. All electrolytes,
organic or inorganic, symmetric or unsymmetric, univalent or multivalent, are
to be represented with this conceptual 1-1 electrolyte segment e together
with the previously defined hydrophobic segment x, polar segments y- and
y+, and hydrophilic segment z in NRTL-SAC. The reference state for ions is by
default an unsymmetric state based on infinite dilution in aqueous solution,
but an option code is available to select the symmetric state of pure fused
salts. When there are no electrolytes present, the segment e is unused and
the current model reduces to the non-electrolyte version of NRTL-SAC present
in earlier releases.
The conceptual segment contribution approach in NRTL-SAC represents a
practical alternative to the UNIFAC functional group contribution approach.
This approach is suitable for use in the industrial practice of carrying out
measurements for a few selected solvents and then using NRTL-SAC to
quickly predict other solvents or solvent mixtures and to generate a list of
suitable solvent systems.
The NRTL-SAC model calculates liquid activity coefficients.
Note: This is the updated version of NRTL-SAC, represented with property
model GMNRTLS and property method NRTL-SAC. This version does not
require the specification of components as oligomers. For the old version, see
NRTLSAC for Segments/Oligomers and ENRTL-SAC.
For the model equations, see NRTL-SAC Model Derivation.
Parameters used in NRTL-SAC
Each component can have up to five parameters, rx,I, ry-,I, ry+,I, rz,I, and re,I,
representing the equivalent number of segments of each type for the NRTL
activity coefficient model. Only one or two of these molecular parameters are
needed for most solvents in practice. These parameters are implemented
together as pure parameter XYZE with five elements representing these five
parameters. Values for this parameter are available for many common
solvents in the NRTL-SAC databank.
116 2 Thermodynamic Property Models

Parameter
Name/
Element
2 Thermodynamic Property Models 117
Symbol Default MDS Lower
Limit
Upper Limit Units
XYZE/1 r x,I — — — — —
XYZE/2 r y-,I — — — — —
XYZE/3 r y+,I — — — — —
XYZE/4 r z,I — — — — —
XYZE/5 r e,I — — — — —
Electrolytes must be modeled as ion pairs in this system, while the individual
ions are components in the Aspen Physical Property System, so for these ion
pairs, the five parameters are stored in binary parameter BXYZE which has
elements corresponding to those of XYZE.
Parameter
Name/
Element
Symbol Default MDS Lower
Limit
Upper Limit Units
BXYZE/1 r x,CA — — — — —
BXYZE/2 r y-,CA — — — — —
BXYZE/3 r y+,CA — — — — —
BXYZE/4 r z,CA — — — — —
BXYZE/5 r e,CA — — — — —
The conceptual segment numbers of a cationic component and
an anionic component come from the dissociation of their
corresponding electrolyte component CA, as defined by the chemical equation
describing the dissociation of the electrolyte:
with
Since an electrolyte component CA can be measured by up to five conceptual
segments , we can calculate ri,C and ri,A as follows for systems of
single electrolyte.
For an electrolyte system where multi-electrolytes may be generated, a
simple mixing rule is used:

where YC is a cationic charge composition fraction and YA is an anionic charge
composition fraction; they are defined as follows:
Notice that electrolyte here is meant to represent an ion-pair composed of a
cationic component and an anionic component in the solutions. The result is
that electrolytes are generated from all possible combinations of ions in the
solution; each generated electrolyte is not necessarily associated with an ionpair
through the dissociation.
Option Codes in NRTL-SAC
Three option codes are available for NRTL-SAC to select the reference state
and to optionally exclude the Flory-Huggins and long-range interaction terms:
Option CodeValue Meaning
1 0 Reference state for ions is unsymmetric: infinite dilution in
aqueous solution (default)
118 2 Thermodynamic Property Models
2 Reference state for ions is symmetric: pure fused salts
2 0 Flory-Huggins term included (default)
1 Flory-Huggins term removed
3 0 Long-range interaction term included (default)
References
1 Long-range interaction term removed
C.-C. Chen and Y. Song, "Extension of Nonrandom Two-Liquid Segment
Activity Coefficient Model for Electrolytes," Ind. Eng. Chem. Res., 2005, 44,
8909.
Y. Song and C.-C. Chen, "Symmetric Nonrandom Two-Liquid Segment Activity
Coefficient Model for Electrolytes," Ind. Eng. Chem. Res., 2009, 48, 5522.

NRTL-SAC Reference States
The NRTL-SAC activity coefficient model for component I is composed of the
local composition term, ln �I lc , the Pitzer-Debye-Hückel long-range interaction
term, ln �I PDH , and the Flory-Huggins term, �I FH :
This equation needs to be normalized based on the reference states of
molecular and ionic components.
Reference state for molecular components
The reference state for a molecular component is defined as follows:
This definition is the so-called standard state of pure liquids for molecular
components and it is also called the symmetric reference state for molecular
components.
Reference state for ionic components
The standard state of pure liquids is hypothetical for ionic components in
electrolyte systems. The symmetric reference state is defined as the pure
fused salt state of each electrolyte component in the system.
However, the conventional reference state for ionic components is the
infinite-dilution activity coefficient in pure water; it is also called the
unsymmetric reference state for ionic components. In NRTL-SAC model, we
will consider both of these reference states; the unsymmetric state is the
default.
Pure fused salt state of an electrolyte component
For an electrolyte component CA, the pure fused salt state can be defined as
follows:
where �± is the mean ionic activity coefficient of the electrolyte component
and is related to the corresponding cationic and anionic activity coefficients �C
and �A by this expression:
where �C is the cationic stoichiometric coefficient and �A is the anionic
stoichiometric coefficient, and �=�C+�A (one mole of salt releases � moles of
ions in solution). They are given by the chemical equation describing the
dissociation of the electrolyte. Therefore Eq. 5 can be written in terms of
charge numbers zC and zA:
2 Thermodynamic Property Models 119
(1)
(2)
(3)
(4)
(5)

At the pure fused salt state:
The symmetric reference state defined by Eq. 3 is restricted to systems
containing a single electrolyte component. For multi-electrolyte systems, the
symmetric reference state can be generalized from Eq. 3 as follows:
120 2 Thermodynamic Property Models
(6)
(7)
(8)
(9)
(10)
where I applies to all molecular components in the system. The symmetric
reference state is a molecular-component-free media.
Infinite-dilution aqueous solution
The condition of infinite-dilution solution for ionic components can be written
as follows:
(11)
This condition applies to all ionic components in the solution. In infinitedilution
aqueous solutions, water must be present and is assumed to
represent the entire solution, so the unsymmetric reference state can be
written as follows:
This equation applies to all ionic components in the solution.
NRTL-SAC Local Composition Term
The segment-based excess Gibbs free energy of the local interactions for
systems with multiple molecular segments m and a single electrolyte segment
e (with a single cation segment c and anion segment a) can be written as
follows:
(12)
(13)
(14)

2 Thermodynamic Property Models 121
(15)
(16)
where I is the component index, i is the segment index, ri,I is the number of
segment i in component I, xI is the mole fraction of component I, xi is the
segment fraction of segment i, and ns is the total number of all segments in
the system.
Since there is only a single 1-1 electrolyte segment, the pair parameters
between a molecular segment and the electrolyte segment can be simplified
as follows:
We can then rewrite the excess Gibbs free energy as follows:
with
(17)
(18)
(19)
(20)
(21)
(22)
The local composition contribution to the segment activity coefficient can be
calculated as follows:
(23)
The local composition contribution to the activity coefficients for molecular
segments, the cationic segment, and the anionic segment can be calculated
out as follows:

The local composition term for the logarithm of the activity coefficient of
component I , before normalization to a chosen reference state, is computed
as the sum of the individual segment contributions.
Specifically, for non-electrolyte (molecular) components, the activity
coefficients are given as follows:
For a cationic component, we have
122 2 Thermodynamic Property Models
(27)
(28)
(24)
(25)
(26)

For an anionic component, we have
Molecular components
2 Thermodynamic Property Models 123
(29)
(30)
Applying Eq. 1, the normalization for molecular components can be done as
follows:
where �m lc,I is the activity coefficient of the molecular segment m contained in
component I,
Ionic components with symmetric reference state
(31)
(32)
Applying Eq. 10, the local composition contribution to the symmetric activity
coefficients for ionic components in multi-electrolyte systems can be
normalized as follows:
where I applies to all molecular components in the solution and Ix 0 is the ionic
strength at the symmetric reference state. In the case that electrolytes are
made up of only the conceptual 1-1 electrolyte segment and none of the
molecular segments, this reference state is equivalent to the molten state of
the conceptual 1-1 electrolyte.
(33)
(34)
(35)
Ionic components with infinite dilution aqueous solution
reference state
Applying Eq. 12, the unsymmetric activity coefficients for ionic components in
aqueous solutions can be normalized as follows:
(36)
(37)

where and are activity coefficients at the infinite dilution aqueous
solution:
NRTL-SAC Long-Range Interaction Term
To account for the long-range ion-ion interactions, the model uses the
symmetric Pitzer-Debye-Hückel (PDH) formula (Pitzer, 1986) on the segment
basis:
with
where ns is the total segment number of the solution, R is the gas constant,
A � is the Debye-Hückel parameter, Ix is the segment-based ionic strength, �
is the closest approach parameter, NA is Avogadro's number, v and � are the
molar volume and dielectric constant of the solvent, Qe is the electron charge,
kB is the Boltzmann constant, zi is the charge number of segment i, and Ix 0
represents Ix at the reference state. Since the "single 1-1 electrolyte segment
e=ca" is defined in the model, we can obtain:
For the symmetric reference state,
And for the unsymmetric reference state,
124 2 Thermodynamic Property Models
(38)
(39)
(40)
(41)
(42)
(43)
(44)
(45)
The long-range contribution to the activity coefficient of segment i can be
derived as follows:
(46)

For a molecular segment, the activity coefficient can be carried out as follows:
2 Thermodynamic Property Models 125
(47)
For the univalent cation or anion segment, the activity coefficient can be
carried out as follows:
(48)
The original Debye-Hückel theory is based on a single electrolyte with water
as the solvent. The molar volume v and the dielectric constant � for the
single solvent water need to be extended for mixed-solvents based on the
molecular solvent properties; a simple composition average mixing rule is
proposed to calculate them as follows:
where S is a solvent component, MS is the solvent molecular weight, and each
sum is over all solvent components in the solution.
The long range interaction term for the logarithm of the activity coefficient of
component I is computed as the sum of the individual segment contributions.
Molecular components
(49)
(50)
(51)
For molecular components, the activity coefficients are given as follows:
(52)
From Eq. 47, it is easy to show that the PDH term activity coefficients for all
molecular components are normalized; that is
where I applies to all molecular components in the system.
(53)

Ionic components with symmetric reference state
Applying Eq. 10, the symmetric activity coefficients for ionic components from
the long range contribution are given as follows:
where I applies to all molecular components in the solution.
126 2 Thermodynamic Property Models
(54)
(55)
(56)
Ionic components with infinite dilution aqueous solution
Applying Eq. 12, the unsymmetric activity coefficients for ionic components
from the long range contribution in aqueous solutions are given as follows:
Segment based Born correction term to activity coefficient
(57)
(58)
If the infinite dilution aqueous solution is chosen as the reference state, we
need to correct the change of the reference state from the mixed-solvent
composition to aqueous solution for the Debye-Hückel term. The Born term
(Robinson and Stokes, 1970; Rashin and Honig, 1985) is used for this
purpose:
where ri is the Born radius of segment species i and �w is the dielectric
constant of water. �G Born is the Born term correction to the unsymmetric
Pitzer-Debye-Hückel formula G ex,PDH .
The Born correction activity coefficient of component i can be derived as
follows:
(60)
For a molecular segment, the correction to the activity coefficient is zero:
(61)
For the univalent cation or anion segment, the activity coefficient can be
carried out as follows:
(59)

Specifically,
The long range interaction term for the logarithm of the activity coefficient of
component I is computed as the sum of the individual segment contributions.
Activity coefficients given by Eq. 65 are already normalized for molecular
components as well as for ionic components with the infinite-dilution aqueous
solution reference state.
References
Pitzer, K.S., J.M. Simonson, "Thermodynamics of Multicomponent, Miscible,
Ionic Systems: Theory and Equations," J. Phys. Chem., 1986, 90, 3005-3009.
2 Thermodynamic Property Models 127
(62)
(63)
(64)
(65)
Robinson, R.A., Stokes, R.H., Electrolyte Solutions, 2nd revised edition,
Dover, 1970.
Rashig, A.A., Honig, B., "Reevaluation of the Born Model of Ion Hydration," J.
Phys. Chem., 1985, 89, 5588.
NRTL-SAC Flory-Huggins Term
We use the Flory-Huggins term to describe the combinatorial term:
(66)
(67)
where G ex,FH is the Flory-Huggins term for the excess Gibbs energy, �I is the
segment fraction of component I, and rI is the number of all conceptual
segments in component I:
(68)
(69)

The contribution to the activity coefficient of component I from the
combinatorial term is thus:
Molecular components
It is easy to show that activity coefficients for molecular components from the
Flory-Huggins term are normalized; that is
where I applies to all molecular components in the solution.
Ionic components with symmetric reference state
Applying Eq. 10, the symmetric activity coefficients for ionic components from
the Flory-Huggins term can be carried out as follows:
with
where I applies to all molecular components in the solution.
128 2 Thermodynamic Property Models
(70)
(71)
(72)
(73)
(74)
(75)
(76)
(77)
Ionic components with infinite dilution aqueous solution
Applying Eq. 12, the unsymmetric activity coefficients for ionic components in
aqueous solutions can be carried out as follows:
(78)
(79)

where and are activity coefficients at the infinite dilution
aqueous solution:
Henry Components in NRTL-SAC
Light gases (i.e. Henry components) are usually supercritical at the
temperature and pressure of the system. In that case pure component vapor
pressure is meaningless and therefore the pure liquid state at the
temperature and pressure of the system cannot serve as the reference state.
The reference state for a Henry component is redefined to be at infinite
dilution (that is, xI�0) and at the temperature and pressure of the system.
2 Thermodynamic Property Models 129
(80)
(81)
The liquid phase reference fugacity, fI *,l , becomes the Henry’s constant for
Henry components in the solution, HI, and the activity coefficient, �I, is
converted to the infinite dilution reference state through the relationship:
where is the infinite dilution activity coefficient of Henry component I
(xI�0) in the solution. By this definition �I* approaches unity as
xI approaches zero. The phase equilibrium relationship for Henry components
becomes:
(82)
(83)
The Henry’s Law is available in all activity coefficient property methods. The
model calculates the Henry’s constant for a dissolved gas component in all
solvent components in the mixture:
(84)
(85)
where HIS and are the Henry’s constant and the infinite dilution activity
coefficient of the dissolved gas component i in the solvent component S
(xI�0 and xS�1, respectively).
Since ionic species exist only in the liquid phase and therefore do not
participate directly in vapor-liquid equilibria, the activities of Henry

components are mainly through the local interactions with solvents. We can
calculate all three activity coefficients for Henry components as follows:
with
Notice that xH�0 applies to all Henry components in the solution.
NRTLSAC for Segments/Oligomers
130 2 Thermodynamic Property Models
(86)
(87)
(88)
(89)
(90)
(91)
(92)
(93)
(94)
This is the original NRTLSAC model added in version 2006, which requires
that components be defined as oligomers. It is retained for compatibility, but
new models should use the NRTL-SAC model.
NRTL-SAC (patent pending) is a segment contribution activity coefficient
model, derived from the Polymer NRTL model, usable in Aspen Properties and
Aspen Polymers. NRTL-SAC can be used for fast, qualitative estimation of the
solubility of complex organic compounds in common solvents. Conceptually,
the model treats the liquid non-ideality of mixtures containing complex
organic molecules (solute) and small molecules (solvent) in terms of
interactions between three pairwise interacting conceptual segments:
hydrophobic segment (x), hydrophilic segment (z), and polar segments (yand
y+). In practice, these conceptual segments become the molecular
descriptors used to represent the molecular surface characteristics of each
solute or solvent molecule. Hexane, water, and acetonitrile are selected as
the reference molecules for the hydrophobic, hydrophilic, and polar segments,
respectively. The molecular parameters for all other solvents can be
determined by regression of available VLE or LLE data for binary systems of
solvent and the reference molecules or their substitutes. The treatment
results in four component-specific molecular parameters: hydrophobicity X,
hydrophilicity Z, and polarity Y- and Y+. The two types of polar segments, Y-

and Y+, are used to reflect the wide variations of interactions between polar
molecules and water.
The conceptual segment contribution approach in NRTL-SAC represents a
practical alternative to the UNIFAC functional group contribution approach.
This approach is suitable for use in the industrial practice of carrying out
measurements for a few selected solvents and then using NRTL-SAC to
quickly predict other solvents or solvent mixtures and to generate a list of
suitable solvent systems.
The NRTL-SAC model calculates liquid activity coefficients.
The equation for the NRTL-SAC model is:
with
G = exp(-��)
Where:
2 Thermodynamic Property Models 131

I, J = Component index
i, j, m = Conceptual segment indexx, y-, y+, z
�I = Activity coefficient of component I
�I C = �I FH = Flory-Huggins term for combinatorial contribution to �I
�I R = �I lc = NRTL term for local composition interaction contribution to
132 2 Thermodynamic Property Models
�I
�I = Segment mole fraction of component I
pI = Effective component size parameter
sI and �I = Empirical parameters for pI
rI = Total segment number of component I
xI = Mole fraction of component I
rI,m = Number of conceptual segment m containing in component
I
xi = Segment mole fraction of conceptual segment i in mixtures
�im = NRTL binary non-randomness factor parameter for
conceptual segments
�im = NRTL binary interaction energy parameter for conceptual
segments
NRTL binary parameters for conceptual segments
The NRTL binary parameters between conceptual segments in NRTLSAC are
determined by available VLE and LLE data between reference molecules
defined above.
Segment 1 x x y- y+ x
Segment 2 y- z z z y+
� 12
� 21
� 12 = � 21
1.643 6.547 -2.000 2.000 1.643
1.834 10.949 1.787 1.787 1.834
0.2 0.2 0.3 0.3 0.2
Parameters used in NRTLSAC
Each component can have up to four parameters, rI,x, rI,y-, rI,y+, and rI,z
although only one or two of these molecular parameters are needed for most
solvents in practice. Since conceptual segments apply to all molecules, these
four molecular parameters are implemented together as a binary parameter,
NRTLXY(I, m) where I represents a component (molecule) index and m
represents a conceptual segment index.
In addition, the Flory-Huggins size parameter, FHSIZE , is used in NRTLSAC
to calculate the effective component size parameter, pI. The Flory-Huggins
combinatorial term can be turned off by setting �I = 0 for each component in
mixtures.

Parameter
Name/
Element
Symbol Default MDS Lower
Limit
2 Thermodynamic Property Models 133
Upper
Limit
Units Comment
NRTLXY r I,m — — — — — Binary,
symmetric
FHSIZE/1 s I 1.0 — 1E-15 1E15 — Unary
FHSIZE/2 � I
Option codes
1.0 — -1E10 1E10 — Unary
The Flory-Huggins term is included by default in the NRTLSAC model. You can
remove this term using the first option code. The table below lists the values
for this option code.
0 Flory-Huggins term included (default)
Others Flory-Huggins term removed
NRTLSAC molecular parameters for common solvents
The molecular parameters are identified for 62 solvents and published.
Solvent name r I,x r I,y- r I,y+ r I,z
ACETIC-ACID 0.045 0.164 0.157 0.217
ACETONE 0.131 0.109 0.513
ACETONITRILE 0.018 0.131 0.883
ANISOLE 0.722
BENZENE 0.607 0.190
1-BUTANOL 0.414 0.007 0.485
2-BUTANOL 0.335 0.082 0.355
N-BUTYL-ACETATE 0.317 0.030 0.330
METHYL-TERT-BUTYL-ETHER 1.040 0.219 0.172
CARBON-TETRACHLORIDE 0.718 0.141
CHLOROBENZENE 0.710 0.424
CHLOROFORM 0.278 0.039
CUMENE 1.208 0.541
CYCLOHEXANE 0.892
1,2-DICHLOROETHANE 0.394 0.691
1,1-DICHLOROETHYLENE 0.529 0.208
1,2-DICHLOROETHYLENE 0.188 0.832
DICHLOROMETHANE 0.321 1.262
1,2-DIMETHOXYETHANE 0.081 0.194 0.858
N,N-DIMETHYLACETAMIDE 0.067 0.030 0.157
N,N-DIMETHYLFORMAMIDE 0.073 0.564 0.372
DIMETHYL-SULFOXIDE 0.532 2.890
1,4-DIOXANE 0.154 0.086 0.401
ETHANOL 0.256 0.081 0.507

Solvent name r I,x r I,y- r I,y+ r I,z
2-ETHOXYETHANOL 0.071 0.318 0.237
ETHYL-ACETATE 0.322 0.049 0.421
ETHYLENE-GLYCOL 0.141 0.338
DIETHYL-ETHER 0.448 0.041 0.165
ETHYL-FORMATE 0.257 0.280
FORMAMIDE 0.089 0.341 0.252
FORMIC-ACID 0.707 2.470
N-HEPTANE 1.340
N-HEXANE 1.000
ISOBUTYL-ACETATE 1.660 0.108
ISOPROPYL-ACETATE 0.552 0.154 0.498
METHANOL 0.088 0.149 0.027 0.562
2-METHOXYETHANOL 0.052 0.043 0.251 0.560
METHYL-ACETATE 0.236 0.337
3-METHYL-1-BUTANOL 0.419 0.538 0.314
METHYL-BUTYL-KETONE 0.673 0.224 0.469
METHYLCYCLOHEXANE 1.162 0.251
METHYL-ETHYL-KETONE 0.247 0.036 0.480
METHYL-ISOBUTYL-KETONE 0.673 0.224 0.469
ISOBUTANOL 0.566 0.067 0.485
N-METHYL-2-PYRROLIDONE 0.197 0.322 0.305
NITROMETHANE 0.025 1.216
N-PENTANE 0.898
1-PENTANOL 0.474 0.223 0.426 0.248
1-PROPANOL 0.375 0.030 0.511
ISOPROPYL-ALCOHOL 0.351 0.070 0.003 0.353
N-PROPYL-ACETATE 0.514 0.134 0.587
PYRIDINE 0.205 0.135 0.174
SULFOLANE 0.210 0.457
TETRAHYDROFURAN 0.235 0.040 0.320
1,2,3,4-TETRAHYDRONAPHTHALENE 0.443 0.555
TOLUENE 0.604 0.304
1,1,1-TRICHLOROETHANE 0.548 0.287
TRICHLOROETHYLENE 0.426 0.285
M-XYLENE 0.758 0.021 0.316
WATER 1.000
TRIETHYLAMINE 0.557 0.105
1-OCTANOL 0.766 0.032 0.624 0.335
134 2 Thermodynamic Property Models

Reference
C.-C. Chen and Y. Song, "Solubility Modeling with a Nonrandom Two-Liquid
Segment Activity Coefficient Model," Ind. Eng. Chem. Res. 43, 8354 (2004).
Using NRTLSAC
NRTLSAC (patent pending) is a segment contribution activity coefficient
model, derived from the Polymer NRTL model, usable in Aspen Properties and
Aspen Polymers. NRTLSAC can be used for fast, qualitative estimation of the
solubility of complex organic compounds in common solvents. For more
information about the model, see NRTLSAC for Segments/Oligomers.
Note: A newer version of NRTL-SAC comes with its own property method
named NRTL-SAC and does not require the specification of a method and
oligomer components as described below.
The NRTLSAC model for Segments/Oligomers in the Aspen Physical Property
System is a liquid activity coefficient model called NRTLSAC. To specify it:
1. On the Properties | Specifications sheet, specify process type ALL.
2. Specify base method NRTLSAC.
In order to use this version of NRTLSAC, all components must be defined as
oligomers. Four conceptual segments also must be defined. On the
Components | Polymers | Oligomers sheet, enter a number for at least
one conceptual segment for each oligomer component, as required by the
definition of an oligomer. These numbers are not used by NRTL-SAC.
On the Properties | Parameters | Binary Interaction | NRTL-1 form,
enter the binary parameters between conceptual segments. In the following
example, the conceptual segments are named X, Y-, Y+, and Z.
Segment 1 X X Y- Y+ X
Segment 2 Y- Z Z Z Y+
AIJ 1.643 6.547 -2.000 2.000 1.643
AJI 1.834 10.949 1.787 1.787 1.834
CIJ 0.2 0.2 0.3 0.3 0.2
On the Properties | Parameters | Binary Interaction | NRTLXY-1 form,
enter a non-zero value for at least one of the four parameters for each
component.
Pitzer Activity Coefficient Model
The Pitzer model was developed as an improvement upon an earlier model
proposed by Guggenheim ( 1935, 1955). The earlier model worked well at low
electrolyte concentrations, but contained discrepancies at higher
concentrations (>0.1M). The Pitzer model resolved these discrepancies,
without resorting to excessive arrays of higher-order terms.
Important: The model can be used for aqueous electrolyte systems, up to 6
molal ionic strength. It cannot be used for systems with any other solvent or
mixed solvents. Any non-water molecular components are considered solutes
and treated as Henry components.
2 Thermodynamic Property Models 135

This section provides theoretical background for the model. All model
equations and parameter requirements are included.
The Pitzer model is commonly used in the calculation of activity coefficients
for aqueous electrolytes up to 6 molal ionic strength. Do not use this model if
a non-aqueous solvent exists. Henry's law parameters are required for all
other components in the aqueous solution. The model development and
working equations are provided in the following sections. Parameter
conversion between the Pitzer notation and our notation is also provided.
The Pitzer model in the Aspen Physical Property System involves usersupplied
parameters that are used in the calculation of binary and ternary
parameters for the electrolyte system.
Five elements (P1 through P5) account for the temperature dependencies of
parameters � (0) , � (1) , � (2) , � (3) , C � , �, and �. These parameters follow the
temperature dependency relation:
Where:
T ref
The user must:
= 298.15 K
� Supply these elements for the binary parameters using a Properties |
Parameters | Binary | T-Dependent form.
� Supply these elements for � on the Properties | Parameters |
Electrolyte Ternary form.
� Specify Comp ID i and Comp ID j (and Comp ID k for �) on these forms,
using the same order that appears on the Components Specifications
Selection sheet.
The parameters are summarized in the following table. There is a Pitzer
parameter databank in the Aspen Physical Property System (see Physical
Property Data).
Parameter
Name
Provides
P1 - P5 for
Cation-Anion Parameters
136 2 Thermodynamic Property Models
No. of
Elements
Default MDS Units
GMPTB0 � (0) 5 0 x —
GMPTB1 � (1) 5 0 x —
GMPTB2 � (2) 5 0 x —
GMPTB3 � (3) 5 0 x —
GMPTC C � 5 0 x —
Cation-Cation Parameters
GMPTTH � cc'
Anion-Anion Parameters
GMPTTH � aa'
Ternary Parameters
5 0 x —
5 0 x —

Parameter
Name
GMPTPS,
GMPTP1,
GMPTP2,
GMPTP3,
GMPTP4
Provides
P1 - P5 for
� ijk
2 Thermodynamic Property Models 137
No. of
Elements
Default MDS Units
1 (in each
parameter)
0 x —
Molecule-Ion and Molecule-Molecule Parameters
GMPTB0 � (0) 5 0 x —
GMPTB1 � (1) 5 0 x —
GMPTC C � 5 0 x —
Model Development
The Pitzer model analyzes "hard-core" effects in the Debye-Hückel theory. It
uses the following expansion as a radial distribution function:
Where:
gij = Distribution function
r = Radius
qij
With:
=
zi = Charge of ion i
Qe = Electron charge
(pair potential of mean force)
�j(r) = Average electric potential for ion j
k = Boltzmann's constant
T = Temperature
This radial distribution function is used in the so-called pressure equation that
relates this function and the intermolecular potential to thermodynamic
properties. From this relation you can obtain an expression for the osmotic
coefficient.
Pitzer proposes a general equation for the excess Gibbs energy. The basic
equation is:
Where:
G E
= Excess Gibbs energy
(1)
(2)

R = Gas constant
T = Temperature
nw = Kilograms of water
mi
With:
138 2 Thermodynamic Property Models
=
xi = Mole fraction of ion i
xw = Mole fraction of water
(molality of ion i)
Mw = Molecular weight of water (g/mol)
ni = Moles of ion i
The function f(I) is an electrostatic term that expresses the effect of longrange
electrostatic forces between ions. This takes into account the hard-core
effects of the Debye-Hückel theory. This term is discussed in detail in the
following section. The parameters �ij are second virial coefficients that
account for the short-range forces between solutes i and j. The parameters
�ijk account for the interactions between solutes, i, j, k. For ion-ion
interactions, �ij is a function of ionic strength. For molecule-ion or moleculemolecule
interactions this ionic strength dependency is neglected. The
dependence of �ijk on ionic strength is always neglected. The matrices �ij and
�ijk are also taken to be symmetric (that is, �ij = �ji).
Pitzer modified this expression for the Gibbs energy by identifying
combinations of functions. He developed interaction parameters that can be
evaluated using experimental data. He selected mathematical expressions for
these parameters that best fit experimental data.
Pitzer's model can be applied to aqueous systems of strong electrolytes and
to aqueous systems of weak electrolytes with molecular solutes. These
applications are discussed in the following section.
In the Aspen Physical Property System, this model is applied using the
reference state of infinite dilution solution in water for non-water molecular
solutes and ionic species. The properties such as DHAQFM are obtained at 25
C and 1 atm.
Application of the Pitzer Model to Aqueous Strong
Electrolyte Systems
Pitzer modified his basic equation to make it more useful for data correlation
of aqueous strong electrolytes. He defined a set of more directly observable
parameters to represent combinations of the second and third virial
coefficients. The modified Pitzer equation is:

zi = Charge of ion i
Subscripts c, c', and a, a' denote cations and anions of the solution. B, C, �,
and � are interaction parameters. f(I) is an electrostatic term as a function of
ionic strength. The cation-anion parameters B and C are characteristic for an
aqueous single-electrolyte system. These parameters can be determined by
the properties of pure (apparent) electrolytes. B is expressed as a function of
� (0) and � (1) , or of � (0) , � (2) , and � (3) (see equations 11 through 15).
The parameters � and � are for the difference of interaction of unlike ions of
the same sign from the mean of like ions. These parameters can be measured
from common-ion mixtures. Examples are NaCl + KCl + H2O or NaCl + NaNO3
+ H2O (sic, Pitzer, 1989). These terms are discussed in detail later in this
section.
Fürst and Renon (1982) propose the following expression as the Pitzer
equation for the excess Gibbs energy:
The difference between equations 3 and 4 is that Pitzer orders cation before
anions. Fürst and Renon do not. All summations are taken over all ions i and j
(both cations and anions). This involves making the parameter matrices Bij,
Cij, �ij, and �ijk symmetric, as follows:
Second-order parameters are written Bij if i and j are ions of different sign. Bij
= 0 if the sign of zi = sign of zj, and Bii = 0. Since cations are not ordered
before anions, Bij = Bji. This eliminates the 2 in the second term in brackets in
Pitzer's original expression (equation 3). Second-order parameters are written
�ij if i and j are ions of the same sign. Thus �ij = 0 if the sign of zi is different
from the sign of zj, and �ii = 0 with �ij = �ji.
Third-order parameters are written Cij if i and j are ions with different signs.
Cij = 0 if the sign of zi = sign of zj, and Cii = 0 with Cij = Cji. The factor of 2 in
the fifth bracketed term in Pitzer's original expression (equation 3) becomes
1/2 in equation 4. The matrix C is symmetric and is extended to all
ions to make the equation symmetric.
2 Thermodynamic Property Models 139
(3)
(4)

�ijk is written for three different ions �ijk = �kij = �jki , and �ikk = 0. �ijk = 0
if the sign of zi =sign of zj =sign of zk. The factor of 1/6 is different from 1/2
in the last term in brackets in Pitzer's original expression. Pitzer distinguishes
between cations and anions. In Pitzer's original model this parameter appears
twice, as �cc'a and �c'ca. In this modified model, it appears six times, as �cc'a;
�c'ca; �acc'; �ac'c; �cac'; and �c'ac. Fürst and Renon's expression, equation 4,
calculates the expressions for activity coefficients and osmotic coefficients.
Pitzer (1975) modified his model by adding the electrostatic unsymmetrical
mixing effects, producing this modified Pitzer equation for the excess Gibbs
energy:
Calculation of Activity Coefficients
The natural logarithm of the activity coefficient for ions is calculated from
equation 4a to give:
140 2 Thermodynamic Property Models
(5)
(4a)
Where � is neglected and �ij and � ' ij are the electrostatic unsymmetric mixing
effects:
The X parameters are calculated differently on the option code.
For option code = –1, there is no unsymmetric mixing correction term:

For option code = 0 (default), the unsymmetric mixing correction term is in
polynomial form:
For option code = 1, the unsymmetric mixing correction term is in integral
form:
For water the logarithm of the activity coefficient is calculated similarly, as
follows:
Applying:
to equation 3 and using:
Where Nw = moles water, gives:
f(I), the electrostatic term, is expressed as a function of ionic strength I :
I, the ionic strength, is defined as:
2 Thermodynamic Property Models 141
(7)
(6)

Taking the derivative of equation 7 with respect to I, gives:
So that:
142 2 Thermodynamic Property Models
(8)
(9)
(10)
This equation is used in equation 6. In equations 7 and 9, is the usual Debye-
Hückel constant for the osmotic coefficient, determined from:
Where:
NA = Avogadro's constant
dw = Water density
�B = Dielectric constant of solvent B
(11)
b is an adjustable parameter, which has been optimized in this model to equal
1.2.
B and B' need expressions so that equations 5 and 6 can completely be solved
for the activity coefficients. The parameter B is determined differently for
different electrolyte pairings. For 1-n electrolytes (1-1, 1-2, 2-1, and so on)
the following expression gives the parameter B:
with �1=2.0.
(12)
For n-m electrolytes, n and m>1 (2-2, 2-3, 3-4, and so on), B is determined
by the following expression:
with �2 = 12.0 and �3 = 1.4.
(13)
By taking appropriate derivatives, expressions for B' can be derived for 1–n
electrolytes:
(14)

and for n-m electrolytes:
2 Thermodynamic Property Models 143
(15)
The parameters � (0) , � (1) , � (2) , � (3) and also C, �, and � can be found in
Pitzer's articles .
After the activity coefficients are calculated, they can be converted to the
mole fraction scale from the molality scale by the following relations:
For solutes:
For water as a solvent:
Where:
�m = Activity coefficient (molality scale)
�x = Activity coefficient (mole fraction scale)
(16)
(17)
Application of the Pitzer Model to Aqueous
Electrolyte Systems with Molecular Solutes
In aqueous weak electrolyte systems with molecular solutes, the second and
third virial coefficients in the basic Pitzer equation for molecule-ion and
molecule-molecule interactions must be considered. The following extensions
of Pitzer's interaction parameters are made.
The second-order parameters Bij are extended to include molecule-molecule
and molecule-ion interaction parameters.
The third-order parameters �ijk are extended to molecule-molecule-molecule
interactions. The following expressions relate �ijk to Pitzer's original �ijk:
�iii = 6�iii
However, molecule-molecule interactions were not taken into account by
Pitzer and coworkers. So �iii is an artificially introduced quantity.

The equations for activity coefficients and the Gibbs free energy are the same
as equations 3 through 6.
Parameters
The Pitzer model in the Aspen Physical Property System involves usersupplied
parameters. These parameters are used in the calculation of binary
and ternary parameters for the electrolyte system. These parameters include
the cation-anion parameters � (0) , � (1) , � (2) , � (3) and C � , cation-cation
parameter �cc', anion-anion parameter �aa', cation1-cation2-common anion
parameter �cc'a, anion1-anion2-common cation parameter �caa', and the
molecule-ion and molecule-molecule parameters � (0) , � (1) , and, C � . The
parameter names in the Aspen Physical Property System and their
requirements are discussed in Pitzer Activity Coefficient Model.
Parameter Conversion
For n-m electrolytes, n and m>1 (2-2, 2-3, 3-4, and so on), the parameter
� (3) corresponds to Pitzer's � (1) . � (2) is the same in both the Aspen Physical
Property System and original Pitzer models. Pitzer refers to the n-m
electrolyte parameters as � (1) , � (2) , � (0) . � (0) and � (2) retain their meanings in
both models, but Pitzer's � (1) is � (3) in the Aspen Physical Property System. Be
careful to make this distinction when entering n-m electrolyte parameters.
Pitzer often gives values of � (0) , � (1) , � (2) , � (3) , and C � that are corrected by
some factors (see Pitzer and Mayorga (1973) for examples). These factors
originate from one of Pitzer's earlier expressions for the excess Gibbs energy:
Where:
144 2 Thermodynamic Property Models
=
na = Mole number of anions
nc = Mole number of cation
(18)
Here � (0) , � (1) , � (2) , and � (3) are multiplied by a factor of 2ncna. C is multiplied
by a factor of 2(ncna) 3/2 .
Aspen Physical Property System accounts for these correcting factors. Enter
the parameters without their correcting factors.
For example, Pitzer gives the values of parameters for MgCl2 as:
4/3� (0) = 0.4698
4/3� (1) = 2.242

= 0.00979
Perform the necessary conversions and enter the parameters as:
= 0.3524
= 1.6815
= 0.00520
Parameter Sources
Binary and ternary parameters for the Pitzer model for various electrolyte
systems are available from Pitzer's series on the thermodynamics of
electrolytes. These papers and the electrolyte parameters they give are:
Reference Parameters available
(Pitzer, 1973) Binary parameters (� (0) , � (1) , C � ) for 13
dilute aqueous electrolytes
(Pitzer and Mayorga, 1973) Binary parameters for 1-1 inorganic
electrolytes, salts of carboxylic acids (1-1),
tetraalkylammonium halids, sulfonic acids
and salts, additional 1-1 organic salts, 2-1
inorganic compounds, 2-1 organic
electrolytes, 3-1 electrolytes, 4-1 and 5-1
electrolytes
(Pitzer and Mayorga, 1974) Binary parameters for 2-2 electrolytes in
water at 25�C
(Pitzer and Kim, 1974) Binary and ternary parameters for mixed
electrolytes, binary mixtures without a
common ion, mixed electrolytes with three
or more solutes
(Pitzer, 1975) Ternary parameters for systems mixing
doubly and singly charged ions
(Pitzer and Silvester, 1976) Parameters for phosphoric acid and its buffer
solutions
(Pitzer, Roy and Silvester, 1977) Parameters and thermodynamic properties
for sulfuric acid
(Silvester and Pitzer, 1977) Data for NaCl and aqueous NaCl solutions
(Pitzer, Silvester, and Peterson, 1978) Rare earth chlorides, nitrates, and
perchlorates
(Peiper and Pitzer, 1982) Aqueous carbonate solutions, including
mixtures of sodium carbonate, bicarbonate,
and chloride
(Phutela and Pitzer, 1983) Aqueous calcium chloride
(Conceicao, de Lima, and Pitzer, 1983) Saturated aqueous solutions, including
mixtures of sodium chloride, potassium
chloride, and cesium chloride
2 Thermodynamic Property Models 145

Reference Parameters available
(Pabalan and Pitzer, 1987) Parameters for polynomial unsymmetric
mixing term
(Kim and Frederick, 1988) Parameters for integral unsymmetric mixing
term
Pitzer References
Conceicao, M., P. de Lima, and K.S. Pitzer, "Thermodynamics of Saturated
Aqueous Solutions Including Mixtures of NaCl, KCl, and CsCl, "J. Solution
Chem, Vol. 12, No. 3, (1983), pp. 171-185.
Fürst, W. and H. Renon, "Effects of the Various Parameters in the Application
of Pitzer's Model to Solid-Liquid Equilibrium. Preliminary Study for Strong 1-1
Electrolytes," Ind. Eng. Chem. Process Des. Dev., Vol. 21, No. 3, (1982),
pp. 396-400.
Guggenheim, E.A., Phil. Mag., Vol. 7, No. 19, (1935), p. 588.
Guggenheim, E.A. and J.C. Turgeon, Trans. Faraday Soc., Vol. 51, (1955), p.
747.
Kim, H. and W.J. Frederick, "Evaluation of Pitzer Ion Interaction Parameters
of Aqueous Mixed Electrolyte Solution at 25C, Part 2: Ternary Mixing
Parameters," J. Chem. Eng. Data, 33, (1988), pp. 278-283.
Pabalan, R.T. and K.S. Pitzer, "Thermodynamics of Concentrated Electrolyte
Mixtures and the Prediction of Mineral Solubilities to High Temperatures for
Mixtures in the system Na-K-Mg-Cl-SO4-OH-H2O," Geochimica Acta, 51,
(1987), pp. 2429-2443.
Peiper, J.C. and K.S. Pitzer, "Thermodynamics of Aqueous Carbonate
Solutions Including Mixtures of Sodium Carbonate, Bicarbonate, and
Chloride," J. Chem. Thermodynamics, Vol. 14, (1982), pp. 613-638.
Phutela, R.C. and K.S. Pitzer, "Thermodynamics of Aqueous Calcium
Chloride," J. Solution Chem., Vol. 12, No. 3, (1983), pp. 201-207.
Pitzer, K.S., "Thermodynamics of Electrolytes. I. Theoretical Basis and
General Equations, " J. Phys. Chem., Vol. 77, No. 2, (1973), pp. 268-277.
Pitzer, K.S., J. Solution Chem., Vol. 4, (1975), p. 249.
Pitzer, K.S., "Fluids, Both Ionic and Non-Ionic, over Wide Ranges of
Temperature and Composition," J. Chen. Thermodynamics, Vol. 21, (1989),
pp. 1-17. (Seventh Rossini lecture of the commission on Thermodynamics of
the IUPAC, Aug. 29, 1988, Prague, ex-Czechoslovakia).
Pitzer, K.S. and J.J. Kim, "Thermodynamics of Electrolytes IV; Activity and
Osmotic Coefficients for Mixed Electrolytes," J.Am. Chem. Soc., Vol. 96
(1974), p. 5701.
Pitzer, K.S. and G. Mayorga, "Thermodynamics of Electrolytes II; Activity and
Osmotic Coefficients for Strong Electrolytes with One or Both Ions Univalent,"
J. Phys. Chem., Vol. 77, No. 19, (1973), pp. 2300-2308.
Pitzer, K.S. and G. Mayorga, J. Solution Chem., Vol. 3, (1974), p. 539.
146 2 Thermodynamic Property Models

Pitzer, K.S., J.R. Peterson, and L.F. Silvester, "Thermodynamics of
Electrolytes. IX. Rare Earth Chlorides, Nitrates, and Perchlorates, "J. Solution
Chem., Vol. 7, No. 1, (1978), pp. 45-56.
Pitzer, K.S., R.N. Roy, and L.F. Silvester, "Thermodynamics of Electrolytes 7
Sulfuric Acid," J. Am. Chem. Soc., Vol. 99, No. 15, (1977), pp. 4930-4936.
Pitzer, K.S. and L.F. Silvester, J. Solution Chem., Vol. 5, (1976), p. 269.
Silvester, L.F. and K.S. Pitzer, "Thermodynamics of Electrolytes 8 High-
Temperature Properties, Including Enthalpy and Heat Capacity, With
Application to Sodium Chloride," J. Phys. Chem., Vol. 81, No. 19, (1977), pp.
1822-1828.
Polynomial Activity Coefficient
This model represents activity coefficient as an empirical function of
composition and temperature. It is used frequently in metallurgical
applications where multiple liquid and solid solution phases can exist.
The equation is:
Where:
Ai
Bi
Ci
Di
Ei
2 Thermodynamic Property Models 147
=
=
=
=
=
For any component i, the value of the activity coefficient can be fixed:
�i = fi
This model is not part of any property method. To use it:
1. On the Properties | Specifications sheet, specify an activity coefficient
model, such as NRTL.
2. Click the Properties | Property Methods folder.
3. In the Object Manager, click New.
4. In the Create New ID dialog box, enter a name for the new method.
5. In the Base Property Method field, select NRTL.
6. Click the Models tab.
7. Change the Model Name for GAMMA from GMRENON to GMPOLY.
Parameter
Symbol Default MDS Lower Upper Units
Name/Element
Limit Limit
GMPLYP/1 a i1 0 x — — —
GMPLYP/2 a i2 0 x — — —
GMPLYP/3 a i3 0 x — — —

Parameter
Name/Element
148 2 Thermodynamic Property Models
Symbol Default MDS Lower
Limit
Upper
Limit
GMPLYP/4 b i1 0 x — — —
GMPLYP/5 b i2 0 x — — —
GMPLYP/6 b i3 0 x — — —
GMPLYP/7 c i1 0 x — — —
GMPLYP/8 c i2 0 x — — —
GMPLYP/9 c i3 0 x — — —
GMPLYP/10 d i1 0 x — — —
GMPLYP/11 d i2 0 x — — —
GMPLYP/12 d i3 0 x — — —
GMPLYP/13 e i1 0 x — — —
GMPLYP/14 e i2 0 x — — —
GMPLYP/15 e i3 0 x — — —
GMPLYO f i — x — — —
Units
Note: If you specify GMPLYP on the Properties | Parameters | Pure
Component | T-Dependent sheet, you can only enter the first 12 elements.
If you want to specify values for elements 13 to 15, you should go to the
Flowsheeting Options | Add-Input | Add After sheet in Aspen Plus or the
Add-Input | Add-Input | Add After sheet in Aspen Properties, and enter
the values of all 15 elements as in the following example:
PROP-DATA GMPLYP-1
IN-UNITS SI
PROP-LIST GMPLYP
PVAL WATER 0.0 1.5 0.0 &
0.0 0.0 0.0 &
0.0 0.0 0.0 &
0.0 0.0 0.0 &
0.0 16. 0.0
Redlich-Kister
This model calculates activity coefficients. It is a polynomial in the difference
between mole fractions in the mixture. It can be used for liquid and solid
mixtures (mixed crystals).
The equation is:
Where:
nc = Number of components
A1,ij = aij / T + bij
A2,ij = cij / T + dij
A3,ij = eij / T + fij

A4,ij = gij / T + hij
A5,ij = mij / T + nij
An,ii = An,jj = 0.0
An,ji = An,ij(-1) (n-1)
An,kj = An,jk(-1) (n-1)
For any component i, the value of the activity coefficient can be fixed:
�i = vi
Parameter Name/
Element
2 Thermodynamic Property Models 149
Symbol Default MDS Lower
Limit
Upper
Limit
GMRKTB/1 a ij 0 x — — —
GMRKTB/2 b ij 0 x — — —
GMRKTB/3 c ij 0 x — — —
GMRKTB/4 d ij 0 x — — —
GMRKTB/5 e ij 0 x — — —
GMRKTB/6 f ij 0 x — — —
GMRKTB/7 g ij 0 x — — —
GMRKTB/8 h ij 0 x — — —
GMRKTB/9 m ij 0 x — — —
GMRKTB/10 n ij 0 x — — —
GMRKTO v i — x — — —
Scatchard-Hildebrand
Units
The Scatchard-Hildebrand model calculates liquid activity coefficients. It is
used in the CHAO-SEA property method and the GRAYSON property method.
The equation for the Scatchard-Hildebrand model is:
Where:
Aij
�i
Vm *,l
=
=
=
Parameter Symbol Default MDS Lower
Name/Element
Limit
Upper
Limit
Units
TC T ci — x 5.0 2000.0 TEMPERATURE

Parameter Symbol Default MDS Lower
Name/Element
Limit
DELTA � i
VLCVT1 V i *,CVT
GMSHVL V i *,l
150 2 Thermodynamic Property Models
— x 10 3
Upper
Limit
10 5
Units
SOLUPARAM
— x 0.0005 1.0 MOLE-
VOLUME
x 0.01 1.0 MOLE-
VOLUME
GMSHXL k ij 0.0 x -5 5 —
Three-Suffix Margules
This model can be used to describe the excess properties of liquid and solid
solutions. It does not find much use in chemical engineering applications, but
is still widely used in metallurgical applications. Note that the binary
parameters for this model do not have physical significance.
The equation is:
Where kij is a binary parameter:
For any component i, the value of the activity coefficient can be fixed:
�i = di
Parameter Name/ Symbol Default MDS Lower
Element
Limit
Upper
Limit
Units
GMMRGB/1 a ij 0 x — — TEMPERATURE
GMMRGB/2 b ij 0 x — — —
GMMRGB/3 c ij 0 x — — —
GMMRGO d i — x — — —
References
M. Margules, "Über die Zusammensetzung der gesättigten Dämpfe von
Mischungen," Sitzungsber. Akad. Wiss. Vienna, Vol. 104, (1895), p. 1293.
D.A. Gaskell, Introduction to Metallurgical Thermodyanics, 2nd ed., (New
York: Hemisphere Publishing Corp., 1981), p. 360.
R.C. Reid, J.M. Prausnitz, and B.E. Poling, The Properties of Gases and
Liquids, 4th ed., (New York: McGraw-Hill, 1987).

Symmetric and Unsymmetric Electrolyte
NRTL Activity Coefficient Model
The Symmetric Electrolyte NRTL activity coefficient model (GMENRTLS) uses a
symmetric reference state for ions as pure fused salts, rather than infinite
dilution in aqueous solution. This basis is easier to use for nonaqueous and
mixed-solvent systems, and eliminates the need to introduce water into
otherwise water-free systems. It also allows the model to reduce to the
standard NRTL model when there are no electrolytes in the system. The
ENRTL-SR property method is based on this model.
Chemical constants, enthalpy, and Gibbs free energy are calculated with
respect to the symmetric ionic reference state.
The Unsymmetric Electrolyte NRTL activity coefficient model (GMENRTLQ)
uses the same equations as GMENRTLS, but the unsymmetric reference state
for ions (infinite dilution in aqueous solution). The ENRTL-RK property method
is based on this model. Unlike the original Electrolyte NRTL activity coefficient
model, GMENRTLQ is also used to calculate enthalpy and Gibbs free energy
from thermodynamics based on the unsymmetric ionic reference state.
These models also handle zwitterions.
Parameters
Both symmetric and unsymmetric models share the same binary and pair
parameters. The adjustable model parameters are the symmetric non-random
factor parameters, �, and the asymmetric binary interaction energy
parameters, �. These parameters exist for molecule-molecule pairs (�mm' =
�m'm while �mm' � �m'm), molecule-electrolyte pairs (�m,ca = �ca,m while �m,ca �
�ca,m where ca represents an ion pair), and electrolyte-electrolyte pairs (�ca,ca'
= �ca',ca and �ca,c'a = �c'a,ca while �ca,ca' � �ca',ca and �ca,c'a � �c'a,ca)
The parameters for ion pairs are temperature-dependent:
2 Thermodynamic Property Models 151

where .
The NRTL parameters are used for molecule-molecule parameters, with
temperature dependence:
The temperature dependency of the dielectric constant is given by:
Option codes can affect the performance of this model. See Option Codes for
Activity Coefficient Models for details.
The following table lists the parameters used by GMENRTLS and GMENRTLQ:
Parameter Symbol No. of Default MDS Units
Name
Elements
Dielectric Constant Unary Parameters
CPDIEC a 1 — — —
152 2 Thermodynamic Property Models
b 1 0 — —
T ref
1 298.15 — TEMPERATURE †
Ionic Born Radius Unary Parameters
RADIUS r i 1 3x10 -10 — LENGTH
Molecule-Molecule Binary Parameters
NRTL/1 a ij — 0 x —
a ji — 0 x —
NRTL/2 b ij — 0 x TEMPERATURE †
b ji — 0 x TEMPERATURE †
NRTL/3 c ij=c ji — .3 x —
NRTL/4 d ij=d ji — 0 x TEMPERATURE
NRTL/5 e ij — 0 x TEMPERATURE
e ji — 0 x TEMPERATURE
NRTL/6 f ji — 0 x TEMPERATURE
f ji — 0 x TEMPERATURE
Electrolyte-Molecule Pair Parameters
GMENCC C ca,m 1 0 x —
C m,ca 1 0 x —

Parameter Symbol No. of
Name
Elements
Dielectric Constant Unary Parameters
2 Thermodynamic Property Models 153
Default MDS Units
GMENCD D ca,m 1 0 x TEMPERATURE †
D m,ca 1 0 x TEMPERATURE †
GMENCE E ca,m 1 0 x —
GMENCN � ca,m = � m,ca
E m,ca 1 0 x —
Electrolyte-Electrolyte Pair Parameters
1 .2 x —
GMENCC C ca,c'a 1 0 x —
C c'a,ca 1 0 x —
C ca,ca' 1 0 x —
C ca',ca 1 0 x —
GMENCD D ca,c'a 1 0 x TEMPERATURE †
D c'a,ca 1 0 x TEMPERATURE †
D ca,ca' 1 0 x TEMPERATURE †
D ca',ca 1 0 x TEMPERATURE †
GMENCE E ca,c'a 1 0 x —
GMENCN � ca,c'a = � c'a,ca
E c'a,ca 1 0 x —
E ca,ca' 1 0 x —
E ca',ca 1 0 x —
� ca,ca' = � ca',ca
1 .2 x —
1 .2 x —
Zwitterions in Symmetric and Unsymmetric
Electrolyte NRTL
The Symmetric and Unsymmetric Electrolyte NRTL models support
zwitterions, compounds with both positive and negative charges but net
charge of zero. Zwitterions are defined as:
� Components of type Conventional, similar to solvents
� Parameter ZWITTER set to 1; all other components in the Aspen Physical
Property System default to zero for ZWITTER
� Parameter PLXANT/1 less than -1.0E10 so that they are non-volatile.
Zwitterions are handled as follows:
� A zwitterion interacts with other molecular species through NRTL
parameters only, excluding any interactions through Henry constants and
pair parameters.
� The activity coefficient is calculated as a solvent.
� The contribution from zwitterions to the solution enthalpy and Gibbs free
energy are calculated as solutes using the infinite dilution heat capacity
model CPAQ0, DGAQFM, and DHAQFM.

Working Equations for Symmetric and
Unsymmetric Electrolyte NRTL
The symmetric and unsymmetric electrolyte NRTL models have two
contributions, one from local interactions that exist at the immediate
neighbourhood of any species, and the other from the long-range ion-ion
interactions that exist beyond the immediate neighbourhood of an ionic
species. To account for the local interactions, the model uses the electrolyte
NRTL expression. To account for the long-range interactions, the model uses
the Pitzer-Debye-Hückel (PDH) formula (Pitzer, 1980, 1986). The following
equation is the basis of the electrolyte NRTL model for the excess Gibbs free
energy of electrolyte systems:
The excess Gibbs free energy Gm ex is defined as:
where Gm is the Gibbs free energy of electrolyte systems and Gm id is the Gibbs
free energy of an ideal solution at the same conditions of temperature,
pressure, and composition.
The activity coefficient �i of component i can be derived from Eq. 1 as follows:
or
Each of these terms will be discussed in subsequent sections.
Reference States in Electrolyte Systems
The activity coefficient needs to be normalized by choosing a reference state
for any molecular and ionic component, respectively.
Reference state for molecular components
The reference state for a molecular component m is defined as follows:
This definition is the so-called standard state of pure liquids for molecular
components and it is also called the symmetric reference state for molecular
components.
154 2 Thermodynamic Property Models
(1)
(2)
(3)
(4)
(5)

Reference state for ionic components
The standard state of pure liquids is hypothetical for ionic components in
electrolyte systems. Instead, the symmetric reference state is defined as the
pure fused salt state of each electrolyte component in the system.
However, the conventional reference state for ionic components is the
infinite-dilution activity coefficients; it is also called the unsymmetric
reference state for ionic components.
GMENRTLS uses the symmetric reference state, while GMENRTLQ uses the
unsymmetric reference state.
Pure fused salt state of an electrolyte component
For an electrolyte component ca, the pure fused salt state can be defined as
follows:
Where �± is the mean ionic activity coefficient of the electrolyte component
and is related to the corresponding cationic and anionic activity coefficients �c
and �a by this expression:
where �c is the cationic stoichiometric coefficient and �a is the anionic
stoichiometric coefficient, and �=�c+�a (one mole of salt releases � moles of
ions in solution). They are given by the chemical equation describing the
dissociation of the electrolyte:
with
2 Thermodynamic Property Models 155
(6)
(7)
(8)
(9)
(10)
Therefore Eq. 4 can be written in terms of charge numbers zc and za:
(11)
At the pure fused salt state, the total moles of ionic components (for one
mole of salt) are:
�=�c+�a
therefore
(12)
(13)

156 2 Thermodynamic Property Models
(14)
(15)
The symmetric reference state defined by Eq. 6 is restricted to systems
containing a single electrolyte component. For multi-electrolyte systems, the
symmetric reference state can be generalized from Eq. 6 as follows:
(16)
where m applies to all molecular components in the system. The symmetric
reference state is a molecular-component-free medium.
Infinite-dilution aqueous solution
The condition of infinite-dilution aqueous solution for ionic components can be
written as follows:
xc=xa=0 (17)
This condition applies to all ionic components in the solution, and water must
be present in the solution for this reference state. In terms of the activity
coefficients for ionic components, the condition for the aqueous solution as
the unsymmetric reference state can be written as follows (where w=water):
(18)
This equation applies to all ionic components in the solution.
Local Interaction Term
In an electrolyte system, all component species can be categorized as one of
three types: molecular species (solvents), m; cationic species (cations), c;
and anionic species (anions), a. The model assumes that there are three
types of local composition interactions. The first type consists of a central
molecular species with other molecular species, cationic species, and anionic
species in the immediate neighbourhood. Here, local electroneutrality is
maintained. The other two types are based on the like-ion repulsion
assumption and have either a cationic or anionic species as the central
species. They also have an immediate neighbourhood consisting of molecular
species and oppositely charged ionic species. Accordingly, the excess Gibbs
energy from local interactions for an electrolyte system can be written as
follows:
or
(19)

with
2 Thermodynamic Property Models 157
(21)
(22)
(20)
where the first term is the contribution when a molecular species is at the
center, the second is the contribution when a cationic species is at the center,
and the third term is the contribution when an anionic species is at the
center. In Eq. 21, Ci=zi (charge number) for ionic species and Ci=1 for
molecular species. Finally, in Eqs. 19 and 20, G and � are local binary
quantities related to each other by the NRTL non-random factor parameter �:
(23)
The contribution to the activity coefficient of component i can be derived as
follows:
The results are:
(24)
(25)
(26)

Binary Parameters
158 2 Thermodynamic Property Models
(27)
The adjustable binary parameters for these models include moleculemolecule,
molecule-electrolyte, and electrolyte-electrolyte binary parameters,
where electrolyte here means an ion-pair composed of a cationic species and
an anionic species. For each of these types, there are asymmetric binary
interaction energy parameters, �, and symmetric non-random factor
parameters, � (for calculating G). That is to say that the following are the
adjustable parameters:
(28)
However, as seen in the preceding equations, we need these parameters for
molecule-molecule, molecule-cation, molecule-anion, and cation-anion pairs.
The molecule-molecule parameters are given directly by the model's
adjustable binary parameters. The remaining parameters �cm, �am, �mc, �ma,
�ca, �ac, �cm, �am, �mc, �ma, �ca, and �ac, are calculated from these parameters.
The � parameters for pairs involving cations and anions are calculated from
the adjustable binary parameters by applying a simple composition-average
mixing rule.
(29)
(30)
(31)
(32)
where Yc is a cationic charge composition fraction and Ya is an anionic charge
composition fraction, defined as follows:
(33)

G for these pairs is calculated the same way:
2 Thermodynamic Property Models 159
(34)
(35)
(36)
(37)
(38)
(39)
(40)
And then the binary parameters � are calculated from G using Eq. 23:
(41)
Normalized contributions to activity coefficients
From Eq. 5, it is easy to show that the local interaction contributions to
activity coefficients for all molecular components are normalized; that is
for all molecular components m in the system.
(42)
For ionic components with symmetric reference state, apply Eq. 16 to find:
(43)
(44)

160 2 Thermodynamic Property Models
(45)
(46)
(47)
(48)
where xm�0 applies to all molecular components in the solution.
For ionic components with infinite-dilution aqueous solution as reference
state, apply Eq. 18 to get:
(49)
(50)
where and are local interaction contributions to activity
coefficients at infinite dilution aqueous solution:
Long-Range Interaction Term
(51)
(52)
To account for the long-range ion-ion interactions, the Symmetric and
Unsymmetric Electrolyte NRTL models use the symmetric Pitzer-Debye-Hückel
(PDH) formula (Pitzer, 1986):
(53)

with
2 Thermodynamic Property Models 161
(54)
(55)
where n is the total mole number of the solution, A� is the Debye-Hückel
parameter, Ix is the ionic strength, � is the closest approach parameter, NA is
Avogadro's number, vs is the molar volume of the solvent, Qe is the electron
charge, �s is the dielectric constant of the solvent, kB is the Boltzmann
constant, zi is the charge number of component i, and Ix 0 represents Ix at the
reference state.
For the unsymmetric reference state, Ix 0 = 0.
For the symmetric reference state, the Debye-Hückel theory is originally
based on a single electrolyte with water as the solvent. Therefore, we can
obtain Ix 0 from Eqs. 13 and 14:
(56)
For multi-electrolyte systems with mixed-solvents, Ix 0 can take this form:
so that
(57)
(58)
(59)
(60)
where xm�0 applies to all molecular components in the solution. This
definition ensures that the excess Gibbs free energy from the long range
interactions will be zero at the symmetric reference state regardless of how
many electrolytes are present in the solution.
The contribution to the activity coefficient from component i can be derived
as:
(61)

For a solvent component, this is:
For a cation or anion component:
For the unsymmetric reference state:
And for the symmetric reference state:
or
162 2 Thermodynamic Property Models
(62)
(63)
(64)
(65)
(66)
(67)
(68)
(69)
The Debye-Hückel theory is original based on a single electrolyte with water
as the solvent. The molar volume vs and the dielectric constant �s for the
single solvent need to be extended for mixed-solvents; a simple composition
average mixing rule is adequate to calculate them as follows:

2 Thermodynamic Property Models 163
(70)
(71)
where s is a solvent component in the mixture and Msis the solvent molecular
weight. Each sum is over all solvent components in the solution.
Born term correction
If the infinite dilution aqueous solution is chosen as the reference state, we
need to correct the the Debye-Hückel term for the change of the reference
state from the mixed-solvent composition to aqueous solution. The Born term
(Robinson and Stokes, 1970; Rashin and Honig, 1985) is used for this
purpose:
(72)
where NA is the Avogadro constant and R is the gas constant. is the
Born term correction to the unsymmetric Pitzer-Debye-Hückel formula,
, and �w is the dielectric constant of water, and ri is the Born radius
of species i.
The Born contribution to the activity coefficient of component i can be derived
as follows:
For a cation or anion component, this is:
(73)
The correction to the activity coefficient for a solvent component is zero:
(75)
Henry Components in the Symmetric and
Unsymmetric Electrolyte NRTL Models
(74)
Light gases (Henry components) are usually supercritical at the temperature
and pressure of the system. In that case, pure component vapor pressure is

meaningless and therefore the pure liquid state at the temperature and
pressure of the system cannot serve as the reference state. The reference
state for a Henry component is redefined to be at infinite dilution (that is, at
xi�0) and at the temperature and pressure of the system.
The liquid phase reference fugacity, fi *,l , becomes the Henry’s constant for
Henry components in the solution, Hi, and the activity coefficient, �i, is
converted to the infinite dilution reference state through the relationship:
164 2 Thermodynamic Property Models
(76)
�
where �i is the infinite dilution activity coefficient of Henry component i
(xi�0) in the solution.
By this definition �i * approaches unity as xi approaches zero. The phase
equilibrium relationship for Henry components becomes:
(77)
The Henry’s Law is available in all activity coefficient property methods. The
model calculates the Henry’s constant for a dissolved gas component in all
solvent components in the mixture:
(78)
(79)
�
where His and �is are the Henry’s constant and the infinite dilution activity
coefficient of the dissolved gas component i in the solvent component s (xi�0
and xs�1), respectively.
Since ionic species exist only in the liquid phase and therefore do not
participate directly in vapor-liquid equilibria, the activities of Henry
components are mainly through the local interactions with solvents. We can
calculate the activity coefficients for Henry components as follows:
(80)
(81)
(82)
where xh�0 applies to all Henry components in the solution.

Activity Coefficient Basis for Henry Components
Regardless of the reference state for ionic components, there are two
�
possibilities for the basis of unsymmetric activity coefficients �h of Henry
components: aqueous and mixed-solvent. This can be specified on the Setup
| Simulation Options | Reactions sheet. Mixed-solvent is the default.
�
For mixed-solvent basis, �h is calculated as follows:
2 Thermodynamic Property Models 165
(83)
where xh�0 applies to all Henry components and xi�0 to all ionic
components in the solution.
For aqueous basis, the unsymmetric activity coefficients of Henry components
are calculated as follows:
Electrolyte Chemical Equilibria
(84)
In determining the composition of an electrolyte system, it is important to
know the equilibrium constants of the reactions taking place. An equilibrium
constant is expressed as the product of the activity of each species raised to
its stoichiometric coefficients. Two different scales are used in Aspen Plus: the
molality scale and the mole fraction scale but both are based on aqueous
electrolyte chemical equilibrium. For instance, the equilibrium constant for the
mole fraction scale in Aspen Plus is written in one of these:
Where:
K = Equilibrium constant
xw = Water mole fraction
�w = Water activity coefficient
xs = Non-water solvent mole fraction
�s = Non-water solvent activity coefficient
(85)
(86)
xi = Mole fraction of solute component (Henry or
ion)
�i * = Unsymmetric activity coefficient of solute
component
�i = Stoichiometric coefficient
The above equations are limited to aqueous electrolyte chemical equilibria
only. Therefore, the chemical constants in Aspen Plus databanks for

electrolyte systems with infinite dilution aqueous reference state cannot be
used for electrolyte systems with the symmetric reference state for ionic
components.
The chemical constants for electrolyte systems with the symmetric reference
state can be written in these forms:
166 2 Thermodynamic Property Models
(87)
(88)
where i indicates a molecular or ionic component and h represents a Henry
component. Eq. 83 or 84 is used for calculation of the unsymmetric activity
coefficients of Henry components. However, the calculation for the activity
coefficients of ionic components is carried out with the symmetric reference
state.
Other Thermophysical Properties
The activity coefficient model can be related to other properties through fundamental
thermodynamic equations. These properties (called excess liquid functions) are relative to the
ideal liquid mixture at the same condition:
Excess molar liquid Gibbs free energy
Excess molar liquid enthalpy
Excess molar liquid entropy
(89)
(90)
(91)
The excess liquid functions given by Equations 89-91 are calculated from the
same activity coefficient model. In practice, however, the activity coefficient �i
is often derived first from the excess liquid Gibbs free energy of a mixture
from an activity coefficient model:
with
(92)
(93)
(94)

Where is the liquid Gibbs free energy of mixing; it is defined as the
difference between the Gibbs free energy of the mixture and that of the pure
component and is the ideal Gibbs free energy of mixing. Once the
excess liquid functions are known, the thermodynamic properties of liquid
mixtures can be computed as follows:
2 Thermodynamic Property Models 167
(95)
(96)
(97)
where Hi l and Hi ig are the enthalpy and ideal gas enthalpy of component i at
the system conditions. Similarly, Gi l and Gi ig are the Gibbs free energy and
ideal gas Gibbs free energy of component i at the system conditions. In Aspen
Plus, both Hi ig and Gi ig are computed by the expressions:
where is the standard enthalpy of formation of ideal gas at
, is the ideal gas heat capacity, and is the
standard Gibbs free energy of formation of ideal gas at .
However, the above equations are directly not applicable to mixtures
containing ionic components because the ideal gas model becomes invalid for
ionic components.
The formulation to calculate the enthalpy and Gibbs free energy for
electrolyte systems can be carried out as follows:
(100)
(101)
(102)
where indexes s, h, and ca are meant to represent the contributions from
solvents, Henry components and ionic components, respectively.
(98)
(99)

Solvents
The contribution from solvents can be written as follows:
168 2 Thermodynamic Property Models
(103)
(104)
(105)
(106)
(107)
(108)
where is the liquid fugacity coefficient of pure solvent
component i, pi sat is the vapor pressure of pure component at the system
temperature T, �i v is the vapor fugacity coefficient of pure component at T
and pi sat (normally calculated from an equation-of-state model), and
is the Poynting pressure correction from pi sat to p,
and Vi l is the liquid molar volume at T and p.
Henry components
The contribution from Henry components can be written as follows:
(109)
(110)
(111)
(112)
(113)

Ionic components
2 Thermodynamic Property Models 169
(114)
(115)
The contribution from ionic components can be written as follows:
(116)
(117)
(118)
(119)
(120)
(121)
where Hi ref and Gi ref are the enthalpy and Gibbs free energy of ionic
component i at the system conditions with a specified reference state
(symmetric or unsymmetric).
The property calculations for solvents and Henry components are the same
when the reference state is changed. Only for ionic components do the
property methods need to be specified with a reference state. The methods
with the unsymmetric reference state are available already in Aspen Plus and
Aspen Properties. New methods are needed only for the symmetric reference
state. Overall, the calculated total enthalpy or Gibbs free energy for the same
electrolyte solution should be the same, regardless of the reference state
specified.
Enthalpy and Gibbs free energy of ionic components with the symmetric
reference state can be written as follows:
(122)
(123)
where and are enthalpy and Gibbs free energy of ionic component
i with the unsymmetric reference state, respectively, and available already in

Aspen Plus and Aspen Properties. �Hi and �Gi are the new contributions from
the symmetric reference state.
The unsymmetric enthalpy for an ionic component is calculated from
the infinite dilution aqueous phase heat capacity as follows:
170 2 Thermodynamic Property Models
(124)
where T ref = 298.15K. By default, is calculated from the aqueous
infinite dilution heat capacity polynomial. If the polynomial model parameters
are not available, is calculated from the Criss-Cobble correlation.
The unsymmetric Gibbs free energy for an ionic component is
calculated from the infinite dilution aqueous phase heat capacity as
follows:
(125)
(126)
where the term RT ln (1000/Mw) is added because and
are based on a molality scale, and is based on a mole fraction scale.
�Hi and �Gi for the symmetric reference state
The reference state for ionic components in the symmetric electrolyte NRTL
model is the pure fused salts containing these ions, so the enthalpy or Gibbs
free energy of the ionic components at the symmetric reference state is the
enthalpy contributions or the Gibbs free energy contributions of these ions to
the system of the pure fused salts. The condition of the pure fused salts can
be defined as follows:
which applies to all molecular components in the solution.
(127)
Given that the calculated total enthalpy or total Gibbs free energy of an
electrolyte solution by any reference state should be the same, the
formulation of enthalpy or Gibbs free energy of the ionic components at the
symmetric reference state can be derived from the unsymmetric electrolyte
NRTL enthalpy or Gibbs free energy calculations at the condition that all
molecular components (solvents and Henry components) approach zero, i.e.

the pure fused salts. Applying Eq. 127, the system enthalpy and Gibbs free
energy with the unsymmetric reference state can be expressed as:
where and are the total enthalpy and total Gibbs
free energy of the solution calculated by the unsymmetric electrolyte NRTL
model at the limit of all molecular components approach zero, that is, the
pure fused salts state, and and are the
excess enthalpy and excess Gibbs free energy of ion i at the same limit
condition.
Applying Eq. 127, the system enthalpy and Gibbs free energy with the
symmetric reference state can be expressed as:
Comparing Eqs. 130 and 131 to Eqs. 128 and 129, we can get:
2 Thermodynamic Property Models 171
(132)
(133)
(130)
(131)
Therefore, the enthalpy and Gibbs free energy of ionic components with the
symmetric reference state can be written as:
(134)
(135)
(128)
(129)

References for Symmetric and Unsymmetric
Electrolyte NRTL
C.-C. Chen and L.B. Evans, "A Local Composition Model for the Excess Gibbs
Energy of Aqueous Electrolyte Systems," AIChE Journal, 1986, 32, 444.
Y. Song and C.-C. Chen, "Symmetric Nonrandom Two-Liquid Activity
Coefficient Model for Electrolytes" (to be published).
K.S. Pitzer, "Electrolytes. From Dilute Solutions to Fused Salts," J. Am. Chem.
Soc., 1980, 102, 2902-2906.
K.S. Pitzer and J.M. Simonson, "Thermodynamics of Multicomponent, Miscible,
Ionic Systems: Theory and Equations," J. Phys. Chem., 1986, 90, 3005-3009.
R.A. Robinson and R.H. Stokes, Electrolyte Solutions, Second Revised Edition.
Butterworths: London, 1970.
A.A. Rashin and B. Honig, "Reevaluation of the Born Model of Ion Hydration,"
J. Phys. Chem., 1985, 89 (26), pp 5588–5593.
UNIFAC Activity Coefficient Model
The UNIFAC model calculates liquid activity coefficients for the following
property methods: UNIFAC, UNIF-HOC, and UNIF-LL. Because the UNIFAC
model is a group-contribution model, it is predictive. All published group
parameters and group binary parameters are stored in the Aspen Physical
Property System.
The equation for the original UNIFAC liquid activity coefficient model is made
up of a combinatorial and residual term:
ln � = ln �i c + ln �i r
ln �i c =
Where the molecular volume and surface fractions are:
and
Where nc is the number of components in the mixture. The coordination
number z is set to 10. The parameters ri and qi are calculated from the group
volume and area parameters:
and
Where �ki is the number of groups of type k in molecule i, and ng is the
number of groups in the mixture.
The residual term is:
172 2 Thermodynamic Property Models

�k is the activity coefficient of a group at mixture composition, and �k i is the
activity coefficient of group k in a mixture of groups corresponding to pure i.
The parameters �k and �k i are defined by:
With:
And:
The parameter Xk is the group mole fraction of group k in the liquid:
Parameter
Name/Element
UFGRP (k,� k, m, � m, ...)
2 Thermodynamic Property Models 173
Symbol Default MDS Lower
Limit
Upper
Limit
— — — — —
GMUFQ Q k — — — — —
GMUFR R k — — — — —
Units
GMUFB b kn — — — — TEMPERATURE
The parameter UFGRP stores the UNIFAC functional group number and
number of occurrences of each group. UFGRP is stored in the Aspen Physical
Property System pure component databank for most components. For
nondatabank components, enter UFGRP on the Properties Molecular Structure
Functional Group sheet. See Physical Property Data, Chapter 3, for a list of
the UNIFAC functional groups.
UNIFAC-PSRK
The PSRK property method uses GMUFPSRK, the UNIFAC-PSRK model, which
is a variation on the standard UNIFAC model. UNIFAC-PSRK has special
groups defined for the light gases CO2, H2, NH3, N2, O2, CO, H2S, and argon,
and the group binary interaction parameters are temperature-dependent,

using the values in parameter UNIFPS, instead of the constant value from
GMUFB used above, so that:
Where a, b, and c are the three elements of UNIFPS.
References
Aa. Fredenslund, J. Gmehling and P. Rasmussen, "Vapor-Liquid Equilibria
using UNIFAC," (Amsterdam: Elsevier, 1977).
Aa. Fredenslund, R.L. Jones and J.M. Prausnitz, AIChE J., Vol. 21, (1975), p.
1086.
H.K. Hansen, P. Rasmussen, Aa. Fredenslund, M. Schiller, and J. Gmehling,
"Vapor-Liquid Equilibria by UNIFAC Group Contribution. 5 Revision and
Extension", Ind. Eng. Chem. Res., Vol. 30, (1991), pp. 2352-2355.
UNIFAC (Dortmund Modified)
The UNIFAC modification by Gmehling and coworkers (Weidlich and
Gmehling, 1987; Gmehling et al., 1993), is slightly different in the
combinatorial part. It is otherwise unchanged compared to the original
UNIFAC:
With:
The temperature dependency of the interaction parameters is:
Parameter
Name/Element
UFGRPD (k,� k, m, � m, ...)
174 2 Thermodynamic Property Models
Symbol Default MDS Lower
Limit
Upper
Limit
— — — — —
GMUFDQ Q k — — — — —
GMUFDR R k — — — — —
Units
UNIFDM/1 a mn,1 0 — — — TEMPERATURE
UNIFDM/2 a mn,2 0 — — — TEMPERATURE
UNIFDM/3 a mn,3 0 — — — TEMPERATURE
The parameter UFGRPD stores the group number and the number of
occurrences of each group. UFGRPD is stored in the Aspen Physical Property
System pure component databank. For nondatabank components, enter
UFGRPD on the Properties Molecular Structure Functional Group sheet. See
Physical Property Data, Chapter 3, for a list of the Dortmund modified UNIFAC
functional groups.

References
U. Weidlich and J. Gmehling, "A Modified UNIFAC Model 1. Prediction of VLE,
h E and ," Ind. Eng. Chem. Res., Vol. 26, (1987), pp. 1372–1381.
J. Gmehling, J. Li, and M. Schiller, "A Modified UNIFAC Model. 2. Present
Parameter Matrix and Results for Different Thermodynamic Properties," Ind.
Eng. Chem. Res., Vol. 32, (1993), pp. 178–193.
UNIFAC (Lyngby Modified)
The equations for the "temperature-dependent UNIFAC" (Larsen et al., 1987)
are similar to the original UNIFAC:
Volume fractions are modified:
With:
2 Thermodynamic Property Models 175
,
Where �k and �k i have the same meaning as in the original UNIFAC, but
defined as:
With:

The temperature dependency of a is described by a function instead of a
constant:
Parameter
Name/Element
UFGRPL (k,� k, m, � m, ...)
176 2 Thermodynamic Property Models
Symbol Default MDS Lower
Limit
Upper
Limit
— — — — —
GMUFLQ Q k — — — — —
GMUFLR R k — — — — —
Units
UNIFLB/1 a mn,1 0 — — — TEMPERATURE
UNIFLB/2 a mn,2 0 — — — TEMPERATURE
UNIFLB/3 a mn,3 0 — — — TEMPERATURE
The parameter UFGRPL stores the modified UNIFAC functional group number
and the number of occurrences of each group. UFGRPL is stored in the Aspen
Physical Property System pure component databank. For nondatabank
components, enter UFGRP on the Properties | Molecular Structure |
Functional Group sheet. See Physical Property Data, Chapter 3, for a list of
the Larsen modified UNIFAC functional groups.
Reference: B. Larsen, P. Rasmussen, and Aa. Fredenslund, "A Modified
UNIFAC Group-Contribution Model for Prediction of Phase Equilibria and Heats
of Mixing," Ind. Eng. Chem. Res., Vol. 26, (1987), pp. 2274 – 2286.
UNIQUAC Activity Coefficient Model
The UNIQUAC model calculates liquid activity coefficients for these property
methods: UNIQUAC, UNIQ-2, UNIQ-HOC, UNIQ-NTH, and UNIQ-RK. It is
recommended for highly non-ideal chemical systems, and can be used for VLE
and LLE applications. This model can also be used in the advanced equations
of state mixing rules, such as Wong-Sandler and MHV2.
The equation for the UNIQUAC model is:
Where:
�i
=
�i' =
�i
li
=
=

ti' =
�ij
2 Thermodynamic Property Models 177
=
z = 10
aij, bij, cij, and dij are unsymmetrical. That is, aij may not be equal to aji, etc.
Absolute temperature units are assumed for the binary parameters aij, bij, cij,
dij, and eij.
can be determined from VLE and/or LLE data regression. The Aspen Physical
Property System has a large number of built-in parameters for the UNIQUAC
model. The binary parameters have been regressed using VLE and LLE data
from the Dortmund Databank. The binary parameters for VLE applications
were regressed using the ideal gas, Redlich-Kwong, and Hayden-O'Connell
equations of state. See Physical Property Data, Chapter 1, for details.
Parameter
Name/Element
Symbol Default MDS Lower
Limit
Upper
Limit
GMUQR r i — x — — —
GMUQQ q i — x — — —
GMUQQ1 q i' q x — — —
UNIQ/1 a ij 0 x -50.0 50.0 —
Units
UNIQ/2 b ij 0 x -15000.0 15000.0 TEMPERATURE
UNIQ/3 c ij 0 x — — TEMPERATURE
UNIQ/4 d ij 0 x — — TEMPERATURE
UNIQ/5 T lower 0 K x — — TEMPERATURE
UNIQ/6 T upper 1000 K x — — TEMPERATURE
UNIQ/7 e ij 0 x — — TEMPERATURE
Absolute temperature units are assumed for elements 2 through 4 and 7 of
UNIQ.
The UNIQ-2 property method uses data set 2 for UNIQ. All other UNIQUAC
methods use data set 1.
References
D.S. Abrams and J.M. Prausnitz, "Statistical Thermodynamics of liquid
mixtures: A new expression for the Excess Gibbs Energy of Partly or
Completely Miscible Systems," AIChE J., Vol. 21, (1975), p. 116.
A. Bondi, "Physical Properties of Molecular Crystals, Liquids and Gases," (New
York: Wiley, 1960).
Simonetty, Yee and Tassios, "Prediction and Correlation of LLE," Ind. Eng.
Chem. Process Des. Dev., Vol. 21, (1982), p. 174.

Van Laar Activity Coefficient Model
The Van Laar model (Van Laar 1910) calculates liquid activity coefficients for
the property methods: VANLAAR, VANL-2, VANL-HOC, VANL-NTH, and VANL-
RK. It can be used for highly nonideal systems.
Where:
zi
Ai
Bi
Ci
Aij
Cij
178 2 Thermodynamic Property Models
=
=
=
=
=
=
Cij = Cji
Aii = Bii = Cii = 0
aij and bij are unsymmetrical. That is, aij may not be equal to aji, and bij may
not be equal to bji.
Parameters Symbol DefaultMDS Lower Limit Upper
Name/Element
Limit
VANL/1 a ij 0 x -50.0 50.0 —
Units
VANL/2 b ij 0 x -15000.0 15000.0 TEMPERATURE
VANL/3 c ij 0 x -50.0 50.0 —
VANL/4 d ij 0 x -15000.0 15000.0 TEMPERATURE
The VANL-2 property method uses data set 2 for VANL. All other Van Laar
methods use data set 1.
References
J.J. Van Laar, "The Vapor Pressure of Binary Mixtures," Z. Phys. Chem., Vol.
72, (1910), p. 723.
R.C. Reid, J.M. Prausnitz, and B.E. Poling, The Properties of Gases and
Liquids, 4th ed. (New York: McGraw-Hill, 1987).

Wagner Interaction Parameter
The Wagner Interaction Parameter model calculates activity coefficients. This
model is used for dilute solutions in metallurgical applications.
The relative activity coefficient with respect to the reference activity
coefficient of a solute i (in a mixture of solutes i, j, and l and solvent A) is:
Where:
The parameter �i ref is the reference activity coefficient of solute i:
kij is a binary parameter:
For any component i, the value of the activity coefficient can be fixed:
�i = gi
This model is recommended for dilute solutions.
Parameter Name/
Element
2 Thermodynamic Property Models 179
Symbol Default MDS Lower
Limit
Upper
Limit
Units
GMWIPR/1 a i 0 x — — TEMPERATURE
GMWIPR/2 b i 0 x — — —
GMWIPR/3 c i 0 x — — —
GMWIPB/1 d ij 0 x — — TEMPERATURE
GMWIPB/2 e ij 0 x — — —
GMWIPB/3 f ij 0 x — — —
GMWIPO g i — x — — —
GMWIPS — 0 x — — —
GMWIPS is used to identify the solvent component. You must set GMWIPS to
1.0 for the solvent component. This model allows only one solvent.
References
A.D. Pelton and C. W. Bale, "A Modified Interaction Parameter Formalism for
Non-Dilute Solutions," Metallurgical Transactions A, Vol. 17A, (July 1986),
p. 1211.
Wilson Activity Coefficient Model
The Wilson model calculates liquid activity coefficients for the following
property methods: WILSON, WILS2, WILS-HOC, WILS-NTH, WILS-RK, WILS-

HF, WILS-LR, and WILS-GLR. It is recommended for highly nonideal systems,
especially alcohol-water systems. It can also be used in the advanced
equation-of-state mixing rules, such as Wong-Sandler and MHV2. This model
cannot be used for liquid-liquid equilibrium calculations.
The equation for the Wilson model is:
Where:
ln Aij
180 2 Thermodynamic Property Models
=
The extended form of ln Aij provides more flexibility in fitting phase
equilibrium and enthalpy data. aij, bij, cij, dij, and eij are unsymmetrical. That
is, aij may not be equal to aji, etc.
The binary parameters aij, bij, cij, dij, and eij must be determined from data
regression or VLE and/or heat-of-mixing data. The Aspen Physical Property
System has a large number of built-in binary parameters for the Wilson
model. The binary parameters have been regressed using VLE data from the
Dortmund Databank. The binary parameters were regressed using the ideal
gas, Redlich-Kwong, and Hayden-O'Connell equations of state. See Physical
Property Data, Chapter 1, for details.
Parameter
Name/Element
Symbol Default MDS Lower Limit Upper
Limit
WILSON/1 a ij 0 x -50.0 50.0 —
†
Units
WILSON/2 b ij 0 x -15000.0 15000.0 TEMPERATURE
††
WILSON/3 c ij 0 x -— — TEMPERATURE
††
WILSON/4 d ij 0 x — — TEMPERATURE
††
WILSON/5 T lower 0 K x — — TEMPERATURE
WILSON/6 T upper 1000 K x — — TEMPERATURE
WILSON/7 e ij 0 x — — TEMPERATURE
††
The WILS-2 property method uses data set 2 for WILSON. All other Wilson
methods use data set 1.
† In the original formulation of the Wilson model, aij = ln Vj/Vi, cij = dij = eij =
0, and
bij = -(�ij - �ii)/R, where Vj and Vi are pure component liquid molar volume at
25�C.
†† If any of biA, ciA, and eiA are non-zero, absolute temperature units are
assumed for all coefficients. If biA, ciA, and eiA are all zero, the others are
interpreted in input units. The temperature limits are always interpreted in
input units.

References
G.M. Wilson, J. Am. Chem. Soc., Vol. 86, (1964), p. 127.
Wilson Model with Liquid Molar Volume
This Wilson model (used in the method WILS-VOL) calculates liquid activity
coefficients using the original formulation of Wilson (Wilson 1964) except that
liquid molar volume is calculated at system temperature, instead of at 25�C.
It is recommended for highly nonideal systems, especially alcohol water
systems. It can be used in any activity coefficient property method or in the
advanced equation of state mixing rules, such as Wong Sandler and MHV2.
This model cannot be used for liquid liquid equilibrium calculations.
The equation for the Wilson model is:
Where:
ln Aij
2 Thermodynamic Property Models 181
=
Vj and Vi are pure component liquid molar volume at the system temperature
calculated using the General Pure Component Liquid Molar Volume model. The
extended form of ln Aij provides more flexibility in fitting phase equilibrium
and enthalpy data. aij, bij, cij, dij, and eij are unsymmetrical. That is, aij may
not be equal to aji, etc.
The binary parameters aij, bij, cij, dij, and eij must be determined from data
regression of VLE and/or heat-of-mixing data. There are no built in binary
parameters for this model.
Parameter
Name/Element
SymbolDefault MDS Lower
Limit
Upper
Limit
WSNVOL/1 a ij 0 x -50.0 50.0 —
†
Units
WSNVOL/2 b ij 0 x -15000.0 15000.0 TEMPERATURE
††
WSNVOL/3 c ij 0 x — — TEMPERATURE
††
WSNVOL/4 d ij 0 x — — TEMPERATURE
††
WSNVOL/5 e ij 0 x — — TEMPERATURE
††
WSNVOL/6 T lower 0 K x — — TEMPERATURE
WSNVOL/7 T upper 1000 K x — — TEMPERATURE
Pure component parameters for the General Pure Component Liquid Molar
Volume model are also required.
† In the original formulation of the Wilson model, aij = cij = dij = eij = 0 and
. Vj and Vi are calculated at 25�C.

†† If any of biA, ciA, and eiA are non-zero, absolute temperature units are
assumed for all coefficients. If biA, ciA, and eiA are all zero, the others are
interpreted in input units. The temperature limits are always interpreted in
input units.
Reference: G.M. Wilson, J. Am. Chem. Soc., Vol. 86, (1964), p. 127.
Vapor Pressure and Liquid
Fugacity Models
The Aspen Physical Property System has the following built-in vapor pressure
and liquid fugacity models. This section describes the vapor pressure and
liquid fugacity models available.
Model Type
General Pure Component Liquid Vapor
Pressure
182 2 Thermodynamic Property Models
Vapor pressure
API Sour Vapor pressure
Braun K-10 Vapor pressure
Chao-Seader Fugacity
Grayson-Streed Fugacity
Kent-Eisenberg Fugacity
Maxwell-Bonnell Vapor pressure
Solid Antoine Vapor pressure
General Pure Component Liquid Vapor
Pressure
The Aspen Physical Property System has several submodels for calculating
vapor pressure of a liquid. It uses parameter THRSWT/3 to determine which
submodel is used. See Pure Component Temperature-Dependent Properties
for details.
If THRSWT/3
is
Then this equation is
used
0 Extended Antoine PLXANT
And this parameter is used
200-211 Barin CPLXP1, CPLXP2, CPIXP1, CPIXP2,
and CPIXP3
301 Wagner WAGNER
302 PPDS Modified Wagner WAGNER
400 PML LNVPEQ and one of LNVP1, LOGVP1,
LNPR1, LOGPR1, LNPR2, LOGPR2
401 IK-CAPE PLPO
501 NIST TDE Polynomial PLTDEPOL
502 NIST Wagner 25 WAGNER25

Extended Antoine Equation
Parameters for many components are available for the extended Antoine
equation from the Aspen Physical Property System pure component databank.
This equation can be used whenever the parameter PLXANT is available.
The equation for the extended Antoine vapor pressure model is:
Extrapolation of ln pi *,l versus 1/T occurs outside of temperature bounds.
Parameter
Name/ Element
2 Thermodynamic Property Models 183
Symbol Default MDS Lower
Limit
Upper
Limit
Units
PLXANT/1 C 1i x PRESSURE,
TEMPERATURE
PLXANT/2 C 2i x TEMPERATURE
PLXANT/3, . . . , 7 C 3i, ..., C 7i 0 x TEMPERATURE
PLXANT/8 C 8i 0 x TEMPERATURE
PLXANT/9 C 9i 1000 x TEMPERATURE
If C5i, C6i, or C7i is non-zero, absolute temperature units are assumed for all
coefficients C1i through C7i. The temperature limits are always in user input
units.
Barin
See Barin Equations for Gibbs Energy, Enthalpy, Entropy, and Heat Capacity
for details about this submodel.
Wagner Vapor Pressure Equation
The Wagner vapor pressure equation is the best equation for correlation. The
equation can be used if the parameter WAGNER is available:
Where:
Tri = T / Tci
pri *,l = pi *,l / pci
Linear extrapolation of ln pi *,l versus T occurs outside of temperature bounds.
Note: Reduced temperature Tr is always calculated using absolute
temperature units.
PPDS Modified Wagner Vapor Pressure Equation
The PPDS equation also uses the same parameter WAGNER as the standard
Wagner equation:

Where:
Tri = T / Tci
pri *,l = pi *,l / pci
Linear extrapolation of ln pi *,l versus T occurs outside of temperature bounds.
Parameter
Name/Element
184 2 Thermodynamic Property Models
Symbol Default MDS Lower
Limit
WAGNER/1 C 1i x
WAGNER/2 C 2i 0 x
WAGNER/3 C 3i 0 x
WAGNER/4 C 4i 0 x
Upper
Limit
Units
WAGNER/5 C 5i 0 x TEMPERATURE
WAGNER/6 C 6i 1000 x TEMPERATURE
TC T ci TEMPERATURE
PC p ci PRESSURE
NIST Wagner 25 Liquid Vapor Pressure Equation
This equation is the same as the PPDS Modified Wagner equation above, but
it uses parameter WAGNER25 instead of WAGNER, and it uses critical
properties from this parameter set also.
Where:
Tri = T / Tci
Linear extrapolation of ln pi *,l versus T occurs outside of temperature bounds.
Parameter
Name/Element
Symbol Default MDS Lower
Limit
WAGNER25/1 C 1i x
WAGNER25/2 C 2i 0 x
WAGNER25/3 C 3i 0 x
WAGNER25/4 C 4i 0 x
WAGNER25/5 ln p ci 0 x
Upper
Limit
Units
WAGNER25/6 T ci x TEMPERATURE
WAGNER25/7 T lower 0 x TEMPERATURE
WAGNER25/8 T upper 1000 x TEMPERATURE

IK-CAPE Vapor Pressure Equation
The IK-CAPE model is a polynomial equation. If the parameter PLPO is
available, the Aspen Physical Property System can use the IK-CAPE vapor
pressure equation:
Linear extrapolation of ln pi *,l versus T occurs outside of temperature bounds.
Parameter
Name/Element
2 Thermodynamic Property Models 185
Symbol DefaultMDS Lower
Limit
Upper
Limit
Units
PLPO/1 C 1i X PRESSURE
TEMPERATURE
PLPO/2, ..., 10 C 2i , ..., C 10i 0 X TEMPERATURE
PLPO/11 C 11i 0 X TEMPERATURE
PLPO/12 C 12i 1000 X TEMPERATURE
PML Vapor Pressure Equations
The PML vapor pressure equations are modified versions of the Antoine and
Wagner equations. Each equation comes in two alternate forms, identical
except for the use of natural or base-10 logarithms. Parameter LNVPEQ/1
specifies the number of the equation used. Each equation uses a separate
parameter: LNVP1 for equation 1, LOGVP1 for 2, LNPR1 for 3, LOGPR1 for 4,
LNPR2 for 5, and LOGPR2 for 6.
Equation 1 (natural logarithm) and 2 (base 10 logarithm):
Equation 3 (natural logarithm) and 4 (base 10 logarithm):
Equation 5 (natural logarithm) and 6 (base 10 logarithm):
Where:
Tri = T / Tci
pri *,l = pi *,l / pci
LNVPEQ/2 and LNVPEQ/3 are the lower and upper temperature limits,
respectively.
In equations 1-4, if elements 4, 7, or 8 are non-zero, absolute temperature
units are assumed for all elements.

Parameter
Name/Element
186 2 Thermodynamic Property Models
Symbol Default MDS Lower
Limit
Upper
Limit
Units
LNVP1/1, ...,8 C 1i, ..., C 8i x PRESSURE
TEMPERATURE
LOGVP1/1, ..., 8 C 1i, ..., C 8i x PRESSURE
TEMPERATURE
LNPR1/1, ..., 8 C 1i, ..., C 8i x PRESSURE
TEMPERATURE
LOGPR1/1, ..., 8 C 1i, ..., C 8i x PRESSURE
TEMPERATURE
LNPR2/1,2 C 1i, C 2i x
LOGPR2/1,2 C 1i, C 2i x
LNVPEQ/1 (equation
number)
LNVPEQ/2 T lower 0 X TEMPERATURE
LNVPEQ/3 T upper 1000 X TEMPERATURE
TC T ci TEMPERATURE
PC p ci PRESSURE
NIST TDE Polynomial for Liquid Vapor Pressure
This equation can be used for calculating vapor pressure when parameter
PLTDEPOL is available.
Linear extrapolation of ln pi *,l versus T occurs outside of temperature bounds.
If elements 2, 3, 6, or 8 are non-zero, absolute temperature units are
assumed for all elements.
Parameter Symbol DefaultMDS Lower Upper Units
Name/Element
Limit Limit
PLTDEPOL/1 C 1i X
PLTDEPOL/2 C 2i 0 X TEMPERATURE
PLTDEPOL/3 C 3i 0 X
PLTDEPOL/4, ..., 8 C 4i , ..., C 8i 0 X TEMPERATURE
PLTDEPOL/9 T lower 0 X TEMPERATURE
PLTDEPOL/10 T upper 1000 X TEMPERATURE
References
Reid, Prausnitz, and Poling, The Properties of Gases and Liquids, 4th ed.,
(New York: McGraw-Hill, 1987).

Harlacher and Braun, "A Four-Parameter Extension of the Theorem of
Corresponding States," Ind. Eng. Chem. Process Des. Dev., Vol. 9, (1970), p.
479.
W. Wagner, Cryogenics, Vol. 13, (1973), pp. 470-482.
D. Ambrose, M. B. Ewing, N. B. Ghiassee, and J. C. Sanchez Ochoa "The
ebulliometric method of vapor-pressure measurement: vapor pressures of
benzene, hexafluorobenzene, and naphthalene," J. Chem. Thermodyn. 22
(1990), p. 589.
API Sour Model
The API Sour model is based on the API sour water model for correlating the
ammonia, carbon dioxide, and hydrogen sulfide volatilities from aqueous sour
water system. The model assumes aqueous phase chemical equilibrium
reactions involving CO2, H2S, and NH3. The model is not usable with chemistry
in the true component approach. Use the apparent component approach with
this model.
The model is applicable from 20 C to 140 C. The authors developed the model
using available phase equilibrium data and reported average errors between
the model and measured partial pressure data as follows
Compound Average Error, %
Up to 60 C Above 60 C
Ammonia 10 36
Carbon dioxide 11 24
Hydrogen sulfide 12 29
Detail of the model is described in the reference below and is too involved to
be reproduced here.
Reference
New Correlation of NH3, CO2, and H2S Volatility Data from Aqueous Sour
Water Systems, API Publication 955, March 1978 (American Petroleum
Institute).
Braun K-10 Model
The BK10 model uses the Braun K-10 K-value correlations, which were
developed from the K10 charts (K-values at 10 psia) for both real and pseudo
components. The form of the equation used is an extended Antoine vapor
pressure equation with coefficients specific to real components and pseudo
component boiling ranges.
This method is strictly applicable to heavy hydrocarbons at low pressures.
However, our model includes coefficients for a large number of hydrocarbons
and light gases. For pseudocomponents the model covers boiling ranges 450
– 700 K (350 – 800F). Heavier fractions can also be handled using the
methods developed by AspenTech.
2 Thermodynamic Property Models 187

References
B.C. Cajander, H.G. Hipkin, and J.M. Lenoir, "Prediction of Equilibrium Ratios
from Nomograms of Improved Accuracy," Journal of Chemical Engineering
Data, vol. 5, No. 3, July 1960, p. 251-259.
J.M. Lenoir, "Predict K Values at Low Temperatures, part 1," Hydrocarbon
Processing, p. 167, September 1969.
J.M. Lenoir, "Predict K Values at Low Temperatures, part 2," Hydrocarbon
Processing, p. 121, October 1969.
Chao-Seader Pure Component Liquid
Fugacity Model
The Chao-Seader model calculates pure component fugacity coefficient, for
liquids. It is used in the CHAO-SEA property method. This is an empirical
model with the Curl-Pitzer form. The general form of the model is:
Where:
188 2 Thermodynamic Property Models
=
Parameter
Name/Element
Symbol Default MDS Lower Limit Upper
Limit
Units
TC T ci — — 5.0 2000.0 TEMPERATURE
PC p ci — — 10 5
OMEGA � i
References
10 8
— — -0.5 2.0 —
PRESSURE
K.C. Chao and J.D. Seader, "A General Correlation of Vapor-Liquid Equilibria
in Hydrocarbon Mixtures," AIChE J., Vol. 7, (1961), p. 598.
Grayson-Streed Pure Component Liquid
Fugacity Model
The Grayson-Streed model calculates pure component fugacity coefficients for
liquids, and is used in the GRAYSON/GRAYSON2 property methods. It is an
empirical model with the Curl-Pitzer form. The general form of the model is:
Where:
Parameter
Name/Element
Symbol Default MDS Lower Limit Upper
Limit
Units
TC T ci — — 5.0 2000.0 TEMPERATURE

Parameter
Name/Element
2 Thermodynamic Property Models 189
Symbol Default MDS Lower Limit Upper
Limit
PC p ci — — 10 5
OMEGA � i
References
10 8
— — -0.5 2.0 —
Units
H.G. Grayson and C.W. Streed, Paper 20-PO7, Sixth World Petroleum
Conference, Frankfurt, June 1963.
Kent-Eisenberg Liquid Fugacity Model
PRESSURE
The Kent-Eisenberg model calculates liquid mixture component fugacity
coefficients and liquid enthalpy for the AMINES property method.
The chemical equilibria in H2S + CO2 + amine systems are described using
these chemical reactions:
Where:
R' = Alcohol substituted alkyl groups
The equilibrium constants are given by:
The chemical equilibrium equations are solved simultaneously with the
balance equations. This obtains the mole fractions of free H2S and CO2 in
solution. The equilibrium partial pressures of H2S and CO2 are related to the
respective free concentrations by Henry's constants:

The apparent fugacities and partial molar enthalpies, Gibbs energies and
entropies of H2S and CO2 are calculated by standard thermodynamic
relationships. The chemical reactions are always considered.
The values of the coefficients for the seven equilibrium constants (A1i, ... A5i)
and for the two Henry's constants B1i and B2i are built into the Aspen Physical
Property System. The coefficients for the equilibrium constants were
determined by regression. All available data for the four amines were used:
monoethanolamine, diethanolamine, disopropanolamine and diglycolamine.
You are not required to enter any parameters for this model.
References
R.L. Kent and B. Eisenberg, Hydrocarbon Processing, (February 1976),
pp. 87-92.
Maxwell-Bonnell Vapor Pressure Model
The Maxwell-Bonnell model calculates vapor pressure using the Maxwell-
Bonnell vapor pressure correlation for all hydrocarbon pseudo-components as
a function of temperature. This is an empirical correlation based on API
procedure 5A1.15, 5A1.13. This model is used in property method MXBONNEL
for calculating vapor pressure and liquid fugacity coefficients (K-values).
References
API procedure 5A1.15 and 5A1.13.
Solid Antoine Vapor Pressure Model
The vapor pressure of a solid can be calculated using the Antoine equation.
Parameters for some components are available for the extended Antoine
equation from the Aspen Physical Property System pure component databank.
This equation can be used whenever the parameter PSANT is available.
The equation for the solid Antoine vapor pressure model is:
Extrapolation of ln pi *,s versus 1/T occurs outside of temperature bounds.
Parameter
Name/
Element
190 2 Thermodynamic Property Models
Symbol Default MDS Lower Limit Upper
Limit
Units
PSANT/1 C 1i — x — — PRESSURE,
TEMPERATURE
PSANT/2 C 2i — x — — TEMPERATURE
PSANT/3 C 3i 0 x — — TEMPERATURE
PSANT/4 C 4i 0 x — — TEMPERATURE
PSANT/5 C 5i 1000 x — — TEMPERATURE

General Pure Component Heat
of Vaporization
The Aspen Physical Property System has several submodels for calculating
pure component heat of vaporization. It uses parameter THRSWT/4 to
determine which submodel is used. See Pure Component Temperature-
Dependent Properties for details.
If THRSWT/4
is
2 Thermodynamic Property Models 191
Then this equation is used And this parameter is
used
0 Watson DHVLWT
106 DIPPR DHVLDP
301 PPDS DHVLDS
401 IK-CAPE DHVLPO
505 NIST TDE Watson equation DHVLTDEW
DIPPR Heat of Vaporization Equation
The DIPPR equation is used to calculate heat of vaporization when THRSWT/4
is set to 106. (Other DIPPR equations may sometimes be used. See Pure
Component Temperature-Dependent Properties for details.)
The equation for the DIPPR heat of vaporization model is:
Where:
Tri = T / Tci
Note: Reduced temperature Tr is always calculated using absolute
temperature units.
Linear extrapolation of �vapHi * versus T occurs outside of temperature bounds,
using the slope at the temperature bound, except that �vapHi * is zero for
.
Parameter Symbol Default MDS Lower
Name/Element
Limit
Upper
Limit
Units
DHVLDP/1 C 1i — x — — MOLE-ENTHALPY
DHVLDP/2, ..., 5 C 2i, ..., C 5i 0 x — — —
DHVLDP/6 C 6i 0 x — — TEMPERATURE
DHVLDP/7 C 7i 1000 x — — TEMPERATURE
TC T ci — — 5.0 2000.0 TEMPERATURE
Watson Heat of Vaporization Equation
The Watson equation is used to calculate heat of vaporization when
THRSWT/4 is set to 0. See Pure Component Temperature-Dependent
Properties for details.

The equation for the Watson model is:
Where:
�vapHi * (T1) = Heat of vaporization at temperature T1
Linear extrapolation of �vapHi * versus T occurs below the minimum
temperature bound, using the slope at the temperature bound.
Parameter
Symbol Default Lower Upper Units
Name/Element
Limit Limit
TC T ci — 5.0 2000.0 TEMPERATURE
DHVLWT/1 � vapH i * (T1) — 5x10 4
192 2 Thermodynamic Property Models
5x10 8
MOLE-ENTHALPY
DHVLWT/2 T 1 — 4.0 3500.0 TEMPERATURE
DHVLWT/3 a i 0.38 -2.0 2.0 —
DHVLWT/4 b i 0 -2.0 2.0 —
DHVLWT/5 T min 0 0.0 1500.0 TEMPERATURE
PPDS Heat of Vaporization Equation
The PPDS equation is used to calculate heat of vaporization when THRSWT/4
is set to 301. See Pure Component Temperature-Dependent Properties for
details.
The equation for the PPDS model is:
where R is the gas constant.
Linear extrapolation of �vapHi * versus T occurs outside of temperature bounds,
using the slope at the temperature bound.
Parameter
Name/Element
Symbol Default MDS Lower
Limit
Upper
Limit
Units
TC T ci — 5.0 2000.0 TEMPERATURE
DHVLDS/1 C 1i — — — — —
DHVLDS/2 C 2i 0 — — — —
DHVLDS/3 C 3i 0 — — — —
DHVLDS/4 C 4i 0 — — — —
DHVLDS/5 C 5i 0 — — — —
DHVLDS/6 C 6i 0 — — TEMPERATURE
DHVLDS/7 C 7i 1000 — — TEMPERATURE

IK-CAPE Heat of Vaporization Equation
The IK-CAPE equation is used to calculate heat of vaporization when
THRSWT/4 is set to 401. See Pure Component Temperature-Dependent
Properties for details.
The equation for the IK-CAPE model is:
Linear extrapolation of �vapHi * versus T occurs outside of temperature bounds,
using the slope at the temperature bound
Parameter
Name/Element
2 Thermodynamic Property Models 193
Symbol Default MDS Lower
Limit
Upper
Limit
Units
DHVLPO/1 C 1i — X — — MOLE-
ENTHALPY
DHVLPO/2, ..., 10C 2i, ..., C 10i 0 X — — MOLE-
ENTHALPY
TEMPERATURE
DHVLPO/11 C 11i 0 X — — TEMPERATURE
DHVLPO/12 C 12i 1000 X — — TEMPERATURE
NIST TDE Watson Heat of Vaporization
Equation
The NIST TDE Watson equation is used to calculate heat of vaporization when
THRSWT/4 is set to 505. See Pure Component Temperature-Dependent
Properties for details.
The equation is:
Linear extrapolation of �vapHi * versus T occurs outside of temperature bounds,
using the slope at the temperature bound
Parameter
Name/Element
Symbol Default MDS Lower
Limit
Upper
Limit
DHVLTDEW/1 C 1i — X — — —
DHVLTDEW/2, 3,
4
C 2i, C 3i, C 4i 0 X — — —
Units
DHVLTDEW/5 T ci — X — — TEMPERATURE
DHVLTDEW/6 nTerms 4 X — — —
DHVLTDEW/7 T lower 0 X — — TEMPERATURE
DHVLTDEW/8 T upper 1000 X — — TEMPERATURE

Clausius-Clapeyron Equation
The Aspen Physical Property System can calculate heat of vaporization using
the Clausius Clapeyron equation:
Where:
Vi *,v
Vi *,l
194 2 Thermodynamic Property Models
= Slope of the vapor pressure curve calculated from the Extended
Antoine equation
= Vapor molar volume calculated from the Redlich Kwong
equation of state
= Liquid molar volume calculated from the Rackett equation
For parameter requirements, see General Pure Component Liquid Vapor
Pressure, the General Pure Component Liquid Molar Volume model, and
Redlich Kwong.
Molar Volume and Density
Models
The Aspen Physical Property System has the following built-in molar volume
and density models available. This section describes the molar volume and
density models.
Model Type
API Liquid Volume Liquid volume
Brelvi-O'Connell Partial molar liquid
volume of gases
Clarke Aqueous Electrolyte Volume Liquid volume
COSTALD Liquid Volume Liquid volume
Debye-Hückel Volume Electrolyte liquid volume
Liquid Constant Molar Volume Model Liquid volume
General Pure Component Liquid Molar
Volume
Rackett/Campbell-Thodos Mixture Liquid
Volume
Liquid volume/liquid
density
Liquid volume
Modified Rackett Liquid volume
General Pure Component Solid Molar Volume Solid volume
Liquid Volume Quadratic Mixing Rule Liquid volume
API Liquid Molar Volume
This model calculates liquid molar volume for a mixture, using the API
procedure and the Rackett model. Ideal mixing is assumed:

Where:
xp = Mole fraction of pseudocomponents
xr = Mole fraction of real components
For pseudocomponents, the API procedure is used:
Where:
fcn = A correlation based on API procedure 6A3.5 (API Technical Data
Book, Petroleum Refining, 4th edition)
At high density, the Ritter equation is used (adapted from Ritter, Lenoir, and
Schweppe, Petrol. Refiner 37 [11] 225 (1958)):
Where SG is the specific gravity, Tb is the mean average boiling point in
Rankine, T is the temperature of the system in Rankine, and the mass volume
is produced in units of cubic feet per pound-mass.
This procedure is valid over the following conditions:
� UOPK: 10.5 - 12.5
� API: 0 - 95
� Mean Average Boiling Point: 0 - 1100 F
� Temperature: 0 - 1000 F
� Calculated density: 0.4 - 1.05 g/cc
The effect of pressure is automatically accounted for using procedure 6A3.10.
This procedure has the following validity range:
� Density at low pressure: 0.7 - 1.0 g/cc
� Pressure: 0 - 100,000 psig
For real components, the mixture Rackett model is used:
Note: Reduced temperature Tr is always calculated using absolute
temperature units.
See the Rackett model for descriptions.
Parameter
Name/Element
2 Thermodynamic Property Models 195
Symbol Default MDS Lower
Limit
Upper
Limit
Units
TB T b — — 4.0 2000.0 TEMPERATURE
API API — — -60.0 500.0 —
TC T c — — 5.0 2000.0 TEMPERATURE

Parameter
Name/Element
196 2 Thermodynamic Property Models
Symbol Default MDS Lower
Limit
PC p c — — 10 5
RKTZRA Z RA
Upper
Limit
10 8
ZC — 0.1 0.5 —
Units
PRESSURE
There are two versions of this model: VL2API and VL2API5. Model VL2API is
used in route VLMX20, while model VL2API5 is used in route VLMX24.
The main difference between the VL2API and VL2API5 models is as follows:
� The VL2API model calculates the liquid density for each pseudocomponent
using the API procedure 6A3.5 (or Ritter equation), then computes the
density of the pseudocomponent mixture as a mole-fraction-weighted
average.
� The VL2API5 model calculates the liquid density of the mixture of the
pseudocomponents as a whole. It first computes the specific gravity and
mean average boiling point of the pseudocomponent mixture, then uses the
API procedure 6A3.5 (or Ritter equation) to compute the mixture liquid
density.
Both models use the same procedure 6A3.10 for pressure correction.
Experience shows that VL2API5 is less sensitive to how the
pseudocomponents are generated from the same assay (number of cut
points, etc.).
Brelvi-O'Connell
The Brelvi-O'Connell model calculates partial molar volume of a supercritical
component i at infinite dilution in pure solvent A. Partial molar volume at
infinite dilution is required to compute the effect of pressure on Henry's
constant. (See Henry's Constant.)
The general form of the Brelvi-O'Connell model is:
Where:
i = Solute or dissolved-gas component
A = Solvent component
The liquid molar volume of solvent is obtained from the Rackett model:
Note: Reduced temperature Tr is always calculated using absolute
temperature units.
Parameter Symbol Default MDS Lower Upper Units
Name/Element
Limit Limit
TC T cA — — 5.0 2000.0 TEMPERATURE
PC p cA — — 10 5
RKTZRA Z A RA
10 8
ZC x 0.1 1.0 —
PRESSURE

Parameter
Name/Element
VLBROC/1 V i BO
2 Thermodynamic Property Models 197
Symbol Default MDS Lower
Limit
Upper
Limit
Units
VC x -1.0 1.0 MOLE-VOLUME
VLBROC/2 — 0 x -0.1 0.1 TEMPERATURE
References
S.W. Brelvi and J.P. O'Connell, AIChE J., Vol. 18, (1972), p. 1239.
S.W. Brelvi and J.P. O'Connell, AIChE J., Vol. 21, (1975), p. 157.
Clarke Aqueous Electrolyte Volume
The Clarke model calculates liquid molar volume for electrolytes solutions.
The model is applicable to mixed solvents and is based on:
� Molar volume of molecular solvents (equation 2)
� The relationship between the partial molar volume of an electrolyte and its
mole fraction in the solvent (equation 4)
All quantities are expressed in terms of apparent components.
If option code 1 is set to 1, the liquid volume quadratic mixing rule is used
instead. The default option uses this equation to calculate the liquid molar
volume for electrolyte solutions:
Where:
Vm l
Vs l
Ve l
(1)
= Liquid molar volume for electrolyte solutions.
= Liquid molar volume for solvent mixtures.
= Liquid molar volume for electrolytes.
Apparent Component Approach
For molecular solvents, the liquid molar volume is calculated by:
Where:
xw = Mole fraction of water
Vw *
(2)
= Molar volume of water from the steam table.
xnws = Sum of the mole fractions of all non-water
solvents.
Vnws l
For electrolytes:
= Liquid molar volume for the mixture of all nonwater
solvents. It is calculated using the
Rackett equation.

Where:
xca = Apparent mole fraction of electrolyte ca
Vca = Liquid molar volume for electrolyte ca
The mole fractions xca are reconstituted arbitrarily from the true ionic
concentrations, even if you use the apparent component approach. This
technique is explained in Electrolyte Calculation in Physical Property Methods.
The result is that electrolytes are generated from all possible combinations of
ions in solution. The following equation is consistently applied to determine
the amounts of each possible apparent electrolyte nca:
Where:
198 2 Thermodynamic Property Models
(3)
(4)
(5)
(6)
(7)
nca = Number of moles of apparent electrolyte ca
zc = Charge of c
zfactor = zc if c and a have the same number of
charges; otherwise 1.
nc = Number of moles of cation c
na = Number of moles of anion a
For example: given an aqueous solution of Ca 2+ , Na + , SO4 2- , Cl - four
electrolytes are found: CaCl2, Na2SO4, CaSO4, and NaCl. The Clarke
parameters of all four electrolytes are used. You can rely on the default,
which calculates the Clarke parameters from ionic parameters. Otherwise, you
must enter parameters for any electrolytes that may not exist in the
components list. If you do not want to use the default, the first step in using
the Clarke model is to add any needed components for electrolytes not in the
components list.
True Component Approach
The true molar volume is obtained from the apparent molar volume:

Where:
Vm l,t = Liquid volume per number of true species
Vm l,a = Liquid volume per number of apparent species, Vm l
of equation 1
n a
n t
= Number of apparent species
= Number of true species
The apparent molar volume is calculated as explained in the preceding
subsection.
Temperature Dependence
The temperature dependence of the molar volume of the solution is
approximately equal to the temperature dependence of the molar volume of
the solvent mixture:
Where Vm l (298.15K) is calculated from equation 1.
Parameter
Name/Element
Applicable
Components
2 Thermodynamic Property Models 199
(8)
(9)
Symbol Default Units
VLCLK/1 Cation-Anion † MOLE-VOLUME
VLCLK/2 Cation-Anion A ca 0.020 MOLE-VOLUME
†If VLCLK/1 is missing, it is calculated based on VLBROC and CHARGE as
follows:
(10)
If VLBROC/1 is missing, the default value of -0.0012 is used. See the Brelvi-
O'Connell model for VLBROC and also Rackett/Campbell-Thodos Mixture
Liquid Volume for additional parameters used in the Rackett equation.
Reference
C.C. Chen, private communication.
COSTALD Liquid Volume
The equation for the COSTALD liquid volume model is:

Where:
Vm R,0 and Vm R,� are functions or Tr for
For , there is a linear interpolation between the liquid density at
Tr = 0.95 and the vapor density at Tr = 1.05. This model can be used to
calculate saturated and compressed liquid molar volume. The compressed
liquid molar volume is calculated using the Tait equation:
Where B and C are functions of T, �, Tc, Pc and P sat is the saturated pressure
at T.
Note: Reduced temperature Tr is always calculated using absolute
temperature units.
Mixing Rules:
Where:
To improve results, the Aspen Physical Property System uses a special
correlation for water when this model is used. Changing the VSTCTD and
OMGCTD parameters for water will not affect the results of the special
correlation.
Parameter
Name/Element
200 2 Thermodynamic Property Models
Symbol Default MDS Lower
Limit
Upper
Limit
Units
TC T ci — — 5.0 2000.0 TEMPERATURE
VSTCTD V r *,CTD
OMGCTD � r
References
VC X 0.001 3.5 MOLE-VOLUME
OMEGA X -0.5 2.0 —
R.W. Hankinson and G.H. Thomson, AIChE J., Vol. 25, (1979), p. 653.
G.H. Thomson, K.R. Brobst, and R.W. Hankinson, AIChE J., Vol. 28, (1982),
p. 4, p. 671.

Debye-Hückel Volume
The Debye-Hückel model calculates liquid molar volume for aqueous
electrolyte solutions.
The equation for the Debye-Hückel volume model is:
Where:
�
Vk is the molar volume for water and is calculated from the ASME steam
table.
Vk is calculated from the Debye-Hückel limiting law for ionic species. It is
assumed to be the infinite dilution partial volume for molecular solutes.
Where:
�
Vk = Partial molar ionic volume at infinite dilution
zk = Charge number of ion k
Av = Debye-Hückel constant for volume
b = 1.2
I =
mk = Molarity of ion k
Av is computed as follows:
Where:
2 Thermodynamic Property Models 201
the ionic strength, with
A� = Debye-Hückel constant for the osmotic
coefficients (Pitzer, 1979)
�w = Density of water (kg / m 3 )
�w = Dielectric constant of water (Fm -1 ), a function
of pressure and temperature (Bradley and
Pitzer, 1979)
Parameter Name Applicable
Components
Symbol Default Units
VLBROC Ions, molecular Solutes �
Vk 0 MOLE-VOLUME

References
D. J. Bradley, K. S. Pitzer, "Thermodynamics of Electrolytes," J. Phys. Chem.,
83 (12), 1599 (1979).
H.C. Helgeson and D.H. Kirkham, "Theoretical prediction of the
thermodynamic behavior of aqueous electrolytes at high pressure and
temperature. I. Thermodynamic/electrostatic properties of the solvent", Am.
J. Sci., 274, 1089 (1974).
K.S. Pitzer, "Theory: Ion Interaction Approach," Activity Coefficients in
Electrolyte Solutions, Pytkowicz, R. ed., Vol. I, (CRC Press Inc., Boca Raton,
Florida, 1979).
Liquid Constant Molar Volume Model
This model, VL0CONS, uses a constant value entered by the user as the pure
component liquid molar volume. It is not a function of temperature or
pressure. This is used with the solids handling property method for modeling
nonconventional solids.
Parameter Name Default MDS Units
VLCONS 1 x MOLE-VOLUME
General Pure Component Liquid Molar
Volume
The Aspen Physical Property System has several submodels for calculating
liquid molar volume. It uses parameter THRSWT/2 to determine which
submodel is used. See Pure Component Temperature-Dependent Properties
for details.
If THRSWT/2 is This equation is used And this parameter is used
0 Rackett RKTZRA
100-116 DIPPR DNLDIP
301 PPDS DNLPDS
401 IK-CAPE VLPO
503 NIST ThermoML
Polynomial
202 2 Thermodynamic Property Models
DNLTMLPO
504 NIST TDE expansion DNLEXSAT
514 NIST TDE Rackett DNLRACK
515 NIST COSTALD DNLCOSTD
For liquid molar volume of mixtures, the Rackett mixture equation is always
used by default. This is not necessarily consistent with the pure component
molar volume or density. If you need consistency, select route VLMX26 on the
Properties | Property Methods form. This route calculates mixture molar
volume from the mole-fraction average of pure component molar volumes.
Many of these equations calculate density first, and return calculate liquid
molar volume based on that density:

DIPPR
DIPPR equation 105 is the default DIPPR equation for most substances:
This equation is similar to the Rackett equation.
DIPPR equation 116 is the default equation for water.
� = 1 - T / Tc
Other DIPPR equations, such as equation 100, may be used for some
substances. Check the value of THRSWT/2 to determine the equation used.
See Pure Component Temperature-Dependent Properties for details about
DIPPR equations.
In either case, linear extrapolation of �i *,l versus T occurs outside of
temperature bounds.
Parameter
Name/Element
2 Thermodynamic Property Models 203
Symbol Default MDS Lower
Limit
Upper
Limit
Units
DNLDIP/1 C 1i — x — — MOLE-DENSITY †
DNLDIP/2 C 2i 0 x — — †
DNLDIP/3 C 3i T ci † x — — TEMPERATURE †
DNLDIP/4 C 4i 0 x — — †
DNLDIP/5 C 5i 0 x — — †
DNLDIP/6 C 6i 0 x — — TEMPERATURE
DNLDIP/7 C 7i 1000 x — — TEMPERATURE
† For equation 116, the units are MOLE-DENSITY for parameters DNLDIP/1
through DNLDIP/5 and the default for DNLDIP/3 is 0. For equation 105,
DNLDIP/5 is not used, and absolute temperature units are assumed for
DNLDIP/3.
PPDS
The PPDS equation is:
Linear extrapolation of �i *,l versus T occurs outside of temperature bounds.
Parameter
Name/Element
Symbol DefaultMDS Lower
Limit
Upper
Limit
MW M i — — 1.0 5000.0 —
Units

Parameter
Name/Element
204 2 Thermodynamic Property Models
Symbol DefaultMDS Lower
Limit
Upper
Limit
Units
VC V ci — — 0.001 3.5 MOLE-VOLUME
TC T ci — — 5.0 2000.0 TEMPERATURE
DNLPDS/1 C 1i — — — — MASS-DENSITY
DNLPDS/2 C 2i 0 — — — MASS-DENSITY
DNLPDS/3 C 3i 0 — — — MASS-DENSITY
DNLPDS/4 C 4i 0 — — — MASS-DENSITY
DNLPDS/5 C 5i 0 x — — TEMPERATURE
DNLPDS/6 C 6i 1000 x — — TEMPERATURE
IK-CAPE
The IK-CAPE equation is:
Linear extrapolation of Vi *,l versus T occurs outside of temperature bounds.
Parameter
Name/Element
Symbol Default MDS Lower
Limit
Upper
Limit
Units
VLPO/1 C 1i — X — — MOLE-
VOLUME
VLPO/2, ..., 10 C 2i, ..., C 10i 0 X — — MOLE-
VOLUME
TEMPERATURE
VLPO/11 C 11i 0 X — — TEMPERATURE
VLPO/12 C 12i 1000 X — — TEMPERATURE
NIST ThermoML Polynomial
This equation can be used when parameter DNLTMLPO is available.
Parameter
Name/Element
Symbol Default MDS Lower
Limit
Upper
Limit
Units
DNLTMLPO/1 C 1i — X — — MOLE-
DENSITY
DNLTMLPO/2, 3,
4
C 2i, C 3i, C 4i 0 X — — MOLE-
DENSITY
TEMPERATURE
DNLTMLPO/5 nTerms 4 X — — —
DNLTMLPO/6 0 X — — TEMPERATURE
DNLTMLPO/7 1000 X — — TEMPERATURE

Rackett
The Rackett equation is:
Where:
Tr = T / Tci
Note: Reduced temperature Tr is always calculated using absolute
temperature units.
Note: Above Tr=0.99 an extrapolation method is used to smooth the
transition to constant molar volume equal to the critical volume.
Parameter
Name/
Element
2 Thermodynamic Property Models 205
Symbol Default MDS Lower
Limit
Upper
Limit
Units
TC T ci — — 5.0 2000.0 TEMPERATURE
PC p ci — — 10 5
RKTZRA Z i *,RA
NIST TDE Rackett Parameters
10 8
ZC x 0.1 1.0 —
PRESSURE
This equation can be used when the parameter DNLRACK is available.
Linear extrapolation of Vi *,l versus T occurs outside of temperature bounds.
Parameter
Name/
Element
Symbol Default MDS Lower
Limit
Upper
Limit
DNLRACK/1 Z c — x — — —
DNLRACK/2 n 2/7 x — — —
Units
DNLRACK/3 T ci — x — — TEMPERATURE
DNLRACK/4 p ci 0 x — — PRESSURE
DNLRACK/5 T lower 0 x — — TEMPERATURE
DNLRACK/6 T upper 1000 x — — TEMPERATURE
NIST COSTALD Parameters
This equation can be used when the parameter DNLCOSTD is available.

Linear extrapolation of Vi *,l versus T occurs outside of temperature bounds.
Parameter
Name/
Element
206 2 Thermodynamic Property Models
Symbol Default MDS Lower
Limit
Upper
Limit
Units
DNLCOSTD/1 V oi — x — — VOLUME
DNLCOSTD/2 � 0 x — — —
DNLCOSTD/3 T ci — x — — TEMPERATURE
DNLCOSTD/4 T lower 0 x — — TEMPERATURE
DNLCOSTD/5 T upper 1000 x — — TEMPERATURE
NIST TDE Expansion
This equation can be used when the parameter DNLEXSAT is available.
Linear extrapolation of Vi *,l versus T occurs outside of temperature bounds.
Parameter
Name/
Element
DNLEXSAT/1 � ci
Symbol Default MDS Lower
Limit
Upper
Limit
Units
— x — — MOLE-
DENSITY
DNLEXSAT/2 C 1i — x — — MOLE-
DENSITY
DNLEXSAT/3, C2i, ..., C6i 0 x — — MOLE-
..., DNLEXSAT/7
DENSITY
DNLEXSAT/8 T ci — x — — TEMPERATURE
DNLEXSAT/9 nTerms 6 x — — —
DNLEXSAT/10 T lower 0 x — — TEMPERATURE
DNLEXSAT/11 T upper 1000 x — — TEMPERATURE
References
H.G. Rackett, J.Chem. Eng. Data., Vol. 15, (1970), p. 514.
C.F. Spencer and R.P. Danner, J. Chem. Eng. Data, Vol. 17, (1972), p. 236.

Rackett/Campbell-Thodos Mixture Liquid
Volume
The Rackett equation calculates liquid molar volume for all activity coefficient
based and petroleum tuned equation of state based property methods. In the
last category of property methods, the equation is used in conjunction with
the API model. The API model is used for pseudocomponents, while the
Rackett model is used for real components. (See API Liquid Volume .)
Campbell-Thodos is a variation on the Rackett model which allows the
compressibility term Zi *,RA to vary with temperature.
Rackett
The equation for the Rackett model is:
Where:
Tc
Zm RA
Vcm
=
=
=
=
Tr = T / Tc
Note: Reduced temperature Tr is always calculated using absolute
temperature units.
Note: Above Tr=0.99 an extrapolation method is used to smooth the
transition to constant molar volume equal to the critical volume.
Parameter
Name/
Element
2 Thermodynamic Property Models 207
Symbol Default MDS Lower
Limit
Upper
Limit
Units
TC T ci — — 5.0 2000.0 TEMPERATURE
PC p ci — — 10 5
10 8
PRESSURE
VCRKT V ci VC x 0.001 3.5 MOLE-
VOLUME
RKTZRA Z i *,RA
ZC x 0.1 1.0 —
RKTKIJ k ij x -5.0 5.0 —

Campbell-Thodos
The Campbell-Thodos model uses the same equation and parameters as the
Rackett model, above, except that Zm RA is allowed to vary with temperature:
Zm RA
=
Campbell-Thodos also uses separately-adjustable versions of the critical
parameters. Tmin and Tmax define the temperature range where the
equation is applicable.
Parameter
Name/
Element
208 2 Thermodynamic Property Models
Symbol Default MDS Lower
Limit
Upper
Limit
Units
RACKET/1 R*T ci/P ci R*Tci/Pci — — — MOLE-
VOLUME
RACKET/2 Z i *,RA
RKTZRA x 0.1 1.0 —
RACKET/3 d i 0 x 0 0.11 —
RACKET/4 T min 0 x — — TEMPERATURE
RACKET/5 T max 1000 x — — TEMPERATURE
The Campbell-Thodos model is used when RACKET/3 is set to a value less
than 0.11. The default value, 2/7, indicates that the standard Rackett
equation should be used. When Campbell-Thodos is not used, RACKET/3
should be kept at its default value of 2/7 for all components.
References
H.G. Rackett, J.Chem, Eng. Data., Vol. 15, (1970), p. 514.
C.F. Spencer and R.P. Danner, J. Chem. Eng. Data, Vol. 17, (1972), p. 236.
Modified Rackett Liquid Molar Volume
The Modified Rackett equation improves the accuracy of liquid mixture molar
volume calculation by introducing additional parameters to compute the pure
component parameter RKTZRA and the binary parameter kij.
The equation for the Modified Rackett model is:
Where:
Tc
kij
=
=
=

Zm RA
Zi *,RA
Vcm
2 Thermodynamic Property Models 209
=
=
=
Tr = T / Tc
Note: Reduced temperature Tr is always calculated using absolute
temperature units.
Note: Above Tr=0.99 an extrapolation method is used to smooth the
transition to constant molar volume equal to the critical volume.
Parameter
Name/Element
Symbol Default MDS Lower
Limit
Upper
Limit
MRKZRA/1 a i RKTZRA x 0.1 0.5 —
MRKZRA/2 b i 0 x — — —
MRKZRA/3 c i 0 x — — —
MRKKIJ/1 A ij x — — —
MRKKIJ/2 B ij 0 x — — —
MRKKIJ/3 C ij 0 x — — —
References
H.G. Rackett, J.Chem, Eng. Data., Vol. 15, (1970), p. 514.
C.F. Spencer and R.P. Danner, J. Chem. Eng. Data, Vol. 17, (1972), p. 236.
Rackett Extrapolation Method
Units
The Rackett equation has a formula involving an exponent of 1+(1-Tr ) 2/7
which is invalid above the critical temperature. As a result, a special
extrapolation method is required for this equation. This method involves the
calculation of an intermediate temperature T00 near the critical temperature.
When the temperature exceeds T00, the volume is constant at the critical
volume. When the temperature is between 0.99Tc and T00, a circle equation is
used to smoothly interpolate the volume between the value and slope at
0.99Tc and the constant value at T00.

Details
First the volume V0 at 0.99Tc and the critical volume Vc are calculated:
Then the volume difference is calculated, as well as the temperature
difference required for the circle equation:
From this, the required intermediate temperature T00 can be calculated:
Then the volume V00 at the circle's center can be calculated:
Finally, the equation of the circle is used to determine any point (T,V) for
0.99Tc < T < T00:
210 2 Thermodynamic Property Models

General Pure Component Solid Molar
Volume
The Aspen Physical Property System has several submodels for calculating
solid molar volume. It uses parameter THRSWT/1 to determine which
submodel is used. See Pure Component Temperature-Dependent Properties
for details.
If THRSWT/1 is This equation is used And this parameter is
used
0 Aspen VSPOLY
100 DIPPR DNSDIP
401 IK-CAPE VSPO
503 NIST ThermoML
polynomial
Aspen Polynomial
2 Thermodynamic Property Models 211
DNSTMLPO
The equation for the Aspen solids volume polynomial is:
Linear extrapolation of Vi *,s versus T occurs outside of temperature bounds.
Parameter
Name
Applicable
Components
Symbol MDS Default Units
VSPOLY/1 Salts, CI solids C 1i x — MOLE-VOLUME
TEMPERATURE
VSPOLY/2, ..., 5 Salts, CI solids C 2i, ..., C 5i x 0 MOLE-VOLUME
TEMPERATURE
VSPOLY/6 Salts, CI solids C 6i x 0 MOLE-VOLUME
TEMPERATURE
VSPOLY/7 Salts, CI solids C 7i x 1000 MOLE-VOLUME
TEMPERATURE
IK-CAPE Equation
The IK-CAPE equation is:
Linear extrapolation of Vi *,s versus T occurs outside of temperature bounds.
Parameter
Name/Element
Symbol Default MDS Lower
Limit
Upper
Limit
Units
VSPO/1 C 1i — X — — MOLE-
VOLUME

Parameter
Name/Element
212 2 Thermodynamic Property Models
Symbol Default MDS Lower
Limit
Upper
Limit
Units
VSPO/2, ..., 10 C 2i, ..., C 10i 0 X — — MOLE-
VOLUME
TEMPERATURE
VSPO/11 C 11i 0 X — — TEMPERATURE
VSPO/12 C 12i 1000 X — — TEMPERATURE
DIPPR
The DIPPR equation is:
Linear extrapolation of �i *,s versus T occurs outside of temperature bounds.
Vi *,s = 1 / �i *,s
(Other DIPPR equations may sometimes be used. See Pure Component
Temperature-Dependent Properties for details.)
The model returns solid molar volume for pure components.
Parameter
Name/Element
Symbol Default MDS Lower
Limit
Upper
Limit
Units
DNSDIP/1 C 1i — x — — MOLE-
DENSITY
DNSDIP/2, ..., 5 C 2i, ..., C 5i 0 x — — MOLE-
DENSITY,
TEMPERATURE
DNSDIP/6 C 6i 0 x — — TEMPERATURE
DNSDIP/7 C 7i 1000 x — — TEMPERATURE
NIST ThermoML Polynomial
Linear extrapolation of �i *,s versus T occurs outside of temperature bounds.
Vi *,s = 1 / �i *,s
Parameter
Name/Element
Symbol Default MDS Lower
Limit
Upper
Limit
Units
DNSTMLPO/1 C 1i — x — — MOLE-
DENSITY
DNSTMLPO/2,...,8 C 2i, ..., C 8i 0 x — — MOLE-
DENSITY,
TEMPERATURE
DNSTMLPO/9 nTerms 8 x — — —
DNSTMLPO/10 T lower 0 x — — TEMPERATURE
DNSTMLPO/11 T upper 1000 x — — TEMPERATURE

Liquid Volume Quadratic Mixing Rule
With i and j being components, the liquid volume quadratic mixing rule is:
Option Codes
Option Code Value Descriptions
1 0 Use normal pure component liquid volume model for all
components (default)
1 Use steam tables for water
2 0 Use mole basis composition (default)
Parameter
Parameter
Name/Element
1 Use mass basis composition
2 Thermodynamic Property Models 213
Symbol Default MDS Lower
Limit
Upper
Limit
VLQKIJ K ij - x - - —
Units
This model is not part of any property method. To use it, you will need to
define a property method on the Properties | Property Methods form.
Specify the route VLMXQUAD for VLMX on the Routes sheet of this form, or
the model VL2QUAD for VLMX on the Models sheet.
Heat Capacity Models
The Aspen Physical Property System has five built-in heat capacity models.
This section describes the heat capacity models available.
Model Type
Aqueous Infinite Dilution Heat Capacity
Polynomial
Criss-Cobble Aqueous Infinite Dilution
Ionic Heat Capacity
General Pure Component Liquid Heat
Capacity
General Pure Component Ideal Gas Heat
Capacity
General Pure Component Solid Heat
Capacity
Electrolyte liquid
Electrolyte liquid
Liquid
Ideal gas
Solid
Aqueous Infinite Dilution Heat Capacity
The aqueous phase infinite dilution enthalpies, entropies, and Gibbs energies
are calculated from the heat capacity polynomial. The values are used in the
calculation of aqueous and mixed solvent properties of electrolyte solutions:

versus T is linearly extrapolated using the slope at C7i for T < C7i
versus T is linearly extrapolated using the slope at C8i for T < C8i
Parameter Applicable
Symbol Default Units
Name/Element Components
CPAQ0/1 Ions, molecular solutes C 1i — TEMPERATURE and
HEAT CAPACITY
CPAQ0/2,…,6 Ions, molecular solutes C 2i, ..., C 6i 0 TEMPERATURE and
HEAT CAPACITY
CPAQ0/7 Ions, molecular solutes C 7i 0 TEMPERATURE
CPAQ0/8 Ions, molecular solutes C 8i 1000 TEMPERATURE
If any of C4i through C6i is non-zero, absolute temperature units are
assumed for C1i through C6i . Otherwise, user input units for temperature are
used. The temperature limits are always interpreted in user input units.
Criss-Cobble Aqueous Infinite Dilution Ionic
Heat Capacity
The Criss-Cobble correlation for aqueous infinite dilution ionic heat capacity is
used if no parameters are available for the aqueous infinite dilution heat
capacity polynomial. From the calculated heat capacity, the thermodynamic
properties entropy, enthalpy and Gibbs energy at infinte dilution in water are
derived:
Parameter
Name
214 2 Thermodynamic Property Models
Applicable
Components
Symbol Default Units
IONTYP Ions Ion Type 0 —
SO25C Anions MOLE-ENTROPY
Cations MOLE-ENTROPY
General Pure Component Liquid Heat
Capacity
The Aspen Physical Property System has several submodels for calculating
liquid heat capacity. It uses parameter THRSWT/6 to determine which
submodel is used. See Pure Component Temperature-Dependent Properties
for details.
If THRSWT/6 is This equation is used And this parameter is used
100 DIPPR CPLDIP

If THRSWT/6 is This equation is used And this parameter is used
200-211 Barin CPLXP1, CPLXP2
301 PPDS CPLPDS
401 IK-CAPE heat capacity
polynomial
403 IK-CAPE liquid heat
capacity
503 NIST ThermoML
polynomial
2 Thermodynamic Property Models 215
CPLPO
CPLIKC
CPLTMLPO
506 NIST TDE equation CPLTDECS
This liquid heat capacity model is used to calculate pure component liquid
heat capacity and pure component liquid enthalpy. To use this model, two
conditions must exist:
� One of the parameters for calculating heat capacity (see table) is
available.
� The component is not supercritical (HENRY-COMP).
The model uses a specific method (see Methods in Property Calculation
Methods and Routes):
Where
= Reference enthalpy calculated at T ref
= Ideal gas enthalpy
= Vapor enthalpy departure
= Enthalpy of vaporization
T ref is the reference temperature; it defaults to 298.15 K. You can enter a
different value for the reference temperature. This is useful when you want to
use this model for very light components or for components that are solids at
298.15K.
Activate this model by specifying the route DHL09 for the property DHL on
the Properties Property Methods Routes sheet. For equation of state property
method, you must also modify the route for the property DHLMX to use a
route with method 2 or 3, instead of method 1. For example, you can use the
route DHLMX00 or DHLMX30. You must ascertain that the route for DHLMX
that you select contains the appropriate vapor phase model and heat of
mixing calculations. Click the View button on the form to see details of the
route.
Optionally, you can specify that this model is used for only certain
components. The properties for the remaining components are then
calculated by the standard model. Use the parameter COMPHL to specify the

components for which this model is used. By default, all components with the
CPLDIP or CPLIKC parameters use this model.
Barin
See Barin Equations for Gibbs Energy, Enthalpy, Entropy, and Heat Capacity
for details about this submodel.
DIPPR Liquid Heat Capacity
The DIPPR equation is used to calculate liquid heat capacity when parameter
THRSWT/6 is 100.
The DIPPR equation is:
Linear extrapolation occurs for Cp *,l versus T outside of bounds.
Parameter
Name/Element
216 2 Thermodynamic Property Models
Symbol Default MDS Lower
Limit
Upper
Limit
Units
CPLDIP/1 C 1i — x — — MOLE-HEAT-
CAPACITY,
TEMPERATURE
CPLDIP/2, ..., 5 C 2i, ..., C 5i 0 x — — MOLE-HEAT-
CAPACITY,
TEMPERATURE
CPLDIP/6 C 6i 0 x — — TEMPERATURE
CPLDIP/7 C 7i 1000 x — — TEMPERATURE
TREFHL T ref
298.15 — — — TEMPERATURE
COMPHL — — — — — —
To specify that the model is used for a component, enter a value of 1.0 for
COMPHL.
(Other DIPPR equations may sometimes be used. See Pure Component
Temperature-Dependent Properties for details.)
PPDS Liquid Heat Capacity
The PPDS equation is used to calculate liquid heat capacity when parameter
THRSWT/6 is 301.
The PPDS equation is:
Where R is the gas constant.
Linear extrapolation occurs for Cp *,l versus T outside of bounds.

Parameter Symbol Default MDS Lower
Name/Element
Limit
2 Thermodynamic Property Models 217
Upper
Limit
CPLPDS/1 C 1i — — — — —
CPLPDS/2 C 2i 0 — — — —
CPLPDS/3 C 3i 0 — — — —
CPLPDS/4 C 4i 0 — — — —
CPLPDS/5 C 5i 0 — — — —
CPLPDS/6 C 6i 0 — — — —
Units
CPLPDS/7 C 7i 0 x — — TEMPERATURE
CPLPDS/8 C 8i 0.99 TC x — — TEMPERATURE
IK-CAPE Liquid Heat Capacity
Two IK-CAPE equations can be used to calculate liquid heat capacity. Linear
extrapolation occurs for Cp *,l versus T outside of bounds for either equation.
When THRSWT/6 is 403, the IK-CAPE liquid heat capacity equation is used.
The equation is:
Parameter Symbol Default MDS Lower
Name/Element
Limit
CPLIKC/1 C 1i —
T
Upper
Limit
Units
x — — MOLE-HEAT-
CAPACITY
CPLIKC/2,...,4 C 2i, ..., C 4i 0 x — — MOLE-HEAT-
CAPACITY,
TEMPERATURE
CPLIKC/5 C 5i 0 x — — MOLE-HEAT-
CAPACITY,
TEMPERATURE †
CPLIKC/6 C 6i 0 x — — TEMPERATURE
CPLIKC/7 C 7i 1000 x — — TEMPERATURE
† If C5i is non-zero, absolute temperature units are assumed for C2i through
C5i. Otherwise, user input units for temperature are used. The temperature
limits are always interpreted in user input units.
When THRSWT/6 is 401, the IK-CAPE heat capacity polynomial is used.The
equation is:
Parameter
Name/Element
Symbol Default MDS Lower
Limit
Upper
Limit
Units
CPLPO/1 C 1i — X — — MOLE-CAPACITY
CPLPO/2,…,10 C 2i, ..., C 10i 0 X — — MOLE-CAPACITY
TEMPERATURE
CPLPO/11 C 11i 0 X — — TEMPERATURE

Parameter
Name/Element
218 2 Thermodynamic Property Models
Symbol Default MDS Lower
Limit
Upper
Limit
Units
CPLPO/12 C 12i 1000 X — — TEMPERATURE
See Pure Component Temperature-Dependent Properties for details on the
THRSWT parameters.
NIST Liquid Heat Capacity
Two NIST equations can be used to calculate liquid heat capacity. Linear
extrapolation occurs for Cp *,l versus T outside of bounds for either equation.
When THRSWT/6 is 503, the ThermoML polynomial is used to calculate liquid
heat capacity:
Parameter
Name/Element
Symbol Default MDS Lower
Limit
Upper
Limit
Units
CPLTMLPO/1 C 1i — X — — J/K^2/mol
CPLTMLPO/2,…,5 C 2i, ..., C 5i 0 X — — J/K^2/mol
CPLTMLPO/6 nTerms 5 X — — —
CPLTMLPO/7 T lower 0 X — — TEMPERATURE
CPLTMLPO/8 T upper 1000 X — — TEMPERATURE
When THRSWT/6 is 506, the TDE equation is used to calculate liquid heat
capacity:
Parameter
Name/Element
Symbol Default MDS Lower
Limit
Upper
Limit
Units
CPLTDECS/1 C 1i — X — — MOLE-HEAT-
CAPACITY
CPLTDECS/2,…,4 C 2i, ..., C 4i 0 X — — MOLE-HEAT-
CAPACITY
CPLTDECS/5 B 0 X — — MOLE-HEAT-
CAPACITY
CPLTDECS/6 T ci — X — — TEMPERATURE
CPLTDECS/7 nTerms 4 X — — —
CPLTDECS/8 T lower 0 X — — TEMPERATURE
CPLTDECS/9 T upper 1000 X — — TEMPERATURE
See Pure Component Temperature-Dependent Properties for details on the
THRSWT parameters.

General Pure Component Ideal Gas Heat
Capacity
The Aspen Physical Property System has several submodels for calculating
ideal gas heat capacity. It uses parameter THRSWT/7 to determine which
submodel is used. See Pure Component Temperature-Dependent Properties
for details.
If THRSWT/7 is This equation is used And this parameter is
used
0 Ideal gas heat capacity
polynomial
2 Thermodynamic Property Models 219
CPIG
107, 127 DIPPR 107 or 127 CPIGDP
200-211 Barin CPIXP1, CPIXP2, CPIXP3
301 PPDS CPIGDS
401 IK-CAPE heat capacity
polynomial
503 NIST ThermoML
polynomial
CPIGPO
CPITMLPO
513 NIST Aly-Lee CPIALEE
These equations are also used to calculate ideal gas enthalpies, entropies,
and Gibbs energies.
Aspen Ideal Gas Heat Capacity Polynomial
The ideal gas heat capacity polynomial is available for components stored in
ASPENPCD, AQUEOUS, and SOLIDS databanks. This model is also used in
PCES.
Cp *,ig is linearly extrapolated using slope at
Parameter
Name/
Element
Symbol Default MDS Lower
Limit
Upper
Limit
Units
CPIG/1 C 1i — — — — MOLE-HEAT-CAPACITY,
TEMPERATURE
CPIG/2, ..., 6 C 2i, ..., C 6i 0 — — — MOLE-HEAT-CAPACITY,
TEMPERATURE
CPIG/7 C 7i 0 — — — TEMPERATURE
CPIG/8 C 8i 1000 — — — TEMPERATURE
CPIG/9, 10,
11
C 9i, C 10i, C 11i — — — — MOLE-HEAT-CAPACITY,
TEMPERATURE †
† If C10i or C11i is non-zero, then absolute temperature units are assumed for
C9i through C11i. Otherwise, user input temperature units are used for all
parameters. User input temperature units are always used for C1i through C8i.

NIST ThermoML Polynomial
This equation can be used when parameter CPITMLPO is available.
Parameter
Name/
Element
Symbol Default MDS Lower
Limit
220 2 Thermodynamic Property Models
Upper
Limit
Units
CPITMLPO /1 C 1i — x — — J/K^2/mol
CPITMLPO /2,
..., 6
C 2i, ..., C 6i 0 x — — J/K^2/mol
CPITMLPO/7 nTerms 6 x — — —
CPITMLPO /8 T lower 0 x — — TEMPERATURE
CPITMLPO /9 T upper 1000 x — — TEMPERATURE
DIPPR Equation 107
The DIPPR ideal gas heat capacity equation 107 by Aly and Lee 1981 is:
No extrapolation is used with this equation.
(Other DIPPR equations may sometimes be used. See Pure Component
Temperature-Dependent Properties for details.)
Parameter Symbol Default MDS Lower Upper Units
Name/Element
Limit Limit
CPIGDP/1 C 1i — x — — MOLE-HEAT-
CAPACITY
CPIGDP/2 C 2i 0 x — — MOLE-HEAT-
CAPACITY
CPIGDP/3 C 3i 0 x — — TEMPERATURE ††
CPIGDP/4 C 4i 0 x — — MOLE-HEAT-
CAPACITY
CPIGDP/5 C 5i 0 x — — TEMPERATURE ††
CPIGDP/6 C 6i 0 x — — TEMPERATURE
CPIGDP/7 C 7i 1000 x — — TEMPERATURE
†† Absolute temperature units are assumed for C3i and C5i. The temperature
limits are always interpreted in user input units.
DIPPR Equation 127
The DIPPR ideal gas heat capacity equation 127 is:

(Other DIPPR equations may sometimes be used. See Pure Component
Temperature-Dependent Properties for details.)
Parameter Symbol Default MDS Lower Upper Units
Name/Element
Limit Limit
CPIGDP/1 C 1i — x — — MOLE-HEAT-
CAPACITY
CPIGDP/2 C 2i 0 x — — MOLE-HEAT-
CAPACITY
CPIGDP/3 C 3i 0 x — — TEMPERATURE ††
CPIGDP/4 C 4i 0 x — — MOLE-HEAT-
CAPACITY
CPIGDP/5 C 5i 0 x — — TEMPERATURE ††
CPIGDP/6 C 6i 0 x — — MOLE-HEAT-
CAPACITY
CPIGDP/7 C 7i 0 x — — TEMPERATURE ††
†† Absolute temperature units are assumed for C3i, C5i and C7i.
Barin
See Barin Equations for Gibbs Energy, Enthalpy, Entropy, and Heat Capacity
for details about this submodel.
NIST Aly-Lee
This equation is the same as the DIPPR Aly and Lee equation 107 above, but
it uses a different parameter set. Note that elements 6 and 7 of the CPIALEE
parameter are not used in the equation.
Parameter Symbol Default MDS Lower
Name/Element
Limit
2 Thermodynamic Property Models 221
Upper
Limit
Units
CPIALEE/1 C 1i — x — — MOLE-HEAT-
CAPACITY
CPIALEE/2 C 2i 0 x — — MOLE-HEAT-
CAPACITY
CPIALEE/3 C 3i 0 x — — TEMPERATURE ††
CPIALEE/4 C 4i 0 x — — MOLE-HEAT-
CAPACITY
CPIALEE/5 C 5i 0 x — — TEMPERATURE ††
CPIALEE/8 C 6i 0 x — — TEMPERATURE
CPIALEE/9 C 7i 1000 x — — TEMPERATURE
†† Absolute temperature units are assumed for C3i and C5i. The temperature
limits are always interpreted in user input units.
PPDS
The PPDS equation is:

where R is the gas constant.
Linear extrapolation of Cp *,ig versus T is performed outside temperature
bounds.
Parameter
Name/Element
222 2 Thermodynamic Property Models
Symbol Default MDS Lower
Limit
Upper
Limit
Units
CPIGDS/1 C 1i — — — — TEMPERATURE
CPIGDS/2, …, 8 C 2i, ..., C 8i 0 — — — —
CPIGDS/9 C 9i 0 — — — TEMPERATURE
CPIGDS/10 C 10i 1000 — — — TEMPERATURE
IK-CAPE Heat Capacity Polynomial
The equation is:
Linear extrapolation of Cp *,ig versus T is performed outside temperature
bounds.
Parameter
Name/Element
Symbol Default MDS Lower
Limit
Upper
Limit
Units
CPIGPO/1 C 1i — X — — MOLE-CAPACITY
CPIGPO/2,…,10 C 2i, ..., C 10i 0 X — — MOLE-CAPACITY
TEMPERATURE
CPIGPO/11 C 11i 0 X — — TEMPERATURE
CPIGPO/12 C 12i 1000 X — — TEMPERATURE
References
Data for the Ideal Gas Heat Capacity Polynomial: Reid, Prausnitz and Poling,
The Properties of Gases and Liquids, 4th ed., (New York: McGraw-Hill, 1987).
The Aspen Physical Property System combustion data bank, JANAF
Thermochemical Data, Compiled and calculated by the Thermal Research
Laboratory of Dow Chemical Company.
F. A. Aly and L. L. Lee, "Self-Consistent Equations for Calculating the Ideal
Gas Heat Capacity, Enthalpy, and Entropy, Fluid Phase Eq., Vol. 6, (1981), p.
169.

General Pure Component Solid Heat
Capacity
The Aspen Physical Property System has several submodels for calculating
solid heat capacity. It uses parameter THRSWT/5 to determine which
submodel is used. See Pure Component Temperature-Dependent Properties
for details.
If THRSWT/5 is This equation is used And this parameter is
used
0 Aspen solid heat capacity CPSPO1
polynomial
100 or 102 DIPPR CPSDIP
200-211 Barin CPSXP1, CPSXP2, …,
CPSXP7
401 IK-CAPE heat capacity
polynomial
503 NIST ThermoML
polynomial
2 Thermodynamic Property Models 223
CPSPO
CPSTMLPO
The enthalpy, entropy, and Gibbs energy of solids are also calculated from
these equations:
Aspen Solid Heat Capacity Polynomial
The Aspen equation is:
Linear extrapolation occurs for Cp,i *,s versus T outside of bounds.
Parameter
Name
Applicable
Components
Symbol MDS Default Units
CPSPO1/1 Solids, Salts C 1i x — †
CPSPO1/2, ..., 6 Solids, Salts C 2i, ..., C 6i x 0 †
CPSPO1/7 Solids, Salts C 7i x 0 †
CPSPO1/8 Solids, Salts C 8i x 1000 †
† The units are TEMPERATURE and HEAT-CAPACITY for all elements. If any of
C4i through C6i are non-zero, absolute temperature units are assumed for
elements C1i through C6i. Otherwise, user input temperature units are
assumed for all elements. The temperature limits are always interpreted in
user input units.
Barin
See Barin Equations for Gibbs Energy, Enthalpy, Entropy, and Heat Capacity
for details about this submodel.
DIPPR
There are two DIPPR equations that may generally be used.
The more common one, DIPPR equation 100, is:

Linear extrapolation occurs for Cp,i *,s versus T outside of bounds.
Parameter
Name/Element
224 2 Thermodynamic Property Models
Symbol Default MDS Lower
Limit
Upper
Limit
Units
CPSDIP/1 C 1i — x — — MOLE-HEAT-
CAPACITY,
TEMPERATURE
CPSDIP/2,...,5 C 2i, ..., C 5i 0 x — — MOLE-HEAT-
CAPACITY,
TEMPERATURE
CPSDIP/6 C 6i 0 x — — TEMPERATURE
CPSDIP/7 C 7i 1000 x — — TEMPERATURE
DIPPR equation 102 is:
Linear extrapolation occurs for Cp,i *,s versus T outside of bounds.
Parameter
Name/Element
Symbol Default MDS Lower
Limit
Upper
Limit
Units
CPSDIP/1 C 1i — x — — MOLE-HEAT-
CAPACITY,
TEMPERATURE
CPSDIP/2 C 2i — x — — —
CPSDIP/3,4 C 3i, C 4i 0 x — — TEMPERATURE
CPSDIP/6 C 6i 0 x — — TEMPERATURE
CPSDIP/7 C 7i 1000 x — — TEMPERATURE
If C3i or C4i are non-zero or C2i is negative, absolute temperature units are
assumed for elements C1i through C4i. Otherwise, user input temperature
units are assumed for all elements. The temperature limits are always
interpreted in user input units.
(Other DIPPR equations may sometimes be used. See Pure Component
Temperature-Dependent Properties for details.)
NIST ThermoML Polynomial
The equation is:
Linear extrapolation occurs for Cp,i *,s versus T outside of bounds.
Parameter
Name/Element
Symbol Default MDS Lower
Limit
Upper
Limit
Units
CPSTMLPO/1 C 1i — x — — J/K^2/mol
CPSTMLPO/2,...,5C 2i, ..., C 5i 0 x — — J/K^2/mol
CPSTMLPO/6 nTerms 5 x — — —
CPSTMLPO/7 T lower 0 x — — TEMPERATURE

Parameter
Name/Element
2 Thermodynamic Property Models 225
Symbol Default MDS Lower
Limit
Upper
Limit
Units
CPSTMLPO/8 T upper 1000 x — — TEMPERATURE
IK-CAPE Heat Capacity Polynomial
The equation is:
Linear extrapolation occurs for Cp,i *,s versus T outside of bounds.
Parameter
Name/Element
Symbol Default MDS Lower
Limit
Upper
Limit
Units
CPSPO/1 C 1i — X — — MOLE-CAPACITY
CPSPO/2,…,10 C 10i 0 X — — MOLE-CAPACITY
TEMPERATURE
CPSPO/11 C 11i 0 X — — TEMPERATURE
CPSPO/12 C 12i 1000 X — — TEMPERATURE
Solubility Correlations
The Aspen Physical Property System has three built-in solubility correlation
models. This section describes the solubility correlation models available.
Model Type
Henry's constant Gas solubility in liquid
Water solubility Water solubility in organic liquid
Hydrocarbon solubility Hydrocarbon solubility in water-rich
liquid
Henry's Constant
The Henry's constant model is used when Henry's Law is applied to calculate
K-values for dissolved gas components in a mixture. Henry's Law is available
in all activity coefficient property methods, such as the WILSON property
method. The model calculates Henry's constant for a dissolved gas component
(i) in one or more solvents (A or B):
Where:
wA
=
ln HiA(T, pA *,l ) =

Linear extrapolation occurs for ln HiA versus T outside of bounds.
HiA(T, P) =
The parameter is obtained from the Brelvi-O'Connell model. pA *,l is
obtained from the Antoine model. is obtained from the appropriate activity
coefficient model.
The Henry's constants aiA, biA, ciA, diA, and eiA are specific to a solute-solvent
pair. They can be obtained from regression of gas solubility data. The Aspen
Physical Property System has a large number of built-in Henry's constants for
many solutes in solvents. These parameters were obtained using data from
the Dortmund Databank. In addition, a small number of Henry's constants
from the literature are available in the BINARY databank. See Physical
Property Data, Chapter 1, for details.
Parameter
Name/Element
226 2 Thermodynamic Property Models
Symbol Default MDS Lower
Limit
Upper
Limit
Units
VC V cA — — 0.001 3.5 MOLE-VOLUME
HENRY/1 a iA †† x — — PRESSURE,
TEMPERATURE †
HENRY/2 b iA 0 x — — TEMPERATURE †
HENRY/3 c iA 0 x — — TEMPERATURE †
HENRY/4 d iA 0 x — — TEMPERATURE †
HENRY/5 T L 0 x — — TEMPERATURE
HENRY/6 T H 2000 x — — TEMPERATURE
HENRY/7 e iA 0 x — — TEMPERATURE †
† If any of biA, ciA, and eiA are non-zero, absolute temperature units are
assumed for all coefficients. If biA, ciA, and eiA are all zero, the others are
interpreted in input units. The temperature limits are always interpreted in
input units.
†† If aiA is missing, is set to zero and the weighting factor wA is
renormalized.
Reference for BINARY Databank
E. Wilhelm, R. Battino, and R.J. Wilcock, "Low-Pressure Solubility of Gases in
Liquid Water," Chemical Reviews, 1977, Vol. 77, No. 2, pp 219 - 262.
Water Solubility
This model calculates solubility of water in a hydrocarbon-rich liquid phase.
The model is used automatically when you model a hydrocarbon-water
system with the free-water option. See Free-Water Immiscibility Simplification
in Free-Water and Three-Phase Calculations for details.

The expression for the liquid mole fraction of water in the ith hydrocarbon
species is:
No extrapolation is used with this equation.
The parameters for about 60 components are stored in the Aspen Physical
Property System pure component databank.
Parameter Symbol Default MDS Lower Upper Units
Name/
Element
Limit Limit
WATSOL/1 C 1i fcn(T bi, SG i, M i) — -10.0 33.0 —
WATSOL/2 C 2i fcn(T bi, SG i, M i) — -10000.0 3000.0 TEMPERATURE †
WATSOL/3 C 3i 0 — -0.05 0.05 TEMPERATURE †
WATSOL/4 C 4i 0 — 0.0 500 TEMPERATURE †
WATSOL/5 C 5i 1000 — 4.0 1000 TEMPERATURE †
† Absolute temperature units are assumed for elements 2 through 5.
Hydrocarbon Solubility
This model calculates solubility of hydrocarbon in a water-rich liquid phase.
The model is used automatically when you model a hydrocarbon-water
system with the dirty-water option. See Free-Water Immiscibility
Simplification in Free-Water and Rigorous Three-Phase Calculations for
details.
The expression for the liquid mole fraction of the ith hydrocarbon species in
water is:
No extrapolation is used with this equation.
The parameters for about 40 components are stored in the Aspen Physical
Property System pure component databank.
Parameter Symbol Default MDS Lower Upper Units
Name/
Element
Limit Limit
HCSOL/1 C 1i fcn(carbon
number) †
2 Thermodynamic Property Models 227
— -1000.0 1000.0 —
HCSOL/2 C 2i 0 — -100000.0 100000.0 TEMPERATURE ††
HCSOL/3 C 3i 0 — -100.0 100.0 TEMPERATURE ††
HCSOL/4 C 4i 0 — 0.0 500 TEMPERATURE
HCSOL/5 C 5i 1000 — 4.0 1000 TEMPERATURE
† For Hydrocarbons and pseudocomponents, the default values are estimated
by the method given by API Procedure 9A2.17 at 25 C.
†† Absolute temperature units are assumed for elements 2 and 3. The
temperature limits are always interpreted in user input units.

Reference
C. Tsonopoulos, Fluid Phase Equilibria, 186 (2001), 185-206.
Other Thermodynamic Property
Models
The Aspen Physical Property System has some built-in additional
thermodynamic property models that do not fit in any other category. This
section describes these models:
� Cavett Liquid Enthalpy Departure
� Barin Equations for Gibbs Energy, Enthalpy, Entropy and Heat Capacity
� Electrolyte NRTL Enthalpy
� Electrolyte NRTL Gibbs Energy
� Liquid Enthalpy from Liquid Heat Capacity Correlation
� Enthalpies Based on Different Reference States
� Helgeson Equations of State
� Quadratic Mixing Rule
Cavett
The general form for the Cavett model is:
Parameter
Name/Element
228 2 Thermodynamic Property Models
Symbol Default MDS Lower
Limit
Upper
Limit
Units
TC T ci — — 5.0 2000.0 TEMPERATURE
PC p ci — — 10 5
DHLCVT ZC X 0.1 0.5 —
10 8
PRESSURE
Barin Equations for Gibbs Energy, Enthalpy,
Entropy, and Heat Capacity
The following equations are used when parameters from the Aspen Physical
Property System inorganic databank are retrieved.
� Gibbs energy:
� Enthalpy:
(2)
(1)

� Entropy:
� Heat capacity:
� refers to an arbitrary phase which can be solid, liquid, or ideal gas. For each
phase, multiple sets of parameters from 1 to n are present to cover multiple
temperature ranges. The value of the parameter n depends on the phase.
(See tables that follow.) When the temperature is outside all these
temperature ranges, linear extrapolation of properties versus T is performed
using the slope at the end of the nearest temperature bound.
The four properties Cp, H, S, and G are interrelated as a result of the
thermodynamic relationships:
There are analytical relationships between the expressions describing the
properties Cp, H, S, and G (equations 1 to 4). The parameters an,i to hn,i can
occur in more than one equation.
The Aspen Physical Property System has other models which can be used to
calculate temperature-dependent properties which the BARIN equations can
calculate. The Aspen Physical Property System uses the parameters in
THRSWT to determine which model is used. See Pure Component
Temperature-Dependent Properties for details.
If this parameter is 200 to 211 Then the BARIN equations are
used to calculate
THRSWT/3 Liquid vapor pressure
THRSWT/5 Solid heat capacity
THRSWT/6 Liquid heat capacity
THRSWT/7 Ideal gas heat capacity
The liquid vapor pressure is computed from Gibbs energy as follows:
ln p = (G L - G V )/RT + ln p ref
where p is the vapor pressure, and p ref is the reference pressure 101325 Pa.
Thus, parameters for both liquid and vapor are necessary to calculate vapor
pressure.
Solid Phase
The parameters in range n are valid for temperature: Tn,l s < T < Tn,h s
2 Thermodynamic Property Models 229
(4)
(3)

When you specify this parameter, be sure to specify at least elements 1
through 3.
Parameter Name †
/Element
CPSXPn/1 T n,l s
CPSXPn/2 T n,h s
CPSXPn/3 a n,i s
CPSXPn/4 b n,i s
CPSXPn/5 c n,i s
CPSXPn/6 d n,i s
CPSXPn/7 e n,i s
CPSXPn/8 f n,i s
CPSXPn/9 g n,i s
CPSXPn/10 h n,i s
230 2 Thermodynamic Property Models
Symbol Default MDS Lower
Limit
Upper
Limit
Units
— x — — TEMPERATURE
— x — — TEMPERATURE
— x — — ††
0 x — — ††
0 x — — ††
0 x — — ††
0 x — — ††
0 x — — ††
0 x — — ††
0 x — — ††
† n is 1 through 7. CPSXP1 vector stores solid parameters for the first
temperature range. CPSXP2 vector stores solid parameters for the second
temperature range, and so on.
†† TEMPERATURE, ENTHALPY, ENTROPY
Liquid Phase
The parameters in range n are valid for temperature: Tn,l l < T < Tn,h l
When you specify this parameter, be sure to specify at least elements 1
through 3.
Parameter Name †
/Element
CPLXPn/1 T n,l l
CPLXPn/2 T n,h l
CPLXPn/3 a n,i l
CPLXPn/4 b n,i l
CPLXPn/5 c n,i l
CPLXPn/6 d n,i l
CPLXPn/7 e n,i l
CPLXPn/8 f n,i l
CPLXPn/9 g n,i l
CPLXPn/10 h n,i l
Symbol Default MDS Lower
Limit
Upper
Limit
Units
— x — — TEMPERATURE
— x — — TEMPERATURE
— x — — ††
0 x — — ††
0 x — — ††
0 x — — ††
0 x — — ††
0 x — — ††
0 x — — ††
0 x — — ††
† n is 1 through 2. CPLXP1 stores liquid parameters for the first temperature
range. CPLXP2 stores liquid parameters for the second temperature range.
†† TEMPERATURE, ENTHALPY, ENTROPY
Ideal Gas Phase
The parameters in range n are valid for temperature: Tn,l ig < T < Tn,h ig
When you specify this parameter, be sure to specify at least elements 1
through 3.

Parameter Name †
/Element
CPIXPn/1 T n,l ig
CPIXPn/2 T n,h ig
CPIXPn/3 a n,i ig
CPIXPn/4 b n,i ig
CPIXPn/5 c n,i ig
CPIXPn/6 d n,i ig
CPIXPn/7 e n,i ig
CPIXPn/8 f n,i ig
CPIXPn/9 g n,i ig
CPIXPn/10 h n,i ig
2 Thermodynamic Property Models 231
Symbol Default MDS Lower
Limit
Upper
Limit
Units
— x — — TEMPERATURE
— x — — TEMPERATURE
— x — — ††
0 x — — ††
0 x — — ††
0 x — — ††
0 x — — ††
0 x — — ††
0 x — — ††
0 x — — ††
† n is 1 through 3. CPIXP1 vector stores ideal gas parameters for the first
temperature range. CPIXP2 vector stores ideal gas parameters for the second
temperature range, and so on.
†† TEMPERATURE, ENTHALPY, ENTROPY
Electrolyte NRTL Enthalpy Model
(HMXENRTL)
The equation for the electrolyte NRTL enthalpy model (HMXENRTL) is:
The molar enthalpy Hm * and the molar excess enthalpy Hm *E are defined with
the asymmetrical reference state: the pure solvent water and infinite dilution
of molecular solutes and ions. (here * refers to the asymmetrical reference
state.)
Hw* is the pure water molar enthalpy, calculated from the Ideal Gas model
and the ASME Steam Table equation-of-state. (here * refers to pure
component.)
Hs *,l is the enthalpy contribution from a non-water solvent. It is calculated as
usual for components in activity coefficient models:
Hs *,l (T) = Hs *,ig + DHVs(T,p) - �Hs,vap(T).
The term DHVs(T,p) = Hs *,v - Hs *,ig is the vapor enthalpy departure
contribution to liquid enthalpy; option code 5 determines how this is
calculated.
�
The aqueous infinite dilution thermodynamic enthalpy Hk is calculated from
the infinite dilution aqueous phase heat capacity as follows:

where the subscript k refers to any ion or molecular solute. By default,
is calculated from the aqueous infinite dilution heat capacity polynomial. If
the polynomial model parameters are not available, is calculated from
the Criss-Cobble correlation for ionic solutes.
For molecular solutes (e.g. Henry components), if the aqueous infinite dilution
�
heat capacity polynomial model parameters are not available, Hk is
calculated from Henry's law:
Hm *E is calculated from the electrolyte NRTL activity coefficient model.
See Criss-Cobble correlation model and Henry's law model for more
information.
Parameter
Name
Applicable
Components
232 2 Thermodynamic Property Models
Symbol Default Units
IONTYP Ions † Ion 0 —
SO25C Cations � ,aq
Sc (T=298) — MOLE-ENTROPY
Anions � ,aq
Sa (T=298) — MOLE-ENTROPY
DHAQFM Ions, Molecular Solutes
††
CPAQ0 Ions, Molecular Solutes
††
� ,aq �f H — MOLE-ENTHALPY
k
� ,aq
C — HEAT-CAPACITY
p,k
DHFORM Molecular Solutes †† � f H i *,ig — MOLE-ENTHALPY
Water, Solvents � f H w *,ig — MOLE-ENTHALPY
CPIG Molecular Solutes C p,i *,ig
Water, Solvents C p,w *,ig
† IONTYP is not needed if CPAQ0 is given for ions.
— †††
— †††
†† DHFORM is not used if DHAQFM and CPAQ0 are given for molecular solutes
(components declared as Henry's components). If CPAQ0 is missing, DHFORM
and Henry's constants are used to calculate infinite dilution enthalpy for
solutes.
††† The unit keywords for CPIG are TEMPERATURE and HEAT-CAPACITY. If
CPIG/10 or CPIG/11 is non-zero, then absolute temperature units are
assumed for CPIG/9 through CPIG/11. Otherwise, user input temperature
units are used for all elements of CPIG. User input temperature units are
always used for other elements of CPIG.

Option Codes for Electrolyte NRTL Enthalpy Model
(HMXENRTL)
The electrolyte NRTL enthalpy model (HMXENRTL) has seven option codes
and the option codes can affect the performance of this model.
Option code 1. Use this option code to specify the default values of pair
parameters for water/solute and solvent/solute; the solute represents a
cation/anion pair. The value (1) sets the default values to zero and the value
(3) sets the default values for water/solute to (8,-4) and for solvent/solute to
(10,-2). The value (3) is the default choice of the option code.
Option code 2. Use this option code to specify the vapor phase equation-ofstate
(EOS) model used for the liquid enthalpy calculation. The value (0) sets
the ideal gas EOS model and the value (1) sets the HF EOS model. The value
(0) is the default.
Option code 3. Always leave this option code set to the value (1) to use the
solvent/solvent binary parameters obtained from NRTL parameters.
Option code 4. Not used.
Option code 5. Use this option code to specify how the vapor phase enthalpy
departure (DHV) is calculated. The value (0) sets DHV = 0, the value (1)
specifies using Redlich-Kwong equation of state, and the value (3) specifies
using Hayden-O’Connell equation of state. The value (0) is the default.
Option code 6. Not used.
Option code 7. Use this option code to specify the method for handling
Henry components and multiple solvents. The value (0) sets the pure liquid
enthalpy to that calculated by aqueous infinite dilution heat capacity (only
water as solvent) and the value (1) sets the pure liquid enthalpy for Henry
components using Henry’s law. Use value (1) when there are multiple
solvents. The value (0) is the default.
Electrolyte NRTL Gibbs Free Energy Model
(GMXENRTL)
The equation for the NRTL Gibbs free energy model (GMXENRTL) is:
The molar Gibbs free energy and the molar excess Gibbs free energy Gm * and
Gm *E are defined with the asymmetrical reference state: as pure water and
infinite dilution of molecular solutes and ions. (* refers to the asymmetrical
reference state.) The ideal mixing term is calculated normally, where j refers
to any component. The molar Gibbs free energy of pure water (or
thermodynamic potential) �w* is calculated from the ideal gas contribution.
This is a function of the ideal gas heat capacity and the departure function.
(here * refers to the pure component.)
The departure function is obtained from the ASME steam tables.
2 Thermodynamic Property Models 233

�s* ,l is the Gibbs free energy contribution from a non-water solvent. It is
calculated as usual for components in activity coefficient models.
�
The aqueous infinite dilution thermodynamic potential �k is calculated from
the infinite dilution aqueous phase heat capacity polynomial model, by
default. Subscript k refers to any ion or molecular solute. If polynomial model
parameters are not available, it is calculated from the Criss-Cobble model for
ionic solutes:
where the subscript k refers to any ion or molecular solute and the term RT
�,aq
are based on a molality
�,aq
ln(1000/Mw) is added because �f Hk and �f Gk
�
scale, while �k is based on mole fraction scale.
By default, is calculated from the aqueous infinite dilution heat
capacity polynomial. If the polynomial model parameters are not available,
is calculated from the Criss-Cobble correlation for ionic solutes.
For molecular solutes (e.g. Henry components), if the aqueous infinite dilution
�
heat capacity polynomial model parameters are not available, �k is
calculated from Henry's law:
Gm *E is calculated from the electrolyte NRTL activity coefficient model.
See the Criss-Cobble correlation model and Henry's law model for more
information.
Parameter
Name
Applicable
Components
234 2 Thermodynamic Property Models
Symbol Default Units
IONTYP Ions † Ion 0 —
SO25C Cations † � ,aq
Sc (T=298) — MOLE-ENTROPY
Anions † � ,aq
Sa (T=298) — MOLE-ENTROPY
DGAQFM Ions, Molecular Solutes
††
CPAQ0 Ions, Molecular Solutes
††
DGFORM Molecular Solutes †† � f G i
Water, Solvents � f G w
� ,aq �f G — MOLE-ENTHALPY
k
� ,aq
C — HEAT-CAPACITY
p,k
— MOLE-ENTHALPY
— MOLE-ENTHALPY

Parameter
Name
Applicable
Components
CPIG Molecular Solutes C p,i *,ig
Water, Solvents C p,w *,ig
2 Thermodynamic Property Models 235
Symbol Default Units
— †††
— †††
† IONTYP and SO25C are not needed if CPAQ0 is given for ions.
†† DGFORM is not needed if DHAQFM and CPAQ0 are given for molecular
solutes.
††† The unit keywords for CPIG are TEMPERATURE and HEAT-CAPACITY. If
CPIG/10 or CPIG/11 is non-zero, then absolute temperature units are
assumed for CPIG/9 through CPIG/11. Otherwise, user input temperature
units are used for all elements of CPIG. User input temperature units are
always used for other elements of CPIG.
Option Codes for Electrolyte NRTL Gibbs Free Energy
Model (GMXENRTL)
The electrolyte NRTL Gibbs free energy model (GMXENRTL) has six option
codes and the option codes can affect the performance of this model.
Option code 1. Use this option code to specify the default values of pair
parameters for water/solute and solvent/solute; the solute represents a
cation/anion pair. The value (1) sets the default values to zero and the value
(3) sets the default values for water/solute to (8,-4) and for solvent/solute to
(10,-2). The value (3) is the default choice of the option code.
Option code 2. Use this option code to specify the vapor phase equation-ofstate
(EOS) model used for the liquid Gibbs free energy calculation. The value
(0) sets the ideal gas EOS model and the value (1) sets the HF EOS model.
The value (0) is the default.
Option code 3. Always leave this option code set to the value (1) to use the
solvent/solvent binary parameters obtained from NRTL parameters.
Option code 4. Not used.
Option code 5. Use this option code to specify how the pure vapor phase
fugacity coefficient (PHIV) is calculated. The value (0) sets PHIV = 1 (ideal
gas law), the value (1) specifies using Redlich-Kwong equation of state, and
the value (3) specifies using Hayden-O’Connell equation of state. The value
(0) is the default.
Option code 6. Use this option code to specify the method for handling
Henry components and multiple solvents. The value (0) sets the pure liquid
Gibbs free energy to that calculated by aqueous infinite dilution heat capacity
(only water as solvent) and the value (1) sets the pure liquid Gibbs free
energy for Henry components using Henry’s law. Use value (1) when there
are multiple solvents. The value (0) is the default.
Liquid Enthalpy from Liquid Heat Capacity
Correlation
Liquid enthalpy is directly calculated by integration of liquid heat capacity:

The reference enthalpy is calculated at T ref as:
Where:
Hi *,ig
Hi *,v - Hi *,ig
= Ideal gas enthalpy
236 2 Thermodynamic Property Models
= Vapor enthalpy departure from equation of state
�vapHi *,l = Heat of vaporization from General model
T ref
= Reference temperature, specified by user. Defaults to
298.15 K
See General Pure Component Heat of Vaporization for parameter requirement
and additional details.
Enthalpies Based on Different Reference
States
Two property methods, WILS-LR and WILS-GLR, are available to calculate
enthalpies based on different reference states. The WILS-LR property method
is based on saturated liquid reference state for all components. The WILS-GLR
property method allows both ideal gas and saturated liquid reference states
for different components.
These property methods use an enthalpy method that optimizes the accuracy
tradeoff between liquid heat capacity, heat of vaporization, and vapor heat
capacity at actual process conditions. This highly recommended method
eliminates many of the problems associated with accurate thermal properties
for both phases, especially the liquid phase.
The liquid enthalpy of mixture is calculated by the following equation (see the
table labeled Liquid Enthalpy Methods):
Where:
Hm ig
Hi *,ig
= Enthalpy of ideal gas mixture
=
= Ideal gas enthalpy of pure component i
(Hm l -Hm ig ) = Enthalpy departure of mixture
For supercritical components, declared as Henry's components, the enthalpy
departure is calculated as follows:

For subcritical components:
Hm l -Hm ig
Hm E,l
HA *,l -HA *,ig
2 Thermodynamic Property Models 237
=
=
= Enthalpy departure of pure component A
H *,ig and H *,l can be calculated based on either saturated liquid or ideal gas as
reference state as described in the sections that follow.
For the WILS-LR property method, H *,ig and H *,l are calculated based on the
saturated liquid reference state for all components.
For the WILS-GLR property method, H *,ig and H *,l can be calculated based on
the saturated liquid reference state for some components and the ideal gas
reference state for other components. You can set the value of a pure
component parameter called RSTATE to specify the reference state for each
component. RSTATE = 1 denotes ideal gas reference state. RSTATE = 2
denotes saturated liquid reference state. If it is not set, the following default
rules apply based on the normal boiling point of the component, i, TB(i):
� If TB(i) 298.15 K, saturated liquid reference state is used.
Saturated Liquid as Reference State
The saturated liquid enthalpy at temperature T is calculated as follows:
Where:
Hi ref,l
Cp,i *,l
= Reference enthalpy for liquid state at Ti ref,l
= Liquid heat capacity of component i
The saturated liquid Gibbs free energy is calculated as follows:
Where:
Gi ref,l
= Reference Gibbs free energy for liquid state at Ti ref,l
�i *,l = Liquid fugacity coefficient of component i
p = System pressure
p ref
= Reference pressure (=101325 N/m 2 )
For the WILS-LR property method, Hi ref,l and Gi ref,l default to zero (0). The
reference temperature Ti ref,l defaults to 273.15K.
For the WILS-GLR property method, the reference temperature Ti ref,l defaults
to 298.15K and Hi ref,l defaults to:

And Gi ref,l defaults to:
Where:
Hi ref,ig
Gi ref,ig
238 2 Thermodynamic Property Models
= Ideal gas enthalpy of formation for liquid state at
298.15K
= Ideal gas Gibbs free energy of formation for liquid
state at 298.15K
�Hi *,v = Vapor enthalpy departure of component i
�Gi *,v = Vapor Gibbs free energy departure of component i
�vapHi * = Enthalpy of vaporization of component i
Note that we cannot default the liquid reference enthalpy and Gibbs free
energy to zero, as is the case for WILS-LR, because it will cause inconsistency
with the enthalpy of components that use ideal-gas reference state. The
default values used result in the enthalpies of all components being on the
same basis. In fact, if you enter values for Hi ref,l and Gi ref,l for a liquidreference
state component you must make sure that they are consistent with
each other and are consistent with the enthalpy basis of the remaining
components in the mixture. If you enter a value for Hi ref,l , you should also
enter a value for Gi ref,l to ensure consistency.
When the liquid-reference state is used, the ideal gas enthalpy at
temperature T is not calculated from the integration of the ideal gas heat
capacity equation (see Ideal Gas as Reference State section below). For
consistency, it is calculated from liquid enthalpy as follows:
Where:
Ti con,l
= Temperature of conversion from liquid to vapor
enthalpy for component i
�vapHi * (Ti con,l ) = Heat of vaporization of component i at
temperature of T con,l
�Hi *,v (Ti con,l , pi *,l ) = Vapor enthalpy departure of component i at the
conversion temperature and vapor pressure pi *,l
pi *,l
= Liquid vapor pressure of component i
= Ideal gas heat capacity of component i
Ti con,l is the temperature at which one crosses from liquid state to the vapor
state. This is a user defined temperature that defaults to the system
temperature T. Ti con,l may be selected such that heat of vaporization for
component i at the temperature is most accurate.

The vapor enthalpy is calculated from ideal gas enthalpy as follows:
Where:
�Hi *,v (T, P) = Vapor enthalpy departure of pure component i at the
system temperature and pressure
The liquid heat capacity and the ideal gas heat capacity can be calculated
from the General Pure Component Liquid Heat Capacity and General Pure
Component Ideal Gas Heat Capacity, or other available models. The heat of
vaporization can be calculated from the General Pure Component Heat of
Vaporization, or other available models. The enthalpy departure is obtained
from an equation-of-state that is being used in the property method. For
WILS-LR and WILS-GLR, the ideal gas equation of state is used.
Parameter Symbol Default MDS Lower
Name/Element
Limit
2 Thermodynamic Property Models 239
Upper
Limit
RSTATE † — 2 — — — —
TREFHL T i ref,l
DHLFRM H i ref,l
DGLFRM G i ref,l
TCONHL T i con,l
Units
†† — — — TEMPERATURE
††† — — — MOLE ENTHALPY
†††† — — — MOLE ENTHALPY
T — — — TEMPERATURE
† Enthalpy reference state given by RSTATE. 2 denotes saturated liquid as
reference state.
†† For WILS-LR property method TREFHL defaults to 273.15K. For WILS-GLR
property method, TREFHL defaults to 298.15 K.
††† For WILS-LR property method, DHLFRM defaults to zero (0). For WILS-
GLR property method, DHLFRM defaults to the equation above.
†††† For WILS-LR property method, DGLFRM defaults to zero (0). For WILS-
GLR property method, DGLFRM defaults to the equation above.
Liquid heat capacity equation is required for all components.
Ideal Gas as Reference State
The saturated liquid enthalpy is calculated as follows:
Where:
Hi ref,ig
Ti ref,ig
= Reference state enthalpy for ideal gas at Ti ref,ig
= Heat of formation of ideal gas at 298.15 K by default
= Reference temperature corresponding to Hi ref,ig .
Defaults to 298.15 K

Ti con,ig
240 2 Thermodynamic Property Models
= The temperature at which one crosses from vapor
state to liquid state. This is a user defined
temperature that defaults to the system temperature
T. Ti con,ig may be selected such that heat of
vaporization of component i at the temperature is
most accurate.
The ideal gas enthalpy is calculated as follows:
The vapor enthalpy is calculated as follows:
The liquid heat capacity and the ideal gas heat capacity can be calculated
from the General Pure Component Liquid Heat Capacity and General Pure
Component Ideal Gas Heat Capacity, or other available models. The heat of
vaporization can be calculated from the General Pure Component Heat of
Vaporization, or other available models. The enthalpy departure is obtained
from an equation of state that is being used in the property method. For
WILS-LR and WILS-GLR, the ideal gas equation of state is used.
Parameter Symbol Default MDS Lower
Name/Element
Limit
Upper
Limit
RSTATE — 1 † — — — —
TREFHI T i ref,ig
DHFORM H i ref,ig
TCONHI T i con,ig
Units
†† — — — TEMPERATURE
— — — — MOLE ENTHALPY
T — — — TEMPERATURE
† Enthalpy reference state RSTATE for a component. Value of 1 denotes ideal
gas.
††For components with TB � 298.15 K, RSTATE defaults to 1 (ideal gas).
TREFHI defaults to 298.15 K. For components with TB > 298.15 K, RSTATE
defaults to 2 (liquid) and TREFHI does not apply to these components. See
the Saturated Liquid as Reference State section for more details.
Helgeson Equations of State
The Helgeson equations of state for standard volume , heat capacity ,
entropy , enthalpy of formation , and Gibbs energy of formation
at infinite dilution in aqueous phase are:

Where:
2 Thermodynamic Property Models 241

Where:
� = Pressure constant for a solvent (2600 bar for water)
� = Temperature constant for a solvent (228 K for
water)
� = Born coefficient
� = Dielectric constant of a solvent
Tr = Reference temperature (298.15 K)
Pr = Reference pressure (1 bar)
Note: Reduced temperature Tr is always calculated using absolute
temperature units.
Parameter Symbol Default MDS Lower Upper Units
Name/Element
Limit Limit
AHGPAR/1, ... ,
4
CHGPAR/1, ... ,
2
242 2 Thermodynamic Property Models
a 1, ..., a 4 0 — — — —
c 1, c 2 x — — — —
DHAQHG 0 — -0.5x10 10 0.5x10 10 MOLE-ENTHALPY
DGAQHG 0 — -0.5x10 10 0.5x10 10 MOLE-ENTHALPY
S25HG 0 — -0.5x10 10 0.5x10 10 MOLE-ENTROPY
OMEGHG 0 — -0.5x10 10 0.5x10 10 MOLE-ENTHALPY
If pressure is under 200 bar, AHGPAR may not be required.
References
Tanger, J.C. IV and H.C. Helgeson, "Calculation of the thermodynamic and
transport properties of aqueous species at high pressures and temperatures:
Revised equation of state for the standard partial properties of ions and
electrolytes," American Journal of Science, Vol. 288, (1988), p. 19-98.
Shock, E.L. and H.C. Helgeson, "Calculation of the thermodynamic and
transport properties of aqueous species at high pressures and temperatures:

Correlation algorithms for ionic species and equation of state predictions to 5
kb and 1000 �C," Geochimica et Cosmochimica Acta, Vol. 52, p. 2009-2036.
Shock, E.L., H.C. Helgeson, and D.A. Sverjensky, "Calculation of the
thermodynamic and transport properties of aqueous species at high pressures
and temperatures: Standard partial molal properties of inorganic neutral
species," Geochimica et Cosmochimica Acta, Vol. 53, p. 2157-2183.
Quadratic Mixing Rule
The quadratic mixing rule is a general-purpose mixing rule which can be
applied to various properties. For a given property Q, with i and j being
components, the rule is:
The pure component properties Qi and Qj are calculated by the default model
for that property, unless modified by option codes. Composition xi and xj is in
mole fraction unless modified by option codes. Kij is a binary parameter
specific to the mixing rule for each property. A variation on the equation using
the logarithm of the property is used for viscosity.
2 Thermodynamic Property Models 243

3 Transport Property Models
This section describes the transport property models available in the Aspen
Physical Property System. The following table provides an overview of the
available models. This table lists the Aspen Physical Property System model
names, and their possible use in different phase types, for pure components
and mixtures.
Viscosity models
These models calculate MUL (pure) and/or MULMX (mixture) for the liquid
phase, and MUV (pure) and/or MUVMX (mixture) for the vapor phase, except
models marked with * calculate MUVLP (pure) and/or MUVMXLP (mixture) for
the vapor phase, and models marked with ** calculate MUVPC (pure) and
MUVMXPC (mixture).
Model Model name Phase(s) Pure Mixture
Andrade Liquid Mixture
Viscosity
General Pure Component
Liquid Viscosity
244 3 Transport Property Models
MUL2ANDR L — X
MUL0ANDR L X —
API Liquid Viscosity MUL2API L — X
API 1997 Liquid Viscosity MULAPI97 L — X
Aspen Liquid Mixture Viscosity MUASPEN L — X
ASTM Liquid Mixture Viscosity MUL2ASTM L — X
General Pure Component
Vapor Viscosity *
Chapman-Enskog-Brokaw-
Wilke Mixing Rule *
Chung-Lee-Starling Low
Pressure *
MUV0CEB V X —
MUV2BROK,
MUV2WILK
MUV0CLSL,
MUV2CLSL
Chung-Lee-Starling MUV0CLS2,
MUV2CLS2,
MUL0CLS2,
MUL2CLS2
Dean-Stiel Pressure Correction
**
MUV0DSPC,
MUV2DSPC
IAPS Viscosity MUV0H2O,
MUL0H2O
V — X
V X X
V L X X
V X X
V L X —

Model Model name Phase(s) Pure Mixture
Jones-Dole Electrolyte
Correction
Letsou-Stiel MUL0LEST,
MUL2LEST
Lucas MUV0LUC,
MUV2LUC
TRAPP viscosity MUL0TRAP,
MUL2TRAP,
MUV0TRAP,
MUV2TRAP
3 Transport Property Models 245
MUL2JONS L — X
L X X
V X X
V L X X
Twu liquid viscosity MUL2TWU L — X
Viscosity quadratic mixing rule MUL2QUAD L — X
Thermal conductivity models
These models calculate KL (pure) and/or KLMX (mixture) for the liquid phase,
and KV (pure) and/or KVMX (mixture) for the vapor phase, except models
marked with * calculate KVLP (pure) and/or KVMXLP (mixture) for the vapor
phase, and models marked with ** calculate KVPC (pure) and KVMXPC
(mixture) for the vapor phase.
Model Model name Phase(s) Pure Mixture
Chung-Lee-Starling Thermal
Conductivtity
IAPS Thermal Conductivity for
Water
KV0CLS2,
KV2CLS2,
KL0CLS2,
KL2CLS2
KV0H2O
KL0H2O
V L X X
Li Mixing Rule KL2LI L X X
Riedel Electrolyte Correction KL2RDL L — X
General Pure Component
Liquid Thermal Conductivity
General Pure Component
Vapor Thermal Conductivity *
Stiel-Thodos Pressure
Correction **
KL0SR,
KL2SRVR
V
L
X
X
—
—
L X X
KV0STLP V X —
KV0STPC,
KV2STPC
TRAPP Thermal Conductivity KV0TRAP,
KV2TRAP,
KL0TRAP,
KL2TRAP
V X X
V L X X
Vredeveld Mixing Rule KL2SRVR L X X
Wassiljewa-Mason-Saxena
mixing rule *
Diffusivity models
KV2WMSM V X X
These models calculate DL (binary) and/or DLMX (mixture) for the liquid
phase, and DV (binary) and/or DVMX (mixture) for the vapor phase.
Model Model name Phase(s) BinaryMixture
Chapman-Enskog-Wilke-Lee
Binary
DV0CEWL V X —

Model Model name Phase(s) BinaryMixture
Chapman-Enskog-Wilke-Lee
Mixture
Dawson-Khoury-Kobayashi
Binary
Dawson-Khoury-Kobayashi
Mixture
Nernst-Hartley Electrolytes DL0NST,
DL1NST
246 3 Transport Property Models
DV1CEWL V — X
DV1DKK V X —
DV1DKK V — X
L X X
Wilke-Chang Binary DL0WC2 L X —
Wilke-Chang Mixture DL1WC L — X
Surface tension models
These models calculate SIGL (pure) and/or SIGLMX (mixture).
Model Model name Phase(s) Pure Mixture
Liquid Mixture Surface Tension SIG2IDL L — X
API Surface Tension SIG2API L — X
General Pure Component
Liquid Surface Tension
SIG0HSS,
SIG2HSS
L X —
IAPS surface tension SIG0H2O L X —
Onsager-Samaras Electrolyte
Correction
SIG2ONSG L — X
Modified MacLeod-Sugden SIG2MS L — X
Viscosity Models
The Aspen Physical Property System has the following built-in viscosity
models:
Model Type
Andrade Liquid Mixture Viscosity Liquid
General Pure Component Liquid Viscosity Pure component liquid
API liquid viscosity Liquid
API 1997 liquid viscosity Liquid
General Pure Component Vapor Viscosity Low pressure vapor,
pure components
Chapman-Enskog-Brokaw-Wilke Mixing Rule Low pressure vapor,
mixture
Chung-Lee-Starling Low Pressure Low pressure vapor
Chung-Lee-Starling Liquid or vapor
Dean-Stiel Pressure correction Vapor
IAPS viscosity Water or steam
Jones-Dole Electrolyte Correction Electrolyte
Letsou-Stiel High temperature liquid
Lucas Vapor
TRAPP viscosity Vapor or liquid

Model Type
Aspen Liquid Mixture Viscosity Liquid
ASTM Liquid Mixture Viscosity Liquid
Twu liquid viscosity Liquid
Viscosity quadratic mixing rule Liquid
Andrade Liquid Mixture Viscosity
The liquid mixture viscosity is calculated by the modified Andrade equation:
Where:
kij
mij
3 Transport Property Models 247
=
=
fi depends on the option code for the model MUL2ANDR.
If first option code of
Then fi is
MUL2ANDR is
0 (Default) Mole fraction of component i
1 Mass fraction of component i
Note that the Andrade liquid mixture viscosity model is called from other
models. The first option codes of these models cause fi to be mole or mass
fraction when Andrade is used in the respective models. To maintain
consistency across models, if you set the first option code for MUL2ANDR to
1, you should also the set the first option code of the other models to 1, if
they are used in your simulation.
Model Model Name
MUL2JONS Jones-Dole Electrolyte Viscosity model
DL0WCA Wilke-Chang Diffusivity model (binary)
DL1WCA Wilke-Chang Diffusivity model (mixture)
DL0NST Nernst-Hartley Electrolyte Diffusivity model (binary)
DL1NST Nernst-Hartley Electrolyte Diffusivity model (mixture)
The binary parameters kij and mij allow accurate representation of complex
liquid mixture viscosity. Both binary parameters default to zero.
Parameter Symbol Default MDS Lower Upper Units
Name/Element
Limit Limit
ANDKIJ/1 a ij 0 — — — —
ANDKIJ/2 b ij 0 — — — —
ANDMIJ/1 c ij 0 — — — —
ANDMIJ/2 d ij 0 — — — —
The pure component liquid viscosity �i *,l is calculated by the General Pure
Component Liquid Viscosity model.

General Pure Component Liquid Viscosity
The Aspen Physical Property System has several submodels for calculating
pure component liquid viscosity. It uses parameter TRNSWT/1 to determine
which submodel is used. See Pure Component Temperature-Dependent
Properties for details.
If TRNSWT/1 is This equation is used And this parameter is used
0 Andrade MULAND
101, 115 DIPPR 101 or 115 MULDIP
301 PPDS MULPDS
401 IK-CAPE polynomial equation MULPO
404 IK-CAPE exponential equation MULIKC
508 NIST TDE equation MULNVE
509 NIST PPDS9 MULPPDS9
Andrade Liquid Viscosity
The Andrade equation is:
Linear extrapolation of ln(viscosity) versus 1/T occurs for temperatures
outside bounds.
Parameter
Name/Element
248 3 Transport Property Models
Symbol Default MDS Lower
Limit
Upper
Limit
Units
MULAND/1 A i — X — — VISCOSITY,
TEMPERATURE †
MULAND/2 B i — X — — TEMPERATURE †
MULAND/3 C i — X — — TEMPERATURE †
MULAND/4 T l 0.0 X — — TEMPERATURE
MULAND/5 T h 500.0 X — — TEMPERATURE
† If Bi or Ci is non-zero, absolute temperature units are assumed for Ai, Bi,
and Ci. Otherwise, all coefficients are interpreted in user input temperature
units. The temperature limits are always interpreted in user input units.
DIPPR Liquid Viscosity
There are two DIPPR equations for liquid viscosity. The value of TRNSWT/1
determines which one is used.
Equation 101 for the DIPPR liquid viscosity model is:
Equation 115 for the DIPPR liquid viscosity model is:
Linear extrapolation of ln(viscosity) versus 1/T occurs for temperatures
outside bounds.

(Other DIPPR equations may sometimes be used. See Pure Component
Temperature-Dependent Properties for details.)
Parameter Symbol Default MDS Lower Upper Units
Name/Element
Limit Limit
MULDIP/1 C 1i — X — — VISCOSITY,
TEMPERATURE ††
MULDIP/2, ..., 5 C 2i, ..., C 5i 0 X — — TEMPERATURE ††
MULDIP/6 C 6i 0 X — — TEMPERATURE
MULDIP/7 C 7i 1000 X — — TEMPERATURE
†† If any of C3i through C5i are non-zero, absolute temperature units are
assumed for C3i through C5i. Otherwise, all coefficients are interpreted in user
input temperature units. The temperature limits are always interpreted in
user input units.
PPDS
The PPDS equation is:
Linear extrapolation of viscosity versus T occurs for temperatures outside
bounds.
Parameter
Name/Element
3 Transport Property Models 249
Symbol Default MDS Lower
Limit
Upper
Limit
MULPDS/1 C 1i — — — — —
MULPDS/2 C 2i — — — —
Units
MULPDS/3 C 3i — — — TEMPERATURE
MULPDS/4 C 4i — — — TEMPERATURE
MULPDS/5 C 5i — — — — VISCOSITY
MULPDS/6 C 6i — — — TEMPERATURE
MULPDS/7 C 7i — — — TEMPERATURE
NIST PPDS9 Equation
This is the same as the PPDS equation above, but it uses parameter
MULPPDS9. Note that the parameters are in a different order.
Parameter Symbol Default MDS Lower Upper Units
Name/Element
Limit Limit
MULPPDS9/1 C 5i — — — — Pa*S
MULPPDS9/2 C 1i — — — —
MULPPDS9/3 C 2i — — — TEMPERATURE
MULPPDS9/4 C 3i — — — TEMPERATURE
MULPPDS9/5 C 4i — — — — TEMPERATURE
MULPPDS9/6 C 6i — — — TEMPERATURE
MULPPDS9/7 C 7i — — — TEMPERATURE

IK-CAPE Liquid Viscosity Model
The IK-CAPE liquid viscosity model includes both exponential and polynomial
equations.
Exponential
Linear extrapolation of viscosity versus T occurs for temperatures outside
bounds.
Parameter
Name/Element
250 3 Transport Property Models
SymbolDefault MDS Lower
Limit
Upper
Limit
Units
MULIKC/1 C 1i — X — — VISCOSITY
MULIKC/2 C 2i 0 X — — TEMPERATURE †††
MULIKC/3 C 3i 0 X — — VISCOSITY
MULIKC/4 C 4i 0 X — — TEMPERATURE
MULIKC/5 C 5i 1000 X — — TEMPERATURE
††† Absolute temperature units are assumed for C2i. The temperature limits
are always interpreted in user input units.
Polynomial
Linear extrapolation of viscosity versus T occurs for temperatures outside
bounds.
Parameter Symbol Default MDS Lower
Name/Element
Limit
Upper
Limit
Units
MULPO/1 C 1i — X — — VISCOSITY
MULPO/2, ..., 10 C 2i, ..., C 10i 0 X — — VISCOSITY,
TEMPERATURE
MULPO/11 C 11i 0 X — — TEMPERATURE
MULPO/12 C 12i 1000 X — — TEMPERATURE
NIST TDE Equation
Linear extrapolation of viscosity versus T occurs for temperatures outside
bounds.
Absolute temperature units are assumed for C2i, C3i, and C4i. The temperature
limits are always interpreted in user input units.
Parameter Symbol Default MDS Lower
Name/Element
Limit
Upper
Limit
MULNVE/1 C 1i — X — — —
Units

Parameter Symbol Default MDS Lower
Name/Element
Limit
3 Transport Property Models 251
Upper
Limit
Units
MULNVE/2, 3, 4 C 2i, C 3i, C 4i 0 X — — TEMPERATURE
MULNVE/5 C 5i 0 X — — TEMPERATURE
MULNVE/6 C 6i 1000 X — — TEMPERATURE
References
R.C. Reid, J.M. Prausnitz, and B.E. Poling, The Properties of Gases and
Liquids, 4th ed., (New York: McGraw-Hill, 1987), p. 439.
API Liquid Viscosity
The liquid mixture viscosity is calculated using a combination of the API and
General equations. This model is recommended for petroleum and
petrochemical applications. It is used in the CHAO-SEA, GRAYSON, LK-PLOCK,
PENG-ROB, and RK-SOAVE option sets.
For pseudocomponents, the API model is used:
Where:
fcn = A correlation based on API Procedures and Figures 11A4.1, 11A4.2,
and 11A4.3 (API Technical Data Book, Petroleum Refining, 4th
edition)
Vm l is obtained from the API liquid volume model.
For real components, the General model is used.
Parameter
Name/Element
Symbol Default MDS Lower
Limit
Upper
Limit
Units
TB T bi — — 4.0 2000.0 TEMPERATURE
API API i — — -60.0 500.0 —
API 1997 Liquid Viscosity
The liquid mixture viscosity is calculated using a combination of the API and
General equations. This model is recommended over the earlier API viscosity
model.
This model is applicable to petroleum fractions with normal boiling points from
150 F to 1200 F and API gravities between 0 and 75. Testing by AspenTech
indicates that this model is slightly more accurate than the Twu model for
light and medium boiling petroleum components, while the Twu model is
superior for heavy fractions.
For pseudocomponents, the API model is used:
Where:

fcn = A correlation based on API Procedures and Figures 11A4.2, 11A4.3,
and 11A4.4 (API Technical Data Book, Petroleum Refining, 1997
edition)
Vm l is obtained from the API liquid volume model.
For real components, the General model is used.
Parameter
Name/Element
252 3 Transport Property Models
Symbol Default MDS Lower
Limit
Upper
Limit
Units
TB T bi — — 4.0 2000.0 TEMPERATURE
API API i — — -60.0 500.0 —
Aspen Liquid Mixture Viscosity
The liquid mixture viscosity is calculated by the equation:
Where:
Xi = Mole fraction or weight fraction of component i
kij = Symmetric binary parameter (kij = kji)
lij = Antisymmetric binary parameter (lij = -lji)
The pure component liquid viscosity �i *,l is calculated by the General Pure
Component Liquid Viscosity model.
The binary parameters kij and lij allow accurate representation of complex
liquid mixture viscosity. Both binary parameters default to zero.
Parameter Symbol Default MDS Lower Upper Units
Name/Element
Limit Limit
MUKIJ k ij 0 — -100.0 100.0 —
MULIJ l ij 0 — 100.0 100.0 —
ASTM Liquid Mixture Viscosity
It is generally difficult to predict the viscosity of a mixture of viscous
components. For hydrocarbons, the following weighting method (ASTM †) is
known to give satisfactory results:
Where:
wi = Weight fraction of component i
�m = Absolute viscosity of the mixture (N-sec/sqm)

�i = Viscosity of component i (N-sec/sqm)
log = Common logarithm (base 10)
f = An adjustable parameter, typically in the
range of 0.5 to 1.0
The individual component viscosities are calculated by the General Pure
Component Liquid Viscosity model. The parameter f can be specified by
setting the value for MULOGF for the first component in the component list
(as defined on the Components | Specifications | Selection sheet).
Parameter
Name/Element
3 Transport Property Models 253
Symbol Default MDS Lower
Limit
Upper
Limit
MULOGF f 1.0 — 0.0 2.0 —
Units
† "Petroleum Refining, 1 Crude Oil, Petroleum Products, Process Flowsheets",
Institut Francais du Petrole Publications, 1995, p. 130.
General Pure Component Vapor Viscosity
The Aspen Physical Property System has several submodels for calculating
pure component low pressure vapor viscosity. It uses parameter TRNSWT/2
to determine which submodel is used. See Pure Component Temperature-
Dependent Properties for details.
If TRNSWT/2 is This equation is used And this parameter is
used
0 Chapman-Enskog-
Brokaw
STKPAR, LJPAR
102 DIPPR MUVDIP
301 PPDS MUVPDS
302 PPDS kinetic theory MUVCEB
401 IK-CAPE polynomial
equation
402 IK-CAPE Sutherland
equation
503 NIST ThermoML
polynomial
Chapman-Enskog-Brokaw
MUVPO
MUVSUT
MUVTMLPO
The equation for the Chapman-Enskog model is:
Where:
�� =
A parameter � is used to determine whether to use the Stockmayer or
Lennard-Jones potential parameters for �/k (energy parameter) and �
(collision diameter). To calculate �, the dipole moment p and either the

Stockmayer parameters or Tb and Vb are needed. The polarity correction is
from Brokaw.
Parameter Symbol Default MDS Lower
Name/Element
Limit
254 3 Transport Property Models
Upper
Limit
MW M i — — 1.0 5000.0 —
MUP p i — — 0.0 5x10 -24
Units
DIPOLEMOMENT
STKPAR/1 (� i/k) ST fcn(T bi, V bi, p i) — X — TEMPERATURE
STKPAR/2 � i ST fcn(T bi, V bi, p i) X — — LENGTH
LJPAR/1 (� i/k) LJ
LJPAR/2 � i LJ
DIPPR Vapor Viscosity
fcn(T ci, � i) X — — TEMPERATURE
fcn(T ci, p ci, � i)
The equation for the DIPPR vapor viscosity model is:
X — — LENGTH
When necessary, the vapor viscosity is extrapolated beyond this temperature
range linearly with respect to T, using the slope at the temperature limits.
(Other DIPPR equations may sometimes be used. See Pure Component
Temperature-Dependent Properties for details.)
PCES uses the DIPPR equation in estimating vapor viscosity.
Parameter
Name/Element
Symbol Default MDS Lower
Limit
Upper
Limit
Units
MUVDIP/1 C 1i — X — — VISCOSITY
MUVDIP/2 C 2i 0 X — — —
MUVDIP/3, 4 C 3i, C 4i 0 X — — TEMPERATURE †
MUVDIP/5 †† 0 X — — —
MUVDIP/6 C 6i 0 X — — TEMPERATURE
MUVDIP/7 C 7i 1000 X — — TEMPERATURE
† If any of C2i through C4i are non-zero, absolute temperature units are
assumed for C1i through C4i. Otherwise, all coefficients are interpreted in user
input temperature units. The temperature limits are always interpreted in
user input units.
†† MUVDIP/5 is not used in this equation. It is normally set to zero. The
parameter is provided for consistency with other DIPPR equations.
PPDS
The PPDS submodel includes both the basic PPDS vapor viscosity equation
and the PPDS kinetic theory vapor viscosity equation. For either equation,
linear extrapolation of viscosity versus T occurs for temperatures outside
bounds.
PPDS Vapor Viscosity
The equation is:

Parameter
Name/Element
3 Transport Property Models 255
Symbol Default MDS Lower
Limit
Upper
Limit
Units
MUVPDS/1 C 1i — — — — VISCOSITY
MUVPDS/2 C 2i 0 — — — —
MUVPDS/3 C 3i 0 — — — —
MUVPDS/4 C 4i 0 — — — TEMPERATURE
MUVPDS/5 C 5i 1000 — — — TEMPERATURE
PPDS Kinetic Theory Vapor Viscosity
The equation is:
Parameter
Name/Element
Symbol Default MDS Lower
Limit
Upper
Limit
MW M i — — 1.0 5000.0 —
Units
MUVCEB/1 C 1i — — — — LENGTH
MUVCEB/2 C 2i — — — — TEMPERATURE †
MUVCEB/3 C 3i 0 — — — —
MUVCEB/4 C 4i 0 — — — TEMPERATURE
MUVCEB/5 C 5i 1000 — — — TEMPERATURE
† Absolute temperature units are assumed for C2i . The temperature limits are
always interpreted in user input units.
IK-CAPE Vapor Viscosity
The IK-CAPE vapor viscosity model includes both the Sutherland equation and
the polynomial equation. For either equation, linear extrapolation of viscosity
versus T occurs for temperatures outside bounds.
Sutherland Equation
Parameter
Name/Element
Symbol Default MDS Lower
Limit
Upper
Limit
Units
MUVSUT/1 C 1i — X — — VISCOSITY
MUVSUT/2 C 2i 0 X — — TEMPERATURE ††
MUVSUT/3 C 3i 0 X — — TEMPERATURE

Parameter
Name/Element
256 3 Transport Property Models
Symbol Default MDS Lower
Limit
Upper
Limit
Units
MUVSUT/4 C 4i 1000 X — — TEMPERATURE
†† If C2i is non-zero, absolute temperature units are assumed for C1i and C2i.
Otherwise, all coefficients are interpreted in user input temperature units. The
temperature limits are always interpreted in user input units.
Polynomial
Parameter
Name/Element
Symbol Default MDS Lower
Limit
Upper
Limit
Units
MUVPO/1 C 1i — X — — VISCOSITY
MUVPO/2, ..., 10 C 2i, ..., C 10i 0 X — — VISCOSITY,
TEMPERATURE
MUVPO/11 C 11i 0 X — — TEMPERATURE
MUVPO/12 C 12i 1000 X — — TEMPERATURE
NIST ThermoML Polynomial
Parameter
Name/Element
Symbol Default MDS Lower
Limit
Upper
Limit
Units
MUVTMLPO/1 C 1i — X — — Pa*s/T
MUVTMLPO/2, ..., 4 C 2i , ..., C 4i 0 X — — Pa*s/T
MUVTMLPO/5 nTerms 4 X — — —
MUVTMLPO/6 T lower 0 X — — TEMPERATURE
MUVTMLPO/7 T upper 1000 X — — TEMPERATURE
References
R.C. Reid, J.M. Prausnitz, and B.E. Poling. The Properties of Gases and
Liquids, 4th ed., (New York: McGraw-Hill, 1987), p. 392.
Chapman-Enskog-Brokaw-Wilke Mixing
Rule
The low pressure vapor mixture viscosity is calculated by the Wilke
approximation of the Chapman-Enskog equation:
For �ij,the formulation by Brokaw is used:

Where:
The Stockmayer or Lennard-Jones potential parameters �/k (energy
parameter) and � (collision diameter) and the dipole moment p are used to
calculate �� The k represents Boltzmann's constant 1.38065 x 10 -23 J/K. If the
Stockmayer parameters are not available, � is estimated from Tb and Vb:
Where p is in debye.
The pure component vapor viscosity �i *,v (p = 0) can be calculated using the
General Pure Component Vapor Viscosity (or another low pressure vapor
viscosity model).
Ensure that you supply parameters for �i *,v (p = 0).
Parameter
Name/
Element
Symbol Default MDS Lower
Limit
3 Transport Property Models 257
Upper
Limit
MW M i — — 1.0 5000.0 —
MUP p i — — 0.0 5x10 -24
Units
DIPOLEMOMENT
STKPAR/1 (� i/k) ST fcn(T bi, V bi, p i) — X — TEMPERATURE

Parameter
Name/
Element
Symbol Default MDS Lower
Limit
258 3 Transport Property Models
Upper
Limit
Units
STKPAR/2 � i ST fcn(T bi, V bi, p i) X — — LENGTH
References
R.C. Reid, J.M. Prausnitz, and T.K. Sherwood, The Properties of Gases and
Liquids, 3rd ed., (New York: McGraw-Hill, 1977), pp. 410–416.
Chung-Lee-Starling Low-Pressure Vapor
Viscosity
The low-pressure vapor viscosity by Chung, Lee, and Starling is:
Where the viscosity collision integral is:
The shape and polarity correction is:
The parameter pr is the reduced dipolemoment:
C1 is a constant of correlation.
The polar parameter � is tabulated for certain alcohols and carboxylic acids.
The previous equations can be used for mixtures when applying these mixing
rules:

Where:
Vcij
=
�ij = 0 (in almost all cases)
Tcij
=
�ij = 0 (in almost all cases)
�ij
Mij
�ij
=
=
=
Note: Reduced temperature Tr is always calculated using absolute
temperature units.
Parameter Symbol Default MDS Lower Upper Units
Name/Element
Limit Limit
TCCLS T ci TC x 5.0 2000.0 TEMPERATURE
VCCLS V ci VC x 0.001 3.5 MOLE-VOLUME
MW M i — — 1.0 5000.0 —
MUP p i — — 0.0 5x10 -24
OMGCLS � i
CLSK � i
CLSKV � ij
CLSKT � ij
3 Transport Property Models 259
OMEGA x -0.5 2.0 —
0.0 x 0.0 0.5 —
0.0 x -0.5 -0.5 —
0.0 x -0.5 0.5 —
DIPOLEMOMENT
The model specific parameters also affect the Chung-Lee-Starling Viscosity
and the Chung-Lee-Starling Thermal Conductivity models.
References
R.C. Reid, J.M. Prausnitz, and B.E. Poling, The Properties of Gases and
Liquids, 4th ed., (New York: McGraw-Hill, 1987), p. 396, p. 413.

Chung-Lee-Starling Viscosity
The Chung-Lee-Starling viscosity equation for vapor and liquid, high and low
pressure is:
With:
f1
f2
FC
=
=
=
The molar density can be calculated using an equation-of-state model (for
example, the Benedict-Webb-Rubin). The parameter pr is the reduced
dipolemoment:
C1 and C2 are constants of correlation.
The polar parameter � is tabulated for certain alcohols and carboxylic acids.
For low pressures, f1 is reduced to 1.0 and f2 becomes negligible. The
equation reduces to the low pressure vapor viscosity model by Chung-Lee and
Starling.
The previous equations can be used for mixtures when applying these mixing
rules:
260 3 Transport Property Models

Where:
Vcij
=
�ij = 0 (in almost all cases)
Tcij
=
�ij = 0 (in almost all cases)
�ij
Mij
�ij
=
=
=
Parameter
Name/Element
3 Transport Property Models 261
Symbol Default MDS Lower
Limit
Upper
Limit
Units
TCCLS T ci TC x 5.0 2000.0 TEMPERATURE
VCCLS V ci VC x 0.001 3.5 MOLE-VOLUME
MW M i — — 1.0 5000.0 —
MUP p i — — 0.0 5x10 -24
OMGCLS � i
CLSK � i
CLSKV � ij
CLSKT � ij
OMEGA x -0.5 2.0 —
0.0 x 0.0 0.5 —
0.0 x -0.5 -0.5 —
0.0 x -0.5 0.5 —
DIPOLEMOMENT
The model specific parameters affect the results of the Chung-Lee-Starling
Thermal Conductivity and Low Pressure Viscosity models as well.
References
R.C. Reid, J.M. Prausnitz, and B.E. Poling, The Properties of Gases and
Liquids, 4th ed., (New York: McGraw-Hill, 1987), p. 427.

Dean-Stiel Pressure Correction
The residual vapor viscosity or the pressure correction to low pressure vapor
viscosity by Dean and Stiel is:
Where � v (p = 0) is obtained from a low pressure viscosity model (for
example, General Pure Component Vapor Viscosity). The dimensionlessmaking
factor � is:
�
Tc
262 3 Transport Property Models
=
=
M =
pc
Vcm
Zcm
=
=
=
�rm = Vcm / Vm v
The parameter Vm v is obtained from Redlich-Kwong equation-of-state.
Parameter
Name/Element
Symbol Default MDS Lower
Limit
Upper
Limit
MW M i — — 1.0 5000.0 —
Units
VC V ci — — 0.001 3.5 MOLE-VOLUME
IAPS Viscosity for Water
The IAPS viscosity models, developed by the International Association for
Properties of Steam, calculate vapor and liquid viscosity for water and steam.
These models are used in option sets STEAMNBS and STEAM-TA.
The general form of the equation for the IAPS viscosity models is:
�w=fcn(T, p)
Where:
fcn = Correlation developed by IAPS
The models are only applicable to water. There are no parameters required
for the models.

Jones-Dole Electrolyte Correction
The Jones-Dole model calculates the correction to the liquid mixture viscosity
of a solvent mixture, due to the presence of electrolytes:
Where:
�solv = Viscosity of the liquid solvent mixture, by default
calculated by the Andrade model
��ca l = Contribution to the viscosity correction due to
apparent electrolyte ca
The parameter �solv can be calculated by different models depending on
option code 3 for MUL2JONS:
Option Code Solvent liquid mixture viscosity
Value
model
0
Andrade liquid mixture viscosity
model (default)
1 Viscosity quadratic mixing rule
2 Aspen liquid mixture viscosity
model
The parameter ��ca l can be calculated by three different equations.
If these parameters are available Use this equation
IONMOB and IONMUB Jones-Dole †
IONMUB Breslau-Miller
— Carbonell
† When the concentration of apparent electrolyte exceeds 0.1 M, the Breslau-
Miller equation is used instead.
Jones-Dole
The Jones-Dole equation is:
Where:
xca a
3 Transport Property Models 263
(1)
= Concentration of apparent electrolyte ca (2)
= Mole fraction of apparent electrolyte ca (3)
Aca = (4)
La = (5)

Lc = (6)
Bca = (7)
When the electrolyte concentration exceeds 0.1 M, the Breslau-Miller equation
is used instead. This behavior can be disabled by setting the second option
code for MUL2JONS to 1.
Breslau-Miller
The Breslau-Miller equation is:
Where the effective volume Vc is given by:
Carbonell
264 3 Transport Property Models
for salts involving univalent ions
for other salts
The Carbonell equation is:
Where:
Mk = Molecular weight of an apparent electrolyte
component k
(8)
(9)
(9a)
(10)
You must provide parameters for the model used for the calculation of the
liquid mixture viscosity of the solvent mixture.
Parameter
Symbol Default Lower Upper Units
Name/Element
Limit Limit
CHARGE z 0.0 — — —
MW M — 1.0 5000.0 —
IONMOB/1 l 1 — — — AREA, MOLES
IONMOB/2 l 2 0.0 — — AREA, MOLES,
TEMPERATURE
IONMUB/1 b 1 — — — MOLE-VOLUME
IONMUB/2 b 2 0,0 — — MOLE-VOLUME,
TEMPERATURE
References
A. L. Horvath, Handbook of Aqueous Electrolyte Solutions, (Chichester: Ellis
Horwood, 1985).

Letsou-Stiel
The Letsou-Stiel model calculates liquid viscosity at high temperatures for
0.76 � Tr � 0.98. This model is used in PCES.
Note: Reduced temperature Tr is always calculated using absolute
temperature units.
The general form for the model is:
� l � = (� l �) 0 + �(� l �) 1
Where:
(� l �) 0 =
(� l �) 1 =
�
�
3 Transport Property Models 265
=
=
Parameter
Name/Element
Symbol Default MDS Lower
Limit
Upper
Limit
MW M i — — 1.0 5000.0 —
Units
TC T ci — — 5.0 2000.0 TEMPERATURE
PC p ci — — 10 5
OMEGA � i
References
10 8
— — -0.5 2.0 —
PRESSURE
R.C. Reid, J.M. Pransnitz, and B.E. Poling, The Properties of Gases and
Liquids, 4th ed., (New York: McGraw-Hill, 1987), p. 471.
Lucas Vapor Viscosity
The equation for the Lucas vapor viscosity model is:
Where the dimensionless low pressure viscosity is given by:
The dimensionless-making group is:
The pressure correction factor Y is:

The polar and quantum correction factors at high and low pressure are:
FP
FQ
266 3 Transport Property Models
=
=
FPi (p = 0) =
FQi (p = 0) = fcn(Tri), but is only nonunity for the quantum
gates i = H2, D2, and He.
Note: Reduced temperature Tr is always calculated using absolute
temperature units.
The Lucas mixing rules are:
Tc
pc
=
=
M =
FP (p = 0) =
FQ (p = 0) =
Where A differs from unity only for certain mixtures.
Parameter
Name/Element
Symbol Default MDS Lower
Limit
Upper
Limit
Units
TCLUC T ci TC x 5.0 2000.0 TEMPERATURE
PCLUC p ci PC x 10 5
ZCLUC Z ci ZC x 0.1 0.5 —
MW M i — — 1.0 5000.0 —
10 8
MUP p i — — 0.0 5x10 -24
References
PRESSURE
DIPOLEMOMENT
R.C. Reid, J.M. Prausnitz, and B.E. Poling, The Properties of Gases and
Liquids, 4th ed., (New York: McGraw-Hill, 1987), p. 421, 431.
TRAPP Viscosity Model
The general form for the TRAPP viscosity model is:

Where:
The parameter is the mole fraction vector; fcn is a corresponding states
correlation based on the model for vapor and liquid viscosity TRAPP, by the
National Bureau of Standards (NBS, currently NIST) . The model can be used
for both pure components and mixtures. The model should be used for
nonpolar components only.
Parameter
Name/Element
3 Transport Property Models 267
Symbol Default MDS Lower
Limit
Upper
Limit
MW M i — — 1.0 5000.0 —
Units
TCTRAP T ci TC x 5.0 2000.0 TEMPERATURE
PCTRAP p ci PC x 10 5
10 8
PRESSURE
VCTRAP V ci VC x 0.001 3.5 MOLE-VOLUME
ZCTRAP Z ci ZC x 0.1 1.0 —
OMGRAP � i
References
OMEGA x -0.5 3.0 —
J.F. Ely and H.J.M. Hanley, "Prediction of Transport Properties. 1. Viscosities
of Fluids and Mixtures," Ind. Eng. Chem. Fundam., Vol. 20, (1981), pp. 323–
332.
Twu Liquid Viscosity
The Twu liquid viscosity model is based upon the work of C.H. Twu (1985).
The correlation uses n-alkanes as a reference fluid and is capable of
predicting liquid viscosity for petroleum fractions with normal boiling points up
to 1340 F and API gravity up to -30.
Given the normal boiling point Tb and the specific gravity SG of the system to
be modeled, the Twu model estimates the viscosity of the n-alkane reference
fluid of the same normal boiling point at 100 F and 210 F, and its specific
gravity. These are used to estimates the viscosity of the system to be
modeled at 100 F and at 210 F, and these viscosities are used to estimate the
viscosity at the temperature of interest.

Where:
SG = Specific gravity of petroleum fraction
Tb = Normal boiling point of petroleum fraction, Rankine
SG° = Specific gravity of reference fluid with normal
boiling point Tb
T = Temperature of petroleum fraction, Rankine
� = Kinematic viscosity of petroleum fraction at T, cSt
�i = Kinematic viscosity of petroleum fraction at 100 F
(i=1) and 210 F (i=2), cSt
�1°, �2° = Kinematic viscosity of reference fluid at 100 F and
210 F, cSt
Tc° = Critical temperature of reference fluid, Rankine
268 3 Transport Property Models

Reference
C.H. Twu, "Internally Consistent Correlation for Predicting Liquid Viscosities of
Petroleum Fractions," Ind. Eng. Chem. Process Des. Dev., Vol. 24 (1985), pp.
1287-1293
Viscosity Quadratic Mixing Rule
With i and j being components, the viscosity quadratic mixing rule is:
The pure component viscosity is calculated by the General Pure Component
Liquid Viscosity model.
Option Codes
Option Code Value Descriptions
1 0 Use mole basis composition (default)
Parameter
Parameter
Name/Element
1 Use mass basis composition
3 Transport Property Models 269
Symbol Default MDS Lower
Limit
Upper
Limit
MLQKIJ K ij - x - - —
Thermal Conductivity Models
Units
The Aspen Physical Property System has eight built-in thermal conductivity
models. This section describes the thermal conductivity models available.
Model Type
Chung-Lee-Starling Vapor or liquid
IAPS Water or steam
Li Mixing Rule Liquid mixture
Riedel Electrolyte Correction Electrolyte
General Pure Component Liquid Thermal
Conductivity
Liquid
Solid Thermal Conductivity Polynomial Solid
General Pure Component Vapor Thermal
Conductivity
Stiel-Thodos Pressure Correction Vapor
Low pressure vapor
TRAPP Thermal Conductivity Vapor or liquid
Vredeveld Mixing Rule Liquid mixture
Wassiljewa-Mason-Saxena Mixing Rule Low pressure vapor

Chung-Lee-Starling Thermal Conductivity
The main equation for the Chung-Lee-Starling thermal conductivity model is:
Where:
f1
f2
�
270 3 Transport Property Models
=
=
=
�(p = 0) can be calculated by the low pressure Chung-Lee-Starling model.
The molar density can be calculated using an equation-of-state model (for
example, the Benedict-Webb-Rubin equation-of-state). The parameter pr is
the reduced dipolemoment:
The polar parameter � is tabulated for certain alcohols and carboxylic acids.
For low pressures, f1 is reduced to 1.0 and f2 is reduced to zero. This gives
the Chung-Lee-Starling expression for thermal conductivity of low pressure
gases.
The same expressions are used for mixtures. The mixture expression for � (p
= 0) must be used. (See Chung-Lee-Starling Low-Pressure Vapor Viscosity.)
Where:

Vcij
3 Transport Property Models 271
=
�ij = 0 (in almost all cases)
Tcij
=
�ij = 0 (in almost all cases)
�ij
Mij
�ij
=
=
=
Parameter
Name/Element
Symbol Default MDS Lower
Limit
Upper
Limit
Units
TCCLS T ci TC x 5.0 2000.0 TEMPERATURE
VCCLS V ci VC x 0.001 3.5 MOLE-VOLUME
MW M i — — 1.0 5000.0 —
MUP p i — — 0.0 5x10 -24
OMGCLS � i
CLSK � i
CLSKV � ij
CLSKT � ij
OMEGA x -0.5 2.0 —
0.0 x 0.0 0.5 —
0.0 x -0.5 -0.5 —
0.0 x -0.5 0.5 —
DIPOLEMOMENT
The model-specific parameters also affect the results of the Chung-Lee-
Starling Viscosity models.
References
R.C. Reid, J.M. Prausnitz, and B.E. Poling, The Properties of Gases and
Liquids, 4th ed., (New York: McGraw-Hill, 1987), p. 505, 523.
IAPS Thermal Conductivity for Water
The IAPS thermal conductivity models were developed by the International
Association for Properties of Steam. These models can calculate vapor and
liquid thermal conductivity for water and steam. They are used in option sets
STEAMNBS and STEAM-TA.
The general form of the equation for the IAPS thermal conductivity models is:
�w=fcn(T, p)
Where:

fcn = Correlation developed by IAPS
The models are only applicable to water. No parameters are required.
Li Mixing Rule
Liquid mixture thermal conductivity is calculated using Li equation (Reid
et.al., 1987):
Where:
The pure component liquid molar volume Vi *,l is calculated from the Rackett
model.
The pure component liquid thermal conductivity �i *,l is calculated by the
General Pure Component Liquid Thermal Conductivity model.
Reference: R.C. Reid, J.M. Prausnitz, and B.E. Poling, The Properties of Gases
and Liquids, 4th ed., (New York: McGraw-Hill, 1987), p. 550.
Riedel Electrolyte Correction
The Riedel model can calculate the correction to the liquid mixture thermal
conductivity of a solvent mixture, due to the presence of electrolytes:
Where:
� l solv = Thermal conductivity of the liquid solvent mixture,
calculated by the General Pure Component Liquid
Thermal Conductivity model using the Vredeveld
mixing rule
xca a
272 3 Transport Property Models
= Mole fraction of the apparent electrolyte ca
ac, aa = Riedel ionic coefficient
Vm l
= Apparent molar volume computed by the Clarke
density model
Apparent electrolyte mole fractions are computed from the true ion molefractions
and ionic charge number. They can also be computed if you use the
apparent component approach. A more detailed discussion of this method is
found in Electrolyte Calculation.

You must provide parameters for the Sato-Riedel model. This model is used
for the calculation of the thermal conductivity of solvent mixtures.
Parameter
Symbol Default Lower Upper Units
Name/Element
Limit Limit
CHARGE z 0.0 — — —
IONRDL a 0.0 — — †
† THERMAL CONDUCTIVITY, MOLE-VOLUME
The behavior of this model can be changed using option codes (these codes
apply to the Vredeveld mixing rule).
Option Option Description
Code Value
1 0 Do not check ratio of KL max / KL min
3 Transport Property Models 273
1 Check ratio. If KL max / KL min > 2, set exponent to 1,
overriding option code 2.
2 0 Exponent is -2
1 Exponent is 0.4
2 Exponent is 1. This uses a weighted average of liquid thermal
conductivities.
General Pure Component Liquid Thermal
Conductivity
The Aspen Physical Property System has several submodels for calculating
pure component liquid thermal conductivity. It uses parameter TRNSWT/3 to
determine which submodel is used. See Pure Component Temperature-
Dependent Properties for details.
If TRNSWT/3 is This equation is used And this parameter is used
0 Sato-Riedel —
100 DIPPR KLDIP
301 PPDS KLPDS
401 IK-CAPE KLPO
503 NIST ThermoML
polynomial
KLTMLPO
510 NIST PPDS8 equation KLPPDS8
Sato-Riedel
The Sato-Riedel equation is (Reid et al., 1987):
Where:
Tbri = Tbi / Tci
Tri = T / Tci

Note: Reduced temperature Tr is always calculated using absolute
temperature units.
Parameter Symbol Default MDS Lower Upper Units
Name/Element
Limit Limit
MW M i — — 1.0 5000.0 —
TC T ci — — 5.0 2000.0 TEMPERATURE
TB T bi — — 4.0 2000.0 TEMPERATURE
PPDS
The equation is:
Linear extrapolation of � *,l versus T occurs outside of bounds.
Parameter
Name/Element
274 3 Transport Property Models
Symbol Default MDS Lower
Limit
Upper
Limit
Units
KLPDS/1 C 1i — — — — THERMAL-
CONDUCTIVITY
KLPDS/2 C 2i 0 — — — —
KLPDS/3 C 3i 0 — — — —
KLPDS/4 C 4i 0 — — — —
KLPDS/5 C 5i 0 — — — TEMPERATURE
KLPDS/6 C 6i 1000 — — — TEMPERATURE
NIST PPDS8 Equation
The equation is
Parameter
Name/Element
Symbol Default MDS Lower
Limit
Upper
Limit
Units
KLPPDS8/1 C 1i — — — — THERMAL-
CONDUCTIVITY
KLPPDS8/2, ..., 7 C 2i , ..., C 7i 0 — — — —
KLPPDS8/8 T Ci — — — — TEMPERATURE
KLPPDS8/9 nTerms 7 — — — —
KLPPDS8/10 T lower 0 — — — TEMPERATURE
KLPPDS8/11 T upper 1000 — — — TEMPERATURE
DIPPR Liquid Thermal Conductivity
The DIPPR equation is:

Linear extrapolation of � *,l versus T occurs outside of bounds.
(Other DIPPR equations may sometimes be used. See Pure Component
Temperature-Dependent Properties for details.)
The DIPPR equation is used by PCES when estimating liquid thermal
conductivity.
Parameter
Name/Element
3 Transport Property Models 275
Symbol Default MDS Lower
Limit
Upper
Limit
Units
KLDIP/1 C 1i — x — — THERMAL-
CONDUCTIVITY,
TEMPERATURE
KLDIP/2, ... , 5 C 2i , ..., C 5i 0 x — — THERMAL-
CONDUCTIVITY,
TEMPERATURE
KLDIP/6 C 6i 0 x — — TEMPERATURE
KLDIP/7 C 7i 1000 x — — TEMPERATURE
NIST ThermoML Polynomial
The equation is:
Linear extrapolation of � *,l versus T occurs outside of bounds.
Parameter
Name/Element
Symbol Default MDS Lower
Limit
Upper
Limit
Units
KLTMLPO/1 C 1i — x — — THERMAL-
CONDUCTIVITY,
TEMPERATURE
KLTMLPO/2, ... ,
4
C 2i , ..., C 4i 0 x — — THERMAL-
CONDUCTIVITY,
TEMPERATURE
KLTMLPO/5 nTerms 4 x — — —
KLTMLPO/6 T lower 0 x — — TEMPERATURE
KLTMLPO/7 T upper 1000 x — — TEMPERATURE
IK-CAPE
The IK-CAPE equation is:
Linear extrapolation of � *,l versus T occurs outside of bounds.
Parameter
Name/Element
Symbol Default MDS Lower
Limit
Upper
Limit
Units
KLPO/1 C 1i — x — — THERMAL-
CONDUCTIVITY

Parameter Symbol Default MDS Lower
Name/Element
Limit
276 3 Transport Property Models
Upper
Limit
Units
KLPO/2, ... , 10 C 2i , ..., C 10i 0 x — — THERMAL-
CONDUCTIVITY,
TEMPERATURE
KLPO/11 C 11i 0 x — — TEMPERATURE
KLPO/12 C 12i 1000 x — — TEMPERATURE
References
R.C. Reid, J.M. Prausnitz, and T.K. Sherwood, The Properties of Gases and
Liquids, 4th ed., (New York: McGraw-Hill, 1977), p. 533.
R.C. Reid, J.M. Prausnitz, and B.E. Poling, The Properties of Gases and
Liquids, 4th ed., (New York: McGraw-Hill, 1987), p. 550.
Solid Thermal Conductivity Polynomial
Thermal conductivity for solid pure components is calculated using the solid
thermal conductivity polynomial. For mixtures, the mole-fraction weighted
average is used.
For pure solids, thermal conductivity is calculated by:
For mixtures:
Linear extrapolation of �i *,s versus T occurs outside of bounds.
Parameter
Name/Element
Symbol Default MDS Lower
Limit
Upper
Limit
Units
KSPOLY/1 a — — — — THERMAL
CONDUCTIVITY
KSPOLY/2, 3, 4, 5 b, c, d, e 0 — — — THERMAL
CONDUCTIVITY,
TEMPERATURE
KSPOLY/6 0 x — — TEMPERATURE
KSPOLY/7 1000 x — — TEMPERATURE
General Pure Component Vapor Thermal
Conductivity
The Aspen Physical Property System has several submodels for calculating
pure component low pressure vapor thermal conductivity. It uses parameter
TRNSWT/4 to determine which submodel is used. See Pure Component
Temperature-Dependent Properties for details.

If TRNSWT/4 is This equation is used And this parameter is
used
0 Stiel-Thodos —
102 DIPPR KVDIP
301 PPDS KVPDS
401 IK-CAPE KVPO
503 NIST ThermoML
polynomial
Stiel-Thodos
The Stiel-Thodos equation is:
Where:
3 Transport Property Models 277
KVTMLPO
�i *,v (p = 0) can be obtained from the General Pure Component Vapor
Viscosity model.
Cpi *,ig is obtained from the General Pure Component Ideal Gas Heat Capacity
model.
R is the universal gas constant.
Parameter
Name/Element
Symbol Default MDS Lower
Limit
Upper
Limit
MW M i — — 1.0 5000.0 —
DIPPR Vapor Thermal Conductivity
The DIPPR equation for vapor thermal conductivity is:
Linear extrapolation of �i *,v versus T occurs outside of bounds.
Units
(Other DIPPR equations may sometimes be used. See Pure Component
Temperature-Dependent Properties for details.)
The DIPPR equation is used in PCES when estimating vapor thermal
conductivity.
Parameter
Name/Element
Symbol Default MDS Lower
Limit
Upper
Limit
Units
KVDIP/1 C 1i — x — — THERMAL
CONDUCTIVITY
KVDIP/2 C 2i 0 x — — —
KVDIP/3, 4 C 3i, C 4i 0 x — — TEMPERATURE †
KVDIP/5 — 0 x — — —
KVDIP/6 C 6i 0 x — — TEMPERATURE
KVDIP/7 C 7i 1000 x — — TEMPERATURE
† If any of C2i through C4i are non-zero, absolute temperature units are
assumed for C1i through C4i. Otherwise, all coefficients are interpreted in user

input temperature units. The temperature limits are always interpreted in
user input units.
PPDS
The equation is:
Linear extrapolation of �i *,v versus T occurs outside of bounds.
Parameter
Name/Element
278 3 Transport Property Models
Symbol Default MDS Lower
Limit
Upper
Limit
Units
KVPDS/1 C 1i — — — — THERMAL-
CONDUCTIVITY
KVPDS/2 C 2i 0 — — — THERMAL-
CONDUCTIVITY
KVPDS/3 C 3i 0 — — — THERMAL-
CONDUCTIVITY
KVPDS/4 C 4i 0 — — — THERMAL-
CONDUCTIVITY
KVPDS/5 C 5i 0 — — — TEMPERATURE
KVPDS/6 C 6i 1000 — — — TEMPERATURE
IK-CAPE Polynomial
Linear extrapolation of �i *,v versus T occurs outside of bounds.
Parameter
Name/Element
Symbol Default MDS Lower
Limit
Upper
Limit
Units
KVPO/1 C 1i — x — — THERMAL-
CONDUCTIVITY
KVPO/2, ... , 10 C 2i, ..., C 10i 0 x — — THERMAL-
CONDUCTIVITY,
TEMPERATURE
KVPO/11 C 11i 0 x — — TEMPERATURE
KVPO/12 C 12i 1000 x — — TEMPERATURE
NIST ThermoML Polynomial
Linear extrapolation of �i *,v versus T occurs outside of bounds.

Parameter
Name/Element
3 Transport Property Models 279
Symbol Default MDS Lower
Limit
Upper
Limit
Units
KVTMLPO/1 C 1i — x — — THERMAL-
CONDUCTIVITY,
TEMPERATURE
KVTMLPO/2, ... ,
4
C 2i, ..., C 4i 0 x — — THERMAL-
CONDUCTIVITY,
TEMPERATURE
KVTMLPO/5 nTerms 4 x — — —
KVTMLPO/6 T lower 0 x — — TEMPERATURE
KVTMLPO/7 T upper 1000 x — — TEMPERATURE
References
R.C. Reid, J.M. Praunitz, and B.E. Poling, The Properties of Gases and Liquid,
4th ed., (New York: McGraw-Hill, 1987), p. 494.
Stiel-Thodos Pressure Correction Model
The pressure correction to a pure component or mixture thermal conductivity
at low pressure is given by:
Where:
�rm
=
The parameter Vm v can be obtained from Redlich-Kwong.
� v (p = 0) can be obtained from the low pressure General Pure Component
Vapor Thermal Conductivity.
This model should not be used for polar substances, hydrogen, or helium.
Parameter Symbol Default MDS Lower Upper Units
Name/Element
Limit Limit
MW M i — — 1.0 5000.0 —
TC T ci — — 5.0 2000.0 TEMPERATURE
PC — — — 10 5
10 8
PRESSURE
VC V ci — — 0.001 3.5 MOLE-VOLUME
ZC Z ci — — 0.1 0.5 —
References
R.C. Reid, J.M. Praunitz, and B.E. Poling, The Properties of Gases and Liquids,
4th ed., (New York: McGraw-Hill, 1987), p. 521.
Vredeveld Mixing Rule
Liquid mixture thermal conductivity is calculated using the Vredeveld equation
(Reid et al., 1977):

Where:
wi = Liquid phase weight fraction of component i
�i *,l = Pure component liquid thermal conductivity of component i
Where n is determined from two option codes on model KL2VR:
If option code 1 is Then n is determined by
0 (default) Option code 2, always
1
If option code 2 is Then n is
0 (default) -2
1 0.4
280 3 Transport Property Models
Option code 2, unless . In this case n is
set to 1.
2 1 (This uses a weighted average of liquid thermal
conductivities.)
For most systems, the ratio of maximum to minimum pure component liquid
thermal conductivity is between 1 and 2, where the exponent -2 is
recommended, and is the default value used.
Pure component liquid thermal conductivity �i *,l is calculated by the General
Pure Component Liquid Thermal Conductivity model.
Reference: R.C. Reid, J.M. Prausnitz, and T.K. Sherwood, The Properties of
Gases and Liquids, 4th ed., (New York: McGraw-Hill, 1977), p. 533.
TRAPP Thermal Conductivity Model
The general form for the TRAPP thermal conductivity model is:
Where:
Cpi *,ig
= Mole fraction vector
= Ideal gas heat capacity calculated using the
General pure component ideal gas heat capacity
model
fcn = Corresponding states correlation based on the
model for vapor and liquid thermal conductivity
made by the National Bureau of standards (NBS,
currently NIST)
The model can be used for both pure components and mixtures. The model
should be used for nonpolar components only.

Parameter
Name/Element
3 Transport Property Models 281
Symbol Default MDS Lower
Limit
Upper
Limit
MW M i — — 1.0 5000.0 —
Units
TCTRAP T ci TC x 5.0 2000.0 TEMPERATURE
PCTRAP p ci PC x 10 5
10 8
PRESSURE
VCTRAP V ci VC x 0.001 3.5 MOLE-VOLUME
ZCTRAP Z ci ZC x 0.1 1.0 —
OMGRAP � i
References
OMEGA x -0.5 3.0 —
J.F. Ely and H.J. M. Hanley, "Prediction of Transport Properties. 2. Thermal
Conductivity of Pure Fluids and Mixtures," Ind. Eng. Chem. Fundam., Vol. 22,
(1983), pp. 90–97.
Wassiljewa-Mason-Saxena Mixing Rule
The vapor mixture thermal conductivity at low pressures is calculated from
the pure component values, using the Wassiljewa-Mason-Saxena equation:
Where:
�i *,v = Calculated by the General Pure Component Vapor
Thermal Conductivity model
�i *,v (p = 0) = Obtained from the General Pure Component Vapor
Viscosity model
You must supply parameters for �i *,v (p = 0) and �i *,v .
Parameter
Name/Element
Symbol Default MDS Lower
Limit
Upper
Limit
MW M i — — 1.0 5000.0 —
References
Units
R.C. Reid, J.M. Prausnitz, and B.E. Poling, The Properties of Gases and
Liquids, 4th ed., (New York: McGraw-Hill, 1987), pp. 530–531.
Diffusivity Models
The Aspen Physical Property System has seven built-in diffusivity models. This
section describes the diffusivity models available.

Model Type
Chapman-Enskog-Wilke-Lee (Binary) Low pressure vapor
Chapman-Enskog-Wilke-Lee (Mixture) Low pressure vapor
Dawson-Khoury-Kobayashi (Binary) Vapor
Dawson-Khoury-Kobayashi (Mixture) Vapor
Nernst-Hartley Electrolyte
Wilke-Chang (Binary) Liquid
Wilke-Chang (Mixture) Liquid
Chapman-Enskog-Wilke-Lee (Binary)
The binary diffusion coefficient at low pressures is calculated using
the Chapman-Enskog-Wilke-Lee model:
Dij v =Dji v
Where:
The collision integral for diffusion is:
�D
282 3 Transport Property Models
=
The binary size and energy parameters are defined as:
�ij
�ij
=
=
A parameter � is used to determine whether to use the Stockmayer or
Lennard-Jones potential parameters for �/k (energy parameter ) and �
(collision diameter). To calculate �, the dipole moment p, and either the
Stockmayer parameters or Tb and Vb are needed.
Parameter Symbol Default MDS Lower
Name/Element
Limit
Upper
Limit
MW M i — — 1.0 5000.0 —
Units
MUP p i — — 0.0 5x10 -24 DIPOLEMOMENT
TB T bi — — 4.0 2000.0 TEMPERATURE
VB V b — — 0.001 3.5 MOLE-VOLUME
OMEGA � i
— — -0.5 2.0 —
STKPAR/1 (� i/k) ST fcn(T bi, V bi, p i) x — — TEMPERATURE

Parameter Symbol Default MDS Lower
Name/Element
Limit
3 Transport Property Models 283
Upper
Limit
Units
STKPAR/2 � i ST fcn(T bi, V bi, p i) x — — LENGTH
LJPAR/1 (� i/k) LJ
LJPAR/2 � i LJ
References
fcn(T ci, � i) x — — TEMPERATURE
fcn(T ci, p ci, � i) x — — LENGTH
R.C. Reid, J.M. Praunitz, and B.E. Poling, The Properties of Gases and Liquids,
4th ed., (New York: McGraw-Hill, 1987), p. 587.
Chapman-Enskog-Wilke-Lee (Mixture)
The diffusion coefficient of a gas into a gas mixture at low pressures is
calculated using an equation of Bird, Stewart, and Lightfoot by default (option
code 0):
If the first option code is set to 1, Blanc's law is used instead:
The binary diffusion coefficient Dij v (p = 0) at low pressures is calculated using
the Chapman-Enskog-Wilke-Lee model. (See Chapman-Enskog-Wilke-Lee
(Binary).)
You must provide parameters for this model.
Parameter
Name/Element
Symbol Default MDS Lower
Limit
Upper
Limit
DVBLNC — 1 x — — —
Units
DVBLNC is set to 1 for a diffusing component and 0 for a non-diffusing
component.
References
R.C. Reid, J.M. Prausnitz, and B.E. Poling, The Properties of Gases and
Liquids, 4th ed., (New York: McGraw-Hill, 1987), p. 597.
Dawson-Khoury-Kobayashi (Binary)
The binary diffusion coefficient Dij v at high pressures is calculated from the
Dawson-Khoury-Kobayashi model:

Dij v =Dji v
Dij v (p = 0) is the low-pressure binary diffusion coefficient obtained from the
Chapman-Enskog-Wilke-Lee model.
The parameters �m v and Vm v are obtained from the Redlich-Kwong equationof-state
model.
You must supply parameters for these two models.
Subscript i denotes a diffusing component. j denotes a solvent.
Parameter Symbol Default MDS Lower Upper Units
Name/Element
Limit Limit
VC V ci — x 0.001 3.5 MOLE-VOLUME
References
R.C. Reid, J.M. Prausnitz, and T.K. Sherwood. The Properties of Gases and
Liquids, 3rd ed., (New York: McGraw-Hill, 1977), pp. 560-565.
Dawson-Khoury-Kobayashi (Mixture)
The diffusion coefficient of a gas into a gas mixture at high pressure is
calculated using an equation of Bird, Stewart, and Lightfoot by default (option
code 0):
If the first option code is set to 1, Blanc's law is used instead:
The binary diffusion coefficient Dij v at high pressures is calculated from the
Dawson-Khoury-Kobayashi model. (See Dawson-Khoury-Kobayashi (Binary).)
At low pressures (up to 1 atm) the binary diffusion coefficient is instead
calculated by the Chapman-Enskog-Wilke-Lee (Binary) model.
You must provide parameters for this model.
284 3 Transport Property Models

Parameter
Name/Element
3 Transport Property Models 285
Symbol Default MDS Lower
Limit
Upper
Limit
DVBLNC — 1 — — — —
Units
DVBLNC is set to 1 for a diffusing component and 0 for a nondiffusing
component.
References
R.C. Reid, J.M. Prausnitz, and B.E. Poling, The Properties of Gases and
Liquids, 4th ed., (New York: McGraw-Hill, 1987), p. 597.
Nernst-Hartley
The effective diffusivity of an ion i in a liquid mixture with electrolytes can be
calculated using the Nernst-Hartley model:
Where:
F = 9.65x10 7 C/kmole (Faraday's number)
xk = Mole fraction of any molecular species k
zi = Charge number of species i
The binary diffusion coefficient of the ion with respect to a molecular species
is set equal to the effective diffusivity of the ion in the liquid mixture:
The binary diffusion coefficient of an ion i with respect to an ion j is set to the
mean of the effective diffusivities of the two ions:
The diffusivity for molecular species is calculated by the Wilke-Chang
(Mixture) model.
Parameter
Name/Element
Symbol Default Lower
Limit
Upper
Limit
CHARGE z 0.0 — — —
(1)
(2)
Units
IONMOB/1 l 1 — † — — AREA, MOLES
IONMOB/2 l 2 0.0 — — AREA, MOLES,
TEMPERATURE
†When IONMOB/1 is missing, the Nernst-Hartley model uses a nominal value
of 5.0 and issues a warning. This parameter should be specified for ions, and
not allowed to default to this value.

References
A. L. Horvath, Handbook of Aqueous Electrolyte Solutions, (Chichester: Ellis
Horwood, Ltd, 1985).
Wilke-Chang (Binary)
The Wilke-Chang model calculates the liquid diffusion coefficient of
component i in a mixture at finite concentrations:
Dij l = Dji l
The equation for the Wilke-Chang model at infinite dilution is:
Where i is the diffusing solute and j the solvent, and:
�j = Association factor of solvent. 2.26 for water, 1.90
for methanol, 1.50 for ethanol, 1.20 for propyl
alchohols and n-butanol, and 1.00 for all other
solvents.
Vbi = Liquid molar volume at Tb of solvent i
�j l = Liquid viscosity of the solvent. This can be obtained
from the General Pure Component Liquid Viscosity
model. You must provide parameters for one of
these models.
� l = Liquid viscosity of the complete mixture of n
components
xi, xj = Apparent binary mole fractions. If the actual mole
Parameter
Name/Element
fractions are then
286 3 Transport Property Models
Symbol Default Lower
Limit
Upper
Limit
MW M j — 1.0 5000.0 —
VB V bi *,l
Units
— 0.001 3.5 MOLE-VOLUME

References
R.C. Reid, J.M. Prausnitz, and B.E. Poling, The Properties of Gases and
Liquids, 4th ed., (New York: McGraw-Hill, 1987), p. 598–600.
Wilke-Chang (Mixture)
The Wilke-Chang model calculates the infinite-dilution liquid diffusion
coefficient of component i in a mixture.
The equation for the Wilke-Chang model is:
With:
Where:
�j = Association factor of solvent. 2.26 for water, 1.90 for
methanol, 1.50 for ethanol, 1.20 for propyl alchohols
and n-butanol, and 1.00 for all other solvents.
n l
= Mixture liquid viscosity of all nondiffusing
components. This can be obtained from the General
Pure Component Liquid Viscosity model. You must
provide parameters for one its submodels.
The parameter DLWC specifies which components diffuse. It is set to 1 for a
diffusing component and 0 for a non-diffusing component.
Parameter
Symbol Default Lower Upper Units
Name/Element
Limit Limit
MW M j — 1.0 5000.0 —
VB V bi *,l
3 Transport Property Models 287
— 0.001 3.5 MOLE-VOLUME
DLWC — 1 — — —
References
R.C. Reid, J.M. Praunsnitz, and B.E. Poling, The Properties of Gases and
Liquids, 4th ed., (New York: McGraw-Hill, 1987), p. 618.
Surface Tension Models
The Aspen Physical Property System has the following built-in surface tension
models.This section describes the surface tension models available.
Model Type
Liquid Mixture Surface Tension Liquid-vapor

Model Type
API Liquid-vapor
IAPS Water-stream
General Pure Component Liquid Surface
Tension
288 3 Transport Property Models
Liquid-vapor
Onsager-Samaras Electrolyte Correction Electrolyte liquid-vapor
Modified MacLeod-Sugden Liquid-vapor
Liquid Mixture Surface Tension
The liquid mixture surface tension is calculated using a general weighted
average expression (R.C. Reid, J.M. Prausnitz, and B.E. Poling, The Properties
of Gases and Liquids, 4th. ed., New York: McGraw-Hill, 1987, p. 643):
Where:
x = Mole fraction
r = Exponent (specified by the option code)
Hadden (S. T. Hadden, Hydrocarbon Process Petrol Refiner, 45(10), 1966, p.
161) suggested that the exponent value r =1 should be used for most
hydrocarbon mixtures. However, Reid recommended the value of r in the
range of -1 to -3. The exponent value r can be specified using the model’s
Option Code (option code = 1, -1, -2, ..., -9 corresponding to the value of r).
The default value of r for this model is 1.
The pure component liquid surface tension �i *,l is calculated by the General
Pure Component Liquid Surface Tension model.
API Surface Tension
The liquid mixture surface tension for hydrocarbons is calculated using the
API model. This model is recommended for petroleum and petrochemical
applications. It is used in the CHAO-SEA, GRAYSON, LK-PLOCK, PENG-ROB,
and RK-SOAVE property models. The general form of the model is:
Where:
fcn = A correlation based on API Procedure 10A32 (API Technical Data
Book, Petroleum Refining, 4th edition)
The original form of this model is only designed for petroleum, and treats all
components as pseudocomponents (estimating surface tension from boiling
point, critical temperature, and specific gravity). If option code 1 is set to 0
(the default), it behaves this way. Set option code 1 to 1 for the model to use
the General Pure Component Liquid Surface Tension model to calculate the
surface tension of real components and the API model for pseudocomponents.

The mixture surface tension is then calculated as a mole-fraction-weighted
average of these surface tensions.
Parameter Symbol Default MDS Lower Upper Units
Name/Element
Limit Limit
TB T bi — — 4.0 2000.0 TEMPERATURE
SG SG — — 0.1 2.0 —
TC T ci — — 5.0 2000 TEMPERATURE
IAPS Surface Tension for Water
The IAPS surface tension model was developed by the International
Association for Properties of Steam. It calculates liquid surface tension for
water and steam. This model is used in option sets STEAMNBS and STEAM-
TA.
The general form of the equation for the IAPS surface tension model is:
�w=fcn(T, p)
Where:
fcn = Correlation developed by IAPS
The model is only applicable to water. No parameters are required.
General Pure Component Liquid Surface
Tension
The Aspen Physical Property System has several submodels for calculating
liquid surface tension. It uses parameter TRNSWT/5 to determine which
submodel is used. See Pure Component Temperature-Dependent Properties
for details.
If TRNSWT/5 is This equation is used And this parameter is
used
0 Hakim-Steinberg-Stiel —
106 DIPPR SIGDIP
301 PPDS SIGPDS
401 IK-CAPE polynomial
equation
505 NIST TDE Watson
equation
3 Transport Property Models 289
SIGPO
SIGTDEW
511 NIST TDE expansion SIGISTE
512 NIST PPDS14 Equation SIGPDS14
Hakim-Steinberg-Stiel
The Hakim-Steinberg-Stiel equation is:
Where:

Qpi =
mi
=
The parameter �i is the Stiel polar factor.
Parameter
Name/Element
290 3 Transport Property Models
Symbol Default Lower
Limit
Upper
Limit
Units
TC T ci — 5.0 2000.0 TEMPERATURE
PC p ci — PRESSURE
OMEGA � i
CHI � i
DIPPR Liquid Surface Tension
— -0.5 2.0 —
0 — — —
The DIPPR equation for liquid surface tension is:
Where:
Tri = T / Tci
Linear extrapolation of �i *,l versus T occurs outside of bounds.
(Other DIPPR equations may sometimes be used. See Pure Component
Temperature-Dependent Properties for details.)
The DIPPR model is used by PCES when estimating liquid surface tension.
Note: Reduced temperature Tr is always calculated using absolute
temperature units.
Parameter Symbol Default Lower Upper Units
Name/Element
Limit Limit
SIGDIP/1 C 1i — — — SURFACE-
TENSION
SIGDIP/2, ..., 5 C 2i, ..., C 5i 0 — — —
SIGDIP/6 C 6i 0 — — TEMPERATURE
SIGDIP/7 C 7i 1000 — — TEMPERATURE
PPDS
The equation is:
Linear extrapolation of �i *,l versus T occurs outside of bounds.
Parameter
Name/Element
Symbol Default MDS Lower
Limit
Upper
Limit
Units
SIGPDS/1 C 1i — — — — SURFACE-
TENSION

Parameter
Name/Element
3 Transport Property Models 291
Symbol Default MDS Lower
Limit
Upper
Limit
SIGPDS/2 C 2i 0 — — — —
SIGPDS/3 C 3i 0 — — — —
Units
SIGPDS/4 C 4i 0 — — — TEMPERATURE
SIGPDS/5 C 5i 1000 — — — TEMPERATURE
NIST PPDS14 Equation
This equation is the same as the PPDS equation above, but it uses its own
parameter set which includes critical temperature.
Parameter Symbol Default MDS Lower Upper Units
Name/Element
Limit Limit
SIGPDS14/1 C 1i — x — — N/m
SIGPDS14/2 C 2i 0 x — — —
SIGPDS14/3 C 3i 0 x — — —
SIGPDS14/4 T ci — x — — TEMPERATURE
SIGPDS14/5 C 4i 0 x — — TEMPERATURE
SIGPDS14/6 C 5i 1000 x — — TEMPERATURE
IK-CAPE Polynomial
The IK-CAPE equation is:
Linear extrapolation of �i *,l versus T occurs outside of bounds.
Parameter
Name/Element
Symbol Default MDS Lower
Limit
Upper
Limit
Units
SIGPO/1 C 1i — x — — SURFACE-
TENSION
SIGPO/2, ..., 10 C 2i, ..., C 10i 0 x — — SURFACE-
TENSION
TEMPERATURE
SIGPO/11 C 11i 0 x — — TEMPERATURE
SIGPO/12 C 12i 1000 x — — TEMPERATURE
NIST TDE Watson Equation
This equation can be used when parameter SIGTDEW is available.
Parameter
Name/Element
Symbol Default MDS Lower
Limit
Upper
Limit
SIGTDEW/1 C 1i — x — — —
Units

Parameter
Name/Element
292 3 Transport Property Models
Symbol Default MDS Lower
Limit
Upper
Limit
SIGTDEW/2, 3, 4 C 2i, C 3i, C 4i 0 x — — —
Units
SIGTDEW/5 T c — x — — TEMPERATURE
SIGTDEW/6 nTerms 4 x — — —
SIGTDEW/7 T lower 0 x — — TEMPERATURE
SIGTDEW/8 T upper 1000 x — — TEMPERATURE
NIST TDE Expansion
This equation can be used when parameter SIGISTE is available.
Parameter
Name/Element
Symbol Default MDS Lower
Limit
Upper
Limit
Units
SIGISTE/1 C 1i — x — — N/m
SIGISTE/2, 3, 4 C 2i, C 3i, C 4i 0 x — — N/m
SIGISTE/5 T ci — x — — TEMPERATURE
SIGISTE/6 nTerms 4 x — — —
SIGISTE/7 T lower 0 x — — TEMPERATURE
SIGISTE/8 T upper 1000 x — — TEMPERATURE
References
R.C. Reid, J.M. Prausnitz, and B.E. Poling, The Properties of Gases and
Liquids, 4th. ed., (New York: McGraw-Hill, 1987), p. 638.
Onsager-Samaras
The Onsager-Samaras model calculates the correction to the liquid mixture
surface tension of a solvent mixture, due to the presence of electrolytes:
Where:
for salt concentration < 0.03
M
�solv = Surface tension of the solvent mixture calculated
by the General Pure Component Liquid Surface
Tension model
xca a
= Mole fraction of the apparent electrolyte ca
��ca = Contribution to the surface tension correction due
to apparent electrolyte ca
For each apparent electrolyte ca, the contribution to the surface tension
correction is calculated as:
(1)

Where:
�solv = Dielectric constant of the solvent mixture
cca a
Vm l
3 Transport Property Models 293
=
= Liquid molar volume calculated by the Clarke
model
Apparent electrolyte mole fractions are computed from the true ion molefractions
and ionic charge number. They are also computed if you use the
apparent component approach. See Apparent Component and True
Component Approaches in the Electrolyte Calculation chapter for a more
detailed discussion of this method.
Above salt concentration 0.03 M, the slope of surface tension vs. mole
fraction is taken to be constant at the value from 0.03 M.
You must provide parameters for the General Pure Component Liquid Surface
Tension model, used for the calculation of the surface tension of the solvent
mixture.
Parameter
Name/Element
Symbol Default Lower
Limit
Upper
Limit
CHARGE z 0.0 — — —
References
(2)
Units
A. L. Horvath, Handbook of Aqueous Electrolyte Solutions, (Chichester: Ellis,
Ltd. 1985).
Modified MacLeod-Sugden
The modified MacLeod-Sugden equation for mixture liquid surface tension can
be derived from the standard MacLeod-Sugden equation by assuming that the
density of the vapor phase is zero. The modified MacLeod-Sugden equation is:
Where:
�i *,l = Surface tension for pure component i, calculated using
the General Pure Component Liquid Surface Tension
model.
Vi *,l = Liquid molar volume for pure component i, calculated
using the General Pure Component Liquid Molar Volume
model.

V l = Mixture liquid molar volume, calculated using the
Rackett model.
References
R.C. Reid, J.M. Prausnitz, and B.E. Poling, The Properties of Gases and
Liquids, 3rd. ed., (New York: McGraw-Hill, 1977).
294 3 Transport Property Models

4 Nonconventional Solid
Property Models
This section describes the nonconventional solid density and enthalpy models
available in the Aspen Physical Property System. The following table lists the
available models and their model names. Nonconventional components are
solid components that cannot be characterized by a molecular formula. These
components are treated as pure components, though they are complex
mixtures.
Nonconventional Solid Property Models
General Enthalpy and
Density Models
4 Nonconventional Solid Property Models 295
Model name Phase(s)
General density polynomial DNSTYGEN S
General heat capacity
polynomial
Enthalpy and Density
Models for Coal and Char
ENTHGEN S
Model name Phase(s)
General coal enthalpy model HCOALGEN S
IGT coal density model DCOALIGT S
IGT char density model DCHARIGT S
General Enthalpy and Density
Models
The Aspen Physical Property System has two built-in general enthalpy and
density models. This section describes the general enthalpy and density
models available:
General Density Polynomial
DNSTYGEN is a general model that gives the density of any nonconventional
solid component. It uses a simple mass fraction weighted average for the
reciprocal temperature-dependent specific densities of its individual

constituents. There may be up to twenty constituents with mass percentages.
You must define these constituents, using the general component attribute
GENANAL. The equations are:
Where:
wij = Mass fraction of the jth constituent in component i
�ij s = Density of the jth consituent in component i
Parameter
Name/Element
296 4 Nonconventional Solid Property Models
Symbol MDS Default Lower
Limit
Upper
Limit
Units
DENGEN/1, 5, 9, …, 77 a i,j1 x — — — MASS-ENTHALPY
and TEMPERATURE
DENGEN/2, 6, 10, …,
78
DENGEN/3, 7, 11, …,
79
DENGEN/4, 8, 12, …,
80
a i,j2 x 0 — — MASS-ENTHALPY
and TEMPERATURE
a i,j3 x 0 — — MASS-ENTHALPY
and TEMPERATURE
a i,j4 x 0 — — MASS-ENTHALPY
and TEMPERATURE
Use the elements of GENANAL to input the mass percentages of the
constituents. The structure of DENGEN is: Elements 1 to 4 are the four
coefficients for the first constituent, elements 5 to 8 are the coefficients for
the second constitutent, and so on, for up to 20 constituents.
General Heat Capacity Polynomial
ENTHGEN is a general model that gives the specific enthalpy of any
nonconventional component as a simple mass-fraction-weighted-average for
the enthalpies of its individual constituents. You may define up to twenty
constituents with mass percentages, using the general component attribute
GENANAL. The specific enthalpy of each constituent at any temperature is
calculated by combining specific enthalpy of formation of the solid with a
sensible heat change. (See Nonconventional Component Enthalpy Calculation
in Physical Property Methods.)
The equations are:
Where:

wij = Mass fraction of the jth constituent in
component i
hi s
4 Nonconventional Solid Property Models 297
= Specific enthalpy of solid component i
�fhj s = Specific enthalpy of formation of constituent j
Cp s
Parameter
Name/Element
= Heat capacity of the jth constituent in
component i
Symbol MDS Default Lower
Limit
Upper
Limit
Units
DHFGEN/J � fh j s x 0 — — MASS-ENTHALPY
HCGEN/1, 5, 9, …, 77 a i,j1 x — — — MASS-ENTHALPY
and
TEMPERATURE
HCGEN/2, 6, 10, …, 78 a i,j2 x 0 — — MASS-ENTHALPY
and
TEMPERATURE
HCGEN/3, 7, 11, …, 79 a i,j3 x 0 — — MASS-ENTHALPY
and
TEMPERATURE
HCGEN/4, 8, 12, …, 80 a i,j4 x 0 — — MASS-ENTHALPY
and
TEMPERATURE
The elements of GENANAL are used to input the mass percentages of the
constituents. The structure for HCGEN is: Elements 1 to 4 are the four
coefficients for the first constituent, elements 5 to 8 are the coefficients for
the second constitutent, and so on, for up to 20 constituents.
Enthalpy and Density Models
for Coal and Char
Coal is modeled in the Aspen Physical Property System as a nonconventional
solid. Coal models are empirical correlations, which require solid material
characterization information. Component attributes are derived from
constituent analyses. Definitions of coal component attributes are given in the
Aspen Plus User Guide, Chapter 6.
Enthalpy and density are the only properties calculated for nonconventional
solids. This section describes the special models available in the Aspen
Physical Property System for the enthalpy and density of coal and char. The
component attributes required by each model are included. The coal models
are:
� General coal enthalpy
� IGT Coal Density
� IGT Char Density

� User models for density and enthalpy. See User Models for
Nonconventional Properties in Chapter 6 of Aspen Plus User Models, for
details on writing the subroutines for these user models.
Notation
Most correlations for the calculation of coal properties require proximate,
ultimate, and other analyses. These are converted to a dry, mineral-matterfree
basis. Only the organic portion of the coal is considered.
Moisture corrections are made for all analyses except hydrogen, according to
the formula:
Where:
w = The value determined for weight fraction
w d
= The value on a dry basis
= The moisture weight fraction
For hydrogen, the formula includes a correction for free-moisture hydrogen:
The mineral matter content is calculated using the modified Parr formula:
The ash term corrects for water lost by decomposition of clays in the ash
determination. The average water constitution of clays is assumed to be 11.2
percent. The sulfur term allows for loss in weight of pyritic sulfur when pyrite
is burned to ferric oxide. The original Parr formula assumed that all sulfur is
pyritic sulfur. This formula included sulfatic and organic sulfur in the mineralmatter
calculation. When information regarding the forms of sulfur is
available, use the modified Parr formula to give a better approximation of the
percent of inorganic material present. Because chlorine is usually small for
United States coals, you can omit chlorine from the calculation.
Correct analyses from a dry basis to a dry, mineral-matter-free basis, using
the formula:
Where:
�w d = Correction factor for other losses, such as the loss
of carbon in carbonates and the loss of hydrogen
present in the water constitution of clays
298 4 Nonconventional Solid Property Models

The oxygen and organic sulfur contents are usually calculated by difference
as:
Where:
Cp = Heat capacity / (J/kgK)
cp = Heat capacity / (cal/gC)
h = Specific enthalpy
�ch = Specific heat of combustion
�fh = Specific heat of formation
Ro = Mean-maximum relectance in oil
T = Temperature/K
t = Temperature/C
w = Weight fraction
� = Specific density
Subscripts:
A = Ash
C = Carbon
Cl = Chlorine
FC = Fixed carbon
H = Hydrogen
H2O = Moisture
MM = Mineral matter
N = Nitrogen
O = Oxygen
So = Organic sulfur
Sp = Pyritic sulfur
St = Total sulfur
S = Other sulfur
VM = Volatile matter
Superscripts:
d = Dry basis
4 Nonconventional Solid Property Models 299

m = Mineral-matter-free basis
General Coal Enthalpy Model
The general coal model for computing enthalpy in the Aspen Physical Property
System is HCOALGEN. This model includes a number of different correlations
for the following:
� Heat of combustion
� Heat of formation
� Heat capacity
You can select one of these correlations using an option code in the Properties
Advanced NC-Props form. (See the Aspen Plus User Guide, Chapter 6). Use
option codes to specify a calculation method for properties. Each element in
the option code vector is used in the calculation of a different property.
The table labeled HCOALGEN Option Codes (below) lists model option codes
for HCOALGEN. The table is followed by a detailed description of the
calculations used for each correlation.
The correlations are described in the following section. The component
attributes are defined in Aspen Plus User Guide, Chapter 6.
Heat of Combustion Correlations
The heat of combustion of coal in the HCOALGEN model is a gross calorific
value. It is expressed in Btu/lb of coal on a dry mineral-matter-free basis.
ASTM Standard D5865-07a defines standard conditions for measuring gross
calorific value. (Earlier ASTM Standard D-2015 used the same conditions.)
Initial oxygen pressure is 20 to 40 atmospheres. Products are in the form of
ash; liquid water; and gaseous CO2, SO2, and NO2.
You can calculate net calorific value from gross calorific value by making a
deduction for the latent heat of vaporization of water.
Heat of combustion values are converted back to a dry, mineral-mattercontaining
basis with a correction for the heat of combustion of pyrite. The
formula is:
The heat of combustion correlations were evaluated by the Institute of Gas
Technology (IGT). They used data for 121 samples of coal from the Penn
State Data Base (IGT, 1976) and 457 samples from a USGS report (Swanson,
et al., 1976). These samples included a wide range of United States coal
fields. The constant terms in the HCOALGEN correlations are bias corrections
obtained from the IGT study.
Boie Correlation:
Parameter Name/Element Symbol Default
BOIEC/1 a 1i 151.2
BOIEC/2 a 2i 499.77
300 4 Nonconventional Solid Property Models

Parameter Name/Element Symbol Default
BOIEC/3 a 3i 45.0
BOIEC/4 a 4i -47.7
BOIEC/5 a 5i 27.0
BOIEC/6 a 6i -189.0
Dulong Correlation:
Parameter Name/Element Symbol Default
DLNGC/1 a 1i 145.44
DLNGC/2 a 2i 620.28
DLNGC/3 a 3i 40.5
DLNGC/4 a 4i -77.54
DLNGC/5 a 5i -16.0
Grummel and Davis Correlation:
Parameter Name/Element Symbol Default
GMLDC/1 a 1i 0.3333
GMLDC/2 a 2i 654.3
GMLDC/3 a 3i 0.125
GMLDC/4 a 4i 0.125
GMLDC/5 a 5i 424.62
GMLDC/6 a 6i -2.0
Mott and Spooner Correlation:
Parameter Name/Element Symbol Default
MTSPC/1 a 1i 144.54
MTSPC/2 a 2i 610.2
MTSPC/3 a 3i 40.3
MTSPC/4 a 4i 62.45
MTSPC/5 a 5i 30.96
MTSPC/6 a 6i 65.88
MTSPC/7 a 7i -47.0
IGT Correlation:
4 Nonconventional Solid Property Models 301

Parameter Name/Element Symbol Default
CIGTC/1 a 1i 178.11
CIGTC/2 a 2i 620.31
CIGTC/3 a 3i 80.93
CIGTC/4 a 4i 44.95
CIGTC/5 a 5i -5153.0
Revised IGT Correlation (Perry's, 7th ed., equation 27-7):
Parameter Name/Element Symbol Default
CIGT2/1 a 1i 146.58
CIGT2/2 a 2i 568.78
CIGT2/3 a 3i 29.4
CIGT2/4 a 4i -6.58
CIGT2/5 a 5i -51.53
User Input Value of Heat Combustion
Parameter Name/Element Symbol Default
HCOMB � ch i d 0
Standard Heat of Formation Correlations
There are two standard heat of formation correlations for the HCOALGEN
model:
� Heat of combustion-based
� Direct
Heat of Combustion-Based Correlation: This is based on the assumption that
combustion results in complete oxidation of all elements except sulfatic sulfur
and ash, which are considered inert. The numerical coefficients are
combinations of stoichiometric coefficients and heat of formation for CO2,
H2O, HCl, and NO2 at 298.15K:
For example, the complete oxidation of hydrogen is based on the reaction
, since the stable phase of water at 298.15 K is
liquid, the heat of vaporization at 298.15 K is needed in the conversion. The
numerical coefficient of is calculated by:
302 4 Nonconventional Solid Property Models

The complete oxidation of carbon is based on the reaction
4 Nonconventional Solid Property Models 303
, and the numerical coefficient of is calculated by:
The complete oxidation of sulfur (pyritic and organic sulfur) is based on the
reaction , and the numerical coefficient of is
calculated by:
The complete oxidation of nitrogen is based on the reaction
, and the numerical coefficient of is calculated by:
The complete oxidation of chlorine is based on the reaction
is calculated by:
, and the numerical coefficient of
Direct Correlation: Normally small, relative to its heat of combustion. An error
of 1% in the heat of a combustion-based correlation produces about a 50%
error when it is used to calculate the heat of formation. For this reason, the
following direct correlation was developed, using data from the Penn State
Data Base. It has a standard deviation of 112.5 Btu/lb, which is close to the
limit, due to measurement in the heat of combustion:
Where:
Parameter Name/Element Symbol Default
HFC/1 a 1i 1810.123
HFC/2 a 2i -502.222
HFC/3 a 3i 329.1087
HFC/4 a 4i 121.766
HFC/5 a 5i -542.393
HFC/6 a 6i 1601.573

Parameter Name/Element Symbol Default
HFC/7 a 7i 424.25
HFC/8 a 8i -525.199
HFC/9 a 9i -11.4805
HFC/10 a 10i 31.585
HFC/11 a 11i 13.5256
HFC/12 a 12i 11.5
HFC/13 a 13i -685.846
HFC/14 a 14i -22.494
HFC/15 a 15i -64836.19
Heat Capacity Kirov Correlations
The Kirov correlation (1965) considered coal to be a mixture of moisture, ash,
fixed carbon, and primary and secondary volatile matter. Secondary volatile
matter is any volatile matter up to 10% on a dry, ash-free basis; the
remaining volatile matter is primary. The correlation developed by Kirov
treats the heat capacity as a weighted sum of the heat capacities of the
constituents:
Where:
i = Component index
j = Constituent index j = 1, 2 , ... , ncn
304 4 Nonconventional Solid Property Models
Where the values of j represent:
1 Moisture
2 Fixed carbon
3 Primary volatile matter
4 Secondary volatile matter
5 Ash
wj = Mass fraction of jth constituent on dry basis
This correlation calculates heat capacity in cal/gram-C using temperature in
C. The parameters must be specified in appropriate units for this conversion.
Parameter Name/Element Symbol Default
CP1C/1 a i,11 1.0
CP1C/2 a i,12 0
CP1C/3 a i,13 0
CP1C/4 a i,14 0
CP1C/5 a i,21 0.165
CP1C/6 a i,22

Parameter Name/Element Symbol Default
CP1C/7 a i,23
CP1C/8 a i,24 0
CP1C/9 a i,31 0.395
CP1C/10 a i,32
CP1C/11 a i,33 0
CP1C/12 a i,34 0
CP1C/13 a i,41 0.71
CP1C/14 a i,42
CP1C/15 a i,43 0
CP1C/16 a i,44 0
CP1C/17 a i,51 0.18
CP1C/18 a i,52
CP1C/19 a i,53 0
CP1C/20 a i,54 0
Cubic Temperature Equation
The cubic temperature equation is:
Parameter Name/Element Symbol Default
CP2C/1 a 1i 0.438
CP2C/2 a 2i
CP2C/3 a 3i
CP2C/4 a 4i
The default values of the parameters were developed by Gomez, Gayle, and
Taylor (1965). They used selected data from three lignites and a
subbituminous B coal, over a temperature range from 32.7 to 176.8�C.
HCOALGEN Option Codes
Option Code Option Code
Number Value †
1 Heat of Combustion
4 Nonconventional Solid Property Models 305
Calculation
Method
Parameter
Names
Component
Attributes
1 Boie correlation BOIEC ULTANAL
SULFANAL
PROXANAL
2 Dulong
correlation
3 Grummel and
Davis correlation
DLNGC ULTANAL
SULFANAL
PROXANAL
GMLDC ULTANAL
SULFANAL
PROXANAL
4 Mott and Spooner
correlation
MTSPC ULTANAL
SULFANAL
PROXANAL

Option Code Option Code
Number Value †
1 Heat of Combustion
306 4 Nonconventional Solid Property Models
Calculation
Method
Parameter
Names
Component
Attributes
5 IGT correlation CIGTC ULTANAL
PROXANAL
6 User input value HCOMB ULTANAL
PROXANAL
7 Revised IGT
correlation
2 Standard Heat of Formation
CIGT2 ULTANAL
PROXANAL
1 Heat-of- — ULTANAL
combustionbased
correlation
SULFANAL
2 Direct correlation HFC ULTANAL
SULFANAL
PROXANAL
3 Heat Capacity
1 Kirov correlation CP1C PROXANAL
2 Cubic
temperature
equation
4 Enthalpy Basis
1 Elements in their —
standard states
at 298.15K and 1
atm
—
2 Component at
298.15 K
† Default = 1 for each option code
References
CP2C —
—
—
— —
Gomez, M., J.B. Gayle, and A.R. Taylor, Jr., Heat Content and Specific Heat of
Coals and Related Products, U.S. Bureau of Mines, R.I. 6607, 1965.
IGT (Institute of Gas Technology), Coal Conversion Systems Technical Data
Book, Section PMa. 44.1, 1976.
Kirov, N.Y., "Specific Heats and Total Heat Contents of Coals and Related
Materials are Elevated Temperatures," BCURA Monthly Bulletin, (1965),
pp. 29, 33.
Swanson, V.E. et al., Collection, Chemical Analysis and Evaluation of Coal
Samples in 1975, U.S. Geological Survey, Open-File Report (1976), pp. 76–
468.
R. H. Perry and D. W. Green, eds., Perry's Chemical Engineers' Handbook, 7th
ed., McGraw-Hill (1997), p. 27-5.
IGT Coal Density Model
The DCOALIGT model gives the true (skeletal or solid-phase) density of coal
on a dry basis. It uses ultimate and sulfur analyses. The model is based on
equations from IGT (1976):

The equation for �i dm is good for a wide range of hydrogen contents, including
anthracities and high temperature cokes. The standard deviation of this
correlation for a set of 190 points collected by IGT from the literature was
12x10 -6 m 3 /kg. The points are essentially uniform over the whole range. This
is equivalent to a standard deviation of about 1.6% for a coal having a
hydrogen content of 5%. It increases to about 2.2% for a coke or anthracite
having a hydrogen content of 1%.
Parameter Name/Element Symbol Default
DENIGT/1 a 1i 0.4397
DENIGT/2 a 2i 0.1223
DENIGT/3 a 3i -0.01715
DENIGT/4 a 4i 0.001077
Reference
IGT (Institute of Gas Technology), Coal Conversion Systems Technical Data
Book, Section PMa. 44.1, 1976.
IGT Char Density Model
The DGHARIGT model gives the true (skeletal or solid-phase) density of char
or coke on a dry basis. It uses ultimate and sulfur analyses. This model is
based on equations from IGT (1976):
Parameter Name/Element Symbol Default
DENIGT/1 a 1i 0.4397
DENIGT/2 a 2i 0.1223
DENIGT/3 a 3i -0.01715
DENIGT/4 a 4i 0.001077
4 Nonconventional Solid Property Models 307

The densities of graphitic high-temperature carbons (including cokes) range
from 2.2x10 3 to 2.26x10 3 kg/m 3 . Densities of nongraphitic high-temperature
carbons (derived from chars) range from 2.0x10 3 to 2.2x10 3 kg/m 3 . Most of
the data used in developing this correlation were for carbonized coking coals.
Although data on a few chars (carbonized non-coking coals) were included,
none has a hydrogen content less than 2%. The correlation is probably not
accurate for high temperature chars.
References
I.M. Chang, B.S. Thesis, Massachusetts Institute of Technology, 1979.
M. Gomez, J.B. Gayle, and A.R. Taylor, Jr., Heat Content and Specific Heat of
Coals and Related Products, U.S. Bureau of Mines, R.I. 6607, 1965.
IGT (Institute of Gas Technology), Coal Conversion Systems Technical Data
Book, Section PMa. 44.1, 1976.
N.Y. Kirov, "Specific Heats and Total Heat Contents of Coals and Related
Materials are Elevated Temperatures," BCURA Monthly Bulletin, (1965),
pp. 29, 33.
V.E. Swanson et al., Collection, Chemical Analysis and Evaluation of Coal
Samples in 1975, U.S. Geological Survey, Open-File Report (1976), pp. 76–
468.
308 4 Nonconventional Solid Property Models

5 Property Model Option
Codes
The following tables list the model option codes available:
� Option Codes for Transport Property Models
� Option Codes for Activity Coefficient Models
� Option Codes for Equation of State Models
� Option Codes for K-value Models
� Option Codes for Enthalpy Models
� Option Codes for Gibbs Energy Models
� Option Codes for Molar Volume Models
Option Codes for Transport
Property Models
Model Name Option
Code
5 Property Model Option Codes 309
Value Descriptions
SIG2HSS 1 1 Exponent in mixing rule (default)
-1,-2,
..., -9
Exponent in mixing rule
SIG2ONSG 1 1 Exponent in mixing rule (default)
-1,-2,
..., -9
Exponent in mixing rule
SIG2API 1 0 Use original API model for all components
MUL2API,
MULAPI92
1 Use API model for pseudocomponents, General
Pure Component Liquid Surface Tension for real
components, and take a mole-fraction-weighted
average of the results.
1 0 Release 9 method. First, the API, SG of the
mixture is calculated, then the API correlation is
used (default)

Model Name Option
Code
MUL2ANDR,
DL0WCA, DL1WCA,
DL0NST, DL1NST
310 5 Property Model Option Codes
Value Descriptions
1 Pre-release 9 method. Liquid viscosity is
calculated for each pseudocomponent using the
API method. Then mixture viscosity is
calculated by mixing rules.
1 0 Mixture viscosity weighted by mole fraction
(default)
1 Mixture viscosity weighted by mass fraction
MUL2JONS 1 0 Mixture viscosity weighted by mole fraction
(default)
MUL2CLS,
MUL2CLS2
1 Mixture viscosity weighted by mass fraction
2 0 Use Breslau and Miller equation instead of Jones
and Dole equation when electrolyte
concentration exceeds 0.1 M.
1 Always use Jones and Dole equation when the
parameters are available.
3 0 Solvent liquid mixture viscosity from Andrade
liquid mixture viscosity model (default)
1 Solvent liquid mixture viscosity from quadratic
mixing rule
2 Solvent liquid mixture viscosity from Aspen
liquid mixture viscosity model
1 0 Original correlation
1 Modified UOP correlation
MUL2QUAD 1 0 Use mole basis composition (default)
1 Use mass basis composition
KL2VR, KL2RDL 1 0 Do not check ratio of KL max / KL min
1 Check ratio. If KL max / KL min > 2, set
exponent to 1, overriding option code 2.
2 0 Exponent is -2
1 Exponent is 0.4
2 Exponent is 1. This uses a weighted average of
liquid thermal conductivities.
Option Codes for Activity
Coefficient Models
Model Name Option
Code
Value Descriptions
GMXSH 1 0 No volume term (default)
1 Includes volume term
WHENRY 1 1 Equal weighting

Model Name Option
Code
5 Property Model Option Codes 311
Value Descriptions
2 Size - VC 1/3
3 Area - VC 2/3 (default)
4 Volume - VC
Electrolyte NRTL Activity Coefficient Model (GMELC and GMENRHG)
GMPT1, GMPT3 (Pitzer)
1 Defaults for pair parameters
1 Pair parameters default to zero
2 Solvent/solute pair parameters default to water
parameters. Water/solute pair parameters default
to zero (default for GMELC)
3 Default water parameters to 8, -4. Default
solvent/solute parameters to 10, -2 (default for
GMENRHG)
2 Not used
3 Solvent/solvent binary parameter values obtained
from
0 Scalar GMELCA, GMELCB and GMELCM (default
for GMELC)
1 Vector NRTL(8) (default for GMENRHG)
1 Defaults for pair mixing rule
-1 No unsymmetric mixing
0 Unsymmetric mixing polynomial (default)
1 Unsymmetric mixing integral
Symmetric and Unsymmetric Electrolyte NRTL Activity Coefficient Model (GMENRTLS and
GMENRTLQ)
COSMOSAC
Hansen
1 PDH long-range term
0 Long-range term calculated (default)
1 Long-range term ignored
1 Model choice
1 COSMO-SAC model by Lin and Sandler (2002)
(Default)
2 COSMO-RS model by Klamt and Eckert (2000)
3 Lin and Sandler model with modified exchange
energy (Lin et al., 2002)
1 0 Hansen volume input by user (default)
1 Hansen volume calculated by Aspen Plus
NRTLSAC (patent pending) for Segments/Oligomers, ENRTLSAC (patent pending)
NRTL-SAC (GMNRTLS)
1 0 Flory-Huggins term included (default)
1 Flory-Huggins term removed
1 0 Reference state for ions is unsymmetric: infinite
dilution in aqueous solution (default)

Model Name Option
Code
312 5 Property Model Option Codes
Value Descriptions
2 Reference state for ions is symmetric: pure fused
salts
2 0 Flory-Huggins term included (default)
1 Flory-Huggins term removed
3 0 Long-range interaction term included (default)
1 Long-range interaction term removed
Option Codes for Equation of
State Models
Model Name Option
Code
Value Descriptions
ESBWRS, ESBWRS0 1 0 Do not use steam tables
ESHOC, ESHOC0,
PHV0HOC
ESPR, ESPR0,
ESPRSTD,
ESPRSTD0
1 Calculate properties (H, S, G, V) of water from
steam table (default; see Note)
2 0 Original RT-Opt root search method (default)
1 VPROOT/LQROOT Aspen Plus root search
method. Use this if the equation-oriented Aspen
Plus solution fails to converge and some
streams with missing phases show the same
properties for the missing phase as for another
phase.
1 0 Hayden-O'Connell model. Use chemical theory
only if one component has HOCETA=4.5
(default)
1 Always use the chemical theory regardless of
HOCETA values
2 Never use the chemical theory regardless of
HOCETA values
2 0 Check high-pressure limit. If exceeded,
calculate volume at cut-off pressure.
1 Ignore high-pressure limit. Calculate volume
model T and P.
1 0 ASPEN Boston/Mathias alpha function when T r
>1, original literature alpha function otherwise.
(default for ESPR)
1 Original literature alpha function (default for
ESPRSTD)
2 Extended Gibbons-Laughton alpha function
3 Twu Generalized alpha function
4 Twu alpha function
2 0 Standard Peng-Robinson mixing rules (default)
1 Asymmetric Kij mixing rule from Dow
3 0 Do not use steam tables (default)

Model Name Option
Code
5 Property Model Option Codes 313
Value Descriptions
1 Calculate water properties (H, S, G, V) from
steam table (see Note)
4 0 Do not use Peneloux liquid volume correction
(default)
1 Apply Peneloux liquid volume correction (See
SRK)
5 0 Use analytical method for root finding (default)
1 Use RTO numerical method for root finding
2 Use VPROOT/LQROOT numerical method for
root finding
ESPRWS,
ESPRWS0, ESPRV1,
ESPRV10, ESPRV2,
ESPRV20,
1 0 ASPEN Boston/Mathias alpha function
ESPSAFT,
ESPSAFT0
ESRKS, ESRKS0,
ESRKSTD,
ESRKSTD0, ESSRK,
ESSRK0, ESRKSML,
ESRKSML0
1 0 Random copolymer (default)
1 Alternative copolymer
2 Block copolymer
2 0 Do not use Sadowski's copolymer model
1 Use Sadowski's copolymer model in which a
copolymer must be built only by two different
types of segments
3 0 Use association term (default)
1 Do not use association term
See Soave-Redlich-Kwong Option Codes
ESRKSW, ESRKSW0 1 0 ASPEN Boston/Mathias alpha function (default)
1 Original literature alpha function
2 Grabowski and Daubert alpha function for H2
above TC (� = 1.202 exp(-0.30228xT ri))
ESRKU, ESRKU0 1 Initial temperature for binary parameter
estimation
0 At TREF=25 C (default)
1 The lower of TB(i) or TB(j)
2 (TB(i) + TB(j))/2
100-
999
Value entered used as temperature in K
2 VLE or LLE UNIFAC
0 VLE (default)
1 LLE
3 Property diagnostic level flag (-1 to 8)

Model Name Option
Code
314 5 Property Model Option Codes
Value Descriptions
4 Vapor phase EOS used in generation of TPxy
data with UNIFAC
0 Hayden-O'Connell (default)
1 Redlich-Kwong
5 Do/do not estimate binary parameters
0 Estimate (default)
1 Set to zero
ESHF, ESHF0 1 0 Equation form for Log(k) expression:
ESRKSWS,
ESRKSWS0,
ESRKSV1,
ESRKSV10,
ESRKSV2,
ESRKSV20,
ESSTEAM,
ESSTEAM0
log(K) = A + B/T + C ln(T) + DT (default)
1 log(K) = A + B/T + CT + DT 2 + E log(P)
1 Original literature alpha function
2 Mathias-Copeman alpha function
3 Schwartzentruber-Renon alpha function
(default)
1 Equation form for alpha function
1 Original literature alpha function
2 Mathias-Copeman alpha function
3 Schwartzentruber-Renon alpha function
(default)
1 0 ASME 1967 correlations
1 NBS 1984 equation of state (default)
2 NBS 1984 equation of state with alternate root
search method (STMNBS2)
2 0 Original fugacity and enthalpy calculations
when used with STMNBS2
1 Rigorous fugacity calculation from Gibbs energy
and corrected enthalpy departure (default)
ESH2O, ESH2O0 1 0 ASME 1967 correlations (default)
1 NBS 1984 equation of state
2 NBS 1984 equation of state with alternate root
search method (STMNBS2)
Note: The enthalpy, entropy, Gibbs energy, and molar volume of water are
calculated from the steam tables when the relevant option is enabled. The
total properties are mole-fraction averages of these values with the properties
calculated by the equation of state for other components. Fugacity coefficient
is not affected.

Soave-Redlich-Kwong Option
Codes
There are five related models all based on the Soave-Redlich-Kwong equation
of state which are very flexible and have many options. These models are:
� Standard Redlich-Kwong-Soave (ESRKSTD0, ESRKSTD)
� Redlich-Kwong-Soave-Boston-Mathias (ESRKS0, ESRKS)
� Soave-Redlich-Kwong (ESSRK, ESSRK0)
� SRK-Kabadi-Danner (ESSRK, ESSRK0)
� SRK-ML (ESRKSML, ESRKSML0)
The options for these models can be selected using the option codes
described in the following table:
Option
Code
Value Description
1 0 Standard SRK alpha function for T r < 1, Boston-Mathias alpha
function for T r > 1
5 Property Model Option Codes 315
1 Standard SRK alpha function for all
2 Grabovsky – Daubert alpha function for H2 and standard SRK
alpha function for others (default)
3 Extended Gibbons-Laughton alpha function for all components
(see notes 1, 2, 3)
4 Mathias alpha function
5 Twu generalized alpha function
2 0 Standard SRK mixing rules (default except for SRK-Kabadi-
Danner)
1 Kabadi – Danner mixing rules (default for SRK-Kabadi-Danner)
(see notes 3, 4, 5)
3 0 Do not calculate water properties from steam table (default for
Redlich-Kwong-Soave models)
1 Calculate properties (H, S, G, V) of water from steam table
(default for SRK models; see note 6)
4 0 Do not apply the Peneloux liquid volume correction (default for
SRK-ML)
1 Apply the liquid volume correction (default for other models)
5 0 Use analytical method for root finding (default)
1 Use RTO numerical method for root finding
2 Use VPROOT/LQROOT numerical method for root finding
6 0 Use true logarithm in calculating properties (default for
Redlich-Kwong-Soave models)
Notes
1 Use smoothed logarithm in calculating properties (default for
SRK models)
1. The standard alpha function is always used for Helium.

2. If extended Gibbons-Laughton alpha function parameters are missing, the
Boston-Mathias extrapolation will be used if T > Tc, and the standard
alpha function will be used if T < Tc.
3. The extended Gibbons-Laughton alpha function should not be used with
the Kabadi-Danner mixing rules.
4. The Kabadi-Danner mixing rules should not be used if Lij parameters are
provided for water with any other components.
5. It is recommended that you use the SRK-KD property method rather than
change this option code.
6. The enthalpy, entropy, Gibbs energy, and molar volume of water are
calculated from the steam tables when this option is enabled. The total
properties are mole-fraction averages of these values with the properties
calculated by the equation of state for other components. Fugacity
coefficient is not affected.
Option Codes for K-Value
Models
Model
Name
Option
Code
316 5 Property Model Option Codes
Value Descriptions
BK10 1 0 Treat pseudocomponents as paraffins (default)
1 Treat pseudocomponents as aromatics
Option Codes for Enthalpy
Models
Model Name Option
Code
Value Descriptions
DHL0HREF 1 1 Use Liquid reference state for all components (Default)
2 Use liquid and gaseous reference states based on the
state of each component
Electrolyte NRTL Enthalpy (HAQELC, HMXELC, and HMXENRHG)
1 Defaults for pair parameters
1 Pair parameters default to zero
2 Solvent/solute pair parameters default to water
parameters. Water/solute pair parameters default to
zero (default for ELC models)
3 Default water parameters to 8, -4. Default
solvent/solute parameters to 10, -2 (default for
HMXENRHG)
2 Vapor phase equation-of-state for liquid enthalpy of HF
0 Ideal gas EOS (default)
1 HF EOS for hydrogen fluoride
3 Solvent/solvent binary parameter values obtained
from:

Model Name Option
Code
HLRELNRT and HLRELELC
5 Property Model Option Codes 317
Value Descriptions
0 Scalar GMELCA, GMELCB and GMELCM (default for ELC
models)
1 Vector NRTL(8) (default for HMXENRHG)
4 Enthalpy calculation method
0 Electrolyte NRTL Enthalpy (default for ELC models and
ELECNRTL property method)
1 Helgeson method (default for HMXENRHG)
5 Vapor phase enthalpy departure contribution to liquid
enthalpy. H liq = H ig + DHV - �H vap; this option indicates
how DHV is calculated.
0 Do not calculate (DHV=0) (default)
1 Calculate using Redlich-Kwong equation of state
2 Calculate using Hayden-O'Connell equation of state
6 Method for calculating corresponding states (for
handling solvents that exist in both subcritical and
supercritical conditions)
0 Original method (default)
1 Corresponding state method. Calculates a pseudocritical
temperature of the solvents and uses it
together with the actual critical temperatures of the
pure solvents to adjust the liquid enthalpy departure.
This results in a smoother transition of the liquid
enthalpy contribution when the component transforms
from subcritical to supercritical.
7 Method for handling Henry components and multiple
solvents
0 Pure liquid enthalpy calculated by aqueous infinite
dilution heat capacity; only water as solvent
1 Pure liquid enthalpy for Henry components calculated
using Henry's law; use this option when there are
multiple solvents.
1 Defaults for pair parameters
1 Pair parameters default to zero
2 Solvent/solute pair parameters default to water
parameters. Water/solute pair parameters default to
zero (default for HLRELELC)
3 Default water parameters to 8, -4. Default
solvent/solute parameters to 10, -2 (default for
HLRENRTL)
2 Solvent/solvent binary parameter values obtained
from:
0 Scalar GMELCA, GMELCB and GMELCM (default)
1 Vector NRTL(8)
3 Mixture density model
0 Rackett equation with Campbell-Thodos modification
1 Quadratic mixing rule for molecular components (mole
basis)

Model Name Option
Code
HIG2ELC, HIG2HG
DHLELC
HAQPT1, HAQPT3 (Pitzer)
318 5 Property Model Option Codes
Value Descriptions
1 Enthalpy calculation method
0 Electrolyte NRTL Enthalpy (default for HIG2ELC)
1 Helgeson method (default for HIG2HG)
1 Steam table for liquid enthalpy of water
0 Use steam table for liquid enthalpy of water (default)
1 Use specified EOS model
2 Vapor phase equation-of-state for liquid enthalpy of HF
0 Use specified EOS model (default)
1 HF EOS for hydrogen fluoride
1 Defaults for pair mixing rule
-1 No unsymmetric mixing
0 Unsymmetric mixing polynomial (default)
1 Unsymmetric mixing integral
2 Standard enthalpy calculation
0 Standard electrolytes method (Pre-release 10)
1 Helgeson method (Default)
3 Estimation of K-stoic temperature dependency
0 Use value at 298.15 K
1 Helgeson Method (default)
HS0POL1, GS0POL1, SS0POL1 (Solid pure component polynomials)
PHILELC
1 Reference temperature usage
0 Use standard reference temperature (default)
1 Use liquid reference temperature
1 Steam table for liquid enthalpy of water
0 Use steam table for liquid enthalpy of water (default)
1 Use specified EOS model
2 Vapor phase equation-of-state for liquid enthalpy of HF
0 Use specified EOS model (default)
1 HF EOS for hydrogen fluoride
Option Codes for Gibbs Free
Energy Models
Model Name Option
Code
Value Descriptions
Electrolyte NRTL Gibbs Energy (GAQELC, GMXELC, and GMXENRHG)
1 Defaults for pair parameters

Model Name Option
Code
GLRELNRT, GLRELELC
5 Property Model Option Codes 319
Value Descriptions
1 Pair parameters default to zero
2 Solvent/solute pair parameters default to water
parameters. Water/solute pair parameters default
to zero (default for ELC models)
3 Default water parameters to 8, -4. Default
solvent/solute parameters to 10, -2 (default for
GMXENRHG)
2 Vapor phase equation-of-state for liquid Gibbs
free energy of HF
0 Ideal gas EOS (default)
1 HF EOS for hydrogen fluoride
3 Solvent/solvent binary parameter values obtained
from
0 Scalar GMELCA, GMELCB and GMELCM (default
for ELC models)
1 Vector NRTL(8) (default for GMXENRHG)
4 Gibbs free energy calculation method
0 Electrolyte NRTL Gibbs free energy (default for
ELC models)
1 Helgeson method (default for GMXENRHG)
5 Vapor phase fugacity coefficient (PHIV)
calculation method.
0 Do not calculate (PHIV=1) (default)
1 Calculate using Redlich-Kwong equation of state
2 Calculate using Hayden-O'Connell equation of
state
6 Method for handling Henry components and
multiple solvents
0 Pure liquid Gibbs free energy calculated by
aqueous infinite dilution heat capacity; only water
as solvent
1 Pure liquid Gibbs free energy for Henry
components calculated using Henry's law; use
this option when there are multiple solvents.
1 Defaults for pair parameters
1 Pair parameters default to zero
2 Solvent/solute pair parameters default to water
parameters. Water/solute pair parameters default
to zero (default for GLRELELC)
3 Default water parameters to 8, -4. Default
solvent/solute parameters to 10, -2 (default for
GLRENRTL)
2 Solvent/solvent binary parameter values obtained
from:
0 Scalar GMELCA, GMELCB and GMELCM (default)
1 Vector NRTL(8)

Model Name Option
Code
GIG2ELC, GIG2HG
GAQPT1, GAQPT3 (Pitzer)
320 5 Property Model Option Codes
Value Descriptions
3 Mixture density model
0 Rackett equation with Campbell-Thodos
modification
1 Quadratic mixing rule for molecular components
(mole basis)
1 Gibbs free energy calculation method
0 Electrolyte NRTL Gibbs free energy (default for
GIG2ELC)
1 Helgeson method (default for GIG2HG)
1 Defaults for pair mixing rule
-1 No unsymmetric mixing
0 Unsymmetric mixing polynomial (default)
1 Unsymmetric mixing integral
2 Standard Gibbs free energy calculation
0 Standard electrolytes method (Pre-release 10)
1 Helgeson method (Default)
3 Estimation of K-stoic temperature dependency
0 Use value at 298.15 K
1 Helgeson Method (default)
Option Codes for Liquid Volume
Models
Model
Name
Option
Code
Value Descriptions
VL2QUAD 1 0 Use normal pure component liquid volume model for
all components (default)
1 Use steam tables for water
2 0 Use mole basis composition (default)
1 Use mass basis composition
VAQCLK 1 0 Use Clarke model
1 Use liquid volume quadratic mixing rule

Index
A
activity coefficient models 86
list of property models 86
alpha functions 69, 73
Peng-Robinson 69
Soave 73
Andrade liquid mixture viscosity
model 247
Andrade/DIPPR viscosity model
248
Antoine/Wagner vapor pressure
model 182
API model 194, 251, 288
liquid molar volume 194
liquid viscosity 251
surface tension 288
API Sour model 187
applications 91
metallurgical 91
aqueous infinite dilution heat
capacity model 213
ASME steam tables 16
Aspen liquid mixture viscosity
model 252
Aspen polynomial equation 211
ASTM 252
liquid viscosity 252
B
Barin equations thermodynamic
property model 228
Benedict-Webb-Rubin-Starling
property model 17
Braun K-10 model 187
Brelvi-O'Connell model 196
Bromley-Pitzer activity coefficient
model 87, 88, 89
Index 321
about 87
parameter conversion 89
working equations 88
BWR-Lee-Starling property model
16
C
Cavett thermodynamic property
model 228
Chao-Seader fugacity model 188
Chapman-Enskog 253, 256, 282,
283
Brokaw/DIPPR viscosity model
253
Brokaw-Wilke mixing rule
viscosity model 256
Wilke-Lee (binary) diffusion
model 282
Wilke-Lee (mixture) diffusion
model 283
Chien-Null activity coefficient
model 89
Chung-Lee-Starling model 258,
260, 270
low pressure vapor viscosity 258
thermal conductivity 270
viscosity 260
Clarke electrolyte liquid volume
model 197
Clausius-Clapeyron equation 194
heat of vaporization 194
coal 297
property models 297
constant activity coefficient model
91
copolymer PC-SAFT EOS property
model 35, 37, 41, 42, 44, 45,
46

about 35
association term 42
chain connectivity 37
dispersion term 41
fundamental equations 35
parameters 45, 46
polar term 44
COSMO-SAC solvation model 91
COSTALD liquid volume model 199
Criss-Cobble aqueous infinite
dilution ionic heat capacity
model 214
D
Dawson-Khoury-Kobayashi
diffusion model 283, 284
binary 283
mixture 284
DCOALIGT coal density model 306
Dean-Stiel pressure correction
viscosity model 262
Debye-Hückel volume model 201
DGHARIGT char density model 307
diffusivity models 281
list 281
DIPPR equation 7, 216
DIPPR model 191, 202, 214, 219,
248, 253, 273, 276, 289
heat of vaporization 191
ideal gas heat capacity 219
liquid heat capacity 214
liquid volume 202
surface tension 289
thermal conductivity 273, 276
viscosity 248, 253
DNSTYGEN nonconventional
component density model 295
E
electrolyte models 197, 231, 233,
263, 272, 285, 292
Clarke liquid volume 197
electrolyte NRTL enthalpy 231
Gibbs energy 233
Jones-Dole viscosity 263
Nernst-Hartley diffusion 285
Onsager-Samaras surface
tension 292
Riedel thermal conductivity 272
electrolyte NRTL 94, 97, 231, 233
activity coefficient model 94, 97
322 Index
enthalpy thermodynamic
property model 231
Gibbs energy thermodynamic
property model 233
eNRTL-SAC activity coefficient
model 108
ENTHGEN nonconventional
component heat capacity
model 296
equation-of-state method 15
property models 15
extrapolation 10
temperature limits 10
G
Grayson-Streed fugacity model 188
group contribution activity
coefficient models 172, 174,
175
Dortmund-modified UNIFAC 174
Lyngby-modified UNIFAC 175
UNIFAC 172
H
Hakim-Steinberg-Stiel/DIPPR
surface tension 289
Hansen solubility parameter model
112
Hayden-O'Connell 22
property model 22
HCOALGEN 300
general coal model for enthalpy
300
heat of vaporization 191
models 191
Helgeson thermodynamic property
model 240
HF equation of state 25
property model 25
Huron-Vidal mixing rules 79
I
IAPS models for water 262, 271,
289
surface tension 289
thermal conductivity 271
viscosity 262
ideal gas heat capacity 219
ideal gas law 29
property model 29

ideal gas/DIPPR heat capacity
model 219
ideal liquid activity coefficient
model 114
IGT density model for 306, 307
char 307
coal 306
IK-CAPE equation 193, 217
heat of vaporization 193
liquid heat capacity 217
J
Jones-Dole electrolyte correction
viscosity model 263
K
Kent-Eisenberg fugacity model 189
L
Lee-Kesler Plöcker property model
31
Lee-Kesler property model 29
Letsou-Stiel viscosity model 265
Li mixing rule thermal conductivity
model 272
liquid constant molar volume
model 202
liquid enthalpy 235
thermodynamic property model
235
liquid heat capacity 216
DIPPR equation 216
liquid mixture 247, 272, 288
surface tension 288
thermal conductivity 272
viscosity 247
liquid thermal conductivity 273
general pure components 273
liquid viscosity 247, 248, 251, 252,
267
Andrade equation 247
API 251
API 1997 251
Aspen 252
ASTM 252
pure components 248
Twu 267
liquid volume quadratic mixing rule
213
Lucas vapor viscosity model 265
Index 323
M
Mathias alpha function 73
Mathias-Copeman alpha function
69, 73
Maxwell-Bonnell vapor pressure
model 190
MHV2 mixing rules 81
mixing rules 79, 81, 82, 84, 213,
243, 256, 269, 272, 279, 281
Brokaw-Wilke viscosity model
256
Huron-Vidal 79
Li 272
liquid volume quadratic 213
MHV2 81
predictive Soave-Redlich-Kwong-
Gmehling 82
quadratic 243
viscosity quadratic 269
Vredeveld 279
Wassiljewa-Mason-Saxena 281
Wong-Sandler 84
modified MacLeod-Sugden surface
tension model 293
N
Nernst-Hartley electrolyte diffusion
model 285
NIST 218
liquid heat capacity 218
NIST TDE Watson equation 193
heat of vaporization 193
nonconventional components 295,
296, 300
coal model for enthalpy 300
density polynomial model 295
enthalpy and density models list
295
heat capacity polynomial model
296
nonconventional solid property
models 295
density 295
enthalpy 295
list of 295
Nothnagel 33
property model 33
NRTL 94, 114
electrolyte NRTL property model
94
property model 114
NRTL-SAC 115, 119, 130

O
for Segments/Oligomers 130
model derivation 119
property model 115
Using 135
Onsager-Samaras electrolyte
surface tension model 292
option codes 309, 310, 312, 315,
316, 318, 320
activity coefficient models 310
enthalpy models 316
equation of state models 312
Gibbs energy models 318
K-value models 316
liquid volume models 320
list 309
Soave-Redlich-Kwong models
315
transport property models 309
P
PC-SAFT property method 35
property model 35
Peng-Robinson 47, 49, 50, 51, 69
alpha functions 69
MHV2 property model 50
property model 47
standard 49
Wong-Sandler property model 51
physical properties 11, 15
models 11, 15
Pitzer activity coefficient model
135, 137, 138, 140, 144
about 135
activity coefficients 140
aqueous strong electrolytes 138
model development 137
parameters 144
polynomial activity coefficient
model 147
PPDS equation 192, 216
heat of vaporization 192
liquid heat capacity 216
predictive Soave-Redlich-Kwong-
Gmehling mixing rules 82
predictive SRK property model
(PSRK) 51
property models 5, 11, 15, 182,
194, 213, 309
equation-of-state list 15
324 Index
fugacity models list 182
heat capacity models list 213
list of 5
molar volume and density
models list 194
option codes 309
thermodynamic list 11
vapor pressure model list 182
property parameters 6
temperature-dependent
properties 6
PSRK 51
property model 51
pure component properties 7
temperature-dependent 7
Q
quadratic mixing rules 243
R
Rackett 207, 208, 209
extrapolation method 209
mixture liquid volume model 207
modified model for molar volume
208
Rackett pure component liquid
volume model 202
Raoult's law 114
Redlich-Kister activity coefficient
model 148
Redlich-Kwong 51, 73
alpha function 73
property model 51
Redlich-Kwong-Aspen property
model 52
Redlich-Kwong-Soave 53, 55, 56,
57, 59, 73
alpha function list 73
Boston-Mathias property model
55
MHV2 property model 57
property model 53
Soave-Redlich-Kwong property
model 59
Wong-Sandler property model 56
Riedel electrolyte correction
thermal conductivity model
272

S
Sato-Riedel/DIPPR thermal
conductivity model 273
Scatchard-Hildebrand activity
coefficient model 149
Schwartzentruber-Renon property
model 57
Soave-Redlich-Kwong 59
property model 59
Soave-Redlich-Kwong models 315
options codes 315
solid Antoine vapor pressure
models 190
solid thermal conductivity
polynomial 276
solids polynomial heat capacity
model 223
solubility correlation models 225,
226, 227
Henry's constant 225
hydrocarbon 227
list 225
water solubility model 226
SRK-Kabadi-Danner property
model 61
SRK-ML property model 63
standard Peng-Robinson property
model 49
standard Redlich-Kwong-Soave
property model 53
steam tables 16, 32
NBS/NRC 32
property models 16
STEAMNBS property method 32
Stiel-Thodos pressure correction
thermal conductivity model
279
Stiel-Thodos thermal conductivity
model 276
surface tension 287, 288, 293
general pure components 289
liquid mixtures 288
models list 287
modified MacLeod-Sugden 293
Symmetric and Unsymmetric
Electrolyte NRTL activity
coefficient model 151, 154
about 151
working equations 154
T
temperature 10
Index 325
extrapolating limits 10
temperature-dependent properties
6, 7
pure component 7
units 6
thermal conductivity 269, 276
models list 269
solids 276
thermo switch 7
thermodynamic property 11, 228
list of additional models 228
models list 11
three-suffix Margules activity
coefficient model 150
THRSWT 7
transport property 244
models list 244
transport switch 7
TRAPP 266, 280
thermal conductivity model 280
viscosity model 266
TRNSWT 7
Twu liquid viscosity model 267
U
UNIFAC 172, 174, 175
activity coefficient model 172
Dortmund modified activity
coefficient model 174
Lyngby modified activity
coefficient model 175
UNIQUAC 176
activity coefficient model 176
V
Van Laar activity coefficient model
178
vapor thermal conductivity 276
general pure components 276
vapor viscosity 253, 256, 258, 265
Brokaw-Wilke mixing rule
viscosity model 256
Chung-Lee-Starling 258
Lucas 265
pure components 253
viscosity 246
models 246
viscosity quadratic mixing rule 269
VPA/IK-CAPE equation of state 64
Vredeveld mixing rule 279

W
Wagner Interaction Parameter
activity coefficient model 179
Wagner vapor pressure model 182
Wassiljewa-Mason-Saxena mixing
rule 281
Watson equation 191
heat of vaporization 191
Wilke-Chang diffusion model 286,
287
binary 286
mixture 287
WILS-GLR property method 236
WILS-LR property method 236
Wilson (liquid molar volume)
activity coefficient model 181
Wilson activity coefficient model
179
Wong-Sandler mixing rules 84
326 Index