AspenPhysPropModelsV7_2-Ref

Aspen PhysicalProperty System

Physical Property Models

Version Number: V7.2July 2010

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Contents 1

Contents

Contents..................................................................................................................1

1 Introduction.........................................................................................................5

Units for Temperature-Dependent Parameters .....................................................6Pure Component Temperature-Dependent Properties............................................7Extrapolation Methods .................................................................................... 10

2 Thermodynamic Property Models .......................................................................11

Equation-of-State Models ................................................................................ 15ASME Steam Tables.............................................................................. 16BWR-Lee-Starling................................................................................. 16Benedict-Webb-Rubin-Starling ............................................................... 17GERG2008 Equation of State ................................................................. 20Hayden-O'Connell ................................................................................ 22HF Equation-of-State ............................................................................ 25IAPWS-95 Steam Tables ....................................................................... 29Ideal Gas ............................................................................................ 29Lee-Kesler........................................................................................... 29Lee-Kesler-Plöcker ............................................................................... 31NBS/NRC Steam Tables ........................................................................ 32Nothnagel ........................................................................................... 33Copolymer PC-SAFT EOS Model.............................................................. 35Peng-Robinson..................................................................................... 47Standard Peng-Robinson ....................................................................... 49Peng-Robinson-MHV2 ........................................................................... 50Predictive SRK (PSRK) .......................................................................... 51Peng-Robinson-Wong-Sandler................................................................ 51Redlich-Kwong..................................................................................... 51Redlich-Kwong-Aspen ........................................................................... 52Redlich-Kwong-Soave ........................................................................... 53Redlich-Kwong-Soave-Boston-Mathias .................................................... 55Redlich-Kwong-Soave-Wong-Sandler ...................................................... 56Redlich-Kwong-Soave-MHV2.................................................................. 57Schwartzentruber-Renon....................................................................... 57Soave-Redlich-Kwong ........................................................................... 59SRK-Kabadi-Danner.............................................................................. 61SRK-ML............................................................................................... 63VPA/IK-CAPE Equation-of-State ............................................................. 64Peng-Robinson Alpha Functions.............................................................. 69Huron-Vidal Mixing Rules ...................................................................... 79MHV2 Mixing Rules ............................................................................... 81Predictive Soave-Redlich-Kwong-Gmehling Mixing Rules ........................... 82

2 Contents

Wong-Sandler Mixing Rules ................................................................... 84Activity Coefficient Models ............................................................................... 86

Bromley-Pitzer Activity Coefficient Model................................................. 87Chien-Null ........................................................................................... 89Constant Activity Coefficient .................................................................. 91COSMO-SAC ........................................................................................ 91Electrolyte NRTL Activity Coefficient Model (GMENRTL) ............................. 94ENRTL-SAC ....................................................................................... 108Hansen ............................................................................................. 112Ideal Liquid ....................................................................................... 114NRTL (Non-Random Two-Liquid) .......................................................... 114NRTL-SAC Model ................................................................................ 115Pitzer Activity Coefficient Model............................................................ 135Polynomial Activity Coefficient ............................................................. 147Redlich-Kister .................................................................................... 148Scatchard-Hildebrand ......................................................................... 149Three-Suffix Margules......................................................................... 150Symmetric and Unsymmetric Electrolyte NRTL Activity Coefficient Model... 151UNIFAC Activity Coefficient Model......................................................... 172UNIFAC (Dortmund Modified)............................................................... 174UNIFAC (Lyngby Modified)................................................................... 175UNIQUAC Activity Coefficient Model ...................................................... 176Van Laar Activity Coefficient Model ....................................................... 178Wagner Interaction Parameter ............................................................. 179Wilson Activity Coefficient Model .......................................................... 179Wilson Model with Liquid Molar Volume ................................................. 181

Vapor Pressure and Liquid Fugacity Models...................................................... 182General Pure Component Liquid Vapor Pressure ..................................... 182API Sour Model .................................................................................. 187Braun K-10 Model .............................................................................. 187Chao-Seader Pure Component Liquid Fugacity Model .............................. 188Grayson-Streed Pure Component Liquid Fugacity Model .......................... 188Kent-Eisenberg Liquid Fugacity Model ................................................... 189Maxwell-Bonnell Vapor Pressure Model.................................................. 190Solid Antoine Vapor Pressure Model ...................................................... 190

General Pure Component Heat of Vaporization ................................................. 191DIPPR Heat of Vaporization Equation .................................................... 191Watson Heat of Vaporization Equation .................................................. 191PPDS Heat of Vaporization Equation ..................................................... 192IK-CAPE Heat of Vaporization Equation ................................................. 193NIST TDE Watson Heat of Vaporization Equation .................................... 193Clausius-Clapeyron Equation ............................................................... 194

Molar Volume and Density Models .................................................................. 194API Liquid Molar Volume ..................................................................... 194Brelvi-O'Connell ................................................................................. 196Clarke Aqueous Electrolyte Volume....................................................... 197COSTALD Liquid Volume ..................................................................... 199Debye-Hückel Volume......................................................................... 201Liquid Constant Molar Volume Model..................................................... 202General Pure Component Liquid Molar Volume ....................................... 202Rackett/Campbell-Thodos Mixture Liquid Volume ................................... 207Modified Rackett Liquid Molar Volume ................................................... 208Rackett Extrapolation Method .............................................................. 209

Contents 3

General Pure Component Solid Molar Volume......................................... 211Liquid Volume Quadratic Mixing Rule .................................................... 213

Heat Capacity Models ................................................................................... 213Aqueous Infinite Dilution Heat Capacity................................................. 213Criss-Cobble Aqueous Infinite Dilution Ionic Heat Capacity ...................... 214General Pure Component Liquid Heat Capacity....................................... 214General Pure Component Ideal Gas Heat Capacity.................................. 219General Pure Component Solid Heat Capacity ........................................ 223

Solubility Correlations................................................................................... 225Henry's Constant................................................................................ 225Water Solubility ................................................................................. 226Hydrocarbon Solubility........................................................................ 227

Other Thermodynamic Property Models........................................................... 228Cavett .............................................................................................. 228Barin Equations for Gibbs Energy, Enthalpy, Entropy, and Heat Capacity... 228Electrolyte NRTL Enthalpy Model (HMXENRTL) ....................................... 231Electrolyte NRTL Gibbs Free Energy Model (GMXENRTL) .......................... 233Liquid Enthalpy from Liquid Heat Capacity Correlation............................. 235Enthalpies Based on Different Reference States ..................................... 236Helgeson Equations of State ................................................................ 240Quadratic Mixing Rule ......................................................................... 243

3 Transport Property Models ...............................................................................244

Viscosity Models........................................................................................... 246Andrade Liquid Mixture Viscosity .......................................................... 247General Pure Component Liquid Viscosity .............................................. 248API Liquid Viscosity ............................................................................ 251API 1997 Liquid Viscosity .................................................................... 251Aspen Liquid Mixture Viscosity ............................................................. 252ASTM Liquid Mixture Viscosity.............................................................. 252General Pure Component Vapor Viscosity .............................................. 253Chapman-Enskog-Brokaw-Wilke Mixing Rule ......................................... 256Chung-Lee-Starling Low-Pressure Vapor Viscosity .................................. 258Chung-Lee-Starling Viscosity ............................................................... 260Dean-Stiel Pressure Correction ............................................................ 262IAPS Viscosity for Water...................................................................... 262Jones-Dole Electrolyte Correction ......................................................... 263Letsou-Stiel ....................................................................................... 265Lucas Vapor Viscosity ......................................................................... 265TRAPP Viscosity Model ........................................................................ 266Twu Liquid Viscosity ........................................................................... 267Viscosity Quadratic Mixing Rule............................................................ 269

Thermal Conductivity Models ......................................................................... 269Chung-Lee-Starling Thermal Conductivity.............................................. 270IAPS Thermal Conductivity for Water .................................................... 271Li Mixing Rule .................................................................................... 272Riedel Electrolyte Correction ................................................................ 272General Pure Component Liquid Thermal Conductivity ............................ 273Solid Thermal Conductivity Polynomial .................................................. 276General Pure Component Vapor Thermal Conductivity............................. 276Stiel-Thodos Pressure Correction Model................................................. 279Vredeveld Mixing Rule......................................................................... 279

4 Contents

TRAPP Thermal Conductivity Model....................................................... 280Wassiljewa-Mason-Saxena Mixing Rule ................................................. 281

Diffusivity Models ......................................................................................... 281Chapman-Enskog-Wilke-Lee (Binary).................................................... 282Chapman-Enskog-Wilke-Lee (Mixture) .................................................. 283Dawson-Khoury-Kobayashi (Binary) ..................................................... 283Dawson-Khoury-Kobayashi (Mixture).................................................... 284Nernst-Hartley ................................................................................... 285Wilke-Chang (Binary) ......................................................................... 286Wilke-Chang (Mixture) ........................................................................ 287

Surface Tension Models................................................................................. 287Liquid Mixture Surface Tension ............................................................ 288API Surface Tension ........................................................................... 288IAPS Surface Tension for Water ........................................................... 289General Pure Component Liquid Surface Tension.................................... 289Onsager-Samaras .............................................................................. 292Modified MacLeod-Sugden ................................................................... 293

4 Nonconventional Solid Property Models ...........................................................295

General Enthalpy and Density Models ............................................................. 295General Density Polynomial ................................................................. 295General Heat Capacity Polynomial ........................................................ 296

Enthalpy and Density Models for Coal and Char................................................ 297General Coal Enthalpy Model ............................................................... 300IGT Coal Density Model ....................................................................... 306IGT Char Density Model ...................................................................... 307

5 Property Model Option Codes ...........................................................................309

Option Codes for Transport Property Models .................................................... 309Option Codes for Activity Coefficient Models .................................................... 310Option Codes for Equation of State Models ...................................................... 312Soave-Redlich-Kwong Option Codes ............................................................... 315Option Codes for K-Value Models.................................................................... 316Option Codes for Enthalpy Models .................................................................. 316Option Codes for Gibbs Free Energy Models..................................................... 318Option Codes for Liquid Volume Models........................................................... 320

Index ..................................................................................................................321

1 Introduction 5

1 Introduction

This manual describes the property models available in the Aspen PhysicalProperty System and defines the parameters used in each model. Thedescription for each model lists the parameter names used to enter values onthe Properties Parameters forms.

This manual also lists the pure component temperature-dependent propertiesthat the Aspen Physical Property System can calculate from a model thatsupports 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 avalue. If a parameter is missing, calculations stop. The lower limit and upperlimit for each parameter, when available, indicate the reasonable bounds forthe parameter. The limits are used to detect grossly erroneous parametervalues.

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. Thefollowing table (below) provides an organizational overview of this manual.The tables labeled Thermodynamic Property Models, Transport PropertyModels, and Nonconventional Solid Property Models present detailed lists ofmodels. These tables also list the Aspen Physical Property System modelnames, and their possible use in different phase types, for pure componentsand mixtures.

Electrolyte and conventional solid property models are presented inThermodynamic Property Models.

6 1 Introduction

Categories of ModelsCategory Sections

ThermodynamicProperty Models

Equation-of-State ModelsActivity Coefficient Models (Including Electrolyte Models)Vapor Pressure and Liquid Fugacity ModelsHeat of Vaporization ModelsMolar Volume and Density ModelsHeat Capacity ModelsSolubility CorrelationsOther

Transport PropertyModels

Viscosity ModelsThermal Conductivity ModelsDiffusivity ModelsSurface Tension Models

Nonconventional SolidProperty Models

General Enthalpy and Density ModelsEnthalpy and Density Models for Coal and Char

Units for Temperature-Dependent ParametersSome temperature-dependent parameters may be based on expressionswhich involve logarithmic or reciprocal temperature terms. When thecoefficient of any such term is non-zero, in many cases the entire expressionmust be calculated assuming that all the coefficients are in absolutetemperature units. In other cases, terms are independent from one another,and only certain terms may require calculation using absolute temperatureunits. Notes in the models containing such terms explain exactly whichcoefficients are affected by this treatment.

When absolute temperature units are forced in this way, this affects the unitsfor coefficients you have entered as input parameters. If your inputtemperature units are Fahrenheit (F), then Rankine (R) is used instead. Ifyour input units are Celsius (C), then Kelvin (K) is used instead.

If only constant and positive powers of temperature are present in theexpression, then your specified input units are used.

If the parameters include temperature limits, the limits are always interpretedin user input units even if the expression is forced to absolute units.

Some equations may include a dimensionless parameter, the reducedtemperature Tr = T / Tc. This reduced temperature is calculated usingabsolute temperature units. In most cases, input parameters associated withsuch equations do not have temperature units.

1 Introduction 7

Pure Component Temperature-Dependent PropertiesThe following table lists the pure component temperature-dependentproperties that the Aspen Physical Property System can calculate from ageneral model that supports several equations or submodels.

For example, the Aspen Physical Property System can calculate heat ofvaporization using these equations:

Watson

DIPPR

PPDS

IK-CAPE

NIST TDE Watson

Pure Component Temperature-Dependent Properties

Property

Submodel-SelectionParameterElementNumber Available Submodels

DIPPR EquationNumbers(† = default)

Solid Volume THRSWT/1 Aspen, DIPPR, IK-CAPE, NIST 100

Liquid Volume THRSWT/2 Aspen (Rackett), DIPPR, PPDS, IK-CAPE, NIST

105†, 116 for wateronly

Liquid VaporPressure

THRSWT/3 Aspen (Extended Antoine),Wagner, BARIN, PPDS, PML, IK-CAPE, NIST

101

Heat ofVaporization

THRSWT/4 Aspen (Watson), DIPPR, PPDS, IK-CAPE, NIST

106

Solid HeatCapacity

THRSWT/5 Aspen, DIPPR, BARIN, IK-CAPE,NIST

100†, 102

Liquid HeatCapacity

THRSWT/6 DIPPR, PPDS, BARIN, IK-CAPE,NIST

100†, 114

Ideal Gas HeatCapacity

THRSWT/7 Aspen, DIPPR, BARIN, PPDS, IK-CAPE, NIST

107, 127†

Second VirialCoefficient

THRSWT/8 DIPPR 104

Liquid Viscosity TRNSWT/1 Aspen (Andrade), DIPPR, PPDS,IK-CAPE, NIST

101†, 115

Vapor Viscosity TRNSWT/2 Aspen (Chapman-Enskog-Brokaw),DIPPR, PPDS, IK-CAPE, NIST

102

Liquid ThermalConductivity

TRNSWT/3 Aspen (Sato-Riedel), DIPPR, PPDS,IK-CAPE, NIST

100

Vapor ThermalConductivity

TRNSWT/4 Aspen (Stiel-Thodos), DIPPR,PPDS, IK-CAPE, NIST

102

Liquid SurfaceTension

TRNSWT/5 Aspen (Hakim-Steinberg-Stiel),DIPPR, PPDS, IK-CAPE, NIST

106

8 1 Introduction

Which equation is actually used to calculate the property for a givencomponent depends on which parameters are available. If parameters areavailable for more than one equation, the Aspen Physical Property Systemuses the parameters that were entered or retrieved first from the databanks.The selection of submodels is driven by the data hierarchy, and controlled bythe submodel-selection parameters.

The thermodynamic properties use the THRSWT (thermo switch) submodel-selection parameter, and the transport properties use the TRNSWT (transportswitch) submodel-selection parameter.

As the previous table shows, a property is associated with an element of thesubmodel-selection parameter. For example, THRSWT element 1 controls thesubmodel for solid volume.

The following table shows the values for THRSWT or TRNSWT, and thecorresponding 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 withthe available parameters. For example, suppose that parameters for theDIPPR equation 106 are available for liquid surface tension. For thatcomponent, TRNSWT element 5 is set to 106 in the databank. If you areretrieving data from an in-house or user databank, you should store theappropriate values for THRSWT and TRNSWT in the databank, using theappropriate equation number. Otherwise, the Aspen Physical Property Systemwill search for the parameters needed for the Aspen form of the equations.

If a component is available in more than one databank, the Aspen PhysicalProperty System uses the data and equations based on the databank listorder on the Components Specifications Selection sheet. For example,suppose the databank search order is ASPENPCD, then PURE10, and that theAspen Physical Property System cannot find the parameters for a particularsubmodel (equation) in the ASPENPCD databank. If the PURE10 databankcontains parameters for another equation, the Aspen Physical PropertySystem will use that equation (most likely the DIPPR equation) to calculatethe 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 PropertiesParameters Pure Component form), the Aspen Physical Property System setsthe corresponding THRSWT and TRNSWT elements for that component to thedefault values shown in the table above. This default setting might not alwaysbe correct. If you know the equation number, you should enter it directly on

1 Introduction 9

the Properties Parameters Pure-Components form. For example, suppose youwant 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 5-8elements to 0. If you want to set the other temperature-dependent propertiesto use what is defined for that component in the databank, leave the elementblank.

The following table lists the available DIPPR equations and the correspondingequation (submodel) number.

Available DIPPR EquationsEquationNumber 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 absolutetemperature units.

The following sections describe the Aspen, DIPPR, BARIN, IK-CAPE, PPDS, andNIST equations for each property. For descriptions of the the BARIN equationsfor heat capacity and enthalpy, see BARIN Equations for Gibbs Energy,Enthalpy, Entropy, and Heat Capacity.

10 1 Introduction

Extrapolation MethodsMany temperature dependent property models have upper and lowertemperature limits. The Aspen Physical Property System usually extrapolateslinearly beyond such limits. It calculates the slope of the property-versus-temperature curve, or the ln(property)-versus-temperature curve for modelsexpressed in logarithmic form, at the upper or lower temperature limit. Fortemperatures beyond the limit, it uses a linear model with this slope whichmeets the curve from the equation at the temperature limit. Thus the modelis:

For T beyond the upper or lower limit, where Tlim is that limit and Z is theproperty or ln(property) as appropriate. Some liquid molar volume models areactually molar density models which then return the reciprocal of the densityas the liquid molar volume. In these models, the extrapolation occurs for thedensity calculation.

There are certain exceptions, detailed below.

Exception 1: Logarithmic Properties Based on ReciprocalTemperature

This applies to property models expressed in the form (where a(T) includesany additional dependency on temperature):

For these models, the extrapolation maintains the slope of ln(property) versus1/T. This applies to the Extended Antoine vapor pressure equation and theAndrade and DIPPR liquid viscosity equations. Note that the equation forHenry'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 forextrapolation at temperatures below the lower limit, which is described in themodel. At high temperatures it follows the usual rule of extrapolatingproperty-versus-temperature linearly.

Exception 3: No Extrapolation

The equations for certain models are used directly at all temperatures, so thatno extrapolation is performed. These models are the Wagner vapor pressureequation, the Aly and Lee equation for the DIPPR Ideal Gas Heat Capacity(using the CPIGDP parameter), and the Water Solubility and HydrocarbonSolubility models. The equations for temperature-dependent binaryinteraction parameters are also used directly at all temperatures with noextrapolation.

2 Thermodynamic Property Models 11

2 Thermodynamic PropertyModels

This section describes the available thermodynamic property models in theAspen Physical Property System. The following table provides a list ofavailable models, with corresponding Aspen Physical Property System modelnames. The table provides phase types for which the model can be used andinformation on use of the model for pure components and mixtures.

Aspen Physical Property System thermodynamic property models includeclassical thermodynamic property models, such as activity coefficient modelsand equations of state, as well as solids and electrolyte models. The modelsare 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 orMixture.

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 modelscalculate 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 alphafunctions 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 —

12 2 Thermodynamic Property Models

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

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 molarvolume

GMWSNVOL L — X

Vapor Pressure and Liquid Fugacity ModelsProperty Model Model

NameProperty Phase(s)Pure Mixture

General Pure Component LiquidVapor Pressure

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 Heatof 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 (puresolid), 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 ElectrolyteVolume

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 LiquidMolar Volume

VL0RKT,VL2RKT L X —

Rackett/Campbell-ThodosMixture Liquid Volume

VL2RKT L X X

Modified Rackett VL2MRK L X X

General Pure Component SolidMolar Volume

VS0POLY S X —

Liquid Volume Quadratic MixingRule

VL2QUAD L — X

Heat Capacity ModelsProperty Model Model


Aqueous Infinite Dilution HeatCapacity Polynomial

— — L — X

Criss-Cobble Aqueous InfiniteDilution Ionic Heat Capacity

— — L — X

General Pure Component LiquidHeat Capacity

HL0DIP HL, DHL L X —

General Pure Component IdealGas Heat Capacity

— CPIG V X X

General Pure Component SolidHeat Capacity

HS0POLY HS S X —

Solubility Correlation ModelsProperty Model Model


Henry's constant HENRY1 HNRY,WHNRY

L — X

Water solubility — — L — X

Hydrocarbon solubility — — L — X

Other ModelsProperty Model Model

NamePropertyPhase(s)Pure Mixture

Cavett Liquid Enthalpy DepartureDHL0CVT,DHL2CVT

DHL,DHLMX

L X X

BARIN Equations for GibbsEnergy, Enthalpy, Entropy andHeat Capacity

— — S L V X —

Bromley-Pitzer Enthalpy HAQPT2 HLMX L — X

Bromley-Pitzer Gibbs Energy GAQPT2 GLMX L — X


Property Model ModelName

PropertyPhase(s)Pure Mixture

Electrolyte NRTL Enthalpy HMXENRTL,HAQELC,HMXELC,HMXENRHG

HLMX L — X

Electrolyte NRTL Gibbs Energy GMXENRTL,GAQELC,GMXELC,GMXENRHG

HLMX L — X

Liquid Enthalpy from Liquid HeatCapacity Correlation

DHL0DIP L X X

Enthalpies Based on DifferentReference States

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 ModelsThe Aspen Physical Property System has the following built-in equation-of-state property models. This section describes the equation-of-state propertymodels 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 TablesThe ASME steam tables are implemented like any other equation-of-state inthe Aspen Physical Property System. The steam tables can calculate anythermodynamic property of water or steam and form the basis of the STEAM-TA property method. There are no parameter requirements. The ASME steamtables 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 EnergyCommision, ASTEM - A Collection of FORTRAN Subroutines to Evaluate the1967 ASME equations of state for water/steam and derivatives of theseequations.

BWR-Lee-StarlingThe Benedict-Webb-Rubin-Lee-Starling equation-of-state is the basis of theBWR-LS property method. It is a generalization by Lee and Starling of thevirial equation-of-state for pure fluids by Benedict, Webb and Rubin. Theequation is used for non-polar components, and can manage hydrogen-containing systems.

General Form:

Where:

Mixing Rules:


Where:

ParameterName/Element

Symbol Default MDS LowerLimit

UpperLimit

Units

TCBWR Tci TC X 5.0 2000.0 TEMPERATURE

VCBWR Vci* VC X 0.001 3.5 MOLE-

VOLUME

BWRGMA iOMEGA X -0.5 3.0 —

BWRKV ij0 X -5.0 1.0 —

BWRKT ij0 X -5.0 1.0 —

Binary interaction parameters BWRKV and BWRKT are available in the AspenPhysical 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-StarlingThe Benedict-Webb-Rubin-Starling equation-of-state is the basis of the BWRSproperty method. It is a modification by Han and Starling of the virialequation-of-state for pure fluids by Benedict, Webb and Rubin. This equation-of-state can be used for hydrocarbon systems that include the common lightgases, 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, n-heptane, n-octane, ethylene, propylene, nitrogen, carbon dioxide, andhydrogen sulfide, values of the parameters in the table below are available inthe EOS-LIT databank in the Aspen Properties Enterprise Database.

If the values of these parameters are not given, and not available from thedatabank, the Aspen Physical Property System will calculate them using the


critical temperature, the critical volume (or critical density), the acentricfactor and generalized correlations given by Han and Starling.

When water is present, by default Benedict-Webb-Rubin-Starling uses thesteam table to calculate the enthalpy, entropy, Gibbs energy, and molarvolume of water. The total properties are mole-fraction averages of thesevalues with the properties calculated by the equation of state for othercomponents. Fugacity coefficient is not affected. An option code can disablethis use of the steam table.

For best results, the binary parameter kij must be regressed using phase-equilibrium data such as VLE data.ParameterName/Element

SymbolDefault MDS LowerLimit

UpperLimit

Units

BWRSTC Tci TC x 5.0 2000.0 TEMPERATURE

BWRSVC Vci VC x 0.001 3.5 MOLE-VOLUME

BWRSOM i OMEGA x –0.5 2.0 –

BWRSA/1 B0i fcn(i ,Vci , Tci) x – – MOLE-VOLUME

BWRSA/2 A0i fcn(i ,Vci , Tci) x – – PRESSURE * MOLE-VOL^2

BWRSA/3 C0i fcn(i ,Vci , Tci) x – – PRESSURE *TEMPERATURE^2 *MOLE-VOLUME^2

BWRSA/4 ifcn(i ,Vci , Tci) x – – MOLE-VOLUME^2

BWRSA/5 bi fcn(i ,Vci , Tci) x – – MOLE-VOLUME^2

BWRSA/6 ai fcn(i ,Vci , Tci) x – – PRESSURE * MOLE-VOL^3

BWRSA/7 i fcn(i ,Vci , Tci) x – – MOLE-VOLUME^3

BWRSA/8 ci fcn(i ,Vci , Tci) x – – PRESSURE *TEMPERATURE^2 *MOLE-VOLUME^3

BWRSA/9 D0i fcn(i ,Vci , Tci) x – – PRESSURE *TEMPERATURE^3 *MOLE-VOLUME^2

BWRSA/10 di fcn(i ,Vci , Tci) x – – PRESSURE *TEMPERATURE * MOLE-VOLUME^3

BWRSA/11 E0i fcn(i ,Vci , Tci) x – – PRESSURE *TEMPERATURE^4 *MOLE-VOLUME^2

BWRAIJ kij – x – – –

Constants Used with the correlations of Han and StarlingParameter Methane Ethane Propane n-Butane

B0i 0.723251 0.826059 0.964762 1.56588

A0i 7520.29 13439.30 18634.70 32544.70

C0i 2.71092x108 2.95195x109 7.96178x109 1.37436x1010

D0i 1.07737x1010 2.57477x1011 4.53708x1011 3.33159x1011

E0i 3.01122x1010 1.46819x1013 2.56053x1013 2.30902x1012


Parameter Methane Ethane Propane n-Butane

bi 0.925404 3.112060 5.462480 9.140660

ai 2574.89 22404.50 40066.40 71181.80

di 47489.1 702189.0 1.50520x107 3.64238x107

i 0.468828 0.909681 2.014020 4.009850

ci 4.37222x108 6.81826x109 2.74461x1010 7.00044x1010

i1.48640 2.99656 4.56182 7.54122

Parameter n-Pentane n-Hexane n-Heptane n-Octane

B0i 2.44417 2.66233 3.60493 4.86965

A0i 51108.20 45333.10 77826.90 81690.60

C0i 2.23931x1010 5.26067x1010 6.15662x1010 9.96546x1010

D0i 1.01769x1012 5.52158x1012 7.77123x1012 7.90575x1012

E0i 3.90860x1013 6.26433x1014 6.36251x1012 3.46419x1013

bi 16.607000 29.498300 27.441500 10.590700

ai 162185.00 434517.00 359087.00 131646.00

di 3.88521x107 3.27460x107 8351150.0 1.85906x108

i 7.067020 9.702300 21.878200 34.512400

ci 1.35286x1011 3.18412x1011 3.74876x1011 6.42053x1011

i11.85930 14.87200 24.76040 21.98880

References

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 Industrialapplications," 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 StateThe GERG2008 equation-of-state model is the basis for the GERG2008property method.

The equation of state is based on a multi-fluid approximation explicit in thereduced Helmholtz free energy:


(1)

Where the ideal-gas contribution o and residual contribution r at a given

mixture density, temperature, and molar composition are:

(2)

(3)

Where the reduced mixture density and inverse reduced mixture

temperature are:

(4)

In eq. (2), the ideal-gas contribution of the reduced Helmholtz free energy forcomponent i is given by:

(5)

In eq. (3), the pure substance contribution to the residual part of the reducedHelmholtz free energy for component i is given by:

(6)

In eq. (3), the mixture contribution to the residual part of the reducedHelmholtz free energy is given by:

(7)

The reduced mixture density is given by:

(8)

And the reduced mixture temperature is given by:


(9)

Where:

R = molar gas constant = 8.314472 J/mol-K.

c,i and Tc,i = critical density and critical temperature

nooi,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 purecomponents

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 OtherMixtures" O. Kunz, R. Klimeck, W. Wagner, M. Jaeschke; GERG TM15 2007;ISBN 978-3-18-355706-6; Published for GERG and printed in Germany byVDI Verlag GmbH (2007).

Kunz, O., Wagner, W., "The new GERG-2004 XT08 wide-range equation ofstate for natural gases and other mixtures." To be submitted to Fluid PhaseEquilibria (beginning of 2010).

Hayden-O'ConnellThe Hayden-O'Connell equation-of-state calculates thermodynamic propertiesfor 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 thechemical theory of dimerization. This model accounts for strong associationand solvation effects, including those found in systems containing organicacids, such as acetic acid. The equation-of-state is:

Where:

For nonpolar, non-associating species:

, with


, where

For polar, associating species:

, with

, where

For chemically bonding species:

, and

Cross-Interactions

The previous equations are valid for dimerization and cross-dimerization ifthese mixing rules are applied:

= 0 unless a special solvation contribution can be justified (for example, iand j are in the same class of compounds). Many values are present in theAspen 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 dimerizingcomponents 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/nt.

This represents true total volume over the true number of species nt.However, the reported molar volume is V/na.

This represents the true total volume over the apparent number of species na.If dimerization does not occur, na is defined as the number of species. V/na

reflects the apparently lower molar volume of an associating gas mixture.

The chemical equilibrium constant for the dimerization reaction on pressurebasis 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 apressure basis

=

ij = 1 for i=j

= 0 for

Apparent mole fractions yia 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 theratio of apparent and true number of moles is added to the molar enthalpy

departure .


Parameter Name/Element


UpperLimit

Units

TC Tci — — 5.0 2000.0 TEMPERATURE

PC pci — — 105 108 PRESSURE

RGYR rigyr — — 10-11 5x10-9 LENGTH

MUP pi — — 0.0 5x10-24 DIPOLEMOMENT

HOCETA 0.0 X — — —

The binary parameters HOCETA for many component pairs are available in theAspen Physical Property System. These parameters are retrievedautomatically 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 SecondVirial Coefficients," Ind. Eng. Chem., Process Des. Dev., Vol. 14,No. 3,(1975), pp. 209 – 216.

HF Equation-of-StateHF forms oligomers in the vapor phase. The non-ideality in the vapor phase isfound in important deviations from ideality in all thermodynamic properties.The HF equation accounts for the vapor phase nonidealities. The model isbased 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 onwhich 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 andtrue species. Abbott and van Ness (1992) provide details and basicthermodynamics of reactive systems.

The temperature-dependent hexamerization equilibrium constant, can fit theexperimentally determined association factors. The built-in functionality is:

(1)

The constants C0 and C1 are from Long et al. (1943), and C2 and C3 are set to0. The correlation is valid between 270 and 330 K, and can be extrapolated toabout 370 K (cf. sec. 4). Different sets of constants can be determined byexperimental 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 orspecies. Assuming the ideal gas law for all true species in terms of (p, V, T)behavior implies:


(2)

Where the true number of species is given by 1/f. The association factor iseasily determined from (p, V, T) experiments. For a critical evaluation of datarefer 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:

(3)

If p1 represents the true partial pressure of the HF monomer, and p6

represents the true partial pressure of the hexamer, then the equilibriumconstant is defined as:

(4)

The true total pressure is:

p = p1 + p6 (5)

If all hexamer were dissociated, the apparent total pressure would be thehypothetical pressure where:

pa = p1 + 6p6 = p + 5p6 (6)

When physical ideality is assumed, partial pressures and mole fractions areproportional. The total pressure in equation 5 represents the true number ofspecies. The apparent total pressure from equation 6 represents the apparentnumber of species:

(7)

Note that the outcome of equation 7 is independent of the assumption ofideality. Equation 7 can be used to compute the number of true species 1/ffor 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 HFcan be calculated using equations 2 and 7. The molar volume calculated is thetrue molar volume for 1 apparent mole of HF. This is because the volume of 1mole of ideal gas (the true molar volume per true number of moles) is alwaysequal 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 HFmole fraction is:

(8)


The denominator of equation 8 is given by equation 6. The numerator (theapparent partial pressure of HF) is the hypothetical partial pressure only if allof the hexamer was dissociated. If you substitute equation 4, then equation 8becomes:

(9)

K is known from Long et al., or can be regressed from (p,V,T) data. Theapparent mole fraction of HF, ya, is known to the user and the simulator, butp1, or y = p1/p must also be known in order to calculate the thermodynamicproperties of the mixture. Equation 9 must be solved for p1.

Equation 9 can be written as a polynomial in p1 of degree 6:

K(6 - 5ya)(p1)6 + p1 - pya = 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 andmole 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 issimilar to the correction applied in equation 2. Since the ideal gas law isassumed, the apparent fugacity coefficient is given by the equation. Allvariables on the right side are known.

(11)

For pure HF, ya = 1:

From the fugacity coefficient, the Gibbs energy departure of the mixture orpure apparent components can be calculated:

(12)

(12a)

Enthalpy and Entropy

For the enthalpy departure, the heat of reaction is considered. For anarbitrary gas phase reaction:


(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 thegeneral equation 14. The second or third equality relates the equilibriumconstant to the Gibbs energy of reaction, which is thus related to the enthalpyof reaction:

(15)

All components are assumed to be ideal. The enthalpy departure is equal tothe heat of reaction, per apparent number of moles:

(16)

(17)

From the Gibbs energy departure and enthalpy departure, the entropydeparture can be calculated:

(18)

Temperature derivatives for the thermodynamic properties can be obtainedby straightforward differentiation.

Usage

The HF equation-of-state should only be used for vapor phase calculations. Itis not suited for liquid phase calculations.

The HF equation-of-state can be used with any activity coefficient model fornonelectrolyte VLE. Using the Electrolyte NRTL model and the data packageMHF2 is strongly recommended for aqueous mixtures (de Leeuw andWatanasiri, 1993).ParameterName/Element


UpperLimit

Units

ESHFK/1 C0 43.65 — — — —

ESHFK/2 C1 -8910 — — — —

ESHFK/3 C2 0 — — — —

ESHFK/4 C3 0 — — — —

References

M. M. Abbott and H. C. van Ness, "Thermodynamics of Solutions ContainingReactive 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 Enthalpiesof the System Water and Hydroflouric Acid Using an HF Equation-of-state inConjunction with the Electrolyte NRTL Activity Coefficient Model," Paperpresented 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 ofGaseous Hydrogen and Deuterium Flourides," J. Am. Chem. Soc., Vol. 65,(1943), pp. 182 – 187.

C. E. Vanderzee and W. WM. Rodenburg, "Gas Imperfections andThermodynamic Excess Properties of Gaseous Hydrogen Fluoride," J. Chem.Thermodynamics, Vol. 2, (1970), pp. 461 – 478.

IAPWS-95 Steam TablesThe IAPWS-95 Steam Tables are implemented like any other equation-of-state in the Aspen Physical Property System. These steam tables can calculateany thermodynamic property of water. The tables form the basis of theIAPWS-95 property method. There are no parameter requirements. They arethe most accurate steam tables in the Aspen Physical Property System.

References

Wanger W. and A. Pruß, ”The IAPWS Formation 1995 for the ThermodynamicProperties of Ordinary Water Substance for General and Scientific Use,” J.Phys. Chem. Ref. Data, 31(2), 387- 535, 2002.

Ideal GasThe ideal gas law (ideal gas equation-of-state) combines the laws of Boyleand Gay-Lussac. It models a vapor as if it consisted of point masses withoutany interactions. The ideal gas law is used as a reference state for equation-of-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-KeslerThis equation-of-state model is based on the work of Lee and Kesler (1975).In this equation, the volumetric and thermodynamic properties of fluids basedon the Curl and Pitzer approach (1958) have been analytically represented bya modified Benedict-Webb-Rubin equation-of-state (1940). The modelcalculates the molar volume, enthalpy departure, Gibbs free energydeparture, and entropy departure of a mixture at a given temperature,pressure, and composition for either a vapor or a liquid phase. Partialderivatives of these quantities with respect to temperature can also becalculated.

Unlike the other equation-of-state models, this model does not calculatefugacity coefficients.


The compressibility factor and other derived thermodynamic functions ofnonpolar and slightly polar fluids can be adequately represented, at constantreduced temperature and pressure, by a linear function of the acentric factor.In particular, the compressibility factor of a fluid whose acentric factor is , isgiven by the following equation:

Z = Z(0) + Z(1)

Where:

Z(0) = Compressibility factor of a simple fluid ( = 0)

Z(1) = 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 andpressure.

Curl and Pitzer (1958) were quite successful in correlating thermodynamicand volumetric properties using the above approach. Their applicationemployed tables of properties in terms of reduced temperature and pressure.A significant weakness of this method is that the various properties (forexample, entropy departure and enthalpy departure) will not be exactlythermodynamically consistent with each other. Lee and Kesler (1975)overcame this drawback by an analytic representation of the tables with anequation-of-state. In addition, the range was extended by including new data.

In the Lee-Kesler implementation, the compressibility factor of any fluid hasbeen 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 generalizedequations of the BWR form in terms of reduced temperature and pressure.Thus,

Equations for the enthalpy departure, Gibbs free energy departure, andentropy departure are obtained from the compressibility factor using standardthermodynamic relationships, thus ensuring thermodynamic consistency.

In the case of mixtures, mixing rules (without any binary parameters) areused 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 volumetricand thermodynamic properties of mixtures containing nonpolar and slightlypolar components.Symbol Parameter Name Default Definition

Tc TCLK TC Critical temperature

Pc PCLK PC Critical pressure

OMGLK OMEGA Acentric factor


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-PlöckerThe Lee-Kesler-Plöcker equation-of-state is the basis for the LK-PLOCKproperty method. This equation-of-state applies to hydrocarbon systems thatinclude the common light gases, such as H2S and CO2. It can be used in gas-processing, 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 isfor a simple fluid, and fR is for reference fluid n-octane.

The mixing rules are:

Vcm =

=

=

Zm =

Where:

Vcij =

Tcij =

Zci =

kij = kji


The binary parameter kij is determined from phase-equilibrium dataregression, such as VLE data. The Aspen Physical Property System stores thebinary parameters for a large number of component pairs. These binaryparameters are used automatically with the LK-PLOCK property method. Ifbinary parameters for certain component pairs are not available, they can beestimated using built-in correlations. The correlations are designed for binaryinteractions among the components CO, CO2, N2, H2, CH4 alcohols andhydrocarbons. If a component is not CO, CO2, N2, H2, CH4 or an alcohol, it isassumed to be a hydrocarbon.ParameterName/Element


UpperLimit

Units

TCLKP Tci TC x 5.0 2000.0 TEMPERATURE

PCLKP pci PC x PRESSURE

VCLKP Vci VC x 0.001 3.5 MOLE-VOLUME

OMGLKP I OMEGA x -0.5 2.0 —

LKPZC Zcifcn() (Method 1)fcn(pci,Vci,Tci)(Method 2)

x 0.1 0.5 —

LKPKIJ kijfcn(TciVci / TcjVcj) x 5.0 5.0 —

Method 1 is the default for LKPZC; Method 2 can be invoked by setting thevalue of LKPZC equal to zero.

Binary interaction parameters LKPKIJ are available for a large number ofcomponents 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-LiquidEquilibria for Mixtures of Low Boiling Substances." Dechema Chemistry DataSeries, Vol. VI.

NBS/NRC Steam TablesThe NBS/NRC Steam Tables are implemented like any other equation-of-statein the Aspen Physical Property System. These steam tables can calculate anythermodynamic property of water. The tables form the basis of theSTEAMNBS and STMNBS2 property methods. There are no parameterrequirements. The STMNBS2 model uses the same equations as STEAMNBSbut with different root search method. The STEAMNBS method isrecommended for use with the SRK, BWRS, MXBONNEL and GRAYSON2property methods.


References

L. Haar, J.S. Gallagher, and J.H. Kell, "NBS/NRC Steam Tables," (Washington:Hemisphere Publishing Corporation, 1984).

NothnagelThe Nothnagel equation-of-state calculates thermodynamic properties for thevapor phase. It is used in property methods NRTL-NTH, UNIQ-NTH, VANL-NTH, and WILS-NTH. It is recommended for systems that exhibit strong vaporphase association. The model incorporates the chemical theory ofdimerization to account for strong association and solvation effects, such asthose 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 dimerizingcomponents i and j is:

The chemical equilibrium constant for the dimerization reaction on pressurebasis 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 apressure basis

When accounting for chemical reactions, the number of true species nt in themixture changes. The true molar volume V/nt is calculated from theequation-of-state. Since both V and nt change in about the same proportion,this number does not change much. However, the reported molar volume isthe total volume over the apparent number of species: V/na. Since theapparent number of species is constant and the total volume decreases with


association, the quantity V/na reflects the apparent contraction in anassociating 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 bydefault the arithmetic mean of the heats of reaction for the dimerizations of

the individual components. Parameter is a small empirical correctionfactor to this value:

The sum of the contributions of all dimerization reactions, corrected for theratio of apparent and true number of moles, is added to the molar enthalpydeparture:

The equilibrium constants can be computed using either built-in calculationsor parameters you entered.

Built-in correlations:

The pure component parameters b, d, and p are stored in the AspenPhysical Property System for many components.

Parameters you entered:

In this method, you enter Ai, Bi, Ci, and Di on the Properties ParametersUnary.T-Dependent form. The units for Kii is pressure-1; use absolute units fortemperature. If you enter Kii and Kjj, then Kij is computed from

If you enter Ai, Bi, Ci, and Di, the equilibrium constants are computed usingthe parameters you entered. Otherwise the equilibrium constants arecomputed using built-in correlations.ParameterName/Element

Symbol Default LowerLimit

Upper Limit Units

TC Tci — 5.0 2000.0 TEMPERATURE

TB Tbi — 4.0 2000.0 TEMPERATURE

PC pci — 105 108 PRESSURE

NTHA/1 bi 0.199 RTci / pci 0.01 1.0 MOLE-VOLUME

NTHA/2 di 0.33 0.01 3.0 —

NTHA/3 pi 0 0.0 1.0 —

NTHK/1 Ai — — — PRESSURE

NTHK/2 Bi 0 — — TEMPERATURE

NTHK/3 Ci 0 — — TEMPERATURE

NTHK/4 Di 0 — — TEMPERATURE




Upper Limit Units

NTHDDH 0† — — MOLE-ENTHALPY

† For the following systems, the values given in Nothnagel et al., 1973 areused 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 Correlationfor 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 ModelThis section describes the Copolymer Perturbed-Chain Statistical AssociatingFluid 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 modeldeveloped by Sadowski and co-workers (Gross and Sadowski, 2001, 2002a,2002b; Gross et al., 2003; Becker et al., 2004; Kleiner et al., 2006). Unlikethe PC-SAFT EOS model (POLYPCSF) in Aspen Plus, the copolymer PC-SAFTincludes the association and polar terms and does not apply mixing rules tocalculate the copolymer parameters from its segments. Its applicability coversfluid 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. Theunderlying idea is to divide the total intermolecular forces into repulsive andattractive contributions. The model uses a hard-chain reference system to


account for the repulsive interactions. The attractive forces are further dividedinto 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 ares 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; ares is defined as:

where a is the Helmholtz energy of a mixture and aig is the Helmholtz energyof 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 fractionstated in the denominator, while all other mole fractions are consideredconstant.

Applying to the departure equations, departure functions of enthalpy,

entropy, and Gibbs free energy can be obtained as follows:

Enthalpy departure:

Entropy departure:


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 offreely-jointed tangent spheres. The contribution from hard-chain fluids as areference system consists of two parts, a nonbonding contribution (i.e., hard-sphere mixtures prior to bonding to form chains) and a bonding contributiondue 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 followingequations:

where mi, i, and i are the segment number, the segment diameter, and

the segment energy parameter of the segment type in the copolymer


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 weightfraction 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 Bii 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 ghsi,j(di,j) is the

radial distribution function of hard-sphere mixtures at contact.

However, the calculation for Bii 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:


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 conditionset by Equation 2.70; the value for C is unity. Therefore:

A special case is the Sadowski’s model for random copolymer with two typesof segments only ( Gross et al., 2003; Becker et al., 2004). In this model, thebonding 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,


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 astatistical 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:


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:


In above equations, the model constants a1i, a2i, a3i, b1i, b2i, and b3i are fittedto pure-component vapor pressure and liquid density data of n-alkanes (Gross and Sadowski, 2001).

Association Term for Copolymer Mixtures - 2BModel

The association term in PC-SAFT model in general needs an iterativeprocedure to calculate the fraction of a species (solvent or segment) that arebounded to each association-site type. Only in pure or binary systems, thefraction can be derived explicitly for some specific models. We start withgeneral expressions for the association contribution for copolymer systems asfollows:

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-sitetype A; it can be estimated as follows:

with

where is the cross effective association volume and is thecross association energy; they are estimated via simple combination rules:

where and are the effective association volume and theassociation energy between the association-site types A and B, of the

segment type in the copolymer component i, respectively.


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 eachassociation-site type associated with a species in a component. In practice,further assumption is needed for efficiency. The commonly used model is theso-called 2B model ( Huang and Radosz, 1990). It assumes that anassociating species (solvent or segment) has two association sites, one isdesigned as the site type A and another as the site type B. Similarly to thehydrogen bonding, type A treats as a donor site with positive charge and typeB as an acceptor site with negative charge; only the donor-acceptorassociation bonding is permitted and this concept applies to both puresystems (self-association such as water) and mixtures (both self-associationand cross-association such as water-methanol). Therefore, we can rewritethese equations as follows:

It is easy to show that

Therefore


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

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), Applicationof 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. Foran 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: solvent-solvent, 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 parametersimplemented in Aspen Plus:




UpperLimit

MDS UnitsKeyword

Comments

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 xp — — — X — Unary

PCSKIJ/1 ai,j0.0 — — X — Binary,

Symmetric

PCSKIJ/2 bi,j0.0 — — X — Binary,

Symmetric

PCSKIJ/3 ci,j0.0 — — X — Binary,

Symmetric

PCSKIJ/4 di,j0.0 — — X — Binary,

Symmetric

PCSKIJ/5 ei,j0.0 — — X — Binary,

Symmetric

PCSKIJ/6 Tref 298.15 — — X TEMP Binary,Symmetric

Parameter Input and Regression for CopolymerPC-SAFT

Since the copolymer PC-SAFT is built based on the segment concept, theunary (pure) parameters must be specified for a solvent or a segment.Specifying a unary parameter for a polymer component (homopolymer orcopolymer) will be ignored by the simulation. For a non-association and non-polar solvent, three unary parameters PCSFTM, PCSFTU, and PCSFTV must bespecified. For a non-association and non-polar segment, these three unaryparameters PCSFTR, PCSFTU, and PCSFTV must be specified. For anassociation species (solvent or segment), two additional unary parametersPCSFAU and PCSFAV must be specified. For a polar species (solvent orsegment), two additional unary parameters PCSFMU and PCSFXP must bespecified.

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 segmentdiameter and in Debye (D) for the dipole moment; these units are not allowedto 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, thebinary parameter is set to be zero.


A databank called PC-SAFT contains both unary and binary PC-SAFTparameters available from literature; it must be used with the PC-SAFTproperty method. The unary parameters available for segments are stored inthe SEGMENT databank. If unary parameters are not available for a species(solvent or segment) in a calculation, the user can perform an Aspen PlusData Regression Run (DRS) to obtain unary parameters. For non-polymercomponents (mainly solvents), the unary parameters are usually obtained byfitting experimental vapor pressure and liquid molar volume data. To obtainunary parameters for a segment, experimental data on liquid density of thehomopolymer that is built by the segment should be regressed. Once theunary parameters are available for a segment, the ideal-gas heat capacityparameter CPIG may be regressed for the same segment using experimentalliquid heat capacity data for the same homopolymer. In addition to unaryparameters, the binary parameter PCSKIJ for each solvent-solvent pair, oreach solvent-segment pair, or each segment-segment pair, can be regressedusing vapor-liquid equilibrium (VLE) data in the form of TPXY data in AspenPlus.

Note: In Data Regression Run, a homopolymer must be defined as anOLIGOMER type, and the number of the segment that builds the oligomermust be specified.

Peng-RobinsonThe Peng-Robinson equation-of-state is the basis for the PENG-ROB and PR-BM property methods. The model has been implemented with choices ofdifferent alpha functions (see Peng-Robinson Alpha Functions) and has beenextended to include advanced asymmetric mixing rules.

Note: You can choose any of the available alpha functions, but you cannotdefine multiple property methods based on this model using different alphafunctions within the same run.

By default, the PENG-ROB property method uses the literature version of thealpha function and mixing rules. The PR-BM property method uses theBoston-Mathias alpha function and standard mixing rules. These defaultproperty methods are recommended for hydrocarbon processing applicationssuch as gas processing, refinery, and petrochemical processes. Their resultsare comparable to those of the property methods that use the standardRedlich-Kwong-Soave equation-of-state.

When advanced alpha function and asymmetric mixing rules are used withappropriately obtained parameters, the Peng-Robinson model can be used toaccurately model polar, non-ideal chemical systems. Similar capability is alsoavailable for the Soave-Redlich-Kwong model.

The equation for the Peng-Robinson model is:

Where:


b =

c =

a = a0+a1

a0 =

(the standard quadratic mixing term, where kij hasbeen made temperature-dependent)

kij =

kij = kji

a1

(an additional, asymmetric term used to modelhighly non-linear systems)

lij =

In general, .

ai =

bi =

ci =

For best results, the binary parameters kij and lij must be determined fromregression of phase equilibrium data such as VLE data. The Aspen PhysicalProperty System also has built-in kij and lij for a large number of componentpairs in the EOS-LIT databank from Knapp et al. These parameters are usedautomatically with the PENG-ROB property method. Values in the databankcan 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, byselecting a different alpha function and other model options. See Peng-Robinson Alpha Functions for a description of the alpha functions. See OptionCodes for Equation of State Models (under ESPR) for a list of the optioncodes.ParameterName/Element


UpperLimit

Units

PRTC Tci TC x 5.0 2000.0 TEMPERATURE

PRPC pci PC x 105 108 PRESSURE

OMGPR iOMEGA x -0.5 2.0 —

PRZRA zRA RKTZRA x — — —




UpperLimit

Units

PRKBV/1 kij(1) 0 x — — —

PRKBV/2 kij(2) 0 x — — TEMPERATURE

PRKBV/3 kij(3) 0 x — — TEMPERATURE

PRKBV/4 Tlower 0 x — — TEMPERATURE

PRKBV/5 Tupper 1000 x — — TEMPERATURE

PRLIJ/1 lij(1) 0 x — — —

PRLIJ/2 lij(2) 0 x — — TEMPERATURE

PRLIJ/3 lij(3) 0 x — — TEMPERATURE

PRLIJ/4 Tlower 0 x — — TEMPERATURE

PRLIJ/5 Tupper 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 rulesfor multicomponent mixtures: the problem of invariance," Fluid PhaseEquilibria, Vol 67, (1991), pp. 31-44.


Standard Peng-RobinsonThe Standard Peng-Robinson equation-of-state is the original formulation ofthe Peng-Robinson equation of state with the standard alpha function (seePeng-Robinson Alpha Functions). It is recommended for hydrocarbonprocessing applications such as gas processing, refinery, and petrochemicalprocesses. Its results are comparable to those of the standard Redlich-Kwong-Soave equation of state.


The equation for this model is:

Where:

b =

a =


ai =

bi =

kij =

The model has option codes which can be used to customize the model, byselecting a different alpha function and other model options. See Peng-Robinson Alpha Functions for a description of the alpha functions. See OptionCodes for Equation of State Models (under ESPRSTD) for a list of the optioncodes.

For best results, the binary parameter kij must be determined from regressionof phase equilibrium data such as VLE data. The Aspen Physical PropertySystem 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-ROBproperty method. Values in the databank can be different than those usedwith other models such as Soave-Redlich-Kwong or Redlich-Kwong-Soave,and this can produce different results.ParameterName/Element


UpperLimit

Units

TCPRS Tci TC x 5.0 2000.0 TEMPERATURE

PCPRS pci PC x 105 108 PRESSURE

OMGPRS iOMEGA x -0.5 2.0 —

PRKBV/1 kij(1) 0 x - - -

PRKBV/2 kij(2) 0 x - - TEMPERATURE

PRKBV/3 kij(3) 0 x - - TEMPERATURE

PRKBV/4 Tlower 0 x - - TEMPERATURE

PRKBV/5 Tupper 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-MHV2This model uses the Peng-Robinson equation-of-state for pure compounds.The mixing rules are the predictive MHV2 rules. Several alpha functions canbe used in the Peng-Robinson-MHV2 equation-of-state model for a moreaccurate description of the pure component behavior. The pure componentbehavior 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 purecompounds. The mixing rules are the predictive Holderbaum rules, or PSRKmethod. Several alpha functions can be used in the PSRK equation-of-statemodel for a more accurate description of the pure component behavior. Thepure component behavior and parameter requirements are described inStandard Redlich-Kwong-Soave and in Soave Alpha Functions.


The PSRK method is an example of modified Huron-Vidal mixing rules. A briefintroduction is provided in Huron-Vidal Mixing Rules. For more details, seePredictive Soave-Redlich-Kwong-Gmehling Mixing Rules.

Peng-Robinson-Wong-SandlerThis model uses the Peng-Robinson equation-of-state for pure compounds.The mixing rules are the predictive Wong-Sandler rules. Several alphafunctions can be used in the Peng-Robinson-Wong-Sandler equation-of-statemodel for a more accurate description of the pure component behavior. Thepure component behavior and parameter requirements are described in Peng-Robinson, and in Peng-Robinson Alpha Functions.


The Wong-Sandler mixing rules are an example of modified Huron-Vidalmixing rules. A brief introduction is provided in Huron-Vidal Mixing Rules. Formore details see Wong-Sandler Mixing Rules., this chapter.

Redlich-KwongThe Redlich-Kwong equation-of-state can calculate vapor phasethermodynamic properties for the following property methods: NRTL-RK,UNIFAC, UNIF-LL, UNIQ-RK, VANL-RK, and WILS-RK. It is applicable forsystems at low to moderate pressures (maximum pressure 10 atm) for whichthe vapor-phase nonideality is small. The Hayden-O'Connell model isrecommended for a more nonideal vapor phase, such as in systemscontaining organic acids. It is not recommended for calculating liquid phaseproperties.

The equation for the model is:

p =

Where:


=

b =

ai =

bi =



UpperLimit

Units



References

O. Redlich and J.N.S. Kwong, "On the Thermodynamics of Solutions V. AnEquation-of-state. Fugacities of Gaseous Solutions," Chem. Rev., Vol. 44,(1979), pp. 223 – 244.

Redlich-Kwong-AspenThe Redlich-Kwong-Aspen equation-of-state is the basis for the RK-ASPENproperty method. It can be used for hydrocarbon processing applications. It isalso used for more polar components and mixtures of hydrocarbons, and forlight 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 phase-equilibrium data regression, such as VLE data.ParameterName/Element


UpperLimit

Units

TCRKA Tci TC x 5.0 2000.0 TEMPERATURE

PCRKA pci PC x 105 108 PRESSURE

OMGRKA iOMEGA x -0.5 2.0 —

RKAPOL i0 x -2.0 2.0 —

RKAKA0 ka,ij0 0 x -5.0 5.0 —

RKAKA1 ka,ij1 0 x -15.0 15.0 TEMPERATURE

RKAKB0 kb,ij0 0 x -5.0 5.0 —

RKAKB1 kb,ij1 0 x -15.0 15.0 TEMPERATURE

References

Mathias, P.M., "A Versatile Phase Equilibrium Equation-of-state", Ind. Eng.Chem. Process Des. Dev., Vol. 22, (1983), pp. 385 – 391.

Redlich-Kwong-SoaveThis is the standard Redlich-Kwong-Soave equation-of-state, and is the basisfor the RK-SOAVE property method. It is recommended for hydrocarbonprocessing applications, such as gas-processing, refinery, and petrochemicalprocesses. Its results are comparable to those of the Peng-Robinsonequation-of-state.

The equation is:

Where:

a0 is the standard quadratic mixing term:

a1 is an additional, asymmetric (polar) term:


b =

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).


The model uses option codes which are described in Soave-Redlich-KwongOption Codes.

For best results, binary parameters kij must be determined from phase-equilibrium data regression (for example, VLE data). The Aspen PhysicalProperty System also has built-in kij for a large number of component pairs inthe EOS-LIT databank from Knapp et al. These binary parameters are usedautomatically with the RK-SOAVE property method. Values of kij in thedatabank can be different than those used with other models such as Soave-Redlich-Kwong or Standard Peng-Robinson, and this can produce differentresults.ParameterName/Element


UpperLimit

Units

TCRKSS Tci TC x 5.0 2000.0 TEMPERATURE

PCRKSS pci PC x 105 108 PRESSURE

OMRKSS iOMEGA x -0.5 2.0 —

RKSKBV/1 kij(1) 0 x -5.0 5.0 —

RKSKBV/2 kij(2) 0 x — — TEMPERATURE


RKSKBV/4 Tk,lower 0 x — — TEMPERATURE

RKSKBV/5 Tk,upper 1000 x — — TEMPERATURE

RKSLBV/1 lij(1) 0 x — — —

RKSLBV/2 lij(2) 0 x — — TEMPERATURE


RKSLBV/4 Tl,lower 0 x — — TEMPERATURE

RKSLBV/5 Tl,upper 1000 x — — TEMPERATURE

References

G. Soave, "Equilibrium Constants for Modified Redlich-Kwong Equation-of-state," Chem. Eng. Sci., Vol. 27, (1972), pp. 1196 – 1203.


J. Schwartzentruber and H. Renon, "Extension of UNIFAC to High Pressuresand 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.


Redlich-Kwong-Soave-Boston-MathiasThe Redlich-Kwong-Soave-Boston-Mathias equation-of-state is the basis forthe RKS-BM property method. It is the Redlich-Kwong-Soave equation-of-state with the Boston-Mathias alpha function (see Soave Alpha Functions). Itis recommended for hydrocarbon processing applications, such as gas-processing, refinery, and petrochemical processes. Its results are comparableto those of the Peng-Robinson-Boston-Mathias equation-of-state.


The equation is:

p =

Where:



b =

ai =

bi =

kij = kji


; ;

The parameter ai is calculated by the standard Soave formulation atsupercritical temperatures. If the component is supercritical, the Boston-Mathias extrapolation is used (see Soave Alpha Functions).


For best results, binary parameters kij must be determined from phase-equilibrium data regression (for example, VLE data).ParameterName/Element


UpperLimit

Units

TCRKS Tci TC x 5.0 2000.0 TEMPERATURE

PCRKS pci PC x 105 108 PRESSURE

OMGRKS iOMEGA x -0.5 2.0 —

RKSKBV/1 kij(1) 0 x -5.0 5.0 —



RKSKBV/4 Tk,lower 0 x — — TEMPERATURE

RKSKBV/5 Tk,upper 1000 x — — TEMPERATURE

RKSLBV/1 lij(1) 0 x — — —



RKSLBV/4 Tl,lower 0 x — — TEMPERATURE

RKSLBV/5 Tl,upper 1000 x — — TEMPERATURE

References

G. Soave, "Equilibrium Constants for Modified Redlich-Kwong Equation-of-state," Chem. Eng. Sci., Vol. 27, (1972), pp. 1196 – 1203.

Redlich-Kwong-Soave-Wong-SandlerThis equation-of-state model uses the Redlich-Kwong-Soave equation-of-statefor 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 purecomponent behavior. The pure component behavior and parameterrequirements are described in Standard Redlich-Kwong-Soave, and in SoaveAlpha Functions.


The Wong-Sandler mixing rules are an example of modified Huron-Vidalmixing rules. A brief introduction is provided in Huron-Vidal Mixing Rules. Formore details, see Wong-Sandler Mixing Rules.


Redlich-Kwong-Soave-MHV2This equation-of-state model uses the Redlich-Kwong-Soave equation-of-statefor pure compounds. The predictive MHV2 mixing rules are used. Severalalpha functions can be used in the RK-Soave-MHV2 equation-of-state modelfor a more accurate description of the pure component behavior. The purecomponent behavior and its parameter requirements are described inStandard Redlich-Kwong-Soave, and in Soave 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.

Schwartzentruber-RenonThe Schwartzentruber-Renon equation-of-state is the basis for the SR-POLARproperty method. It can be used to model chemically nonideal systems withthe same accuracy as activity coefficient property methods, such as theWILSON property method. This equation-of-state is recommended for highlynon-ideal systems at high temperatures and pressures, such as in methanolsynthesis and supercritical extraction applications.

The equation for the model is:

p =

Where:

a =

b =

c =

ai =

bi =

ci =

(for T < Tci)

ka,ij =

lij =


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 mostcases, ka,ij

0 and lij0 are sufficient to represent the system of interest.

VLE calculations are independent of c. However, c does influence the fugacityvalues and can be adjusted to (liquid) molar volumes. For a wide temperaturerange, adjust ci0 to the molar volume at 298.15K or at boiling temperature.

The ai are calculated using the Extended Mathias Alpha Function, as describedin Soave Alpha Functions.

Warning: Using c1i and c2i can cause anomalous behavior in enthalpy andheat capacity. Their use is strongly discouraged.ParameterName/Element


UpperLimit

Units

TCRKU Tci TC x 5.0 2000.0 TEMPERATURE

PCRKU pci PC x 105 108 PRESSURE

OMGRKU iOMEGA x -0.5 2.0 —

RKUPP0 †† q0i — x — — —

RKUPP1 †† q1i 0 x — — —

RKUPP2 †† q2i 0 x — — —

RKUC0 c0i 0 x — — ‡

RKUC1 c1i 0 x — — ‡

RKUC2 c2i 0 x — — ‡

RKUKA0 ††† ka,ij0 0 x — — —

RKUKA1 ††† ka,ij1 0 x — — TEMPERATURE

RKUKA2 ††† ka,ij2 0 x — — TEMPERATURE †

RKULA0 ††† lij0 0 x — — —

RKULA1 ††† lij1 0 x — — TEMPERATURE

RKULA2 ††† lij2 0 x — — TEMPERATURE †

RKUKB0 ††† kb,ij0 0 x — — —

RKUKB1 ††† kb,ij1 0 x — — TEMPERATURE

RKUKB2 ††† kb,ij2 0 x — — TEMPERATURE †

† Absolute temperature units are assumed for ka,ij2, lij

2, and kb,ij2.

†† For polar components (dipole moment >> 0), if you do not enter q0i, thesystem estimates q0i, q1i, q2i from vapor pressures using the Antoine vaporpressure model.

††† If you do not enter at least one of the binary parameters ka,ij0, ka,ij

2, lij0,

lij2, kb,ij

0, or kb,ij2 the system estimates ka,ij

0, ka,ij2, lij

0, and lij2 from the UNIFAC

or Hayden O'Connell models.


‡ RKUC0, RKUC1, and RKUC2 are treated as having units m3/kmol. No unitconversion to other molar volume units is done.

References

G. Soave, "Equilibrium Constants for Modified Redlich-Kwong Equation-of-state," Chem. Eng. Sci., Vol. 27, (1972), pp. 1196 - 1203.

J. Schwartzentruber and H. Renon, "Extension of UNIFAC to High Pressuresand Temperatures by the Use of a Cubic Equation-of-State," Ind. Eng. Chem.Res., Vol. 28, (1989), pp. 1049 – 1955.


Soave-Redlich-KwongThe Soave-Redlich-Kwong equation-of-state is the basis of the SRK propertymethod. 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 toimprove molar liquid volume calculated from the cubic equation of state.

Improvement in water properties is achieved by using the NBS SteamTable.

Improvement in speed of computation for equation based calculation isachieved by using composition independent fugacity.

Optional Kabadi-Danner mixing rules for improved phase equilibriumcalculations in water-hydrocarbon systems (see SRK-Kabadi-Danner)

Optional Mathias alpha function


This equation-of-state can be used for hydrocarbon systems that include thecommon light gases, such as H2S, CO2 and N2.


Where:


Where:

;



Where:

; ;

The enthalpy, entropy, Gibbs energy, and molar volume of water arecalculated from the steam tables. The total properties are mole-fractionaverages of these values with the properties calculated by the equation ofstate for other components. Fugacity coefficient is not affected.

For best results, the binary parameter kij must be determined from phaseequilibrium data regression (for example, VLE data). The Aspen PhysicalProperty System also has built-in kij for a large number of component pairs inthe SRK-ASPEN databank, regressed by AspenTech. These parameters areused automatically with the SRK property method. Values of kij in thedatabank can be different than those used with other models such asStandard Redlich-Kwong-Soave or Standard Redlich-Kwong-Soave, and thiscan produce different results.

The model uses option codes which are described in Soave-Redlich-KwongOption Codes.ParameterName/Element


UpperLimit

Units

SRKTC Tci TC x 5.0 2000.0 TEMPERATURE

SRKPC pci PC x 105 108 PRESSURE

SRKOMG iOMEGA x –0.5 2.0 —

SRKZRA zRA RKTZRA x — — —

SRKKIJ/1 kij(1) 0 x — — —

SRKKIJ/2 kij(2) 0 x — — TEMPERATURE


SRKKIJ/4 Tlower 0 x — — TEMPERATURE

SRKKIJ/5 Tupper 1000 x — — TEMPERATURE

SRKLIJ/1 lij(1) 0 x — — —

SRKLIJ/2 lij(2) 0 x — — TEMPERATURE




UpperLimit

Units

SRKLIJ/3 lij(3) 0 x — — TEMPERATURE

SRKLIJ/4 Tlower 0 x — — TEMPERATURE

SRKLIJ/5 Tupper 1000 x — — TEMPERATURE

References

G. Soave, "Equilibrium Constants for Modified Redlich-Kwong Equation-of-state," Chem. Eng. Sci., Vol. 27, (1972), pp. 1196 - 1203.


P.M. Mathias, H.C. Klotz, and J.M. Prausnitz, "Equation of state mixing rulesfor multicomponent mixtures: the problem of invariance," Fluid PhaseEquilibria, Vol 67, (1991), pp. 31-44.

SRK-Kabadi-DannerThe SRK-Kabadi-Danner property model uses the SRK equation-of-state withimproved phase equilibrium calculations for mixtures containing water andhydrocarbons. These improvements are achieved by using the Kabadi-Dannermixing rules.


Where:


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 Serieswith WaterHomologous series kwj

Alkanes 0.500

Alkenes 0.393

Dialkenes 0.311


Homologous series kwj

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 amolecule of hydrocarbon i.

gl is the group contribution parameter for groups constituting hydrocarbons.

Groups Constituting Hydrocarbons and Their GroupContribution ParametersGroup l gl , atm m6 x 105

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.


SRK-Kabadi-Danner uses the same parameters as SRK, with addedinteraction parameters. Do not specify values for the SRKLIJ parameterswhen using SRK-KD.




UpperLimit

Units

SRKTC Tci TC x 5.0 2000.0 TEMPERATURE

SRKPC pci PC x 105 108 PRESSURE

SRKOMG i OMEGA x –0.5 2.0 —

SRKWF Gi 0 x — — —

SRKZRA zRA RKTZRA x — — —

SRKKIJ/1 kij(1) 0 x — — —



SRKKIJ/4 Tlower 0 x — — TEMPERATURE

SRKKIJ/5 Tupper 0 x — — TEMPERATURE

References

V. Kabadi and R. P. Danner, "A Modified Soave-Redlich-Kwong Equation ofState for Water-Hydrocarbon Phase Equilibria", Ind. Eng. Chem. Process Des.Dev., Vol. 24, No. 3, (1985), pp. 537-541.

SRK-MLThe SRK-ML property model is the same as the Soave-Redlich-Kwong modelwith two exceptions:

kij does not equal kji for non-ideal systems; they are unsymmetric, and adifferent set of parameters is used, as shown below.

The lij are calculated from the equation lij = kji - kij



UpperLimit

Units

SMLTC Tci TC x 5.0 2000.0 TEMPERATURE

SMLPC pci PC x 105 108 PRESSURE

SMLOMG iOMEGA x –0.5 2.0 —

SMLZRA zRA RKTZRA x — — —

SMLCMP — 0 x — — —

SRKMLP — † x -2.0 2.0 †

SRKGLP — † x — — †

SMLKIJ/1 kij(1) 0 x — — —

SMLKIJ/2 kij(2) 0 x — — TEMPERATURE

SMLKIJ/3 kij(3) 0 x — — TEMPERATURE

SMLKIJ/4 Tlower 0 x — — TEMPERATURE

SMLKIJ/5 Tupper 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 settingoption code 4 to 1, but is disabled by default (in which case this parameter isnot used).

SMLCMP is the Composition Independent Fugacity Calculation Flag. You canuse this flag to indicate the component for which its fugacity coefficient in themixture will be calculated such that it is independent of composition. Thecalculated fugacity coefficient of that component is simply the pure-component fugacity coefficient. This is a simplification. Enter a value of 1 forthe element i to indicate that the fugacity coefficient of component i isindependent 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-StateThe VPA/IK-CAPE equation of state is similar to the HF equation of state butallows dimerization, tetramerization and hexamerization to occursimultaneously. The main assumption of the model is that only molecularassociation causes the gas phase nonideality. Attractive forces between themolecules 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 ofassociation can occur simultaneously, for example, in a mixture containingacetic acid and HF. Up to five components can associate, and any number ofinert components are allowed. This is the only difference between this modeland 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 ofassociation n=1, 2, 4, 6

zMij = True concentration of cross-dimers of components iand j, for i,j 1 to 5.

p0 = Reference pressure

k = Number of components


Association Equilibria

Every association equilibrium reaction

(1)

(2)

is described by the equilibrium constants

(3)

(4)

By setting

(5)

(6)

their temperature dependence can be reproduced.

To evaluate the true concentration of every complex zin, the followingnonlinear systems of equations are to be solved:

Total mass balance:The sum of true concentrations is unity.

(7)

Mass balance for every component i>1:The ratio of the monomers of each component i>1 and component i=1occurring in the various complexes must be equal to the ratio of theirapparent concentrations.

(8)

Thus, a system of k nonlinear equations for k unknowns zi1 has beendeveloped. After having solved it, all the zin and zMij can be determined using


equations (3, 4). This is the main step to evaluate all the properties neededfor a calculation.

Specific Volume of the Gas Phase

The compressibility factor is defined by the ratio between the number ofcomplexes and the number of monomers in the complexes.

(9)

The compressibility factor itself is

(10)

Fugacity Coefficient

As is well-known from thermodynamics, the fugacity coefficient can becalculated by

(11)

Isothermal Enthalpy Departure

According to the ASPEN enthalpy model, an equation of state must supply anexpression to compute the isothermal molar enthalpy departure between zeropressure 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 enthalpyper mole can be written as

(12)

with

(13)

to evaluate ha, a mixture consisting of N monomers integrated in the

complexes is considered. The quota of monomers i being integrated in acomplex of degree n is given by


(14)

and

(16)

respectively. For the reactions mentioned above:

(1)

(2)

the enthalpies of reaction are

(17)

(18)

as the van't Hoff equation

(19)

holds for this case.

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

(22)

and

(23)

(24)

Using the association model, more different species occur than can bedistinguished. Thus, the equivalent expression for the entropy of mixingshould be written with the true concentrations. As eq. 24 refers to 1 molemonomers, the expression should be weighted by the compressibility factorrepresenting the true number of moles. The new expression is

(25)

For ga we obtain

(26)

and, analogously,

(27)



UpperLimit

Units

DMER/1 Ai2 0 X – – –

DMER/2 Bi2 0 X – – TEMPERATURE

TMER/1 Ai4 0 X – – –

TMER/2 Bi4 0 X – – TEMPERATURE

HMER/1 Ai6 0 X – – –

HMER/2 Bi6 0 X – – TEMPERATURE

References

M. M. Abbott and H. C. van Ness, "Thermodynamics of Solutions ContainingReactive 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 Enthalpiesof the System Water and Hydrofluoric Acid Using an HF Equation-of-state inConjunction with the Electrolyte NRTL Activity Coefficient Model," PaperPresented at the 13th European Seminar on Applied Thermodynamics, June9–12, Carry-le-Rouet, France, 1993.


R. W. Long, J. H. Hildebrand, and W. E. Morrell, "The Polymerization ofGaseous Hydrogen and Deuterium Fluorides," J. Am. Chem. Soc., Vol. 65,(1943), pp. 182–187.

C. E. Vanderzee and W. Wm. Rodenburg, "Gas Imperfections andThermodynamic Excess Properties of Gaseous Hydrogen Fluoride," J. Chem.Thermodynamics, Vol. 2, (1970), pp. 461–478.

Peng-Robinson Alpha FunctionsThe pure component parameters for the Peng-Robinson equation-of-state arecalculated as follows:

(1)

(2)

These expressions are derived by applying the critical constraints to theequation-of-state under these conditions:

(3)

The parameter is a temperature function. It was originally introduced by

Soave in the Redlich-Kwong equation-of-state. This parameter improves thecorrelation of the pure component vapor pressure.

Note: You can choose any of the alpha functions described here, but youcannot define multiple property methods based on this model using differentalpha functions within the same run.

This approach was also adopted by Peng and Robinson:

(4)

Equation 3 is still represented. The parameter mi can be correlated with theacentric factor:

(5)

Equations 1 through 5 are the standard Peng-Robinson formulation. ThePeng-Robinson alpha function is adequate for hydrocarbons and othernonpolar compounds, but is not sufficiently accurate for polar compounds.

Note: Reduced temperature Tr is always calculated using absolutetemperature units.ParameterName/Element


UpperLimit

Units

TCPR Tci TC X 5.0 2000.0 TEMPERATURE

PCPR pci PC X 105 108 PRESSURE

OMGPR iOMEGA X -0.5 2.0 —


Boston-Mathias Extrapolation

For light gases at high reduced temperatures (> 5), equation 4 givesunrealistic 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 fortemperatures higher than critical:

(6)

With

=

=

Where mi is computed by equation 5, and equation 4 is used for subcriticaltemperatures. Additional parameters are not needed.

Extended Gibbons-Laughton Alpha Function

The extended Gibbons-Laughton alpha function is suitable for use with bothpolar and nonpolar components. It has the flexibility to fit the vapor pressureof most substances from the triple point to the critical point.

Where Tr is the reduced temperature; Xi, Yi and Zi are substance dependentparameters.

This function is equivalent to the standard Peng-Robinson alpha function if



UpperLimit

Units

PRGLP/1 X — X — — —

PRGLP/2 Y 0 X — — —

PRGLP/3 Z 0 X — — —

PRGLP/4 n 2 X — — —

PRGLP/5 Tlower 0 X — — TEMPERATURE

PRGLP/6 Tupper 1000 X — — TEMPERATURE

Twu Generalized Alpha Function

The Twu generalized alpha function is a theoretically-based function that iscurrently recognized as the best available alpha function. It behaves betterthan other functions at supercritical conditions (T > Tc) and when the acentricfactor is large. The improved behavior at high values of acentric factor isimportant for high molecular weight pseudocomponents. There is no limit onthe 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 ofstate and whether the temperature is above or below the critical temperatureof the component.

For Peng-Robinson equation of state:Subcritical T Supercritical T

L(0) 0.272838 0.373949

M(0) 0.924779 4.73020

N(0) 1.19764 -0.200000

L(1) 0.625701 0.0239035

M(1) 0.792014 1.24615

N(1) 2.46022 -8.000000

Twu Alpha Function

The Twu alpha function is a theoretically-based function that is currentlyrecognized as the best available alpha function. It behaves better than otherfunctions at supercritical conditions (T > Tc).

Where the L, M, and N are substance-dependent parameters that must bedetermined from regression of pure-component vapor pressure data or otherdata such as liquid heat capacity.ParameterName/Element


UpperLimit

Units

PRTWUP/1 L — X — — —

PRTWUP/2 M 0 X — — —

PRTWUP/3 N 0 X — — —

Mathias-Copeman Alpha Function

This is an extension of the Peng-Robinson alpha function which provides amore accurate fit of vapor pressure for polar compounds.

(7)

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 thetemperature is subcritical to regress the constants. If the temperature issupercritical, c2,i and c3,i are set to 0.ParameterName/Element


UpperLimit

Units






UpperLimit

Units

PRMCP/1 c1,i — X — — —

PRMCP/2 c2,i 0 X — — —

PRMCP/3 c3,i 0 X — — —

Schwartzentruber-Renon-Watanasiri Alpha Function

The Schwartzentruber-Renon-Watanasiri alpha function is:

(8)

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 polarparameters 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:

(9)

(10)



UpperLimit

Units



OMGPR iOMEGA X -0.5 2.0 —

PRSRP/1 — X — — —

PRSRP/2 0 X — — —

PRSRP/3 0 X — — —

Use of Alpha Functions

The alpha functions in Peng-Robinson-based equation-of-state models isprovided in the following table. You can verify and change the value ofpossible 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

ESPR0, ESPRESPRWS0, ESPRWSESPRV20, ESPRV2

000

Extended Gibbons-Laughton

ESPR0, ESPR 2

Twu Generalized alphafunction

ESPR0, ESPR 3

Twu alpha function ESPR0, ESPR 4


Alpha function Model name First Option code

Mathias-Copeman ESPRWS0, ESPRWSESPRV20, ESPRV2

22

Schwartzentruber-Renon-Watanasiri

ESPRWS0, ESPRWSESPRV20, ESPRV2

3 (default)3 (default)

References

J. F. Boston and P.M. Mathias, "Phase Equilibria in a Third-Generation ProcessSimulator" in Proceedings of the 2nd International Conference on PhaseEquilibria 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 Equation-of-state To Complex Mixtures: Evaluation of the Various Forms of the LocalComposition Concept",Fluid Phase Eq., Vol. 13, (1983), p. 91.

J. Schwartzentruber, H. Renon, and S. Watanasiri, "K-values for Non-IdealSystems:An Easier Way," Chem. Eng., March 1990, pp. 118-124.

G. Soave, "Equilibrium Constants for a Modified Redlich-Kwong Equation-of-state," 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 ofState 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 arecalculated as:

(1)

(2)

These expressions are derived by applying the critical constraint to theequation-of-state under these conditions:

(3)

Note: You can choose any of the alpha functions described here, but youcannot define multiple property methods based on this model using differentalpha functions within the same run.

In the Redlich-Kwong equation-of-state, alpha is:


(4)



UpperLimit

Units



Soave Modification

The parameter i is a temperature function introduced by Soave in theRedlich-Kwong equation-of-state to improve the correlation of the purecomponent vapor pressure:

(5)

Equation 3 still holds. The parameter mi can be correlated with the acentricfactor:

(6)

Equations 1, 2, 3, 5 and 6 are the standard Redlich-Kwong-Soaveformulation. The Soave alpha function is adequate for hydrocarbons and othernonpolar compounds, but is not sufficiently accurate for polar compounds.ParameterName/Element


UpperLimit

Units

TCRKS Tci TC X 5.0 2000.0 TEMPERATURE

PCRKS pci PC X 105 108 PRESSURE

OMGRKS i OMEGA X -0.5 2.0 —

Boston-Mathias Extrapolation

For light gases at high reduced temperatures (> 5), equation 5 givesunrealistic results. The boundary conditions are that attraction between

molecules should vanish for extremely high temperatures, and reducesasymptotically to zero. Boston and Mathias derived an alternative function fortemperatures higher than critical:

(7)

With

di =

ci =

Where:


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 moreaccurate fit of vapor pressure for polar compounds.

(8)

For i=0, equation 8 reduces to the standard Redlich-Kwong-Soaveformulation, equations 5 and 6. For temperatures above critical, the Boston-Mathias extrapolation is used, that is, equation 7 with:

(9)

(10)

The Mathias alpha function is used in the Redlich-Kwong-Aspen model, whichis the basis for the RK-ASPEN property method. This alpha function is alsoavailable as an option for SRK, SRKKD, SRK-ML, RK-SOAVE, and RKS-BM.See Soave-Redlich-Kwong Option Codes for more information.ParameterName/Element


UpperLimit

Units

TCRKA Tci TC X 5.0 2000.0 TEMPERATURE

PCRKA pci PC X 105 108 PRESSURE

OMGRKA i OMEGA X -0.5 2.0 —

† i — X -2.0 2.0 —

† RKAPOL for Redlich-Kwong-Aspen, SRKPOL for SRK and SRKKD, SRKMLP forSRK-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-Soaveformulation. You can use vapor pressure data to regress the constants if thetemperature is subcritical. Equation 11 is used only for temperatures belowcritical.

The Boston-Mathias extrapolation is used for temperatures above critical, thatis, with:

(12)


(13)

This alpha function is used in the Redlich-Kwong-UNIFAC model which is thebasis for the SR-POLAR property method.ParameterName/Element


UpperLimit

Units

TCRKU Tci TC X 5.0 2000.0 TEMPERATURE

PCRKU pci PC X 105 108 PRESSURE

OMGRKU i OMEGA X -0.5 2.0 —

RKUPP0 p1,i — X — — —

RKUPP1 p2,i 0 X — — —

RKUPP2 p3,i 0 X — — —

Mathias-Copeman Alpha Function

The Mathias-Copeman alpha function is suitable for use with both polar andnonpolar components. It has the flexibility to fit the vapor pressure of mostsubstances 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 vaporpressure data to regress the constants. If the temperature is supercritical, setc2,i and c3,i to 0.ParameterName/Element


UpperLimit

Units



RKSMCP/1 c1,i — X — — —

RKSMCP/2 c2,i 0 X — — —

RKSMCP/3 c3,i 0 X — — —

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 andp3,i are comparable with the c parameters of the Mathias-Copemanexpression. Equation 15 reduces to the standard Redlich-Kwong-Soaveformulation if the polar parameters are zero. Equation 15 is very similar tothe extended Mathias equation, but it is easier to use in data regression. It isused only for temperatures below critical. The Boston-Mathias extrapolation isused for temperatures above critical, that is, use equation 7 with:

(16)


(17)



UpperLimit

Units



OMGRKS i OMEGA X -0.5 2.0 —

RKSSRP/1 p1,i — X — — —

RKSSRP/2 p2,i 0 X — — —

RKSSRP/3 p3,i 0 X — — —

Extended Gibbons-Laughton Alpha Function

The extended Gibbons-Laughton alpha function is suitable for use with bothpolar and nonpolar components. It has the flexibility to fit the vapor pressureof most substances from the triple point to the critical point.

Where Tr is the reduced temperature; Xi, Yi and Zi are substance dependentparameters.

This function is equivalent to the standard Soave alpha function if

This function is not intended for use in supercritical conditions. To avoidpredicting negative alpha, when Tri>1 the Boston-Mathias alpha function isused instead.ParameterName/Element


UpperLimit

Units

SRKGLP/1 X — X — — —

SRKGLP/2 Y 0 X — — —

SRKGLP/3 Z 0 X — — —

SRKGLP/4 n 2 X — — —

SRKGLP/5 Tlower 0 X — — TEMPERATURE

SRKGLP/6 Tupper 1000 X — — TEMPERATURE

Twu Generalized Alpha Function

The Twu generalized alpha function is a theoretically-based function that iscurrently recognized as the best available alpha function. It behaves betterthan other functions at supercritical conditions (T > Tc) and when the acentricfactor is large. The improved behavior at high values of acentric factor isimportant for high molecular weight pseudocomponents. There is no limit onthe 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 ofstate and whether the temperature is above or below the critical temperatureof the component.

For Soave-Redlich-Kwong:Subcritical T Supercritical T

L(0) 0.544000 0.379919

M(0) 1.01309 5.67342

N(0) 0.935995 -0.200000

L(1) 0.544306 0.0319134

M(1) 0.802404 1.28756

N(1) 3.10835 -8.000000

Use of Alpha Functions

The use of alpha functions in Soave-Redlich-Kwong based equation-of-statemodels is given in the following table. You can verify and change the value ofpossible option codes on the Properties | Property Methods | Modelssheet.Alpha Function Model Name First Option Code

original RK ESRK0, ESRK —

standard RKS ESRKSTD0, ESRKSTD*

—1, 2 (default)

standard RKS/Boston-Mathias *ESRKSWS0, ESRKSWSESRKSV10, ESRKV1ESRKSV20, ESRKSV2

0111

Mathias/Boston-Mathias ESRKA0, ESRKA —

Extended Mathias/Boston-Mathias

ESRKU0, ESRKU —

Mathias-Copeman ESRKSV10, ESRKSV1ESRKSV20, ESRKSV2

22

Schwartzentruber-Renon-Watanasiri

ESPRWS0, ESPRWSESRKSV10, ESRKSV1ESRKSV20, ESRKSV2

3 (default)3 (default)3 (default)

Twu generalized * 5

Gibbons-Laughton with Patelextension

* 3

Mathias for T < Tc; Boston-Mathias for T > Tc

* 4

* 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 ProcessSimulator" in Proceedings of the 2nd International Conference on PhaseEquilibria 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 Equation-of-state To Complex Mixtures: Evaluation of the Various Forms of the LocalComposition Concept", Fluid Phase Eq., Vol. 13, (1983), p. 91.

O. Redlich and J. N. S. Kwong, "On the Thermodynamics of Solutions V. AnEquation-of-state. Fugacities of Gaseous Solutions," Chem. Rev., Vol. 44,(1949), pp. 223–244.

J. Schwartzentruber and H. Renon, "Extension of UNIFAC to High Pressuresand 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-IdealSystems:An Easier Way," Chem. Eng., March 1990, pp. 118-124.

G. Soave, "Equilibrium Constants for a Modified Redlich-Kwong Equation-of-state," Chem Eng. Sci., Vol. 27, (1972), pp. 1196-1203.

C.H. Twu, W.D. Sim, and V. Tassone, "Getting a Handle on Advanced CubicEquations of State", Chemical Engineering Progress, Vol. 98 #11 (November2002) pp. 58-65.

Huron-Vidal Mixing RulesHuron and Vidal (1979) used a simple thermodynamic relationship to equatethe excess Gibbs energy to expressions for the fugacity coefficient ascomputed by equations of state:

(1)

Equation 1 is valid at any pressure, but cannot be evaluated unless someassumptions are made. If Equation 1 is evaluated at infinite pressure, themixture must be liquid-like and extremely dense. It can be assumed that:

(2)

(3)

Using equations 2 and 3 in equation 1 results in an expression for a/b thatcontains the excess Gibbs energy at an infinite pressure:

(4)


Where:

(5)

The parameters 1and 2depend on the equation-of-state used. In general a

cubic equation-of-state can be written as:

(6)

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 theparameter. The mixing rule for b is fixed by equation 3. Even when used atother pressures, this expression contains the excess Gibbs energy at infinitepressure. You can use any activity coeffecient model to evaluate the excessGibbs energy at infinite pressure. Binary interaction coefficients must beregressed. The mixing rule used contains as many binary parameters as theactivity coefficient model chosen.

This mixing rule has been used successfully for polar mixtures at highpressures, such as systems containing light gases. In theory, any activitycoefficient model can be used. But the NRTL equation (as modified by Huronand Vidal) has demonstrated better performance.

The Huron-Vidal mixing rules combine extreme flexibility with thermodynamicconsistency, unlike many other mole-fraction-dependent equation-of-statemixing rules. The Huron-Vidal mixing rules do not allow flexibility in thedescription of the excess molar volume, but always predict reasonable excessvolumes.

The Huron-Vidal mixing rules are theoretically incorrect for low pressure,because quadratic mole fraction dependence of the second virial coefficient (ifderived from the equation-of-state) is not preserved. Since equations of stateare primarily used at high pressure, the practical consequences of thisdrawback are minimal.

The Gibbs energy at infinite pressure and the Gibbs energy at an arbitraryhigh pressure are similar. But the correspondence is not close enough tomake the mixing rule predictive.

There are several methods for modifying the Huron-Vidal mixing rule to makeit more predictive. The following three methods are used in Aspen PhysicalProperty 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)


These mixing rules are discussed separately in the following sections. Theyhave major advantages over other composition-dependent equation-of-statemixing rules.

References

M.- J. Huron and J. Vidal, "New Mixing Rules in Simple Equations of State forrepresenting Vapour-liquid equilibria of strongly non-ideal mixtures," FluidPhase Eq., Vol. 3, (1979), pp. 255-271.

MHV2 Mixing RulesDahl and Michelsen (1990) use a thermodynamic relationship between excessGibbs energy and the fugacity computed by equations of state. Thisrelationship is equivalent to the one used by Huron and Vidal:

(1)

The advantage is that the expressions for mixture and pure componentfugacities do not contain the pressure. They are functions of compacity V/b

and :

(2)

Where:

(3)

and

(4)

With:

(5)

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 conditionof 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:

(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:

(7)

Since q()is a universal function (for each equation-of-state), the

combination of equations 6 and 7 form the MHV2 mixing rule. Excess Gibbsenergies, 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-Vidalmixing rules:

(8)

This equation is equivalent to the assumption of zero excess molar volume.

The MHV2 mixing rule was the first successful predictive mixing rule forequations of state. This mixing rule uses previously determined activitycoefficient parameters for predictions at high pressures. UNIFAC was chosenas a default for its predictive character. The Lyngby modified UNIFACformulation was chosen for optimum performance (see UNIFAC (LyngbyModified)). However, any activity coefficient model can be used when itsbinary interaction parameters are known.

Like the Huron-Vidal mixing rules, the MHV2 mixing rules are not flexible inthe description of the excess molar volume. The MHV2 mixing rules aretheoretically incorrect at the low pressure limit. But the practicalconsequences of this drawback are minimal (see Huron-Vidal Mixing Rules,this chapter).

Reference: S. Dahl and M.L. Michelsen, "High-Pressure Vapor-LiquidEquilibrium with a UNIFAC-based Equation-of-state," AIChE J., Vol. 36,(1990), pp. 1829-1836.

Predictive Soave-Redlich-Kwong-GmehlingMixing RulesThese mixing rules by Holderbaum and Gmehling (1991) use a relationshipbetween the excess Helmholtz energy and equation-of-state. They do not usea relationship between equation-of-state properties and excess Gibbs energy,as in the Huron-Vidal mixing rules. The pressure-explicit expression for theequation-of-state is substituted in the thermodynamic equation:

(1)

The Helmholtz energy is calculated by integration. AE is obtained by:

(2)


Where both Ai* and Am are calculated by using equation 1. Ai* and Am arewritten in terms of equation-of-state parameters.

The simplification of constant packing fraction (Vm / b) is used:

(3)

With:

(4)

Therefore:

(5)

The mixing rule is:

(6)

Where ' is slightly different from for the Huron-Vidal mixing rule:

(7)

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 goesto 1. The excess Helmholtz energy is equal to the excess Gibbs energy. TheHuron-Vidal mixing rules are recovered.

The goal of these mixing rules is to be able to use binary interactionparameters for activity coefficient models at any pressure. These parametershave been optimized at low pressures. UNIFAC is chosen for its predictivecharacter. Two issues exist: the packing fraction is not equal to one, and theexcess Gibbs and Helmholtz energy are not equal at the low pressure wherethe UNIFAC parameters have been derived.

Fischer (1993) determined that boiling point, the average packing fraction forabout 80 different liquids with different chemical natures was 1.1. Adoptingthis value, the difference between liquid excess Gibbs energy and liquidexcess Helmholtz energy can be computed as:

(8)

The result is a predictive mixing rule for cubic equations of state. But theoriginal UNIFAC formulation gives the best performance for any binary pairwith interactions available from UNIFAC. Gas-solvent interactions areunavailable. However, it has poor accuracy for highly asymmetric such as CH4


– n-C10H22. To address the issue, the Li correction (Li et al., 1998) isapplied.

With the Li correction, the R and Q parameters for groups CH3, CH2, CH, andC in UNIFAC are modified. R* and Q*, the effective values of R and Q, arecalculated based on the original values and nc, the number of alkyl carbons(single-bonded carbons in CH3, CH2, CH, and C groups), as follows, fornc<45:

At the University of Oldenburg in Germany, the UNIFAC groups wereextended with often-occurring gases. New group interactions weredetermined from gas-solvent data, specific to the Redlich-Kwong-Soaveequation-of-state. The new built-in parameters to the Aspen Physical PropertySystem are activated when using the PSRK equation-of-state model.

The PSRK method has a lot in common with the Huron-Vidal mixing rules. Themole fraction is dependent on the second virial coefficient and excess volumeis predicted. These are minor disadvantages.

References

K. Fischer, "Die PSRK-Methode: Eine Zustandsgleichung unter Verwendungdes UNIFAC-Gruppenbeitragsmodells," (Düsseldorf: VDI Fortschrittberichte,Reihe 3: Verfahrenstechnik, Nr. 324, VDI Verlag GmbH, 1993).

T. Holderbaum and J. Gmehling, "PSRK: A Group Contribution Equation-of-state based on UNIFAC," Fluid Phase Eq., Vol. 70, (1991), pp. 251-265.

J. Li, K. Fischer, and J. Gmehling, "Prediction of vapor-liquid equilibria forasymmetric systems at low and high pressures with the PSRK model," FluidPhase Equilib., 1998, 143, 71-82

Wong-Sandler Mixing RulesThese mixing rules use a relationship between the excess Helmholtz energyand 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 thethermodynamic equation:

(1)

The Helmholtz energy is obtained by integration, AE is obtained by:

(2)

Where both Ai* and Am are calculated by using equation 1. Ai* and Am arewritten in terms of equation-of-state parameters.


Like Huron and Vidal, the limiting case of infinite pressure is used. Thissimplifies the expressions for Ai* and Am. Equation 2 becomes:

(3)

Where depends on the equation-of-state (see Huron-Vidal Mixing Rules).

Equation 3 is completely analogous to the Huron-Vidal mixing rule for theexcess Gibbs energy at infinite pressure. (See equation 4, Huron-Vidal MixingRules.) The excess Helmholtz energy can be approximated by the excessGibbs energy at low pressure from any liquid activity coefficient model. Usingthe Helmholtz energy permits another mixing rule for b than the linear mixingrule. The mixing rule for b is derived as follows. The second virial coefficientmust depend quadratically on the mole fraction:

(4)

With:

(5)

The relationship between the equation-of-state at low pressure and the virialcoefficient is:

(6)

(7)

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 beapproximated by the Gibbs energy at low pressure. The difference betweenthe two functions is corrected by fitting kij until the excess Gibbs energy fromthe equation-of-state (using the mixing rules 3 and 8) is equal to the excessGibbs energy computed by an activity coeffecient model. This is done at aspecific mole fraction and temperature.

This mixing rule accurately predicts the VLE of polar mixtures at highpressures. UNIFAC or other activity coeffecient models and parameters fromthe literature are used. Gas solubilities are not predicted. They must beregressed from experimental data.

Unlike other (modified) Huron-Vidal mixing rules, the Wong and Sandlermixing rule meets the theoretical limit at low pressure. The use of kij does


influence excess molar volume behavior. For calculations where densities areimportant, check whether they are realistic.

References

D. S. Wong and S. I. Sandler, "A Theoretically Correct New Mixing Rule forCubic 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 forNon-ideal Mixtures Using Available Activity Coefficient Model Parameters andThat 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-statePredictions at High Temperatures and Pressures Using the Existing UNIFACModel," Fluid Phase Eq., Vol. 85, (1993), pp. 41 – 54.

Activity Coefficient ModelsThe Aspen Physical Property System has the following built-in activitycoefficient models. This section describes the activity coefficient modelsavailable.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 saltreference 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


Model Type

Wilson Local composition

Wilson with Liquid Molar Volume Local composition

Bromley-Pitzer Activity Coefficient ModelThe Bromley-Pitzer activity coefficient model is a simplified Pitzer activitycoefficient model with Bromley correlations for the interaction parameters.See Working Equations for a detailed description. This model has predictivecapabilities. It can be used to compute activity coefficients for aqueouselectrolytes up to 6 molal ionic strength, but is less accurate than the Pitzermodel if the parameter correlations are used. The model should not be usedfor mixed-solvent electrolyte systems.

The Bromley-Pitzer model in the Aspen Physical Property System involvesuser-supplied parameters, used in the calculation of binary parameters for theelectrolyte system.

Parameters (0), (1), (2), (3), and have five elements to account for

temperature dependencies. Elements P1 through P5 follow the temperaturedependency relation:

Where:

Tref = 298.15K

The user must:

Supply these elements using a Properties Parameters Binary T-Dependentform.

Specify Comp ID i and Comp ID j on this form, using the same order thatappears on the Components Specifications Selection sheet form.

Parameter Name Symbol No. of ElementsDefault Units

Ionic Unary Parameters

GMBPB ion1 0 —

GMBPD ion1 0 —

Cation-Anion Parameters

GMBPB0 (0) 5 0 —

GMBPB1 (1) 5 0 —

GMBPB2 (2) 5 0 —

GMBPB3 (3) 5 0 —

Cation-Cation Parameters

GMBPTH cc'5 0 —

Anion-Anion Parameters

GMBPTH aa'5 0 —

Molecule-Ion and Molecule-Molecule Parameters

GMBPB0 (0) 5 0 —


Parameter Name Symbol No. of ElementsDefault Units

Ionic Unary Parameters

GMBPB1 (1) 5 0 —

Working Equations

The complete Pitzer equation (Fürst and Renon, 1982) for the excess Gibbsenergy is (see also equation 4):

(1)

Where:

GE = Excess Gibbs energy

R = Gas constant

T = Temperature

nw = Kilograms of water

zi = Charge number of ion i

= molality of ion i

Where:

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 ActivityCoefficient 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.

(2)

Where:

Bij = f(ij(0),ij

(1),ij(2),ij

(3))


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 PropertyData, 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 ActivityCoefficient Model.

References

L.A. Bromley, "Thermodynamic Properties of Strong Electrolytes in AqueousSolution, " AIChE J., Vol. 19, No. 2, (1973), pp. 313 – 320.

W. Fürst and H. Renon, "Effects of the Various Parameters in the Applicationof Pitzer's Model to Solid-Liquid Equilibrium. Preliminary Study for Strong 1-1Electrolytes," 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-NullThe Chien-Null model calculates liquid activity coefficients and it can be usedfor highly non-ideal systems. The generalized expression used in its derivationcan be adapted to represent other well known formalisms for the activitycoefficient by properly defining its binary terms. This characteristic allows themodel the use of already available binary parameters regressed for thoseother liquid activity models with thermodynamic consistency.

The equation for the Chien-Null liquid activity coeficient is:

Where:

Rji = Aji / Aij

Aii = 0


Aij = aij + bij / T

Subscripts i and j are component indices.

The choice of model and parameters can be set for each binary pairconstituting the process mixture by assigning the appropriate value to theICHNUL parameter.

The Regular Solution and Scatchard-Hamer models are regained bysubstituting in the general expression (ICHNUL = 1 or 2).

Vji = Sji = Vj*,l / Vi

*,l

Where:

Vj*,l = Liquid molar volume of component i

The Chien-Null activity coefficient model collapses to the Margules liquidactivity coefficient expression by setting (ICHNUL = 3):

Vji = Sji = 1

The Van Laar Liquid activity coefficient model is obtained when the V and Sparameters in the Chien-Null models are set to the ratio of the cross terms ofA (ICHNUL = 4:)

Vji = Sji = Aji / Aij

Finally, the Renon or NRTL model is obtained when we make the followingsusbstitutions in the Chien-Null expression for the liquid activity (ICHNUL =5).

Sji = RjiAji / Aij

Aji = 2jiGji

Vji = Gji

The following are defined for the Non-Random Two-Liquid activity coefficientmodel, 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 bedetermined from regression of VLE and/or LLE data. Also, if you haveparameters 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 selectingthe proper code (ICHNUL) to identify the source model and entering theappropriate activity model parameters.




UpperLimit

Units

ICHNUL — 3 1 6 —

CHNULL/1 aij 0 — — —

CHNULL/2 bij 0 — — —

CHNULL/3 Vij 0 — — —

The parameter ICHNUL is used to identify the activity model parametersavailable for each binary pair of interest. The following values are allowed forICHNUL:

ICHNUL = 1 or 2, sets the model to the Scatchard-Hamer or regular solutionmodel for the associated binary;

ICHNUL = 3, sets the model to the Three-Suffix Margules activity model forthe associated binary;

ICHNUL = 4, sets the model to the Van Laar formalism for the activity modelfor the associated binary;

ICHNUL = 5, sets the model to the NRTL (Renon) formalism for the activitymodel for the associated binary.

ICHNUL = 6, sets the model to the full Chien-Null formalism for the activitymodel for the associated binary.

When you specify a value for the ICHNUL parameter that is different than thedefault, you must enter the appropriate binary model parameters for thechosen activity model directly. The routine will automatically convert theexpressions and parameters to conform to the Chien-Null formulation.

Constant Activity CoefficientThis approach is used exclusively in metallurgical applications where multipleliquid and solid phases can coexist. You can assign any value to the activitycoefficient of component i. Use the Properties Parameters Unary Scalar form.The equation is:

i = ai


Symbol Default MDS UpperLimit

LowerLimit

Units

GMCONS ai 1.0 x — — —

COSMO-SACCosmo-SAC is a solvation model that describes the electric fields on themolecular surface of species that are polarizable. It requires a fairlycomplicated quantum mechanical calculation, but this calculation must bedone only once for a particular molecule; then the results can be stored. In itsfinal form, it uses individual atoms as the building blocks for predicting phaseequilibria instead of functional groups. This model formulation provides aconsiderably larger range of applicability than group-contribution methods.

The calculation for liquid nonideality is only slightly more computationallyintensive than activity-coefficient models such as NRTL or UNIQUAC. Cosmo-


SAC complements the UNIFAC group-contribution method, because it isapplicable to virtually any mixture.

The Cosmo-SAC model calculates liquid activity coefficients. The equation forthe Cosmo-SAC model is:

With


Where:

i= Activity coefficient of component i

iSG = Staverman-Guggenheim model for combinatorial

contribution to i

i(m) = Segment activity coefficient of segment m in

component i

S(m) = Segment activity coefficient of segment m in

solvent mixture

pi(m) = Sigma profile of component i

pi(m) = Sigma profile of solvent mixture

= Surface charge density

W(m,n) = Exchange energy between segments m and n

WHB(m,n) = Hydrogen-bonding contribution to exchange energy

between segments m and n

z = Coordination number, 10

Vi = Molecular volume of component i

Ai = Molecular surface area of component i

aeff = Standard segment surface area, 7.50 Å2

Veff = Standard component volume, 66.69 Å3

Aeff = Standard component surface area, 79.53 Å2

' = Misfit energy constant

The Cosmo-SAC model does not require binary parameters. For eachcomponent, it has six input parameters. CSACVL is the component volumeparameter which is always defined in cubic angstroms, regardless of chosenunits sets. SGPRF1 to SGPRF5 are five component sigma profile parameters;each can store up to 12 points of sigma profile values. All six inputparameters are obtained from COSMO calculation. The Aspen PhysicalProperty System includes a database of sigma profiles for over 1400compounds from Mullins et al. (2006). The parameters were obtained bypermission from the Virginia Tech Sigma Profile Database website(http://www.design.che.vt.edu/VT-2004.htm). Aspen Technology, Inc. doesnot claim proprietary rights to these parameters.

Note: Starting in version V7.2, additional parameters SGPRF6 throughSGPRF9 and SGPR10 through SGPR14 are available in Aspen Plus andAspen Properties, as part of a planned expansion to allow larger sigmaprofiles to be used. However, the model is not yet updated to use theseparameters and you should not yet try to use sigma profiles larger than 51elements.




UpperLimit

Units

CSACVL Vi — x — — VOLUME (Å3)

SGPRF1 Ai pi(1-12) — x — — —

SGPRF2 Ai pi(13-24) — x — — —

SGPRF3 Ai pi(25-36) — x — — —

SGPRF4 Ai pi(37-48) — x — — —

SGPRF5 Ai pi(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 tablebelow:OptionCode

Description

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 (Linet al., 2002)

References

A. Klamt, "Conductor-like Screening Model for Real Solvents: A New Approachto 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-BondingSystems from a New Expression for COSMO Solvation Models," presented atthe AIChE Annual Meeting, Indianapolis, IN, 3-8 November (2002).

S.-T. Lin and S. I. Sandler, "A Priori Phase Equilibrium Prediction from aSegment Contribution Solvation Model," Ind. Eng. Chem. Res. 41, 899(2002).

E. Mullins, et al. "Sigma-Profile Database for Using COSMO-BasedThermodynamic Methods," Ind. Eng. Chem. Res. 45, 4389 (2006).

Electrolyte NRTL Activity Coefficient Model(GMENRTL)The Electrolyte NRTL activity coefficient model (GMENRTL) is a versatilemodel for the calculation of activity coefficients. Using binary and pairparameters, the model can represent aqueous electrolyte systems as well asmixed solvent electrolyte systems over the entire range of electrolyteconcentrations. This model can calculate activity coefficients for ionic speciesand molecular species in aqueous electrolyte systems as well as in mixedsolvent electrolyte systems. The model reduces to the well-known NRTLmodel when electrolyte concentrations become zero (Renon and Prausnitz,1969).


The electrolyte NRTL model uses the infinite dilution aqueous solution as thereference state for ions. It adopts the Born equation to account for thetransformation of the reference state of ions from the infinite dilution mixedsolvent solution to the infinite dilution aqueous solution.

Water must be present in the electrolyte system in order to compute thetransformation of the reference state of ions. Thus, it is necessary tointroduce a trace amount of water to use the model for nonaqueouselectrolyte systems.

The Aspen Physical Property System uses the electrolyte NRTL model tocalculate activity coefficients, enthalpies, and Gibbs energies for electrolytesystems. Model development and working equations are provided inTheoretical 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, andelectrolyte-electrolyte pairs

The pure component dielectric constant coefficients of nonaqueous solventsand Born radius of ionic species are required only for mixed-solventelectrolyte systems. The temperature dependency of the dielectric constant ofsolvent 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 mustshare either one common cation or one common anion:


Where:

Tref = 298.15K

Many parameter pairs are included in the electrolyte NRTL model parameterdatabank (see Physical Property Data, Chapter 1).ParameterName

Symbol No. ofElements

Default MDS Units

Dielectric Constant Unary Parameters

CPDIEC AB 1 — — —

BB 1 0 — —

CB 1 298.15 — TEMPERATURE†

Ionic Born Radius Unary Parameters

RADIUS ri 1 3x10-10 — LENGTH

Molecule-Molecule Binary Parameters

NRTL/1 ABB' — 0 x —

AB'B — 0 x —

NRTL/2 BBB' — 0 x TEMPERATURE†

BB'B — 0 x TEMPERATURE†

NRTL/3 BB' = B'B— .3 x —

NRTL/4 — — 0 x TEMPERATURE

NRTL/5 FBB' — 0 x TEMPERATURE

FB'B — 0 x TEMPERATURE

NRTL/6 GBB' — 0 x TEMPERATURE

GB'B — 0 x TEMPERATURE

Electrolyte-Molecule Pair Parameters

GMELCC Cca,B 1 0 x —

CB,ca 1 0 x —

GMELCD Dca,B 1 0 x TEMPERATURE†

DB,ca 1 0 x TEMPERATURE†

GMELCE Eca,B 1 0 x —

EB,ca 1 0 x —

GMELCN ca,B = B,ca1 .2 x —

Electrolyte-Electrolyte Pair Parameters

GMELCC Cca',ca'' 1 0 x —

Cca'',ca' 1 0 x —

Cc'a,c''a 1 0 x —

Cc''a,c'a 1 0 x —

GMELCD Dca',ca'' 1 0 x TEMPERATURE †

Dca'',ca' 1 0 x TEMPERATURE†

Dc'a,c''a 1 0 x TEMPERATURE†

Dc''a,c'a 1 0 x TEMPERATURE†

GMELCE Eca',ca'' 1 0 x —


ParameterName


Default MDS Units


Eca'',ca' 1 0 x —

Ec'a,c''a 1 0 x —

Ec''a,c'a 1 0 x —

GMELCN ca',ca'' = ca'',ca'1 .2 x —

c'a,c''a = c''a,c'a1 .2 x —

† Certain Electrolyte NRTL activity coefficient model parameters are used withreciprocal temperature terms:

CPDIEC

NRTL/2

GMELCD for electrolyte-electrolyte or electrolyte-molecule pairs

When any of these parameters is specified, absolute temperature units areused for the calculations in this model.

Reference: H. Renon, and J.M. Prausnitz, "Local Compositions inThermodynamic 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 workingequations are given. The different ways parameters can be obtained arediscussed with references to the databank directories and the DataRegression System (DRS). The parameter requirements of the model aregiven in Electrolyte NRTL Activity Coefficient Model.

Development of the Model

The Electrolyte NRTL model was originally proposed by Chen et al., foraqueous electrolyte systems. It was later extended to mixed solventelectrolyte systems (Mock et al., 1984, 1986). The model is based on twofundamental assumptions:

The like-ion repulsion assumption: states that the local composition ofcations around cations is zero (and likewise for anions around anions).This is based on the assumption that the repulsive forces between ions oflike charge are extremely large. This assumption may be justified on thebasis that repulsive forces between ions of the same sign are very strongfor neighboring species. For example, in salt crystal lattices the immediateneighbors of any central ion are always ions of opposite charge.

The local electroneutrality assumption: states that the distribution ofcations and anions around a central molecular species is such that the netlocal ionic charge is zero. Local electroneutrality has been observed forinterstitial molecules in salt crystals.

Chen proposed an excess Gibbs energy expression which contains twocontributions: one contribution for the long-range ion-ion interactions thatexist beyond the immediate neighborhood of a central ionic species, and the


other related to the local interactions that exist at the immediateneighborhood of any central species.

The unsymmetric Pitzer-Debye-Hückel model and the Born equation are usedto represent the contribution of the long-range ion-ion interactions, and theNon-Random Two Liquid (NRTL) theory is used to represent the localinteractions. The local interaction contribution model is developed as asymmetric model, based on reference states of pure solvent and purecompletely dissociated liquid electrolyte. The model is then normalized byinfinite dilution activity coefficients in order to obtain an unsymmetric model.This NRTL expression for the local interactions, the Pitzer-Debye-Hückelexpression, and the Born equation are added to give equation 1 for theexcess Gibbs energy (see the following note).

(1)

This leads to

(2)

Note: The notation using * to denote an unsymmetric reference state is well-accepted in electrolyte thermodynamics and will be maintained here. Thereader should be warned not to confuse it with the meaning of * in classicalthermodynamics 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 Modelfor Excess Gibbs Energy of Electrolyte Systems: Part I: Single Solvent, SingleCompletely 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 GibbsEnergy 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-SolventElectrolyte Systems: A New Thermodynamic Model," Proceedings of the 1984Summer Computer Simulation Conference, p. 558.

B. Mock, L.B. Evans, and C.-C. Chen, "Thermodynamic Representation ofPhase 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 forsolvent and zero for electrolytes, is used to represent the long-rangeinteraction contribution.


with

(3)

(4)

(5)

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)


zi = Charge number of ion i

= "Closest approach" parameter

Taking the appropriate derivative of equation 3, an expression for the activitycoefficient can then be derived.

(6)

The Born equation is used to account for the Gibbs energy of transfer of ionicspecies from the infinite dilution state in a mixed-solvent to the infinitedilution state in aqueous phase.

(7)

Where:

w= Dielectric constant of water

ri = Born radius of the ionic species i


The expression for the activity coefficient can be derived from (7):

(8)

The Debye-Hückel theory is based on the infinite dilution reference state forionic species in the actual solvent media. For systems with water as the onlysolvent, the reference state is the infinite dilution aqueous solution. Formixed-solvent systems, the reference state for which the Debye-Hückeltheory remains valid is the infinite dilution solution with the correspondingmixed-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 areadequate to calculate them as follows:

(6a)

(7a)

(8a)

(8b)

(8c)

(8d)

Where:

xm = Mole fraction of the solvent m in the solution

Mm = Molecular weight of the solvent m

Vml = 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-watersolvents.

Vnwsl = Liquid molar volume for the mixture of all non-

water solvents. It is calculated using theRackett 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 TwoLiquid theory. The basic assumption of the NRTL model is that the nonidealentropy of mixing is negligible compared to the heat of mixing: this is indeedthe case for electrolyte systems. This model was adopted because of itsalgebraic simplicity and its applicability to mixtures that exhibit liquid phasesplitting. The model does not require specific volume or area data.

The effective local mole fractions Xji and Xii of species j and i, respectively, inthe neighborhood of i are related by:

(9)

Where:

Xj = xjCj

(Cj = zj for ions and Cj = unity for molecules)

Gji =

ji=

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,

(10)

Where:

Gji,ki =

ji,ki=

ji,ki= Nonrandomness factor

Apparent Binary Systems

The derivations that follow are based on a simple system of one completelydissociated liquid electrolyte ca and one solvent B. They will be later extended


to multicomponent systems. In this simple system, three differentarrangements exist:

In the case of a central solvent molecule with other solvent molecules,cations, and anions in its immediate neighborhood, the principle of localelectroneutrality is followed: the surrounding cations and anions are such thatthe neighborhood of the solvent is electrically neutral. In the case of a centralcation (anion) with solvent molecules and anions (cations) in its immediateneighborhood, the principle of like-ion repulsion is followed: no ions of likecharge exist anywhere near each other, whereas opposite charged ions arevery close to each other.

The effective local mole fractions are related by the following expressions:

(central solvent cells)(11)

(central cation cells)(12)

(central anion cells)(13)

Using equation 11 through 13 and the notation introduced in equations 9 and10 above, expressions for the effective local mole fractions in terms of theoverall 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 Gibbsenergies, per mole of cells of central cation, anion, or solvent, respectively, be

, , and . These are then related to theeffective local mole fractions:

(17)

(18)

(19)


The reference Gibbs energy is determined for the reference states ofcompletely dissociated liquid electrolyte and of pure solvent. The referenceGibbs energies per mole are then:

(20)

(21)

(22)

Where:

zc = Charge number on cations

za = Charge number on anions

The molar excess Gibbs energy can be found by summing all changes inresidual Gibbs energy per mole that result when the electrolyte and solvent intheir reference state are mixed to form the existing electrolyte system. Theexpression is:

(23)

Using the previous relation for the excess Gibbs energy and the expressionsfor the residual and reference Gibbs energy (equations 17 to 19 and 20 to22), the following expression for the excess Gibbs energy is obtained:

(24)

The assumption of local electroneutrality applied to cells with central solventmolecules may be stated as:

(25)

Combining this expression with the expression for the effective local molefractions given in equations 9 and 10, the following equality is obtained:

(26)

The following relationships are further assumed for nonrandomness factors:

(27)

(28)

and,

(29)

It can be inferred from equations 9, 10, and 26 to 29 that:

(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 normalizedto the infinite dilution reference state for ions:

(32)

This leads to:

(33)

By taking the appropriate derivatives of equation 33, expressions for theactivity coefficients of all three species can be determined.

(34)

(35)

(36)

Multicomponent Systems

The Electrolyte NRTL model can be extended to handle multicomponentsystems.

The excess Gibbs energy expression is:


(37)

Where:

j and k can be any species (a, C, or B)

The activity coefficient equation for molecular components is given by:

(38)

The activity coefficient equation for cations is given by:

(39)

The activity coefficient equation for anions is given by:

(40)

Where:


(41)

(42)

(43)

(44)

(45)

(46)

(47)

(48)

It should be understood that and remained constant inequation 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 electrolytesmust 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 solventsand Born radius of ionic species are required only for mixed-solventelectrolyte systems.

The temperature dependency relations of these parameters are given inElectrolyte NRTL Activity Coefficient Model.

Heat of mixing is calculated from temperature derivatives of activitycoefficients. Heat capacity is calculated from secondary temperaturederivative of the activity coefficient. As a result, the temperature dependentparameters are critical for modeling enthalpy correctly. It is recommendedthat enthalpy data and heat capacity data be used to obtain thesetemperature dependency parameters. See also Electrolyte NRTL Enthalpy andElectrolyte NRTL Gibbs Energy.

Obtaining Parameters

In the absence of electrolytes, the electrolyte NRTL model reduces to theNRTL equation which is widely used for non-electrolyte systems. Therefore,molecule-molecule binary parameters can be obtained from binarynonelectrolyte systems.

Electrolyte-molecule pair parameters can be obtained from data regression ofapparent single electrolyte systems.

Electrolyte-electrolyte pair parameters are required only for mixedelectrolytes with a common ion. Electrolyte-electrolyte pair parameters canaffect trace ionic activity precipitation. Electrolyte-electrolyte pair parameterscan be obtained by regressing solubility data of multiple componentelectrolyte systems.

When the electrolyte-molecule and electrolyte-electrolyte pair parameters arezero, the electrolyte NRTL model reduces to the Debye-Hückel limiting law.Calculation results with electrolyte-molecule and electrolyte-electrolyte pairparameters fixed to zero should be adequate for very dilute weak electrolytesystems; however, for concentrated systems, pair parameters are requiredfor accurate representation.

See Physical Property Data, Chapter 1, for the pair parameters available fromthe electrolyte NRTL model databank. The table contains pair parameters forsome electrolytes in aqueous solution at 100C. These values were obtainedby using the Aspen Physical Property Data Regression System (DRS) toregress vapor pressure and mole fraction data at T=100C 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), vaporpressure (mmHg), and mole fractions were set at 0.2, 1.0, and 0.001,respectively. In addition, complete dissociation of the electrolyte wasassumed for all cases.

Option Codes for Electrolyte NRTL ActivityCoefficient Model (GMENRTL)

The electrolyte NRTL activity coefficient model (GMENRTL) has three optioncodes and the option codes can affect the performance of this model.


Option code 1. Use this option code to specify the default values of pairparameters for water/solute and solvent/solute; the solute represents acation/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 thesolvent/solvent binary parameters obtained from NRTL parameters.

ENRTL-SACeNRTL-SAC (ENRTLSAC, patent pending) is an extension of the nonrandomtwo-liquid segment activity coefficient model (NRTL-SAC, patent pending) byChen and Song (Ind. Eng. Chem. Res., 2004, 43, 8354) to includeelectrolytes in the solution. It can be used in usable in Aspen Properties andAspen Polymers. It is intended for the computation of ionic activitycoefficients and solubilities of electrolytes, organic and inorganic, in commonsolvents and solvent mixtures. In addition to the three types of molecularparameters defined for organic nonelectrolytes in NRTL-SAC (hydrophobicityX, hydrophilicity Z, and polarity Y- and Y+), an electrolyte parameter, E, isintroduced to characterize both local and long-range ion-ion and ion-moleculeinteractions attributed to ionized segments of electrolytes.

In applying the segment contribution concept to electrolytes, a newconceptual electrolyte segment e corresponding to the electrolyte parameterE, is introduced. This conceptual segment e would completely dissociate to acationic segment (c) and an anionic segment (a), both of unity charge. Allelectrolytes, organic or inorganic, symmetric or unsymmetric, univalent ormultivalent, are to be represented with this conceptual uni-univalentelectrolyte segment e together with previously defined hydrophobic segmentx, polar segments y- and y+, and hydrophilic segment z in NRTL-SAC.

A major consideration in the extension of NRTL-SAC for electrolytes is thetreatment of the reference state for activity coefficient calculations. While theconventional reference state for nonelectrolyte systems is the pure liquidcomponent, the conventional reference state for electrolytes in solution is theinfinite-dilution aqueous solution and the corresponding activity coefficient isunsymmetric. The equation for the logarithm of the unsymmetric activitycoefficient of an ionic species is

With



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


I*PDH = Pitzer-Debye-Hückel term

I*FH = Flory-Huggins term

= 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/cm3

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 aredetermined by available VLE and LLE data between reference moleculesdefined in NRTLSAC.Segment (1) x x y- y+ x

Segment (2) y- z z z y+

121.643 6.547 -2.000 2.000 1.643

211.834 10.949 1.787 1.787 1.834

12 = 210.2 0.2 0.3 0.3 0.2

NaCl is used as the reference electrolyte for the conceptual electrolytesegment e. The NRTL binary parameters between conceptual molecular


segments and the electrolyte segment e are determined from literature dataor preset as follows:Segment (1) x y- y+ z

Segment (2) e e e e

1215 12 12 8.885

215 -3 -3 -4.549

12 = 210.2 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 solventsand 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 aconceptual segment index.

Option codes

There are three option codes in ENRTLSAC. The first is used to enable ordisable the Flory-Huggins term. The other two are only used internally andyou should not change their values. The Flory-Huggins term is included bydefault in eNRTL-SAC model. You can remove this term using the first optioncode. 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-LiquidSegment Activity Coefficient Model," Ind. Eng. Chem. Res. 43, 8354 (2004).

C.-C. Chen and Y. Song, "Extension of Nonrandom Two-Liquid SegmentActivity Coefficient Model for Electrolytes," Ind. Eng. Chem. Res. 44, 8909(2005).

HansenHansen is a solubility parameter model and is commonly used in the solventselection process. It is based on the regular solution theory and Hansensolubility parameters. This model has no binary parameters and its applicationmerely follows the empirical guide like dissolves like.

The Hansen model calculates liquid activity coefficients. The equation for theHansen model is:

with


Where:

i= Activity coefficient of component i

Vi = Molar volume of component i

id = Hansen solubility parameter of component i for nonpolar

effect

ip = Hansen solubility parameter of component i for polar effect

ih = Hansen solubility parameter of component i for hydrogen-

bonding effect

i= Volume 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.ParameterName/Element


UpperLimit

Units

DELTAD id — x — — PRESSURE^0.5

DELTAP ip — x — — PRESSURE^0.5

DELTAH ih — x — — PRESSURE^0.5

HANVOL Vi — x — — VOLUME

Option codes

The Hansen volume is implemented as an input parameter. If the Hansenvolume is not input by the user it will be calculated by an Aspen Plus internalmethod. You can also request the Aspen Plus method using Option Codes inAspen Plus Interface. The table below lists the option codes.

First Option Code in Hansen model

0 Hansen volume input by user (default)


Other values Hansen volume calculated by Aspen Plus

Reference

Frank, T. C.; Downey, J. R.; Gupta, S. K. "Quickly Screen Solvents forOrganic Solids," Chemical Engineering Progress 1999, December, 41.

Hansen, C. M. Hansen Solubility Parameters: A User’s Handbook; CRC Press,2000.

Ideal LiquidThis 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 carbonnumber. It can be used as a reference to compare the results of other activitycoefficient models.

The equation is:

ln i = 0

NRTL (Non-Random Two-Liquid)The NRTL model calculates liquid activity coefficients for the followingproperty methods: NRTL, NRTL-2, NRTL-HOC, NRTL-NTH, and NRTL-RK. It isrecommended for highly non-ideal chemical systems, and can be used for VLEand LLE applications. The model can also be used in the advanced equation-of-state mixing rules, such as Wong-Sandler and MHV2.

The equation for the NRTL model is:

for Tlower T Tupper

Where:

Gij =

ij=

ij =

ii= 0

Gii = 1

aij, bij, eij, and fij are unsymmetrical. That is, aij may not be equal to aji, etc.


Recommended cij Values for Different Types of Mixturescij Mixtures

0.30 Nonpolar substances; nonpolar with polar non-associated liquids; smalldeviations from ideality

0.20 Saturated hydrocarbons with polar non-associated liquids and systems thatexhibit 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 VLEand/or LLE data regression. The Aspen Physical Property System has a largenumber of built-in binary parameters for the NRTL model. The binaryparameters have been regressed using VLE and LLE data from the DortmundDatabank. The binary parameters for the VLE applications were regressedusing the ideal gas, Redlich-Kwong, and Hayden O'Connell equations of state.See Physical Property Data, Chapter 1, for details.ParameterName/Element


UpperLimit

Units

NRTL/1 aij 0 x -100.0 100.0 —

NRTL/2 bij 0 x -30000 30000.0 TEMPERATURE

NRTL/3 cij 0.30 x 0.0 1.0 —

NRTL/4 dij 0 x -0.02 0.02 TEMPERATURE

NRTL/5 eij 0 x — — TEMPERATURE

NRTL/6 fij 0 x — — TEMPERATURE

NRTL/7 Tlower 0 x — — TEMPERATURE

NRTL/8 Tupper 1000 x — — TEMPERATURE

Note: If any of bij, dij, or eij is non-zero, absolute temperature units areassumed for bij, dij, eij, and fij. Otherwise, user input units for temperature areused. The temperature limits are always interpreted in user input units.

The NRTL-2 property method uses data set 2 for NRTL. All other NRTLmethods use data set 1.

References

H. Renon and J.M. Prausnitz, "Local Compositions in Thermodynamic ExcessFunctions for Liquid Mixtures," AIChE J., Vol. 14, No. 1, (1968), pp. 135 –144.

NRTL-SAC ModelNRTL-SAC (patent pending) is a segment contribution activity coefficientmodel, derived from the Polymer NRTL model and extended to handleelectrolytes, but usable in Aspen Plus or Aspen Properties without AspenPolymers. NRTL-SAC can be used for fast, qualitative estimation of thesolubility of complex organic compounds in common solvents. It can also beused as a general activity coefficient model in Aspen Plus, Aspen Properties,and HYSYS.

Conceptually, the model treats the liquid non-ideality of mixtures containingcomplex organic molecules (solute) and small molecules (solvent) in terms ofinteractions between three pairwise interacting conceptual segments:


hydrophobic segment (x), hydrophilic segment (z), and polar segments (y-and y+). In practice, these conceptual segments become the moleculardescriptors used to represent the molecular surface characteristics of eachsolute or solvent molecule. Hexane, water, and acetonitrile are selected asthe reference molecules for the hydrophobic, hydrophilic, and polar segments,respectively. The molecular parameters for all other solvents can bedetermined by regression of available VLE or LLE data for binary systems ofsolvent 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 ofpolar segments, Y- and Y+, are used to reflect the wide variations ofinteractions between polar molecules and water.

NRTL-SAC can also be used to model electrolyte systems. In this case, anelectrolyte segment e, corresponding to the electrolyte parameter E, isintroduced. This conceptual segment e completely dissociates to a cationicsegment (c) and an anionic segment (a), both of unit charge. All electrolytes,organic or inorganic, symmetric or unsymmetric, univalent or multivalent, areto be represented with this conceptual 1-1 electrolyte segment e togetherwith the previously defined hydrophobic segment x, polar segments y- andy+, and hydrophilic segment z in NRTL-SAC. The reference state for ions is bydefault an unsymmetric state based on infinite dilution in aqueous solution,but an option code is available to select the symmetric state of pure fusedsalts. When there are no electrolytes present, the segment e is unused andthe current model reduces to the non-electrolyte version of NRTL-SAC presentin earlier releases.

The conceptual segment contribution approach in NRTL-SAC represents apractical alternative to the UNIFAC functional group contribution approach.This approach is suitable for use in the industrial practice of carrying outmeasurements for a few selected solvents and then using NRTL-SAC toquickly predict other solvents or solvent mixtures and to generate a list ofsuitable solvent systems.

The NRTL-SAC model calculates liquid activity coefficients.

Note: This is the updated version of NRTL-SAC, represented with propertymodel GMNRTLS and property method NRTL-SAC. This version does notrequire the specification of components as oligomers. For the old version, seeNRTLSAC 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 NRTLactivity coefficient model. Only one or two of these molecular parameters areneeded for most solvents in practice. These parameters are implementedtogether as pure parameter XYZE with five elements representing these fiveparameters. Values for this parameter are available for many commonsolvents in the NRTL-SAC databank.




Upper Limit Units

XYZE/1 rx,I — — — — —

XYZE/2 ry-,I — — — — —

XYZE/3 ry+,I — — — — —

XYZE/4 rz,I — — — — —

XYZE/5 re,I — — — — —

Electrolytes must be modeled as ion pairs in this system, while the individualions are components in the Aspen Physical Property System, so for these ionpairs, the five parameters are stored in binary parameter BXYZE which haselements corresponding to those of XYZE.ParameterName/Element


Upper Limit Units

BXYZE/1 rx,CA — — — — —

BXYZE/2 ry-,CA — — — — —

BXYZE/3 ry+,CA — — — — —

BXYZE/4 rz,CA — — — — —

BXYZE/5 re,CA — — — — —

The conceptual segment numbers of a cationic component and

an anionic component come from the dissociation of theircorresponding electrolyte component CA, as defined by the chemical equationdescribing 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 ofsingle electrolyte.

For an electrolyte system where multi-electrolytes may be generated, asimple mixing rule is used:


where YC is a cationic charge composition fraction and YA is an anionic chargecomposition fraction; they are defined as follows:

Notice that electrolyte here is meant to represent an ion-pair composed of acationic component and an anionic component in the solutions. The result isthat electrolytes are generated from all possible combinations of ions in thesolution; each generated electrolyte is not necessarily associated with an ion-pair through the dissociation.

Option Codes in NRTL-SAC

Three option codes are available for NRTL-SAC to select the reference stateand to optionally exclude the Flory-Huggins and long-range interaction terms:Option CodeValue Meaning

1 0 Reference state for ions is unsymmetric: infinite dilution inaqueous solution (default)

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

References

C.-C. Chen and Y. Song, "Extension of Nonrandom Two-Liquid SegmentActivity Coefficient Model for Electrolytes," Ind. Eng. Chem. Res., 2005, 44,8909.

Y. Song and C.-C. Chen, "Symmetric Nonrandom Two-Liquid Segment ActivityCoefficient 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 Ilc, the Pitzer-Debye-Hückel long-range interaction

term, ln IPDH, and the Flory-Huggins term, I

FH:

(1)

This equation needs to be normalized based on the reference states ofmolecular and ionic components.

Reference state for molecular components

The reference state for a molecular component is defined as follows:

(2)

This definition is the so-called standard state of pure liquids for molecularcomponents and it is also called the symmetric reference state for molecularcomponents.

Reference state for ionic components

The standard state of pure liquids is hypothetical for ionic components inelectrolyte systems. The symmetric reference state is defined as the purefused salt state of each electrolyte component in the system.

However, the conventional reference state for ionic components is theinfinite-dilution activity coefficient in pure water; it is also called theunsymmetric reference state for ionic components. In NRTL-SAC model, wewill consider both of these reference states; the unsymmetric state is thedefault.

Pure fused salt state of an electrolyte component

For an electrolyte component CA, the pure fused salt state can be defined asfollows:

(3)

(4)

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:

(5)

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 thedissociation of the electrolyte. Therefore Eq. 5 can be written in terms ofcharge numbers zC and zA:


(6)

At the pure fused salt state:

(7)

(8)

(9)

The symmetric reference state defined by Eq. 3 is restricted to systemscontaining a single electrolyte component. For multi-electrolyte systems, thesymmetric reference state can be generalized from Eq. 3 as follows:

(10)

where I applies to all molecular components in the system. The symmetricreference state is a molecular-component-free media.

Infinite-dilution aqueous solution

The condition of infinite-dilution solution for ionic components can be writtenas follows:

(11)

This condition applies to all ionic components in the solution. In infinite-dilution aqueous solutions, water must be present and is assumed torepresent the entire solution, so the unsymmetric reference state can bewritten as follows:

(12)

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 forsystems with multiple molecular segments m and a single electrolyte segmente (with a single cation segment c and anion segment a) can be written asfollows:

(13)

(14)


(15)

(16)

where I is the component index, i is the segment index, ri,I is the number ofsegment i in component I, xI is the mole fraction of component I, xi is thesegment fraction of segment i, and ns is the total number of all segments inthe system.

Since there is only a single 1-1 electrolyte segment, the pair parametersbetween a molecular segment and the electrolyte segment can be simplifiedas follows:

(17)

(18)

(19)

(20)

We can then rewrite the excess Gibbs free energy as follows:

(21)

with

(22)

The local composition contribution to the segment activity coefficient can becalculated as follows:

(23)

The local composition contribution to the activity coefficients for molecularsegments, the cationic segment, and the anionic segment can be calculatedout as follows:


(24)

(25)

(26)

The local composition term for the logarithm of the activity coefficient ofcomponent I , before normalization to a chosen reference state, is computedas the sum of the individual segment contributions.

(27)

Specifically, for non-electrolyte (molecular) components, the activitycoefficients are given as follows:

(28)

For a cationic component, we have


(29)

For an anionic component, we have

(30)

Molecular components

Applying Eq. 1, the normalization for molecular components can be done asfollows:

(31)

where mlc,I is the activity coefficient of the molecular segment m contained in

component I,

(32)

Ionic components with symmetric reference state

Applying Eq. 10, the local composition contribution to the symmetric activitycoefficients for ionic components in multi-electrolyte systems can benormalized as follows:

(33)

(34)

(35)

where I applies to all molecular components in the solution and Ix0 is the ionic

strength at the symmetric reference state. In the case that electrolytes aremade up of only the conceptual 1-1 electrolyte segment and none of themolecular segments, this reference state is equivalent to the molten state ofthe conceptual 1-1 electrolyte.

Ionic components with infinite dilution aqueous solutionreference state

Applying Eq. 12, the unsymmetric activity coefficients for ionic components inaqueous solutions can be normalized as follows:

(36)

(37)


where and are activity coefficients at the infinite dilution aqueoussolution:

(38)

(39)

NRTL-SAC Long-Range Interaction Term

To account for the long-range ion-ion interactions, the model uses thesymmetric Pitzer-Debye-Hückel (PDH) formula (Pitzer, 1986) on the segmentbasis:

(40)

with

(41)

(42)

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 segmente=ca" is defined in the model, we can obtain:

(43)

For the symmetric reference state,

(44)

And for the unsymmetric reference state,

(45)

The long-range contribution to the activity coefficient of segment i can bederived as follows:

(46)


For a molecular segment, the activity coefficient can be carried out as follows:

(47)

For the univalent cation or anion segment, the activity coefficient can becarried 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 themolecular solvent properties; a simple composition average mixing rule isproposed to calculate them as follows:

(49)

(50)

where S is a solvent component, MS is the solvent molecular weight, and eachsum is over all solvent components in the solution.

The long range interaction term for the logarithm of the activity coefficient ofcomponent I is computed as the sum of the individual segment contributions.

(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 allmolecular components are normalized; that is

(53)

where I applies to all molecular components in the system.



Applying Eq. 10, the symmetric activity coefficients for ionic components fromthe long range contribution are given as follows:

(54)

(55)

(56)

where I applies to all molecular components in the solution.

Ionic components with infinite dilution aqueous solution

Applying Eq. 12, the unsymmetric activity coefficients for ionic componentsfrom the long range contribution in aqueous solutions are given as follows:

(57)

(58)

Segment based Born correction term to activity coefficient

If the infinite dilution aqueous solution is chosen as the reference state, weneed to correct the change of the reference state from the mixed-solventcomposition to aqueous solution for the Debye-Hückel term. The Born term(Robinson and Stokes, 1970; Rashin and Honig, 1985) is used for thispurpose:

(59)

where ri is the Born radius of segment species i and w is the dielectric

constant of water. GBorn is the Born term correction to the unsymmetric

Pitzer-Debye-Hückel formula Gex,PDH.

The Born correction activity coefficient of component i can be derived asfollows:

(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 becarried out as follows:


(62)

Specifically,

(63)

(64)

The long range interaction term for the logarithm of the activity coefficient ofcomponent I is computed as the sum of the individual segment contributions.

(65)

Activity coefficients given by Eq. 65 are already normalized for molecularcomponents as well as for ionic components with the infinite-dilution aqueoussolution 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.

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 Gex,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 conceptualsegments in component I:

(68)

(69)


The contribution to the activity coefficient of component I from thecombinatorial term is thus:

(70)


It is easy to show that activity coefficients for molecular components from theFlory-Huggins term are normalized; that is

(71)



Applying Eq. 10, the symmetric activity coefficients for ionic components fromthe Flory-Huggins term can be carried out as follows:

(72)

(73)

with

(74)

(75)

(76)

(77)


Ionic components with infinite dilution aqueous solution

Applying Eq. 12, the unsymmetric activity coefficients for ionic components inaqueous solutions can be carried out as follows:

(78)

(79)


where and are activity coefficients at the infinite dilutionaqueous solution:

(80)

(81)

Henry Components in NRTL-SAC

Light gases (i.e. Henry components) are usually supercritical at thetemperature and pressure of the system. In that case pure component vaporpressure is meaningless and therefore the pure liquid state at thetemperature 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, xI0) 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:

(82)

where is the infinite dilution activity coefficient of Henry component I

(xI0) in the solution. By this definition I* approaches unity as

xI approaches zero. The phase equilibrium relationship for Henry componentsbecomes:

(83)

The Henry’s Law is available in all activity coefficient property methods. Themodel calculates the Henry’s constant for a dissolved gas component in allsolvent components in the mixture:

(84)

(85)

where HIS and are the Henry’s constant and the infinite dilution activitycoefficient of the dissolved gas component i in the solvent component S

(xI0 and xS1, respectively).

Since ionic species exist only in the liquid phase and therefore do notparticipate directly in vapor-liquid equilibria, the activities of Henry


components are mainly through the local interactions with solvents. We cancalculate all three activity coefficients for Henry components as follows:

(86)

(87)

(88)

with

(89)

(90)

(91)

(92)

(93)

(94)

Notice that xH0 applies to all Henry components in the solution.

NRTLSAC for Segments/Oligomers

This is the original NRTLSAC model added in version 2006, which requiresthat components be defined as oligomers. It is retained for compatibility, butnew models should use the NRTL-SAC model.

NRTL-SAC (patent pending) is a segment contribution activity coefficientmodel, derived from the Polymer NRTL model, usable in Aspen Properties andAspen Polymers. NRTL-SAC can be used for fast, qualitative estimation of thesolubility of complex organic compounds in common solvents. Conceptually,the model treats the liquid non-ideality of mixtures containing complexorganic molecules (solute) and small molecules (solvent) in terms ofinteractions between three pairwise interacting conceptual segments:hydrophobic segment (x), hydrophilic segment (z), and polar segments (y-and y+). In practice, these conceptual segments become the moleculardescriptors used to represent the molecular surface characteristics of eachsolute or solvent molecule. Hexane, water, and acetonitrile are selected asthe reference molecules for the hydrophobic, hydrophilic, and polar segments,respectively. The molecular parameters for all other solvents can bedetermined by regression of available VLE or LLE data for binary systems ofsolvent and the reference molecules or their substitutes. The treatmentresults 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 polarmolecules and water.

The conceptual segment contribution approach in NRTL-SAC represents apractical alternative to the UNIFAC functional group contribution approach.This approach is suitable for use in the industrial practice of carrying outmeasurements for a few selected solvents and then using NRTL-SAC toquickly predict other solvents or solvent mixtures and to generate a list ofsuitable solvent systems.

The NRTL-SAC model calculates liquid activity coefficients.

The equation for the NRTL-SAC model is:

with

G = exp(-)

Where:


I, J = Component index

i, j, m = Conceptual segment indexx, y-, y+, z

I= Activity coefficient of component I

IC = I

FH = Flory-Huggins term for combinatorial contribution to I

IR = I

lc = NRTL term for local composition interaction contribution to

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 componentI

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 aredetermined by available VLE and LLE data between reference moleculesdefined above.Segment 1 x x y- y+ x

Segment 2 y- z z z y+

121.643 6.547 -2.000 2.000 1.643

211.834 10.949 1.787 1.787 1.834

12 = 210.2 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 mostsolvents in practice. Since conceptual segments apply to all molecules, thesefour molecular parameters are implemented together as a binary parameter,NRTLXY(I, m) where I represents a component (molecule) index and mrepresents a conceptual segment index.

In addition, the Flory-Huggins size parameter, FHSIZE , is used in NRTLSACto 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.




UpperLimit

Units Comment

NRTLXY rI,m — — — — — Binary,symmetric

FHSIZE/1 sI 1.0 — 1E-15 1E15 — Unary

FHSIZE/2 I1.0 — -1E10 1E10 — Unary

Option codes

The Flory-Huggins term is included by default in the NRTLSAC model. You canremove this term using the first option code. The table below lists the valuesfor 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 rI,x rI,y- rI,y+ rI,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 rI,x rI,y- rI,y+ rI,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-TETRAHYDRONAPHTHALENE0.443 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


Reference

C.-C. Chen and Y. Song, "Solubility Modeling with a Nonrandom Two-LiquidSegment Activity Coefficient Model," Ind. Eng. Chem. Res. 43, 8354 (2004).

Using NRTLSAC

NRTLSAC (patent pending) is a segment contribution activity coefficientmodel, derived from the Polymer NRTL model, usable in Aspen Properties andAspen Polymers. NRTLSAC can be used for fast, qualitative estimation of thesolubility of complex organic compounds in common solvents. For moreinformation about the model, see NRTLSAC for Segments/Oligomers.

Note: A newer version of NRTL-SAC comes with its own property methodnamed NRTL-SAC and does not require the specification of a method andoligomer components as described below.

The NRTLSAC model for Segments/Oligomers in the Aspen Physical PropertySystem 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 asoligomers. Four conceptual segments also must be defined. On theComponents | Polymers | Oligomers sheet, enter a number for at leastone conceptual segment for each oligomer component, as required by thedefinition 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 followingexample, 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 eachcomponent.

Pitzer Activity Coefficient ModelThe Pitzer model was developed as an improvement upon an earlier modelproposed by Guggenheim ( 1935, 1955). The earlier model worked well at lowelectrolyte concentrations, but contained discrepancies at higherconcentrations (>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 6molal ionic strength. It cannot be used for systems with any other solvent ormixed solvents. Any non-water molecular components are considered solutesand treated as Henry components.


This section provides theoretical background for the model. All modelequations and parameter requirements are included.

The Pitzer model is commonly used in the calculation of activity coefficientsfor aqueous electrolytes up to 6 molal ionic strength. Do not use this model ifa non-aqueous solvent exists. Henry's law parameters are required for allother components in the aqueous solution. The model development andworking equations are provided in the following sections. Parameterconversion between the Pitzer notation and our notation is also provided.

The Pitzer model in the Aspen Physical Property System involves user-supplied parameters that are used in the calculation of binary and ternaryparameters 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:

Tref = 298.15 K

The user must:

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 SpecificationsSelection sheet.

The parameters are summarized in the following table. There is a Pitzerparameter databank in the Aspen Physical Property System (see PhysicalProperty Data).ParameterName

ProvidesP1 - P5 for

No. ofElements

Default MDS Units

Cation-Anion Parameters

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'5 0 x —

Anion-Anion Parameters

GMPTTH aa'5 0 x —

Ternary Parameters


ParameterName

ProvidesP1 - P5 for

No. ofElements

Default MDS Units

GMPTPS,GMPTP1,GMPTP2,GMPTP3,GMPTP4

ijk1 (in eachparameter)

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. Ituses the following expansion as a radial distribution function:

(1)

Where:

gij = Distribution function

r = Radius

qij =

(pair potential of mean force)

With:

zi = Charge of ion i

Qe = Electron charge

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 thatrelates this function and the intermolecular potential to thermodynamicproperties. From this relation you can obtain an expression for the osmoticcoefficient.

Pitzer proposes a general equation for the excess Gibbs energy. The basicequation is:

(2)

Where:

GE = Excess Gibbs energy


R = Gas constant

T = Temperature

nw = Kilograms of water

mi =

(molality of ion i)

With:

xi = Mole fraction 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 long-range electrostatic forces between ions. This takes into account the hard-coreeffects 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 molecule-

molecule 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 identifyingcombinations of functions. He developed interaction parameters that can beevaluated using experimental data. He selected mathematical expressions forthese parameters that best fit experimental data.

Pitzer's model can be applied to aqueous systems of strong electrolytes andto aqueous systems of weak electrolytes with molecular solutes. Theseapplications are discussed in the following section.

In the Aspen Physical Property System, this model is applied using thereference state of infinite dilution solution in water for non-water molecularsolutes and ionic species. The properties such as DHAQFM are obtained at 25C and 1 atm.

Application of the Pitzer Model to Aqueous StrongElectrolyte Systems

Pitzer modified his basic equation to make it more useful for data correlationof aqueous strong electrolytes. He defined a set of more directly observableparameters to represent combinations of the second and third virialcoefficients. The modified Pitzer equation is:


(3)

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 anaqueous single-electrolyte system. These parameters can be determined bythe 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 measuredfrom common-ion mixtures. Examples are NaCl + KCl + H2O or NaCl + NaNO3

+ H2O (sic, Pitzer, 1989). These terms are discussed in detail later in thissection.

Fürst and Renon (1982) propose the following expression as the Pitzerequation for the excess Gibbs energy:

(4)

The difference between equations 3 and 4 is that Pitzer orders cation beforeanions. 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 orderedbefore anions, Bij = Bji. This eliminates the 2 in the second term in brackets inPitzer'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 inthe 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 allions to make the equation symmetric.


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 1/2in the last term in brackets in Pitzer's original expression. Pitzer distinguishesbetween 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 unsymmetricalmixing effects, producing this modified Pitzer equation for the excess Gibbsenergy:

(4a)

Calculation of Activity Coefficients

The natural logarithm of the activity coefficient for ions is calculated fromequation 4a to give:

(5)

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 inpolynomial form:

For option code = 1, the unsymmetric mixing correction term is in integralform:

For water the logarithm of the activity coefficient is calculated similarly, asfollows:

Applying:

to equation 3 and using:

Where Nw = moles water, gives:

(6)

f(I), the electrostatic term, is expressed as a function of ionic strength I :

(7)

I, the ionic strength, is defined as:


(8)

Taking the derivative of equation 7 with respect to I, gives:

(9)

So that:

(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:

(11)

Where:

NA = Avogadro's constant

dw = Water density

B= Dielectric constant of solvent B

b is an adjustable parameter, which has been optimized in this model to equal1.2.

B and B' need expressions so that equations 5 and 6 can completely be solvedfor the activity coefficients. The parameter B is determined differently fordifferent electrolyte pairings. For 1-n electrolytes (1-1, 1-2, 2-1, and so on)the following expression gives the parameter B:

(12)

with 1=2.0.

For n-m electrolytes, n and m>1 (2-2, 2-3, 3-4, and so on), B is determinedby the following expression:

(13)

with 2 = 12.0 and 3 = 1.4.

By taking appropriate derivatives, expressions for B' can be derived for 1–nelectrolytes:

(14)


and for n-m electrolytes:

(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 themole fraction scale from the molality scale by the following relations:

For solutes:

(16)

For water as a solvent:

(17)

Where:

m= Activity coefficient (molality scale)

x= Activity coefficient (mole fraction scale)

Application of the Pitzer Model to AqueousElectrolyte Systems with Molecular Solutes

In aqueous weak electrolyte systems with molecular solutes, the second andthird virial coefficients in the basic Pitzer equation for molecule-ion andmolecule-molecule interactions must be considered. The following extensionsof Pitzer's interaction parameters are made.

The second-order parameters Bij are extended to include molecule-moleculeand 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 = 6iii

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 sameas equations 3 through 6.

Parameters

The Pitzer model in the Aspen Physical Property System involves user-supplied parameters. These parameters are used in the calculation of binaryand 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 theirrequirements 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 factorsoriginate from one of Pitzer's earlier expressions for the excess Gibbs energy:

(18)

Where:

=

na = Mole number of anions

nc = Mole number of cation

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. Enterthe 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 electrolytesystems are available from Pitzer's series on the thermodynamics ofelectrolytes. 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 inorganicelectrolytes, salts of carboxylic acids (1-1),tetraalkylammonium halids, sulfonic acidsand salts, additional 1-1 organic salts, 2-1inorganic compounds, 2-1 organicelectrolytes, 3-1 electrolytes, 4-1 and 5-1electrolytes

(Pitzer and Mayorga, 1974) Binary parameters for 2-2 electrolytes inwater at 25C

(Pitzer and Kim, 1974) Binary and ternary parameters for mixedelectrolytes, binary mixtures without acommon ion, mixed electrolytes with threeor more solutes

(Pitzer, 1975) Ternary parameters for systems mixingdoubly and singly charged ions

(Pitzer and Silvester, 1976) Parameters for phosphoric acid and its buffersolutions

(Pitzer, Roy and Silvester, 1977) Parameters and thermodynamic propertiesfor sulfuric acid

(Silvester and Pitzer, 1977) Data for NaCl and aqueous NaCl solutions

(Pitzer, Silvester, and Peterson, 1978) Rare earth chlorides, nitrates, andperchlorates

(Peiper and Pitzer, 1982) Aqueous carbonate solutions, includingmixtures of sodium carbonate, bicarbonate,and chloride

(Phutela and Pitzer, 1983) Aqueous calcium chloride

(Conceicao, de Lima, and Pitzer, 1983) Saturated aqueous solutions, includingmixtures of sodium chloride, potassiumchloride, and cesium chloride


Reference Parameters available

(Pabalan and Pitzer, 1987) Parameters for polynomial unsymmetricmixing term

(Kim and Frederick, 1988) Parameters for integral unsymmetric mixingterm

Pitzer References

Conceicao, M., P. de Lima, and K.S. Pitzer, "Thermodynamics of SaturatedAqueous Solutions Including Mixtures of NaCl, KCl, and CsCl, "J. SolutionChem, Vol. 12, No. 3, (1983), pp. 171-185.

Fürst, W. and H. Renon, "Effects of the Various Parameters in the Applicationof Pitzer's Model to Solid-Liquid Equilibrium. Preliminary Study for Strong 1-1Electrolytes," 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 Parametersof Aqueous Mixed Electrolyte Solution at 25C, Part 2: Ternary MixingParameters," J. Chem. Eng. Data, 33, (1988), pp. 278-283.

Pabalan, R.T. and K.S. Pitzer, "Thermodynamics of Concentrated ElectrolyteMixtures and the Prediction of Mineral Solubilities to High Temperatures forMixtures 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 CarbonateSolutions Including Mixtures of Sodium Carbonate, Bicarbonate, andChloride," J. Chem. Thermodynamics, Vol. 14, (1982), pp. 613-638.

Phutela, R.C. and K.S. Pitzer, "Thermodynamics of Aqueous CalciumChloride," J. Solution Chem., Vol. 12, No. 3, (1983), pp. 201-207.

Pitzer, K.S., "Thermodynamics of Electrolytes. I. Theoretical Basis andGeneral 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 ofTemperature and Composition," J. Chen. Thermodynamics, Vol. 21, (1989),pp. 1-17. (Seventh Rossini lecture of the commission on Thermodynamics ofthe IUPAC, Aug. 29, 1988, Prague, ex-Czechoslovakia).

Pitzer, K.S. and J.J. Kim, "Thermodynamics of Electrolytes IV; Activity andOsmotic Coefficients for Mixed Electrolytes," J.Am. Chem. Soc., Vol. 96(1974), p. 5701.

Pitzer, K.S. and G. Mayorga, "Thermodynamics of Electrolytes II; Activity andOsmotic 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.


Pitzer, K.S., J.R. Peterson, and L.F. Silvester, "Thermodynamics ofElectrolytes. IX. Rare Earth Chlorides, Nitrates, and Perchlorates, "J. SolutionChem., Vol. 7, No. 1, (1978), pp. 45-56.

Pitzer, K.S., R.N. Roy, and L.F. Silvester, "Thermodynamics of Electrolytes 7Sulfuric 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, WithApplication to Sodium Chloride," J. Phys. Chem., Vol. 81, No. 19, (1977), pp.1822-1828.

Polynomial Activity CoefficientThis model represents activity coefficient as an empirical function ofcomposition and temperature. It is used frequently in metallurgicalapplications where multiple liquid and solid solution phases can exist.

The equation is:

Where:

Ai =

Bi =

Ci =

Di =

Ei =

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 coefficientmodel, 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.ParameterName/Element


UpperLimit

Units

GMPLYP/1 ai1 0 x — — —






UpperLimit

Units

GMPLYP/4 bi1 0 x — — —



GMPLYP/7 ci1 0 x — — —



GMPLYP/10 di1 0 x — — —

GMPLYP/11 di2 0 x — — —

GMPLYP/12 di3 0 x — — —

GMPLYP/13 ei1 0 x — — —

GMPLYP/14 ei2 0 x — — —

GMPLYP/15 ei3 0 x — — —

GMPLYO fi — x — — —

Note: If you specify GMPLYP on the Properties | Parameters | PureComponent | 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 theFlowsheeting Options | Add-Input | Add After sheet in Aspen Plus or theAdd-Input | Add-Input | Add After sheet in Aspen Properties, and enterthe values of all 15 elements as in the following example:

PROP-DATA GMPLYP-1IN-UNITS SIPROP-LIST GMPLYPPVAL 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-KisterThis model calculates activity coefficients. It is a polynomial in the differencebetween mole fractions in the mixture. It can be used for liquid and solidmixtures (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)


i = vi



UpperLimit

Units

GMRKTB/1 aij 0 x — — —

GMRKTB/2 bij 0 x — — —

GMRKTB/3 cij 0 x — — —

GMRKTB/4 dij 0 x — — —

GMRKTB/5 eij 0 x — — —

GMRKTB/6 fij 0 x — — —

GMRKTB/7 gij 0 x — — —

GMRKTB/8 hij 0 x — — —

GMRKTB/9 mij 0 x — — —

GMRKTB/10 nij 0 x — — —

GMRKTO vi — x — — —

Scatchard-HildebrandThe Scatchard-Hildebrand model calculates liquid activity coefficients. It isused in the CHAO-SEA property method and the GRAYSON property method.

The equation for the Scatchard-Hildebrand model is:

Where:

Aij =

i=

Vm*,l =



UpperLimit

Units

TC Tci — x 5.0 2000.0 TEMPERATURE




UpperLimit

Units

DELTA i— x 103 105 SOLUPARAM

VLCVT1 Vi*,CVT — x 0.0005 1.0 MOLE-

VOLUME

GMSHVL Vi*,l x 0.01 1.0 MOLE-

VOLUME

GMSHXL kij 0.0 x -5 5 —

Three-Suffix MargulesThis model can be used to describe the excess properties of liquid and solidsolutions. It does not find much use in chemical engineering applications, butis still widely used in metallurgical applications. Note that the binaryparameters for this model do not have physical significance.

The equation is:

Where kij is a binary parameter:


i = di



UpperLimit

Units

GMMRGB/1 aij 0 x — — TEMPERATURE

GMMRGB/2 bij 0 x — — —

GMMRGB/3 cij 0 x — — —

GMMRGO di — x — — —

References

M. Margules, "Über die Zusammensetzung der gesättigten Dämpfe vonMischungen," Sitzungsber. Akad. Wiss. Vienna, Vol. 104, (1895), p. 1293.

D.A. Gaskell, Introduction to Metallurgical Thermodyanics, 2nd ed., (NewYork: Hemisphere Publishing Corp., 1981), p. 360.

R.C. Reid, J.M. Prausnitz, and B.E. Poling, The Properties of Gases andLiquids, 4th ed., (New York: McGraw-Hill, 1987).


Symmetric and Unsymmetric ElectrolyteNRTL Activity Coefficient ModelThe Symmetric Electrolyte NRTL activity coefficient model (GMENRTLS) uses asymmetric reference state for ions as pure fused salts, rather than infinitedilution in aqueous solution. This basis is easier to use for nonaqueous andmixed-solvent systems, and eliminates the need to introduce water intootherwise water-free systems. It also allows the model to reduce to thestandard NRTL model when there are no electrolytes in the system. TheENRTL-SR property method is based on this model.

Chemical constants, enthalpy, and Gibbs free energy are calculated withrespect to the symmetric ionic reference state.

The Unsymmetric Electrolyte NRTL activity coefficient model (GMENRTLQ)uses the same equations as GMENRTLS, but the unsymmetric reference statefor ions (infinite dilution in aqueous solution). The ENRTL-RK property methodis based on this model. Unlike the original Electrolyte NRTL activity coefficientmodel, GMENRTLQ is also used to calculate enthalpy and Gibbs free energyfrom thermodynamics based on the unsymmetric ionic reference state.

These models also handle zwitterions.

Parameters

Both symmetric and unsymmetric models share the same binary and pairparameters. 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:


where .

The NRTL parameters are used for molecule-molecule parameters, withtemperature dependence:

The temperature dependency of the dielectric constant is given by:

Option codes can affect the performance of this model. See Option Codes forActivity Coefficient Models for details.

The following table lists the parameters used by GMENRTLS and GMENRTLQ:ParameterName


Default MDS Units


CPDIEC a 1 — — —

b 1 0 — —

Tref 1 298.15 — TEMPERATURE†

Ionic Born Radius Unary Parameters

RADIUS ri 1 3x10-10 — LENGTH

Molecule-Molecule Binary Parameters

NRTL/1 aij — 0 x —

aji — 0 x —

NRTL/2 bij — 0 x TEMPERATURE†

bji — 0 x TEMPERATURE†

NRTL/3 cij=cji — .3 x —

NRTL/4 dij=dji — 0 x TEMPERATURE

NRTL/5 eij — 0 x TEMPERATURE

eji — 0 x TEMPERATURE

NRTL/6 fji — 0 x TEMPERATURE

fji — 0 x TEMPERATURE

Electrolyte-Molecule Pair Parameters

GMENCC Cca,m 1 0 x —

Cm,ca 1 0 x —


ParameterName


Default MDS Units


GMENCD Dca,m 1 0 x TEMPERATURE†

Dm,ca 1 0 x TEMPERATURE†

GMENCE Eca,m 1 0 x —

Em,ca 1 0 x —

GMENCN ca,m = m,ca1 .2 x —

Electrolyte-Electrolyte Pair Parameters

GMENCC Cca,c'a 1 0 x —

Cc'a,ca 1 0 x —

Cca,ca' 1 0 x —

Cca',ca 1 0 x —

GMENCD Dca,c'a 1 0 x TEMPERATURE†

Dc'a,ca 1 0 x TEMPERATURE†

Dca,ca' 1 0 x TEMPERATURE†

Dca',ca 1 0 x TEMPERATURE†

GMENCE Eca,c'a 1 0 x —

Ec'a,ca 1 0 x —

Eca,ca' 1 0 x —

Eca',ca 1 0 x —

GMENCN ca,c'a = c'a,ca1 .2 x —

ca,ca' = ca',ca1 .2 x —

Zwitterions in Symmetric and UnsymmetricElectrolyte NRTL

The Symmetric and Unsymmetric Electrolyte NRTL models supportzwitterions, compounds with both positive and negative charges but netcharge of zero. Zwitterions are defined as:

Components of type Conventional, similar to solvents

Parameter ZWITTER set to 1; all other components in the Aspen PhysicalProperty 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 NRTLparameters only, excluding any interactions through Henry constants andpair parameters.

The activity coefficient is calculated as a solvent.

The contribution from zwitterions to the solution enthalpy and Gibbs freeenergy are calculated as solutes using the infinite dilution heat capacitymodel CPAQ0, DGAQFM, and DHAQFM.


Working Equations for Symmetric andUnsymmetric Electrolyte NRTL

The symmetric and unsymmetric electrolyte NRTL models have twocontributions, one from local interactions that exist at the immediateneighbourhood of any species, and the other from the long-range ion-ioninteractions that exist beyond the immediate neighbourhood of an ionicspecies. To account for the local interactions, the model uses the electrolyteNRTL expression. To account for the long-range interactions, the model usesthe Pitzer-Debye-Hückel (PDH) formula (Pitzer, 1980, 1986). The followingequation is the basis of the electrolyte NRTL model for the excess Gibbs freeenergy of electrolyte systems:

(1)

The excess Gibbs free energy Gmex is defined as:

(2)

where Gm is the Gibbs free energy of electrolyte systems and Gmid 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:

(3)

or

(4)

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 statefor any molecular and ionic component, respectively.

Reference state for molecular components

The reference state for a molecular component m is defined as follows:

(5)

This definition is the so-called standard state of pure liquids for molecularcomponents and it is also called the symmetric reference state for molecularcomponents.


Reference state for ionic components

The standard state of pure liquids is hypothetical for ionic components inelectrolyte systems. Instead, the symmetric reference state is defined as thepure fused salt state of each electrolyte component in the system.

However, the conventional reference state for ionic components is theinfinite-dilution activity coefficients; it is also called the unsymmetricreference state for ionic components.

GMENRTLS uses the symmetric reference state, while GMENRTLQ uses theunsymmetric reference state.

Pure fused salt state of an electrolyte component

For an electrolyte component ca, the pure fused salt state can be defined asfollows:

(6)

(7)

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:

(8)

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 thedissociation of the electrolyte:

(9)

with

(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 onemole of salt) are:

=c+a(12)

therefore

(13)


(14)

(15)

The symmetric reference state defined by Eq. 6 is restricted to systemscontaining a single electrolyte component. For multi-electrolyte systems, thesymmetric reference state can be generalized from Eq. 6 as follows:

(16)

where m applies to all molecular components in the system. The symmetricreference state is a molecular-component-free medium.

Infinite-dilution aqueous solution

The condition of infinite-dilution aqueous solution for ionic components can bewritten as follows:

xc=xa=0 (17)

This condition applies to all ionic components in the solution, and water mustbe present in the solution for this reference state. In terms of the activitycoefficients for ionic components, the condition for the aqueous solution asthe 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 ofthree types: molecular species (solvents), m; cationic species (cations), c;and anionic species (anions), a. The model assumes that there are threetypes of local composition interactions. The first type consists of a centralmolecular species with other molecular species, cationic species, and anionicspecies in the immediate neighbourhood. Here, local electroneutrality ismaintained. The other two types are based on the like-ion repulsionassumption and have either a cationic or anionic species as the centralspecies. They also have an immediate neighbourhood consisting of molecularspecies and oppositely charged ionic species. Accordingly, the excess Gibbsenergy from local interactions for an electrolyte system can be written asfollows:

(19)

or


(20)

with

(21)

(22)

where the first term is the contribution when a molecular species is at thecenter, 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 thecenter. 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 asfollows:

(24)

The results are:

(25)

(26)


(27)

Binary Parameters

The adjustable binary parameters for these models include molecule-molecule, molecule-electrolyte, and electrolyte-electrolyte binary parameters,where electrolyte here means an ion-pair composed of a cationic species andan 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 formolecule-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-averagemixing rule.

(29)

(30)

(31)

(32)

where Yc is a cationic charge composition fraction and Ya is an anionic chargecomposition fraction, defined as follows:

(33)


(34)

G for these pairs is calculated the same way:

(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 toactivity coefficients for all molecular components are normalized; that is

(42)

for all molecular components m in the system.

For ionic components with symmetric reference state, apply Eq. 16 to find:

(43)

(44)


(45)

(46)

(47)

(48)

where xm0 applies to all molecular components in the solution.

For ionic components with infinite-dilution aqueous solution as referencestate, apply Eq. 18 to get:

(49)

(50)

where and are local interaction contributions to activitycoefficients at infinite dilution aqueous solution:

(51)

(52)

Long-Range Interaction Term

To account for the long-range ion-ion interactions, the Symmetric andUnsymmetric Electrolyte NRTL models use the symmetric Pitzer-Debye-Hückel(PDH) formula (Pitzer, 1986):

(53)


with

(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 Ix0 represents Ix at the

reference state.

For the unsymmetric reference state, Ix0 = 0.

For the symmetric reference state, the Debye-Hückel theory is originallybased on a single electrolyte with water as the solvent. Therefore, we canobtain Ix

0 from Eqs. 13 and 14:

(56)

For multi-electrolyte systems with mixed-solvents, Ix0 can take this form:

(57)

(58)

(59)

so that

(60)

where xm0 applies to all molecular components in the solution. This

definition ensures that the excess Gibbs free energy from the long rangeinteractions will be zero at the symmetric reference state regardless of howmany electrolytes are present in the solution.

The contribution to the activity coefficient from component i can be derivedas:

(61)


For a solvent component, this is:

(62)

For a cation or anion component:

(63)

For the unsymmetric reference state:

(64)

And for the symmetric reference state:

(65)

(66)

(67)

or

(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 compositionaverage mixing rule is adequate to calculate them as follows:


(70)

(71)

where s is a solvent component in the mixture and Msis the solvent molecularweight. 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, weneed to correct the the Debye-Hückel term for the change of the referencestate from the mixed-solvent composition to aqueous solution. The Born term(Robinson and Stokes, 1970; Rashin and Honig, 1985) is used for thispurpose:

(72)

where NA is the Avogadro constant and R is the gas constant. is theBorn 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 derivedas follows:

(73)

For a cation or anion component, this is:

(74)

The correction to the activity coefficient for a solvent component is zero:

(75)

Henry Components in the Symmetric andUnsymmetric Electrolyte NRTL Models

Light gases (Henry components) are usually supercritical at the temperatureand pressure of the system. In that case, pure component vapor pressure is


meaningless and therefore the pure liquid state at the temperature andpressure of the system cannot serve as the reference state. The referencestate for a Henry component is redefined to be at infinite dilution (that is, at

xi0) 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:

(76)

where i

is the infinite dilution activity coefficient of Henry component i

(xi0) 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. Themodel calculates the Henry’s constant for a dissolved gas component in allsolvent 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 (xi0

and xs1), respectively.

Since ionic species exist only in the liquid phase and therefore do notparticipate directly in vapor-liquid equilibria, the activities of Henrycomponents are mainly through the local interactions with solvents. We cancalculate the activity coefficients for Henry components as follows:

(80)

(81)

(82)

where xh0 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:

(83)

where xh0 applies to all Henry components and xi0 to all ionic

components in the solution.

For aqueous basis, the unsymmetric activity coefficients of Henry componentsare calculated as follows:

(84)

Electrolyte Chemical Equilibria

In determining the composition of an electrolyte system, it is important toknow the equilibrium constants of the reactions taking place. An equilibriumconstant is expressed as the product of the activity of each species raised toits stoichiometric coefficients. Two different scales are used in Aspen Plus: themolality scale and the mole fraction scale but both are based on aqueouselectrolyte chemical equilibrium. For instance, the equilibrium constant for themole fraction scale in Aspen Plus is written in one of these:

(85)

(86)

Where:

K = Equilibrium constant

xw = Water mole fraction

w= Water activity coefficient

xs = Non-water solvent mole fraction

s= Non-water solvent activity coefficient

xi = Mole fraction of solute component (Henry orion)

i* = Unsymmetric activity coefficient of solute

component

i= Stoichiometric coefficient

The above equations are limited to aqueous electrolyte chemical equilibriaonly. Therefore, the chemical constants in Aspen Plus databanks for


electrolyte systems with infinite dilution aqueous reference state cannot beused for electrolyte systems with the symmetric reference state for ioniccomponents.

The chemical constants for electrolyte systems with the symmetric referencestate can be written in these forms:

(87)

(88)

where i indicates a molecular or ionic component and h represents a Henrycomponent. Eq. 83 or 84 is used for calculation of the unsymmetric activitycoefficients of Henry components. However, the calculation for the activitycoefficients of ionic components is carried out with the symmetric referencestate.

Other Thermophysical PropertiesThe activity coefficient model can be related to other properties through fundamentalthermodynamic equations. These properties (called excess liquid functions) are relative to theideal liquid mixture at the same condition:Excess molar liquid Gibbs free energy

(89)

Excess molar liquid enthalpy

(90)

Excess molar liquid entropy

(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 mixturefrom an activity coefficient model:

(92)

with

(93)

(94)


Where is the liquid Gibbs free energy of mixing; it is defined as thedifference between the Gibbs free energy of the mixture and that of the pure

component and is the ideal Gibbs free energy of mixing. Once theexcess liquid functions are known, the thermodynamic properties of liquidmixtures can be computed as follows:

(95)

(96)

(97)

where Hil and Hi

ig are the enthalpy and ideal gas enthalpy of component i atthe system conditions. Similarly, Gi

l and Giig are the Gibbs free energy and

ideal gas Gibbs free energy of component i at the system conditions. In AspenPlus, both Hi

ig and Giig are computed by the expressions:

(98)

(99)

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 mixturescontaining ionic components because the ideal gas model becomes invalid forionic components.

The formulation to calculate the enthalpy and Gibbs free energy forelectrolyte systems can be carried out as follows:

(100)

(101)

(102)

where indexes s, h, and ca are meant to represent the contributions fromsolvents, Henry components and ionic components, respectively.


Solvents

The contribution from solvents can be written as follows:

(103)

(104)

(105)

(106)

(107)

(108)

where is the liquid fugacity coefficient of pure solventcomponent i, pi

sat is the vapor pressure of pure component at the system

temperature T, iv is the vapor fugacity coefficient of pure component at T

and pisat (normally calculated from an equation-of-state model), and

is the Poynting pressure correction from pisat to p,

and Vil 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)


(114)

(115)

Ionic components

The contribution from ionic components can be written as follows:

(116)

(117)

(118)

(119)

(120)

(121)

where Hiref and Gi

ref are the enthalpy and Gibbs free energy of ioniccomponent i at the system conditions with a specified reference state(symmetric or unsymmetric).

The property calculations for solvents and Henry components are the samewhen the reference state is changed. Only for ionic components do theproperty methods need to be specified with a reference state. The methodswith the unsymmetric reference state are available already in Aspen Plus andAspen Properties. New methods are needed only for the symmetric referencestate. Overall, the calculated total enthalpy or Gibbs free energy for the sameelectrolyte solution should be the same, regardless of the reference statespecified.

Enthalpy and Gibbs free energy of ionic components with the symmetricreference state can be written as follows:

(122)

(123)

where and are enthalpy and Gibbs free energy of ionic componenti 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:

(124)

where Tref = 298.15K. By default, is calculated from the aqueousinfinite 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 asfollows:

(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 NRTLmodel is the pure fused salts containing these ions, so the enthalpy or Gibbsfree energy of the ionic components at the symmetric reference state is theenthalpy contributions or the Gibbs free energy contributions of these ions tothe system of the pure fused salts. The condition of the pure fused salts canbe defined as follows:

(127)

which applies to all molecular components in the solution.

Given that the calculated total enthalpy or total Gibbs free energy of anelectrolyte solution by any reference state should be the same, theformulation of enthalpy or Gibbs free energy of the ionic components at thesymmetric reference state can be derived from the unsymmetric electrolyteNRTL enthalpy or Gibbs free energy calculations at the condition that allmolecular components (solvents and Henry components) approach zero, i.e.


the pure fused salts. Applying Eq. 127, the system enthalpy and Gibbs freeenergy with the unsymmetric reference state can be expressed as:

(128)

(129)

where and are the total enthalpy and total Gibbsfree energy of the solution calculated by the unsymmetric electrolyte NRTLmodel at the limit of all molecular components approach zero, that is, the

pure fused salts state, and and are theexcess enthalpy and excess Gibbs free energy of ion i at the same limitcondition.

Applying Eq. 127, the system enthalpy and Gibbs free energy with thesymmetric reference state can be expressed as:

(130)

(131)

Comparing Eqs. 130 and 131 to Eqs. 128 and 129, we can get:

(132)

(133)

Therefore, the enthalpy and Gibbs free energy of ionic components with thesymmetric reference state can be written as:

(134)

(135)


References for Symmetric and UnsymmetricElectrolyte NRTL

C.-C. Chen and L.B. Evans, "A Local Composition Model for the Excess GibbsEnergy of Aqueous Electrolyte Systems," AIChE Journal, 1986, 32, 444.

Y. Song and C.-C. Chen, "Symmetric Nonrandom Two-Liquid ActivityCoefficient 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 ModelThe UNIFAC model calculates liquid activity coefficients for the followingproperty methods: UNIFAC, UNIF-HOC, and UNIF-LL. Because the UNIFACmodel is a group-contribution model, it is predictive. All published groupparameters and group binary parameters are stored in the Aspen PhysicalProperty System.

The equation for the original UNIFAC liquid activity coefficient model is madeup of a combinatorial and residual term:

ln = ln ic + ln i

r

ln ic =

Where the molecular volume and surface fractions are:

and

Where nc is the number of components in the mixture. The coordinationnumber z is set to 10. The parameters ri and qi are calculated from the groupvolume 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:


k is the activity coefficient of a group at mixture composition, and ki is the

activity coefficient of group k in a mixture of groups corresponding to pure i.

The parameters k and ki are defined by:

With:

And:

The parameter Xk is the group mole fraction of group k in the liquid:


Symbol DefaultMDS LowerLimit

UpperLimit

Units

UFGRP (k,k, m, m, ...) — — — — —

GMUFQ Qk — — — — —

GMUFR Rk — — — — —

GMUFB bkn — — — — TEMPERATURE

The parameter UFGRP stores the UNIFAC functional group number andnumber of occurrences of each group. UFGRP is stored in the Aspen PhysicalProperty System pure component databank for most components. Fornondatabank components, enter UFGRP on the Properties Molecular StructureFunctional Group sheet. See Physical Property Data, Chapter 3, for a list ofthe UNIFAC functional groups.

UNIFAC-PSRK

The PSRK property method uses GMUFPSRK, the UNIFAC-PSRK model, whichis a variation on the standard UNIFAC model. UNIFAC-PSRK has specialgroups 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 fromGMUFB 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 Equilibriausing 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 andExtension", Ind. Eng. Chem. Res., Vol. 30, (1991), pp. 2352-2355.

UNIFAC (Dortmund Modified)The UNIFAC modification by Gmehling and coworkers (Weidlich andGmehling, 1987; Gmehling et al., 1993), is slightly different in thecombinatorial part. It is otherwise unchanged compared to the originalUNIFAC:

With:

The temperature dependency of the interaction parameters is:



UpperLimit

Units

UFGRPD (k,k, m, m, ...) — — — — —

GMUFDQ Qk — — — — —

GMUFDR Rk — — — — —

UNIFDM/1 amn,1 0 — — — TEMPERATURE



The parameter UFGRPD stores the group number and the number ofoccurrences of each group. UFGRPD is stored in the Aspen Physical PropertySystem pure component databank. For nondatabank components, enterUFGRPD on the Properties Molecular Structure Functional Group sheet. SeePhysical Property Data, Chapter 3, for a list of the Dortmund modified UNIFACfunctional groups.


References

U. Weidlich and J. Gmehling, "A Modified UNIFAC Model 1. Prediction of VLE,

hE and ," Ind. Eng. Chem. Res., Vol. 26, (1987), pp. 1372–1381.

J. Gmehling, J. Li, and M. Schiller, "A Modified UNIFAC Model. 2. PresentParameter 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:

Where k and ki 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 aconstant:



UpperLimit

Units

UFGRPL (k,k, m, m, ...) — — — — —

GMUFLQ Qk — — — — —

GMUFLR Rk — — — — —

UNIFLB/1 amn,1 0 — — — TEMPERATURE



The parameter UFGRPL stores the modified UNIFAC functional group numberand the number of occurrences of each group. UFGRPL is stored in the AspenPhysical Property System pure component databank. For nondatabankcomponents, enter UFGRP on the Properties | Molecular Structure |Functional Group sheet. See Physical Property Data, Chapter 3, for a list ofthe Larsen modified UNIFAC functional groups.

Reference: B. Larsen, P. Rasmussen, and Aa. Fredenslund, "A ModifiedUNIFAC Group-Contribution Model for Prediction of Phase Equilibria and Heatsof Mixing," Ind. Eng. Chem. Res., Vol. 26, (1987), pp. 2274 – 2286.

UNIQUAC Activity Coefficient ModelThe UNIQUAC model calculates liquid activity coefficients for these propertymethods: UNIQUAC, UNIQ-2, UNIQ-HOC, UNIQ-NTH, and UNIQ-RK. It isrecommended for highly non-ideal chemical systems, and can be used for VLEand LLE applications. This model can also be used in the advanced equationsof state mixing rules, such as Wong-Sandler and MHV2.

The equation for the UNIQUAC model is:

Where:

i =

i' =

i =

li =


ti' =

ij=

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 PhysicalProperty System has a large number of built-in parameters for the UNIQUACmodel. The binary parameters have been regressed using VLE and LLE datafrom the Dortmund Databank. The binary parameters for VLE applicationswere regressed using the ideal gas, Redlich-Kwong, and Hayden-O'Connellequations of state. See Physical Property Data, Chapter 1, for details.ParameterName/Element


UpperLimit

Units

GMUQR ri — x — — —

GMUQQ qi — x — — —

GMUQQ1 qi' q x — — —

UNIQ/1 aij 0 x -50.0 50.0 —

UNIQ/2 bij 0 x -15000.0 15000.0 TEMPERATURE

UNIQ/3 cij 0 x — — TEMPERATURE

UNIQ/4 dij 0 x — — TEMPERATURE

UNIQ/5 Tlower 0 K x — — TEMPERATURE

UNIQ/6 Tupper 1000 K x — — TEMPERATURE

UNIQ/7 eij 0 x — — TEMPERATURE

Absolute temperature units are assumed for elements 2 through 4 and 7 ofUNIQ.

The UNIQ-2 property method uses data set 2 for UNIQ. All other UNIQUACmethods use data set 1.

References

D.S. Abrams and J.M. Prausnitz, "Statistical Thermodynamics of liquidmixtures: A new expression for the Excess Gibbs Energy of Partly orCompletely Miscible Systems," AIChE J., Vol. 21, (1975), p. 116.

A. Bondi, "Physical Properties of Molecular Crystals, Liquids and Gases," (NewYork: 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 ModelThe Van Laar model (Van Laar 1910) calculates liquid activity coefficients forthe 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 =

Cij = Cji

Aii = Bii = Cii = 0

aij and bij are unsymmetrical. That is, aij may not be equal to aji, and bij maynot be equal to bji.ParametersName/Element

Symbol DefaultMDS Lower Limit UpperLimit

Units

VANL/1 aij 0 x -50.0 50.0 —

VANL/2 bij 0 x -15000.0 15000.0 TEMPERATURE

VANL/3 cij 0 x -50.0 50.0 —

VANL/4 dij 0 x -15000.0 15000.0 TEMPERATURE

The VANL-2 property method uses data set 2 for VANL. All other Van Laarmethods 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 andLiquids, 4th ed. (New York: McGraw-Hill, 1987).


Wagner Interaction ParameterThe Wagner Interaction Parameter model calculates activity coefficients. Thismodel is used for dilute solutions in metallurgical applications.

The relative activity coefficient with respect to the reference activitycoefficient of a solute i (in a mixture of solutes i, j, and l and solvent A) is:

Where:

The parameter iref is the reference activity coefficient of solute i:

kij is a binary parameter:


i = gi

This model is recommended for dilute solutions.Parameter Name/Element


UpperLimit

Units

GMWIPR/1 ai 0 x — — TEMPERATURE

GMWIPR/2 bi 0 x — — —

GMWIPR/3 ci 0 x — — —

GMWIPB/1 dij 0 x — — TEMPERATURE

GMWIPB/2 eij 0 x — — —

GMWIPB/3 fij 0 x — — —

GMWIPO gi — x — — —

GMWIPS — 0 x — — —

GMWIPS is used to identify the solvent component. You must set GMWIPS to1.0 for the solvent component. This model allows only one solvent.

References

A.D. Pelton and C. W. Bale, "A Modified Interaction Parameter Formalism forNon-Dilute Solutions," Metallurgical Transactions A, Vol. 17A, (July 1986),p. 1211.

Wilson Activity Coefficient ModelThe Wilson model calculates liquid activity coefficients for the followingproperty 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 advancedequation-of-state mixing rules, such as Wong-Sandler and MHV2. This modelcannot be used for liquid-liquid equilibrium calculations.

The equation for the Wilson model is:

Where:

ln Aij = †

The extended form of ln Aij provides more flexibility in fitting phaseequilibrium and enthalpy data. aij, bij, cij, dij, and eij are unsymmetrical. Thatis, aij may not be equal to aji, etc.

The binary parameters aij, bij, cij, dij, and eij must be determined from dataregression or VLE and/or heat-of-mixing data. The Aspen Physical PropertySystem has a large number of built-in binary parameters for the Wilsonmodel. The binary parameters have been regressed using VLE data from theDortmund Databank. The binary parameters were regressed using the idealgas, Redlich-Kwong, and Hayden-O'Connell equations of state. See PhysicalProperty Data, Chapter 1, for details.ParameterName/Element

Symbol Default MDS Lower LimitUpperLimit

Units

WILSON/1 aij 0 x -50.0 50.0 —

WILSON/2 bij 0 x -15000.0 15000.0 TEMPERATURE††

WILSON/3 cij 0 x -— — TEMPERATURE††

WILSON/4 dij 0 x — — TEMPERATURE††

WILSON/5 Tlower 0 K x — — TEMPERATURE

WILSON/6 Tupper 1000 K x — — TEMPERATURE

WILSON/7 eij 0 x — — TEMPERATURE††

The WILS-2 property method uses data set 2 for WILSON. All other Wilsonmethods 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

25C.

†† If any of biA, ciA, and eiA are non-zero, absolute temperature units areassumed for all coefficients. If biA, ciA, and eiA are all zero, the others areinterpreted in input units. The temperature limits are always interpreted ininput units.


References

G.M. Wilson, J. Am. Chem. Soc., Vol. 86, (1964), p. 127.

Wilson Model with Liquid Molar VolumeThis Wilson model (used in the method WILS-VOL) calculates liquid activitycoefficients using the original formulation of Wilson (Wilson 1964) except thatliquid molar volume is calculated at system temperature, instead of at 25C.It is recommended for highly nonideal systems, especially alcohol watersystems. It can be used in any activity coefficient property method or in theadvanced 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 = †

Vj and Vi are pure component liquid molar volume at the system temperaturecalculated using the General Pure Component Liquid Molar Volume model. Theextended form of ln Aij provides more flexibility in fitting phase equilibriumand enthalpy data. aij, bij, cij, dij, and eij are unsymmetrical. That is, aij maynot be equal to aji, etc.

The binary parameters aij, bij, cij, dij, and eij must be determined from dataregression of VLE and/or heat-of-mixing data. There are no built in binaryparameters for this model.ParameterName/Element

SymbolDefaultMDS LowerLimit

UpperLimit

Units

WSNVOL/1 aij 0 x -50.0 50.0 —

WSNVOL/2 bij 0 x -15000.0 15000.0 TEMPERATURE††

WSNVOL/3 cij 0 x — — TEMPERATURE††

WSNVOL/4 dij 0 x — — TEMPERATURE††

WSNVOL/5 eij 0 x — — TEMPERATURE††

WSNVOL/6 Tlower 0 K x — — TEMPERATURE

WSNVOL/7 Tupper 1000 K x — — TEMPERATURE

Pure component parameters for the General Pure Component Liquid MolarVolume model are also required.

† In the original formulation of the Wilson model, aij = cij = dij = eij = 0 and

. Vj and Vi are calculated at 25C.


†† If any of biA, ciA, and eiA are non-zero, absolute temperature units areassumed for all coefficients. If biA, ciA, and eiA are all zero, the others areinterpreted in input units. The temperature limits are always interpreted ininput units.

Reference: G.M. Wilson, J. Am. Chem. Soc., Vol. 86, (1964), p. 127.

Vapor Pressure and LiquidFugacity ModelsThe Aspen Physical Property System has the following built-in vapor pressureand liquid fugacity models. This section describes the vapor pressure andliquid fugacity models available.Model Type

General Pure Component Liquid VaporPressure

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 VaporPressureThe Aspen Physical Property System has several submodels for calculatingvapor pressure of a liquid. It uses parameter THRSWT/3 to determine whichsubmodel is used. See Pure Component Temperature-Dependent Propertiesfor details.If THRSWT/3is

Then this equation isused

And this parameter is used

0 Extended Antoine PLXANT

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 Antoineequation 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.

ParameterName/ Element


UpperLimit

Units

PLXANT/1 C1i x PRESSURE,TEMPERATURE

PLXANT/2 C2i x TEMPERATURE

PLXANT/3, . . . , 7 C3i, ..., C7i 0 x TEMPERATURE

PLXANT/8 C8i 0 x TEMPERATURE

PLXANT/9 C9i 1000 x TEMPERATURE

If C5i, C6i, or C7i is non-zero, absolute temperature units are assumed for allcoefficients C1i through C7i. The temperature limits are always in user inputunits.

Barin

See Barin Equations for Gibbs Energy, Enthalpy, Entropy, and Heat Capacityfor details about this submodel.

Wagner Vapor Pressure Equation

The Wagner vapor pressure equation is the best equation for correlation. Theequation 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.


PPDS Modified Wagner Vapor Pressure Equation

The PPDS equation also uses the same parameter WAGNER as the standardWagner equation:


Where:

Tri = T / Tci

pri*,l = pi

*,l / pci




UpperLimit

Units

WAGNER/1 C1i x

WAGNER/2 C2i 0 x

WAGNER/3 C3i 0 x

WAGNER/4 C4i 0 x

WAGNER/5 C5i 0 x TEMPERATURE

WAGNER/6 C6i 1000 x TEMPERATURE

TC Tci TEMPERATURE

PC pci PRESSURE

NIST Wagner 25 Liquid Vapor Pressure Equation

This equation is the same as the PPDS Modified Wagner equation above, butit uses parameter WAGNER25 instead of WAGNER, and it uses criticalproperties from this parameter set also.

Where:

Tri = T / Tci




UpperLimit

Units

WAGNER25/1 C1i x

WAGNER25/2 C2i 0 x

WAGNER25/3 C3i 0 x

WAGNER25/4 C4i 0 x

WAGNER25/5 ln pci 0 x

WAGNER25/6 Tci x TEMPERATURE

WAGNER25/7 Tlower 0 x TEMPERATURE

WAGNER25/8 Tupper 1000 x TEMPERATURE


IK-CAPE Vapor Pressure Equation

The IK-CAPE model is a polynomial equation. If the parameter PLPO isavailable, the Aspen Physical Property System can use the IK-CAPE vaporpressure equation:




UpperLimit

Units

PLPO/1 C1i X PRESSURETEMPERATURE

PLPO/2, ..., 10 C2i , ..., C10i 0 X TEMPERATURE

PLPO/11 C11i 0 X TEMPERATURE

PLPO/12 C12i 1000 X TEMPERATURE

PML Vapor Pressure Equations

The PML vapor pressure equations are modified versions of the Antoine andWagner equations. Each equation comes in two alternate forms, identicalexcept for the use of natural or base-10 logarithms. Parameter LNVPEQ/1specifies the number of the equation used. Each equation uses a separateparameter: 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):



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 temperatureunits are assumed for all elements.




UpperLimit

Units

LNVP1/1, ...,8 C1i, ..., C8i x PRESSURETEMPERATURE

LOGVP1/1, ..., 8 C1i, ..., C8i x PRESSURETEMPERATURE

LNPR1/1, ..., 8 C1i, ..., C8i x PRESSURETEMPERATURE

LOGPR1/1, ..., 8 C1i, ..., C8i x PRESSURETEMPERATURE

LNPR2/1,2 C1i, C2i x

LOGPR2/1,2 C1i, C2i x

LNVPEQ/1 (equationnumber)

LNVPEQ/2 Tlower 0 X TEMPERATURE

LNVPEQ/3 Tupper 1000 X TEMPERATURE

TC Tci TEMPERATURE

PC pci PRESSURE

NIST TDE Polynomial for Liquid Vapor Pressure

This equation can be used for calculating vapor pressure when parameterPLTDEPOL is available.


If elements 2, 3, 6, or 8 are non-zero, absolute temperature units areassumed for all elements.ParameterName/Element


UpperLimit

Units

PLTDEPOL/1 C1i X

PLTDEPOL/2 C2i 0 X TEMPERATURE

PLTDEPOL/3 C3i 0 X

PLTDEPOL/4, ..., 8 C4i , ..., C8i 0 X TEMPERATURE

PLTDEPOL/9 Tlower 0 X TEMPERATURE

PLTDEPOL/10 Tupper 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 ofCorresponding 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 "Theebulliometric method of vapor-pressure measurement: vapor pressures ofbenzene, hexafluorobenzene, and naphthalene," J. Chem. Thermodyn. 22(1990), p. 589.

API Sour ModelThe API Sour model is based on the API sour water model for correlating theammonia, carbon dioxide, and hydrogen sulfide volatilities from aqueous sourwater system. The model assumes aqueous phase chemical equilibriumreactions involving CO2, H2S, and NH3. The model is not usable with chemistryin the true component approach. Use the apparent component approach withthis model.

The model is applicable from 20 C to 140 C. The authors developed the modelusing available phase equilibrium data and reported average errors betweenthe model and measured partial pressure data as followsCompound 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 tobe reproduced here.

Reference

New Correlation of NH3, CO2, and H2S Volatility Data from Aqueous SourWater Systems, API Publication 955, March 1978 (American PetroleumInstitute).

Braun K-10 ModelThe BK10 model uses the Braun K-10 K-value correlations, which weredeveloped from the K10 charts (K-values at 10 psia) for both real and pseudocomponents. The form of the equation used is an extended Antoine vaporpressure equation with coefficients specific to real components and pseudocomponent boiling ranges.

This method is strictly applicable to heavy hydrocarbons at low pressures.However, our model includes coefficients for a large number of hydrocarbonsand light gases. For pseudocomponents the model covers boiling ranges 450– 700 K (350 – 800F). Heavier fractions can also be handled using themethods developed by AspenTech.


References

B.C. Cajander, H.G. Hipkin, and J.M. Lenoir, "Prediction of Equilibrium Ratiosfrom Nomograms of Improved Accuracy," Journal of Chemical EngineeringData, vol. 5, No. 3, July 1960, p. 251-259.

J.M. Lenoir, "Predict K Values at Low Temperatures, part 1," HydrocarbonProcessing, p. 167, September 1969.

J.M. Lenoir, "Predict K Values at Low Temperatures, part 2," HydrocarbonProcessing, p. 121, October 1969.

Chao-Seader Pure Component LiquidFugacity ModelThe Chao-Seader model calculates pure component fugacity coefficient, forliquids. It is used in the CHAO-SEA property method. This is an empiricalmodel with the Curl-Pitzer form. The general form of the model is:

Where:

=



Units



OMEGA i— — -0.5 2.0 —

References

K.C. Chao and J.D. Seader, "A General Correlation of Vapor-Liquid Equilibriain Hydrocarbon Mixtures," AIChE J., Vol. 7, (1961), p. 598.

Grayson-Streed Pure Component LiquidFugacity ModelThe Grayson-Streed model calculates pure component fugacity coefficients forliquids, and is used in the GRAYSON/GRAYSON2 property methods. It is anempirical model with the Curl-Pitzer form. The general form of the model is:

Where:



Units





Units


OMEGA i— — -0.5 2.0 —

References

H.G. Grayson and C.W. Streed, Paper 20-PO7, Sixth World PetroleumConference, Frankfurt, June 1963.

Kent-Eisenberg Liquid Fugacity ModelThe Kent-Eisenberg model calculates liquid mixture component fugacitycoefficients and liquid enthalpy for the AMINES property method.

The chemical equilibria in H2S + CO2 + amine systems are described usingthese chemical reactions:

Where:

R' = Alcohol substituted alkyl groups

The equilibrium constants are given by:

The chemical equilibrium equations are solved simultaneously with thebalance equations. This obtains the mole fractions of free H2S and CO2 insolution. The equilibrium partial pressures of H2S and CO2 are related to therespective free concentrations by Henry's constants:


The apparent fugacities and partial molar enthalpies, Gibbs energies andentropies of H2S and CO2 are calculated by standard thermodynamicrelationships. 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 PhysicalProperty System. The coefficients for the equilibrium constants weredetermined 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 ModelThe Maxwell-Bonnell model calculates vapor pressure using the Maxwell-Bonnell vapor pressure correlation for all hydrocarbon pseudo-components asa function of temperature. This is an empirical correlation based on APIprocedure 5A1.15, 5A1.13. This model is used in property method MXBONNELfor calculating vapor pressure and liquid fugacity coefficients (K-values).

References

API procedure 5A1.15 and 5A1.13.

Solid Antoine Vapor Pressure ModelThe vapor pressure of a solid can be calculated using the Antoine equation.

Parameters for some components are available for the extended Antoineequation 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.



Units

PSANT/1 C1i — x — — PRESSURE,TEMPERATURE

PSANT/2 C2i — x — — TEMPERATURE

PSANT/3 C3i 0 x — — TEMPERATURE




General Pure Component Heatof VaporizationThe Aspen Physical Property System has several submodels for calculatingpure component heat of vaporization. It uses parameter THRSWT/4 todetermine which submodel is used. See Pure Component Temperature-Dependent Properties for details.If THRSWT/4is

Then this equation is usedAnd this parameter isused

0 Watson DHVLWT

106 DIPPR DHVLDP

301 PPDS DHVLDS

401 IK-CAPE DHVLPO

505 NIST TDE Watson equation DHVLTDEW

DIPPR Heat of Vaporization EquationThe DIPPR equation is used to calculate heat of vaporization when THRSWT/4is set to 106. (Other DIPPR equations may sometimes be used. See PureComponent Temperature-Dependent Properties for details.)

The equation for the DIPPR heat of vaporization model is:

Where:

Tri = T / Tci


Linear extrapolation of vapHi* versus T occurs outside of temperature bounds,

using the slope at the temperature bound, except that vapHi* is zero for

.ParameterName/Element


UpperLimit

Units

DHVLDP/1 C1i — x — — MOLE-ENTHALPY

DHVLDP/2, ..., 5 C2i, ..., C5i 0 x — — —

DHVLDP/6 C6i 0 x — — TEMPERATURE

DHVLDP/7 C7i 1000 x — — TEMPERATURE


Watson Heat of Vaporization EquationThe Watson equation is used to calculate heat of vaporization whenTHRSWT/4 is set to 0. See Pure Component Temperature-DependentProperties 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.ParameterName/Element


UpperLimit

Units


DHVLWT/1 vapHi*(T1) — 5x104 5x108 MOLE-ENTHALPY

DHVLWT/2 T1 — 4.0 3500.0 TEMPERATURE

DHVLWT/3 ai 0.38 -2.0 2.0 —

DHVLWT/4 bi 0 -2.0 2.0 —

DHVLWT/5 Tmin 0 0.0 1500.0 TEMPERATURE

PPDS Heat of Vaporization EquationThe PPDS equation is used to calculate heat of vaporization when THRSWT/4is set to 301. See Pure Component Temperature-Dependent Properties fordetails.

The equation for the PPDS model is:

where R is the gas constant.


using the slope at the temperature bound.ParameterName/Element


UpperLimit

Units


DHVLDS/1 C1i — — — — —

DHVLDS/2 C2i 0 — — — —

DHVLDS/3 C3i 0 — — — —

DHVLDS/4 C4i 0 — — — —

DHVLDS/5 C5i 0 — — — —

DHVLDS/6 C6i 0 — — TEMPERATURE

DHVLDS/7 C7i 1000 — — TEMPERATURE


IK-CAPE Heat of Vaporization EquationThe IK-CAPE equation is used to calculate heat of vaporization whenTHRSWT/4 is set to 401. See Pure Component Temperature-DependentProperties for details.

The equation for the IK-CAPE model is:


using the slope at the temperature boundParameterName/Element


UpperLimit

Units

DHVLPO/1 C1i — X — — MOLE-ENTHALPY

DHVLPO/2, ..., 10C2i, ..., C10i 0 X — — MOLE-ENTHALPYTEMPERATURE

DHVLPO/11 C11i 0 X — — TEMPERATURE

DHVLPO/12 C12i 1000 X — — TEMPERATURE

NIST TDE Watson Heat of VaporizationEquationThe NIST TDE Watson equation is used to calculate heat of vaporization whenTHRSWT/4 is set to 505. See Pure Component Temperature-DependentProperties for details.

The equation is:


using the slope at the temperature boundParameterName/Element


UpperLimit

Units

DHVLTDEW/1 C1i — X — — —

DHVLTDEW/2, 3,4

C2i, C3i, C4i 0 X — — —

DHVLTDEW/5 Tci — X — — TEMPERATURE

DHVLTDEW/6 nTerms 4 X — — —

DHVLTDEW/7 Tlower 0 X — — TEMPERATURE

DHVLTDEW/8 Tupper 1000 X — — TEMPERATURE


Clausius-Clapeyron EquationThe Aspen Physical Property System can calculate heat of vaporization usingthe Clausius Clapeyron equation:

Where:

= Slope of the vapor pressure curve calculated from the ExtendedAntoine equation

Vi*,v = Vapor molar volume calculated from the Redlich Kwong

equation of state

Vi*,l = Liquid molar volume calculated from the Rackett equation

For parameter requirements, see General Pure Component Liquid VaporPressure, the General Pure Component Liquid Molar Volume model, andRedlich Kwong.

Molar Volume and DensityModelsThe Aspen Physical Property System has the following built-in molar volumeand density models available. This section describes the molar volume anddensity models.Model Type

API Liquid Volume Liquid volume

Brelvi-O'Connell Partial molar liquidvolume 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 MolarVolume

Liquid volume/liquiddensity

Rackett/Campbell-Thodos Mixture LiquidVolume

Liquid volume

Modified Rackett Liquid volume

General Pure Component Solid Molar Volume Solid volume

Liquid Volume Quadratic Mixing Rule Liquid volume

API Liquid Molar VolumeThis model calculates liquid molar volume for a mixture, using the APIprocedure 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 DataBook, Petroleum Refining, 4th edition)

At high density, the Ritter equation is used (adapted from Ritter, Lenoir, andSchweppe, Petrol. Refiner 37 [11] 225 (1958)):

Where SG is the specific gravity, Tb is the mean average boiling point inRankine, T is the temperature of the system in Rankine, and the mass volumeis 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:


See the Rackett model for descriptions.ParameterName/Element


UpperLimit

Units

TB Tb — — 4.0 2000.0 TEMPERATURE

API API — — -60.0 500.0 —

TC Tc — — 5.0 2000.0 TEMPERATURE




UpperLimit

Units

PC pc — — 105 108 PRESSURE

RKTZRA ZRA ZC — 0.1 0.5 —

There are two versions of this model: VL2API and VL2API5. Model VL2API isused 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 pseudocomponentusing the API procedure 6A3.5 (or Ritter equation), then computes thedensity of the pseudocomponent mixture as a mole-fraction-weightedaverage.

The VL2API5 model calculates the liquid density of the mixture of thepseudocomponents as a whole. It first computes the specific gravity andmean average boiling point of the pseudocomponent mixture, then uses theAPI procedure 6A3.5 (or Ritter equation) to compute the mixture liquiddensity.

Both models use the same procedure 6A3.10 for pressure correction.Experience shows that VL2API5 is less sensitive to how thepseudocomponents are generated from the same assay (number of cutpoints, etc.).

Brelvi-O'ConnellThe Brelvi-O'Connell model calculates partial molar volume of a supercriticalcomponent i at infinite dilution in pure solvent A. Partial molar volume atinfinite dilution is required to compute the effect of pressure on Henry'sconstant. (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:



UpperLimit

Units

TC TcA — — 5.0 2000.0 TEMPERATURE

PC pcA — — 105 108 PRESSURE

RKTZRA ZARA ZC x 0.1 1.0 —




UpperLimit

Units

VLBROC/1 ViBO 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 VolumeThe 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 itsmole 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 usedinstead. The default option uses this equation to calculate the liquid molarvolume for electrolyte solutions:

(1)

Where:

Vml = Liquid molar volume for electrolyte solutions.

Vsl = Liquid molar volume for solvent mixtures.

Vel = Liquid molar volume for electrolytes.

Apparent Component Approach

For molecular solvents, the liquid molar volume is calculated by:

(2)

Where:


Vw* = Molar volume of water from the steam table.

xnws = Sum of the mole fractions of all non-watersolvents.

Vnwsl = Liquid molar volume for the mixture of all non-

water solvents. It is calculated using theRackett equation.

For electrolytes:


(3)

(4)

(5)

(6)

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 ionicconcentrations, even if you use the apparent component approach. Thistechnique is explained in Electrolyte Calculation in Physical Property Methods.

The result is that electrolytes are generated from all possible combinations ofions in solution. The following equation is consistently applied to determinethe amounts of each possible apparent electrolyte nca:

(7)

Where:

nca = Number of moles of apparent electrolyte ca

zc = Charge of c

zfactor = zc if c and a have the same number ofcharges; otherwise 1.

nc = Number of moles of cation c

na = Number of moles of anion a

For example: given an aqueous solution of Ca2+, Na+, SO42-, Cl- four

electrolytes are found: CaCl2, Na2SO4, CaSO4, and NaCl. The Clarkeparameters of all four electrolytes are used. You can rely on the default,which calculates the Clarke parameters from ionic parameters. Otherwise, youmust enter parameters for any electrolytes that may not exist in thecomponents list. If you do not want to use the default, the first step in usingthe Clarke model is to add any needed components for electrolytes not in thecomponents list.

True Component Approach

The true molar volume is obtained from the apparent molar volume:


(8)

Where:

Vml,t = Liquid volume per number of true species

Vml,a = Liquid volume per number of apparent species, Vm

l

of equation 1

na = Number of apparent species

nt = Number of true species

The apparent molar volume is calculated as explained in the precedingsubsection.

Temperature Dependence

The temperature dependence of the molar volume of the solution isapproximately equal to the temperature dependence of the molar volume ofthe solvent mixture:

(9)

Where Vml(298.15K) is calculated from equation 1.


ApplicableComponents

Symbol Default Units

VLCLK/1 Cation-Anion † MOLE-VOLUME

VLCLK/2 Cation-Anion Aca 0.020 MOLE-VOLUME

†If VLCLK/1 is missing, it is calculated based on VLBROC and CHARGE asfollows:

(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 MixtureLiquid Volume for additional parameters used in the Rackett equation.

Reference

C.C. Chen, private communication.

COSTALD Liquid VolumeThe equation for the COSTALD liquid volume model is:


Where:

VmR,0 and Vm

R, are functions or Tr for

For , there is a linear interpolation between the liquid density atTr = 0.95 and the vapor density at Tr = 1.05. This model can be used tocalculate saturated and compressed liquid molar volume. The compressedliquid molar volume is calculated using the Tait equation:

Where B and C are functions of T, , Tc, Pc and Psat is the saturated pressure

at T.


Mixing Rules:

Where:

To improve results, the Aspen Physical Property System uses a specialcorrelation for water when this model is used. Changing the VSTCTD andOMGCTD parameters for water will not affect the results of the specialcorrelation.ParameterName/Element


UpperLimit

Units


VSTCTD Vr*,CTD VC X 0.001 3.5 MOLE-VOLUME

OMGCTD rOMEGA X -0.5 2.0 —

References

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 VolumeThe Debye-Hückel model calculates liquid molar volume for aqueouselectrolyte 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 isassumed 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 =

the ionic strength, with

mk = Molarity of ion k

Av is computed as follows:

Where:

A = Debye-Hückel constant for the osmoticcoefficients (Pitzer, 1979)

w= Density of water (kg / m3)

w= Dielectric constant of water (Fm-1), a function

of pressure and temperature (Bradley andPitzer, 1979)

Parameter Name ApplicableComponents


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 thethermodynamic behavior of aqueous electrolytes at high pressure andtemperature. I. Thermodynamic/electrostatic properties of the solvent", Am.J. Sci., 274, 1089 (1974).

K.S. Pitzer, "Theory: Ion Interaction Approach," Activity Coefficients inElectrolyte Solutions, Pytkowicz, R. ed., Vol. I, (CRC Press Inc., Boca Raton,Florida, 1979).

Liquid Constant Molar Volume ModelThis model, VL0CONS, uses a constant value entered by the user as the purecomponent liquid molar volume. It is not a function of temperature orpressure. This is used with the solids handling property method for modelingnonconventional solids.Parameter Name Default MDS Units

VLCONS 1 x MOLE-VOLUME

General Pure Component Liquid MolarVolumeThe Aspen Physical Property System has several submodels for calculatingliquid molar volume. It uses parameter THRSWT/2 to determine whichsubmodel is used. See Pure Component Temperature-Dependent Propertiesfor 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 ThermoMLPolynomial

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 alwaysused by default. This is not necessarily consistent with the pure componentmolar volume or density. If you need consistency, select route VLMX26 on theProperties | Property Methods form. This route calculates mixture molarvolume from the mole-fraction average of pure component molar volumes.

Many of these equations calculate density first, and return calculate liquidmolar 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 somesubstances. Check the value of THRSWT/2 to determine the equation used.See Pure Component Temperature-Dependent Properties for details aboutDIPPR equations.

In either case, linear extrapolation of i*,l versus T occurs outside of

temperature bounds.ParameterName/Element


UpperLimit

Units

DNLDIP/1 C1i — x — — MOLE-DENSITY †

DNLDIP/2 C2i 0 x — — †

DNLDIP/3 C3i Tci † x — — TEMPERATURE †



DNLDIP/6 C6i 0 x — — TEMPERATURE

DNLDIP/7 C7i 1000 x — — TEMPERATURE

† For equation 116, the units are MOLE-DENSITY for parameters DNLDIP/1through DNLDIP/5 and the default for DNLDIP/3 is 0. For equation 105,DNLDIP/5 is not used, and absolute temperature units are assumed forDNLDIP/3.

PPDS

The PPDS equation is:

Linear extrapolation of i*,l versus T occurs outside of temperature bounds.



UpperLimit

Units

MW Mi — — 1.0 5000.0 —




UpperLimit

Units

VC Vci — — 0.001 3.5 MOLE-VOLUME


DNLPDS/1 C1i — — — — MASS-DENSITY

DNLPDS/2 C2i 0 — — — MASS-DENSITY



DNLPDS/5 C5i 0 x — — TEMPERATURE

DNLPDS/6 C6i 1000 x — — TEMPERATURE

IK-CAPE

The IK-CAPE equation is:

Linear extrapolation of Vi*,l versus T occurs outside of temperature bounds.



UpperLimit

Units

VLPO/1 C1i — X — — MOLE-VOLUME

VLPO/2, ..., 10 C2i, ..., C10i 0 X — — MOLE-VOLUMETEMPERATURE

VLPO/11 C11i 0 X — — TEMPERATURE

VLPO/12 C12i 1000 X — — TEMPERATURE

NIST ThermoML Polynomial

This equation can be used when parameter DNLTMLPO is available.



UpperLimit

Units

DNLTMLPO/1 C1i — X — — MOLE-DENSITY

DNLTMLPO/2, 3,4

C2i, C3i, C4i 0 X — — MOLE-DENSITYTEMPERATURE

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 absolutetemperature units.Note: Above Tr=0.99 an extrapolation method is used to smooth thetransition to constant molar volume equal to the critical volume.ParameterName/Element


UpperLimit

Units



RKTZRA Zi*,RA ZC x 0.1 1.0 —

NIST TDE Rackett Parameters

This equation can be used when the parameter DNLRACK is available.




UpperLimit

Units

DNLRACK/1 Zc — x — — —

DNLRACK/2 n 2/7 x — — —

DNLRACK/3 Tci — x — — TEMPERATURE

DNLRACK/4 pci 0 x — — PRESSURE

DNLRACK/5 Tlower 0 x — — TEMPERATURE

DNLRACK/6 Tupper 1000 x — — TEMPERATURE

NIST COSTALD Parameters

This equation can be used when the parameter DNLCOSTD is available.





UpperLimit

Units

DNLCOSTD/1 Voi — x — — VOLUME

DNLCOSTD/2 0 x — — —

DNLCOSTD/3 Tci — x — — TEMPERATURE

DNLCOSTD/4 Tlower 0 x — — TEMPERATURE

DNLCOSTD/5 Tupper 1000 x — — TEMPERATURE

NIST TDE Expansion

This equation can be used when the parameter DNLEXSAT is available.




UpperLimit

Units

DNLEXSAT/1 ci— x — — MOLE-

DENSITY

DNLEXSAT/2 C1i — x — — MOLE-DENSITY

DNLEXSAT/3,..., DNLEXSAT/7

C2i, ..., C6i 0 x — — MOLE-DENSITY

DNLEXSAT/8 Tci — x — — TEMPERATURE

DNLEXSAT/9 nTerms 6 x — — —

DNLEXSAT/10 Tlower 0 x — — TEMPERATURE

DNLEXSAT/11 Tupper 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 LiquidVolumeThe Rackett equation calculates liquid molar volume for all activity coefficientbased and petroleum tuned equation of state based property methods. In thelast category of property methods, the equation is used in conjunction withthe API model. The API model is used for pseudocomponents, while theRackett model is used for real components. (See API Liquid Volume .)Campbell-Thodos is a variation on the Rackett model which allows thecompressibility term Zi

*,RA to vary with temperature.

Rackett

The equation for the Rackett model is:

Where:

Tc =

=

ZmRA =

Vcm =

Tr = T / Tc



UpperLimit

Units



VCRKT Vci VC x 0.001 3.5 MOLE-VOLUME

RKTZRA Zi*,RA ZC x 0.1 1.0 —

RKTKIJ kij x -5.0 5.0 —


Campbell-Thodos

The Campbell-Thodos model uses the same equation and parameters as theRackett model, above, except that Zm

RAis allowed to vary with temperature:

ZmRA =

Campbell-Thodos also uses separately-adjustable versions of the criticalparameters. Tmin and Tmax define the temperature range where theequation is applicable.ParameterName/Element


UpperLimit

Units

RACKET/1 R*Tci/Pci R*Tci/Pci — — — MOLE-VOLUME

RACKET/2 Zi*,RA RKTZRA x 0.1 1.0 —

RACKET/3 di 0 x 0 0.11 —

RACKET/4 Tmin 0 x — — TEMPERATURE

RACKET/5 Tmax 1000 x — — TEMPERATURE

The Campbell-Thodos model is used when RACKET/3 is set to a value lessthan 0.11. The default value, 2/7, indicates that the standard Rackettequation should be used. When Campbell-Thodos is not used, RACKET/3should 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.


Modified Rackett Liquid Molar VolumeThe Modified Rackett equation improves the accuracy of liquid mixture molarvolume calculation by introducing additional parameters to compute the purecomponent parameter RKTZRA and the binary parameter kij.

The equation for the Modified Rackett model is:

Where:

Tc =

kij =

=


ZmRA =

Zi*,RA =

Vcm =

Tr = T / Tc



UpperLimit

Units

MRKZRA/1 ai RKTZRA x 0.1 0.5 —

MRKZRA/2 bi 0 x — — —

MRKZRA/3 ci 0 x — — —

MRKKIJ/1 Aij x — — —

MRKKIJ/2 Bij 0 x — — —

MRKKIJ/3 Cij 0 x — — —

References

H.G. Rackett, J.Chem, Eng. Data., Vol. 15, (1970), p. 514.


Rackett Extrapolation MethodThe 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 specialextrapolation method is required for this equation. This method involves thecalculation of an intermediate temperature T00 near the critical temperature.When the temperature exceeds T00, the volume is constant at the criticalvolume. When the temperature is between 0.99Tc and T00, a circle equation isused to smoothly interpolate the volume between the value and slope at0.99Tc 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 temperaturedifference 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) for0.99Tc < T < T00:


General Pure Component Solid MolarVolumeThe Aspen Physical Property System has several submodels for calculatingsolid molar volume. It uses parameter THRSWT/1 to determine whichsubmodel is used. See Pure Component Temperature-Dependent Propertiesfor 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 ThermoMLpolynomial

DNSTMLPO

Aspen Polynomial

The equation for the Aspen solids volume polynomial is:

Linear extrapolation of Vi*,s versus T occurs outside of temperature bounds.

ParameterName


Symbol MDS Default Units

VSPOLY/1 Salts, CI solids C1i x — MOLE-VOLUMETEMPERATURE

VSPOLY/2, ..., 5 Salts, CI solids C2i, ..., C5i x 0 MOLE-VOLUMETEMPERATURE

VSPOLY/6 Salts, CI solids C6i x 0 MOLE-VOLUMETEMPERATURE

VSPOLY/7 Salts, CI solids C7i x 1000 MOLE-VOLUMETEMPERATURE

IK-CAPE Equation


Linear extrapolation of Vi*,s versus T occurs outside of temperature bounds.



UpperLimit

Units

VSPO/1 C1i — X — — MOLE-VOLUME




UpperLimit

Units

VSPO/2, ..., 10 C2i, ..., C10i 0 X — — MOLE-VOLUMETEMPERATURE

VSPO/11 C11i 0 X — — TEMPERATURE

VSPO/12 C12i 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 ComponentTemperature-Dependent Properties for details.)

The model returns solid molar volume for pure components.ParameterName/Element


UpperLimit

Units

DNSDIP/1 C1i — x — — MOLE-DENSITY

DNSDIP/2, ..., 5 C2i, ..., C5i 0 x — — MOLE-DENSITY,TEMPERATURE

DNSDIP/6 C6i 0 x — — TEMPERATURE

DNSDIP/7 C7i 1000 x — — TEMPERATURE


Linear extrapolation of i*,s versus T occurs outside of temperature bounds.

Vi*,s = 1 / i

*,s



UpperLimit

Units

DNSTMLPO/1 C1i — x — — MOLE-DENSITY

DNSTMLPO/2,...,8 C2i, ..., C8i 0 x — — MOLE-DENSITY,TEMPERATURE

DNSTMLPO/9 nTerms 8 x — — —

DNSTMLPO/10 Tlower 0 x — — TEMPERATURE

DNSTMLPO/11 Tupper 1000 x — — TEMPERATURE


Liquid Volume Quadratic Mixing RuleWith i and j being components, the liquid volume quadratic mixing rule is:

Option CodesOption Code Value Descriptions

1 0 Use normal pure component liquid volume model for allcomponents (default)

1 Use steam tables for water

2 0 Use mole basis composition (default)

1 Use mass basis composition

ParameterParameterName/Element


UpperLimit

Units

VLQKIJ Kij - x - - —

This model is not part of any property method. To use it, you will need todefine a property method on the Properties | Property Methods form.Specify the route VLMXQUAD for VLMX on the Routes sheet of this form, orthe model VL2QUAD for VLMX on the Models sheet.

Heat Capacity ModelsThe 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 CapacityPolynomial

Electrolyte liquid

Criss-Cobble Aqueous Infinite DilutionIonic Heat Capacity

Electrolyte liquid

General Pure Component Liquid HeatCapacity

Liquid

General Pure Component Ideal Gas HeatCapacity

Ideal gas

General Pure Component Solid HeatCapacity

Solid

Aqueous Infinite Dilution Heat CapacityThe aqueous phase infinite dilution enthalpies, entropies, and Gibbs energiesare calculated from the heat capacity polynomial. The values are used in thecalculation 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




CPAQ0/1 Ions, molecular solutes C1i — TEMPERATURE andHEAT CAPACITY

CPAQ0/2,…,6 Ions, molecular solutes C2i, ..., C6i 0 TEMPERATURE andHEAT CAPACITY

CPAQ0/7 Ions, molecular solutes C7i 0 TEMPERATURE

CPAQ0/8 Ions, molecular solutes C8i 1000 TEMPERATURE

If any of C4i through C6i is non-zero, absolute temperature units areassumed for C1i through C6i . Otherwise, user input units for temperature areused. The temperature limits are always interpreted in user input units.

Criss-Cobble Aqueous Infinite Dilution IonicHeat CapacityThe Criss-Cobble correlation for aqueous infinite dilution ionic heat capacity isused if no parameters are available for the aqueous infinite dilution heatcapacity polynomial. From the calculated heat capacity, the thermodynamicproperties entropy, enthalpy and Gibbs energy at infinte dilution in water arederived:

ParameterName



IONTYP Ions Ion Type 0 —

SO25C Anions MOLE-ENTROPY

Cations MOLE-ENTROPY

General Pure Component Liquid HeatCapacityThe Aspen Physical Property System has several submodels for calculatingliquid heat capacity. It uses parameter THRSWT/6 to determine whichsubmodel is used. See Pure Component Temperature-Dependent Propertiesfor 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 capacitypolynomial

CPLPO

403 IK-CAPE liquid heatcapacity

CPLIKC


CPLTMLPO

506 NIST TDE equation CPLTDECS

This liquid heat capacity model is used to calculate pure component liquidheat capacity and pure component liquid enthalpy. To use this model, twoconditions must exist:

One of the parameters for calculating heat capacity (see table) isavailable.

The component is not supercritical (HENRY-COMP).

The model uses a specific method (see Methods in Property CalculationMethods and Routes):

Where

= Reference enthalpy calculated at Tref

= Ideal gas enthalpy

= Vapor enthalpy departure

= Enthalpy of vaporization

Tref is the reference temperature; it defaults to 298.15 K. You can enter adifferent value for the reference temperature. This is useful when you want touse this model for very light components or for components that are solids at298.15K.

Activate this model by specifying the route DHL09 for the property DHL onthe Properties Property Methods Routes sheet. For equation of state propertymethod, you must also modify the route for the property DHLMX to use aroute with method 2 or 3, instead of method 1. For example, you can use theroute DHLMX00 or DHLMX30. You must ascertain that the route for DHLMXthat you select contains the appropriate vapor phase model and heat ofmixing calculations. Click the View button on the form to see details of theroute.

Optionally, you can specify that this model is used for only certaincomponents. The properties for the remaining components are thencalculated by the standard model. Use the parameter COMPHL to specify the


components for which this model is used. By default, all components with theCPLDIP or CPLIKC parameters use this model.

Barin


DIPPR Liquid Heat Capacity

The DIPPR equation is used to calculate liquid heat capacity when parameterTHRSWT/6 is 100.


Linear extrapolation occurs for Cp*,l versus T outside of bounds.



UpperLimit

Units

CPLDIP/1 C1i — x — — MOLE-HEAT-CAPACITY,TEMPERATURE

CPLDIP/2, ..., 5 C2i, ..., C5i 0 x — — MOLE-HEAT-CAPACITY,TEMPERATURE

CPLDIP/6 C6i 0 x — — TEMPERATURE

CPLDIP/7 C7i 1000 x — — TEMPERATURE

TREFHL Tref 298.15 — — — TEMPERATURE

COMPHL — — — — — —

To specify that the model is used for a component, enter a value of 1.0 forCOMPHL.


PPDS Liquid Heat Capacity

The PPDS equation is used to calculate liquid heat capacity when parameterTHRSWT/6 is 301.


Where R is the gas constant.

Linear extrapolation occurs for Cp*,l versus T outside of bounds.




UpperLimit

Units

CPLPDS/1 C1i — — — — —

CPLPDS/2 C2i 0 — — — —

CPLPDS/3 C3i 0 — — — —

CPLPDS/4 C4i 0 — — — —

CPLPDS/5 C5i 0 — — — —

CPLPDS/6 C6i 0 — — — —

CPLPDS/7 C7i 0 x — — TEMPERATURE

CPLPDS/8 C8i 0.99 TC x — — TEMPERATURE

IK-CAPE Liquid Heat Capacity

Two IK-CAPE equations can be used to calculate liquid heat capacity. Linearextrapolation 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:



UpperLimit

Units

CPLIKC/1 C1i —T

x — — MOLE-HEAT-CAPACITY

CPLIKC/2,...,4 C2i, ..., C4i 0 x — — MOLE-HEAT-CAPACITY,TEMPERATURE

CPLIKC/5 C5i 0 x — — MOLE-HEAT-CAPACITY,TEMPERATURE †

CPLIKC/6 C6i 0 x — — TEMPERATURE

CPLIKC/7 C7i 1000 x — — TEMPERATURE

† If C5i is non-zero, absolute temperature units are assumed for C2i throughC5i. Otherwise, user input units for temperature are used. The temperaturelimits are always interpreted in user input units.

When THRSWT/6 is 401, the IK-CAPE heat capacity polynomial is used.Theequation is:



UpperLimit

Units

CPLPO/1 C1i — X — — MOLE-CAPACITY

CPLPO/2,…,10 C2i, ..., C10i 0 X — — MOLE-CAPACITYTEMPERATURE

CPLPO/11 C11i 0 X — — TEMPERATURE




UpperLimit

Units

CPLPO/12 C12i 1000 X — — TEMPERATURE

See Pure Component Temperature-Dependent Properties for details on theTHRSWT parameters.

NIST Liquid Heat Capacity

Two NIST equations can be used to calculate liquid heat capacity. Linearextrapolation occurs for Cp

*,l versus T outside of bounds for either equation.

When THRSWT/6 is 503, the ThermoML polynomial is used to calculate liquidheat capacity:



UpperLimit

Units

CPLTMLPO/1 C1i — X — — J/K^2/mol

CPLTMLPO/2,…,5 C2i, ..., C5i 0 X — — J/K^2/mol

CPLTMLPO/6 nTerms 5 X — — —

CPLTMLPO/7 Tlower 0 X — — TEMPERATURE

CPLTMLPO/8 Tupper 1000 X — — TEMPERATURE

When THRSWT/6 is 506, the TDE equation is used to calculate liquid heatcapacity:



UpperLimit

Units

CPLTDECS/1 C1i — X — — MOLE-HEAT-CAPACITY

CPLTDECS/2,…,4 C2i, ..., C4i 0 X — — MOLE-HEAT-CAPACITY

CPLTDECS/5 B 0 X — — MOLE-HEAT-CAPACITY

CPLTDECS/6 Tci — X — — TEMPERATURE

CPLTDECS/7 nTerms 4 X — — —

CPLTDECS/8 Tlower 0 X — — TEMPERATURE

CPLTDECS/9 Tupper 1000 X — — TEMPERATURE

See Pure Component Temperature-Dependent Properties for details on theTHRSWT parameters.


General Pure Component Ideal Gas HeatCapacityThe Aspen Physical Property System has several submodels for calculatingideal gas heat capacity. It uses parameter THRSWT/7 to determine whichsubmodel is used. See Pure Component Temperature-Dependent Propertiesfor details.If THRSWT/7 is This equation is used And this parameter is

used

0 Ideal gas heat capacitypolynomial

CPIG

107, 127 DIPPR 107 or 127 CPIGDP

200-211 Barin CPIXP1, CPIXP2, CPIXP3

301 PPDS CPIGDS


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 inASPENPCD, AQUEOUS, and SOLIDS databanks. This model is also used inPCES.

Cp*,ig is linearly extrapolated using slope at



UpperLimit

Units

CPIG/1 C1i — — — — MOLE-HEAT-CAPACITY,TEMPERATURE

CPIG/2, ..., 6 C2i, ..., C6i 0 — — — MOLE-HEAT-CAPACITY,TEMPERATURE

CPIG/7 C7i 0 — — — TEMPERATURE

CPIG/8 C8i 1000 — — — TEMPERATURE

CPIG/9, 10,11

C9i, C10i, C11i — — — — MOLE-HEAT-CAPACITY,TEMPERATURE †

† If C10i or C11i is non-zero, then absolute temperature units are assumed forC9i through C11i. Otherwise, user input temperature units are used for allparameters. User input temperature units are always used for C1i through C8i.



This equation can be used when parameter CPITMLPO is available.



UpperLimit

Units

CPITMLPO /1 C1i — x — — J/K^2/mol

CPITMLPO /2,..., 6

C2i, ..., C6i 0 x — — J/K^2/mol

CPITMLPO/7 nTerms 6 x — — —

CPITMLPO /8 Tlower 0 x — — TEMPERATURE

CPITMLPO /9 Tupper 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 ComponentTemperature-Dependent Properties for details.)ParameterName/Element


UpperLimit

Units

CPIGDP/1 C1i — x — — MOLE-HEAT-CAPACITY

CPIGDP/2 C2i 0 x — — MOLE-HEAT-CAPACITY

CPIGDP/3 C3i 0 x — — TEMPERATURE ††



CPIGDP/6 C6i 0 x — — TEMPERATURE

CPIGDP/7 C7i 1000 x — — TEMPERATURE

†† Absolute temperature units are assumed for C3i and C5i. The temperaturelimits are always interpreted in user input units.

DIPPR Equation 127

The DIPPR ideal gas heat capacity equation 127 is:




UpperLimit

Units

CPIGDP/1 C1i — x — — MOLE-HEAT-CAPACITY







†† Absolute temperature units are assumed for C3i, C5i and C7i.

Barin


NIST Aly-Lee

This equation is the same as the DIPPR Aly and Lee equation 107 above, butit uses a different parameter set. Note that elements 6 and 7 of the CPIALEEparameter are not used in the equation.ParameterName/Element


UpperLimit

Units

CPIALEE/1 C1i — x — — MOLE-HEAT-CAPACITY

CPIALEE/2 C2i 0 x — — MOLE-HEAT-CAPACITY

CPIALEE/3 C3i 0 x — — TEMPERATURE ††

CPIALEE/4 C4i 0 x — — MOLE-HEAT-CAPACITY

CPIALEE/5 C5i 0 x — — TEMPERATURE ††

CPIALEE/8 C6i 0 x — — TEMPERATURE

CPIALEE/9 C7i 1000 x — — TEMPERATURE

†† Absolute temperature units are assumed for C3i and C5i. The temperaturelimits are always interpreted in user input units.

PPDS



where R is the gas constant.

Linear extrapolation of Cp*,ig versus T is performed outside temperature

bounds.ParameterName/Element


UpperLimit

Units

CPIGDS/1 C1i — — — — TEMPERATURE

CPIGDS/2, …, 8 C2i, ..., C8i 0 — — — —

CPIGDS/9 C9i 0 — — — TEMPERATURE

CPIGDS/10 C10i 1000 — — — TEMPERATURE

IK-CAPE Heat Capacity Polynomial

The equation is:

Linear extrapolation of Cp*,ig versus T is performed outside temperature

bounds.ParameterName/Element


UpperLimit

Units

CPIGPO/1 C1i — X — — MOLE-CAPACITY

CPIGPO/2,…,10 C2i, ..., C10i 0 X — — MOLE-CAPACITYTEMPERATURE

CPIGPO/11 C11i 0 X — — TEMPERATURE

CPIGPO/12 C12i 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, JANAFThermochemical Data, Compiled and calculated by the Thermal ResearchLaboratory of Dow Chemical Company.

F. A. Aly and L. L. Lee, "Self-Consistent Equations for Calculating the IdealGas Heat Capacity, Enthalpy, and Entropy, Fluid Phase Eq., Vol. 6, (1981), p.169.


General Pure Component Solid HeatCapacityThe Aspen Physical Property System has several submodels for calculatingsolid heat capacity. It uses parameter THRSWT/5 to determine whichsubmodel is used. See Pure Component Temperature-Dependent Propertiesfor details.If THRSWT/5 is This equation is used And this parameter is

used

0 Aspen solid heat capacitypolynomial

CPSPO1

100 or 102 DIPPR CPSDIP

200-211 Barin CPSXP1, CPSXP2, …,CPSXP7


CPSPO


CPSTMLPO

The enthalpy, entropy, and Gibbs energy of solids are also calculated fromthese equations:

Aspen Solid Heat Capacity Polynomial

The Aspen equation is:

Linear extrapolation occurs for Cp,i*,s versus T outside of bounds.

ParameterName


Symbol MDS Default Units

CPSPO1/1 Solids, Salts C1i x — †

CPSPO1/2, ..., 6 Solids, Salts C2i, ..., C6i x 0 †

CPSPO1/7 Solids, Salts C7i x 0 †

CPSPO1/8 Solids, Salts C8i x 1000 †

† The units are TEMPERATURE and HEAT-CAPACITY for all elements. If any ofC4i through C6i are non-zero, absolute temperature units are assumed forelements C1i through C6i. Otherwise, user input temperature units areassumed for all elements. The temperature limits are always interpreted inuser input units.

Barin


DIPPR

There are two DIPPR equations that may generally be used.

The more common one, DIPPR equation 100, is:





UpperLimit

Units

CPSDIP/1 C1i — x — — MOLE-HEAT-CAPACITY,TEMPERATURE

CPSDIP/2,...,5 C2i, ..., C5i 0 x — — MOLE-HEAT-CAPACITY,TEMPERATURE

CPSDIP/6 C6i 0 x — — TEMPERATURE


DIPPR equation 102 is:




UpperLimit

Units

CPSDIP/1 C1i — x — — MOLE-HEAT-CAPACITY,TEMPERATURE

CPSDIP/2 C2i — x — — —

CPSDIP/3,4 C3i, C4i 0 x — — TEMPERATURE



If C3i or C4i are non-zero or C2i is negative, absolute temperature units areassumed for elements C1i through C4i. Otherwise, user input temperatureunits are assumed for all elements. The temperature limits are alwaysinterpreted in user input units.



The equation is:




UpperLimit

Units

CPSTMLPO/1 C1i — x — — J/K^2/mol

CPSTMLPO/2,...,5C2i, ..., C5i 0 x — — J/K^2/mol

CPSTMLPO/6 nTerms 5 x — — —

CPSTMLPO/7 Tlower 0 x — — TEMPERATURE




UpperLimit

Units

CPSTMLPO/8 Tupper 1000 x — — TEMPERATURE

IK-CAPE Heat Capacity Polynomial

The equation is:




UpperLimit

Units

CPSPO/1 C1i — X — — MOLE-CAPACITY

CPSPO/2,…,10 C10i 0 X — — MOLE-CAPACITYTEMPERATURE

CPSPO/11 C11i 0 X — — TEMPERATURE

CPSPO/12 C12i 1000 X — — TEMPERATURE

Solubility CorrelationsThe Aspen Physical Property System has three built-in solubility correlationmodels. 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-richliquid

Henry's ConstantThe Henry's constant model is used when Henry's Law is applied to calculateK-values for dissolved gas components in a mixture. Henry's Law is availablein all activity coefficient property methods, such as the WILSON propertymethod. 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 activitycoefficient model.

The Henry's constants aiA, biA, ciA, diA, and eiA are specific to a solute-solventpair. They can be obtained from regression of gas solubility data. The AspenPhysical Property System has a large number of built-in Henry's constants formany solutes in solvents. These parameters were obtained using data fromthe Dortmund Databank. In addition, a small number of Henry's constantsfrom the literature are available in the BINARY databank. See PhysicalProperty Data, Chapter 1, for details.ParameterName/Element


UpperLimit

Units

VC VcA — — 0.001 3.5 MOLE-VOLUME

HENRY/1 aiA †† x — — PRESSURE,TEMPERATURE †

HENRY/2 biA 0 x — — TEMPERATURE †

HENRY/3 ciA 0 x — — TEMPERATURE †

HENRY/4 diA 0 x — — TEMPERATURE †

HENRY/5 TL 0 x — — TEMPERATURE

HENRY/6 TH 2000 x — — TEMPERATURE

HENRY/7 eiA 0 x — — TEMPERATURE †

† If any of biA, ciA, and eiA are non-zero, absolute temperature units areassumed for all coefficients. If biA, ciA, and eiA are all zero, the others areinterpreted in input units. The temperature limits are always interpreted ininput units.

†† If aiA is missing, is set to zero and the weighting factor wA isrenormalized.

Reference for BINARY Databank

E. Wilhelm, R. Battino, and R.J. Wilcock, "Low-Pressure Solubility of Gases inLiquid Water," Chemical Reviews, 1977, Vol. 77, No. 2, pp 219 - 262.

Water SolubilityThis model calculates solubility of water in a hydrocarbon-rich liquid phase.The model is used automatically when you model a hydrocarbon-watersystem with the free-water option. See Free-Water Immiscibility Simplificationin Free-Water and Three-Phase Calculations for details.


The expression for the liquid mole fraction of water in the ith hydrocarbonspecies is:


The parameters for about 60 components are stored in the Aspen PhysicalProperty System pure component databank.ParameterName/Element


UpperLimit

Units

WATSOL/1 C1i fcn(Tbi, SGi, Mi) — -10.0 33.0 —

WATSOL/2 C2i fcn(Tbi, SGi, Mi) — -10000.0 3000.0 TEMPERATURE †

WATSOL/3 C3i 0 — -0.05 0.05 TEMPERATURE †

WATSOL/4 C4i 0 — 0.0 500 TEMPERATURE †

WATSOL/5 C5i 1000 — 4.0 1000 TEMPERATURE †

† Absolute temperature units are assumed for elements 2 through 5.

Hydrocarbon SolubilityThis model calculates solubility of hydrocarbon in a water-rich liquid phase.The model is used automatically when you model a hydrocarbon-watersystem with the dirty-water option. See Free-Water ImmiscibilitySimplification in Free-Water and Rigorous Three-Phase Calculations fordetails.

The expression for the liquid mole fraction of the ith hydrocarbon species inwater is:


The parameters for about 40 components are stored in the Aspen PhysicalProperty System pure component databank.ParameterName/Element


UpperLimit

Units

HCSOL/1 C1i fcn(carbonnumber) †

— -1000.0 1000.0 —

HCSOL/2 C2i 0 — -100000.0 100000.0 TEMPERATURE ††

HCSOL/3 C3i 0 — -100.0 100.0 TEMPERATURE ††

HCSOL/4 C4i 0 — 0.0 500 TEMPERATURE

HCSOL/5 C5i 1000 — 4.0 1000 TEMPERATURE

† For Hydrocarbons and pseudocomponents, the default values are estimatedby the method given by API Procedure 9A2.17 at 25 C.

†† Absolute temperature units are assumed for elements 2 and 3. Thetemperature limits are always interpreted in user input units.


Reference

C. Tsonopoulos, Fluid Phase Equilibria, 186 (2001), 185-206.

Other Thermodynamic PropertyModelsThe Aspen Physical Property System has some built-in additionalthermodynamic property models that do not fit in any other category. Thissection 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

CavettThe general form for the Cavett model is:



UpperLimit

Units



DHLCVT ZC X 0.1 0.5 —

Barin Equations for Gibbs Energy, Enthalpy,Entropy, and Heat CapacityThe following equations are used when parameters from the Aspen PhysicalProperty System inorganic databank are retrieved.

Gibbs energy:

(1)

Enthalpy:

(2)


Entropy:

(3)

Heat capacity:

(4)

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 multipletemperature ranges. The value of the parameter n depends on the phase.(See tables that follow.) When the temperature is outside all thesetemperature ranges, linear extrapolation of properties versus T is performedusing the slope at the end of the nearest temperature bound.

The four properties Cp, H, S, and G are interrelated as a result of thethermodynamic relationships:

There are analytical relationships between the expressions describing theproperties Cp, H, S, and G (equations 1 to 4). The parameters an,i to hn,i canoccur in more than one equation.

The Aspen Physical Property System has other models which can be used tocalculate temperature-dependent properties which the BARIN equations cancalculate. The Aspen Physical Property System uses the parameters inTHRSWT to determine which model is used. See Pure ComponentTemperature-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 = (GL - GV)/RT + ln pref

where p is the vapor pressure, and pref is the reference pressure 101325 Pa.Thus, parameters for both liquid and vapor are necessary to calculate vaporpressure.

Solid Phase

The parameters in range n are valid for temperature: Tn,ls < T < Tn,h

s


When you specify this parameter, be sure to specify at least elements 1through 3.Parameter Name †/Element


UpperLimit

Units

CPSXPn/1 Tn,ls — x — — TEMPERATURE

CPSXPn/2 Tn,hs — x — — TEMPERATURE

CPSXPn/3 an,is — x — — ††

CPSXPn/4 bn,is 0 x — — ††

CPSXPn/5 cn,is 0 x — — ††

CPSXPn/6 dn,is 0 x — — ††

CPSXPn/7 en,is 0 x — — ††

CPSXPn/8 fn,is 0 x — — ††

CPSXPn/9 gn,is 0 x — — ††

CPSXPn/10 hn,is 0 x — — ††

† n is 1 through 7. CPSXP1 vector stores solid parameters for the firsttemperature range. CPSXP2 vector stores solid parameters for the secondtemperature range, and so on.

†† TEMPERATURE, ENTHALPY, ENTROPY

Liquid Phase

The parameters in range n are valid for temperature: Tn,ll < T < Tn,h

l

When you specify this parameter, be sure to specify at least elements 1through 3.Parameter Name †/Element


UpperLimit

Units

CPLXPn/1 Tn,ll — x — — TEMPERATURE

CPLXPn/2 Tn,hl — x — — TEMPERATURE

CPLXPn/3 an,il — x — — ††

CPLXPn/4 bn,il 0 x — — ††

CPLXPn/5 cn,il 0 x — — ††

CPLXPn/6 dn,il 0 x — — ††

CPLXPn/7 en,il 0 x — — ††

CPLXPn/8 fn,il 0 x — — ††

CPLXPn/9 gn,il 0 x — — ††

CPLXPn/10 hn,il 0 x — — ††

† n is 1 through 2. CPLXP1 stores liquid parameters for the first temperaturerange. CPLXP2 stores liquid parameters for the second temperature range.


Ideal Gas Phase

The parameters in range n are valid for temperature: Tn,lig < T < Tn,h

ig

When you specify this parameter, be sure to specify at least elements 1through 3.


Parameter Name †/Element


UpperLimit

Units

CPIXPn/1 Tn,lig — x — — TEMPERATURE

CPIXPn/2 Tn,hig — x — — TEMPERATURE

CPIXPn/3 an,iig — x — — ††

CPIXPn/4 bn,iig 0 x — — ††

CPIXPn/5 cn,iig 0 x — — ††

CPIXPn/6 dn,iig 0 x — — ††

CPIXPn/7 en,iig 0 x — — ††

CPIXPn/8 fn,iig 0 x — — ††

CPIXPn/9 gn,iig 0 x — — ††

CPIXPn/10 hn,iig 0 x — — ††

† n is 1 through 3. CPIXP1 vector stores ideal gas parameters for the firsttemperature range. CPIXP2 vector stores ideal gas parameters for the secondtemperature range, and so on.


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 withthe asymmetrical reference state: the pure solvent water and infinite dilutionof molecular solutes and ions. (here * refers to the asymmetrical referencestate.)

Hw* is the pure water molar enthalpy, calculated from the Ideal Gas modeland the ASME Steam Table equation-of-state. (here * refers to purecomponent.)

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 departurecontribution to liquid enthalpy; option code 5 determines how this iscalculated.

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 fromthe 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 moreinformation.ParameterName



IONTYP Ions † Ion 0 —

SO25C Cations Sc,aq (T=298) — MOLE-ENTROPY

Anions Sa,aq (T=298) — MOLE-ENTROPY

DHAQFM Ions, Molecular Solutes††

f Hk,aq — MOLE-ENTHALPY

CPAQ0 Ions, Molecular Solutes††

Cp,k,aq — HEAT-CAPACITY

DHFORM Molecular Solutes †† f Hi*,ig — MOLE-ENTHALPY

Water, Solvents f Hw*,ig — MOLE-ENTHALPY

CPIG Molecular Solutes Cp,i*,ig — †††

Water, Solvents Cp,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, DHFORMand Henry's constants are used to calculate infinite dilution enthalpy forsolutes.

††† The unit keywords for CPIG are TEMPERATURE and HEAT-CAPACITY. IfCPIG/10 or CPIG/11 is non-zero, then absolute temperature units areassumed for CPIG/9 through CPIG/11. Otherwise, user input temperatureunits are used for all elements of CPIG. User input temperature units arealways used for other elements of CPIG.


Option Codes for Electrolyte NRTL Enthalpy Model(HMXENRTL)

The electrolyte NRTL enthalpy model (HMXENRTL) has seven option codesand the option codes can affect the performance of this model.


Option code 2. Use this option code to specify the vapor phase equation-of-state (EOS) model used for the liquid enthalpy calculation. The value (0) setsthe ideal gas EOS model and the value (1) sets the HF EOS model. The value(0) is the default.



Option code 5. Use this option code to specify how the vapor phase enthalpydeparture (DHV) is calculated. The value (0) sets DHV = 0, the value (1)specifies using Redlich-Kwong equation of state, and the value (3) specifiesusing Hayden-O’Connell equation of state. The value (0) is the default.


Option code 7. Use this option code to specify the method for handlingHenry components and multiple solvents. The value (0) sets the pure liquidenthalpy to that calculated by aqueous infinite dilution heat capacity (onlywater as solvent) and the value (1) sets the pure liquid enthalpy for Henrycomponents using Henry’s law. Use value (1) when there are multiplesolvents. 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 asymmetricalreference state.) The ideal mixing term is calculated normally, where j refersto 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.


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, bydefault. Subscript k refers to any ion or molecular solute. If polynomial modelparameters are not available, it is calculated from the Criss-Cobble model forionic solutes:

where the subscript k refers to any ion or molecular solute and the term RT

ln(1000/Mw) is added because f Hk,aq and f Gk

,aq are based on a molality

scale, while k

is based on mole fraction scale.

By default, is calculated from the aqueous infinite dilution heatcapacity 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 moreinformation.ParameterName



IONTYP Ions † Ion 0 —

SO25C Cations † Sc,aq (T=298) — MOLE-ENTROPY

Anions † Sa,aq (T=298) — MOLE-ENTROPY

DGAQFM Ions, Molecular Solutes††

f Gk,aq — MOLE-ENTHALPY

CPAQ0 Ions, Molecular Solutes††

Cp,k,aq — HEAT-CAPACITY

DGFORM Molecular Solutes †† f Gi— MOLE-ENTHALPY

Water, Solvents f Gw— MOLE-ENTHALPY


ParameterName



CPIG Molecular Solutes Cp,i*,ig — †††

Water, Solvents Cp,w*,ig — †††

† IONTYP and SO25C are not needed if CPAQ0 is given for ions.

†† DGFORM is not needed if DHAQFM and CPAQ0 are given for molecularsolutes.

††† The unit keywords for CPIG are TEMPERATURE and HEAT-CAPACITY. IfCPIG/10 or CPIG/11 is non-zero, then absolute temperature units areassumed for CPIG/9 through CPIG/11. Otherwise, user input temperatureunits are used for all elements of CPIG. User input temperature units arealways used for other elements of CPIG.

Option Codes for Electrolyte NRTL Gibbs Free EnergyModel (GMXENRTL)

The electrolyte NRTL Gibbs free energy model (GMXENRTL) has six optioncodes and the option codes can affect the performance of this model.


Option code 2. Use this option code to specify the vapor phase equation-of-state (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 5. Use this option code to specify how the pure vapor phasefugacity coefficient (PHIV) is calculated. The value (0) sets PHIV = 1 (idealgas law), the value (1) specifies using Redlich-Kwong equation of state, andthe 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 handlingHenry components and multiple solvents. The value (0) sets the pure liquidGibbs free energy to that calculated by aqueous infinite dilution heat capacity(only water as solvent) and the value (1) sets the pure liquid Gibbs freeenergy for Henry components using Henry’s law. Use value (1) when thereare multiple solvents. The value (0) is the default.

Liquid Enthalpy from Liquid Heat CapacityCorrelationLiquid enthalpy is directly calculated by integration of liquid heat capacity:


The reference enthalpy is calculated at Tref as:

Where:

Hi*,ig = Ideal gas enthalpy

Hi*,v - Hi

*,ig = Vapor enthalpy departure from equation of state

vapHi*,l = Heat of vaporization from General model

Tref = Reference temperature, specified by user. Defaults to298.15 K

See General Pure Component Heat of Vaporization for parameter requirementand additional details.

Enthalpies Based on Different ReferenceStatesTwo property methods, WILS-LR and WILS-GLR, are available to calculateenthalpies based on different reference states. The WILS-LR property methodis based on saturated liquid reference state for all components. The WILS-GLRproperty method allows both ideal gas and saturated liquid reference statesfor different components.

These property methods use an enthalpy method that optimizes the accuracytradeoff between liquid heat capacity, heat of vaporization, and vapor heatcapacity at actual process conditions. This highly recommended methodeliminates many of the problems associated with accurate thermal propertiesfor both phases, especially the liquid phase.

The liquid enthalpy of mixture is calculated by the following equation (see thetable labeled Liquid Enthalpy Methods):

Where:

Hmig = Enthalpy of ideal gas mixture

=

Hi*,ig = Ideal gas enthalpy of pure component i

(Hml-Hm

ig) = Enthalpy departure of mixture

For supercritical components, declared as Henry's components, the enthalpydeparture is calculated as follows:


For subcritical components:

Hml-Hm

ig =

HmE,l =

HA*,l-HA

*,ig = Enthalpy departure of pure component A

H*,ig and H*,l can be calculated based on either saturated liquid or ideal gas asreference state as described in the sections that follow.

For the WILS-LR property method, H*,ig and H*,l are calculated based on thesaturated liquid reference state for all components.

For the WILS-GLR property method, H*,ig and H*,l can be calculated based onthe saturated liquid reference state for some components and the ideal gasreference state for other components. You can set the value of a purecomponent parameter called RSTATE to specify the reference state for eachcomponent. RSTATE = 1 denotes ideal gas reference state. RSTATE = 2denotes saturated liquid reference state. If it is not set, the following defaultrules apply based on the normal boiling point of the component, i, TB(i):

If TB(i) <= 298.15 K, ideal gas reference state is used

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:

Hiref,l = Reference enthalpy for liquid state at Ti

ref,l

Cp,i*,l = Liquid heat capacity of component i

The saturated liquid Gibbs free energy is calculated as follows:

Where:

Giref,l = Reference Gibbs free energy for liquid state at Ti

ref,l

i*,l = Liquid fugacity coefficient of component i

p = System pressure

pref = Reference pressure (=101325 N/m2)

For the WILS-LR property method, Hiref,l and Gi

ref,l default to zero (0). Thereference temperature Ti

ref,l defaults to 273.15K.

For the WILS-GLR property method, the reference temperature Tiref,l defaults

to 298.15K and Hiref,l defaults to:


And Giref,l defaults to:

Where:

Hiref,ig = Ideal gas enthalpy of formation for liquid state at

298.15K

Giref,ig = 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 freeenergy to zero, as is the case for WILS-LR, because it will cause inconsistencywith the enthalpy of components that use ideal-gas reference state. Thedefault values used result in the enthalpies of all components being on thesame basis. In fact, if you enter values for Hi

ref,l and Giref,l for a liquid-

reference state component you must make sure that they are consistent witheach other and are consistent with the enthalpy basis of the remainingcomponents in the mixture. If you enter a value for Hi

ref,l, you should alsoenter a value for Gi

ref,l to ensure consistency.

When the liquid-reference state is used, the ideal gas enthalpy attemperature T is not calculated from the integration of the ideal gas heatcapacity equation (see Ideal Gas as Reference State section below). Forconsistency, it is calculated from liquid enthalpy as follows:

Where:

Ticon,l = Temperature of conversion from liquid to vapor

enthalpy for component i

vapHi*(Ti

con,l) = Heat of vaporization of component i attemperature of Tcon,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

Ticon,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 systemtemperature T. Ti

con,l may be selected such that heat of vaporization forcomponent 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 calculatedfrom the General Pure Component Liquid Heat Capacity and General PureComponent Ideal Gas Heat Capacity, or other available models. The heat ofvaporization can be calculated from the General Pure Component Heat ofVaporization, or other available models. The enthalpy departure is obtainedfrom an equation-of-state that is being used in the property method. ForWILS-LR and WILS-GLR, the ideal gas equation of state is used.ParameterName/Element


UpperLimit

Units

RSTATE † — 2 — — — —

TREFHL Tiref,l †† — — — TEMPERATURE

DHLFRM Hiref,l ††† — — — MOLE ENTHALPY

DGLFRM Giref,l †††† — — — MOLE ENTHALPY

TCONHL Ticon,l T — — — TEMPERATURE

† Enthalpy reference state given by RSTATE. 2 denotes saturated liquid asreference state.

†† For WILS-LR property method TREFHL defaults to 273.15K. For WILS-GLRproperty 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:

Hiref,ig = Reference state enthalpy for ideal gas at Ti

ref,ig

= Heat of formation of ideal gas at 298.15 K by default

Tiref,ig = Reference temperature corresponding to Hi

ref,ig.Defaults to 298.15 K


Ticon,ig = The temperature at which one crosses from vapor

state to liquid state. This is a user definedtemperature that defaults to the system temperatureT. Ti

con,igmay be selected such that heat ofvaporization of component i at the temperature ismost 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 calculatedfrom the General Pure Component Liquid Heat Capacity and General PureComponent Ideal Gas Heat Capacity, or other available models. The heat ofvaporization can be calculated from the General Pure Component Heat ofVaporization, or other available models. The enthalpy departure is obtainedfrom an equation of state that is being used in the property method. ForWILS-LR and WILS-GLR, the ideal gas equation of state is used.ParameterName/Element


UpperLimit

Units

RSTATE — 1 † — — — —

TREFHI Tiref,ig †† — — — TEMPERATURE

DHFORM Hiref,ig — — — — MOLE ENTHALPY

TCONHI Ticon,ig T — — — TEMPERATURE

† Enthalpy reference state RSTATE for a component. Value of 1 denotes idealgas.

††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, RSTATEdefaults to 2 (liquid) and TREFHI does not apply to these components. Seethe 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 formationat infinite dilution in aqueous phase are:


Where:


Where:

= Pressure constant for a solvent (2600 bar for water)

= Temperature constant for a solvent (228 K forwater)

= Born coefficient

= Dielectric constant of a solvent

Tr = Reference temperature (298.15 K)

Pr = Reference pressure (1 bar)



UpperLimit

Units

AHGPAR/1, ... ,4

a1, ..., a4 0 — — — —

CHGPAR/1, ... ,2

c1, c2 x — — — —

DHAQHG 0 — -0.5x1010 0.5x1010 MOLE-ENTHALPY

DGAQHG 0 — -0.5x1010 0.5x1010 MOLE-ENTHALPY

S25HG 0 — -0.5x1010 0.5x1010 MOLE-ENTROPY

OMEGHG 0 — -0.5x1010 0.5x1010 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 andtransport properties of aqueous species at high pressures and temperatures:Revised equation of state for the standard partial properties of ions andelectrolytes," American Journal of Science, Vol. 288, (1988), p. 19-98.

Shock, E.L. and H.C. Helgeson, "Calculation of the thermodynamic andtransport properties of aqueous species at high pressures and temperatures:


Correlation algorithms for ionic species and equation of state predictions to 5kb and 1000 C," Geochimica et Cosmochimica Acta, Vol. 52, p. 2009-2036.

Shock, E.L., H.C. Helgeson, and D.A. Sverjensky, "Calculation of thethermodynamic and transport properties of aqueous species at high pressuresand temperatures: Standard partial molal properties of inorganic neutralspecies," Geochimica et Cosmochimica Acta, Vol. 53, p. 2157-2183.

Quadratic Mixing RuleThe quadratic mixing rule is a general-purpose mixing rule which can beapplied to various properties. For a given property Q, with i and j beingcomponents, the rule is:

The pure component properties Qi and Qj are calculated by the default modelfor that property, unless modified by option codes. Composition xi and xj is inmole fraction unless modified by option codes. Kij is a binary parameterspecific to the mixing rule for each property. A variation on the equation usingthe logarithm of the property is used for viscosity.

244 3 Transport Property Models

3 Transport Property Models

This section describes the transport property models available in the AspenPhysical Property System. The following table provides an overview of theavailable models. This table lists the Aspen Physical Property System modelnames, and their possible use in different phase types, for pure componentsand mixtures.

Viscosity models

These models calculate MUL (pure) and/or MULMX (mixture) for the liquidphase, and MUV (pure) and/or MUVMX (mixture) for the vapor phase, exceptmodels marked with * calculate MUVLP (pure) and/or MUVMXLP (mixture) forthe vapor phase, and models marked with ** calculate MUVPC (pure) andMUVMXPC (mixture).Model Model name Phase(s) Pure Mixture

Andrade Liquid MixtureViscosity

MUL2ANDR L — X

General Pure ComponentLiquid Viscosity

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 ComponentVapor Viscosity *

MUV0CEB V X —

Chapman-Enskog-Brokaw-Wilke Mixing Rule *

MUV2BROK,MUV2WILK

V — X

Chung-Lee-Starling LowPressure *

MUV0CLSL,MUV2CLSL

V X X

Chung-Lee-Starling MUV0CLS2,MUV2CLS2,MUL0CLS2,MUL2CLS2

V L X X

Dean-Stiel Pressure Correction**

MUV0DSPC,MUV2DSPC

V X X

IAPS Viscosity MUV0H2O,MUL0H2O

V L X —

3 Transport Property Models 245

Model Model name Phase(s) Pure Mixture

Jones-Dole ElectrolyteCorrection

MUL2JONS L — X

Letsou-Stiel MUL0LEST,MUL2LEST

L X X

Lucas MUV0LUC,MUV2LUC

V X X

TRAPP viscosity MUL0TRAP,MUL2TRAP,MUV0TRAP,MUV2TRAP

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 modelsmarked with * calculate KVLP (pure) and/or KVMXLP (mixture) for the vaporphase, and models marked with ** calculate KVPC (pure) and KVMXPC(mixture) for the vapor phase.Model Model name Phase(s) Pure Mixture

Chung-Lee-Starling ThermalConductivtity

KV0CLS2,KV2CLS2,KL0CLS2,KL2CLS2

V L X X

IAPS Thermal Conductivity forWater

KV0H2OKL0H2O

VL

XX

——

Li Mixing Rule KL2LI L X X

Riedel Electrolyte Correction KL2RDL L — X

General Pure ComponentLiquid Thermal Conductivity

KL0SR,KL2SRVR

L X X

General Pure ComponentVapor Thermal Conductivity *

KV0STLP V X —

Stiel-Thodos PressureCorrection **

KV0STPC,KV2STPC

V X X

TRAPP Thermal Conductivity KV0TRAP,KV2TRAP,KL0TRAP,KL2TRAP

V L X X

Vredeveld Mixing Rule KL2SRVR L X X

Wassiljewa-Mason-Saxenamixing rule *

KV2WMSM V X X

Diffusivity models

These models calculate DL (binary) and/or DLMX (mixture) for the liquidphase, and DV (binary) and/or DVMX (mixture) for the vapor phase.Model Model name Phase(s) BinaryMixture

Chapman-Enskog-Wilke-LeeBinary

DV0CEWL V X —


Model Model name Phase(s) BinaryMixture

Chapman-Enskog-Wilke-LeeMixture

DV1CEWL V — X

Dawson-Khoury-KobayashiBinary

DV1DKK V X —

Dawson-Khoury-KobayashiMixture

DV1DKK V — X

Nernst-Hartley Electrolytes DL0NST,DL1NST

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 ComponentLiquid Surface Tension

SIG0HSS,SIG2HSS

L X —

IAPS surface tension SIG0H2O L X —

Onsager-Samaras ElectrolyteCorrection

SIG2ONSG L — X

Modified MacLeod-Sugden SIG2MS L — X

Viscosity ModelsThe Aspen Physical Property System has the following built-in viscositymodels: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 ViscosityThe liquid mixture viscosity is calculated by the modified Andrade equation:

Where:

kij =

mij =

fi depends on the option code for the model MUL2ANDR.If first option code ofMUL2ANDR is

Then fi 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 othermodels. The first option codes of these models cause fi to be mole or massfraction when Andrade is used in the respective models. To maintainconsistency across models, if you set the first option code for MUL2ANDR to1, you should also the set the first option code of the other models to 1, ifthey 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 complexliquid mixture viscosity. Both binary parameters default to zero.ParameterName/Element


UpperLimit

Units

ANDKIJ/1 aij 0 — — — —

ANDKIJ/2 bij 0 — — — —

ANDMIJ/1 cij 0 — — — —

ANDMIJ/2 dij 0 — — — —

The pure component liquid viscosity i*,l is calculated by the General Pure

Component Liquid Viscosity model.


General Pure Component Liquid ViscosityThe Aspen Physical Property System has several submodels for calculatingpure component liquid viscosity. It uses parameter TRNSWT/1 to determinewhich submodel is used. See Pure Component Temperature-DependentProperties 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 equationMULIKC

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 temperaturesoutside bounds.ParameterName/Element


UpperLimit

Units

MULAND/1 Ai — X — — VISCOSITY,TEMPERATURE †

MULAND/2 Bi — X — — TEMPERATURE †

MULAND/3 Ci — X — — TEMPERATURE †

MULAND/4 Tl 0.0 X — — TEMPERATURE

MULAND/5 Th 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 temperatureunits. 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/1determines 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 temperaturesoutside bounds.




UpperLimit

Units

MULDIP/1 C1i — X — — VISCOSITY,TEMPERATURE ††

MULDIP/2, ..., 5 C2i, ..., C5i 0 X — — TEMPERATURE ††

MULDIP/6 C6i 0 X — — TEMPERATURE

MULDIP/7 C7i 1000 X — — TEMPERATURE

†† If any of C3i through C5i are non-zero, absolute temperature units areassumed for C3i through C5i. Otherwise, all coefficients are interpreted in userinput temperature units. The temperature limits are always interpreted inuser input units.

PPDS


Linear extrapolation of viscosity versus T occurs for temperatures outsidebounds.ParameterName/Element


UpperLimit

Units

MULPDS/1 C1i — — — — —

MULPDS/2 C2i — — — —

MULPDS/3 C3i — — — TEMPERATURE


MULPDS/5 C5i — — — — VISCOSITY



NIST PPDS9 Equation

This is the same as the PPDS equation above, but it uses parameterMULPPDS9. Note that the parameters are in a different order.ParameterName/Element


UpperLimit

Units

MULPPDS9/1 C5i — — — — Pa*S

MULPPDS9/2 C1i — — — —

MULPPDS9/3 C2i — — — TEMPERATURE


MULPPDS9/5 C4i — — — — TEMPERATURE




IK-CAPE Liquid Viscosity Model

The IK-CAPE liquid viscosity model includes both exponential and polynomialequations.

Exponential



UpperLimit

Units

MULIKC/1 C1i — X — — VISCOSITY

MULIKC/2 C2i 0 X — — TEMPERATURE †††

MULIKC/3 C3i 0 X — — VISCOSITY

MULIKC/4 C4i 0 X — — TEMPERATURE

MULIKC/5 C5i 1000 X — — TEMPERATURE

††† Absolute temperature units are assumed for C2i. The temperature limitsare always interpreted in user input units.

Polynomial



UpperLimit

Units

MULPO/1 C1i — X — — VISCOSITY

MULPO/2, ..., 10 C2i, ..., C10i 0 X — — VISCOSITY,TEMPERATURE

MULPO/11 C11i 0 X — — TEMPERATURE

MULPO/12 C12i 1000 X — — TEMPERATURE

NIST TDE Equation

Linear extrapolation of viscosity versus T occurs for temperatures outsidebounds.

Absolute temperature units are assumed for C2i, C3i, and C4i. The temperaturelimits are always interpreted in user input units.ParameterName/Element


UpperLimit

Units

MULNVE/1 C1i — X — — —




UpperLimit

Units

MULNVE/2, 3, 4 C2i, C3i, C4i 0 X — — TEMPERATURE

MULNVE/5 C5i 0 X — — TEMPERATURE

MULNVE/6 C6i 1000 X — — TEMPERATURE

References

R.C. Reid, J.M. Prausnitz, and B.E. Poling, The Properties of Gases andLiquids, 4th ed., (New York: McGraw-Hill, 1987), p. 439.

API Liquid ViscosityThe liquid mixture viscosity is calculated using a combination of the API andGeneral equations. This model is recommended for petroleum andpetrochemical 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, 4thedition)

Vml is obtained from the API liquid volume model.

For real components, the General model is used.ParameterName/Element


UpperLimit

Units

TB Tbi — — 4.0 2000.0 TEMPERATURE

API APIi — — -60.0 500.0 —

API 1997 Liquid ViscosityThe liquid mixture viscosity is calculated using a combination of the API andGeneral equations. This model is recommended over the earlier API viscositymodel.

This model is applicable to petroleum fractions with normal boiling points from150 F to 1200 F and API gravities between 0 and 75. Testing by AspenTechindicates that this model is slightly more accurate than the Twu model forlight and medium boiling petroleum components, while the Twu model issuperior 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, 1997edition)

Vml is obtained from the API liquid volume model.

For real components, the General model is used.ParameterName/Element


UpperLimit

Units


API APIi — — -60.0 500.0 —

Aspen Liquid Mixture ViscosityThe 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 complexliquid mixture viscosity. Both binary parameters default to zero.ParameterName/Element


UpperLimit

Units

MUKIJ kij 0 — -100.0 100.0 —

MULIJ lij 0 — 100.0 100.0 —

ASTM Liquid Mixture ViscosityIt is generally difficult to predict the viscosity of a mixture of viscouscomponents. For hydrocarbons, the following weighting method (ASTM †) isknown 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 therange of 0.5 to 1.0

The individual component viscosities are calculated by the General PureComponent Liquid Viscosity model. The parameter f can be specified bysetting the value for MULOGF for the first component in the component list(as defined on the Components | Specifications | Selection sheet).ParameterName/Element


UpperLimit

Units

MULOGF f 1.0 — 0.0 2.0 —

† "Petroleum Refining, 1 Crude Oil, Petroleum Products, Process Flowsheets",Institut Francais du Petrole Publications, 1995, p. 130.

General Pure Component Vapor ViscosityThe Aspen Physical Property System has several submodels for calculatingpure component low pressure vapor viscosity. It uses parameter TRNSWT/2to 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 polynomialequation

MUVPO

402 IK-CAPE Sutherlandequation

MUVSUT


MUVTMLPO

Chapman-Enskog-Brokaw

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 isfrom Brokaw.ParameterName/Element


UpperLimit

Units

MW Mi — — 1.0 5000.0 —


STKPAR/1 (i/k)ST fcn(Tbi, Vbi, pi) — X — TEMPERATURE

STKPAR/2 iST fcn(Tbi, Vbi, pi) X — — LENGTH

LJPAR/1 (i/k)LJ fcn(Tci, i) X — — TEMPERATURE

LJPAR/2 iLJ fcn(Tci, pci, i) X — — LENGTH

DIPPR Vapor Viscosity

The equation for the DIPPR vapor viscosity model is:

When necessary, the vapor viscosity is extrapolated beyond this temperaturerange linearly with respect to T, using the slope at the temperature limits.


PCES uses the DIPPR equation in estimating vapor viscosity.ParameterName/Element


UpperLimit

Units

MUVDIP/1 C1i — X — — VISCOSITY

MUVDIP/2 C2i 0 X — — —

MUVDIP/3, 4 C3i, C4i 0 X — — TEMPERATURE †

MUVDIP/5 †† 0 X — — —

MUVDIP/6 C6i 0 X — — TEMPERATURE

MUVDIP/7 C7i 1000 X — — TEMPERATURE

† If any of C2i through C4i are non-zero, absolute temperature units areassumed for C1i through C4i. Otherwise, all coefficients are interpreted in userinput temperature units. The temperature limits are always interpreted inuser input units.

†† MUVDIP/5 is not used in this equation. It is normally set to zero. Theparameter is provided for consistency with other DIPPR equations.

PPDS

The PPDS submodel includes both the basic PPDS vapor viscosity equationand the PPDS kinetic theory vapor viscosity equation. For either equation,linear extrapolation of viscosity versus T occurs for temperatures outsidebounds.

PPDS Vapor Viscosity

The equation is:




UpperLimit

Units

MUVPDS/1 C1i — — — — VISCOSITY

MUVPDS/2 C2i 0 — — — —

MUVPDS/3 C3i 0 — — — —

MUVPDS/4 C4i 0 — — — TEMPERATURE

MUVPDS/5 C5i 1000 — — — TEMPERATURE

PPDS Kinetic Theory Vapor Viscosity

The equation is:



UpperLimit

Units

MW Mi — — 1.0 5000.0 —

MUVCEB/1 C1i — — — — LENGTH

MUVCEB/2 C2i — — — — TEMPERATURE †

MUVCEB/3 C3i 0 — — — —

MUVCEB/4 C4i 0 — — — TEMPERATURE

MUVCEB/5 C5i 1000 — — — TEMPERATURE

† Absolute temperature units are assumed for C2i . The temperature limits arealways interpreted in user input units.

IK-CAPE Vapor Viscosity

The IK-CAPE vapor viscosity model includes both the Sutherland equation andthe polynomial equation. For either equation, linear extrapolation of viscosityversus T occurs for temperatures outside bounds.

Sutherland Equation



UpperLimit

Units

MUVSUT/1 C1i — X — — VISCOSITY

MUVSUT/2 C2i 0 X — — TEMPERATURE ††

MUVSUT/3 C3i 0 X — — TEMPERATURE




UpperLimit

Units

MUVSUT/4 C4i 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. Thetemperature limits are always interpreted in user input units.

Polynomial



UpperLimit

Units

MUVPO/1 C1i — X — — VISCOSITY

MUVPO/2, ..., 10 C2i, ..., C10i 0 X — — VISCOSITY,TEMPERATURE

MUVPO/11 C11i 0 X — — TEMPERATURE

MUVPO/12 C12i 1000 X — — TEMPERATURE




UpperLimit

Units

MUVTMLPO/1 C1i — X — — Pa*s/T

MUVTMLPO/2, ..., 4 C2i , ..., C4i 0 X — — Pa*s/T

MUVTMLPO/5 nTerms 4 X — — —

MUVTMLPO/6 Tlower 0 X — — TEMPERATURE

MUVTMLPO/7 Tupper 1000 X — — TEMPERATURE

References

R.C. Reid, J.M. Prausnitz, and B.E. Poling. The Properties of Gases andLiquids, 4th ed., (New York: McGraw-Hill, 1987), p. 392.

Chapman-Enskog-Brokaw-Wilke MixingRuleThe low pressure vapor mixture viscosity is calculated by the Wilkeapproximation 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 vaporviscosity model).

Ensure that you supply parameters for i*,v (p = 0).



UpperLimit

Units

MW Mi — — 1.0 5000.0 —


STKPAR/1 (i/k)ST fcn(Tbi, Vbi, pi) — X — TEMPERATURE




UpperLimit

Units

STKPAR/2 iST fcn(Tbi, Vbi, pi) X — — LENGTH

References

R.C. Reid, J.M. Prausnitz, and T.K. Sherwood, The Properties of Gases andLiquids, 3rd ed., (New York: McGraw-Hill, 1977), pp. 410–416.

Chung-Lee-Starling Low-Pressure VaporViscosityThe 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 mixingrules:


Where:

Vcij =

ij= 0 (in almost all cases)

Tcij =


ij=

Mij =

ij=



UpperLimit

Units

TCCLS Tci TC x 5.0 2000.0 TEMPERATURE

VCCLS Vci VC x 0.001 3.5 MOLE-VOLUME

MW Mi — — 1.0 5000.0 —


OMGCLS iOMEGA x -0.5 2.0 —

CLSK i0.0 x 0.0 0.5 —

CLSKV ij0.0 x -0.5 -0.5 —

CLSKT ij0.0 x -0.5 0.5 —

The model specific parameters also affect the Chung-Lee-Starling Viscosityand the Chung-Lee-Starling Thermal Conductivity models.

References

R.C. Reid, J.M. Prausnitz, and B.E. Poling, The Properties of Gases andLiquids, 4th ed., (New York: McGraw-Hill, 1987), p. 396, p. 413.


Chung-Lee-Starling ViscosityThe Chung-Lee-Starling viscosity equation for vapor and liquid, high and lowpressure is:

With:

f1 =

f2 =

FC =

The molar density can be calculated using an equation-of-state model (forexample, the Benedict-Webb-Rubin). The parameter pr is the reduceddipolemoment:

C1 and C2 are constants of correlation.


For low pressures, f1 is reduced to 1.0 and f2 becomes negligible. Theequation reduces to the low pressure vapor viscosity model by Chung-Lee andStarling.

The previous equations can be used for mixtures when applying these mixingrules:


Where:

Vcij =


Tcij =


ij=

Mij =

ij=



UpperLimit

Units



MW Mi — — 1.0 5000.0 —



CLSK i0.0 x 0.0 0.5 —

CLSKV ij0.0 x -0.5 -0.5 —

CLSKT ij0.0 x -0.5 0.5 —

The model specific parameters affect the results of the Chung-Lee-StarlingThermal Conductivity and Low Pressure Viscosity models as well.

References



Dean-Stiel Pressure CorrectionThe residual vapor viscosity or the pressure correction to low pressure vaporviscosity 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 dimensionless-

making factor is:

=

Tc =

M =

pc =

Vcm =

Zcm =

rm= Vcm / Vm

v

The parameter Vmv is obtained from Redlich-Kwong equation-of-state.



UpperLimit

Units

MW Mi — — 1.0 5000.0 —


IAPS Viscosity for WaterThe IAPS viscosity models, developed by the International Association forProperties 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 requiredfor the models.


Jones-Dole Electrolyte CorrectionThe Jones-Dole model calculates the correction to the liquid mixture viscosityof a solvent mixture, due to the presence of electrolytes:

Where:

solv= Viscosity of the liquid solvent mixture, by default

calculated by the Andrade model

cal = 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 CodeValue

Solvent liquid mixture viscositymodel

0Andrade liquid mixture viscositymodel (default)

1 Viscosity quadratic mixing rule

2 Aspen liquid mixture viscositymodel

The parameter cal 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:

(1)

Where:

= Concentration of apparent electrolyte ca (2)

xcaa = 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 equationis used instead. This behavior can be disabled by setting the second optioncode for MUL2JONS to 1.

Breslau-Miller

The Breslau-Miller equation is:

(8)

Where the effective volume Vc is given by:

for salts involving univalent ions

(9)

for other salts

(9a)

Carbonell

The Carbonell equation is:

(10)

Where:

Mk = Molecular weight of an apparent electrolytecomponent k

You must provide parameters for the model used for the calculation of theliquid mixture viscosity of the solvent mixture.ParameterName/Element


UpperLimit

Units

CHARGE z 0.0 — — —

MW M — 1.0 5000.0 —

IONMOB/1 l1 — — — AREA, MOLES

IONMOB/2 l2 0.0 — — AREA, MOLES,TEMPERATURE

IONMUB/1 b1 — — — MOLE-VOLUME

IONMUB/2 b2 0,0 — — MOLE-VOLUME,TEMPERATURE

References

A. L. Horvath, Handbook of Aqueous Electrolyte Solutions, (Chichester: EllisHorwood, 1985).


Letsou-StielThe Letsou-Stiel model calculates liquid viscosity at high temperatures for

0.76 Tr 0.98. This model is used in PCES.


The general form for the model is:

l = (l)0 + (l)1

Where:

(l)0 =

(l)1 =

=

=



UpperLimit

Units

MW Mi — — 1.0 5000.0 —



OMEGA i— — -0.5 2.0 —

References

R.C. Reid, J.M. Pransnitz, and B.E. Poling, The Properties of Gases andLiquids, 4th ed., (New York: McGraw-Hill, 1987), p. 471.

Lucas Vapor ViscosityThe 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 =

FPi (p = 0) =

FQi (p = 0) = fcn(Tri), but is only nonunity for the quantumgates i = H2, D2, and He.


The Lucas mixing rules are:

Tc =

pc =

M =

FP (p = 0) =

FQ (p = 0) =

Where A differs from unity only for certain mixtures.ParameterName/Element


UpperLimit

Units

TCLUC Tci TC x 5.0 2000.0 TEMPERATURE

PCLUC pci PC x 105 108 PRESSURE

ZCLUC Zci ZC x 0.1 0.5 —

MW Mi — — 1.0 5000.0 —


References

R.C. Reid, J.M. Prausnitz, and B.E. Poling, The Properties of Gases andLiquids, 4th ed., (New York: McGraw-Hill, 1987), p. 421, 431.

TRAPP Viscosity ModelThe general form for the TRAPP viscosity model is:


Where:

The parameter is the mole fraction vector; fcn is a corresponding statescorrelation based on the model for vapor and liquid viscosity TRAPP, by theNational Bureau of Standards (NBS, currently NIST) . The model can be usedfor both pure components and mixtures. The model should be used fornonpolar components only.ParameterName/Element


UpperLimit

Units

MW Mi — — 1.0 5000.0 —

TCTRAP Tci TC x 5.0 2000.0 TEMPERATURE

PCTRAP pci PC x 105 108 PRESSURE

VCTRAP Vci VC x 0.001 3.5 MOLE-VOLUME

ZCTRAP Zci ZC x 0.1 1.0 —

OMGRAP iOMEGA x -0.5 3.0 —

References

J.F. Ely and H.J.M. Hanley, "Prediction of Transport Properties. 1. Viscositiesof Fluids and Mixtures," Ind. Eng. Chem. Fundam., Vol. 20, (1981), pp. 323–332.

Twu Liquid ViscosityThe 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 ofpredicting liquid viscosity for petroleum fractions with normal boiling points upto 1340 F and API gravity up to -30.

Given the normal boiling point Tb and the specific gravity SG of the system tobe modeled, the Twu model estimates the viscosity of the n-alkane referencefluid of the same normal boiling point at 100 F and 210 F, and its specificgravity. These are used to estimates the viscosity of the system to bemodeled at 100 F and at 210 F, and these viscosities are used to estimate theviscosity 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 normalboiling 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 and210 F, cSt

Tc° = Critical temperature of reference fluid, Rankine


Reference

C.H. Twu, "Internally Consistent Correlation for Predicting Liquid Viscosities ofPetroleum Fractions," Ind. Eng. Chem. Process Des. Dev., Vol. 24 (1985), pp.1287-1293

Viscosity Quadratic Mixing RuleWith i and j being components, the viscosity quadratic mixing rule is:

The pure component viscosity is calculated by the General Pure ComponentLiquid Viscosity model.

Option CodesOption Code Value Descriptions



ParameterParameterName/Element


UpperLimit

Units

MLQKIJ Kij - x - - —

Thermal Conductivity ModelsThe Aspen Physical Property System has eight built-in thermal conductivitymodels. 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 ThermalConductivity

Liquid

Solid Thermal Conductivity Polynomial Solid

General Pure Component Vapor ThermalConductivity

Low pressure vapor

Stiel-Thodos Pressure Correction Vapor

TRAPP Thermal Conductivity Vapor or liquid

Vredeveld Mixing Rule Liquid mixture

Wassiljewa-Mason-Saxena Mixing Rule Low pressure vapor


Chung-Lee-Starling Thermal ConductivityThe main equation for the Chung-Lee-Starling thermal conductivity model is:

Where:

f1 =

f2 =

=

(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 (forexample, the Benedict-Webb-Rubin equation-of-state). The parameter pr isthe reduced dipolemoment:


For low pressures, f1 is reduced to 1.0 and f2 is reduced to zero. This givesthe Chung-Lee-Starling expression for thermal conductivity of low pressuregases.

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 =


Tcij =


ij=

Mij =

ij=



UpperLimit

Units



MW Mi — — 1.0 5000.0 —



CLSK i0.0 x 0.0 0.5 —

CLSKV ij0.0 x -0.5 -0.5 —

CLSKT ij0.0 x -0.5 0.5 —

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 andLiquids, 4th ed., (New York: McGraw-Hill, 1987), p. 505, 523.

IAPS Thermal Conductivity for WaterThe IAPS thermal conductivity models were developed by the InternationalAssociation for Properties of Steam. These models can calculate vapor andliquid thermal conductivity for water and steam. They are used in option setsSTEAMNBS and STEAM-TA.

The general form of the equation for the IAPS thermal conductivity models is:

w=fcn(T, p)

Where:



The models are only applicable to water. No parameters are required.

Li Mixing RuleLiquid mixture thermal conductivity is calculated using Li equation (Reidet.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 Gasesand Liquids, 4th ed., (New York: McGraw-Hill, 1987), p. 550.

Riedel Electrolyte CorrectionThe Riedel model can calculate the correction to the liquid mixture thermalconductivity of a solvent mixture, due to the presence of electrolytes:

Where:

lsolv

= Thermal conductivity of the liquid solvent mixture,calculated by the General Pure Component LiquidThermal Conductivity model using the Vredeveldmixing rule

xcaa = Mole fraction of the apparent electrolyte ca

ac, aa = Riedel ionic coefficient

Vml = Apparent molar volume computed by the Clarke

density model

Apparent electrolyte mole fractions are computed from the true ion mole-fractions and ionic charge number. They can also be computed if you use theapparent component approach. A more detailed discussion of this method isfound in Electrolyte Calculation.


You must provide parameters for the Sato-Riedel model. This model is usedfor the calculation of the thermal conductivity of solvent mixtures.ParameterName/Element


UpperLimit

Units

CHARGE z 0.0 — — —

IONRDL a 0.0 — — †

† THERMAL CONDUCTIVITY, MOLE-VOLUME

The behavior of this model can be changed using option codes (these codesapply to the Vredeveld mixing rule).OptionCode

OptionValue

Description

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 thermalconductivities.

General Pure Component Liquid ThermalConductivityThe Aspen Physical Property System has several submodels for calculatingpure component liquid thermal conductivity. It uses parameter TRNSWT/3 todetermine 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


KLTMLPO

510 NIST PPDS8 equation KLPPDS8

Sato-Riedel

The Sato-Riedel equation is (Reid et al., 1987):

Where:

Tbri = Tbi / Tci

Tri = T / Tci




UpperLimit

Units

MW Mi — — 1.0 5000.0 —



PPDS

The equation is:

Linear extrapolation of *,l versus T occurs outside of bounds.



UpperLimit

Units

KLPDS/1 C1i — — — — THERMAL-CONDUCTIVITY

KLPDS/2 C2i 0 — — — —

KLPDS/3 C3i 0 — — — —

KLPDS/4 C4i 0 — — — —

KLPDS/5 C5i 0 — — — TEMPERATURE

KLPDS/6 C6i 1000 — — — TEMPERATURE

NIST PPDS8 Equation

The equation is



UpperLimit

Units

KLPPDS8/1 C1i — — — — THERMAL-CONDUCTIVITY

KLPPDS8/2, ..., 7 C2i , ..., C7i 0 — — — —

KLPPDS8/8 TCi — — — — TEMPERATURE

KLPPDS8/9 nTerms 7 — — — —

KLPPDS8/10 Tlower 0 — — — TEMPERATURE

KLPPDS8/11 Tupper 1000 — — — TEMPERATURE

DIPPR Liquid Thermal Conductivity





The DIPPR equation is used by PCES when estimating liquid thermalconductivity.ParameterName/Element


UpperLimit

Units

KLDIP/1 C1i — x — — THERMAL-CONDUCTIVITY,TEMPERATURE

KLDIP/2, ... , 5 C2i , ..., C5i 0 x — — THERMAL-CONDUCTIVITY,TEMPERATURE

KLDIP/6 C6i 0 x — — TEMPERATURE

KLDIP/7 C7i 1000 x — — TEMPERATURE


The equation is:




UpperLimit

Units

KLTMLPO/1 C1i — x — — THERMAL-CONDUCTIVITY,TEMPERATURE

KLTMLPO/2, ... ,4

C2i , ..., C4i 0 x — — THERMAL-CONDUCTIVITY,TEMPERATURE

KLTMLPO/5 nTerms 4 x — — —

KLTMLPO/6 Tlower 0 x — — TEMPERATURE

KLTMLPO/7 Tupper 1000 x — — TEMPERATURE

IK-CAPE





UpperLimit

Units

KLPO/1 C1i — x — — THERMAL-CONDUCTIVITY




UpperLimit

Units

KLPO/2, ... , 10 C2i , ..., C10i 0 x — — THERMAL-CONDUCTIVITY,TEMPERATURE

KLPO/11 C11i 0 x — — TEMPERATURE

KLPO/12 C12i 1000 x — — TEMPERATURE

References

R.C. Reid, J.M. Prausnitz, and T.K. Sherwood, The Properties of Gases andLiquids, 4th ed., (New York: McGraw-Hill, 1977), p. 533.


Solid Thermal Conductivity PolynomialThermal conductivity for solid pure components is calculated using the solidthermal conductivity polynomial. For mixtures, the mole-fraction weightedaverage is used.

For pure solids, thermal conductivity is calculated by:

For mixtures:

Linear extrapolation of i*,s versus T occurs outside of bounds.



UpperLimit

Units

KSPOLY/1 a — — — — THERMALCONDUCTIVITY

KSPOLY/2, 3, 4, 5 b, c, d, e 0 — — — THERMALCONDUCTIVITY,TEMPERATURE

KSPOLY/6 0 x — — TEMPERATURE

KSPOLY/7 1000 x — — TEMPERATURE

General Pure Component Vapor ThermalConductivityThe Aspen Physical Property System has several submodels for calculatingpure component low pressure vapor thermal conductivity. It uses parameterTRNSWT/4 to determine which submodel is used. See Pure ComponentTemperature-Dependent Properties for details.


If TRNSWT/4 is This equation is used And this parameter isused

0 Stiel-Thodos —

102 DIPPR KVDIP

301 PPDS KVPDS

401 IK-CAPE KVPO


KVTMLPO

Stiel-Thodos

The Stiel-Thodos equation is:

Where:

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.ParameterName/Element


UpperLimit

Units

MW Mi — — 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.


The DIPPR equation is used in PCES when estimating vapor thermalconductivity.ParameterName/Element


UpperLimit

Units

KVDIP/1 C1i — x — — THERMALCONDUCTIVITY

KVDIP/2 C2i 0 x — — —

KVDIP/3, 4 C3i, C4i 0 x — — TEMPERATURE †

KVDIP/5 — 0 x — — —

KVDIP/6 C6i 0 x — — TEMPERATURE

KVDIP/7 C7i 1000 x — — TEMPERATURE

† If any of C2i through C4i are non-zero, absolute temperature units areassumed for C1i through C4i. Otherwise, all coefficients are interpreted in user


input temperature units. The temperature limits are always interpreted inuser input units.

PPDS

The equation is:




UpperLimit

Units

KVPDS/1 C1i — — — — THERMAL-CONDUCTIVITY

KVPDS/2 C2i 0 — — — THERMAL-CONDUCTIVITY



KVPDS/5 C5i 0 — — — TEMPERATURE

KVPDS/6 C6i 1000 — — — TEMPERATURE

IK-CAPE Polynomial




UpperLimit

Units

KVPO/1 C1i — x — — THERMAL-CONDUCTIVITY

KVPO/2, ... , 10 C2i, ..., C10i 0 x — — THERMAL-CONDUCTIVITY,TEMPERATURE

KVPO/11 C11i 0 x — — TEMPERATURE

KVPO/12 C12i 1000 x — — TEMPERATURE






UpperLimit

Units

KVTMLPO/1 C1i — x — — THERMAL-CONDUCTIVITY,TEMPERATURE

KVTMLPO/2, ... ,4

C2i, ..., C4i 0 x — — THERMAL-CONDUCTIVITY,TEMPERATURE

KVTMLPO/5 nTerms 4 x — — —

KVTMLPO/6 Tlower 0 x — — TEMPERATURE

KVTMLPO/7 Tupper 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 ModelThe pressure correction to a pure component or mixture thermal conductivityat low pressure is given by:

Where:

rm=

The parameter Vmv 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.ParameterName/Element


UpperLimit

Units

MW Mi — — 1.0 5000.0 —


PC — — — 105 108 PRESSURE


ZC Zci — — 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 RuleLiquid 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

1Option code 2, unless . In this case n isset to 1.

If option code 2 is Then n is

0 (default) -2

1 0.4

2 1 (This uses a weighted average of liquid thermalconductivities.)

For most systems, the ratio of maximum to minimum pure component liquidthermal conductivity is between 1 and 2, where the exponent -2 isrecommended, 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 ofGases and Liquids, 4th ed., (New York: McGraw-Hill, 1977), p. 533.

TRAPP Thermal Conductivity ModelThe general form for the TRAPP thermal conductivity model is:

Where:

= Mole fraction vector

Cpi*,ig = Ideal gas heat capacity calculated using the

General pure component ideal gas heat capacitymodel

fcn = Corresponding states correlation based on themodel for vapor and liquid thermal conductivitymade by the National Bureau of standards (NBS,currently NIST)

The model can be used for both pure components and mixtures. The modelshould be used for nonpolar components only.




UpperLimit

Units

MW Mi — — 1.0 5000.0 —

TCTRAP Tci TC x 5.0 2000.0 TEMPERATURE

PCTRAP pci PC x 105 108 PRESSURE

VCTRAP Vci VC x 0.001 3.5 MOLE-VOLUME

ZCTRAP Zci ZC x 0.1 1.0 —

OMGRAP iOMEGA x -0.5 3.0 —

References

J.F. Ely and H.J. M. Hanley, "Prediction of Transport Properties. 2. ThermalConductivity of Pure Fluids and Mixtures," Ind. Eng. Chem. Fundam., Vol. 22,(1983), pp. 90–97.

Wassiljewa-Mason-Saxena Mixing RuleThe vapor mixture thermal conductivity at low pressures is calculated fromthe 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.



UpperLimit

Units

MW Mi — — 1.0 5000.0 —

References

R.C. Reid, J.M. Prausnitz, and B.E. Poling, The Properties of Gases andLiquids, 4th ed., (New York: McGraw-Hill, 1987), pp. 530–531.

Diffusivity ModelsThe Aspen Physical Property System has seven built-in diffusivity models. Thissection 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 usingthe Chapman-Enskog-Wilke-Lee model:

Dijv=Dji

v

Where:

The collision integral for diffusion is:

D=

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.ParameterName/Element


UpperLimit

Units

MW Mi — — 1.0 5000.0 —



VB Vb — — 0.001 3.5 MOLE-VOLUME

OMEGA i— — -0.5 2.0 —

STKPAR/1 (i/k)ST fcn(Tbi, Vbi, pi) x — — TEMPERATURE




UpperLimit

Units

STKPAR/2 iST fcn(Tbi, Vbi, pi) x — — LENGTH

LJPAR/1 (i/k)LJ fcn(Tci, i) x — — TEMPERATURE

LJPAR/2 iLJ fcn(Tci, pci, i) x — — LENGTH

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. 587.

Chapman-Enskog-Wilke-Lee (Mixture)The diffusion coefficient of a gas into a gas mixture at low pressures iscalculated using an equation of Bird, Stewart, and Lightfoot by default (optioncode 0):

If the first option code is set to 1, Blanc's law is used instead:

The binary diffusion coefficient Dijv(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.ParameterName/Element


UpperLimit

Units

DVBLNC — 1 x — — —

DVBLNC is set to 1 for a diffusing component and 0 for a non-diffusingcomponent.

References


Dawson-Khoury-Kobayashi (Binary)The binary diffusion coefficient Dij

v at high pressures is calculated from theDawson-Khoury-Kobayashi model:


Dijv=Dji

v

Dijv(p = 0) is the low-pressure binary diffusion coefficient obtained from the

Chapman-Enskog-Wilke-Lee model.

The parameters mv and Vm

v are obtained from the Redlich-Kwong equation-

of-state model.

You must supply parameters for these two models.

Subscript i denotes a diffusing component. j denotes a solvent.ParameterName/Element


UpperLimit

Units

VC Vci — x 0.001 3.5 MOLE-VOLUME

References

R.C. Reid, J.M. Prausnitz, and T.K. Sherwood. The Properties of Gases andLiquids, 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 iscalculated using an equation of Bird, Stewart, and Lightfoot by default (optioncode 0):

If the first option code is set to 1, Blanc's law is used instead:

The binary diffusion coefficient Dijv 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 insteadcalculated by the Chapman-Enskog-Wilke-Lee (Binary) model.

You must provide parameters for this model.




UpperLimit

Units

DVBLNC — 1 — — — —

DVBLNC is set to 1 for a diffusing component and 0 for a nondiffusingcomponent.

References


Nernst-HartleyThe effective diffusivity of an ion i in a liquid mixture with electrolytes can becalculated using the Nernst-Hartley model:

(1)

Where:

F = 9.65x107C/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 speciesis set equal to the effective diffusivity of the ion in the liquid mixture:

(2)

The binary diffusion coefficient of an ion i with respect to an ion j is set to themean of the effective diffusivities of the two ions:

The diffusivity for molecular species is calculated by the Wilke-Chang(Mixture) model.ParameterName/Element


UpperLimit

Units

CHARGE z 0.0 — — —

IONMOB/1 l1 — † — — AREA, MOLES

IONMOB/2 l2 0.0 — — AREA, MOLES,TEMPERATURE

†When IONMOB/1 is missing, the Nernst-Hartley model uses a nominal valueof 5.0 and issues a warning. This parameter should be specified for ions, andnot allowed to default to this value.


References

A. L. Horvath, Handbook of Aqueous Electrolyte Solutions, (Chichester: EllisHorwood, Ltd, 1985).

Wilke-Chang (Binary)The Wilke-Chang model calculates the liquid diffusion coefficient ofcomponent i in a mixture at finite concentrations:

Dijl = 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 propylalchohols and n-butanol, and 1.00 for all othersolvents.

Vbi = Liquid molar volume at Tb of solvent i

jl = Liquid viscosity of the solvent. This can be obtained

from the General Pure Component Liquid Viscositymodel. You must provide parameters for one ofthese models.

l = Liquid viscosity of the complete mixture of ncomponents

xi, xj = Apparent binary mole fractions. If the actual mole

fractions are then



UpperLimit

Units

MW Mj — 1.0 5000.0 —

VB Vbi*,l — 0.001 3.5 MOLE-VOLUME


References

R.C. Reid, J.M. Prausnitz, and B.E. Poling, The Properties of Gases andLiquids, 4th ed., (New York: McGraw-Hill, 1987), p. 598–600.

Wilke-Chang (Mixture)The Wilke-Chang model calculates the infinite-dilution liquid diffusioncoefficient 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 alchoholsand n-butanol, and 1.00 for all other solvents.

nl = Mixture liquid viscosity of all nondiffusingcomponents. This can be obtained from the GeneralPure Component Liquid Viscosity model. You mustprovide parameters for one its submodels.

The parameter DLWC specifies which components diffuse. It is set to 1 for adiffusing component and 0 for a non-diffusing component.ParameterName/Element


UpperLimit

Units

MW Mj — 1.0 5000.0 —

VB Vbi*,l — 0.001 3.5 MOLE-VOLUME

DLWC — 1 — — —

References

R.C. Reid, J.M. Praunsnitz, and B.E. Poling, The Properties of Gases andLiquids, 4th ed., (New York: McGraw-Hill, 1987), p. 618.

Surface Tension ModelsThe Aspen Physical Property System has the following built-in surface tensionmodels.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 SurfaceTension

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 weightedaverage expression (R.C. Reid, J.M. Prausnitz, and B.E. Poling, The Propertiesof 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 mosthydrocarbon mixtures. However, Reid recommended the value of r in therange of -1 to -3. The exponent value r can be specified using the model’sOption 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 TensionThe liquid mixture surface tension for hydrocarbons is calculated using theAPI model. This model is recommended for petroleum and petrochemicalapplications. 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 DataBook, Petroleum Refining, 4th edition)

The original form of this model is only designed for petroleum, and treats allcomponents as pseudocomponents (estimating surface tension from boilingpoint, 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 usethe General Pure Component Liquid Surface Tension model to calculate thesurface tension of real components and the API model for pseudocomponents.


The mixture surface tension is then calculated as a mole-fraction-weightedaverage of these surface tensions.ParameterName/Element


UpperLimit

Units


SG SG — — 0.1 2.0 —

TC Tci — — 5.0 2000 TEMPERATURE

IAPS Surface Tension for WaterThe IAPS surface tension model was developed by the InternationalAssociation for Properties of Steam. It calculates liquid surface tension forwater 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:


The model is only applicable to water. No parameters are required.

General Pure Component Liquid SurfaceTensionThe Aspen Physical Property System has several submodels for calculatingliquid surface tension. It uses parameter TRNSWT/5 to determine whichsubmodel is used. See Pure Component Temperature-Dependent Propertiesfor 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 polynomialequation

SIGPO

505 NIST TDE Watsonequation

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.



UpperLimit

Units


PC pci — PRESSURE

OMEGA i— -0.5 2.0 —

CHI i0 — — —

DIPPR Liquid Surface Tension

The DIPPR equation for liquid surface tension is:

Where:

Tri = T / Tci

Linear extrapolation of i*,l versus T occurs outside of bounds.


The DIPPR model is used by PCES when estimating liquid surface tension.



UpperLimit

Units

SIGDIP/1 C1i — — — SURFACE-TENSION

SIGDIP/2, ..., 5 C2i, ..., C5i 0 — — —

SIGDIP/6 C6i 0 — — TEMPERATURE

SIGDIP/7 C7i 1000 — — TEMPERATURE

PPDS

The equation is:




UpperLimit

Units

SIGPDS/1 C1i — — — — SURFACE-TENSION




UpperLimit

Units

SIGPDS/2 C2i 0 — — — —

SIGPDS/3 C3i 0 — — — —

SIGPDS/4 C4i 0 — — — TEMPERATURE

SIGPDS/5 C5i 1000 — — — TEMPERATURE

NIST PPDS14 Equation

This equation is the same as the PPDS equation above, but it uses its ownparameter set which includes critical temperature.ParameterName/Element


UpperLimit

Units

SIGPDS14/1 C1i — x — — N/m

SIGPDS14/2 C2i 0 x — — —

SIGPDS14/3 C3i 0 x — — —

SIGPDS14/4 Tci — x — — TEMPERATURE

SIGPDS14/5 C4i 0 x — — TEMPERATURE

SIGPDS14/6 C5i 1000 x — — TEMPERATURE

IK-CAPE Polynomial





UpperLimit

Units

SIGPO/1 C1i — x — — SURFACE-TENSION

SIGPO/2, ..., 10 C2i, ..., C10i 0 x — — SURFACE-TENSIONTEMPERATURE

SIGPO/11 C11i 0 x — — TEMPERATURE

SIGPO/12 C12i 1000 x — — TEMPERATURE

NIST TDE Watson Equation

This equation can be used when parameter SIGTDEW is available.



UpperLimit

Units

SIGTDEW/1 C1i — x — — —




UpperLimit

Units

SIGTDEW/2, 3, 4 C2i, C3i, C4i 0 x — — —

SIGTDEW/5 Tc — x — — TEMPERATURE

SIGTDEW/6 nTerms 4 x — — —

SIGTDEW/7 Tlower 0 x — — TEMPERATURE

SIGTDEW/8 Tupper 1000 x — — TEMPERATURE

NIST TDE Expansion

This equation can be used when parameter SIGISTE is available.



UpperLimit

Units

SIGISTE/1 C1i — x — — N/m

SIGISTE/2, 3, 4 C2i, C3i, C4i 0 x — — N/m

SIGISTE/5 Tci — x — — TEMPERATURE

SIGISTE/6 nTerms 4 x — — —

SIGISTE/7 Tlower 0 x — — TEMPERATURE

SIGISTE/8 Tupper 1000 x — — TEMPERATURE

References

R.C. Reid, J.M. Prausnitz, and B.E. Poling, The Properties of Gases andLiquids, 4th. ed., (New York: McGraw-Hill, 1987), p. 638.

Onsager-SamarasThe Onsager-Samaras model calculates the correction to the liquid mixturesurface tension of a solvent mixture, due to the presence of electrolytes:

for salt concentration < 0.03M

(1)

Where:

solv= Surface tension of the solvent mixture calculated

by the General Pure Component Liquid SurfaceTension model

xcaa = 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 tensioncorrection is calculated as:


(2)

Where:

solv= Dielectric constant of the solvent mixture

ccaa =

Vml = Liquid molar volume calculated by the Clarke

model

Apparent electrolyte mole fractions are computed from the true ion mole-fractions and ionic charge number. They are also computed if you use theapparent component approach. See Apparent Component and TrueComponent Approaches in the Electrolyte Calculation chapter for a moredetailed discussion of this method.

Above salt concentration 0.03 M, the slope of surface tension vs. molefraction is taken to be constant at the value from 0.03 M.

You must provide parameters for the General Pure Component Liquid SurfaceTension model, used for the calculation of the surface tension of the solventmixture.ParameterName/Element


UpperLimit

Units

CHARGE z 0.0 — — —

References

A. L. Horvath, Handbook of Aqueous Electrolyte Solutions, (Chichester: Ellis,Ltd. 1985).

Modified MacLeod-SugdenThe modified MacLeod-Sugden equation for mixture liquid surface tension canbe derived from the standard MacLeod-Sugden equation by assuming that thedensity 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 Tensionmodel.

Vi*,l = Liquid molar volume for pure component i, calculated

using the General Pure Component Liquid Molar Volumemodel.


V l = Mixture liquid molar volume, calculated using theRackett model.

References

R.C. Reid, J.M. Prausnitz, and B.E. Poling, The Properties of Gases andLiquids, 3rd. ed., (New York: McGraw-Hill, 1977).

4 Nonconventional Solid Property Models 295

4 Nonconventional SolidProperty Models

This section describes the nonconventional solid density and enthalpy modelsavailable in the Aspen Physical Property System. The following table lists theavailable models and their model names. Nonconventional components aresolid components that cannot be characterized by a molecular formula. Thesecomponents are treated as pure components, though they are complexmixtures.

Nonconventional Solid Property ModelsGeneral Enthalpy andDensity Models

Model name Phase(s)

General density polynomial DNSTYGEN S

General heat capacitypolynomial

ENTHGEN S

Enthalpy and DensityModels for Coal and Char

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 DensityModelsThe Aspen Physical Property System has two built-in general enthalpy anddensity models. This section describes the general enthalpy and densitymodels available:

General Density PolynomialDNSTYGEN is a general model that gives the density of any nonconventionalsolid component. It uses a simple mass fraction weighted average for thereciprocal temperature-dependent specific densities of its individual

296 4 Nonconventional Solid Property Models

constituents. There may be up to twenty constituents with mass percentages.You must define these constituents, using the general component attributeGENANAL. The equations are:

Where:

wij = Mass fraction of the jth constituent in component i

ijs = Density of the jth consituent in component i


Symbol MDS Default LowerLimit

UpperLimit

Units

DENGEN/1, 5, 9, …, 77 ai,j1 x — — — MASS-ENTHALPYand TEMPERATURE

DENGEN/2, 6, 10, …,78

ai,j2 x 0 — — MASS-ENTHALPYand TEMPERATURE

DENGEN/3, 7, 11, …,79


DENGEN/4, 8, 12, …,80


Use the elements of GENANAL to input the mass percentages of theconstituents. The structure of DENGEN is: Elements 1 to 4 are the fourcoefficients for the first constituent, elements 5 to 8 are the coefficients forthe second constitutent, and so on, for up to 20 constituents.

General Heat Capacity PolynomialENTHGEN is a general model that gives the specific enthalpy of anynonconventional component as a simple mass-fraction-weighted-average forthe enthalpies of its individual constituents. You may define up to twentyconstituents with mass percentages, using the general component attributeGENANAL. The specific enthalpy of each constituent at any temperature iscalculated by combining specific enthalpy of formation of the solid with asensible heat change. (See Nonconventional Component Enthalpy Calculationin Physical Property Methods.)

The equations are:

Where:


wij = Mass fraction of the jth constituent incomponent i

his = Specific enthalpy of solid component i

fhjs = Specific enthalpy of formation of constituent j

Cps = Heat capacity of the jth constituent in

component i


Symbol MDS Default LowerLimit

UpperLimit

Units

DHFGEN/J fhjs x 0 — — MASS-ENTHALPY

HCGEN/1, 5, 9, …, 77 ai,j1 x — — — MASS-ENTHALPYandTEMPERATURE

HCGEN/2, 6, 10, …, 78 ai,j2 x 0 — — MASS-ENTHALPYandTEMPERATURE



The elements of GENANAL are used to input the mass percentages of theconstituents. The structure for HCGEN is: Elements 1 to 4 are the fourcoefficients for the first constituent, elements 5 to 8 are the coefficients forthe second constitutent, and so on, for up to 20 constituents.

Enthalpy and Density Modelsfor Coal and CharCoal is modeled in the Aspen Physical Property System as a nonconventionalsolid. Coal models are empirical correlations, which require solid materialcharacterization information. Component attributes are derived fromconstituent analyses. Definitions of coal component attributes are given in theAspen Plus User Guide, Chapter 6.

Enthalpy and density are the only properties calculated for nonconventionalsolids. This section describes the special models available in the AspenPhysical Property System for the enthalpy and density of coal and char. Thecomponent attributes required by each model are included. The coal modelsare:

General coal enthalpy

IGT Coal Density

IGT Char Density


User models for density and enthalpy. See User Models forNonconventional Properties in Chapter 6 of Aspen Plus User Models, fordetails 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-matter-free basis. Only the organic portion of the coal is considered.

Moisture corrections are made for all analyses except hydrogen, according tothe formula:

Where:

w = The value determined for weight fraction

wd = 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 ashdetermination. The average water constitution of clays is assumed to be 11.2percent. The sulfur term allows for loss in weight of pyritic sulfur when pyriteis burned to ferric oxide. The original Parr formula assumed that all sulfur ispyritic sulfur. This formula included sulfatic and organic sulfur in the mineral-matter calculation. When information regarding the forms of sulfur isavailable, use the modified Parr formula to give a better approximation of thepercent of inorganic material present. Because chlorine is usually small forUnited States coals, you can omit chlorine from the calculation.

Correct analyses from a dry basis to a dry, mineral-matter-free basis, usingthe formula:

Where:

wd = Correction factor for other losses, such as the lossof carbon in carbonates and the loss of hydrogenpresent in the water constitution of clays


The oxygen and organic sulfur contents are usually calculated by differenceas:

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


m = Mineral-matter-free basis

General Coal Enthalpy ModelThe general coal model for computing enthalpy in the Aspen Physical PropertySystem is HCOALGEN. This model includes a number of different correlationsfor the following:

Heat of combustion

Heat of formation

Heat capacity

You can select one of these correlations using an option code in the PropertiesAdvanced NC-Props form. (See the Aspen Plus User Guide, Chapter 6). Useoption codes to specify a calculation method for properties. Each element inthe option code vector is used in the calculation of a different property.

The table labeled HCOALGEN Option Codes (below) lists model option codesfor HCOALGEN. The table is followed by a detailed description of thecalculations used for each correlation.

The correlations are described in the following section. The componentattributes 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 calorificvalue. It is expressed in Btu/lb of coal on a dry mineral-matter-free basis.ASTM Standard D5865-07a defines standard conditions for measuring grosscalorific value. (Earlier ASTM Standard D-2015 used the same conditions.)Initial oxygen pressure is 20 to 40 atmospheres. Products are in the form ofash; liquid water; and gaseous CO2, SO2, and NO2.

You can calculate net calorific value from gross calorific value by making adeduction for the latent heat of vaporization of water.

Heat of combustion values are converted back to a dry, mineral-matter-containing basis with a correction for the heat of combustion of pyrite. Theformula is:

The heat of combustion correlations were evaluated by the Institute of GasTechnology (IGT). They used data for 121 samples of coal from the PennState Data Base (IGT, 1976) and 457 samples from a USGS report (Swanson,et al., 1976). These samples included a wide range of United States coalfields. The constant terms in the HCOALGEN correlations are bias correctionsobtained from the IGT study.

Boie Correlation:

Parameter Name/Element Symbol Default

BOIEC/1 a1i 151.2

BOIEC/2 a2i 499.77



BOIEC/3 a3i 45.0

BOIEC/4 a4i -47.7

BOIEC/5 a5i 27.0

BOIEC/6 a6i -189.0

Dulong Correlation:


DLNGC/1 a1i 145.44

DLNGC/2 a2i 620.28

DLNGC/3 a3i 40.5

DLNGC/4 a4i -77.54

DLNGC/5 a5i -16.0

Grummel and Davis Correlation:


GMLDC/1 a1i 0.3333

GMLDC/2 a2i 654.3

GMLDC/3 a3i 0.125

GMLDC/4 a4i 0.125

GMLDC/5 a5i 424.62

GMLDC/6 a6i -2.0

Mott and Spooner Correlation:


MTSPC/1 a1i 144.54

MTSPC/2 a2i 610.2

MTSPC/3 a3i 40.3

MTSPC/4 a4i 62.45

MTSPC/5 a5i 30.96

MTSPC/6 a6i 65.88

MTSPC/7 a7i -47.0

IGT Correlation:



CIGTC/1 a1i 178.11

CIGTC/2 a2i 620.31

CIGTC/3 a3i 80.93

CIGTC/4 a4i 44.95

CIGTC/5 a5i -5153.0

Revised IGT Correlation (Perry's, 7th ed., equation 27-7):


CIGT2/1 a1i 146.58

CIGT2/2 a2i 568.78

CIGT2/3 a3i 29.4

CIGT2/4 a4i -6.58

CIGT2/5 a5i -51.53

User Input Value of Heat CombustionParameter Name/Element Symbol Default

HCOMB chid 0

Standard Heat of Formation Correlations

There are two standard heat of formation correlations for the HCOALGENmodel:

Heat of combustion-based

Direct

Heat of Combustion-Based Correlation: This is based on the assumption thatcombustion results in complete oxidation of all elements except sulfatic sulfurand ash, which are considered inert. The numerical coefficients arecombinations 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 isliquid, the heat of vaporization at 298.15 K is needed in the conversion. The

numerical coefficient of is calculated by:


The complete oxidation of carbon is based on the reaction

, 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

, and the numerical coefficient of

is calculated by:

Direct Correlation: Normally small, relative to its heat of combustion. An errorof 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, thefollowing direct correlation was developed, using data from the Penn StateData Base. It has a standard deviation of 112.5 Btu/lb, which is close to thelimit, due to measurement in the heat of combustion:

Where:Parameter Name/Element Symbol Default

HFC/1 a1i 1810.123

HFC/2 a2i -502.222

HFC/3 a3i 329.1087

HFC/4 a4i 121.766

HFC/5 a5i -542.393

HFC/6 a6i 1601.573



HFC/7 a7i 424.25

HFC/8 a8i -525.199

HFC/9 a9i -11.4805

HFC/10 a10i 31.585

HFC/11 a11i 13.5256

HFC/12 a12i 11.5

HFC/13 a13i -685.846

HFC/14 a14i -22.494

HFC/15 a15i -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 volatilematter is any volatile matter up to 10% on a dry, ash-free basis; theremaining volatile matter is primary. The correlation developed by Kirovtreats the heat capacity as a weighted sum of the heat capacities of theconstituents:

Where:

i = Component index

j = Constituent index j = 1, 2 , ... , ncn

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 inC. The parameters must be specified in appropriate units for this conversion.Parameter Name/Element Symbol Default

CP1C/1 ai,11 1.0

CP1C/2 ai,12 0

CP1C/3 ai,13 0

CP1C/4 ai,14 0

CP1C/5 ai,21 0.165

CP1C/6 ai,22



CP1C/7 ai,23

CP1C/8 ai,24 0

CP1C/9 ai,31 0.395

CP1C/10 ai,32

CP1C/11 ai,33 0

CP1C/12 ai,34 0

CP1C/13 ai,41 0.71

CP1C/14 ai,42

CP1C/15 ai,43 0

CP1C/16 ai,44 0

CP1C/17 ai,51 0.18

CP1C/18 ai,52

CP1C/19 ai,53 0

CP1C/20 ai,54 0

Cubic Temperature Equation

The cubic temperature equation is:


CP2C/1 a1i 0.438

CP2C/2 a2i

CP2C/3 a3i

CP2C/4 a4i

The default values of the parameters were developed by Gomez, Gayle, andTaylor (1965). They used selected data from three lignites and asubbituminous B coal, over a temperature range from 32.7 to 176.8C.

HCOALGEN Option CodesOption CodeNumber

Option CodeValue†

CalculationMethod

ParameterNames

ComponentAttributes

1 Heat of Combustion

1 Boie correlation BOIEC ULTANALSULFANALPROXANAL

2 Dulongcorrelation

DLNGC ULTANALSULFANALPROXANAL

3 Grummel andDavis correlation

GMLDC ULTANALSULFANALPROXANAL

4 Mott and Spoonercorrelation

MTSPC ULTANALSULFANALPROXANAL


Option CodeNumber

Option CodeValue†

CalculationMethod

ParameterNames

ComponentAttributes

1 Heat of Combustion

5 IGT correlation CIGTC ULTANALPROXANAL

6 User input value HCOMB ULTANALPROXANAL

7 Revised IGTcorrelation

CIGT2 ULTANALPROXANAL

2 Standard Heat of Formation

1 Heat-of-combustion-based correlation

— ULTANALSULFANAL

2 Direct correlation HFC ULTANALSULFANALPROXANAL

3 Heat Capacity

1 Kirov correlation CP1C PROXANAL

2 Cubictemperatureequation

CP2C —

4 Enthalpy Basis

1 Elements in theirstandard statesat 298.15K and 1atm

——

——

2 Component at298.15 K

— —

† Default = 1 for each option code

References

Gomez, M., J.B. Gayle, and A.R. Taylor, Jr., Heat Content and Specific Heat ofCoals and Related Products, U.S. Bureau of Mines, R.I. 6607, 1965.

IGT (Institute of Gas Technology), Coal Conversion Systems Technical DataBook, Section PMa. 44.1, 1976.

Kirov, N.Y., "Specific Heats and Total Heat Contents of Coals and RelatedMaterials are Elevated Temperatures," BCURA Monthly Bulletin, (1965),pp. 29, 33.

Swanson, V.E. et al., Collection, Chemical Analysis and Evaluation of CoalSamples 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, 7thed., McGraw-Hill (1997), p. 27-5.

IGT Coal Density ModelThe DCOALIGT model gives the true (skeletal or solid-phase) density of coalon a dry basis. It uses ultimate and sulfur analyses. The model is based onequations from IGT (1976):


The equation for idm is good for a wide range of hydrogen contents, including

anthracities and high temperature cokes. The standard deviation of thiscorrelation for a set of 190 points collected by IGT from the literature was12x10-6 m3/kg. The points are essentially uniform over the whole range. Thisis equivalent to a standard deviation of about 1.6% for a coal having ahydrogen content of 5%. It increases to about 2.2% for a coke or anthracitehaving a hydrogen content of 1%.Parameter Name/Element Symbol Default

DENIGT/1 a1i 0.4397

DENIGT/2 a2i 0.1223

DENIGT/3 a3i -0.01715

DENIGT/4 a4i 0.001077

Reference


IGT Char Density ModelThe DGHARIGT model gives the true (skeletal or solid-phase) density of charor coke on a dry basis. It uses ultimate and sulfur analyses. This model isbased on equations from IGT (1976):


DENIGT/1 a1i 0.4397

DENIGT/2 a2i 0.1223

DENIGT/3 a3i -0.01715

DENIGT/4 a4i 0.001077


The densities of graphitic high-temperature carbons (including cokes) rangefrom 2.2x103 to 2.26x103 kg/m3. Densities of nongraphitic high-temperaturecarbons (derived from chars) range from 2.0x103 to 2.2x103 kg/m3. Most ofthe 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 notaccurate 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 ofCoals and Related Products, U.S. Bureau of Mines, R.I. 6607, 1965.


N.Y. Kirov, "Specific Heats and Total Heat Contents of Coals and RelatedMaterials are Elevated Temperatures," BCURA Monthly Bulletin, (1965),pp. 29, 33.

V.E. Swanson et al., Collection, Chemical Analysis and Evaluation of CoalSamples in 1975, U.S. Geological Survey, Open-File Report (1976), pp. 76–468.

5 Property Model Option Codes 309

5 Property Model OptionCodes

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 TransportProperty ModelsModel Name Option

CodeValue 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

1 Use API model for pseudocomponents, GeneralPure Component Liquid Surface Tension for realcomponents, and take a mole-fraction-weightedaverage of the results.

MUL2API,MULAPI92

1 0 Release 9 method. First, the API, SG of themixture is calculated, then the API correlation isused (default)

310 5 Property Model Option Codes

Model Name OptionCode

Value Descriptions

1 Pre-release 9 method. Liquid viscosity iscalculated for each pseudocomponent using theAPI method. Then mixture viscosity iscalculated by mixing rules.

MUL2ANDR,DL0WCA, DL1WCA,DL0NST, DL1NST

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)

1 Mixture viscosity weighted by mass fraction

2 0 Use Breslau and Miller equation instead of Jonesand Dole equation when electrolyteconcentration exceeds 0.1 M.

1 Always use Jones and Dole equation when theparameters are available.

3 0 Solvent liquid mixture viscosity from Andradeliquid mixture viscosity model (default)

1 Solvent liquid mixture viscosity from quadraticmixing rule

2 Solvent liquid mixture viscosity from Aspenliquid mixture viscosity model

MUL2CLS,MUL2CLS2

1 0 Original correlation

1 Modified UOP correlation

MUL2QUAD 1 0 Use mole basis composition (default)


KL2VR, KL2RDL 1 0 Do not check ratio of KL max / KL min

1 Check ratio. If KL max / KL min > 2, setexponent 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 ofliquid thermal conductivities.

Option Codes for ActivityCoefficient ModelsModel Name Option


GMXSH 1 0 No volume term (default)

1 Includes volume term

WHENRY 1 1 Equal weighting



Value Descriptions

2 Size - VC1/3

3 Area - VC2/3 (default)

4 Volume - VC

Electrolyte NRTL Activity Coefficient Model (GMELC and GMENRHG)

1 Defaults for pair parameters

1 Pair parameters default to zero

2 Solvent/solute pair parameters default to waterparameters. Water/solute pair parameters defaultto zero (default for GMELC)

3 Default water parameters to 8, -4. Defaultsolvent/solute parameters to 10, -2 (default forGMENRHG)

2 Not used

3 Solvent/solvent binary parameter values obtainedfrom

0 Scalar GMELCA, GMELCB and GMELCM (defaultfor GMELC)

1 Vector NRTL(8) (default for GMENRHG)

GMPT1, GMPT3 (Pitzer)

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 andGMENRTLQ)

1 PDH long-range term

0 Long-range term calculated (default)

1 Long-range term ignored

COSMOSAC

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 exchangeenergy (Lin et al., 2002)

Hansen

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 Reference state for ions is unsymmetric: infinitedilution in aqueous solution (default)



Value Descriptions

2 Reference state for ions is symmetric: pure fusedsalts



3 0 Long-range interaction term included (default)

1 Long-range interaction term removed

Option Codes for Equation ofState ModelsModel Name Option


ESBWRS, ESBWRS01 0 Do not use steam tables

1 Calculate properties (H, S, G, V) of water fromsteam table (default; see Note)

2 0 Original RT-Opt root search method (default)

1 VPROOT/LQROOT Aspen Plus root searchmethod. Use this if the equation-oriented AspenPlus solution fails to converge and somestreams with missing phases show the sameproperties for the missing phase as for anotherphase.

ESHOC, ESHOC0,PHV0HOC

1 0 Hayden-O'Connell model. Use chemical theoryonly if one component has HOCETA=4.5(default)

1 Always use the chemical theory regardless ofHOCETA values

2 Never use the chemical theory regardless ofHOCETA values

2 0 Check high-pressure limit. If exceeded,calculate volume at cut-off pressure.

1 Ignore high-pressure limit. Calculate volumemodel T and P.

ESPR, ESPR0,ESPRSTD,ESPRSTD0

1 0 ASPEN Boston/Mathias alpha function when Tr

>1, original literature alpha function otherwise.(default for ESPR)

1 Original literature alpha function (default forESPRSTD)

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)



Value Descriptions

1 Calculate water properties (H, S, G, V) fromsteam table (see Note)

4 0 Do not use Peneloux liquid volume correction(default)

1 Apply Peneloux liquid volume correction (SeeSRK)

5 0 Use analytical method for root finding (default)

1 Use RTO numerical method for root finding

2 Use VPROOT/LQROOT numerical method forroot finding

ESPRWS,ESPRWS0, ESPRV1,ESPRV10, ESPRV2,ESPRV20,

1 0 ASPEN Boston/Mathias alpha function

ESPSAFT,ESPSAFT0

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 acopolymer must be built only by two differenttypes of segments

3 0 Use association term (default)

1 Do not use association term

ESRKS, ESRKS0,ESRKSTD,ESRKSTD0, ESSRK,ESSRK0, ESRKSML,ESRKSML0

See Soave-Redlich-Kwong Option Codes

ESRKSW, ESRKSW01 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(-0.30228xTri))

ESRKU, ESRKU0 1 Initial temperature for binary parameterestimation

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)



Value Descriptions

4 Vapor phase EOS used in generation of TPxydata 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:

log(K) = A + B/T + C ln(T) + DT (default)

1 log(K) = A + B/T + CT + DT2 + E log(P)


2 Mathias-Copeman alpha function

3 Schwartzentruber-Renon alpha function(default)

ESRKSWS,ESRKSWS0,ESRKSV1,ESRKSV10,ESRKSV2,ESRKSV20,

1 Equation form for alpha function


2 Mathias-Copeman alpha function

3 Schwartzentruber-Renon alpha function(default)

ESSTEAM,ESSTEAM0

1 0 ASME 1967 correlations

1 NBS 1984 equation of state (default)

2 NBS 1984 equation of state with alternate rootsearch method (STMNBS2)

2 0 Original fugacity and enthalpy calculationswhen used with STMNBS2

1 Rigorous fugacity calculation from Gibbs energyand 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 rootsearch method (STMNBS2)

Note: The enthalpy, entropy, Gibbs energy, and molar volume of water arecalculated from the steam tables when the relevant option is enabled. Thetotal properties are mole-fraction averages of these values with the propertiescalculated by the equation of state for other components. Fugacity coefficientis not affected.


Soave-Redlich-Kwong OptionCodesThere are five related models all based on the Soave-Redlich-Kwong equationof 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 codesdescribed in the following table:OptionCode

Value Description

1 0 Standard SRK alpha function for Tr < 1, Boston-Mathias alphafunction for Tr > 1

1 Standard SRK alpha function for all

2 Grabovsky – Daubert alpha function for H2 and standard SRKalpha 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 forRedlich-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 forSRK-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 forRedlich-Kwong-Soave models)

1 Use smoothed logarithm in calculating properties (default forSRK models)

Notes

1. The standard alpha function is always used for Helium.


2. If extended Gibbons-Laughton alpha function parameters are missing, theBoston-Mathias extrapolation will be used if T > Tc, and the standardalpha function will be used if T < Tc.

3. The extended Gibbons-Laughton alpha function should not be used withthe Kabadi-Danner mixing rules.

4. The Kabadi-Danner mixing rules should not be used if Lij parameters areprovided for water with any other components.

5. It is recommended that you use the SRK-KD property method rather thanchange this option code.

6. The enthalpy, entropy, Gibbs energy, and molar volume of water arecalculated from the steam tables when this option is enabled. The totalproperties are mole-fraction averages of these values with the propertiescalculated by the equation of state for other components. Fugacitycoefficient is not affected.

Option Codes for K-ValueModelsModelName

OptionCode

Value Descriptions

BK10 1 0 Treat pseudocomponents as paraffins (default)

1 Treat pseudocomponents as aromatics

Option Codes for EnthalpyModelsModel Name Option


DHL0HREF 1 1 Use Liquid reference state for all components (Default)

2 Use liquid and gaseous reference states based on thestate of each component

Electrolyte NRTL Enthalpy (HAQELC, HMXELC, and HMXENRHG)



2 Solvent/solute pair parameters default to waterparameters. Water/solute pair parameters default tozero (default for ELC models)

3 Default water parameters to 8, -4. Defaultsolvent/solute parameters to 10, -2 (default forHMXENRHG)

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 obtainedfrom:



Value Descriptions

0 Scalar GMELCA, GMELCB and GMELCM (default for ELCmodels)

1 Vector NRTL(8) (default for HMXENRHG)

4 Enthalpy calculation method

0 Electrolyte NRTL Enthalpy (default for ELC models andELECNRTL property method)

1 Helgeson method (default for HMXENRHG)

5 Vapor phase enthalpy departure contribution to liquidenthalpy. Hliq = Hig + DHV - Hvap; this option indicateshow 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 (forhandling solvents that exist in both subcritical andsupercritical conditions)

0 Original method (default)

1 Corresponding state method. Calculates a pseudo-critical temperature of the solvents and uses ittogether with the actual critical temperatures of thepure solvents to adjust the liquid enthalpy departure.This results in a smoother transition of the liquidenthalpy contribution when the component transformsfrom subcritical to supercritical.

7 Method for handling Henry components and multiplesolvents

0 Pure liquid enthalpy calculated by aqueous infinitedilution heat capacity; only water as solvent

1 Pure liquid enthalpy for Henry components calculatedusing Henry's law; use this option when there aremultiple solvents.

HLRELNRT and HLRELELC



2 Solvent/solute pair parameters default to waterparameters. Water/solute pair parameters default tozero (default for HLRELELC)

3 Default water parameters to 8, -4. Defaultsolvent/solute parameters to 10, -2 (default forHLRENRTL)


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 (molebasis)



Value Descriptions

HIG2ELC, HIG2HG

1 Enthalpy calculation method

0 Electrolyte NRTL Enthalpy (default for HIG2ELC)

1 Helgeson method (default for HIG2HG)

DHLELC

1 Steam table for liquid enthalpy of water

0 Use steam table for liquid enthalpy of water (default)

1 Use specified EOS model


0 Use specified EOS model (default)


HAQPT1, HAQPT3 (Pitzer)





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)

1 Reference temperature usage

0 Use standard reference temperature (default)

1 Use liquid reference temperature

PHILELC

1 Steam table for liquid enthalpy of water

0 Use steam table for liquid enthalpy of water (default)

1 Use specified EOS model


0 Use specified EOS model (default)


Option Codes for Gibbs FreeEnergy ModelsModel Name Option


Electrolyte NRTL Gibbs Energy (GAQELC, GMXELC, and GMXENRHG)




Value Descriptions


2 Solvent/solute pair parameters default to waterparameters. Water/solute pair parameters defaultto zero (default for ELC models)

3 Default water parameters to 8, -4. Defaultsolvent/solute parameters to 10, -2 (default forGMXENRHG)

2 Vapor phase equation-of-state for liquid Gibbsfree energy of HF

0 Ideal gas EOS (default)


3 Solvent/solvent binary parameter values obtainedfrom

0 Scalar GMELCA, GMELCB and GMELCM (defaultfor ELC models)

1 Vector NRTL(8) (default for GMXENRHG)

4 Gibbs free energy calculation method

0 Electrolyte NRTL Gibbs free energy (default forELC 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 ofstate

6 Method for handling Henry components andmultiple solvents

0 Pure liquid Gibbs free energy calculated byaqueous infinite dilution heat capacity; only wateras solvent

1 Pure liquid Gibbs free energy for Henrycomponents calculated using Henry's law; usethis option when there are multiple solvents.

GLRELNRT, GLRELELC



2 Solvent/solute pair parameters default to waterparameters. Water/solute pair parameters defaultto zero (default for GLRELELC)

3 Default water parameters to 8, -4. Defaultsolvent/solute parameters to 10, -2 (default forGLRENRTL)


0 Scalar GMELCA, GMELCB and GMELCM (default)

1 Vector NRTL(8)



Value Descriptions

3 Mixture density model

0 Rackett equation with Campbell-Thodosmodification

1 Quadratic mixing rule for molecular components(mole basis)

GIG2ELC, GIG2HG

1 Gibbs free energy calculation method

0 Electrolyte NRTL Gibbs free energy (default forGIG2ELC)

1 Helgeson method (default for GIG2HG)

GAQPT1, GAQPT3 (Pitzer)





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 VolumeModelsModelName

OptionCode

Value Descriptions

VL2QUAD 1 0 Use normal pure component liquid volume model forall components (default)

1 Use steam tables for water



VAQCLK 1 0 Use Clarke model

1 Use liquid volume quadratic mixing rule

Index 321

Index

A

activity coefficient models 86list of property models 86

alpha functions 69, 73Peng-Robinson 69Soave 73

Andrade liquid mixture viscositymodel 247

Andrade/DIPPR viscosity model248

Antoine/Wagner vapor pressuremodel 182

API model 194, 251, 288liquid molar volume 194liquid viscosity 251surface tension 288

API Sour model 187applications 91

metallurgical 91aqueous infinite dilution heat

capacity model 213ASME steam tables 16Aspen liquid mixture viscosity

model 252Aspen polynomial equation 211ASTM 252

liquid viscosity 252

B

Barin equations thermodynamicproperty model 228

Benedict-Webb-Rubin-Starlingproperty model 17

Braun K-10 model 187Brelvi-O'Connell model 196Bromley-Pitzer activity coefficient

model 87, 88, 89

about 87parameter conversion 89working equations 88

BWR-Lee-Starling property model16

C

Cavett thermodynamic propertymodel 228

Chao-Seader fugacity model 188Chapman-Enskog 253, 256, 282,

283Brokaw/DIPPR viscosity model

253Brokaw-Wilke mixing rule

viscosity model 256Wilke-Lee (binary) diffusion

model 282Wilke-Lee (mixture) diffusion

model 283Chien-Null activity coefficient

model 89Chung-Lee-Starling model 258,

260, 270low pressure vapor viscosity 258thermal conductivity 270viscosity 260

Clarke electrolyte liquid volumemodel 197

Clausius-Clapeyron equation 194heat of vaporization 194

coal 297property models 297

constant activity coefficient model91

copolymer PC-SAFT EOS propertymodel 35, 37, 41, 42, 44, 45,46

322 Index

about 35association term 42chain connectivity 37dispersion term 41fundamental equations 35parameters 45, 46polar term 44

COSMO-SAC solvation model 91COSTALD liquid volume model 199Criss-Cobble aqueous infinite

dilution ionic heat capacitymodel 214

D

Dawson-Khoury-Kobayashidiffusion model 283, 284

binary 283mixture 284

DCOALIGT coal density model 306Dean-Stiel pressure correction

viscosity model 262Debye-Hückel volume model 201DGHARIGT char density model 307diffusivity models 281

list 281DIPPR equation 7, 216DIPPR model 191, 202, 214, 219,

248, 253, 273, 276, 289heat of vaporization 191ideal gas heat capacity 219liquid heat capacity 214liquid volume 202surface tension 289thermal conductivity 273, 276viscosity 248, 253

DNSTYGEN nonconventionalcomponent density model 295

E

electrolyte models 197, 231, 233,263, 272, 285, 292

Clarke liquid volume 197electrolyte NRTL enthalpy 231Gibbs energy 233Jones-Dole viscosity 263Nernst-Hartley diffusion 285Onsager-Samaras surface

tension 292Riedel thermal conductivity 272

electrolyte NRTL 94, 97, 231, 233activity coefficient model 94, 97

enthalpy thermodynamicproperty model 231

Gibbs energy thermodynamicproperty model 233

eNRTL-SAC activity coefficientmodel 108

ENTHGEN nonconventionalcomponent heat capacitymodel 296

equation-of-state method 15property models 15

extrapolation 10temperature limits 10

G

Grayson-Streed fugacity model 188group contribution activity

coefficient models 172, 174,175

Dortmund-modified UNIFAC 174Lyngby-modified UNIFAC 175UNIFAC 172

H

Hakim-Steinberg-Stiel/DIPPRsurface tension 289

Hansen solubility parameter model112

Hayden-O'Connell 22property model 22

HCOALGEN 300general coal model for enthalpy

300heat of vaporization 191

models 191Helgeson thermodynamic property

model 240HF equation of state 25

property model 25Huron-Vidal mixing rules 79

I

IAPS models for water 262, 271,289

surface tension 289thermal conductivity 271viscosity 262

ideal gas heat capacity 219ideal gas law 29

property model 29

Index 323

ideal gas/DIPPR heat capacitymodel 219

ideal liquid activity coefficientmodel 114

IGT density model for 306, 307char 307coal 306

IK-CAPE equation 193, 217heat of vaporization 193liquid heat capacity 217

J

Jones-Dole electrolyte correctionviscosity model 263

K

Kent-Eisenberg fugacity model 189

L

Lee-Kesler Plöcker property model31

Lee-Kesler property model 29Letsou-Stiel viscosity model 265Li mixing rule thermal conductivity

model 272liquid constant molar volume

model 202liquid enthalpy 235

thermodynamic property model235

liquid heat capacity 216DIPPR equation 216

liquid mixture 247, 272, 288surface tension 288thermal conductivity 272viscosity 247

liquid thermal conductivity 273general pure components 273

liquid viscosity 247, 248, 251, 252,267

Andrade equation 247API 251API 1997 251Aspen 252ASTM 252pure components 248Twu 267

liquid volume quadratic mixing rule213

Lucas vapor viscosity model 265

M

Mathias alpha function 73Mathias-Copeman alpha function

69, 73Maxwell-Bonnell vapor pressure

model 190MHV2 mixing rules 81mixing rules 79, 81, 82, 84, 213,

243, 256, 269, 272, 279, 281Brokaw-Wilke viscosity model

256Huron-Vidal 79Li 272liquid volume quadratic 213MHV2 81predictive Soave-Redlich-Kwong-

Gmehling 82quadratic 243viscosity quadratic 269Vredeveld 279Wassiljewa-Mason-Saxena 281Wong-Sandler 84

modified MacLeod-Sugden surfacetension model 293

N

Nernst-Hartley electrolyte diffusionmodel 285

NIST 218liquid heat capacity 218

NIST TDE Watson equation 193heat of vaporization 193

nonconventional components 295,296, 300

coal model for enthalpy 300density polynomial model 295enthalpy and density models list

295heat capacity polynomial model

296nonconventional solid property

models 295density 295enthalpy 295list of 295

Nothnagel 33property model 33

NRTL 94, 114electrolyte NRTL property model

94property model 114

NRTL-SAC 115, 119, 130

324 Index

for Segments/Oligomers 130model derivation 119property model 115Using 135

O

Onsager-Samaras electrolytesurface tension model 292

option codes 309, 310, 312, 315,316, 318, 320

activity coefficient models 310enthalpy models 316equation of state models 312Gibbs energy models 318K-value models 316liquid volume models 320list 309Soave-Redlich-Kwong models

315transport property models 309

P

PC-SAFT property method 35property model 35

Peng-Robinson 47, 49, 50, 51, 69alpha functions 69MHV2 property model 50property model 47standard 49Wong-Sandler property model 51

physical properties 11, 15models 11, 15

Pitzer activity coefficient model135, 137, 138, 140, 144

about 135activity coefficients 140aqueous strong electrolytes 138model development 137parameters 144

polynomial activity coefficientmodel 147

PPDS equation 192, 216heat of vaporization 192liquid 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

fugacity models list 182heat capacity models list 213list of 5molar volume and density

models list 194option codes 309thermodynamic list 11vapor pressure model list 182

property parameters 6temperature-dependent

properties 6PSRK 51

property model 51pure component properties 7

temperature-dependent 7

Q

quadratic mixing rules 243

R

Rackett 207, 208, 209extrapolation method 209mixture liquid volume model 207modified model for molar volume

208Rackett pure component liquid

volume model 202Raoult's law 114Redlich-Kister activity coefficient

model 148Redlich-Kwong 51, 73

alpha function 73property model 51

Redlich-Kwong-Aspen propertymodel 52

Redlich-Kwong-Soave 53, 55, 56,57, 59, 73

alpha function list 73Boston-Mathias property model

55MHV2 property model 57property model 53Soave-Redlich-Kwong property

model 59Wong-Sandler property model 56

Riedel electrolyte correctionthermal conductivity model272

Index 325

S

Sato-Riedel/DIPPR thermalconductivity model 273

Scatchard-Hildebrand activitycoefficient model 149

Schwartzentruber-Renon propertymodel 57

Soave-Redlich-Kwong 59property model 59

Soave-Redlich-Kwong models 315options codes 315

solid Antoine vapor pressuremodels 190

solid thermal conductivitypolynomial 276

solids polynomial heat capacitymodel 223

solubility correlation models 225,226, 227

Henry's constant 225hydrocarbon 227list 225water solubility model 226

SRK-Kabadi-Danner propertymodel 61

SRK-ML property model 63standard Peng-Robinson property

model 49standard Redlich-Kwong-Soave

property model 53steam tables 16, 32

NBS/NRC 32property models 16

STEAMNBS property method 32Stiel-Thodos pressure correction

thermal conductivity model279

Stiel-Thodos thermal conductivitymodel 276

surface tension 287, 288, 293general pure components 289liquid mixtures 288models list 287modified MacLeod-Sugden 293

Symmetric and UnsymmetricElectrolyte NRTL activitycoefficient model 151, 154

about 151working equations 154

T

temperature 10

extrapolating limits 10temperature-dependent properties

6, 7pure component 7units 6

thermal conductivity 269, 276models list 269solids 276

thermo switch 7thermodynamic property 11, 228

list of additional models 228models list 11

three-suffix Margules activitycoefficient model 150

THRSWT 7transport property 244

models list 244transport switch 7TRAPP 266, 280

thermal conductivity model 280viscosity model 266

TRNSWT 7Twu liquid viscosity model 267

U

UNIFAC 172, 174, 175activity coefficient model 172Dortmund modified activity

coefficient model 174Lyngby modified activity

coefficient model 175UNIQUAC 176

activity coefficient model 176

V

Van Laar activity coefficient model178

vapor thermal conductivity 276general pure components 276

vapor viscosity 253, 256, 258, 265Brokaw-Wilke mixing rule

viscosity model 256Chung-Lee-Starling 258Lucas 265pure components 253

viscosity 246models 246

viscosity quadratic mixing rule 269VPA/IK-CAPE equation of state 64Vredeveld mixing rule 279

326 Index

W

Wagner Interaction Parameteractivity coefficient model 179

Wagner vapor pressure model 182Wassiljewa-Mason-Saxena mixing

rule 281Watson equation 191

heat of vaporization 191Wilke-Chang diffusion model 286,

287binary 286mixture 287

WILS-GLR property method 236WILS-LR property method 236Wilson (liquid molar volume)

activity coefficient model 181Wilson activity coefficient model

179Wong-Sandler mixing rules 84

AspenPhysPropModelsV7_2-Ref

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