Aspen Plus. Physical Property Methods and Models. Version STEADY STATE SIMULATION. AspenTech

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1 Aspen Plus STEADY STATE SIMULATION Verson 10 Physcal Property Methods and Models REFERENCE MANUAL AspenTech

2 COPYRIGHT Aspen Technology, Inc. ALL RIGHTS RESERVED The flowsheet graphcs and plot components of ASPEN PLUS were developed by MY-Tech, Inc. ADVENT, Aspen Custom Modeler, Aspen Dynamcs, ASPEN PLUS, AspenTech, BoProcess Smulator (BPS), DynaPLUS, ModelManager, Plantellgence, the Plantellgence logo, POLYMERS PLUS, PROPERTIES PLUS, SPEEDUP, and the aspen leaf logo are ether regstered trademarks, or trademarks of Aspen Technology, Inc., n the Unted States and/or other countres. BATCHFRAC and RATEFRAC are trademarks of Koch Engneerng Company, Inc. Actvator s a trademark of Software Securty, Inc. Ranbow SentnelSuperPro s a trademark of Ranbow Technologes, Inc. Élan Lcense Manager s a trademark of Élan Computer Group, Inc., Mountan Vew, Calforna, USA. Mcrosoft Wndows, Wndows NT, and Wndows 95 are ether regstered trademarks or trademarks of Mcrosoft Corporaton n the Unted States and/or other countres. All other brand and product names are trademarks or regstered trademarks of ther respectve companes. The Lcense Manager porton of ths product s based on: Élan Lcense Manager Élan Computer Group, Inc. All rghts reserved Use of ASPEN PLUS and Ths Manual Ths manual s ntended as a gude to usng ASPEN PLUS process modelng software. Ths documentaton contans AspenTech propretary and confdental nformaton and may not be dsclosed, used, or coped wthout the pror consent of AspenTech or as set forth n the applcable lcense agreement. Users are solely responsble for the proper use of ASPEN PLUS and the applcaton of the results obtaned. Although AspenTech has tested the software and revewed the documentaton, the sole warranty for ASPEN PLUS may be found n the applcable lcense agreement between AspenTech and the user. ASPENTECH MAKES NO WARRANTY OR REPRESENTATION, EITHER EXPRESS OR IMPLIED, WITH RESPECT TO THIS DOCUMENTATION, ITS QUALITY, PERFORMANCE, MERCHANTABILITY, OR FITNESS FOR A PARTICULAR PURPOSE.

3 Contents About Physcal Property Methods and Models For More Informaton...v Techncal Support...v 1 Overvew of ASPEN PLUS Property Methods Thermodynamc Property Methods Equaton-of-State Method Vapor-Lqud Equlbra Pressure-Temperature Dagram Retrograde Condensaton Lqud-Lqud and Lqud-Lqud-Vapor Equlbra Lqud Phase Nondealty Crtcal Soluton Temperature Calculaton of Propertes Usng an Equaton-of-State Property Method Advantages and Dsadvantages of the Equaton-of-State Method References Actvty Coeffcent Method Vapor-Lqud Equlbra Lqud Phase Reference Fugacty Electrolyte and Multcomponent VLE Lqud-Lqud and Lqud-Lqud-Vapor Equlbra Phase Equlbra Involvng Solds Salt Precptaton Phase Equlbra Involvng Solds for Metallurgcal Applcatons Calculaton of Other Propertes Usng Actvty Coeffcents Advantages and Dsadvantages of the Actvty Coeffcent Method References Equaton-of-State Models Cubc Equatons of State Pure Components Mxtures Vral Equatons of State Vapor Phase Assocaton References Actvty Coeffcent Models Molecular Models Group Contrbuton Models Electrolyte Models References Transport Property Methods Vscosty and Thermal Conductvty Methods Dffuson Coeffcent Methods Surface Tenson Methods Physcal Property Methods and Models Release 10

4 References Nonconventonal Component Enthalpy Calculaton Footnotes Property Method Descrptons Classfcaton of Property Methods and Recommended Use IDEAL Property Method Mxture Types Range Use of Henry s Law Property Methods for Petroleum Mxtures Lqud Fugacty and K-Value Model Property Methods BK Mxture Types Range CHAO-SEA Mxture Types Range GRAYSON Mxture Types Range Petroleum-Tuned Equaton-of-State Property Methods PENG-ROB Mxture Types Range RK-SOAVE Mxture Types Range Common Models Equaton-of-State Property Methods for Hgh-Pressure Hydrocarbon Applcatons BWR-LS Mxture Types Range LK-PLOCK Mxture Types Range PR-BM Mxture Types Range RKS-BM Mxture Types Range Common Models Flexble and Predctve Equaton-of-State Property Methods PRMHV Mxture Types Range PRWS Mxture Types Range v Physcal Property Methods and Models Verson 10

5 PSRK Mxture Types Range RK-ASPEN Mxture Types Range RKSMHV Mxture Types Range RKSWS Mxture Types Range SR-POLAR Mxture Types Range Common Models Lqud Actvty Coeffcent Property Methods Equatons of State Ideal Gas Law Mxture Types Range Redlch-Kwong Mxture Types Range Nothnagel Mxture Types Range Hayden-O Connell Mxture Types Range HF Equaton of State Mxture Types Range Actvty Coeffcent Models NRTL Mxture Types Range UNIFAC Mxture Types Range UNIQUAC Mxture Types Range Van Laar Mxture Types Range Wlson Mxture Types Range Common Models Electrolyte Property Methods Physcal Property Methods and Models Release 10 v

6 AMINES Range APISOUR ELECNRTL Mxture Types Range ENRTL-HF Mxture Types Range ENRTL-HG Mxture Types Range PITZER Mxture Types Range B-PITZER Mxture Types Range PITZ-HG Mxture Types Range General and Transport Property Model Parameter Requrements Solds Handlng Property Method Steam Tables STEAM-TA Range STEAMNBS Range Property Model Descrptons Thermodynamc Property Models Equaton-of-State Models ASME Steam Tables References BWR-Lee-Starlng References Hayden-O Connell Cross-Interactons Chemcal Theory References HF Equaton-of-State Molar Volume Calculaton True Mole Fracton (Partal Pressure) Calculaton Gbbs Energy and Fugacty Enthalpy and Entropy Usage References Ideal Gas Lee-Kesler References v Physcal Property Methods and Models Verson 10

7 Lee-Kesler-Plöcker References NBS/NRC Steam Tables References Nothnagel References Peng-Robnson-Boston-Mathas References Peng-Robnson-MHV Predctve SRK (PSRK) Peng-Robnson-Wong-Sandler Redlch-Kwong References Redlch-Kwong-Aspen References Redlch-Kwong-Soave-Boston-Mathas References Redlch-Kwong-Soave-Wong-Sandler Redlch-Kwong-Soave-MHV Schwartzentruber-Renon References Standard Peng-Robnson References Standard Redlch-Kwong-Soave References Peng-Robnson Alpha Functons Boston-Mathas Extrapolaton Mathas-Copeman Alpha Functon Schwartzentruber-Renon-Watanasr Alpha Functon Use of Alpha Functons References Soave Alpha Functons Soave Modfcaton Boston-Mathas Extrapolaton Mathas Alpha Functon Extended Mathas Alpha Functon Mathas-Copeman Alpha Functon Schwartzentruber-Renon-Watanasr Alpha Functon Use of Alpha Functons References Huron-Vdal Mxng Rules References MHV2 Mxng Rules References Predctve Soave-Redlch-Kwong-Gmehlng Mxng Rules References Wong-Sandler Mxng Rules References Actvty Coeffcent Models Bromley-Ptzer Actvty Coeffcent Model Chen-Null Constant Actvty Coeffcent Physcal Property Methods and Models Release 10 v

8 Electrolyte NRTL Actvty Coeffcent Model Ideal Lqud NRTL (Non-Random Two-Lqud) References Ptzer Actvty Coeffcent Model Polynomal Actvty Coeffcent Redlch-Kster Scatchard-Hldebrand Three-Suffx Margules References UNIFAC References UNIFAC (Dortmund Modfed) References UNIFAC (Lyngby Modfed) References UNIQUAC References Van Laar References Wagner Interacton Parameter References Wlson References Wlson Model wth Lqud Molar Volume References Vapor Pressure and Lqud Fugacty Models Extended Antone/Wagner Extended Antone Equaton Wagner Vapor Pressure Equaton References Chao-Seader References Grayson-Streed References Kent-Esenberg References Heat of Vaporzaton Model DIPPR Equaton Watson Equaton Clausus-Clapeyron Equaton Molar Volume and Densty Models API Lqud Volume Brelv-O Connell References Clarke Aqueous Electrolyte Volume Apparent Component Approach True Component Approach Temperature Dependence COSTALD Lqud Volume References Debje-Hückel Volume v Physcal Property Methods and Models Verson 10

9 References Rackett/DIPPR Pure Component Lqud Volume DIPPR Rackett References Rackett Mxture Lqud Volume References Modfed Rackett References Solds Volume Polynomal Heat Capacty Models Aqueous Infnte Dluton Heat Capacty Crss-Cobble Aqueous Infnte Dluton Ionc Heat Capacty DIPPR Lqud Heat Capacty Ideal Gas Heat Capacty/DIPPR DIPPR Ideal Gas Heat Capacty Polynomal References Solds Heat Capacty Polynomal Solublty Correlatons Henry s Constant Water Solublty Other Thermodynamc Property Models Cavett BARIN Equatons for Gbbs Energy, Enthalpy, Entropy, and Heat Capacty Sold Phase Lqud Phase Ideal Gas Phase Electrolyte NRTL Enthalpy Electrolyte NRTL Gbbs Energy Lqud Enthalpy from Lqud Heat Capacty Correlaton Enthalpes Based on Dfferent Reference States Saturated Lqud as Reference State Ideal Gas as Reference State Helgeson Equatons of State References Transport Property Models Vscosty Models Andrade/DIPPR Andrade DIPPR Lqud Vscosty References API Lqud Vscosty Chapman-Enskog-Brokaw/DIPPR Chapman-Enskog-Brokaw DIPPR Vapor Vscosty References Chapman-Enskog-Brokaw-Wlke Mxng Rule References Chung-Lee-Starlng Low-Pressure Vapor Vscosty References Chung-Lee-Starlng Vscosty Physcal Property Methods and Models Release 10 x

10 References Dean-Stel Pressure Correcton IAPS Vscosty for Water Jones-Dole Electrolyte Correcton Jones-Dole Breslau-Mller Carbonell References Letsou-Stel References Lucas Vapor Vscosty References TRAPP Vscosty Model References Thermal Conductvty Models Chung-Lee-Starlng Thermal Conductvty References IAPS Thermal Conductvty for Water L Mxng Rule Redel Electrolyte Correcton Sato-Redel/DIPPR Sato-Redel DIPPR Vredeveld Mxng Rule References Stel-Thodos/DIPPR Stel-Thodos DIPPR Vapor Thermal Conductvty References Stel-Thodos Pressure Correcton Model References TRAPP Thermal Conductvty Model References Wassljewa-Mason-Saxena Mxng Rule References Dffusvty Models Chapman-Enskog-Wlke-Lee (Bnary) References Chapman-Enskog-Wlke-Lee (Mxture) References Dawson-Khoury-Kobayash (Bnary) References Dawson-Khoury-Kobayash (Mxture) References Nernst-Hartley References Wlke-Chang (Bnary) References Wlke-Chang (Mxture) References Surface Tenson Models API Surface Tenson x Physcal Property Methods and Models Verson 10

11 IAPS Surface Tenson for Water Hakm-Stenberg-Stel/DIPPR Hakm-Stenberg-Stel DIPPR Lqud Surface Tenson References Onsager-Samaras References Nonconventonal Sold Property Models General Enthalpy and Densty Models General Densty Polynomal General Heat Capacty Polynomal Enthalpy and Densty Models for Coal and Char Notaton General Coal Enthalpy Model Heat of Combuston Correlatons Standard Heat of Formaton Correlatons Heat Capacty Krov Correlatons Cubc Temperature Equaton IGT Coal Densty Model IGT Char Densty Model References Property Calculaton Methods and Routes Introducton Physcal Propertes n ASPEN PLUS Methods Routes And Models Concept of Routes Models Property Model Opton Codes Tracng a Route Modfyng and Creatng Property Method Modfyng Exstng Property Methods Replacng Routes Replacng Models and Usng Multple Data Sets Conflctng Route and Model Specfcatons Creatng New Property Methods Usng Multple Data Sets n Multple Property Methods Modfyng and Creatng Routes Electrolyte Smulaton Soluton Chemstry Apparent Component and True Component Approaches Choosng the True or Apparent Approach Reconsttuton of Apparent Component Mole Fractons Electrolyte Thermodynamc Models Ptzer Equaton Electrolyte NRTL Equaton Zemats Equaton (Bromley-Ptzer Model) Future Models Physcal Property Methods and Models Release 10 x

12 Electrolyte Data Regresson References Free-Water and Rgorous Three-Phase Calculatons Free-Water Immscblty Smplfcaton Specfyng Free-Water Calculatons Free-Water Phase Propertes Organc Phase Propertes Rgorous Three-Phase Calculatons Petroleum Components Characterzaton Methods Property Methods for Characterzaton of Petroleum Components References Property Parameter Estmaton Descrpton of Estmaton Methods Molecular Weght (MW) Normal Bolng Pont (TB) Joback Method Ogata-Tsuchda Method Gan Method Man Method Crtcal Temperature (TC) Joback Method Lydersen Method Ambrose Method Fedors Method Smple Method Gan Method Man Method Crtcal Pressure (PC) Joback Method Lydersen Method Ambrose Method Gan Method Crtcal Volume (VC) Joback Method Lydersen Method Ambrose Method Redel Method Fedors Method Gan Method Crtcal Compressblty Factor (ZC) Acentrc Factor (OMEGA) Defnton Method Lee-Kesler Method Standard Enthalpy of Formaton (DHFORM) Benson Method Joback Method BensonR8 Method x Physcal Property Methods and Models Verson 10

13 Gan Method Standard Gbbs Free Energy of Formaton (DGFORM) Benson Method Joback Method Gan Method Heat of Vaporzaton at TB (DHVLB) Lqud Molar Volume at TB (VB) Standard Lqud Volume (VLSTD) Radus of Gyraton (RGYR) Solublty Parameter (DELTA) UNIQUAC R and Q Parameters (GMUQR, GMUQQ) Parachor (PARC) Ideal Gas Heat Capacty (CPIG) Benson Method Joback Method Data Method Vapor Pressure (PLXANT) Data Method Redel Method L-Ma Method Man Method Heat of Vaporzaton (DHVLWT) Data Method Defnton Method Vetere Method Gan Method Ducros Method L-Ma Method Lqud Molar Volume (RKTZRA) Gunn-Yamada Method Le Bas Method Data Method Lqud Vscosty (MULAND) Orrck-Erbar Method Letsou-Stel Method Data Method Vapor Vscosty (MUVDIP) Rechenberg Method Data Method Lqud Thermal Conductvty (KLDIP) Sato-Redel Method Data Method Vapor Thermal Conductvty (KVDIP) Surface Tenson (SIGDIP) Data Method Brock-Brd Method Macleod-Sugden Method L-Ma Method Lqud Heat Capacty (CPLDIP) Data Method Ruzcka Method Sold Heat Capacty (CPSPO1) Physcal Property Methods and Models Release 10 x

14 Data Method Mostafa Method Sold Standard Enthalpy of Formaton (DHSFRM) Mostafa Method Sold Standard Gbbs Free Energy of Formaton (DGSFRM) Mostafa Method Standard Enthalpy of Formaton of Aqueous Speces (DHAQHG) AQU-DATA Method THERMO Method AQU-EST1 Method AQU-EST2 Method Standard Gbbs Free Energy of Formaton of Aqueous Speces (DGAQHG) AQU-DATA Method THERMO Method AQU-EST1 Method AQU-EST2 Method Absolute Entropy of Aqueous Speces (S25HG) AQU-DATA Method THERMO Method AQU-EST1 Method AQU-EST2 Method Born Coeffcent (OMEGHG) Helgeson Capacty Parameters (CHGPAR) HG-AQU Method HG-CRIS Method HG-EST Method Bnary Parameters (WILSON, NRTL, UNIQ) UNIFAC R and Q Parameters (GMUFR, GMUFQ, GMUFDR, GMUFDQ, GMUFLR, GMUFLQ) A Bromley-Ptzer Actvty Coeffcent Model Workng Equatons...A-1 Parameter Converson...A-2 References...A-3 B Electrolyte NRTL Actvty Coeffcent Model Theoretcal Bass and Workng Equatons...B-1 Development of the Model...B-2 Long-Range Interacton Contrbuton...B-3 Local Interacton Contrbuton...B-4 Apparent Bnary Systems...B-5 Multcomponent Systems...B-9 Parameters...B-11 Obtanng Parameters...B-11 References...B-12 C Ptzer Actvty Coeffcent Model Model Development...C-1 Applcaton of the Ptzer Model to Aqueous Strong Electrolyte Systems...C-3 xv Physcal Property Methods and Models Verson 10

15 Calculaton of Actvty Coeffcents... C-5 Applcaton of the Ptzer Model to Aqueous Electrolyte Systems wth Molecular Solutes... C-8 Parameters... C-9 Parameter Converson... C-9 Parameter Sources... C-10 References... C-11 Index Index-1 Physcal Property Methods and Models Release 10 xv

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17 About Physcal Property Methods and Models Physcal Property Methods and Models provdes an overvew of ASPEN PLUS physcal property methods and detaled techncal reference nformaton on property opton sets, property calculaton methods and routes, property models, and parameter estmaton. Ths volume also ncludes techncal reference nformaton for handlng physcal propertes n electrolytes smulatons, rgorous and three-phase calculatons, and petroleum components characterzaton methods. Much of ths nformaton s also avalable n onlne prompts and help. At Release 9.3, correctons were made to property models n Chapter 3. Many property models have been added to ASPEN PLUS Release 9.3 and are now documented, for example the Wlson model wth lqud molar volume, the L mxng rules for lqud thermal conductvty and the new enthalpy methods. For nformaton and lstngs for all ASPEN PLUS databanks, electrolytes data, group contrbuton method functonal groups, and property sets, see ASPEN PLUS Physcal Property Data. An overvew of the ASPEN PLUS physcal property system, and nformaton about how to use ts full range and power, s n the ASPEN PLUS User Gude, as well as n onlne help and prompts n ASPEN PLUS. Physcal Property Methods and Models Verson 10 xv

18 For More Informaton Onlne Help ASPEN PLUS has a complete system of onlne help and context-senstve prompts. The help system contans both context-senstve help and reference nformaton. For more nformaton about usng ASPEN PLUS help, see the ASPEN PLUS User Gude, Chapter 3. ASPEN PLUS Gettng Started Buldng and Runnng a Process Model Ths tutoral ncludes several hands-on sessons to famlarze you wth ASPEN PLUS. The gude takes you step-by-step to learn the full power and scope of ASPEN PLUS. ASPEN PLUS User Gude The three-volume ASPEN PLUS User Gude provdes step-by-step procedures for developng and usng an ASPEN PLUS process smulaton model. The gude s task-orented to help you accomplsh the engneerng work you need to do, usng the powerful capabltes of ASPEN PLUS. ASPEN PLUS reference manual seres ASPEN PLUS reference manuals provde detaled techncal reference nformaton. These manuals nclude background nformaton about the unt operaton models and the physcal propertes methods and models avalable n ASPEN PLUS, tables of ASPEN PLUS databank parameters, group contrbuton method functonal groups, and a wde range of other reference nformaton. The set comprses: Unt Operaton Models Physcal Property Methods and Models Physcal Property Data User Models System Management Summary Fle Toolkt ASPEN PLUS applcaton examples A sute of sample onlne ASPEN PLUS smulatons llustratng specfc processes s delvered wth ASPEN PLUS. ASPEN PLUS Installaton Gudes These gudes provde nstructons on platform and network nstallaton of ASPEN PLUS. The set comprses: ASPEN PLUS Installaton Gude for Wndows ASPEN PLUS Installaton Gude for OpenVMS ASPEN PLUS Installaton Gude for UNIX The ASPEN PLUS manuals are delvered n Adobe portable document format (PDF) on the ASPEN PLUS Documentaton CD. You can also order prnted manuals from AspenTech. xv Physcal Property Methods and Models Verson 10.0

19 Techncal Support World Wde Web For addtonal nformaton about AspenTech products and servces, check the AspenTech World Wde Web home page on the Internet at: Techncal resources To obtan n-depth techncal support nformaton on the Internet, vst the Techncal Support homepage. Regster at: Approxmately three days after regsterng, you wll receve a confrmaton e-mal and you wll then be able to access ths nformaton. The most current Hotlne contact nformaton s lsted. Other nformaton ncludes: Frequently asked questons Product tranng courses Techncal tps AspenTech Hotlne If you need help from an AspenTech Customer Support engneer, contact our Hotlne for any of the followng locatons: If you are located n: Phone Number Fax Number E-Mal Address North Amerca & the Carbbean / / (toll free) / support@aspentech.com South Amerca (Argentna offce) +54-1/ / tecnoba@aspentech.com (Brazl offce) / / tecnosp@aspentech.com Europe, Gulf Regon, & Afrca (Brussels offce) +32-2/ / atesupport@aspentech.com (UK offce) / / atuksupport@aspentech.com Japan +81-3/ / atjsupport@aspentech.com Asa & Australa +85-2/ / atasupport@aspentech.com Physcal Property Methods and Models Verson 10 xx

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21 Chapter 1 1 Overvew of ASPEN PLUS Property Methods All unt operaton models need property calculatons to generate results. The most often requested propertes are fugactes for thermodynamc equlbrum (flash calculaton). Enthalpy calculatons are also often requested. Fugactes and enthalpes are often suffcent nformaton to calculate a mass and heat balance. However, other thermodynamc propertes (and, f requested, transport propertes) are calculated for all process streams. The mpact of property calculaton on the smulaton result s great. Ths s due to the qualty and the choce of the equlbrum and property calculatons. Equlbrum calculaton and the bases of property calculaton are explaned n ths chapter. The understandng of these bases s mportant to choose the approprate property calculaton. Chapter 2 gves more help on ths subject. The qualty of the property calculaton s determned by the model equatons themselves and by the usage. For optmal usage, you may need detals on property calculaton. These are gven n the Chapters 3 and 4. Ths chapter contans three sectons: Thermodynamc property methods Transport property methods Nonconventonal component enthalpy calculaton The thermodynamc property methods secton dscusses the two methods of calculatng vapor-lqud equlbrum (VLE): the equaton-of-state method and the actvty coeffcent method. Each method contans the followng: Fundamental concepts of phase equlbra and the equatons used Applcaton to vapor-lqud equlbra and other types of equlbra, such as lqud-lqud Calculatons of other thermodynamc propertes The last part of ths secton gves an overvew of the current equaton of state and actvty coeffcent technology. Physcal Property Methods and Models 1-1 Verson 10

22 Overvew of ASPEN PLUS Property Methods The table labeled Symbol Defntons on page 1-38 defnes the symbols used n equatons. Thermodynamc Property Methods The key thermodynamc property calculaton performed n a smulaton s phase equlbrum. The basc relatonshp for every component n the vapor and lqud phases of a system at equlbrum s: f v = f l (1) Where: f v = Fugacty of component n the vapor phase f l = Fugacty of component n the lqud phase Appled thermodynamcs provdes two methods for representng the fugactes from the phase equlbrum relatonshp n terms of measurable state varables, the equaton-of-state method and the actvty coeffcent method. In the equaton of state method: f f v l =ϕ v y p l =ϕ x p (2) (3) Wth α 1 Vα p RT α lnϕ = ln m RT n V dv Z TVn,, ej (4) Where: α = v or l V = Total volume n = Mole number of component 1-2 Physcal Property Methods and Models Verson 10

23 Chapter 1 Equatons 2 and 3 are dentcal wth the only dfference beng the phase to whch the varables apply. The fugacty coeffcent ϕ α s obtaned from the equaton of state, represented by p n equaton 4. See equaton 45 for an example of an equaton of state. In the actvty coeffcent method: f v v = ϕ yp (5) f l = x γ f *, l (6) Where ϕ v s calculated accordng to equaton 4, γ = Lqud actvty coeffcent of component *, l f = Lqud fugacty of pure component at mxture temperature Equaton 5 s dentcal to equaton 2. Agan, the fugacty coeffcent s calculated from an equaton of state. Equaton 6 s totally dfferent. Each property method n ASPEN PLUS s based on ether the equaton-of-state method or the actvty coeffcent method for phase equlbrum calculatons. The phase equlbrum method determnes how other thermodynamc propertes, such as enthalpes and molar volumes, are calculated. Wth an equaton-of-state method, all propertes can be derved from the equaton of state, for both phases. Usng an actvty coeffcent method, the vapor phase propertes are derved from an equaton of state, exactly as n the equaton-of- state method. However the lqud propertes are determned from summaton of the pure component propertes to whch a mxng term or an excess term s added. Equaton-of-State Method The partal pressure of a component n a gas mxture s: p = y p (7) The fugacty of a component n an deal gas mxture s equal to ts partal pressure. The fugacty n a real mxture s the effectve partal pressure: f v =ϕ v y p (8) Physcal Property Methods and Models 1-3 Verson 10

24 Overvew of ASPEN PLUS Property Methods The correcton factor ϕ v s the fugacty coeffcent. For a vapor at moderate pressures, ϕ v s close to unty. The same equaton can be appled to a lqud: f l l =ϕ x p (9) A lqud dffers from an deal gas much more than a real gas dffers from an deal gas. Thus fugacty coeffcents for a lqud are very dfferent from unty. For example, the fugacty coeffcent of lqud water at atmospherc pressure and room temperature s about 0.03 (Haar et al., 1984). An equaton of state descrbes the pressure, volume and temperature (p,v,t) behavor of pure components and mxtures. Usually t s explct n pressure. Most equatons of state have dfferent terms to represent attractve and repulsve forces between molecules. Any thermodynamc property, such as fugacty coeffcents and enthalpes, can be calculated from the equaton of state. Equaton-of-state propertes are calculated relatve to the deal gas propertes of the same mxture at the same condtons. See Calculaton of Propertes Usng an Equaton-of-State Property Method on page 1-7. Vapor-Lqud Equlbra The relatonshp for vapor-lqud equlbrum s obtaned by substtutng equatons 8 and 9 n equaton 1 and dvdng by p: ϕ v l y = ϕx (10) Fugacty coeffcents are obtaned from the equaton of state (see equaton 4 and Calculaton of Propertes Usng an Equaton-of-State Property Method on page 1-7). The calculaton s the same for supercrtcal and subcrtcal components (see Actvty Coeffcent Method on page 1-10). 1-4 Physcal Property Methods and Models Verson 10

25 Chapter 1 Pressure-Temperature Dagram Flud phase equlbra depend not only on temperature but also on pressure. At constant temperature (and below the mxture crtcal temperature), a multcomponent mxture wll be n the vapor state at very low pressure and n the lqud state at very hgh pressure. There s an ntermedate pressure range for whch vapor and lqud phases co-exst. Comng from low pressures, frst a dew pont s found. Then more and more lqud wll form untl the vapor dsappears at the bubble pont pressure. Ths s llustrated n the fgure labeled Phase Envelope of a Methane-Rch Hydrocarbon Mxture. Curves of constant vapor fracton (0.0, 0.2, 0.4, 0.6, 0.8 and 1.0) are plotted as a functon of temperature. A vapor fracton of unty corresponds to a dew-pont; a vapor fracton of zero corresponds to a bubble pont. The area confned between dew-pont and bubble-pont curves s the twophase regon. The dew-pont and bubble-pont curves meet at hgh temperatures and pressures at the crtcal pont. The other lnes of constant vapor fractons meet at the same pont. In Phase Envelope of a Methane-Rch Hydrocarbon Mxture, the crtcal pont s found at the pressure maxmum of the phase envelope (crcondenbar). Ths s not a general rule. At the crtcal pont the dfferences between vapor and lqud vansh; the mole fractons and propertes of the two phases become dentcal. Equaton 10 can handle ths phenomenon because the same equaton of state s used to evaluate ϕ v and ϕ l. Engneerng type equatons of state can model the pressure dependence of vapor-lqud equlbra very well. However, they cannot yet model crtcal phenomena accurately (see Equaton-of-State Models on page 1-22). Phase Envelope of a Methane-Rch Hydrocarbon Mxture Physcal Property Methods and Models 1-5 Verson 10

26 Overvew of ASPEN PLUS Property Methods Retrograde Condensaton Compressng the methane-rch mxture shown n the fgure labeled Phase Envelope of a Methane-Rch Hydrocarbon Mxture at 270 K (above the mxture crtcal temperature) wll show a dew-pont. Then lqud wll be formed up to a vapor fracton of about 0.75 (110 bar). Upon further compresson the vapor fracton wll decrease agan untl a second dew-pont s reached. If the process s carred out wth decreasng pressure, lqud s formed when expandng. Ths s the opposte of the more usual condensaton upon compresson. It s called retrograde condensaton and t happens often n natural gas mxtures. Lqud-Lqud and Lqud-Lqud-Vapor Equlbra Lqud-lqud equlbra are less pressure dependent than vapor-lqud equlbra, but certanly not pressure ndependent. The actvty coeffcent method can model lqud-lqud and lqud-lqud-vapor equlbra at low pressure as a functon of temperature. However, wth varyng pressure the equaton of state method s needed (compare Actvty Coeffcent Method on page 1-10, Lqud-Lqud and Lqud-Lqud-Vapor Equlbra). The equaton-of-state method (equaton 10) can be appled to lqud-lqud equlbra: ϕ x = ϕ x l l l l (11) and also to lqud-lqud-vapor equlbra: v l l l ϕ y = ϕ x = ϕ x l2 (12) Fugacty coeffcents n all the phases are calculated usng the same equaton of state. Fugacty coeffcents from equatons of state are a functon of composton, temperature, and pressure. Therefore, the pressure dependency of lqud-lqud equlbra can be descrbed. Lqud Phase Nondealty Lqud-lqud separaton occurs n systems wth very dssmlar molecules. Ether the sze or the ntermolecular nteractons between components may be dssmlar. Systems that demx at low pressures, have usually strongly dssmlar ntermolecular nteractons, as for example n mxtures of polar and non-polar molecules. In ths case, the mscblty gap s lkely to exst at hgh pressures as well. An examples s the system dmethyl-ether and water (Pozo and Street, 1984). Ths behavor also occurs n systems of a fully- or near fully-fluornated alphatc or alcyclc fluorocarbon wth the correspondng hydrocarbon (Rowlnson and Swnton, 1982), for example cyclohexane and perfluorocyclohexane (Dyke et al., 1959; Hcks and Young, 1971). Systems whch have smlar nteractons, but whch are very dfferent n sze, do demx at hgher pressures. For bnary systems, ths happens often n the vcnty of the crtcal pont of the lght component (Rowlnson and Swnton, 1982). 1-6 Physcal Property Methods and Models Verson 10

27 Chapter 1 Examples are: Methane wth hexane or heptane (van der Koo, 1981; Davenport and Rowlnson, 1963; Kohn, 1961) Ethane wth n-alkanes wth carbon numbers from 18 to 26 (Peters et al., 1986) Carbon doxde wth n-alkanes wth carbon numbers from 7 to 20 (Fall et al., 1985) The more the demxng compounds dffer n molecular sze, the more lkely t s that the lqud-lqud and lqud-lqud-vapor equlbra wll nterfere wth soldfcaton of the heavy component. For example, ethane and pentacosane or hexacosane show ths. Increasng the dfference n carbon number further causes the lqud-lqud separaton to dsappear. For example n mxtures of ethane wth n-alkanes wth carbon numbers hgher than 26, the lqud-lqud separaton becomes metastable wth respect to the sold-flud (gas or lqud) equlbra (Peters et al., 1986). The sold cannot be handled by an equaton-of-state method. Crtcal Soluton Temperature In lqud-lqud equlbra, mutual solubltes depend on temperature and pressure. Solubltes can ncrease or decrease wth ncreasng or decreasng temperature or pressure. The trend depends on thermodynamc mxture propertes but cannot be predcted a pror. Immscble phases can become mscble wth ncreasng or decreasng temperature or pressure. In that case a lqud-lqud crtcal pont occurs. Equatons 11 and 12 can handle ths behavor, but engneerng type equatons of state cannot model these phenomena accurately. Calculaton of Propertes Usng an Equaton-of-State Property Method The equaton of state can be related to other propertes through fundamental thermodynamc equatons : Fugacty coeffcent: v v f =ϕ yp (13) Enthalpy departure: V g RT ( H H ) p ( ) ( ) V dv RT V g m m = ln TS S RTZ g + m m + m 1 (14) V Entropy departure: V g p R ( S S ) T V dv R V m m = g + ln (15) v V Gbbs energy departure: V g RT ( G G ) p ( ) V dv RT V m m = ln RT Z g + m 1 (16) V Physcal Property Methods and Models 1-7 Verson 10

28 Overvew of ASPEN PLUS Property Methods Molar volume: Solve ptv (, m ) for V m. From a gven equaton of state, fugactes are calculated accordng to equaton 13. The other thermodynamc propertes of a mxture can be computed from the departure functons: Vapor enthalpy: v g v g Hm = Hm + ( Hm Hm ) (17) Lqud enthalpy: l g l g H = H + H H (18) g C p, f m m ( m m ) The molar deal gas enthalpy, H m g T g g g Hm = y f H + Cp() T dt ref, T (19) Where: = Ideal gas heat capacty s computed by the expresson g H = Standard enthalpy of formaton for deal gas at K and 1 atm T ref = Reference temperature = K Entropy and Gbbs energy can be computed n a smlar manner: v g v g G = G + G G m m ( m m ) l g ( m m ) v g ( m m ) l g ( m m ) l g G = G + G G m m v g S = S + S S m m l g S = S + S S m m Vapor and lqud volume s computed by solvng p(t,v m ) for V m or computed by an emprcal correlaton. Advantages and Dsadvantages of the Equaton-of-State Method You can use equatons of state over wde ranges of temperature and pressure, ncludng subcrtcal and supercrtcal regons. For deal or slghtly non-deal systems, thermodynamc propertes for both the vapor and lqud phases can be computed wth a mnmum amount of component data. Equatons of state are sutable for modelng hydrocarbon systems wth lght gases such as CO 2, N 2, and HS 2. (20) (21) (22) (23) 1-8 Physcal Property Methods and Models Verson 10

29 Chapter 1 For the best representaton of non-deal systems, you must obtan bnary nteracton parameters from regresson of expermental vapor-lqud equlbrum (VLE) data. Equaton of state bnary parameters for many component pars are avalable n ASPEN PLUS. The assumptons n the smpler equatons of state (Redlch-Kwong-Soave, Peng- Robnson, Lee-Kesler-Plöcker) are not capable of representng hghly non-deal chemcal systems, such as alcohol-water systems. Use the actvty-coeffcent optons sets for these systems at low pressures. At hgh pressures, use the flexble and predctve equatons of state. References A.J. Davenport and J.S. Rowlnson, Trans. Faraday Soc., Vol. 59 (1963), p. 78, (cted after van der Koo, 1981). D.E.L. Dyke, J.S. Rowlnson and R. Thacker, Trans. Faraday Soc., Vol. 55, (1959), p. 903, (cted after Rowlnson and Swnton, 1982). D.J. Fall, J.L. Fall, and K.D. Luks, "Lqud-lqud-vapor mmscblty Lmts n Carbon Doxde + n-paraffn Mxtures," J. Chem. Eng. Data, Vol. 30, No. 1, (1985), pp L. Haar, J.S. Gallagher, and J.H. Kell, NBSINRC Steam Tables (Washngton: Hemsphere Publshng Corporaton, 1984). C.P. Hcks and C.L. Young, Trans. Faraday Soc., Vol. 67, (1971), p.1605, (cted after Rowlnson and Swnton, 1982). J.P. Kohn, AIChE J., Vol 7, (1961), p. 514, (cted after van der Koo, 1981). H.J. van der Koo, Metngen en berekenngen aan het systeem methaan-nescosaan, Ph.D. thess, Delft Unversty of Technology (Delft: Delftse Unverstare Pers, 1981) (In Dutch). C.J. Peters, R.N. Lchtenthaler, and J. de Swaan Arons, "Three Phase Equlbra In Bnary Mxtures Of Ethane And Hgher N-Alkanes," Flud Phase Eq., Vol. 29, (1986), pp M.E. Pozo and W.B. Street, "Flud Phase Equlbra for the System Dmethyl Ether/Water from 50 to 200 C and Pressures to 50.9 MPa," J. Chem. Eng. Data, Vol. 29, No. 3, (1984), pp J.S. Rowlnson and F.L. Swnton, Lquds and Lqud Mxtures, 3rd ed. (London, etc.:butterworths, 1982), ch. 6. Physcal Property Methods and Models 1-9 Verson 10

30 Overvew of ASPEN PLUS Property Methods Actvty Coeffcent Method In an deal lqud soluton, the lqud fugacty of each component n the mxture s drectly proportonal to the mole fracton of the component. f l = x f *, l (24) The deal soluton assumes that all molecules n the lqud soluton are dentcal n sze and are randomly dstrbuted. Ths assumpton s vald for mxtures contanng molecules of smlar sze and character. An example s a mxture of pentane (n-pentane) and 2,2-dmethylpropane (neopentane) (Gmehlng et al., 1980, pp ). For ths mxture, the molecules are of smlar sze and the ntermolecular nteractons between dfferent component molecules are small (as for all nonpolar systems). Idealty can also exst between polar molecules, f the nteractons cancel out. An example s the system water and 1,2-ethanedol (ethyleneglycol) at 363 K (Gmehlng et al., 1988, p. 124). In general, you can expect non-dealty n mxtures of unlke molecules. Ether the sze and shape or the ntermolecular nteractons between components may be dssmlar. For short these are called sze and energy asymmetry. Energy asymmetry occurs between polar and non-polar molecules and also between dfferent polar molecules. An example s a mxture of alcohol and water. The actvty coeffcent γ represents the devaton of the mxture from dealty (as defned by the deal soluton): l f = x γ f *, l (25) The greater γ devates from unty, the more non-deal the mxture. For a pure component x = 1 and γ = 1, so by ths defnton a pure component s deal. A mxture that behaves as the sum of ts pure components s also defned as deal (compare equaton 24). Ths defnton of dealty, relatve to the pure lqud, s totally dfferent from the defnton of the dealty of an deal gas, whch has an absolute meanng (see Equaton-of-State Method on page 1-3). These forms of dealty can be used next to each other. In the majorty of mxtures, γ s greater than unty. The result s a hgher fugacty than deal (compare equaton 25 to equaton 24). The fugacty can be nterpreted as the tendency to vaporze. If compounds vaporze more than n an deal soluton, then they ncrease ther average dstance. So actvty coeffcents greater than unty ndcate repulson between unlke molecules. If the repulson s strong, lqud-lqud separaton occurs. Ths s another mechansm that decreases close contact between unlke molecules. It s less common that γ s smaller than unty. Usng the same reasonng, ths can be nterpreted as strong attracton between unlke molecules. In ths case, lqud-lqud separaton does not occur. Instead formaton of complexes s possble Physcal Property Methods and Models Verson 10

31 Chapter 1 Vapor-Lqud Equlbra In the actvty coeffcent approach, the basc vapor-lqud equlbrum relatonshp s represented by: ϕ v yp= xγ f *, l (26) The vapor phase fugacty coeffcent ϕ v s computed from an equaton of state (see Equaton-of-State Method on page 1-3). The lqud actvty coeffcent γ s computed from an actvty coeffcent model. For an deal gas, ϕ v = 1. For an deal lqud, γ = 1. Combnng ths wth equaton 26 gves Raoult s law: yp= xp *, l (27) At low to moderate pressures, the man dfference between equatons 26 and 27 s due to the actvty coeffcent. If the actvty coeffcent s larger than unty, the system s sad to show postve devatons from Raoults law. Negatve devatons from Raoult s law occur when the actvty coeffcent s smaller than unty. Lqud Phase Reference Fugacty The lqud phase reference fugacty f ways: *, l from equaton 26 can be computed n three For solvents: The reference state for a solvent s defned as pure component n the lqud state, at the temperature and pressure of the system. By ths defnton γ approaches unty as x approaches unty. The lqud phase reference fugacty f l (, ) *, l s computed as *, l *, v *, *, l *,l f =ϕ T p p θ (28) Where: *, v ϕ = Fugacty coeffcent of pure component at the system temperature and vapor pressures, as calculated from the vapor phase equaton of state *, l p = Lqud vapor pressures of component at the system temperature *, l θ = Poyntng correcton for pressure = 1 exp RT p *, p l V *, l dp Physcal Property Methods and Models 1-11 Verson 10

32 Overvew of ASPEN PLUS Property Methods At low pressures, the Poyntng correcton s near unty, and can be gnored. For dssolved gases: Lght gases (such as O 2 and N 2 ) are usually supercrtcal at the temperature and pressure of the soluton. In that case pure component vapor pressure s meanngless and therefore t cannot serve as the reference fugacty. The reference state for a dssolved gas s redefned to be at nfnte dluton and at the temperature and pressure of the mxtures. The lqud phase *, l reference fugacty f becomes H (the Henry s constant for component n the mxture). The actvty coeffcent γ s converted to the nfnte dluton reference state through the relatonshp ( ) γ * = γ γ (29) Where: γ = The nfnte dluton actvty coeffcent of component n the mxture By ths defnton γ * approaches unty as x approaches zero. The phase equlbrum relatonshp for dssolved gases becomes ϕ v * yp= xγ H (30) To compute H, you must supply the Henry s constant for the dssolved-gas component n each subcrtcal solvent component. Usng an Emprcal Correlaton: The reference state fugacty s calculated usng an emprcal correlaton. Examples are the Chao-Seader or the Grayson- Streed model. Electrolyte and Multcomponent VLE The vapor-lqud equlbrum equatons 26 and 30, only apply for components whch occur n both phases. Ions are components whch do not partcpate drectly n vapor-lqud equlbrum. Ths s true as well for solds whch do not dssolve or vaporze. However, ons nfluence actvty coeffcents of the other speces by nteractons. As a result they partcpate ndrectly n the vapor-lqud equlbra. An example s the lowerng of the vapor pressure of a soluton upon addton of an electrolyte. For more on electrolyte actvty coeffcent models, see Actvty Coeffcent Models on page Physcal Property Methods and Models Verson 10

33 Chapter 1 Multcomponent vapor-lqud equlbra are calculated from bnary parameters. These parameters are usually ftted to bnary phase equlbrum data (and not multcomponent data) and represent therefore bnary nformaton. The predcton of multcomponent phase behavor from bnary nformaton s generally good. Lqud-Lqud and Lqud-Lqud-Vapor Equlbra The basc lqud-lqud-vapor equlbrum relatonshp s: l1 l1 *, l l2 l2 *, l v x γ f = x γ f = ϕ y p (31) Equaton 31 can be derved from the lqud-vapor equlbrum relatonshp by analogy. For lqud-lqud equlbra, the vapor phase term can be omtted, and the pure component lqud fugacty cancels out: x γ = x γ l1 l1 l2 l2 (32) The actvty coeffcents depend on temperature, and so do lqud-lqud equlbra. However, equaton 32 s ndependent of pressure. The actvty coeffcent method s very well suted for lqud-lqud equlbra at low to moderate pressures. Mutual solubltes do not change wth pressure n ths case. For hgh-pressure lqud-lqud equlbra, mutual solubltes become a functon of pressure. In that case, use an equaton-of-state method. For the computaton of the dfferent terms n equatons 31 and 32, see Vapor- Lqud Equlbra on page 1-4. Mult-component lqud-lqud equlbra cannot be relably predcted from bnary nteracton parameters ftted to bnary data only. In general, regresson of bnary parameters from mult-component data wll be necessary. See the ASPEN PLUS User Gude, Chapter 31 for detals. The ablty of actvty coeffcent models n descrbng expermental lqud-lqud equlbra dffers. The Wlson model cannot descrbe lqud-lqud separaton at all; UNIQUAC, UNIFAC and NRTL are sutable. For detals, see Actvty Coeffcent Models on page Actvty coeffcent models sometmes show anomalous behavor n the metastable and unstable composton regon. Phase equlbrum calculaton usng the equalty of fugactes of all components n all phases (as n equatons 31 and 32), can lead to unstable solutons. Instead, phase equlbrum calculaton usng the mnmzaton of Gbbs energy always yelds stable solutons. Physcal Property Methods and Models 1-13 Verson 10

34 Overvew of ASPEN PLUS Property Methods The fgure labeled (T,x,x,y) Dagram of Water and Butanol-1 at bar, a graphcal Gbbs energy mnmzaton of the system n-butanol + water, shows ths: (T,x,x,y) Dagram of Water and Butanol-1 at bar The phase dagram of n-butanol + water at 1 bar s shown n ths fgure. There s lqud-lqud separaton below 367 K and there are vapor-lqud equlbra above ths temperature. The dagram s calculated usng the UNIFAC actvty coeffcent model wth the lqud-lqud data set Physcal Property Methods and Models Verson 10

35 Chapter 1 The Gbbs energes of vapor and lqud phases at 1 bar and 365 K are gven n the fgure labeled Molar Gbbs Energy of Butanol-1 and Water at 365 K and 1 atm 1. Ths corresponds to a secton of the phase dagram at 365 K. The Gbbs energy of the vapor phase s hgher than that of the lqud phase at any mole fracton. Ths means that the vapor s unstable wth respect to the lqud at these condtons. The mnmum Gbbs energy of the system as a functon of the mole fracton can be found graphcally by stretchng an magnary strng from below around the Gbbs curves. For the case of the fgure labeled Molar Gbbs Energy of Butanol-1 and Water at 365 K and 1 atm, the strng never touches the vapor Gbbs energy curve. For the lqud the stuaton s more subtle: the strng touches the curve at the extremtes but not at mole fractons between 0.56 and In that range the strng forms a double tangent to the curve. A hypothetcal lqud mxture wth mole fracton of 0.8 has a hgher Gbbs energy and s unstable wth respect to two lqud phases wth mole fractons correspondng to the ponts where the tangent and the curve touch. The overall Gbbs energy of these two phases s a lnear combnaton of ther ndvdual Gbbs energes and s found on the tangent (on the strng). The mole fractons of the two lqud phases found by graphcal Gbbs energy mnmzaton are also ndcated n the fgure labeled (T,x,x,y) Dagram of Water and Butanol-1 at bar. Molar Gbbs Energy of Butanol-1 and Water at 365 K and 1 atm Physcal Property Methods and Models 1-15 Verson 10

36 Overvew of ASPEN PLUS Property Methods At a temperature of 370 K, the vapor has become stable n the mole fracton range of 0.67 to 0.90 (see the fgure labeled Molar Gbbs Energy of Butanol-1 and Water at 370 K and 1 atm). Graphcal Gbbs energy mnmzaton results n two vapor-lqud equlbra, ndcated n the fgure labeled Molar Gbbs Energy of Butanol-1 and Water at 370 K and 1 atm. Ignorng the Gbbs energy of the vapor and usng a double tangent to the lqud Gbbs energy curve a lqud-lqud equlbrum s found. Ths s unstable wth respect to the vapor-lqud equlbra. Ths unstable equlbrum wll not be found wth Gbbs mnmzaton (unless the vapor s gnored) but can easly be found wth the method of equalty of fugactes. Molar Gbbs Energy of Butanol-1 and Water at 370 K and 1 atm The technque of Gbbs energy mnmzaton can be used for any number of phases and components, and gves accurate results when handled by a computer algorthm. Ths technque s always used n the equlbrum reactor unt operaton model RGbbs, and can be used optonally for lqud phase separaton n the dstllaton model RadFrac. Phase Equlbra Involvng Solds In most nstances, solds are treated as nert wth respect to phase equlbrum (CISOLID). Ths s useful f the components do not dssolve or vaporze. An example s sand n a water stream. CISOLID components are stored n separate substreams Physcal Property Methods and Models Verson 10

37 Chapter 1 There are two areas of applcaton where phase equlbrum nvolvng solds may occur: Salt precptaton n electrolyte solutons Pyrometallurgcal applcatons Salt Precptaton Electrolytes n soluton often have a sold solublty lmt. Sold solubltes can be calculated f the actvty coeffcents of the speces and the solublty product are known (for detals see Chapter 5). The actvty of the onc speces can be computed from an electrolyte actvty coeffcent model (see Actvty Coeffcent Models on page 1-32). The solublty product can be computed from the Gbbs energes of formaton of the speces partcpatng n the precptaton reacton or can be entered as the temperature functon (K-SALT) on the Reactons Chemstry Equlbrum Constants sheet. Salt precptaton s only calculated when the component s declared as a Salt on the Reactons Chemstry Stochometry sheet. The salt components are part of the MIXED substream, because they partcpate n phase equlbrum. The types of equlbra are lqud-sold or vapor-lqud-sold. Each precptatng salt s treated as a separate, pure component, sold phase. Sold compounds, whch are composed of stochometrc amounts of other components, are treated as pure components. Examples are salts wth crystal water, lke CaSO 4, HO 2. Phase Equlbra Involvng Solds for Metallurgcal Applcatons Mneral and metallc solds can undergo phase equlbra n a smlar way as organc lquds. Typcal pyrometallurgcal applcatons have specfc characterstcs: Smultaneous occurrence of multple sold and lqud phases Occurrence of smultaneous phase and chemcal equlbra Occurrence of mxed crystals or sold solutons These specfc characterstcs are ncompatble wth the chemcal and phase equlbrum calculatons by flash algorthms as used for chemcal and petrochemcal applcatons. Instead, these equlbra can be calculated by usng Gbbs energy mnmzaton technques. In ASPEN PLUS, the unt operaton model RGbbs s specally desgned for ths purpose. Gbbs energy mnmzaton technques are equvalent to phase equlbrum computatons based on equalty of fugactes. If the dstrbuton of the components of a system s found, such that the Gbbs energy s mnmal, equlbrum s obtaned. (Compare the dscusson of phase equlbrum calculaton usng Gbbs energy mnmzaton n Equlbra on page 1-6) As a result, the analog of equaton 31 holds: l1 l1 *, l l2 l2 *, l s1 s1 *, s s2 s2 *, s v x γ f = x γ f =... x γ f = x γ f =... ϕ y p (33) Physcal Property Methods and Models 1-17 Verson 10

38 Overvew of ASPEN PLUS Property Methods Ths equaton can be smplfed for pure component solds and lquds, or be extended for any number of phases. For example, the pure component vapor pressure (or sublmaton) curve can be calculated from the pure component Gbbs energes of vapor and lqud (or sold). The fgure labeled Thermodynamc Potental of Mercury at 7, 5, 10, and 20 bar shows the pure component molar Gbbs energy or thermodynamc potental of lqud and vapor mercury as a functon of temperature and at four dfferent pressures: 1,5,10 and 20 bar 2. The thermodynamc potental of the lqud s not dependent on temperature and ndependent of pressure: the four curves concde. The vapor thermodynamc potental s clearly dfferent at each pressure. The ntersecton pont of the lqud and vapor thermodynamc potentals at 1 bar s at about 630 K. At ths pont the thermodynamc potentals of the two phases are equal, so there s equlbrum. A pont of the vapor pressure curve s found. Below ths temperature the lqud has the lower thermodynamc potental and s the stable phase; above ths temperature the vapor has the lower thermodynamc potental. Repeatng the procedure for all four pressures gves the four ponts ndcated on the vapor pressure curve (see the fgure labeled Vapor Pressure Curve of Lqud Mercury). Ths s a smlar result as a drect calculaton wth the Antone equaton. The procedure can be repeated for a large number of pressures to construct the curve wth suffcent accuracy. The sublmaton curve can also be calculated usng an Antone type model, smlar to the vapor pressure curve of a lqud. Thermodynamc Potental of Mercury at 7, 5, 10, and 20 bar 1-18 Physcal Property Methods and Models Verson 10

39 Chapter 1 Vapor Pressure Curve of Lqud Mercury The majorty of sold databank components occur n the INORGANIC databank. In that case, pure component Gbbs energy, enthalpy and entropy of sold, lqud or vapor are calculated by polynomals (see Chapter 3). The pure component sold propertes (Gbbs energy and enthalpy) together wth the lqud and vapor mxture propertes are suffcent nput to calculate chemcal and phase equlbra nvolvng pure sold phases. In some cases mxed crystals or sold solutons can occur. These are separate phases. The concept of dealty and nondealty of sold solutons are smlar to those of lqud phases (see Vapor- Lqud Equlbra on page 1-4). The actvty coeffcent models used to descrbe nondealty of the sold phase are dfferent than those generally used for lqud phases. However some of the models (Margules, Redlch-Kster) can be used for lquds as well. If multple lqud and sold mxture phases occur smultaneously, the actvty coeffcent models used can dffer from phase to phase. To be able to dstngush pure component solds from sold solutons n the stream summary, the pure component solds are placed n the CISOLID substream and the sold solutons n the MIXED substream. Calculaton of Other Propertes Usng Actvty Coeffcents Propertes can be calculated for vapor, lqud or sold phases: Physcal Property Methods and Models 1-19 Verson 10

40 Overvew of ASPEN PLUS Property Methods Vapor phase: Vapor enthalpy, entropy, Gbbs energy and densty are computed from an equaton of state (see Calculaton of Propertes Usng an Equaton-of- State Property Method on page 1-7). Lqud phase: Lqud mxture enthalpy s computed as v ( ) l *, * El, H = x H H + H (34) m Where: vap m *, v H = Pure component vapor enthalpy at T and vapor pressure vap H * = Component vaporzaton enthalpy El, H m = Excess lqud enthalpy El, Excess lqud enthalpy H m expresson s related to the actvty coeffcent through the El, ln γ Hm = RT 2 x T Lqud mxture Gbbs free energy and entropy are computed as: S l m 1 = T H ( l G l m m) (35) (36) l v l El G = G RT ϕ + G (37) m Where: m ln *,, m El, G = RT x ln γ m (38) Lqud densty s computed usng an emprcal correlaton. Sold phase: Sold mxture enthalpy s computed as: s s s Hm = x H *, + H Es, m (39) Where: *, s H = Pure component sold enthalpy at T 1-20 Physcal Property Methods and Models Verson 10

41 Chapter 1 Es, H m = The excess sold enthalpy Es, Excess sold enthalpy H m s related to the actvty coeffcent through the Es, ln γ expresson Hm = RT 2 x T (40) Sold mxture Gbbs energy s computed as: s s Es s s G = x µ *, + G, + RT x ln x (41) m Where: m Es, s s G = RT x ln γ (42) m The sold mxture entropy follows from the Gbbs energy and enthalpy: S s m 1 = T H ( s G s m m) (43) Advantages and Dsadvantages of the Actvty Coeffcent Method The actvty coeffcent method s the best way to represent hghly non-deal lqud mxtures at low pressures. You must estmate or obtan bnary parameters from expermental data, such as phase equlbrum data. Bnary parameters for the Wlson, NRTL, and UNIQUAC models are avalable n ASPEN PLUS for a large number of component pars. These bnary parameters are used automatcally. See ASPEN PLUS Physcal Property Data, Chapter 1, for detals. Bnary parameters are vald only over the temperature and pressure ranges of the data. Bnary parameters outsde the vald range should be used wth cauton, especally n lqud-lqud equlbrum applcatons. If no parameters are avalable, the predctve UNIFAC models can be used. The actvty coeffcent approach should be used only at low pressures (below 10 atm). For systems contanng dssolved gases at low pressures and at small concentratons, use Henry s law. For hghly non-deal chemcal systems at hgh pressures, use the flexble and predctve equatons of state. References Collecton, Alphatc Hydrocarbons, C4 - C6, Chemstry Data Seres Vol 1, Part 6a, D. Berens and R.Eckerman, eds., (Frankfurt/Man: Dechema, 1980). Physcal Property Methods and Models 1-21 Verson 10

42 Overvew of ASPEN PLUS Property Methods J. Gmehlng, U. Onken and W. Arlt, "Vapor-Lqud Equlbrum Data Collecton, Aqueous-Organc Systems, Supplement 2," Chemstry Data Seres Vol 1, Part 1b, D. Berens and R.Eckerman, eds., (Frankfurt/Man: Dechema, 1988). H.A.J. Oonk, Phase Theory, The Thermodynamcs of Heterogeneous Equlbra, (Amsterdam, etc.: Elsever Scentfc Publshng Company, 1981), Ch. 4. Equaton-of-State Models The smplest equaton of state s the deal gas law: p = RT V m (44) The deal gas law assumes that molecules have no sze and that there are no ntermolecular nteractons. Ths can be called absolute dealty, n contrast to dealty defned relatve to pure component behavor, as used n the actvty coeffcent approach (see Actvty Coeffcent Method on page 1-10). There are two man types of engneerng equatons of state: cubc equatons of state and the vral equatons of state. Steam tables are an example of another type of equaton of state. Cubc Equatons of State In an deal gas, molecules have no sze and therefore no repulson. To correct the deal gas law for repulson, the total volume must be corrected for the volume of the molecule(s), or covolume b. (Compare the frst term of equaton 45 to equaton 44. The covolume can be nterpreted as the molar volume at closest packng. The attracton must decrease the total pressure compared to an deal gas, so a negatve term s added, proportonal to an attracton parameter a. Ths term s dvded by an expresson wth dmenson m 3, because attractve forces are proportonal to 1, wth r beng the dstance between molecules. An example of 6 r ths class of equatons s the Soave-Redlch-Kwong equaton of state (Soave, 1972): p= RT ( V b) at ( ) ( + ) V V b m m m (45) 1-22 Physcal Property Methods and Models Verson 10

43 Chapter 1 Equaton 45 can be wrtten as a cubc polynomal n V m. Wth the two terms of equaton 45 and usng smple mxng rules (see Mxtures, ths chapter). the Soave-Redlch-Kwong equaton of state can represent non-dealty due to compressblty effects. The Peng-Robnson equaton of state (Peng and Robnson, 1976) s smlar to the Soave-Redlch-Kwong equaton of state. Snce the publcaton of these equatons, many mprovements and modfcatons have been suggested. A selecton of mportant modfcatons s avalable n ASPEN PLUS. The orgnal Redlch-Kwong-Soave and Peng-Robnson equatons wll be called standard cubc equatons of state. Cubc equatons of state n ASPEN PLUS are based on the Redlch-Kwong-Soave and Peng-Robnson equatons of state. Equatons are lsted n the followng table. Cubc Equatons of State n ASPEN PLUS Redlch-Kwong(-Soave) based Redlch-Kwong Standard Redlch-Kwong-Soave Redlch-Kwong-Soave Redlch-Kwong-ASPEN Peng-Robnson based Standard Peng-Robnson Peng-Robnson Peng-Robnson-MHV2 Peng-Robnson-WS Schwartzentruber-Renon Redlch-Kwong-Soave-MHV2 Predctve SRK Redlch-Kwong-Soave-WS Pure Components In a standard cubc equaton of state, the pure component parameters are calculated from correlatons based on crtcal temperature, crtcal pressure, and acentrc factor. These correlatons are not accurate for polar compounds or long chan hydrocarbons. Introducng a more flexble temperature dependency of the attracton parameter (the alpha-functon), the qualty of vapor pressure representaton mproves. Up to three dfferent alpha functons are bult-n to the followng cubc equaton-of-state models n ASPEN PLUS: Redlch-Kwong-Aspen, Schwartzenruber-Renon, Peng-Robnson-MHV2, Peng-Robnson-WS, Predctve RKS, Redlch-Kwong-Soave-MHV2, and Redlch-Kwong-Soave-WS. Cubc equatons of state do not represent lqud molar volume accurately. To correct ths you can use volume translaton, whch s ndependent of VLE computaton. The Schwartzenruber-Renon equaton of state model has volume translaton. Physcal Property Methods and Models 1-23 Verson 10

44 Overvew of ASPEN PLUS Property Methods Mxtures The cubc equaton of state calculates the propertes of a flud as f t conssted of one (magnary) component. If the flud s a mxture, the parameters a and b of the magnary component must be calculated from the pure component parameters of the real components usng mxng rules. The classcal mxng rules, wth one bnary nteracton parameter for the attracton parameter, are not suffcently flexble to descrbe mxtures wth strong shape and sze asymmetry: ( ) ( ) 1 2 a = x x a a 1 k, (46) j j j a j b bj b= xb = xx j 2 j (47) A second nteracton coeffcent s added for the b parameter n the Redlch- Kwong-Aspen (Mathas, 1983) and Schwartzentruber-Renon (Schwartzentruber and Renon, 1989) equatons of state: b bj b= xx j ( 1 kbj, ) (48) 2 j Ths s effectve to ft vapor-lqud equlbrum data for systems wth strong sze and shape asymmetry but t has the dsadvantage that k bj, s strongly correlated wth k aj, and that k bj, affects the excess molar volume (Lermte and Vdal, 1988). For strong energy asymmetry, n mxtures of polar and non-polar compounds, the nteracton parameters should depend on composton to acheve the desred accuracy of representng VLE data. Huron-Vdal mxng rules use actvty coeffcent models as mole fracton functons (Huron and Vdal, 1979). These mxng rules are extremely successful n fttng because they combne the advantages of flexblty wth a mnmum of drawbacks (Lermte and Vdal, 1988). However, wth the orgnal Huron-Vdal approach t s not possble to use actvty coeffcent parameters, determned at low pressures, to predct the hgh pressure equaton-of-state nteractons. Several modfcatons of Huron-Vdal mxng rules exst whch use actvty coeffcent parameters obtaned at low pressure drectly n the mxng rules (see the table labeled Cubc Equatons of State n ASPEN PLUS). They accurately predct bnary nteractons at hgh pressure. In practce ths means that the large database of actvty coeffcent data at low pressures (DECHEMA Chemstry Data Seres, Dortmund DataBank) s now extended to hgh pressures. The MHV2 mxng rules (Dahl and Mchelsen, 1990), use the Lyngby modfed UNIFAC actvty coeffcent model (See Actvty Coeffcent Models on page 1-32). The qualty of the VLE predctons s good Physcal Property Methods and Models Verson 10

45 Chapter 1 The predctve SRK method (Holderbaum and Gmehlng, 1991; Fscher, 1993) uses the orgnal UNIFAC model. The predcton of VLE s good. The mxng rules can be used wth any equaton of state, but t has been ntegrated wth the Redlch-Kwong-Soave equaton of state n the followng way: new UNIFAC groups have been defned for gaseous components, such as hydrogen. Interacton parameters for the new groups have been regressed and added to the exstng parameter matrx. Ths extends the exstng low pressure actvty coeffcent data to hgh pressures, and adds predcton of gas solubltes at hgh pressures. The Wong-Sandler mxng rules (Wong and Sandler, 1992; Orbey et al., 1993) predct VLE at hgh pressure equally well as the MHV2 mxng rules. Specal attenton has been pad to the theoretcal correctness of the mxng rules at pressures approachng zero. Vral Equatons of State Vral equatons of state n ASPEN PLUS are: Hayden-O Connell BWR-Lee-Starlng Lee-Kesler-Plöcker Ths type of equaton of state s based on a selecton of powers of the expanson: 1 B C p= RT (49) V 3 3 V V m m m Truncaton of equaton 49 after the second term and the use of the second vral coeffcent B can descrbe the behavor of gases up to several bar. The Hayden- O'Connell equaton of state uses a complex computaton of B to account for the assocaton and chemcal bondng n the vapor phase (see Vapor Phase Assocaton on page 1-26). Lke cubc equatons of state, some of these terms must be related to ether repulson or attracton. To descrbe lqud and vapor propertes, hgher order terms are needed. The order of the equatons n V s usually hgher than cubc. The Benedct-Webb-Rubn equaton of state s a good example of ths approach. It had many parameters generalzed n terms of crtcal propertes and acentrc factor by Lee and Starlng (Brulé et al., 1982). The Lee-Kesler-Plöcker equaton of state s another example of ths approach. Vral equatons of state for lqud and vapor are more flexble n descrbng a (p,v) sotherm because of the hgher degree of the equaton n the volume. They are more accurate than cubc equatons of state. Generalzatons have been focused manly on hydrocarbons, therefore these compounds obtan excellent results. They are not recommended for polar compounds. The standard mxng rules gve good results for mxtures of hydrocarbons and lght gases. Physcal Property Methods and Models 1-25 Verson 10

46 Overvew of ASPEN PLUS Property Methods Vapor Phase Assocaton Nonpolar substances n the vapor phase at low pressures behave almost deally. Polar substances can exhbt nondeal behavor or even assocaton n the vapor phase. Assocaton can be expected n systems wth hydrogen bondng such as alcohols, aldehydes and carboxylc acds. Most hydrogen bondng leads to dmers. HF s an excepton; t forms manly hexamers. Ths secton uses dmerzaton as an example to dscuss the chemcal theory used to descrbe strong assocaton. Chemcal theory can be used for any type of reacton. If assocaton occurs, chemcal reactons take place. Therefore, a model based on physcal forces s not suffcent. Some reasons are: Two monomer molecules form one dmer molecule, so the total number of speces decreases. As a result the mole fractons change. Ths has nfluence on VLE and molar volume (densty). The heat of reacton affects thermal propertes lke enthalpy C p. The equlbrum constant of a dmerzaton reacton 2A A2 (50) n the vapor phase s defned n terms of fugactes: K f A2 = 2 f A (51) Wth: f v =ϕ v y p (52) and realzng that ϕ v s approxmately unty at low pressures: K y A2 = 2 y p A (53) Equatons are expressed n terms of true speces propertes. Ths may seem natural, but unless measurements are done, the true compostons are not known. On the contrary, the composton s usually gven n terms of unreacted or apparent speces (Abbott and van Ness, 1992), whch represents the magnary state of the system f no reacton takes place. Superscrpts t and a are used to dstngush clearly between true and apparent speces. (For more on the use of apparent and true speces approach, see Chapter 5) Physcal Property Methods and Models Verson 10

47 Chapter 1 K n equaton 53 s only a functon of temperature. If the pressure approaches A zero at constant temperature, y 2,whch s a measure of the degree of 2 y A assocaton, must decrease. It must go to zero for zero pressure where the deal gas behavor s recovered. The degree of assocaton can be consderable at atmospherc pressure: for example acetc acd at 293 K and 1 bar s dmerzed at about 95% (Prausntz et al., 1986). The equlbrum constant s related to the thermodynamc propertes of reacton: rg rh rs ln K = = + RT RT R (54) The Gbbs energy, the enthalpy, and the entropy of reacton can be approxmated as ndependent of temperature. Then from equaton 54 t follows that ln K plotted aganst 1 T s approxmately a straght lne wth a postve slope (snce the reacton s exothermc) wth ncreasng 1 T. Ths represents a decrease of ln K wth ncreasng temperature. From ths t follows (usng equaton 53) that the degree of assocaton decreases wth ncreasng temperature. It s convenent to calculate equlbra and to report mole fractons n terms of apparent components. The concentratons of the true speces have to be calculated, but are not reported. Vapor-lqud equlbra n terms of apparent components requre apparent fugacty coeffcents. The fugacty coeffcents of the true speces are expected to be close to unty (deal) at atmospherc pressure. However the apparent fugacty coeffcent needs to reflect the decrease n apparent partal pressure caused by the decrease n number of speces. The a apparent partal pressure s represented by the term yp n the vapor fugacty equaton appled to apparent components: f =ϕ av, av, a y p (55) In fact the apparent and true fugacty coeffcents are drectly related to each other by the change n number of components (Nothnagel et al., 1973; Abbott and van Ness, 1992): ϕ = ϕ av, tv, y y t a (56) Physcal Property Methods and Models 1-27 Verson 10

48 Overvew of ASPEN PLUS Property Methods Ths s why apparent fugacty coeffcents of assocatng speces are well below unty. Ths s llustrated n the fgure labeled Apparent Fugacty of Vapor Benzene and Proponc Acd for the system benzene + proponc acd at 415 K and kpa (1 atm) (Nothnagel et al., 1973). The effect of dmerzaton clearly decreases below apparent proponc acd mole fractons of about 0.2 (partal pressures of 20 kpa). The effect vanshes at partal pressures of zero, as expected from the pressure dependence of equaton 53. The apparent fugacty coeffcent of benzene ncreases wth ncreasng proponc acd mole fracton. Ths s because the true mole fracton of proponc acd s hgher than ts apparent mole fracton (see equaton 56). Apparent Fugacty of Vapor Benzene and Proponc Acd The vapor enthalpy departure needs to be corrected for the heat of assocaton. The true heat of assocaton can be obtaned from the equlbrum constant: r H T d G dt t ( ) ( ) t 2 r m 2 ln m = = RT d K dt (57) The value obtaned from equaton 57 must be corrected for the rato of true to apparent number of speces to be consstent wth the apparent vapor enthalpy departure. Wth the enthalpy and Gbbs energy of assocaton (equatons 57 and 54), the entropy of assocaton can be calculated Physcal Property Methods and Models Verson 10

49 Chapter 1 The apparent heat of vaporzaton of assocatng components as a functon of temperature can show a maxmum. The ncrease of the heat of vaporzaton wth temperature s probably related to the decrease of the degree of assocaton wth ncreasng temperature. However, the heat of vaporzaton must decrease to zero when the temperature approaches the crtcal temperature. The fgure labeled Lqud and Vapor Enthalpy of Acetc Acd llustrates the enthalpc behavor of acetc acd. Note that the enthalpy effect due to assocaton s very large. Lqud and Vapor Enthalpy of Acetc Acd The true molar volume of an assocatng component s close to the true molar volume of a non-assocatng component. At low pressures, where the deal gas law s vald, the true molar volume s constant and equal to p/rt, ndependent of assocaton. Ths means that assocated molecules have a hgher molecular mass than ther monomers, but they behave as an deal gas, just as ther monomers. Ths also mples that the mass densty of an assocated gas s hgher than that of a gas consstng of the monomers. The apparent molar volume s defned as the true total volume per apparent number of speces. Snce the number of apparent speces s hgher than the true number of speces the apparent molar volume s clearly smaller than the true molar volume. The chemcal theory can be used wth any equaton of state to compute true fugacty coeffcents. At low pressures, the deal gas law can be used. Physcal Property Methods and Models 1-29 Verson 10

50 Overvew of ASPEN PLUS Property Methods For dmerzaton, two approaches are commonly used: the Nothagel and the Hayden-O Connel equatons of state. For HF hexamerzaton a dedcated equaton of state s avalable n ASPEN PLUS. Nothnagel et al. (1973) used a truncated van der Waals equaton of state. They correlated the equlbrum constants wth the covolume b, a polarty parameter p and the parameter d. b can be determned from group contrbuton methods (Bond, 1968) (or a correlaton of the crtcal temperature and pressure (as n ASPEN PLUS). D and p are adjustable parameters. Many values for d and p are avalable n the Nothnagel equaton of state n ASPEN PLUS. Also correcton terms for the heats of assocaton of unlke molecules are bult-n. The equlbrum constant, K, has been correlated to T b, T c, b, d, and p. Hayden and O Connell (1975) used the vral equaton of state (equaton 49), truncated after the second term. They developed a correlaton for the second vral coeffcent of polar, nonpolar and assocatng speces based on the crtcal temperature and pressure, the dpole moment and the mean radus of gyraton. Assocaton of lke and unlke molecules s descrbed wth the adjustable parameter η. Pure component and bnary values for η are avalable n ASPEN PLUS. The HF equaton of state (de Leeuw and Watanasr, 1993) assumes the formaton of hexamers only. The fugactes of the true speces are assumed to be deal, and s therefore suted for low pressures. Specal attenton has been pad to the robustness of the algorthm, and the consstency of the results wth theory. The equaton of state has been ntegrated wth the electrolyte NRTL actvty coeffcent model to allow the rgorous representaton of absorpton and strppng of HF wth water. It can be used wth other actvty coeffcent models for hydrocarbon + HF mxtures. References M. Abbott and M. C. Van Ness, "Thermodynamcs of Solutons Contanng Reactve Speces: A Gude to Fundamentals and Applcatons," Flud Phase Equlbra, Vol 77, (1992), pp Bond, "Physcal Propertes of Moelcular Lquds, Crystals, and Glasses," Wley, New York, M.R. Brulé, C.T. Ln, L.L. Lee, and K.E. Starlng, "Multparameter Correspondng States Correlaton of Coal-Flud Thermodynamc Propertes," AIChE J., Vol. 28, No. 4, (1982), pp Dahl and M.L. Mchelsen, "Hgh-Pressure Vapor-Lqud Equlbrum wth a UNIFAC-based Equaton of State", AIChE J., Vol. 36, No. 12 (1990), pp Physcal Property Methods and Models Verson 10

51 Chapter 1 Fscher, De PSRK-Methode: Ene Zustandsglechung unter Verwendung des UNIFAC-Gruppenbetragsmodells, VDI Fortschrttberchte, Rehe 3: Verfahrenstechnk, Nr. 324 (Düsseldorf: VDI Verlag GmbH, 1993). J.G. Hayden and J.P. O'Connell, " A Generalzed Method for Predctng Second Vral Coeffcents, " Ind. Eng. Chem. Process Des. Dev., Vol. 14, No. 3, (1975), pp Holderbaum and J. Gmehlng, "PSRK: A Group Contrbuton Equaton of State based on UNIFAC", Flud Phase Eq., Vol. 70, (1991), pp M.-J. Huron and J. Vdal, "New Mxng Rules n Smple Equatons of state for representng Vapour-Lqud Equlbra of Strongly Non-deal Mxtures," Flud Phase Eq., Vol. 3, (1979), pp V.V. de Leeuw and S. Watanasr, " Modellng Phase Equlbra And Enthalpes Of The System Water And Hydrofluorc Acd Usng A 'HF Equaton Of State' In Conjuncton Wth The Electrolyte NRTL Actvty Coeffcent Model," Presented at the 13 th European Semnar on Appled Thermodynamcs, 9 th -12 th June 1993, Carry-le-Rouet, France. Ch. Lermte and J. Vdal, "Les règles de mélange applquées aux équatons d'état." Revue de l'insttut Franças du Pétrole, Vol. 43, No. 1, (1988), pp P.M. Mathas, "A Versatle Phase Equlbrum Equaton of State," Ind. Eng. Chem. Process Des. Dev. Vol. 22, (1983), pp K.-H. Nothnagel, D.S. Abrams, and J.M. Prausntz, "Generalzed Correlaton for Fugacty Coeffcents n Mxtures at Moderate Pressures. Applcatons of Chemcal Theory of Vapor Imperfectons," Ind. Eng. Chem. Process Des. Dev., Vol. 12, No. 1, (1973), pp Orbey, S.I. Sandler, and D.S. Wong, "Accurate equaton of state predctons at hgh temperatures and pressures usng the exstng UNIFAC model," Flud Phase Eq., Vol. 85, (1993), pp D.-Y. Peng and D.B. Robnson, "A New Two-Constant Equaton of state," Ind. Eng. Chem. Fundam., Vol. 15, (1976), pp J.M. Prausntz, R.N. Lchtenthaler, and E. Gomes de Azevedo, Molecular Thermodynamcs of Flud-Phase Equlbra, 2 nd ed., (Englewood Clffs: Prentce- Hall Inc., 1986), pp Schwartzentruber and H. Renon, "Extenson of UNIFAC to Hgh Pressures and Temperatures by the Use of a Cubc Equaton of State," Ind. Eng. Chem. Res., Vol. 28, (1989), pp Soave, "Equlbrum Constants for a Modfed Redlch-Kwong Equaton of State," Chem. Eng. Sc., Vol. 27, (1972), pp Physcal Property Methods and Models 1-31 Verson 10

52 Overvew of ASPEN PLUS Property Methods D.S. Wong and S.I. Sandler, "A Theoretcally Correct New Mxng Rule for Cubc Equatons of State for Both Hghly and Slghtly Non-deal Mxtures," AIChE J., Vol. 38, (1992), pp Actvty Coeffcent Models Ths secton dscusses the characterstcs of actvty coeffcent models. The descrpton s dvded nto the followng categores: Molecular models (correlatve models for non-electrolyte solutons ) Group contrbuton models (predctve models for non-electrolyte solutons) Electrolyte actvty coeffcent models Molecular Models The early actvty coeffcent models such as van Laar and Scatchard-Hldebrand, are based on the same assumptons and prncples of regular solutons. Excess entropy and excess molar volume are assumed to be zero, and for unlke nteractons, London s geometrc mean rule s used. Bnary parameters were estmated from pure component propertes. The van Laar model s only useful as correlatve model. The Scatchard-Hldebrand can predct nteractons from solublty parameters for non-polar mxtures. Both models predct only postve devatons from Raoult s law (see Actvty Coeffcent Method on page 1-10). The three-suffx Margules and the Redlch-Kster actvty coeffcent models are flexble arthmetc expressons. Local composton models are very flexble, and the parameters have much more physcal sgnfcance. These models assume orderng of the lqud soluton, accordng to the nteracton energes between dfferent molecules. The Wlson model s suted for many types of non-dealty but cannot model lqud-lqud separaton. The NRTL and UNIQUAC models can be used to descrbe VLE, LLE and enthalpc behavor of hghly non-deal systems. The WILSON, NRTL and UNIQUAC models are well accepted and are used on a regular bass to model hghly non-deal systems at low pressures. A detaled dscusson of molecular actvty coeffcent models and underlyng theores can be found n Prausntz et al. (1986) Physcal Property Methods and Models Verson 10

53 Chapter 1 Group Contrbuton Models The UNIFAC actvty coeffcent model s an extenson of the UNIQUAC model. It apples the same theory to functonal groups that UNIQUAC uses for molecules. A lmted number of functonal groups s suffcent to form an nfnte number of dfferent molecules. The number of possble nteractons between groups s very small compared to the number of possble nteractons between components from a pure component database (500 to 2000 components). Group-group nteractons determned from a lmted, well chosen set of expermental data are suffcent to predct actvty coeffcents between almost any par of components. UNIFAC (Fredenslund et al., 1975; 1977) can be used to predct actvty coeffcents for VLE. For LLE a dfferent dataset must be used. Mxture enthalpes, derved from the actvty coeffcents (see Actvty Coeffcent Method on page 1-10) are not accurate. UNIFAC has been modfed at the Techncal Unversty of Lyngby (Denmark). The modfcaton ncludes an mproved combnatoral term for entropy and the group-group nteracton has been made temperature dependent. The three UNIFAC models are avalable n ASPEN PLUS. For detaled nformaton on each model, see Chapter 3. Ths model can be appled to VLE, LLE and enthalpes (Larsen et al., 1987). Another UNIFAC modfcaton comes from the Unversty of Dortmund (Germany). Ths modfcaton s smlar to Lyngby modfed UNIFAC, but t can also predct actvty coeffcents at nfnte dluton (Wedlch and Gmehlng, 1987). Electrolyte Models In electrolyte solutons a larger varety of nteractons and phenomena exst than n non-electrolyte solutons. Besdes physcal and chemcal molecule-molecule nteractons, onc reactons and nteractons occur (molecule-on and on-on). Electrolyte actvty coeffcent models (Electrolyte NRTL, Ptzer) are therefore more complcated than non-electrolyte actvty coeffcent models. Electrolytes dssocate so a few components can form many speces n a soluton. Ths causes a multtude of nteractons, some of whch are strong. Ths secton gves a summary of the capabltes of the electrolyte actvty coeffcent models n ASPEN PLUS. For detals, see Chapter 3 and Appendces A, B, and C. The Ptzer electrolyte actvty coeffcent model can be used for the representaton of aqueous electrolyte solutons up to 6 molal strength (for lterature references, see Appendx C). The model handles gas solubltes. Excellent results can be obtaned, but many parameters are needed. Physcal Property Methods and Models 1-33 Verson 10

54 Overvew of ASPEN PLUS Property Methods The Electrolyte NRTL model s an extenson of the molecular NRTL model (for lterature references, see Appendx B). It can handle electrolyte solutons of any strength, and s suted for solutons wth multple solvents, and dssolved gases. The flexblty of ths model makes t very sutable for any low-to-moderate pressure applcaton. Electrolyte parameter databanks and data packages for ndustrally mportant applcatons have been developed for both models (see ASPEN PLUS Physcal Property Data, Chapter 1). If parameters are not avalable, use data regresson, or the Bromley-Ptzer actvty coeffcent model. The Bromley-Ptzer actvty coeffcent model s a smplfcaton of the Ptzer model (for lterature references, see Appendx A). A correlaton s used to calculate the nteracton parameters. The model s lmted n accuracy, but predctve. References Fredenslund, R.L. Jones, and J.M. Prausntz, "Group-Contrbuton Estmaton of Actvty Coeffcents n Nondeal Lqud Mxtures," AIChE J., Vol. 21, (1975), pp Fredenslund, J. Gmehlng, and P. Rasmussen, Vapor-Lqud Equlbra Usng UNIFAC, (Amsterdam: Elsever, 1977). B.L. Larsen, P. Rasmussen, and Aa. Fredenslund, "A Modfed UNIFAC Group- Contrbuton Model for the Predcton of Phase Equlbra and Heats of Mxng," Ind. Eng. Chem. Res., Vol. 26, (1987), pp J.M. Prausntz, R.N. Lchtenthaler, and E. Gomes de Azevedo, Molecular Thermodynamcs of Flud-Phase Equlbra, 2 nd ed., (Englewood Clffs: Prentce- Hall Inc., 1986), pp Wedlch and J. Gmehlng, "A Modfed UNIFAC Model. 1. Predcton of VLE, h E, γ," Ind. Eng. Chem. Res., Vol. 26, (1987), pp Transport Property Methods ASPEN PLUS property methods can compute the followng transport propertes: Vscosty Thermal conductvty Dffuson coeffcent Surface tenson 1-34 Physcal Property Methods and Models Verson 10

55 Chapter 1 Each pure component property s calculated ether from an emprcal equaton or from a sem-emprcal (theoretcal) correlaton. The coeffcents for the emprcal equaton are determned from expermental data and are stored n the ASPEN PLUS databank. The mxture propertes are calculated usng approprate mxng rules. Ths secton dscusses the methods for transport property calculaton. The propertes that have the most n common n ther behavor are vscosty and thermal conductvty. Ths s reflected n smlar methods that exst for these propertes and therefore they are dscussed together. Vscosty and Thermal Conductvty Methods When the pressure approaches zero, vscosty and thermal conductvty are lnear functons of temperature wth a postve slope. At a gven temperature, vscosty and thermal conductvty ncrease wth ncreasng densty (densty ncreases for any flud wth ncreasng pressure). Detaled molecular theores exst for gas phase vscosty and thermal conductvty at low pressures. Some of these can account for polarty. These low pressure propertes are not exactly deal gas propertes because non-dealty s taken nto account. Examples are the Chapman-Enskog-Brokaw and the Chung- Lee-Starlng low pressure vapor vscosty models and the Stel-Thodos low pressure vapor thermal conductvty model. Resdual property models are avalable to account for pressure or densty effects. These models calculate the dfference of a certan property wth respect to the low pressure value. The method used s: ( ) ( ) = ( = ) + ( ) ( = ) x p x p 0 x p x p 0 (58) Where: x = Vscosty or thermal conductvty Most of the low pressure models requre mxng rules for calculatng mxture propertes. Another class of models calculate the hgh pressure property drectly from molecular parameters and state varables. For example the TRAPP models for hydrocarbons use crtcal parameters and acentrc factor as molecular parameters. The models use temperature and pressure as state varables. The Chung-Lee-Starlng models use crtcal parameters, acentrc factor, and dpole moment as molecular parameters. The models use temperature and densty as state varables. These models generally use mxng rules for molecular parameters, rather than mxng rules for pure component propertes. Physcal Property Methods and Models 1-35 Verson 10

56 Overvew of ASPEN PLUS Property Methods Vapor vscosty, thermal conductvty, and vapor dffusvty are nterrelated by molecular theores. Many thermal conductvty methods therefore requre low pressure vapor vscosty ether n calculatng thermal conductvty or n the mxng rules. Lqud propertes are often descrbed by emprcal, correlatve models: Andrade/DIPPR for lqud vscosty and Sato-Redel for thermal conductvty. These are accurate n the temperature and pressure ranges of the expermental data used n the ft. Mxng rules for these propertes do not provde a good descrpton for the excess propertes. Correspondng-states models such as Chung-Lee-Starlng and TRAPP can descrbe both lqud and vapor propertes. These models are more predctve and less accurate than a correlatve model, but extrapolate well wth temperature and pressure. Chung-Lee-Starlng allows the use of bnary nteracton parameters and an assocaton parameter, whch can be adjusted to expermental data. Dffuson Coeffcent Methods It s evdent that dffuson s related to vscosty, so several dffuson coeffcent methods, requre vscosty, for both lqud and for vapor dffuson coeffcents. (Chapman-Enskog-Wlke-Lee and Wlke-Chang models). Vapor dffuson coeffcents can be calculated from molecular theores smlar to those dscussed for low pressure vapor vscosty and thermal conductvty. Smlarly, pressure correcton methods exst. The Dawson-Khoury-Kobayash model calculates a pressure correcton factor whch requres the densty as nput. Lqud dffuson coeffcents depend on actvty and lqud vscosty. Bnary dffuson coeffcents are requred n processes where mass transfer s lmted. Bnary dffuson coeffcents descrbe the dffuson of one component at nfnte dluton n another component. In multcomponent systems ths corresponds to a matrx of values. The average dffuson coeffcent of a component n a mxture does not have any quanttatve applcatons; t s an nformatve property. It s computed usng a mxng rule for vapor dffuson coeffcents and usng mxture nput parameters for the Wlke-Chang model Physcal Property Methods and Models Verson 10

57 Chapter 1 Surface Tenson Methods Surface tenson s calculated by emprcal, correlatve models such as Hakm- Stenberg-Stel/DIPPR. An emprcal lnear mxng rule s used to compute mxture surface tenson. References R.C. Red, J.M. Prausntz, and B.E. Polng, The Propertes Of Gases And Lquds, 4 th ed., (New York, etc: McGraw-Hll Book Company, 1987). Nonconventonal Component Enthalpy Calculaton Nonconventonal components generally do not partcpate n phase equlbrum calculatons, but are ncluded n enthalpy balances. For a process unt n whch no chemcal change occurs, only sensble heat effects of nonconventonal components are sgnfcant. In ths case, the enthalpy reference state may be taken as the component at any arbtrary reference temperatures (for example, K). If a nonconventonal component s nvolved n a chemcal reacton, an enthalpy balance s meanngful only f the enthalpy reference state s consstent wth that adopted for conventonal components: the consttuents elements must be n ther standard states at 1 atm and K. The enthalpy s calculated as: T = f + T s s s H h C dt ref p (59) s Frequently the heat of formaton f h s unknown and cannot be obtaned drectly because the molecular structure of the component s unknown. In many cases, t s possble to calculate the heat of formaton from the heat of combuston s c h, because the combuston products and elemental composton of the components are known: s s h = h + h f c f s cp (60) f h s the sum of the heats of formaton of the combuston products multpled s cp by the mass fractons of the respectve elements n the nonconventonal component. Ths s the approach used n the coal enthalpy model HCOALGEN (see Chapter 3). Ths approach s recommended for computng DHFGEN for the ENTHGEN model. Physcal Property Methods and Models 1-37 Verson 10

58 Overvew of ASPEN PLUS Property Methods Symbol Defntons Roman Letters a b B C p C f G H H k K n p R S T V x,y Z Defntons Equaton of state energy parameter Equaton of state co-volume Second vral coeffcent Heat capacty at constant pressure Thrd vral coeffcent Fugacty Gbbs energy Henry s constant Enthalpy Equaton of state bnary parameter Chemcal equlbrum constant Mole number Pressure Unversal gas constant Entropy Temperature Volume Molefracton Compressblty factor Greek Letters γ θ ϕ Defntons Actvty coeffcent Poyntng correcton Fugacty coeffcent µ Thermodynamc potental Superscrpts c I f Defntons Combuston property Component ndex Formaton property contnued 1-38 Physcal Property Methods and Models Verson 10

59 Chapter 1 Symbol Defntons (Contnued) Roman Letters m vap r ref Defntons Molar property Vaporzaton property Reacton property Reference state property * Pure component property, asymmetrc conventon a At nfnte dluton Apparent property E g l l2 l1 s t v Excess property Ideal gas property Lqud property Second lqud property Frst lqud property Sold property True property Vapor property Footnotes 1 The Gbbs energy has been transformed by a contrbuton lnear n the mole fracton, such that the Gbbs energy of pure lqud water (thermodynamc potental of water) has been shfted to the value of pure lqud n-butanol. Ths s done to make the Gbbs energy mnmzaton vsble on the scale of the graph. Ths transformaton has no nfluence on the result of Gbbs energy mnmzaton (Oonk, 1981). 2 The pure component molar Gbbs energy s equal to the pure component thermodynamc potental. The ISO and IUPAC recommendaton to use the thermodynamc potental s followed. Physcal Property Methods and Models 1-39 Verson 10

60 Overvew of ASPEN PLUS Property Methods 1-40 Physcal Property Methods and Models Verson 10

61 Chapter 2 2 Property Method Descrptons Ths chapter descrbes the ASPEN PLUS property methods. Topcs nclude: Classfcaton of property methods Recommended use Property method descrptons, organzed by applcaton Snce ASPEN PLUS property methods are talored to classes of compounds and operatng condtons, they ft most engneerng needs. Customzaton of property methods s explaned n Chapter 4. Physcal Property Methods and Models 2-1 Verson 10

62 Property Method Descrptons Classfcaton of Property Methods and Recommended Use A property method s a collecton of property calculaton routes. (For more on routes, see Chapter 4). The propertes nvolved are needed by unt operaton models. Thermodynamc propertes: Fugacty coeffcent (or equvalent: chemcal potental, K-value) Enthalpy Entropy Gbbs energy Volume Transport propertes: Vscosty Thermal conductvty Dffuson coeffcent Surface tenson Property methods allow you to specfy a collecton of property calculaton procedures as one entty, for example, you mght use them n a unt operaton, or n a flowsheet (see ASPEN PLUS User Gude, Chapter 7). It s mportant to choose the rght property method for an applcaton to ensure the success of your smulaton. To help you choose a property method, frequently encountered applcatons are lsted wth recommended property methods. (Multple property methods often apply. A class of property methods s recommended, as opposed to an ndvdual property method.) The classes of property methods avalable are: IDEAL Lqud fugacty and K-value correlatons Petroleum tuned equatons of state Equatons of state for hgh pressure hydrocarbon applcatons Flexble and predctve equatons of state Lqud actvty coeffcents Electrolyte actvty coeffcents and correlatons Solds processng Steam tables After you have decded whch property method class your applcaton needs, refer to the correspondng secton n ths chapter for more detaled recommendatons. See Chapter 3 for detaled nformaton on models and ther parameter requrements. General usage ssues, such as usng Henry s law and the free-water approxmaton, are dscussed n ASPEN PLUS User Gude, Chapter Physcal Property Methods and Models Verson 10

63 Chapter 2 Recommended Classes of Property Methods for Dfferent Applcatons Ol and Gas Producton Applcaton Reservor systems Platform separaton Transportaton of ol and gas by ppelne Recommended Property Method Equatons of state for hgh pressure hydrocarbon applcatons Equatons of state for hgh pressure hydrocarbon applcatons Equatons of state for hgh pressure hydrocarbon applcatons Refnery Applcaton Low pressure applcatons(up to several atm) Vacuum tower Atmospherc crude tower Medum pressure applcatons (up to several tens of atm) Coker man fractonator, FCC man fractonator Hydrogen-rch applcatons Reformer Hydrofner Lube ol unt De-asphaltng unt Recommended Property Method Petroleum fugacty and K-value correlatons (and assay data analyss) Petroleum fugacty and K-value correlatons Petroleum-tuned equatons of state (and assay data analyss) Selected petroleum fugacty correlatons Petroleum-tuned equatons of state (and assay data analyss) Petroleum-tuned equatons of state (and assay data analyss) Gas Processng Applcaton Hydrocarbon separatons Demethanzer C3- spltter Cryogenc gas processng Ar separaton Gas dehydraton wth glycols Acd gas absorpton wth Methanol (rectsol) NMP (pursol) Recommended Property Method Equatons of state for hgh pressure hydrocarbon applcatons (wth k j ) Equatons of state for hgh pressure hydrocarbon applcatons Flexble and predctve equatons of state Flexble and predctve equatons of state Flexble and predctve equatons of state Contnued Physcal Property Methods and Models 2-3 Verson 10

64 Property Method Descrptons Gas Processng (contnued) Applcaton Acd gas absorpton wth Water Ammona Amnes Amnes + methanol (amsol) Caustc Lme Hot carbonate Claus process Recommended Property Method Electrolyte actvty coeffcents Flexble and predctve equatons of state Petrochemcals Applcaton Ethylene plant Prmary fractonator Lght hydrocarbons separaton tran Quench tower Aromatcs BTX extracton Substtuted hydrocarbons VCM plant Acrylontrle plant Ether producton MTBE, ETBE, TAME Ethylbenzene and styrene plants Terephthalc acd Recommended Property Method Petroleum fugacty correlatons (and assay data analyss) Equatons of state for hgh pressure hydrocarbon applcatons Equatons of state for hgh pressure hydrocarbon applcatons Lqud actvty coeffcents (very senstve to parameters) Equatons of state for hgh pressure hydrocarbon applcatons Lqud actvty coeffcents Equatons of state for hgh pressure hydrocarbon applcatons and Ideal (wth Watsol) or lqud actvty coeffcent Lqud actvty coeffcents (wth dmerzaton n acetc acd secton) Chemcals Applcaton Azeotropc separatons Alcohol separaton Carboxylc acds Acetc acd plant Phenol plant Recommended Property Method Lqud actvty coeffcents Lqud actvty coeffcents Lqud actvty coeffcents Lqud phase reactons Estrfcaton Lqud actvty coeffcents contnued 2-4 Physcal Property Methods and Models Verson 10

65 Chapter 2 Chemcals (contnued) Applcaton Recommended Property Method Ammona plant Equatons of state for hgh pressure hydrocarbon applcatons (wth k j ) Fluorochemcals Inorganc Chemcals Caustc Acds Phosphorc acd Sulphurc acd Ntrc acd Hydrochlorc acd Hydrofluorc acd Lqud actvty coeffcents (and HF equaton of state) Electrolyte actvty coeffcents Electrolyte actvty coeffcent (and HF equaton of state) Coal Processng Applcaton Sze reducton crushng, grndng Separaton and cleanng sevng, cyclones, precptton, washng Combuston Acd gas absorpton Coal gasfcaton and lquefacton Recommended Property Method Solds processng (wth coal analyss and partcle sze dstrbuton) Solds processng (wth coal analyss and and partcle sze dstrbuton) Equatons of state for hgh pressure hydrocarbon applcatons (wth combuston databank) See Gas Processng earler n ths dscusson. See Synthetc Fuel later n ths dscusson. Power Generaton Applcaton Combuston Coal Ol Steam cycles Compressors Turbnes Acd gas absorpton Recommended Property Method Equatons of state for hgh pressure hydrocarbon applcatons (wth combuston databank) (and assay analys wth coal correlatons) (and assay analys) Steam tables See Gas Processng earler n ths dscusson. contnued Physcal Property Methods and Models 2-5 Verson 10

66 Property Method Descrptons Synthetc Fuel Applcaton Synthess gas Coal gasfcaton Coal lquefacton Recommended Property Method Equatons of state for hgh pressure hydrocarbon applcatons Equatons of state for hgh pressure hydrocarbon applcatons Equatons of state for hgh pressure hydrocarbon applcatons wth k j and assay analyss wth coal correlatons) Envronmental Applcaton Solvent recovery (Substtuted) hydrocarbon strppng Acd gas strppng from Methanol (rectsol) NMP (pursol) Acd gas strppng from Water Ammona Amnes Amnes + methanol (amsol) Caustc Lme Hot carbonate Claus process Acds Strppng Neutralzaton Recommended Property Method Lqud actvty coeffcents Lqud actvty coeffcents Flexble and predctve equatons of state Electrolyte actvty coeffcents Flexble and predctve equatons of state Electrolyte actvty coeffcents Water and Steam Applcaton Steam systems Coolant Recommended Property Method Steam tables Steam tables contnued 2-6 Physcal Property Methods and Models Verson 10

67 Chapter 2 Mneral and Metallurgcal Processes Applcaton Recommended Property Method Mechancal processng crushng, grndng, sevng, washng Hydrometallurgy Mneral leachng Pyrometallurgy Smelter Converter Solds Processng (wth norganc databank) Electrolyte actvty coeffcents Solds Processng (wth norganc databank) IDEAL Property Method The IDEAL property method accommodates both Raoult s law and Henry s law. Ths method uses the: Ideal actvty coeffcent model for the lqud phase ( χ = 1) Ideal gas equaton of state Pv = RT for the vapor phase Rackett model for lqud molar volume The IDEAL property method s recommended for systems n whch deal behavor can be assumed, such as: Systems at vacuum pressures Isomerc systems at low pressures In the vapor phase, small devatons from the deal gas law are allowed. These devatons occur at: Low pressures (ether below atmospherc pressure, or at pressures not exceedng 2 bar) Very hgh temperatures Ideal behavor n the lqud phase s exhbted by molecules wth ether: Very small nteractons (for example, paraffn of smlar carbon number) Interactons that cancel each other out (for example, water and acetone) The IDEAL property method: Can be used for systems wth and wthout noncondensable components. Permanent gases can be dssolved n the lqud. You can use Henry s law, whch s vald at low concentratons, to model ths behavor. Does not nclude the Poyntng correcton Returns heat of mxng of zero Is used to ntalze FLASH algorthm The transport property models for the vapor phase are all well suted for deal gases. The transport property models for the lqud phase are emprcal equatons for fttng expermental data. Physcal Property Methods and Models 2-7 Verson 10

68 Property Method Descrptons The IDEAL property method s sometmes used for solds processng where VLE s unmportant (for example, n coal processng). For these, however, the SOLIDS property method s recommended. See Solds Handlng Property Method on page 2-67 for documentaton on sold phase propertes. Mxture Types Ideal mxtures wth and wthout noncondensable components. You should not use IDEAL for nondeal mxtures. Range IDEAL s approprate only at low pressure and low lqud mole fractons of the noncondensable components (f present). Use of Henry s Law To use Henry s law for noncondensable components, you must desgnate these components as Henry s components on the Components Henry-Comps form. Henry's constant model parameters (HENRY) must be avalable for the solute wth at least one solvent. Use the Propertes Parameters Bnary Interacton form (HENRY-1) to enter Henry's constants or to revew bult-n parameters. ASPEN PLUS contans an extensve collecton of Henry s constants for many solutes n solvents. Solvents are water and other organc components. ASPEN PLUS uses these parameters automatcally when you specfy the IDEAL property method. The followng table lsts thermodynamc and transport property models used n IDEAL, and ther mnmum parameter requrements. Parameters Requred for the IDEAL Property Method General Property/Purpose Mass balance, Converson Mass-bass Mole-bass Converson Stdvol-bass Mole-bass Usng Free-water opton: solublty of water n organc phase Enthalpy of reacton Gbbs energy of reacton Parameter Requrements MW VLSTD WATSOL DHFORM DGFORM contnued 2-8 Physcal Property Methods and Models Verson 10

69 Chapter 2 Thermodynamc Propertes Propertes Models Parameter Requrements Vapor mxture Fugacty coeffcent Enthalpy, entropy, Gbbs energy Densty Lqud mxture Fugacty coeffcent Ideal gas law Ideal gas heat capacty Ideal gas law Ideal lqud actvty coeffcent Extended Antone vapor pressure Henry s constant Brelv-O Connell CPIG or CPIGDP PLXANT Solvent: VC, Solute-solvent: HENRY Solvent: TC, PC, (ZC or RKTZRA), Solute: (VC or VLBROC) Enthalpy, entropy Watson/DIPPR TC, (DHVLWT or DHVLDP) Densty Rackett TC, PC, (VC or VCRKT), (ZC or RKTZRA) Transport Propertes Propertes Models Parameter Requrements Vapor mxture Vscosty Thermal conductvty Dffusvty Surface tenson Lqud mxture Vscosty Thermal Conductvty Dffusvty Chapman-Enskog-Brokaw/ DIPPR Stel-Thodos low pres./ DIPPR Chapman-Enskog-Wlke-Lee Hakm-Stenberg-Stel/ DIPPR Andrade/DIPPR Sato-Redel/DIPPR Wlke-Chan MW; (MUP and (STKPAR or LJPAR)) or MUVDIP MW or KVDIP MW; MUP and (STKPAR or LJPAR) (TC, PC, OMEGA) or SIGDIP MULAND or MULDIP (MW, TC, TB) or KLDIP MW, VB Physcal Property Methods and Models 2-9 Verson 10

70 Property Method Descrptons Property Methods for Petroleum Mxtures The property methods n the followng table are desgned for mxtures of hydrocarbons and lght gases. K-value models and lqud fugacty correlatons are used at low and medum pressures. Petroleum-tuned equatons of state are used at hgh pressures. The hydrocarbons can be from natural gas or crude ol: that s, complex mxtures that are treated usng pseudocomponents. These property methods are often used for refnery applcatons. Densty and transport propertes are calculated by API procedures when possble. The followng table lsts the common and the dstnctve models of the property methods. The parameter requrements of the dstnctve models are gven n the tables labeled Parameters Requred for the CHAO-SEA Property Method on page 2-13, Parameters Requred for the GRAYSON Property Method on page 2-15, Parameters Requred for the PENG-ROB Property Method on page 2-16, and Parameters Requred for the RK-SOAVE Property Method on page Parameter requrements for the common models are n the table labeled Parameters Requred for Common Models on page For detals on these models, see Chapter 3 Property Methods for Petroleum Mxtures Lqud Fugacty and K-Value Models Property Method Name Models BK10 CHAO-SEA GRAYSON Braun K10 K-value model Chao-Seader lqud fugacty, Scatchard-Hldebrand actvty coeffcent Grayson-Streed lqud fugacty, Scatchard-Hldebrand actvty coeffcent Petroleum-Tuned Equatons of State Property Method Name Models PENG-ROB RK-SOAVE Peng-Robnson Redlch-Kwong-Soave Common Models for Property Methods for Petroleum Mxtures Property Model Lqud enthalpy Lqud molar volume Lee-Kesler API contnued 2-10 Physcal Property Methods and Models Verson 10

71 Chapter 2 Common Models for Property Methods for Petroleum Mxtures (Contnued) Property Model Vapor vscosty Vapor thermal conductvty Vapor dffusvty Surface tenson Lqud vscosty Lqud thermal conductvty Lqud dffusvty Chapman-Enskog-Brokaw Stel-Thodos/DIPPR Dawson-Khoury-Kobayash API surface tenson API Sato-Redel/DIPPR Wlke-Chang Lqud Fugacty and K-Value Model Property Methods The BK10 property method s generally used for vacuum and low pressure applcatons (up to several atm). The CHAO-SEA property method and the GRAYSON property method can be used at hgher pressures. GRAYSON has the wdest ranges of applcablty (up to several tens of atm). For hydrogen-rch systems, GRAYSON s recommended. These property methods are less suted for hgh-pressure applcatons n refnery (above about 50 atm). Petroleum-tuned equaton of state property methods are preferred for hgh pressures. These property methods are not suted for condtons close to crtcalty, as occur n lght ol reservors, transportaton of gas by ppelnes, and n some gas processng applcatons. Standard equatons of state for non-polar components are preferred. If polar compounds are present, such as n gas treatment, use flexble and predctve equatons of state for polar compounds. BK10 The BK10 property method uses the Braun K-10 K-value correlatons. The correlatons were developed from the K10 charts for both real components and ol fractons. The real components nclude 70 hydrocarbons and lght gases. The ol fractons cover bolng ranges K ( F). Propretary methods were developed to cover heaver ol fractons. Physcal Property Methods and Models 2-11 Verson 10

72 Property Method Descrptons Mxture Types Best results are obtaned wth purely alphatc or purely aromatc mxtures wth normal bolng ponts rangng from 450 to 700 K. For mxtures of alphatc and aromatc components, or naphtenc mxtures, the accuracy decreases. For mxtures wth lght gases, and medum pressures, CHAO-SEA or GRAYSON are recommended. Range The BK10 property method s suted for vacuum and low pressure applcatons (up to several atm). For hgh pressures, petroleum-tuned equatons of state are best suted. The applcable temperature range of the K10 chart s K ( F). It can be used up to 1100 K (1520 F). The parameters for the Braun K-10 are all bult-n. You do not need to supply them. See the table Parameters Requred for Common Models on page 2-18 for parameter requrements of models common to petroleum property methods. CHAO-SEA The CHAO-SEA property method uses the: Chao-Seader correlaton for reference state fugacty coeffcent Scatchard-Hldebrand model for actvty coeffcent Redlch-Kwong equaton of state for vapor phase propertes Lee-Kesler equaton of state for lqud and vapor enthalpy API method for lqud molar volume, vscosty and surface tenson Models lsted n the tables labeled Parameters Requred for the CHAO-SEA Property Method on page 2-13 and Parameters Requred for Common Models on page 2-18 The tables labeled Parameters Requred for the CHAO-SEA Property Method on page 2-13 and Parameters Requred for Common Models on page 2-18 provde thermodynamc and transport property models, and ther parameter requrements. The CHAO-SEA property method s predctve. It can be used for crude towers, vacuum towers, and some parts of the ethylene process. It s not recommended for systems contanng hydrogen Physcal Property Methods and Models Verson 10

73 Chapter 2 Mxture Types The CHAO-SEA property method was developed for systems contanng hydrocarbons and lght gases, such as carbon doxde and hydrogen sulfde, but wth the excepton of hydrogen. If the system contans hydrogen, use the GRAYSON property method. Range Use the CHAO-SEA property method for systems wth temperature and pressure lmts of 200 < T < 533 K 0.5 < T r < 1.3 T rm < 0.93 P < 140 atm Where: T r = Reduced temperature of a component T rm = Reduced temperature of the mxture Do not use ths property method at very hgh pressures, especally near the mxture crtcal pont, because of anomalous behavor n these regons. Parameters Requred for the CHAO-SEA Property Method Thermodynamc Propertes Models Parameter Requrements Vapor mxture Fugacty coeffcent, Densty Enthalpy, entropy, Gbbs free energy Lqud mxture Fugacty coeffcent, Gbbs free energy Redlch-Kwong Ideal gas heat capacty, Redlch-Kwong Scatchard-Hldebrand actvty coeffcent Chao-Seader pure component fugacty coeffcent TC, PC CPIG or CPIGDP TC, PC TC, DELTA, VLCVT1; GMSHVL TC, PC, OMEGA Physcal Property Methods and Models 2-13 Verson 10

74 Property Method Descrptons GRAYSON The GRAYSON property method uses the: Grayson-Streed correlaton for reference state fugacty coeffcents Scratchard-Hldlebrand model for actvty coeffcents Redlch-Kwong equaton of state for vapor phase propertes Lee-Kesler equaton of state for lqud and vapor enthalpy API method for lqud molar volume, vscosty and surface tenson Refer to the tables labeled Parameters Requred for the GRAYSON Property Method on page 2-15 and Parameters Requred for Common Models on page 2-18 for thermodynamc and transport property models, and ther parameter requrements. The GRAYSON property method s predctve. It can be used for crude towers, vacuum towers, and some parts of the ethylene process. It s recommended for systems contanng hydrogen. Mxture Types The GRAYSON property method was developed for systems contanng hydrocarbons and lght gases, such as carbon doxde and hydrogen sulfde. It s recommended over the CHAO-SEA property method when the system contans hydrogen. Range Use the GRAYSON property method for systems wth temperature and pressure lmts of: 200K < T < 700K 05. <T r P < 210 atm Where: T r = Reduced temperature coeffcent Do not use ths property method at very hgh pressures, especally near the mxture crtcal pont, because of anomalous behavor n these regons Physcal Property Methods and Models Verson 10

75 Chapter 2 Parameters Requred for the GRAYSON Property Method Thermodynamc Propertes Models Parameter Requrements Vapor mxture Fugacty coeffcent, Densty Enthalpy, entropy, Gbbs free energy Lqud mxture Fugacty coeffcent, Gbbs free energy Redlch-Kwong Ideal gas heat capacty, Redlch-Kwong Scatchard-Hldebrand actvty coeffcent Grayson-Streed pure component fugacty coeffcent TC, PC CPIG or CPIGDP TC, PC TC, DELTA, VLCVT1;GMSHVL TC, PC, OMEGA Petroleum-Tuned Equaton-of-State Property Methods Petroleum-tuned equaton-of-state property methods are based on equatons of state for nonpolar compounds wth bult-n bnary parameters. These property methods use the API/Rackett model for lqud densty to overcome the drawback of poor lqud densty calculated by cubc equatons of state. Lqud vscosty and surface tensons are calculated by API models. Equatons of state are comparable n performance when comparng VLE. BWR- LS s recommended for hydrogen-rch systems. Property methods based on lqud fugacty correlatons or K-value models are generally preferred for low pressure refnery applcatons. Petroleum-tuned equaton-of-state models can handle crtcal ponts, but some other models of the property methods (such as lqud densty and lqud vscosty) are not suted for condtons close to crtcalty, as occur n lght ol reservors, transportaton of gas by ppe lnes, and n some gas processng applcatons. For these cases, equatonof-state property methods for hgh pressure hydrocarbon applcatons are preferred. If polar compounds are present, such as n gas treatment, use flexble and predctve equatons of state for polar compounds. PENG-ROB The PENG-ROB property method uses the: Peng-Robnson cubc equaton of state for all thermodynamc propertes except lqud molar volume API method for lqud molar volume of pseudocomponents and the Rackett model for real components Physcal Property Methods and Models 2-15 Verson 10

76 Property Method Descrptons Refer to the tables labeled Parameters Requred for the PENG-ROB Property Method on page 16 and Parameters Requred for Common Models on page 2-18 for thermodynamc and transport property models, and ther requred parameters. Ths property method s comparable to the RK-SOAVE property method. It s recommended for gas-processng, refnery, and petrochemcal applcatons. Sample applcatons nclude gas plants, crude towers, and ethylene plants. For accurate results n your VLE or LLE calculatons, you must use bnary parameters, such as the ASPEN PLUS bult-n bnary parameters. Use the Propertes Parameters Bnary Interacton PRKIJ-1 form to revew avalable bult-n bnary parameters. You can also use the Data Regresson System (DRS) to determne the bnary parameters from expermental phase equlbrum data (usually bnary VLE data). Mxture Types Use the PENG-ROB property method for nonpolar or mldly polar mxtures. Examples are hydrocarbons and lght gases, such as carbon doxde, hydrogen sulfde, and hydrogen. For systems wth polar components, use the SR-POLAR, PRWS, RKSWS, PRMHV2, RKSMHV2, PSRK, WILSON, NRTL, VANLAAR, or UNIQUAC property methods. Ths property method s partcularly sutable n the hgh temperature and hgh pressure regons, such as n hydrocarbon processng applcatons or supercrtcal extractons. Range You can expect reasonable results at all temperatures and pressures. The PENG- ROB property method s consstent n the crtcal regon. Therefore, t does not exhbt anomalous behavor, unlke the actvty coeffcent property methods. Results are least accurate n the regon near the mxture crtcal pont. Parameters Requred for the PENG-ROB Property Method Thermodynamc Propertes Models Parameter Requrements Vapor mxture Fugacty coeffcent Densty Enthalpy, entropy, Gbbs free energy Lqud mxture Fugacty coeffcent Enthalpy, entropy, Gbbs energy Peng-Robnson Ideal gas heat capacty, Peng-Robnson Peng-Robnson Ideal gas heat capacty, Peng-Robnson TCPR or TC; PCPR or PC; OMGPR or OMEGA CPIG or CPIGDP TCPR or TC; PCPR or PC; OMGPR or OMEGA CPIG or CPIGDP 2-16 Physcal Property Methods and Models Verson 10

77 Chapter 2 RK-SOAVE The RK-SOAVE property method uses the: Redlch-Kwong-Soave (RKS) cubc equaton of state for all thermodynamc propertes except lqud molar volume API method for lqud molar volume of pseudocomponents and the Rackett model for real components Refer to the tables labeled Parameters Requred for the RK-SOAVE Property Method on page 2-18 and Parameters Requred for Common Models on page 2-18 for thermodynamc and transport property models, and requred parameters for ths property method. Ths property method s comparable to the PENG-ROB property method. It s recommended for gas-processng, refnery, and petrochemcal applcatons. Example applcatons nclude gas plants, crude towers, and ethylene plants. The RK-SOAVE property method has bult-n bnary parameters, RKSKIJ, that are used automatcally n ASPEN PLUS. For accurate results n your VLE and LLE calculatons, you must use bnary parameters. You can use the ASPEN PLUS bult-n parameters. Use the Propertes Parameters Bnary Interacton RKSKIJ-1 form to revew avalable bult-n bnary parameters. You can also use the Data Regresson System (DRS) to determne the bnary parameters from expermental phase equlbrum data (usually bnary VLE data). Mxture Types Use the RK-SOAVE property method for nonpolar or mldly polar mxtures. Examples are hydrocarbons and lght gases, such as carbon doxde, hydrogen sulfde, and hydrogen. For systems wth polar components, such as alcohols, use the SR-POLAR, WILSON, NRTL, VANLAAR, or UNIQUAC property methods. Ths property method s partcularly sutable n the hgh temperature and hgh pressure regons, such as n hydrocarbon processng applcatons or supercrtcal extractons. Range You can expect reasonable results at all temperatures and pressures. The RK- SOAVE property method s consstent n the crtcal regon. Therefore, unlke the actvty coeffcent property methods, t does not exhbt anomalous behavor. Results are least accurate n the regon near the mxture crtcal pont. Physcal Property Methods and Models 2-17 Verson 10

78 Property Method Descrptons Parameters Requred for the RK-SOAVE Property Method Thermodynamc Propertes Models Parameter Requrements Vapor mxture Fugacty coeffcent, Densty Enthalpy, entropy Gbbs free energy Lqud mxture Fugacty coeffcent Enthalpy, entropy, Gbbs free energy Redlch-Kwong-Soave Ideal gas heat capacty, Redlch-Kwong-Soave Redlch-Kwong-Soave Ideal gas heat capacty, Redlch-Kwong-Soave TC, PC, OMEGA CPIG or CPIGDP, TC, PC, OMEGA TC, PC, OMEGA CPIG or CPIGDP TC, PC, OMEGA Common Models The followng table lsts the models used n all petroleum property methods and ther parameter requrements. Parameters Requred for Common Models General Property/Purpose Mass balance, Converson Mass-bass Mole-bass Converson Stdvol-bass Mole-bass Intalzaton of Flash calculatons Usng Free-water opton: solublty of water n organc phase Enthalpy of reacton Gbbs energy of reacton Parameter Requrements MW VLSTD PLXANT WATSOL DHFORM DGFORM 2-18 Physcal Property Methods and Models Verson 10

79 Chapter 2 Thermodynamc Propertes Property Models Parameter Requrements Lqud mxture Enthalpy, Entropy Densty Ideal heat capacty, Lee-Kesler Real components: Rackett/DIPPR Pseudo components: (CPIG or CPIGDP) TC, PC, OMEGA TC, PC, VCRKT TB, API Transport Propertes Property Models Paremeter Requrements Vapor mxture Vscosty Thermal Conductvty Dffusvty Lqud mxture Vscosty Thermal Conductvty Dffusvty Chapman-Enskog-Brokaw/ DIPPR Stel-Thodos/ DIPPR Dawson Khoury-Kobayash - API Sato-Redel/ DIPPR Wlke-Chang MW, (MUP and (STKPAR or LJPAR)) or MUVDIP MW or KVDIP (and vapor vscosty parameters) MW, MUP, (STKPAR or LJPAR), VC TB, API (MW, TB, TC) or KLDIP MW, VB Surface tenson API TB, TC, SG Physcal Property Methods and Models 2-19 Verson 10

80 Property Method Descrptons Equaton-of-State Property Methods for Hgh-Pressure Hydrocarbon Applcatons The followng table, Equaton of State Property Methods for Hydrocarbons at Hgh Pressure, lsts property methods for mxtures of hydrocarbons and lght gases. The property methods can deal wth hgh pressures and temperatures, and mxtures close to ther crtcal pont (for example, ppelne transportaton of gas or supercrtcal extracton). All thermodynamc propertes of vapor and lqud phases are calculated from the equatons of state. (See Chapter 1). The TRAPP models for vscosty and thermal conductvty can descrbe the contnuty of gas and lqud beyond the crtcal pont, comparable to an equaton of state. The hydrocarbons can be from complex crude or gas mxtures treated usng pseudocomponents. But the property methods for petroleum mxtures are better tuned for these applcatons at low to medum pressures. Unless you use ftted bnary nteracton parameters, no great accuracy should be expected close to the crtcal pont. Lqud denstes are not accurately predcted for the cubc equatons of state. In the presence of polar components (for example, n gas treatment), flexble and predctve equatons of state should be used. For mxtures of polar and nonpolar compounds at low pressures, use an actvty-coeffcent-based property method. The followng table lsts the common and dstnctve models of the property methods BWR-LS, LK-PLOCK, PR-BM, and RKS-BM. The parameter requrements of the common models are gven n the table labeled Parameters Requred for Common Models on page The parameter requrements for the dstnctve models are n the tables labeled Parameters Requred for the BWR-LS Property Method on page 2-22, Parameters Requred for the LK-PLOCK Property Method on page 2-23, Parameters Requred for the PR-BM Property Method on page 2-24, and Parameters Requred for the RKS-BM Property Method on page Equaton-of-State Property Methods for Hydrocarbons at Hgh Pressure Property Method Name BWR-LS LK-PLOCK PR-BM RKS-BM Models BWR-Lee-Starlng Lee-Kesler-Plöcker Peng-Robnson-Boston-Mathas Redlch-Kwong-Soave-Boston-Mathas contnued 2-20 Physcal Property Methods and Models Verson 10

81 Chapter 2 Equaton-of-State Property Methods for Hydrocarbons at Hgh Pressure Property Vapor vscosty Vapor thermal conductvty Vapor dffusvty Surface tenson Lqud vscosty Lqud thermal conductvty Lqud dffusvty Common Models TRAPP TRAPP Dawson-Khoury-Kobayash API surface tenson TRAPP TRAPP Wlke-Chang BWR-LS The BWR-LS property method s based on the BWR-Lee-Starlng equaton of state. It s the generalzaton (n terms of pure component crtcal propertes) of the Benedct-Webb-Rubn vral equaton of state. The property method uses the equaton of state for all thermodynamc propertes. Refer to the table labeled Parameters Requred for the BWR-LS Property Method on page 2-22 and Parameters Requred for Common Models on page 2-25 for thermodynamc and transport property models and ther parameter requrements. The BWR-LS property method s comparable to PENG-ROB, RK-SOAVE, and LK- PLOCK for phase equlbrum calculatons, but s more accurate than PENG- ROB and RK-SOAVE for lqud molar volume and enthalpy. You can use t for gas processng and refnery applcatons. It s suted for hydrogen-contanng systems, and has shown good results n coal lquefacton applcatons. For accurate results, use the bnary nteracton parameters. Bult-n bnary parameters BWRKV and BWRKT are avalable for a large number of component pars. ASPEN PLUS uses these bnary parameters automatcally. Use the Propertes Parameters Bnary Interacton BWRKV-1 and BWRKT-1 forms to revew avalable bult-n bnary parameters. You can also use the Data Regresson System (DRS) to determne the bnary parameters from expermental phase equlbrum data (usually bnary VLE data). Mxture Types Use the BWR-LS property method for nonpolar or slghtly polar mxtures, and lght gases. Asymmetrc nteractons between long and short molecules are well predcted. Physcal Property Methods and Models 2-21 Verson 10

82 Property Method Descrptons Range You can expect reasonable results up to medum pressures. At very hgh pressures, unrealstc lqud-lqud demxng may be predcted. Hgh pressure lqud-lqud demxng occurs between short and long chan hydrocarbons and also, for example, between carbon doxde and longer hydrocarbon chans at hgh pressures. Parameters Requred for the BWR-LS Property Method Thermodynamc Propertes Models Parameter Requrements Vapor mxture Fugacty coeffcent, Densty Enthalpy, Entropy, Gbbs energy Lqud mxture Fugacty coeffcent, Densty Enthalpy, Entropy, Gbbs energy BWR-Lee-Starlng Ideal heat capacty, BWR-Lee-Starlng BWR-Lee-Starlng Ideal heat capacty, BWR-Lee-Starlng TC, VC, OMEGA (CPIG or CPIGDP) and TC, VC, OMEGA TC, VC, OMEGA (CPIG or CPIGDP) and TC, VC, OMEGA LK-PLOCK The LK-PLOCK property method s based on the Lee-Kesler-Plöcker equaton of state, whch s a vral-type equaton. LK-PLOCK uses the: EOS to calculate all thermodynamc propertes except lqud molar volume API method for lqud molar volume of pseudocomponents and the Rackett model for real components You can use LK-PLOCK for gas-processng and refnery applcatons, but the RK- SOAVE or the PENG-ROB property methods are preferred. Refer to the tables labeled Parameters Requred for the LK-PLOCK Property Method on page 2-23 and Parameters Requred for Common Models on page 2-25 for thermodynamc and transport property models, and ther parameter requrements. For accurate results n VLE calculatons, use bnary parameters. Bult-n bnary parameters LKPKIJ are avalable for a large number of component pars. ASPEN PLUS uses these bnary parameters automatcally. Use the Propertes Parameters Bnary Interacton LKPKIJ-1 form to revew avalable bult-n bnary parameters. You can also use the Data Regresson System (DRS) to determne the bnary parameters from expermental phase equlbrum data (usually bnary VLE data) Physcal Property Methods and Models Verson 10

83 Chapter 2 Ths property method also has bult-n correlatons for estmatng bnary parameters among the components CO, CO 2, N 2, H 2, CH 4, alcohols, and hydrocarbons. Components not belongng to the classes lsted above are assumed to be hydrocarbons. Mxture Types Use the LK-PLOCK property method for nonpolar or mldly polar mxtures. Examples are hydrocarbons and lght gases, such as carbon doxde, hydrogen sulfde, and hydrogen. Range You can expect reasonable results at all temperatures and pressures. The LK-PLOCK property method s consstent n the crtcal regon. It does not exhbt anomalous behavor, unlke the actvty coeffcent property methods. Results are least accurate n the regon near the mxture crtcal pont. Parameters Requred for the LK-PLOCK Property Method Thermodynamc Propertes Models Parameter Requrements Vapor mxture Fugacty coeffcent, Densty Enthalpy, entropy Gbbs free energy Lqud mxture Fugacty coeffcent, Densty Enthalpy, entropy Gbbs free energy Lee-Kesler-Plöcker Ideal gas heat capacty, Lee-Kesler-Plöcker Lee-Kesler-Plöcker Ideal gas heat capacty, Lee-Kesler-Plöcker TC, PC, VC, OMEGA (CPIG or CPIGDP) and TC, PC, VC, OMEGA TC, PC, VC, OMEGA (CPIG or CPIGDP) and TC, PC, VC, OMEGA PR-BM The PR-BM property method uses the Peng Robnson cubc equaton of state wth the Boston-Mathas alpha functon for all thermodynamc propertes. Refer to the tables labeled Parameters Requred for the PR-BM Property Method on page 2-24 and Parameters Requred for Common Models on page 2-25 for thermodynamc and transport property models, and ther requred parameters. Ths property method s comparable to the RKS-BM property method. It s recommended for gas-processng, refnery, and petrochemcal applcatons. Sample applcatons nclude gas plants, crude towers, and ethylene plants. Physcal Property Methods and Models 2-23 Verson 10

84 Property Method Descrptons For accurate results n your VLE calculatons, you must use bnary parameters. ASPEN PLUS does not have bult-n bnary parameters for ths property method. Mxture Types Use the PR-BM property method for nonpolar or mldly polar mxtures. Examples are hydrocarbons and lght gases, such as carbon doxde, hydrogen sulfde, and hydrogen. Range You can expect reasonable results at all temperatures and pressures. The PR-BM property method s consstent n the crtcal regon. Results are least accurate n the regon near the mxture crtcal pont. Parameters Requred for the PR-BM Property Method Thermodynamc Propertes Models Parameter Requrements Vapor or lqud mxture Fugacty coeffcent Densty Enthalpy, entropy, Gbbs free energy Peng-Robnson Ideal gas heat capacty, Peng-Robnson PC, TC, OMEGA CPIG or CPIGDP, TC,PC, OMEGA RKS-BM The RKS-BM property method uses the Redlch-Kwong-Soave (RKS) cubc equaton of state wth Boston-Mathas alpha functon for all thermodynamc propertes. Ths property method s comparable to the PR-BM property method. It s recommended for gas-processng, refnery, and petrochemcal applcatons. Example applcatons nclude gas plants, crude towers, and ethylene plants. For accurate results n your VLE calculatons, you must use bnary parameters. ASPEN PLUS does not have bult-n bnary parameters for ths property method. Mxture Types Use the RKS-BM property method for nonpolar or mldly polar mxtures. Examples are hydrocarbons and lght gases, such as carbon doxde, hydrogen sulfde, and hydrogen Physcal Property Methods and Models Verson 10

85 Chapter 2 Range You can expect reasonable results at all temperatures and pressures. The RKS-BM property method s consstent n the crtcal regon. Results are least accurate n the regon near the mxture crtcal pont. Refer to the tables labeled Parameters Requred for the RKS-BM Property Method on page 2-25 and Parameters Requred for Common Models on page 2-25 for thermodynamc and transport property models, and ther requred parameters. Parameters Requred for the RKS-BM Property Method Thermodynamc Propertes Models Parameter Requrements Vapor or lqud mxture Fugacty coeffcent Densty Enthalpy, entropy, Gbbs free energy Redlch-Kwong-Soave Ideal gas heat capacty, Redlch-Kwong-Soave TC, PC, OMEGA CPIG or CPIGDP, TC,PC, OMEGA Common Models The followng table labeled Parameters Requred for Common Models lsts the models common to equaton-of-state property methods for hgh pressure hydrocarbon applcatons and ther parameter requrements. Parameters Requred for Common Models General Property/Purpose Mass balance, Converson Massbass Mole-bass Converson Stdvol-bass Mole-bass Intalzaton of Flash calculatons Usng Free-water opton: solublty of water n organc phase Enthalpy of reacton Gbbs energy of reacton Parameter Requrements MW VLSTD PLXANT WATSOL DHFORM DGFORM contnued Physcal Property Methods and Models 2-25 Verson 10

86 Property Method Descrptons Transport Property Models Parameter Requrements Vapor Mxture Vscosty Thermal Conductvty Dffusvty TRAPP TRAPP Dawson-Khoury-Kobayash TC, PC, OMEGA TC, PC, OMEGA MW, MUP, (STKPAR or LJPAR), VC Surface tenson API TB, TC, SG Lqud mxture Vscosty Thermal Conductvty Dffusvty TRAPP TRAPP Wlke-Chang TC, PC, OMEGA TC, PC, OMEGA MW, VB Flexble and Predctve Equaton-of-State Property Methods The table labeled Flexble and Predctve Equaton-of-State Property Methods on page 2-28 lsts property methods for mxtures of polar and non-polar components and lght gases. The property methods can deal wth hgh pressures and temperatures, mxtures close to ther crtcal pont, and lqud-lqud separaton at hgh pressure. Examples of applcatons are gas dryng wth glycols, gas sweetenng wth methanol, and supercrtcal extracton. Pure component thermodynamc behavor s modeled usng the Peng-Robnson or Redlch-Kwong-Soave equatons of state. They are extended wth flexble alphafunctons wth up to three parameters, for very accurate fttng of vapor pressures. Ths s mportant n separatons of very closely bolng systems and for polar compounds. In some cases they are extended wth a volume translaton term for accurate fttng of lqud denstes (see the table labeled Flexble and Predctve Equaton-of-State Property Methods on page 2-28). Parameters for the Schwartzentruber-Renon and Mathas-Copeman alpha functons are avalable for many components n the PURECOMP databank Physcal Property Methods and Models Verson 10

87 Chapter 2 Mxng rules for these models vary. Extended classcal mxng rules are used for fttng hydrogen-rch systems or systems wth strong sze and shape asymmetry (Redlch-Kwong-Aspen). Composton and temperature-dependent mxng rules ft strongly non-deal hgh pressure systems (SR-POLAR). Modfed Huron-Vdal mxng rules can predct non-dealty at hgh pressure from low-pressure (groupcontrbuton) actvty coeffent models (Wong-Sandler, MHV2, PSRK). The predctve capabltes of modfed Huron-Vdal mxng rules are superor to the predctve capabltes of SR-POLAR. The dfferences among capabltes of the modfed Huron-Vdal mxng rules are small (see Chapter 3). The Wong-Sandler, MHV2, and Holderbaum-Gmehlng mxng rules use actvty coeffcent models to calculate excess Gbbs or Helmholtz energy for the mxng rules. The property methods wth these mxng rules use the UNIFAC or Lyngby modfed UNIFAC group contrbuton models. Therefore, they are predctve. You can use any ASPEN PLUS actvty coeffcent models wth these mxng rules, ncludng user models. Use the Propertes Methods Models sheet to modfy the property method. See Chapter 4 for detals on how to modfy a property method. The Chung-Lee-Starlng models for vscosty and thermal conductvty can descrbe the contnuty of gas and lqud beyond the crtcal pont. Ths s comparable to an equaton of state. These models can ft the behavor of polar and assocatng components. Detals about the pure component models and mxng rules are found n Chapter 3. For mxtures of polar and non-polar compounds at low pressures, actvty coeffcent models are preferred. For non-polar mxtures of petroleum fluds and lght gases at low to medum pressures, the property methods for petroleum mxtures are recommended. The flexble and predctve equatons of state are not suted for electrolyte solutons. The followng table, Flexble and Predctve Equaton-of-State Property Methods, lsts flexble and predctve equaton-of-state property methods, the dstnctve equaton-of-state models on whch they are based, and some of ther characterstcs. The table also gves the models that the property methods have n common. Parameter requrements of the common models are gven n the table labeled Parameters Requred for Common Flexble and Predctve Models on page Parameter requrements for the dstnctve models are n the tables labeled Parameters Requred for the PRMHV2 Property Method on page 2-29, Parameters Requred for the PRWS Property Method on page 2-30, Parameters Requred for the PSRK Property Method on page 2-31, Parameters Requred for the RK-ASPEN Property Method on page 2-32, Parameters Requred for the RKSMHV2 Property Method on page 2-33, Parameters Requred for the RKSWS Property Method on page 2-34, and Parameters Requred for the SR-POLAR Property Method on page Physcal Property Methods and Models 2-27 Verson 10

88 Property Method Descrptons Flexble and Predctve Equaton-of-State Property Methods Property Method Name Equaton of State Volume Shft Mxng Rule Predctve PRMHV2 Peng-Robnson MHV2 X PRWS Peng-Robnson Wong-Sandler X PSRK Redlch-Kwong-Soave Holderbaum-Gmehlng X RK-ASPEN Redlch-Kwong-Soave Mathas RKSMHV2 Redlch-Kwong-Soave MHV2 X RKSWS Redlch-Kwong-Soave Wong-Sandler X SR-POLAR Redlch-Kwong-Soave X Schwartzentruber-Renon Property Vapor vscosty Vapor thermal conductvty Vapor dffusvty Surface tenson Lqud vscosty Thermal conductvty Lqud dffusvty Common Models Chung-Lee-Starlng Chung-Lee-Starlng Dawson-Khoury-Kobayash Hakm-Stenberg-Stel/DIPPR Chung-Lee-Starlng Chung-Lee-Starlng Wlke-Chang lqud An X ndcates volume shft s ncluded n the property method. An X ndcates that the property method s predctve. PRMHV2 The PRMHV2 property method s based on the Peng-Robnson-MHV2 equaton-ofstate model, whch s an extenson of the Peng-Robnson equaton of state. The UNIFAC model s used by default to calculate excess Gbbs energy n the MHV2 mxng rules. Other modfed UNIFAC models and actvty coeffcent models can be used for excess Gbbs energy. Besdes the acentrc factor, up to three polar parameters can be used to ft more accurately the vapor pressure of polar compounds. The MHV2 mxng rules predct the bnary nteractons at any pressure. Usng the UNIFAC model the MHV2 mxng rules are predctve for any nteracton that can be predcted by the UNIFAC model at low pressure Physcal Property Methods and Models Verson 10

89 Chapter 2 The mnmum parameter requrements of the PRMHV2 property method are gven n the tables labeled Parameters Requred for the PRMHV2 Property Method on page 2-29 and Parameters Requred for Common Flexble and Predctve Models on page For detals about optonal parameters, and calculaton of pure component and mxture propertes, see Chapter 3. Mxture Types You can use the PRMHV2 property method for mxtures of non-polar and polar compounds. For lght gases UNIFAC does not provde any nteracton. Range You can use the PRMHV2 property method up to hgh temperatures and pressures. You can expect accurate predctons (4% n pressure and 2% n mole fracton at gven temperature) up to about 150 bar. You can expect reasonable results at any condton, provded the UNIFAC nteracton parameters are avalable. Results are least accurate close to the crtcal pont. Parameters Requred for the PRMHV2 Property Method Thermodynamc Propertes Models Parameter Requrements Vapor and lqud mxture Fugacty coeffcent, Densty Peng-Robnson-MHV2, UNIFAC TC, PC, OMEGA, UFGRP, GMUFQ, GMUFR Enthalpy, Entropy, Gbbs energy Ideal heat capacty, Peng-Robnson-MHV2, UNIFAC (CPIG or CPIGDP), TC, PC, OMEGA, UFGRP, GMUFQ, GMUFR PRWS The PRWS property method s based on the Peng-Robnson-Wong-Sandler equaton-of-state model, whch s based on an extenson of the Peng-Robnson equaton of state. The UNIFAC model s used to calculate excess Helmholtz energy for the mxng rules. Besdes the acentrc factor, you can use up to three polar parameters to ft more accurately the vapor pressure of polar compounds. The Wong-Sandler mxng rules predct the bnary nteractons at any pressure. Usng the UNIFAC model the PRWS property method s predctve for any nteracton that can be predcted by UNIFAC at low pressure. Physcal Property Methods and Models 2-29 Verson 10

90 Property Method Descrptons The mnmum parameter requrements of the property method are gven n the tables labeled Parameters Requred for the PRWS Property Method on page 2-30 and Parameters Requred for Common Flexble and Predctve Models on page For detals about the optonal parameters, and about calculaton of pure component and mxture propertes, see Chapter 3. Mxture Types You can use the PRWS property method for mxtures of non-polar and polar compounds, n combnaton wth lght gases. Range You can use the PRWS property method up to hgh temperatures and pressures. You can expect accurate predctons (3% n pressure and 2% n mole fracton at a gven temperature) up to about 150 bar. You can expect reasonable results at any condton, provded UNIFAC nteracton parameters are avalable. Results are least accurate close to the crtcal pont. Parameters Requred for the PRWS Property Method Thermodynamc Propertes Models Parameter Requrements Vapor and lqud mxture Fugacty coeffcent, Densty Enthalpy, Entropy, Gbbs energy Peng-Robnson-WS, UNIFAC Ideal heat capacty, PengRobnson-WS, UNIFAC TC, PC, OMEGA, UFGRP, GMUFR, GMUFQ (CPIG or CPIGDP),TC, PC, OMEGA, UFGRP, GMUFR, GMUFQ PSRK The PSRK property method s based on the Predctve Soave-Redlch-Kwong equaton-of-state model, whch s an extenson of the Redlch-Kwong-Soave equaton of state. Besdes the acentrc factor, you can use up to three polar parameters to ft more accurately the vapor pressure of polar compounds. The Holderbaum-Gmehlng mxng rules or PSRK method predct the bnary nteractons at any pressure. Usng UNIFAC the PSRK method s predctve for any nteracton that can be predcted by UNIFAC at low pressure. The UNIFAC nteracton parameter table has been extended for gases, for the PSRK method Physcal Property Methods and Models Verson 10

91 Chapter 2 The mnmum parameter requrements of the PSRK property method are gven n the tables labeled Parameters Requred for the PSRK Property Method on page 2-31 and Parameters Requred for Common Flexble and Predctve Models on page For detals about the optonal parameters, and about calculaton of pure component and mxture propertes, see Chapter 3. Mxture Types You can use the PSRK property method for mxtures of non-polar and polar compounds, n combnaton wth lght gases. Range You can use the PSRK property method up to hgh temperatures and pressures. You can expect accurate predctons at any condtons provded UNIFAC nteracton parameters are avalable. Results are least accurate close to the crtcal pont. Parameters Requred for the PSRK Property Method Thermodynamc Propertes Models Parameter Requrements Vapor and lqud mxture Fugacty coeffcent, Densty Enthalpy, Entropy, Gbbs energy PSRK, UNIFAC Ideal heat capacty, PSKR, UNIFAC TC, PC, OMEGA, UFGRP, GMUFR, GMUFQ (CPIG or CPIGDP),TC, PC, OMEGA, UFGRP, GMUFR, GMUFQ RK-ASPEN The RK-ASPEN property method s based on the Redlch-Kwong-Aspen equatonof-state model, whch s an extenson of Redlch-Kwong-Soave. Ths property method s smlar to RKS-BM, but t also apples to polar components such as alcohols and water. RKS-BM requres polar parameters that must be determned from regresson of expermental vapor pressure data usng DRS. Use the bnary parameters to obtan best possble results for phase equlbra. RK-ASPEN allows temperature-dependent bnary parameters. If the polar parameters are zero for all components and the bnary parameters are constant, RK-ASPEN s dentcal to RKS-BM. Physcal Property Methods and Models 2-31 Verson 10

92 Property Method Descrptons The mnmum parameter requrements of the RK-ASPEN property method are gven n the tables labeled Parameters Requred for the RK-ASPEN Property Method on page 2-32 and Parameters Requred for Common Flexble and Predctve Models on page For detals about the optonal parameters for ths model, see Chapter 3. Mxture Types You can use the RK-ASPEN property method for mxtures of non-polar and slghtly polar compounds, n combnaton wth lght gases. It s especally suted for combnatons of small and large molecules, such as ntrogen wth n-decane, or hydrogen-rch systems. Range You can use the RK-ASPEN property method up to hgh temperatures and pressures. You can expect reasonable results at any condton, but results are least accurate close to the crtcal pont. Parameters Requred for the RK-ASPEN Property Method Thermodynamc Propertes Models Parameter Requrements Vapor and lqud mxture Fugacty coeffcent, Densty Enthalpy, Entropy, Gbbs energy Redlch-Kwong-Aspen Ideal heat capacty, Redlch-Kwong-Aspen TC, PC, OMEGA, UFGRP, GMUFR, GMUFQ (CPIG or CPIGDP) and TC, PC, OMEGA RKSMHV2 The RKSMHV2 property method s based on the Redlch-Kwong-Soave MHV2 equaton-of-state model, whch s an extenson of the Redlch-Kwong-Soave equaton of state. The Lyngby modfed UNIFAC model s used to calculate excess Gbbs energy for the MHV2 mxng rules. Besdes the acentrc factor, you can use up to three polar parameters to ft more accurately the vapor pressure of polar compounds. The MHV2 mxng rules predct the bnary nteractons at any pressure. Usng the Lyngby modfed UNIFAC model, the Redlch-Kwong-Soave MHV2 model s predctve for any nteracton that can be predcted by Lyngby modfed UNIFAC at low pressure. The Lyngby modfed UNIFAC nteracton parameter table has been extended for gases for the MHV2 method Physcal Property Methods and Models Verson 10

93 Chapter 2 The mnmum parameter requrements of the RKSMHV2 property method are gven n the tables labeled Parameters Requred for the RKSMHV2 Property Method on page 2-33 and Parameters Requred for Common Flexble and Predctve Models on page For detals about optonal parameters and calculaton of pure component and mxture propertes, see Chapter 3. Mxture Types You can use the RKSMHV2 property method for mxtures of non-polar and polar compounds, n combnaton wth lght gases. Range You can use the RKSMHV2 property method up to hgh temperatures and pressures. You can expect accurate predctons (4% n pressure and 2% n mole fracton at gven temperature) up to about 150 bar. You can expect reasonable results at any condton, provded Lyngby modfed UNIFAC nteractons are avalable. Results are least accurate close to the crtcal pont. Parameters Requred for the RKSMHV2 Property Method Thermodynamc Propertes Models Parameter Requrements Vapor and lqud mxture Fugacty coeffcent, Densty Enthalpy, Entropy, Gbbs energy Redlch-Kwong-Soave-MHV2, Lyngby modfed UNIFAC Ideal heat capacty, Redlch-Kwong-Soave-MHV2, Lyngby modfed UNIFAC TC, PC, OMEGA, UFGRPL, GMUFLR, GMUFLQ (CPIG or CPIGDP),TC, PC, OMEGA, UFGRPL, GMUFLR, GMUFLQ RKSWS The RKSWS property method s based on the Redlch-Kwong-Soave-Wong-Sandler equaton-of-state model, whch s an extenson of the Redlch-Kwong-Soave equaton of state. The UNIFAC model s used to calculate excess Helmholtz energy for the mxng rules. Besdes the acentrc factor,you can use up to three polar parameters to ft more accurately the vapor pressure of polar compounds. The Wong-Sandler mxng rules predct the bnary nteractons at any pressure. Usng the UNIFAC model t s predctve for any nteracton that can be predcted by UNIFAC at low pressure. Physcal Property Methods and Models 2-33 Verson 10

94 Property Method Descrptons The mnmum parameter requrements of the RKSWS property method are gven n the tables labeled Parameters Requred for the RKSWS Property Method on page 2-34 and Parameters Requred for Common Flexble and Predctve Models on page For detals about optonal parameters and calculaton of pure component and mxture propertes, see Chapter 3. Mxture Types You can use the RKSWS property method for mxtures of non-polar and polar compounds, n combnaton wth lght gases. Range You can use the RKSWS property method up to hgh temperatures and pressures. You can expect accurate predctons (3% n pressure and 2% n mole fracton at a gven temperature) up to about 150 bar. You can expect reasonable results at any condton, provded UNIFAC nteracton parameters are avalable. But results are least accurate close to the crtcal pont. Parameters Requred for the RKSWS Property Method Thermodynamc Propertes Models Parameter Requrements Vapor and lqud mxture Fugacty coeffcent, Densty Enthalpy, Entropy, Gbbs energy Redlch-Kwong-Soave-WS, UNIFAC Ideal heat capacty, Redlch-Kwong-Soave-WS, UNIFAC TC, PC, OMEGA, UFGRP, GMUFR, GMUFQ (CPIG or CPIGDP),TC, PC, OMEGA, UFGRP, GMUFR, GMUFQ SR-POLAR The SR-POLAR property method s based on an equaton-of-state model by Schwarzentruber and Renon, whch s an extenson of the Redlch-Kwong-Soave equaton of state. You can apply the SR-POLAR method to both non-polar and hghly polar components, and to hghly nondeal mxtures. Ths method s recommended for hgh temperature and pressure applcatons SR-POLAR requres: Polar parameters for polar components. These parameters are determned automatcally usng vapor pressure data generated from the extended Antone model. Bnary parameters to accurately represent phase equlbra. The bnary parameters are temperature-dependent Physcal Property Methods and Models Verson 10

95 Chapter 2 If you do not enter bnary parameters, ASPEN PLUS estmates them automatcally usng VLE data generated from the UNIFAC group contrbuton method. Therefore, the SR-POLAR property method s predctve for any nteracton that UNIFAC can predct at low pressures. The accuracy of the predcton decreases wth ncreasng pressure. You cannot use UNIFAC to predct nteractons wth lght gases. SR-POLAR s an alternatve property method that you can use for nondeal systems, nstead of usng an actvty coeffcent property method, such as WILSON. Parameter requrements for the SR-POLAR property method are n the tables labeled Parameters Requred for the SR-POLAR Property Method on page 2-35 and Parameters Requred for Common Flexble and Predctve Models on page For detals about optonal parameters, and calculaton of pure component and mxture propertes, see Chapter 3. Mxture Types You can use the SR-POLAR property method for mxtures of non-polar and polar compounds, n combnaton wth lght gases. Range You can use the SR-POLAR property method up to hgh temperatures and pressures. You can expect far predctons up to about 50 bar. You can expect reasonable results at any condton, provded UNIFAC nteracton parameters are avalable. But results are least accurate close to the crtcal pont. Parameters Requred for the SR-POLAR Property Method Thermodynamc Propertes Models Parameter Requrements Vapor and lqud mxture Fugacty coeffcent, Densty Enthalpy, Entropy, Gbbs energy Schwartzentruber-Renon Ideal gas heat capacty/dippr Schwartzentruber-Renon TC, PC, OMEGA, Optonal: RKUPPn, RKUCn, RKUKAn, RKULAn, RKUKBn n = 0, 1, 2 (CPIG or CPIGDP) Optonal: RKUPPn, RKUCn, RKUKAn, RKULAn, RKUKBn n = 0, 1, 2 Physcal Property Methods and Models 2-35 Verson 10

96 Property Method Descrptons Common Models The followng table descrbes the models common to flexble and predctve property methods and ther parameter requrements. Parameters Requred for Common Flexble and Predctve Models General Property/Purpose Mass balance, Converson Massbass Mole-bass Converson Stdvol-bass Mole-bass Intalzaton of Flash calculatons Usng Free-water opton: solublty of water n organc phase Enthalpy of reacton Gbbs energy of reacton Parameter Requrements MW VLSTD PLXANT WATSOL DHFORM DGFORM Transport Propertes Property Models Parameter Requrements Vapor mxture Vscosty Thermal Conductvty Dffusvty Chung-Lee-Starlng Chung-Lee-Starlng Dawson-Khoury-Kobayash TC, PC, OMEGA TC, PC, OMEGA MW, MUP, (STKPAR or LJPAR), VC Surface tenson Hakm-Stenberg-Stel/ DIPPR (TC, PC, OMEGA) or SIGDIP Lqud mxture Vscosty Thermal Conductvty Dffusvty Chung-Lee-Starlng Chung-Lee-Starlng Wlke-Chang TC, PC, OMEGA TC, PC, OMEGA MW, VB 2-36 Physcal Property Methods and Models Verson 10

97 Chapter 2 Lqud Actvty Coeffcent Property Methods The table labeled Lqud Actvty Coeffcent Property Methods on page 2-38 lsts property methods for nondeal and strongly nondeal mxtures at low pressures (maxmum 10 atm). You can model permanent gases n lqud soluton usng Henry s law. Bnary parameters for many component pars are avalable n the ASPEN PLUS databanks. The UNIFAC based property methods are predctve. These property methods are not suted for electrolytes. In that case use an electrolyte actvty coeffcent property method. Model polar mxtures at hgh pressures wth flexble and predctve equatons of state. Non-polar mxtures are more convenently modeled wth equatons-of-state. Petroleum mxtures are more accurately modeled wth lqud fugacty correlatons and equatons of state. In the table labeled Lqud Actvty Coeffcent Property Methods on page 2-38,there are fve dfferent actvty coeffcent models and sx dfferent equatonof-state models. Each actvty coeffcent model s pared wth a number of equaton-of-state models to form 26 property methods. The descrpton of the property methods are therefore dvded nto two parts: Equaton of state Actvty coeffcent model Each part dscusses the characterstcs of the specfc model and ts parameter requrements. Parameters of the models occurrng n all property methods are gven n the table labeled Parameters Requred For Common Models on page Equatons of State Ths secton dscusses the characterstcs and parameter requrements of the followng equatons of state: Ideal gas law Redlch-Kwong Nothnagel Hayden-O Connell HF equaton of state Physcal Property Methods and Models 2-37 Verson 10

98 Property Method Descrptons Lqud Actvty Coeffcent Property Methods Property Method Gamma Model Name Vapor Phase EOS Name NRTL NRTL Ideal gas law NRTL-2 NRTL Ideal gas law NRTL-RK NRTL Redlch-Kwong NRTL-HOC NRTL Hayden-O Connell NRTL-NTH NRTL Nothnagel UNIFAC UNIFAC Redlch-Kwong UNIF-LL UNIFAC Redlch-Kwong UNIF-HOC UNIFAC Hayden-O Connell UNIF-DMD Dortmund modfed UNIFAC Redlch-Kwong-Soave UNIF-LBY Lyngby modfed UNIFAC Ideal Gas law UNIQUAC UNIQUAC Ideal gas law UNIQ-2 UNIQUAC Ideal gas law UNIQ-RK UNIQUAC Redlch-Kwong UNIQ-HOC UNIQUAC Hayden-O Connell UNIQ-NTH UNIQUAC Nothnagel VANLAAR Van Laar Ideal gas law VANL-2 Van Laar Ideal gas law VANL-RK Van Laar Redlch-Kwong VANL-HOC Van Laar Hayden-O Connell VANL-NTH Van Laar Nothnagel WILSON Wlson Ideal gas law WILS-2 Wlson Ideal gas law WILS-GLR Wlson Ideal gas law WILS-LR Wlson Ideal gas law WILS-RK Wlson Redlch-Kwong WILS-HOC Wlson Hayden-O Connell WILS-NTH Wlson Nothnagel WILS-HF Wlson HF equaton of state 2-38 Physcal Property Methods and Models Verson 10

99 Chapter 2 Property Vapor pressure Lqud molar volume Heat of vaporzaton Vapor vscosty Vapor thermal conductvty Vapor dffusvty Surface tenson Lqud vscosty Lqud thermal conductvty Lqud dffusvty Common Models Extended Antone Rackett Watson Chapman-Enskog-Brokaw Stel-Thodos/DIPPR Dawson-Khoury-Kobayash Hakm-Stenberg-Stel/DIPPR Andrade/DIPPR Sato-Redel/DIPPR Wlke-Chang Ideal Gas Law The property methods that use the deal gas law as the vapor phase model are: NRTL NRTL-2 UNIF-LBY UNIQUAC UNIQ-2 VANLAAR VANL-2 WILSON WILS-2 WILS-GLR WILS-LR The deal gas law s the smplest equaton of state. It s also known as the combned laws of Boyle and Gay-Lussac. Mxture Types The deal gas law cannot model assocaton behavor n the vapor phase, as occurs wth carboxylc acds. Choose Hayden-O Connell or Nothnagel to model ths behavor. Range The deal gas law s vald for low pressures. It s not suted for modelng pressures exceedng several atm. For medum pressures, choose a Redlch-Kwong-based property method. There are no component-specfc parameters assocated wth the deal gas law. Physcal Property Methods and Models 2-39 Verson 10

100 Property Method Descrptons Redlch-Kwong The property methods that use the Redlch-Kwong equaton of state as the vapor phase model are: NRTL-RK UNIFAC UNIF-LL UNIQ-RK VANL-RK WILS-RK The Redlch-Kwong equaton of state s a smple cubc equaton of state. Mxture Types The Redlch-Kwong equaton of state cannot model assocaton behavor n the vapor phase, as occurs wth carboxylc acds. Range The Redlch-Kwong equaton of state descrbes vapor phase propertes accurately up to medum pressures. The parameter requrements for the Redlch-Kwong equaton of state are gven n the followng table. For detals about the model, see Chapter 3. Parameters Requred for Redlch-Kwong Property Methods Thermodynamc Propertes Models Parameter Requrements Vapor mxture Fugacty coeffcent, Densty Enthalpy, Entropy, Gbbs energy Redlch-Kwong Ideal heat capacty, Redlch-Kwong TC, PC (CPIG or CPIGDP), TC, PC Nothnagel The property methods that use the Nothnagel equaton of state as vapor phase model are: NRTL-NTH UNIQ-NTH VANL-NTH WILS-NTH 2-40 Physcal Property Methods and Models Verson 10

101 Chapter 2 The Nothnagel equaton of state accounts for dmerzaton n the vapor phase at low pressure. Dmerzaton affects VLE; vapor phase propertes, such as enthalpy and densty; and lqud phase propertes, such as enthalpy. Mxture Types The Nothnagel equaton of state can model dmerzaton n the vapor phase, as occurs wth mxtures contanng carboxylc acds. Range Do not use the Nothnagel based property methods at pressures exceedng several atm. For vapor phase assocaton up to medum pressure choose the Hayden- O Connell equaton. Parameter requrements for the Nothnagel equaton of state are gven n the followng table. Enter equlbrum constants of assocaton drectly (NTHK). Or calculate them from the pure component parameters NTHA, elements 1 to 3 (b, p and d ). If parameters are not avalable, ASPEN PLUS uses default values. For predcton, the Hayden-O Connell correlaton s more accurate. For detals about the models, see Chapter 3. Parameters Requred for Nothnagel Property Methods Thermodynamc Propertes Models Parameter Requrements Vapor mxture Fugacty coeffcent, Densty Enthalpy, Entropy, Gbbs energy Nothnagel Ideal heat capacty, Nothnagel TB, TC, PC and (NTHA or NTHK) (CPIG or CPIGDP), TB, TC, PC and (NTHA or NTHK) Hayden-O Connell The property methods that use the Hayden-O Connell equaton of state as vapor phase model are: NRTL-HOC UNIF-HOC UNIQ-HOC VANL-HOC WILS-HOC The Hayden-O Connell equaton of state predcts solvaton and dmerzaton n the vapor phase, up to medum pressure. Dmerzaton affects VLE; vapor phase propertes, such as enthalpy and densty; and lqud phase propertes, such as enthalpy. Physcal Property Methods and Models 2-41 Verson 10

102 Property Method Descrptons Mxture Types The Hayden-O Connell equaton relably predcts solvaton of polar compounds and dmerzaton n the vapor phase, as occurs wth mxtures contanng carboxylc acds. Range Do not use the Hayden-O Connell-based property methods at pressures exceedng 10 to 15 atm. Parameter requrements for the Hayden-O Connell equaton of state are gven n the followng table. For detals about the model, see Chapter 3. Parameters Requred for Hayden-O Connell Property Methods Thermodynamc Propertes Models Parameter Requrements Vapor mxture Fugacty coeffcent, Densty Enthalpy, Entropy, Gbbs energy Hayden-O Connell Ideal heat capacty, Hayden-O Connell TC, PC, RGYR, MUP, HOCETA (CPIG or CPIGDP), TC, PC, RGYR, MUP, HOCETA HF Equaton of State The only property method that has the HF equaton of state as the vapor phase model s WILS-HF. For HF-hydrocarbon mxtures, the Wlson actvty coeffcent model s usually best suted for preventng nonrealstc lqud phase splttng. The HF equaton of state predcts the strong assocaton of HF the vapor phase at low pressures. Assocaton (manly hexamerzaton) affects VLE, vapor phase propertes, such as enthalpy and densty, and lqud phase propertes, such as enthalpy. Mxture Types The HF equaton of state relably predcts the strong assocaton effects of HF n a mxture. Range Do not use the WILS-HF property method at pressures exceedng 3 atm Physcal Property Methods and Models Verson 10

103 Chapter 2 Parameters for the HF equaton of state are bult-n for temperatures up to 373 K. You can enter parameters and regress them usng the ASPEN PLUS Data Regresson System (DRS), f necessary. For detals about the model, see Chapter 3. Actvty Coeffcent Models Ths secton dscusses the characterstcs and parameter requrements of the followng actvty coeffcent models: NRTL UNIFAC UNIQUAC Van Laar Wlson NRTL The property methods that use the NRTL actvty coeffcent model are lsted n the followng table. NRTL Property Methods Bnary Parameters Property Method Dataset Number VLE Name Lt Reg LLE Lt Reg Henry Lt Reg Vapor Phase EOS Name Poyntng Correcton NRTL 1 X X X X X Ideal Gas law NRTL-2 2 X X X X X Ideal Gas law NRTL-RK 1 X X X Redlch-Kwong X NRTL-HOC 1 X X X Hayden-O'Connell X NRTL-NTH 1 X X Nothnagel X An X ndcates the parameters were obtaned from the lterature. An X ndcates the parameters were regressed by AspenTech from expermental data n the Dortmund Databank (DDB). The NRTL model can descrbe VLE and LLE of strongly nondeal solutons. The model requres bnary parameters. Many bnary parameters for VLE and LLE, from lterature and from regresson of expermental data, are ncluded n the ASPEN PLUS databanks. For detals, see ASPEN PLUS Physcal Property Data, Chapter 1. Physcal Property Methods and Models 2-43 Verson 10

104 Property Method Descrptons You can model the solublty of supercrtcal gases usng Henry s law. Henry coeffcents are avalable n the ASPEN PLUS databanks for many solutes wth water and other solvents (see ASPEN PLUS Physcal Property Data, Chapter 1). The property methods wth a vapor phase model that can be used up to moderate pressures, have the Poyntng correcton ncluded n the lqud fugacty coeffcent calculaton (see the table labeled NRTL Property Methods on page Heat of mxng s calculated usng the NRTL model. You can use separate data sets for the NRTL bnary parameters to model propertes or equlbra at dfferent condtons. It s also possble to use one data set for VLE and a second data set for LLE (use NRTL and NRTL-2) property methods are dentcal except for the data set number they use. For example, you can use these property methods n dfferent flowsheet sectons or column sectons. Mxture Types The NRTL model can handle any combnaton of polar and non-polar compounds, up to very strong nondealty. Range Parameters should be ftted n the temperature, pressure, and composton range of operaton. No component should be close to ts crtcal temperature. Parameter requrements for the NRTL actvty coeffcent model are gven n the table labeled Parameters Requred for NRTL Property Methods on page For detals about the model, see Chapter Physcal Property Methods and Models Verson 10

105 Chapter 2 Parameters Requred for NRTL Property Methods Thermodynamc Propertes Models Parameter Requrements Lqud mxture Fugacty coeffcent, Gbbs energy Enthalpy, Entropy Densty NRTL lqud actvty coeffcent Extended Antone vapor pressure Henry s constant Brelv-O Connell Ideal gas heat capacty Watson/DIPPR heat of vaporzaton NRTL lqud actvty coeffcent Rackett NRTL PLXANT Solvent: VC, Solute-solvent: HENRY Solvent: TC, PC, (ZC or RKTZRA), Solute: (VC or VLBROC) CPIG or CPIGDP TC, (DHVLWT or DHVLDP) NRTL TC, PC, (VC or VCRKT), (ZC or ZCRKT) UNIFAC UNIFAC s an actvty coeffcent model, lke NRTL or UNIQUAC. But t s based on group contrbutons, rather than molecular contrbutons. Wth a lmted number of group parameters and group-group nteracton parameters, UNIFAC can predct actvty coeffcents. The followng table lsts the property methods based on UNIFAC. Physcal Property Methods and Models 2-45 Verson 10

106 Property Method Descrptons UNIFAC Property Methods Property Method Name Model Name Parameters Rev. Yr Tmn /K Tmax /K Henry Lt Reg Vapor Phase EOS Name Poyntng Correcton UNIFAC UNIFAC 5, X X Redlch- Kwong UNIF-LL UNIFAC, X X Redlch- Kwong UNIF-HOC UNIFAC 5, X X Hayden- O'Connell UNIF-DMD DMD-UNIF 1, X X Redlch- Kwong- Soave UNIF-LBY LBY-UNIF, X X Ideal Gas law X X X X An X ndcates the parameters were obtaned from the lterature. An X ndcates the parameters were regressed by AspenTech from expermental data n the Dortmund Databank (DDB). The orgnal verson of UNIFAC can predct VLE and LLE, usng two sets of parameters. So there are two property methods based on the orgnal UNIFAC model, one usng the VLE datas et (UNIFAC), the other usng the LLE data set (UNIF-LL). There are two modfcatons to the UNIFAC model. They are named after the locaton of the unverstes where they were developed: Lyngby n Denmark, and Dortmund n Germany. The correspondng property methods are UNIF-LBY and UNIF-DMD. Both modfcatons: Include more temperature-dependent terms of the group-group nteracton parameters Predct VLE and LLE wth a sngle set of parameters Predct heats of mxng better In the Dortmund modfcaton, the predcton for actvty coeffcents at nfnte dluton s mproved. For detals on the models, see Chapter 3. You can model the solublty of supercrtcal gases usng Henry s law. Henry coeffcents are avalable n the ASPEN PLUS databanks for many solutes wth water and other solvents (see ASPEN PLUS Physcal Property Data, Chapter 1). The optons sets wth a vapor phase model that can be used up to moderate pressures, have the Poyntng correcton ncluded n the lqud fugacty coeffcent calculaton (see the table labeled UNIFAC Property Methods on page 2-47). Heats of mxng are calculated usng the UNIFAC or modfed UNIFAC models Physcal Property Methods and Models Verson 10

107 Chapter 2 Mxture Types The UNIFAC and modfed UNIFAC models can handle any combnaton of polar and nonpolar compounds. Dssolved gas n solutons can be handled wth Henry s Law. However, gas-solvent nteractons are not predcted by UNIFAC. Range No component should be close to ts crtcal temperature. Approxmate temperature ranges are ndcated n the table labeled UNIFAC Property Methods on page The parameter sets for all UNIFAC models are regularly revsed and extended. The table labeled UNIFAC Property Methods on page 2-47 gves the revson number currently used n ASPEN PLUS. For detals on the parameters used, see Physcal Property Data, Chapter 3. The mnmum parameter requrements for the UNIFAC and modfed UNIFAC models are gven n the followng table. For detals about the models, see Chapter 3. Parameters Requred for the UNIFAC Property Methods Thermodynamc Propertes Models Parameter Requrements Lqud mxture Fugacty coeffcent, UNIFAC UFGRPD Gbbs energy or: Dortmund modfed UNIFAC UFGRPL or: Lyngby modfed UNIFAC Extended Antone vapor pressure Henry s constant Brelv-O Connell PLXANT Solvent: VC, Solute-solvent: HENRY Solvent: TC, PC, (ZC or RKTZRA), Solute: (VC or VLBROC) Enthalpy, Entropy Ideal gas heat capacty CPIG or CPIGDP Watson/DIPPR heat of vaporzaton UNIFAC TC, (DHVLWT or DHVLDP) UFGRP or: Dortmund modfed UNIFAC UFGRPD or: Lyngby modfed UNIFAC UFGRPL Densty Rackett TC, PC, (VC or VCRKT), (ZC or ZCRKT) Physcal Property Methods and Models 2-47 Verson 10

108 Property Method Descrptons UNIQUAC The property methods that use the UNIQUAC actvty coeffcent model are lsted n the followng table. UNIQUAC Property Methods Bnary Parameters Property Method Dataset Number VLE Name Lt Reg LLE Lt Reg Henry Lt Reg Vapor Phase EOS Name Poyntng Correcton UNIQUAC 1 X X X X X X Ideal Gas law UNIQ-2 2 X X X X X X Ideal Gas law UNIQ-RK 1 X X X Redlch-Kwong X UNIQ-HOC 1 X X X Hayden-O'Connell X UNIQ-NTH 1 X X Nothnagel X An X ndcates the parameters were obtaned from the lterature. An X ndcates the parameters were regressed by AspenTech from expermental data n the Dortmund Databank (DDB). The UNIQUAC model can descrbe strongly nondeal lqud solutons and lqudlqud equlbra. The model requres bnary parameters. Many bnary parameters for VLE and LLE, from lterature and from regresson of expermental data, are ncluded n the ASPEN PLUS databanks (for detals, see ASPEN PLUS Physcal Property Data, Chapter 1). You can model the solublty of supercrtcal gases usng Henry s law. Henry coeffcents are avalable from the databank (see ASPEN PLUS Physcal Property Data, Chapter 1). The property methods wth a vapor phase model that can be used up to moderate pressures, have the Poyntng correcton ncluded n the lqud fugacty coeffcent calculaton (see the table labeled UNIQUAC Property Methods on page 2-49). Heats of mxng are calculated usng the UNIQUAC model. You can use separate data sets for the UNIQUAC bnary parameters to model propertes or equlbra at dfferent condtons. It s also possble to use one data set for VLE and a second data set for LLE (use UNIQUAC and UNIQ-2). The property methods are dentcal except for the data set number they use. For example, you can use these optons sets n dfferent flowsheet sectons or column sectons Physcal Property Methods and Models Verson 10

109 Chapter 2 Mxture Types The UNIQUAC model can handle any combnaton of polar and non-polar compounds, up to very strong nondealty. Range Parameters should be ftted n the temperature, pressure, and composton range of operaton. No component should be close to ts crtcal temperature. Parameter requrements for the UNIQUAC actvty coeffcent model are gven n the followng table. For detals about the model, see Chapter 3. Parameters Requred for UNIQUAC Property Methods Thermodynamc Propertes Models Parameter Requrements Lqud mxture Fugacty coeffcent, Gbbs energy UNIQUAC lqud actvty coeffcent GMUQR, GMUQQ, UNIQ Extended Antone vapor pressure Henry s constant Brelv-O Connell PLXANT Solvent: VC, Solute-solvent: HENRY Solvent: TC, PC, (ZC or RKTZRA), Solute: (VC or VLBROC) Enthalpy, Entropy Ideal gas heat capacty CPIG or CPIGDP Watson/DIPPR heat of vaporzaton UNIQUAC lqud actvty coeffcent TC, (DHVLWT or DHVLDP) GMUQR, GMUQQ, UNIQ Densty Rackett TC, PC, (VC or VCRKT), (ZC or ZCRKT) Van Laar The property methods that use the Van Laar actvty coeffcent model are lsted n the followng table. Physcal Property Methods and Models 2-49 Verson 10

110 Property Method Descrptons Van Laar Property Methods Bnary Parameters Property Method Dataset number VLE Name Lt Reg LLE Lt Reg Henry Vapor Phase EOS Name Poyntng Lt Reg Correcton VANLAAR 1 X X Ideal Gas law VANL-2 2 X X Ideal Gas law VANL-RK 1 X X Redlch-Kwong X VANL-HOC 1 X X Hayden-O'Connell X VANL-NTH 1 X X Nothnagel X An X ndcates the parameters were obtaned from the lterature. An X ndcates the parameters were regressed by AspenTech from expermental data n the Dortmund Databank (DDB). The Van Laar model can descrbe nondeal lqud solutons wth postve devatons from Raoult s law (see Chapter 1). The model requres bnary parameters. You can model the solublty of supercrtcal gases usng Henry s law. Henry coeffcents are avalable from the ASPEN PLUS databank (see ASPEN PLUS Physcal Property Data, Chapter 1). The property methods wth a vapor phase model that can be used up to moderate pressures, have the Poyntng correcton ncluded n the lqud fugacty coeffcent calculaton (see the table labeled Van Laar Property Methods on page 2-51). Heats of mxng are calculated usng the Van Laar model. You can use separate data sets to model propertes or equlbra at dfferent condtons (use VANLAAR and VANL-2). The property methods are dentcal except for the data set number they use. For example, you can use these property methods n dfferent flowsheet or column sectons. Mxture Types The Van Laar model can handle any combnaton of polar and non-polar compounds wth postve devatons from Raoult s law. Range Parameters should be ftted n the temperature range of operaton. No component should be close to ts crtcal temperature. Parameter requrements for the Van Laar actvty coeffcent model are gven n the table labeled Parameters Requred for Van Laar Property Methods on page For detals about the model, see Chapter Physcal Property Methods and Models Verson 10

111 Chapter 2 Parameters Requred for Van Laar Property Methods Thermodynamc Propertes Models Parameter Requrements Lqud mxture Fugacty coeffcent, Gbbs energy Van Laar lqud actvty coeffcent VANL Extended Antone vapor pressure Henry s constant Brelv-O Connell PLXANT Solvent: VC, Solute-solvent: HENRY Solvent: TC, PC, ( ZC or RKTZRA), Solute: (VC or VLBROC) Enthalpy, Entropy Ideal gas heat capacty CPIG or CPIGDP Watson/DIPPR heat of vaporzaton Van Laar lqud actvty coeffcent TC, (DHVLWT or DHVLDP) VANL Densty Rackett TC, PC, (VC or VCRKT), (ZC or ZCRKT) Wlson The property methods that use the Wlson actvty coeffcent model are lsted n the followng table. Wlson Property Methods Bnary Parameters Property Method Dataset number VLE Name Lt Reg LLE Lt Reg Henry Lt Reg Vapor Phase EOS Name Poyntng Correcton WILSON 1 X X X X Ideal Gas law WILS-2 2 X X X X Ideal Gas law WILS-GLR 1 X X Ideal Gas law ---- WILS-LR 1 X X Ideal Gas law ---- WILS-RK 1 X X X Redlch-Kwong X WILS-HOC 1 X X X Hayden-O'Connell X WILS-NTH 1 X X Nothnagel X An X ndcates the parameters were obtaned from the lterature. An X ndcates the parameters were regressed by AspenTech from expermental data n the Dortmund Databank (DDB). Physcal Property Methods and Models 2-51 Verson 10

112 Property Method Descrptons The Wlson model can descrbe strongly nondeal lqud solutons. The model cannot handle two lqud phases. In that case use NRTL or UNIQUAC. The model requres bnary parameters. Many bnary parameters for VLE, from lterature and from regresson of expermental data, are ncluded n the ASPEN PLUS databanks (for detals, see ASPEN PLUS Physcal Property Data, Chapter 1). The solublty of supercrtcal gases can be modeled usng Henry s law. Henry coeffcents are avalable from the databank for many solutes wth water and other solvents (see ASPEN PLUS Physcal Property Data, Chapter 1). The property methods wth a vapor phase model that can be used up to moderate pressures, have the Poyntng correcton ncluded n the lqud fugacty coeffcent calculaton (see the table labeled Wlson Property Methods on page 2-52). Heats of mxng are calculated usng the Wlson model. You can use separate data sets for the Wlson bnary parameters to model propertes or equlbra at dfferent condtons (use WILSON and WILS-2). The property methods are dentcal except for the data set number they use. For example, you can use these property methods n dfferent flowsheet or column sectons. Mxture Types The Wlson model can handle any combnaton of polar and non-polar compounds, up to very strong nondealty. Range Parameters should be ftted n the temperature, pressure, and composton range of operaton. No component should be close to ts crtcal temperature. Parameter requrements for the Wlson actvty coeffcent model are gven n the table below. For detals about the model, see Chapter 3. Parameters Requred for the Wlson Property Methods Thermodynamc Propertes Models Parameter Requrements Lqud mxture Fugacty coeffcent, Gbbs energy Wlson lqud actvty coeffcent WILSON Extended Antone vapor pressure Henry s constant PLXANT Solvent: VC, Solute-solvent: HENRY Brelv-O Connell Solvent: TC, PC, (ZC or RKTZRA), Solute: (VC or VLBROC) 2-52 Physcal Property Methods and Models Verson 10

113 Chapter 2 Parameters Requred for the Wlson Property Methods (contnued) Thermodynamc Propertes Models Parameter Requrements Enthalpy, Entropy Ideal gas heat capacty Watson/DIPPR heat of vaporzaton Wlson lqud actvty coeffcent CPIG or CPIGDP TC, (DHVLWT or DHVLDP) WILSON Densty Rackett TC, PC, (VC or VCRKT), (ZC or ZCRKT) Common Models The followng table descrbes the models common to actvty coeffcent property methods and ther parameter requrements. Parameters Requred For Common Models General Property/Purpose Mass balance, Converson Mass-bass Mole-bass Converson Stdvol-bass Mole-bass Usng Free-water opton: solublty of water n organc phase Enthalpy of reacton Gbbs energy of reacton Parameter Requrements MW VLSTD WATSOL DHFORM DGFORM Transport Propertes Property Models Parameter Requrements Vapor mxture Vscosty Chapman-Enskog-Brokaw/ DIPPR MW; (MUP and (STKPAR or LJPAR)) or MUVDIP Thermal conductvty Stel-Thodos low pres./ DIPPR MW or KVDIP Dffusvty Chapman-Enskog-Wlke-Lee MW; MUP and (STKPAR or LJPAR) Surface tenson Hakm-Stenberg-Stel/ DIPPR (TC, PC, OMEGA) or SIGDIP Lqud mxture Vscosty Andrade/DIPPR MULAND or MULDIP Thermal Conductvty Sato-Redel/DIPPR (MW, TC, TB) or KLDIP Dffusvty Wlke-Chang MW, VB Physcal Property Methods and Models 2-53 Verson 10

114 Property Method Descrptons Electrolyte Property Methods The followng table lsts property methods for electrolyte solutons. Electrolyte solutons are extremely nondeal because of the presence of charged speces. Property methods based on correlatons can handle specfc components under well-descrbed condtons; rgorous models are generally applcable. The ELECNRTL property method can handle mxed solvent systems at any concentraton. The PITZER property method s accurate for aqueous solutons up to 6M. Bnary parameters for many component pars are avalable n the databanks. B-PITZER s predctve but less accurate. You can use these property methods at low pressures (maxmum 10 atm). ENRTL-HF s smlar to ELECNRTL, but wth a vapor phase model for the strong HF assocaton. Ths property method should be used at low pressures (maxmum 3 atm). Permanent gases n lqud soluton can be modeled by usng Henry s law. Transport propertes are calculated by standard correlatons wth correctons for the presence of electrolytes. Electrolyte Property Methods Correlaton-Based Property Methods Property Method Correlaton System AMINES Kent-Esenberg MEA, DEA, DIPA, DGA APISOUR API Sour water correlaton H2O, NH3, CO2, H2S Actvty Coeffcent Model-Based Property Methods Property Method Gamma Model Name Vapor Phase EOS Name ELECNRTL Electrolyte NRTL Redlch-Kwong ENRTL-HF Electrolyte NRTL HF equaton of state ENRTL-HG Electrolyte NRTL Redlch-Kwong PITZER Ptzer Redlch-Kwong-Soave PITZ-HG Ptzer Redlch-Kwong-Soave B-PITZER Bromley-Ptzer Redlch-Kwong-Soave Common Models For Rgorous Property Methods Property Model Vapor pressure Lqud molar volume Extended Antone Rackett/Clarke contnued 2-54 Physcal Property Methods and Models Verson 10

115 Chapter 2 Common Models For Rgorous Property Methods (contnued) Property Model Heat of vaporzaton Infnte dluton heat capacty Vapor vscosty Vapor thermal conductvty Vapor dffusvty Surface tenson Lqud vscosty Lqud thermal conductvty Lqud dffusvty Watson/DIPPR Crss-Cobble Chapman-Enskog-Brokaw Stel-Thodos/DIPPR Dawson-Khoury-Kobayash Hakm-Stenberg-Stel/DIPPR - Onsager-Samara Andrade/DIPPR - Jones-Dole Sato-Redel/DIPPR - Redel Wlke-Chang - Nernst-Hartley Do not use the electrolyte property methods for nonelectrolyte systems. See Classfcaton of Property Methods and Recommended Use on page 2-2 for more help. For general thermodynamc prncples, see Chapter 1. Chapter 5 contans specfcs on electrolyte smulaton. For detals on methods, see Chapter 4. The property method descrptons gve the mnmum parameter requrements for the thermodynamc property models used, also of the common thermodynamc property models. The general and transport property parameter requrements for coeffcent-based property methods are n the table labeled Parameters Requred for General and Transport Property Models on page For detals on models, see Chapter 3. AMINES The AMINES property methoduses the Kent-Esenberg method for K-values and enthalpy. It s desgned for systems contanng water, one of four ethanolamnes, hydrogen sulfde, carbon doxde, and other components typcally present n gassweetenng processes. It can be used for the followng four amnes: Monoethanolamne (MEA) Dethanolamne (DEA) Dsopropanolamne (DIPA) Dglycolamne (DGA) Physcal Property Methods and Models 2-55 Verson 10

116 Property Method Descrptons Range Use the AMINES property method for amne systems wth ranges of: MEA DEA DIPA DGA Temperature ( F) Maxmum H2s or CO2 Loadng (moles gas/mole amne) Amne Concentraton n Soluton (mass percent) If the amne concentraton s outsde the recommended range, the Chao-Seader method s used for K-values (only for that partcular property evaluaton). Refer to the followng table for parameter requrements for ths property method. Parameters Requred for the AMINES Property Method General Property/Purpose Mass balance, Converson Mass-bass Mole-bass Converson Stdvol-bass Mole-bass Usng free-water opton: solublty of water n organc phase Enthalpy of reacton Gbbs energy of reacton Parameter Requrements MW VLSTD WATSOL DHFORM DGFORM Thermodynamc Propertes Propertes Models Parameter Requrements Vapor mxture Fugacty coeffcent Densty Redlch-Kwong, TC; PC Enthalpy, entropy Ideal gas heat capacty/dippr CPIG or CPIGDP Lqud mxture Fugacty coeffcent Gbbs energy Scatchard-Hldebrand actvty coeffcent Chao-Seader pure component fugacty coeffcent TC; DELTA; VLCVT1; GMSHVL TC; PC; OMEGA contnued 2-56 Physcal Property Methods and Models Verson 10

117 Chapter 2 Thermodynamc Propertes (contnued) Propertes Models Parameter Requrements Extended Antone vapor pressure (amnes and water only) PLXANT Kent-Esenberg (H2S and CO2 only) Enthalpy, entropy Watson heat of vaporzaton and DIPPR model TC; PC;DHVLWT or DHVLDP Densty Rackett molar volume TC; PC: VC or VCRKT; ZC or ZCRKT Transport Propertes Propertes Models Parameter Requrements Vapor mxture Dean-Stel Vscosty MW; (MUP and (STKPAR or LJPAR)) or MUVDIP; TC, PC, VC Thermal conductvty Stel-Thodos MW, TC, PC, VC, ZC Dffusvty Dawson-Khoury-Kobayask MW; MUP and (STKPAR or LJPAR); VC Surface tenson Hakm-Stenberg-Stel/ DIPPR (TC, PC, OMEGA) or SIGDIP Lqud mxture Vscosty Andrade/DIPPR MULAND or MULDIP Thermal Conductvty Sato-Redel/DIPPR (MW, TC, TB) or KLDIP Dffusvty Wlke-Chang MW, VB APISOUR The APISOUR property method: Uses the API procedure for K-values and enthalpy of sour water systems. Is desgned for sour water systems contanng only water, ammona, hydrogen sulfde and carbon doxde. Is applcable n the temperature range of C. Has an overall average error between measured and predcted partal pressures of about 30% for ammona, carbon doxde, and hydrogen sulfde. Does not requre any user-suppled parameters. Is recommended for fast smulaton of sour water systems at lmted concentraton. For more accurate results, use the ELECNRTL property method. Parameter requrements for the APISOUR property method are lsted n the followng table. Physcal Property Methods and Models 2-57 Verson 10

118 Property Method Descrptons Parameters Requred for the APISOUR Property Method General Property/Purpose Mass balance, Converson Mass-bass Mole-bass Converson Stdvol-bass Mole-bass Usng Free-water opton: solublty of water n organc phase Enthalpy of reacton Gbbs energy of reacton Parameter Requrements MW VLSTD WATSOL DHFORM DGFORM Transport Propertes Propertes Models Parameter Requrements Vapor mxture Vscosty Chapman-Enskog-Brokaw/ DIPPR MW; (MUP and (STKPAR or LJPAR)) or MUVDIP Thermal conductvty Stel-Thodos low pres./ DIPPR MW or KVDIP Dffusvty Chapman-Enskog-Wlke-Lee MW; MUP and (STKPAR or LJPAR) Surface tenson Hakm-Stenberg-Stel/ DIPPR (TC, PC, OMEGA) or SIGDIP Lqud mxture Vscosty Andrade/DIPPR MULAND or MULDIP Thermal Conductvty Sato-Redel/DIPPR (MW, TC, TB) or KLDIP Dffusvty Wlke-Chang MW, VB ELECNRTL The ELECNRTL property methods the most versatle electrolyte property method. It can handle very low and very hgh concentratons. It can handle aqueous and mxed solvent systems. The ELECNRTL s fully consstent wth the NRTL-RK property method: the molecular nteractons are calculated exactly the same way, therefore ELECNRTL can use the databank for bnary molecular nteracton parameters for the NRTL-RK property method. Many bnary and par parameters and chemcal equlbrum constants from regresson of expermental data are ncluded n ASPEN PLUS databanks. See ASPEN PLUS Physcal Property Data, Chapter 2, for detals on the systems ncluded, the sources of the data, and the ranges of applcaton Physcal Property Methods and Models Verson 10

119 Chapter 2 The solublty of supercrtcal gases can be modeled usng Henry s law. Henry coeffcents are avalable from the databank (see Chapter 1). Heats of mxng are calculated usng the electrolyte NRTL model. The Redlch-Kwong equaton of state s used for all vapor phase propertes, whch cannot model assocaton behavor n the vapor phase as occurs wth carboxylc acds or HF. For carboxylc acds, choose Hayden-O Connell or Nothnagel; for HF choose ENRTL-HF. Mxture Types Any lqud electrolyte soluton unless there s assocaton n the vapor phase. Range Vapor phase propertes are descrbed accurately up to medum pressures. Interacton parameters should be ftted n the range of operaton. The parameter requrements for the ELECNRTL property method are gven n the followng table, Parameters Requred for the ELECNRTL Property Method, and Parameters Requred for General and Transport Property Models on page For detals about the model see Chapter 3. Parameters Requred for the ELECNRTL Property Method Thermodynamc Propertes Models Parameter Requrements Vapor mxture Fugacty coeffcent, Densty Redlch-Kwong TC, PC Enthalpy, Entropy, Gbbs energy Lqud mxture Fugacty coeffcent, Gbbs energy [Ideal gas heat capacty/ DIPPR/ Barn correlaton and Redlch-Kwong Electrolyte NRTL Extended Antone vapor pressure Henry s constant CPIG or CPIGDP or CPIXP1, CPIXP2, CPIXP3] TC, PC Mol.: CPDIEC Ion: RADIUS Mol.-Mol.: NRTL Mol.-Ion, Ion-Ion: GMELCC, GMELCD GMELCE, GMELCN PLXANT Solvent: VC, Mol. solute-solvent: HENRY contnued Physcal Property Methods and Models 2-59 Verson 10

120 Property Method Descrptons Parameters Requred for the ELECNRTL Property Method (contnued) Thermodynamc Propertes Models Parameter Requrements Enthalpy, Entropy Brelv-O Connell [Ideal gas heat capacty/ DIPPR and Watson/DIPPR heat of vaporzaton or [Infnte dluton heat capacty / Crss-Cobble Electrolyte NRTL Solvent: TC, PC, (ZC or RKTZRA), Mol. solute: (VC or VLBROC) CPIG or CPIGDP Solvent: TC, (DHVLWT or DHVLDP)] Ions: CPAQ0 or Ions: IONTYP, S025C ] Mol.: CPDIEC Ion: RADIUS Mol.-Mol.: NRTL Mol.-Ion, Ion-Ion: GMELCC, GMELCD GMELCE, GMELCN Densty Rackett/Clarke Mol.: TC, PC, (VC or VCRKT), (ZC or ZCRKT) Ion-on: VLCLK Sold pure (and mxture) Enthalpy, Entropy Solds heat capacty polynomal/ Barn correlaton CPSP01 or CPSXP1 to CPSXP7 Densty Solds molar volume polynomal VSPOLY ENRTL-HF The ENRTL-HF property method s smlar to the ELECNRTL property method except that t uses the HF equaton of state as vapor phase model. The HF equaton of state predcts the strong assocaton of HF n the vapor phase at low pressures. Assocaton (manly hexamerzaton) affects both vapor phase propertes (for example, enthalpy and densty) and lqud phase propertes (for example, enthalpy). A data package s avalable to accurately model vapor and lqud phases of HF and water mxtures n any proporton. Mxture Types The HF equaton of state relably predcts the strong assocaton effects of HF n the vapor phase. The lqud can be any lqud electrolyte soluton. Range Usage should not exceed pressures of 3 atm Physcal Property Methods and Models Verson 10

121 Chapter 2 Parameters for the HF equaton of state are bult-n for temperatures up to 373 K. Parameters can be entered and regressed usng the ASPEN PLUS Data Regresson System (DRS) f needed. For detals about the model, see Chapter 3. For the parameter requrements for the electrolyte NRTL model, refer to the ELECNRTL property method, n the table labeled Parameters Requred for the ELECNRTL Property Method on page For general and transport property parameter requrements, see the table labeled Parameters Requred for General and Transport Property Models on page ENRTL-HG The ENRTL-HG property method s smlar to the ELECNRTL property method, except t uses the Helgeson model for standard propertes calculatons. The Helgeson model s a very accurate and flexble equaton of state that calculates standard enthalpy, entropy, Gbbs free energy and volume for components n aqueous solutons. The Helgeson model should provde more accurate enthalpy and Gbbs free energy of process streams up to hgh temperatures and pressures. The model s also used to calculate Gbbs free energy for use n estmatng chemcal equlbrum constants (for both equlbrum and salt precptaton reactons) when they are mssng. Equlbrum constants calculated usng the Helgeson model have been found to be reasonably accurate and extrapolate well wth respect to temperature. Mxture Types Any lqud electrolyte soluton s acceptable, unless there s assocaton n the vapor phase. Range Vapor phase propertes are descrbed accurately up to medum pressures. Interacton parameters should be ftted n the range of operaton. For parameter requrements for the electrolyte NRTL model, see the ELECNRTL property method, n the table labeled Parameters Requred for the ELECNRTL Property Method on page For general and transport property parameter requrements, see the table labeled Parameters Requred for General and Transport Property Models on page Physcal Property Methods and Models 2-61 Verson 10

122 Property Method Descrptons PITZER The PITZER property method s based on an aqueous electrolyte actvty coeffcent model. It has no overlap wth other actvty coeffcent models. It can accurately calculate the behavor of aqueous electrolyte solutons wth or wthout molecular solutes up to 6 molal onc strength. Many nteracton parameters from regresson of expermental data are ncluded n databanks and data packages (for detals, see Chapter 1). You can model the solublty of supercrtcal gases usng Henry s law. Henry coeffcents are avalable from the ASPEN PLUS databanks (see Chapter 1). Heats of mxng are calculated usng the Ptzer model. The Redlch-Kwong-Soave equaton of state s used for the vapor phase fugacty coeffcent, all other vapor phase propertes are assumed deal. Redlch-Kwong- Soave cannot model assocaton behavor n the vapor phase (for example, carboxylc acds or HF). For carboxylc acds, choose a non-electrolyte actvty coeffcent model wth Hayden-O Connell or Nothnagel; for HF choose ENRTL- HF or WILS-HF. Mxture Types You can use the Ptzer model for any aqueous electrolyte soluton up to 6M onc strength, not showng assocaton n the vapor phase. Range Vapor phase fugactes are descrbed accurately up to medum pressures. Interacton parameters should be ftted n the range of operaton. The parameter requrements for the PITZER property method are gven n the table labeled Parameters Requred for the PITZER Property Method on page 2-63 and the table labeled Parameters Requred for General and Transport Property Models on page For detals about the model, see Chapter Physcal Property Methods and Models Verson 10

123 Chapter 2 Parameters Requred for the PITZER Property Method Thermodynamc Propertes Models Parameter Requrements Vapor mxture Fugacty coeffcent, Densty Enthalpy, Entropy, Gbbs energy Lqud mxture Fugacty coeffcent, Gbbs energy Enthalpy, Entropy Redlch-Kwong-Soave [Ideal gas heat capacty/ DIPPR/ Barn correlaton and Redlch-Kwong Ptzer Extended Antone vapor pressure Henry's constant Brelv-O'Connell [Ideal gas heat capacty/ DIPPR and Watson/DIPPR heat of vaporzaton or [Infnte dluton heat capacty / TC, PC, OMEGA CPIG or CPIGDP or CPIXP1, CPIXP2, CPIXP3] TC, PC, OMEGA Caton-anon: GMPTB0, GMPTB1, GMPTB2, GMPTB3, GMPTC Caton-caton: GMPTTH Anon-anon: GMPTTH Caton1-caton2-common anon: GMPTPS Anon1-anon2-common caton: GMPTPS Molecule-on, Mol. Mol.: GMPTB0, GMPTB1, GMPTC PLXANT Solvent: VC, Mol. Solute-solvent: HENRY Solvent: TC, PC, (ZC or RKTZRA), Mol. Solute: (VC or VLBROC) CPIG or CPIGDP Solvent: TC, (DHVLWT or DHVLDP)] Ions: CPAQ0 or Crss-Cobble Ions: IONTYP, S025C ] Ptzer Caton-anon: GMPTB0,GMPTB1,GMPTB2,GMPTB3,GMPT C Caton-caton: GMPTTH Anon-anon: GMPTTH Caton1-caton2-common anon: GMPTPS Anon1-anon2-common caton: GMPTPS Molecule-on, Mol. Mol.: GMPTB0,GMPTB1,GMPTC Densty Rackett/Clarke Mol.: TC, PC, (VC or VCRKT), (ZC or ZCRKT) Ion-on: VLCLK contnued Physcal Property Methods and Models 2-63 Verson 10

124 Property Method Descrptons Parameters Requred for the PITZER Property Method (contnued) Thermodynamc Propertes Models Parameter Requrements Sold pure (and mxture) Enthalpy, Entropy Solds heat capacty polynomal/ Barn correlaton CPSP01 or CPSXP1 to CPSXP7 Densty Solds molar volume polynomal VSPOLY B-PITZER The B-PITZER property method s based on the smplfed Ptzer aqueous electrolyte actvty coeffcent model, whch neglects thrd order nteractons. It can predct the behavor of aqueous electrolyte solutons up to 6 molal onc strength. It s not as accurate as ELECNRTL or PITZER wth ftted parameters. But, t s better than usng these property methods wthout nteracton parameters. You can model the solublty of supercrtcal gases usng Henry s law. Henry coeffcents are avalable from the ASPEN PLUS databanks (see Chapter 1). Heats of mxng are calculated usng the Bromley-Ptzer model. The Redlch-Kwong-Soave equaton of state s used for the vapor phase fugacty coeffcent. All other vapor phase propertes are assumed deal. Redlch-Kwong- Soave cannot model assocaton behavor n the vapor phase (for example wth carboxylc acds or HF). For carboxylc acds, choose a non-electrolyte actvty coeffcent model wth Hayden-O Connell or Nothnagel; for HF, choose ENRTL- HF or WILS-HF. Mxture Types You can use the B-PITZER model for any aqueous electrolyte soluton up to 6M onc strength, not showng assocaton n the vapor phase. Range Vapor phase fugactes are descrbed accurately up to medum pressures. Interacton parameters should be ftted n the range of operaton. The parameter requrements for the B-PITZER property method are gven n the table labeled Parameters Requred for the B-PITZER Property Method on page 2-65 and the table labeled Parameters Requred for General and Transport Property Models on page For detals about the model, see Chapter Physcal Property Methods and Models Verson 10

125 Chapter 2 Parameters Requred for the B-PITZER Property Method Thermodynamc Propertes Models Parameter Requrements Vapor mxture Fugacty coeffcent, Densty Redlch-Kwong-Soave TC, PC, OMEGA Enthalpy, Entropy, Gbbs energy Lqud mxture Fugacty coeffcent, Gbbs energy Enthalpy, Entropy [Ideal gas heat capacty/ DIPPR/ Barn correlaton and Redlch-Kwong Bromley-Ptzer Extended Antone vapor pressure Henry s constant Brelv-O Connell [Ideal gas heat capacty/ DIPPR and Watson/DIPPR heat of vaporzaton or[infnte dluton heat capacty / Crss-Cobble Bromley-Ptzer CPIG or CPIGDP or CPIXP1, CPIXP2, CPIXP3] TC, PC, OMEGA Ionc: GMBPB, GMBPD Optonal: Caton-anon: GMPTB0, GMPTB1, GMPTB2, GMPTB3 Caton-caton: GMPTTH Anon-anon: GMPTTH Molecule-on, Mol.-Mol.: GMPTB0, GMPTB1 PLXANT Solvent: VC, Mol. Solute-solvent: HENRY Solvent: TC, PC, (ZC or RKTZRA), Mol. Solute: (VC or VLBROC) CPIG or CPIGDP Solvent: TC, (DHVLWT or DHVLDP)] Ions: CPAQ0 or Ions: IONTYP, S025C ] Ionc: GMBPB, GMBPD Optonal: Caton-anon: GMPTB0, GMPTB1, GMPTB2, GMPTB3 Caton-caton:GMPTTH Anon-anon: GMPTTH Molecule-on, Mol.-Mol.: GMPTB0, GMPTB1 Densty Rackett/Clarke Mol.: TC, PC, (VC or VCRKT), (ZC or ZCRKT) Ion-on: VLCLK Sold pure (and mxture) Enthalpy, Entropy Solds heat capacty polynomal/ Barn correlaton CPSP01 or CPSXP1 to CPSXP7 Densty Solds molar volume polynomal VSPOLY Physcal Property Methods and Models 2-65 Verson 10

126 Property Method Descrptons PITZ-HG The PITZ-HG property method s smlar to the PITZER property method, except t uses the Helgeson model for standard propertes calculatons. The Helgeson model s a very accurate and flexble equaton of state that calculates standard enthalpy, entropy, Gbbs free energy and volume for components n aqueous solutons. The Helgeson model should provde more accurate enthalpy and Gbbs free energy of process streams up to hgh temperatures and pressures. The Helgeson model s also used to calculate Gbbs free energy for use n estmatng chemcal equlbrum constants (for both equlbrum and salt precptaton reactons) when they are mssng. Equlbrum constants calculated usng the Helgeson model have been found to be reasonably accurate and extrapolate well wth respect to temperature. Mxture Types You can use ths property method for any aqueous electrolyte soluton up to 6M onc strength, not showng assocaton n the vapor phase. Range Vapor phase fugactes are descrbed accurately up to medum pressures. Interacton parameters should be ftted n the range of operaton. The parameter requrements for the PITZ-HG property method are gven n the table labeled Parameters Requred for the PITZER Property Method on page 2-63 and the followng table, Parameters Requred for General and Transport Property Models. For detals about the model, see Chapter 3. General and Transport Property Model Parameter Requrements The followng table descrbes the general and transport property models used and ther parameter requrements for actvty coeffcent-based electrolyte property methods. Parameters Requred for General and Transport Property Models General Property/Purpose Parameter Requrements Mass balance, Contnued 2-66 Physcal Property Methods and Models Verson 10

127 Chapter 2 General (contnued) Property/Purpose Converson Massbass Mole-bass Enthalpy of reacton Gbbs energy of reacton Parameter Requrements MW Solvents, Mol. Solutes: DHFORM Solds, Salts: (DHSFRM or CPSXP1 to CPSXP7) Ions: DHAQFM Solvents, Mol. Solutes: DGFORM Solds,Salts: (DGSFRM or CPSXP1 to CPSXP7) Ions: DGAQFM Transport Propertes Property Models Parameter Requrements Vapor mxture Vscosty Chapman-Enskog-Brokaw/ DIPPR MW; (MUP and (STKPAR or LJPAR)) or MUVDIP Thermal conductvty Stel-Thodos low pres./ DIPPR MW or KVDIP Dffusvty Chapman-Enskog-Wlke-Lee MW; MUP and (STKPAR or LJPAR) Surface tenson Lqud mxture Hakm-Stenberg-Stel/ DIPPR Onsager- Samaras Solv., Mol.sol.: (TC, PC, OMEGA) or SIGDIP Ion: CHARGE Vscosty Andrade/DIPPR Jones-Dole Solv., Mol.sol.: MULAND or MULDIP Ion: IONMUB, IONMOB Thermal Conductvty Sato-Redel/ DIPPR Redel Solv., Mol.sol.: (MW, TC, TB) or KLDIP Ion: IONRDL Dffusvty Wlke-Chang/ Nernst-Hartley Solv., Mol.sol.: MW, VB Ion: CHARGE, IONMOB Only for rgorous electrolyte property methods Solds Handlng Property Method The SOLIDS property method s desgned for many knds of solds processng: Coal processng Pyrometallurgcal processes Mscellaneous other solds processng (such as starch and polymers) Physcal Property Methods and Models 2-67 Verson 10

128 Property Method Descrptons The propertes of solds and flud phases cannot be calculated wth the same type of models. Therefore the components are dstrbuted over the substreams of types MIXED, CISOLID and NC and ther propertes are calculated wth approprate models (for detals on the use of substreams, see ASPEN PLUS User Gude, Chapter 9). Durng the mechancal processng of raw materals (ore, coal, wood), physcal propertes can often be handled as nonconventonal components wth an overall densty and an overall heat capacty. The characterzaton of nonconventonal components and the specfcaton of property models s dscussed n the ASPEN PLUS User Gude, Chapter 7. Detals on nonconventonal property methods and models are gven n chapters 1 and 3 of ths manual, respectvely. When the solds are decomposed nto ndvdual components (for example, to selectvely undergo chemcal reactons), they occur n the CISOLID substream. The property models for these components are pure component property models of the polynomal type. The components are not n phase equlbrum wth the flud components. Some examples are coal dust n ar, burnng carbon, and sand n water. In pyrometallurgcal applcatons, a CISOLID component can be n smultaneous phase and chemcal equlbrum. Ths can happen only n the RGIBBS model, an equlbrum reactor based on Gbbs energy mnmzaton. Under other condtons, the CISOLID component can undergo reactons but not phase equlbrum. As another excepton, homogeneous sold mxture phases can occur n the same reactor. The nondealty of sold mxtures can be handled usng actvty coeffcent models. To dstngush a sold mxture from sngle CISOLID components, they are placed n the MIXED substream. In pyrometallurgcal applcatons, many phases can occur smultaneously. These phases may need to be treated wth dfferent actvty coeffcent models (use the SOLIDS property method). For detals, see ASPEN PLUS Gettng Started Modelng Processes wth Solds. Flud components always occur n the MIXED substream. They are treated wth the same flud phase models as dscussed n IDEAL. If non-dealty n the lqud phase occurs, the deal actvty coeffcent model can be replaced. Permanent gases may be dssolved n the lqud. You can model them usng Henry s law, whch s vald at low concentratons. Hydrometallurgcal applcatons cannot be handled by the SOLIDS property method. Use an electrolyte property method. The transport property models for the vapor phase are all well suted for deal gases. The transport property models for the lqud phase are emprcal equatons for fttng of expermental data. The followng table lsts the models used n the SOLIDS property method and ther parameter requrements. For detals on these models, see Chapter Physcal Property Methods and Models Verson 10

129 Chapter 2 Parameters Requred for the SOLIDS Property Method General Property/Purpose Mass balance, Converson Massbass Mole-bass Converson Stdvol-bass Mole-bass Free-water opton: solublty of water n organc phase Enthalpy of reacton Gbbs energy of reacton Parameter Requrements MW VLSTD WATSOL DHFORM, (DHSFRM or CPSXP1 to CPSXP7) DGFORM, (DGSFRM or CPSXP1 to CPSXP7) Thermodynamc Propertes Property Models Parameter Requrements Vapor pure and mxture Fugacty Coeffcent Enthalpy, Entropy, Gbbs energy Ideal gas law Ideal gas heat capacty/ DIPPR/ Barn correlaton CPIG or CPIGDP or CPIXP1, CPIXP2, CPIXP3 Densty Lqud pure and mxture Fugacty Coeffcent, Gbbs energy Ideal gas law Extended Antone vapor pressure/ Barn correlaton PLXANT or CPIXP1, CPIXP2 Ideal lqud actvty coeffcent Henry's constant Brelv-O'Connell Solvent: VC, Solute-solvent: HENRY Solvent: TC, PC, (ZC or RKTZRA), Solute: (VC or VLBROC) Lqud pure and mxture Enthalpy, Entropy [Ideal gas heat capacty/ DIPPR and Watson/DIPPR heat of vaporzaton CPIG or CPIGDP TC, (DHVLWT or DHVLDP)] contnued Physcal Property Methods and Models 2-69 Verson 10

130 Property Method Descrptons Thermodynamc Propertes (contnued) Property Models Parameter Requrements Densty Sold pure (and mxture) Fugacty Coeffcent, Gbbs energy DIPPR heat capacty correlaton/ Barn correlaton Constant Volume, Ideal mxng Extended Antone vapor pressure/ Barn correlaton (CPLDIP or CPLXP1, CPLXP2 VLCONS PLXANT CPSXP1 to CPSXP7 Ideal lqud actvty coeffcent Enthalpy, Entropy Solds heat capacty polynomal/ Barn correlaton CPSP01 or CPSXP1 to CPSXP7 Densty Solds molar volume polynomal VSPOLY Transport Propertes Property Models Parameter Requrements Vapor pure and mxture Vscosty Thermal conductvty DIPPR Chapman-Enskog-Brokaw/ DIPPR Stel-Thodos low pres./ KVDIP MW; (MUP and (STKPAR or LJPAR)) or MUVDIP MW or Dffusvty Chapman-Enskog-Wlke-Lee MW; MUP and (STKPAR or LJPAR) Surface tenson Lqud pure and mxture Hakm-Stenberg-Stel/ DIPPR (TC, PC, OMEGA) or SIGDIP Vscosty Andrade/DIPPR MULAND or MULDIP Thermal Conductvty Sato-Redel/DIPPR (MW, TC, TB) or KLDIP Dffusvty Wlke-Chang MW, VB Solds pure Thermal Conductvty Solds, polynomal KSPOLY 2-70 Physcal Property Methods and Models Verson 10

131 Chapter 2 Steam Tables The followng table lsts the names of the two steam table property methods avalable n ASPEN PLUS. Steam Tables Property Methods Property Method Name Models Steam Tables: STEAM-TA STEAMNBS ASME 1967 NBS/NRC 1984 Common models: IAPS vapor vscosty IAPS vapor thermal conductvty IAPS surface tenson IAPS lqud vscosty IAPS lqud thermal conductvty Steam tables can calculate all thermodynamc propertes for systems contanng pure water or steam. For mxtures of water and other components, refer to the begnnng of ths chapter for more help. The NBS/NRC steam tables are more recent and accurate. The transport property models for both property methods are from the Internatonal Assocaton for Propertes of Steam (IAPS). All models have bult-n parameters. For detals, see Chapter 3. STEAM-TA The STEAM-TA property method uses the: 1967 ASME steam table correlatons for thermodynamc propertes Internatonal Assocaton for Propertes of Steam (IAPS) correlatons for transport propertes Use ths property method for pure water and steam. ASPEN PLUS uses STEAM-TA as the default property method for the free-water phase, when freewater calculatons are performed. Physcal Property Methods and Models 2-71 Verson 10

132 Property Method Descrptons Range Use the STEAM-TA property method for pure water and steam wth temperature ranges of K to 1073 K. The maxmum pressure s 1000 bar. STEAMNBS The STEAMNBS property method uses: 1984 NBS/NRC steam table correlatons for thermodynamc propertes Internatonal Assocaton for Propertes of Steam (IAPS) correlatons for transport propertes Use ths property method for pure water and steam. Range Use the STEAMNBS property method for pure water and steam wth temperature ranges of K to 2000 K. The maxmum pressure s over bar Physcal Property Methods and Models Verson 10

133 Chapter 3 3 Property Model Descrptons Ths chapter descrbes the property models avalable n ASPEN PLUS and defnes the parameters used n each model. The descrpton for each model lsts the parameter names used to enter values n ASPEN PLUS on the Propertes Parameters forms. Many parameters have default values ndcated n the Default column. A dash ( ) ndcates that the parameter has no default value and you must provde a value. If a parameter s mssng, smulaton calculatons stop. The lower lmt and upper lmt for each parameter, when avalable, ndcate the reasonable bounds for the parameter. The lmts are used to detect grossly erroneous parameter values. The property models are dvded nto the followng categores: Thermodynamc property models Transport property models Nonconventonal sold property models The property types for each category are dscussed n separate sectons of ths chapter. The followng table provdes an organzatonal overvew of ths chapter. The tables labeled Thermodynamc Property Models, Transport Property Models, and Nonconventonal Sold Property Models n ths chapter present detaled lsts of models. These tables also lst the ASPEN PLUS model names, and ther possble use n dfferent phase types, for pure components and mxtures. Electrolyte and conventonal sold property models are presented n Thermodynamc Property Models, ths chapter. For more detals on electrolyte coeffcent models, see Appendces A, B, and C. Physcal Property Methods and Models 3-1 Verson 10

134 Property Model Descrptons Categores of Models Category Sectons Detals Thermodynamc Property Models Transport Property Models Nonconventonal Sold Property Models Equaton-of-State Models Actvty Coeffcent Models Vapor Pressure and Lqud Fugacty Models Heat of Vaporzaton Models Molar Volume and Densty Models Heat Capacty Models Solublty Correlatons Other Vscosty Models Thermal Conductvty Models Dffusvty Models Surface Tenson Models General Enthalpy and Densty Models Enthalpy and Densty Models for Coal and Char Thermodynamc Property Models Transport Property Models Nonconventonal Sold Property Models 3-2 Physcal Property Methods and Models Verson10

135 Chapter 3 Thermodynamc Property Models Ths secton descrbes the avalable thermodynamc property models n ASPEN PLUS. The followng table provdes a lst of avalable models, wth correspondng ASPEN PLUS model names. The table provdes phase types for whch the model can be used and nformaton on use of the model for pure components and mxtures. ASPEN PLUS thermodynamc property models nclude classcal thermodynamc property models, such as actvty coeffcent models and equatons of state, as well as solds and electrolyte models. The models are grouped accordng to the type of property they descrbe. Thermodynamc Property Models Equaton-of-State Models Property Model Model Name(s) Phase(s) Pure Mxture ASME Steam Tables ESH2O0, ESH2O V L X BWR-Lee-Starlng ESBWR0, ESCSTBWR V L X X Hayden-O'Connell ESHOC0, ESHOC V X X HF equaton-of-state ESHF0, ESHF V X X Ideal Gas 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 Nothnagel ESNTH0, ESNTH V X X Peng-Robnson-Boston-Mathas ESPR0, ESPR V L X X Peng-Robnson-Wong-Sandler ESPRWS0, ESPRWS V L X X Peng-Robnson-MHV2 ESPRV20, ESPRV2 V L X X Predctve SRK ESRKSV10, ESRKSV1 V L X X Redlch-Kwong ESRK0, ESRK V X X Redlch-Kwong-Aspen ESRKA0, ESRKA V L X X Redlch-Kwong-Soave-Boston-Mathas ESRKS0, ESRKS V L X X Redlch-Kwong-Soave-Wong-Sandler ESRKSWS0, ESRKSWS V L X X V = Vapor; L = Lqud; S = Sold An X ndcates applcable to Pure or Mxture contnued Physcal Property Methods and Models 3-3 Verson 10

136 Property Model Descrptons Equaton-of-State Models (contnued) Property Model Model Name(s) Phase(s) Pure Mxture Redlch-Kwong-Soave-MHV2 ESRKSV20, ESRKSV2 V L X X Standard Peng-Robnson ESPRSTD0, ESPRSTD V L X X Standard Redlch-Kwong-Soave ESRKSTD0, ESRKSTD V L X X Peng-Robnson Alpha functons V L X RK-Soave Alpha functons V L X Huron-Vdal mxng rules V L X MHV2 mxng rules V L X PSRK mxng rules V L X Wong-Sandler mxng rules V L X Actvty Coeffcent Models Property Model Model Name Phase(s) Pure Mxture Bromley-Ptzer (Chen-Null) GMPT2 L X Chen-Null GMCHNULL L X Constant Actvty Coeffcent GMCONS S X Electrolyte NRTL GMELC L L1 L2 X Ideal Lqud GMIDL L X NRTL (Non-Random-Two-Lqud) GMRENON L L1 L2 X Ptzer GMPT1 L X Polynomal Actvty Coeffcent GMPOLY S X Redlch-Kster GMREDKIS L S X Scatchard-Hldebrand GMXSH L X Three-Suffx Margules GMMARGUL L S X UNIFAC GMUFAC L L1 L2 X UNIFAC (Lyngby modfed) GMUFLBY L L1 L2 X UNIFAC (Dortmund modfed) GMUFDMD L L1 L2 X UNIQUAC GMUQUAC L L1 L2 X van Laar GMVLAAR L X V = Vapor; L = Lqud; S = Sold An X ndcates applcable to Pure or Mxture contnued 3-4 Physcal Property Methods and Models Verson10

137 Chapter 3 Vapor Pressure and Lqud Fugacty Models (contnued) Property Model Model Name Phase(s) Pure Mxture Wagner nteracton parameter GMWIP S X Wlson GMWILSON L X Wlson model wth lqud molar volume GMWSNVOL L X Extended Antone/Wagner PL0XANT L L1 L2 X Chao-Seader PHL0CS L X Grayson-Streed PHL0GS L X Kent-Esenberg ESAMIN L X Heat of Vaporzaton Models Property Model Model Name Phase(s) Pure Mxture Watson / DIPPR DHVLWTSN L X Clausus-Clapeyron Equaton DHVLWTSN L X Molar Volume and Densty Models Property Model Model Name Phase(s) Pure Mxture API Lqud Volume VL2API L X Brelv-O'Connell VL1BROC L X Clarke Aqueous Electrolyte Volume VAQCLK L X Costald Lqud Volume VL0CTD, VL2CTD L X X Debje-Hückel Volume VAQDH L X Rackett / DIPPR Lqud Volume VL0RKT, VL2RKT L X Rackett Mxture Lqud Volume VL2RKT L X X Modfed Rackett VL2MRK L X X Solds Volume Polynomal VS0POLY S X V = Vapor; L = Lqud; S = Sold An X ndcates applcable to Pure or Mxture contnued Physcal Property Methods and Models 3-5 Verson 10

138 Property Model Descrptons Heat Capacty Models Property Model Model Name Phase(s) Pure Mxture Aqueous Infnte Dluton Heat Capacty Polynomal Crss-Cobble Aqueous Infnte Dluton Ionc Heat Capacty L X L X DIPPR Lqud Heat Capacty HL0DIP L X Ideal Gas Heat Capacty / DIPPR V X X Solds Heat Capacty Polynomal HS0POLY S X Solublty Correlaton Models Property Model Model Name Phase(s) Pure Mxture Henry s constant HENRY1 L X Water solublty L X Other Models Property Model Model Name Phase(s) Pure Mxture Cavett Lqud Enthalpy Departure DHL0CVT, DHL2CVT L X X BARIN Equatons for Gbbs Energy, Enthalpy, Entropy and Heat Capacty S L V X Electrolyte NRTL Enthalpy HAQELC, HMXELC L X Electrolyte NRTL Gbbs Energy GAQELC, GMXELC L X Lqud Enthalpy from Lqud Heat Capacty Correlaton Enthalpes Based on Dfferent Reference Status DHL0DIP L X X DHL0HREF L V X X V = Vapor; L = Lqud; S = Sold An X ndcates applcable to Pure or Mxture 3-6 Physcal Property Methods and Models Verson10

139 Chapter 3 Equaton-of-State Models ASPEN PLUS has 20 bult-n equaton-of-state property models. Ths secton descrbes the equaton-of-state property models avalable. Model ASME Steam Tables BWR-Lee-Starlng Hayden-O Connell HF Huron-Vdal mxng rules Ideal Gas Lee-Kesler Lee-Kesler-Plöcker MHV2 mxng rules NBS/NCR Steam Tables Nothnagel Peng-Robnson alpha functons Peng-Robnson-Boston-Mathas Peng-Robnson-MHV2 Peng-Robnson-Wong-Sandler Predctve SRK PSRK mxng rules Redlch-Kwong Redlch-Kwong-Aspen Redlch-Kwong-Soave-Boston-Mathas Redlch-Kwong-Soave-MHV2 Redlch-Kwong-Soave-Wong-Sandler RK-Soave alpha functons Schwartzentruber-Renon Standard Peng-Robnson Standard Redlch-Kwong-Soave Wong-Sandler mxng rules Type Fundamental Vral Vral and assocaton Ideal and assocaton Mxng rules Ideal Vral Vral Mxng rules Fundamental Ideal Alpha functons Cubc Cubc Cubc Cubc Mxng rules Cubc Cubc Cubc Cubc Cubc Alpha functons Cubc Cubc Cubc Mxng rules Physcal Property Methods and Models 3-7 Verson 10

140 Property Model Descrptons ASME Steam Tables The ASME steam tables (1967) are mplemented lke any other equaton-of-state n ASPEN PLUS. The steam tables can calculate any thermodynamc property of water or steam and form the bass of the STEAM-TA property method. There are no parameter requrements. The ASME steam tables are less accurate than the NBS/NRC steam tables. References ASME Steam Tables, Thermodynamc and Transport Propertes of Steam, (1967). K. V. Moore, Aerojet Nuclear Company, prepared for the U.S. Atomc Energy Commson, ASTEM - A Collecton of FORTRAN Subroutnes to Evaluate the 1967 ASME equatons of state for water/steam and dervatves of these equatons. BWR-Lee-Starlng The Benedct-Webb-Rubn-Lee-Starlng equaton-of-state s the bass of the BWR-LS property method. It s a generalzaton by Lee and Starlng of the vral equaton-of-state for pure fluds by Benedct, Webb and Rubn. The equaton s used for non-polar components, and can manage hydrogen-contanng systems. General Form: 0 Z = Z + γz ( ) (1) m m m Where: ( 0) (1) Z, Z = fcn( T, T, V, V ) m m c m cm Mxng Rules: V a cm b V T cm = xxv j *, a j cj = x x T V b c j cj cj j b VcmT = x x γ V Where: c c j j cj j a = b= 45. / 3; c= 35. / 5 V = ( 1 ε ) ( V V ) 3 * * 1/ 2 cj j c cj 3-8 Physcal Property Methods and Models Verson10

141 Chapter 3 T = ( 1 n )( T T ) / cj j c cj γ ( γ γ ) / ιϕ = j Parameter Name/Element Symbol Default MDS Lower Lmt Upper Lmt Unts TCBWR T c TC X TEMPERATURE VCBWR V c * VC X MOLE-VOLUME BWRGMA γ OMEGA X BWRKV ε j 0 X BWRKT η j 0 X Bnary nteracton parameters BWRKV and BWRKT are avalable n ASPEN PLUS for a large number of components. (See ASPEN PLUS Physcal Property Data, Chapter 1). References M.R. Brulé, C.T. Ln, L.L. Lee, and K.E. Starlng, AIChE J., Vol. 28, (1982) p Brulé et al., Chem. Eng., (Nov., 1979) p Watanasr et al., AIChE J., Vol. 28, (1982) p Hayden-O Connell The Hayden-O'Connell equaton-of-state calculates thermodynamc propertes for the vapor phase. It s used n property methods NRTL-HOC, UNIF-HOC, UNIQ-HOC, VANL-HOC, and WILS-HOC, and s recommended for nonpolar, polar, and assocatng compounds. Hayden-O'Connell ncorporates the chemcal theory of dmerzaton. Ths model accounts for strong assocaton and solvaton effects, ncludng those found n systems contanng organc acds, such as acetc acd. The equaton-of-state s: Z m = 1+ Bp RT Where: B = x x B ( T) j j j B = ( B ) + ( B ) + ( B ) + ( B ) + ( B ) j free nonpolar j free polar j metastable j bound j chem j Physcal Property Methods and Models 3-9 Verson 10

142 Property Model Descrptons For nonpolar, non-assocatng speces: Bfree nonpolar = fi( σnp, εnp, ω np, T), wth σ ε = g 1 ( ω, T, p ) np np c c = g 2 ( ω, T), where np np c ω np gyr = f 2 ( r ) For polar, assocatng speces: Bfree nonpolar = f 3 ( σ fp, ε fp, ω np, T), wth σ = g 3 ( σ, ω, ξ) fp np np ε = g 4 ( ε, ω, ξ), where fp np np ξ = γ 5 ( σ, ε, ω, p, ) np np np T For chemcally bondng speces: B + B = f 4 ( σ, ε, p, T), and metastable bound c c B = f 5 ( σ, ε, η, T) chem c c σ = g 3 ( σ, ω, ξ) c np np ε = g 6 ( ε, ω, ξ, η) c np np Cross-Interactons The prevous equatons are vald for dmerzaton and cross-dmerzaton f these mxng rules are appled: ε = 07 ε ε /.( j). ε ε j σ =( σ σ ) / j 12 ε = 07 ε ε /.( j). ε ε j σ =( σ σ ) / j 12 ω np ( ωnp, + ωnpj, ) = Physcal Property Methods and Models Verson10

143 Chapter 3 p =( p p ) / j 12 η=0 unless a specal solvaton contrbuton can be justfed (for example, and j are n the same class of compounds). Many η values are present n ASPEN PLUS. Chemcal Theory When a compound wth strong assocaton ( η 45. ) s present n a mxture, the entre mxture s treated accordng to the chemcal theory of dmerzaton. The chemcal reacton for the general case of a mxture of dmerzng components and j s: K j + j= j Where and j refer to the same component. The equaton-of-state becomes: pv RT nc nc t Bp = n 1 + wth B = y B RT ( ) = 1 j= 1 In ths case, molar volume s equal to: V n t j free j Ths represents true total volume over the true number of speces n t. However, the reported molar volume s: V n a Ths represents the true total volume over the apparent number of speces n a. If V dmerzaton does not occur, n a s defned as the number of speces. n reflects a the apparently lower molar volume of an assocatng gas mxture. The chemcal equlbrum constant for the dmerzaton reacton on pressure bass K p, s related to the true mole fractons and fugacty coeffcents: yj yy j ϕj Kj p ϕϕ = j Physcal Property Methods and Models 3-11 Verson 10

144 Property Model Descrptons Where: y and y j = True mole fractons of monomers y j = True mole fracton of dmer ϕ = True fugacty coeffcent of component K j = Equlbrum constant for the dmerzaton of and j, on a pressure bass δ j = 1 for =j = ( B + B + B ) ( )/ RT bound metastable chem j 2 δj = 0 for j Apparent mole fractons y a are reported, but n the calculaton real mole fractons y, y j, and y j are used. The heat of reacton due to each dmerzaton s calculated accordng to: r H m d( rgm) d(ln Kj ) = T 2 = RT 2 dt dt The sum of the contrbutons of all dmerzaton reactons, corrected for the rato of apparent and true number of moles s added to the molar enthalpy departure H ν g H. m m Parameter Name/ Element Symbol Default MDS Lower Lmt Upper Lmt Unts TC T c TEMPERATURE PC p c PRESSURE RGYR gyr r x 9 MUP p x 24 LENGTH DIPOLEMOMENT HOCETA η 0.0 x The bnary parameters HOCETA for many component pars are avalable n ASPEN PLUS. These parameters are retreved automatcally when you specfy any of the followng property methods: NRTL- HOC, UNIF-HOC, UNIQ-HOC, VANL-HOC, and WILS-HOC Physcal Property Methods and Models Verson10

145 Chapter 3 References J.G. Hayden and J.P. O Connell, "A Generalzed Method for Predctng Second Vral Coeffcents," Ind. Eng. Chem., Process Des. Dev., Vol. 14,No. 3, (1974), pp HF Equaton-of-State HF forms olgomers n the vapor phase. The non-dealty n the vapor phase s found n mportant devatons from dealty n all thermodynamc propertes. The HF equaton accounts for the vapor phase nondealtes. The model s based on chemcal theory and assumes the formaton of hexamers. Speces lke HF that assocate lnearly behave as sngle speces. For example, they have a vapor pressure curve, lke pure components. The component on whch a hypothetcal unreacted system s based s often called the apparent (or parent) component. Apparent components react to the true speces. Electrolyte Smulaton, Chapter 5, dscusses apparent and true speces. Abbott and van Ness (1992) provde detals and basc thermodynamcs of reactve systems. The temperature-dependent hexamerzaton equlbrum constant, can ft the expermentally determned assocaton factors. The bult-n functonalty s: 10 log K C T 1 = C0 + + C2 ln T + C3T (1) The constants C 0 and C 1 are from Long et al. (1943), and C 2 and C 3 are set to 0. The correlaton s vald between 270 and 330 K, and can be extrapolated to about 370 K (cf. sec. 4). Dfferent sets of constants can be determned by expermental data regresson. Molar Volume Calculaton The non-dealty of HF s often expressed usng the assocaton factor, f, ndcatng the rato of apparent number of speces to the real number or speces. Assumng the deal gas law for all true speces n terms of (p, V, T) behavor mples: pv = m 1 RT f (2) Where the true number of speces s gven by 1 f. The assocaton factor s easly determned from (p, V, T) experments. For a crtcal evaluaton of data refer to Vanderzee and Rodenburg (1970). If only one reacton s assumed for a mxture of HF and ts assocated speces, (refer to Long et al., 1943), then: Physcal Property Methods and Models 3-13 Verson 10

146 Property Model Descrptons ( ) 6HF HF 6 (3) If p 1 represents the true partal pressure of the HF monomer, and p 6 represents the true partal pressure of the hexamer, then the equlbrum constant s defned as: K p ( p ) 6 = 6 1 (4) The true total pressure s: p = p1 + p6 (5) If all hexamer were dssocated, the apparent total pressure would be the hypothetcal pressure where: p a = p + 6p = p+ 5 p (6) When physcal dealty s assumed, partal pressures and mole fractons are proportonal. The total pressure n equaton 5 represents the true number of speces. The apparent total pressure from equaton 6 represents the apparent number of speces: f a p = = p p1 + 6p6 p+ 5p = p + p p = 1+ 5 y (7) 6 Note that the outcome of equaton 7 s ndependent of the assumpton of dealty. Equaton 7 can be used to compute the number of true speces 1 f for a mxture contanng HF, but the assocaton factor s defned dfferently. If p 1 and p 6 are known, the molar volume or densty of a vapor contanng HF can be calculated usng equatons 2 and 7. The molar volume calculated s the true molar volume for 1 apparent mole of HF. Ths s because the volume of 1 mole of deal gas (the true molar volume per true number of moles) s always equal to about m3/mol at K. True Mole Fracton (Partal Pressure) Calculaton If you assume the deal gas law for a mxture contanng HF, the apparent HF mole fracton s: y a a p p + 6p = = a p p+ 5p (8) 3-14 Physcal Property Methods and Models Verson10

147 Chapter 3 The denomnator of equaton 8 s gven by equaton 6. The numerator (the apparent partal pressure of HF) s the hypothetcal partal pressure only f all of the hexamer was dssocated. If you substtute equaton 4, then equaton 8 becomes: y a = p1 + 6K( p1) p+ 5K( p ) (9) K s known from Long et al., or can be regressed from (p,v,t) data. The apparent mole fracton of HF, y a, s known to the user and the smulator, but p p 1, or y = 1 must also be known n order to calculate the thermodynamc p propertes of the mxture. Equaton 9 must be solved for p 1 Equaton 9 can be wrtten as a polynomal n p 1 of degree 6: K y a 6 a ( 6 5 )( p ) + p py = 0 (9a) 1 1 A second order Newton-Raphson technque s used to determne p 1. Then p 6 can be calculated by equaton 5, and f s known (equaton 7). Gbbs Energy and Fugacty The apparent fugacty coeffcent s related to the true fugacty coeffcent and mole fractons: a y ln ϕ = ln ϕ = ln a 1 y (10) Equaton 10 represents a correcton to the deal mxng term of the fugacty. The rato of the true number of speces to the apparent number of speces s smlar to the correcton appled n equaton 2. Snce the deal gas law s assumed, the apparent fugacty coeffcent s gven by the equaton. All varables on the rght sde are known. ϕ a y = = y p py 1 1 a a (11) For pure HF, y a = 1: ln *, a ϕ = ln y1 Physcal Property Methods and Models 3-15 Verson 10

148 Property Model Descrptons From the fugacty coeffcent, the Gbbs energy departure of the mxture or pure apparent components can be calculated: g a p G G = RT ln ϕ + RT ln (12) ref p *, g *, a µ µ = RT ln ϕ + RT ln p p ref (12a) Enthalpy and Entropy For the enthalpy departure, the heat of reacton s consdered. For an arbtrary gas phase reacton: vaa+ vbb = vcc+ vdd (13) RT ln K = RT ln p p v C v A c A p p v D v B D B (14) Where µ * s the pure component thermodynamc potental or molar Gbbs energy of a component. Equaton 4 represents the frst two terms of the general equaton 14. The second or thrd equalty relates the equlbrum constant to the Gbbs energy of reacton, whch s thus related to the enthalpy of reacton: r H m d rgm = T = RT dt 2 2 (ln K ) T (15) All components are assumed to be deal. The enthalpy departure s equal to the heat of reacton, per apparent number of moles: H m g Hm = 1 r H m f (16) H g HHF = 1 rhm (17) f * *, HF From the Gbbs energy departure and enthalpy departure, the entropy departure can be calculated: Gm = Hm TSm (18) Temperature dervatves for the thermodynamc propertes can be obtaned by straghtforward dfferentaton. Usage The HF equaton-of-state should only be used for vapor phase calculatons. It s not suted for lqud phase calculatons Physcal Property Methods and Models Verson10

149 Chapter 3 The HF equaton-of-state can be used wth any actvty coeffcent model for nonelectrolyte VLE. Usng the Electrolyte NRTL model and the data package MHF2 s strongly recommended for aqueous mxtures (de Leeuw and Watanasr, 1993). Parameter Name/Element Symbol Default MDS Lower Lmt Upper Lmt Unts ESHFK/1 C ESHFK/2 C ESHFK/3 C 2 0 ESHFK/4 C 3 0 References M. M. Abbott and H. C. van Ness, "Thermodynamcs of Solutons Contanng Reactve Speces, a Gude to Fundamentals and Applcatons," Flud Phase Eq., Vol. 77, (1992) pp V. V. De Leeuw and S. Watanasr, "Modellng Phase Equlbra and Enthalpes of the System Water and Hydroflourc Acd Usng an HF Equaton-of-state n Conjuncton wth the Electrolyte NRTL Actvty Coeffcent Model," Paper presented at the 13th European Semnar on Appled Thermodynamcs, June 9 12, Carry-le-Rouet, France, R. W. Long, J. H. Hldebrand, and W. E. Morrell, "The Polymerzaton of Gaseous Hydrogen and Deuterum Flourdes," J. Am. Chem. Soc., Vol. 65, (1943), pp C. E. Vanderzee and W. WM. Rodenburg, "Gas Imperfectons and Thermodynamc Excess Propertes of Gaseous Hydrogen Flourde," J. Chem. Thermodynamcs, Vol. 2, (1970), pp Ideal Gas The deal gas law (deal gas equaton-of-state) combnes the laws of Boyle and Gay-Lussac. It models a vapor as f t conssted of pont masses wthout any nteractons. The deal gas law s used as a reference state for equaton-of-state calculatons, and can be used to model gas mxtures at low pressures (wthout specfc gas phase nteractons). The equaton s: RT p = V m Physcal Property Methods and Models 3-17 Verson 10

150 Property Model Descrptons Lee-Kesler Ths equaton-of-state model s based on the work of Lee and Kesler (1975). In ths equaton, the volumetrc and thermodynamc propertes of fluds based on the Curl and Ptzer approach (1958) have been analytcally represented by a modfed Benedct-Webb-Rubn equaton-of-state (1940). The model calculates the molar volume, enthalpy departure, Gbbs free energy departure, and entropy departure of a mxture at a gven temperature, pressure, and composton for ether a vapor or a lqud phase. Partal dervatves of these quanttes wth respect to temperature can also be calculated. Unlke the other equaton-of-state models, ths model does not calculate fugacty coeffcents. The compressblty factor and other derved thermodynamc functons of nonpolar and slghtly polar fluds can be adequately represented, at constant reduced temperature and pressure, by a lnear functon of the acentrc factor. In partcular, the compressblty factor of a flud whose acentrc factor s ω, s gven by the followng equaton: Z = Z + ωz Where: ( 0) ( 1) Z ( 0 ) = Compressblty factor of a smple flud ( ω=0) Z ( 1 ) = Devaton of the compressblty factor of the real flud from Z ( 0) Z ( 0) and Z ( 1) are assumed unversal functons of the reduced temperature and pressure. Curl and Ptzer (1958) were qute successful n correlatng thermodynamc and volumetrc propertes usng the above approach. Ther applcaton employed tables of propertes n terms of reduced temperature and pressure. A sgnfcant weakness of ths method s that the varous propertes (for example, entropy departure and enthalpy departure) wll not be exactly thermodynamcally consstent wth each other. Lee and Kesler (1975) overcame ths drawback by an analytc representaton of the tables wth an equaton-of-state. In addton, the range was extended by ncludng new data. In the Lee-Kesler mplementaton, the compressblty factor of any flud has been wrtten n terms of a smple flud and a reference as follows: ( ) ( Z = Z + Z r ) ( ) ( Z ) ( r) 0 0 ω ω In the above equaton both Z ( 0) and Z ( 1) are represented as generalzed equatons of the BWR form n terms of reduced temperature and pressure. Thus, ( 0) ( 0 Z = f ) ( T P T P ) c, c 3-18 Physcal Property Methods and Models Verson10

151 Chapter 3 Z ( ) = f ( ) ( ) r r T T P P c, c Equatons for the enthalpy departure, Gbbs free energy departure, and entropy departure are obtaned from the compressblty factor usng standard thermodynamc relatonshps, thus ensurng thermodynamc consstency. In the case of mxtures, mxng rules (wthout any bnary parameters) are used to obtan the mxture values of the crtcal temperature and pressure, and the acentrc factor. Ths equaton has been found to provde a good descrpton of the volumetrc and thermodynamc propertes of mxtures contanng nonpolar and slghtly polar components. Symbol Parameter Name Default Defnton T c TCLK TC Crtcal temperature P c PCLK PC Crtcal pressure ω OMGLK OMEGA Acentrc factor References B. I. Lee and M.G. Kesler, AIChEJ, Vol. 21, (1975), p R. F. Curl and K.S. Ptzer, Ind. Eng. Chem., Vol. 50, (1958), p M. Benedct, G. B. Webb, and L. C. Rubn, J. Chem. Phys., Vol. 8, (1940), p Lee-Kesler-Plöcker The Lee-Kesler-Plöcker equaton-of-state s the bass for the LK-PLOCK property method. Ths equaton-of-state apples to hydrocarbon systems that nclude the common lght gases, such as HS 2 and CO 2. It can be used n gas-processng, refnery, and petrochemcal applcatons. The general form of the equaton s: o ω o R Zm = Zm + Z Z R m m ω ( ) Where: o Z = f ( T, T, V, V ) m o c m cm R Z = f ( T, T, V, V ) m R c m cm Physcal Property Methods and Models 3-19 Verson 10

152 Property Model Descrptons The f o and f R parameters are functons of the BWR form. The f o parameter s for a smple flud, and f R s for reference flud n-octane. pc = ZcmRTc / Vcm The mxng rules are: V cm = xxv j j cj V 1 4 = cm Tc ω = x ω 1 xxv 4 T Z m = xz Where: j j cj cj c V cj = [ Vc + Vcj ] T cj = ( 1+ k )( T T ) j c cj Z c = ω ( Method 1) pv c c ( 2) RT Method c 1 2 k j = k j The bnary parameter k j s determned from phase-equlbrum data regresson, such as VLE data. ASPEN PLUS stores the bnary parameters for a large number of component pars. These bnary parameters are used automatcally wth the LK-PLOCK property method. If bnary parameters for certan component pars are not avalable, they can be estmated usng bult-n correlatons. The correlatons are desgned for bnary nteractons among the components CO, CO2, N 2, H2, CH4 alcohols and hydrocarbons. If a component s not CO, CO, N, H, CH or an alcohol, t s assumed to be a hydrocarbon Physcal Property Methods and Models Verson10

153 Chapter 3 Parameter Name/Element Symbol Default MDS Upper Lmt Lower Lmt Unts TCLKP T c TC x TEMPERATURE PCLKP p c PC x PRESSURE VCLKP V c VC x MOLE-VOLUME OMGLKP ω I OMEGA x LKPZC Z c fcn( ω) (Method 1) fcn( pc, Vc, Tc ) (Method 2) x LKPKIJ k j fcn T c V c ( TV ) x cj cj Method 1 s the default; Method 2 can be nvoked by settng the value of LKPZC equal to zero. Bnary nteracton parameters LKPKIJ are avalablefor a large number of components n ASPEN PLUS. References B.I. Lee and M.G. Kesler, AIChE J., Vol. 21, (1975) p. 510; errata: AIChE J., Vol. 21, (1975) p V. Plöcker, H. Knapp, and J.M. Prausntz, Ind. Eng. Chem., Process Des. Dev., Vol. 17, (1978), p NBS/NRC Steam Tables The NBS/NRC Steam Tables are mplemented lke any other equaton-of-state n ASPEN PLUS. These steam tables can calculate any thermodynamc property of water. The tables form the bass of the STEAMNBS property method. There are no parameter requrements. They are the most accurate steam tables n ASPEN PLUS. References L. Haar, J.S. Gallagher, and J.H. Kell, "NBS/NRC Steam Tables," (Washngton: Hemsphere Publshng Corporaton, 1984). Physcal Property Methods and Models 3-21 Verson 10

154 Property Model Descrptons Nothnagel The Nothnagel equaton-of-state calculates thermodynamc propertes for the vapor phase. It s used n property methods NRTL-NTH, UNIQ-NTH, VANL- NTH, and WILS-NTH. It s recommended for systems that exhbt strong vapor phase assocaton. The model ncorporates the chemcal theory of dmerzaton to account for strong assocaton and solvaton effects, such as those found n organc acds, lke acetc acd. The equaton-of-state s: p RT = V b m Where: b = nc = 1 yb + nc y b j j = 1 j= 1 1 b j = ( b + bj ) 8 nc = Number of components n the mxture The chemcal reacton for the general case of a mxture of dmerzng components and j s: K + j = j The chemcal equlbrum constant for the dmerzaton reacton on pressure bass K p s related to the true mole fractons and fugacty coeffcents: y j yy j ϕj Kj p ϕϕ = j Where: y and y j = True mole fractons of monomers y j = True mole fracton of dmer ϕ = True fugacty coeffcent of component K j = Equlbrum constant for the dmerzaton of and j, on a pressure bass 3-22 Physcal Property Methods and Models Verson10

155 Chapter 3 When accountng for chemcal reactons, the number of true speces n t n the V mxture changes. The true molar volume s calculated from the equaton-ofstate. Snce both V and n t change n about the same proporton, ths number n t does not change much. However, the reported molar volume s the total volume over the apparent number of speces: V. Snce the apparent number of speces s a n constant and the total volume decreases wth assocaton, the quantty V n a reflects the apparent contracton n an assocatng mxture. The heat of reacton due to each dmerzaton can be calculated: r r m j Hm T d G RT d K 2 ( ) (ln ) 2 = = dt dt The sum of the contrbutons of all dmerzaton reactons, corrected for the rato of apparent and true number of moles, s added to the molar enthalpy departure: v g ( H H ) m m The equlbrum constants can be computed usng ether bult-n calculatons or parameters you entered. Bult-n correlatons: ln( RTK IJ ) = fcn( T, b, bj, d, d j, p, p j ) The pure component parameters b, d, and p are stored n ASPEN PLUS for many components. Parameters you entered: B ln K = A + T + C ln T + DT In ths method, you enter A B, C, and D on the Propertes Parameters Unary.T-Dependent form. The unts for K s pressure 1 ; use absolute unts for temperature. If you enter K and K, then jj K s computed from jj Kj = 2 KK jj If you enter A B, C, and D, the equlbrum constants are computed usng the parameters you entered. Otherwse the equlbrum constants are computed usng bult-n correlatons. Physcal Property Methods and Models 3-23 Verson 10

156 Property Model Descrptons Parameter Name/Element Symbol Default Upper Lmt Lower Lmt Unts TC T c TEMPERATURE TB T b TEMPERATURE PC p c PRESSURE NTHA/1 b RTc p c MOLE-VOLUME NTHA/2 d NTHA/3 p NTHK/1 A PRESSURE NTHK/2 B 0 TEMPERATURE NTHK/3 C 0 TEMPERATURE NTHK/4 D 0 TEMPERATURE References K.-H. Nothnagel, D. S. Abrams, and J.M. Prausntz, "Generalzed Correlaton for Fugacty Coeffcents n Mxtures at Moderate Pressures," Ind. Eng. Chem., Process Des. Dev., Vol. 12, No. 1 (1973), pp Physcal Property Methods and Models Verson10

157 Chapter 3 Peng-Robnson-Boston-Mathas The Peng-Robnson-Boston-Mathas equaton-of-state s the bass for the PR-BM property method. It s the Peng-Robnson equaton-of-state wth the Boston- Mathas alpha functon (see Peng-Robnson Alpha Functons). It s recommended for hydrocarbon processng applcatons such as gas processng, refnery, and petrochemcal processes. Its results are comparable to those of the Redlch- Kwong-Soave equaton-of-state. The equaton for the BM model s: p = RT a V b V ( V + b) + b( V b) Where: b = xb m m m m a = xx ( aa ) 05. ( 1 k ) b = fcn( T, p ) j c j j j a = fcn( T, T, p, ω ) c c c k j = k j The parameter α s calculated by the standard Peng-Robnson formulaton at supercrtcal temperatures. If the component s supercrtcal, the Boston-Mathas extrapolaton s used (see Peng-Robnson Alpha Functons on page 3-36). For best results, the bnary parameter k j must be determned from phase equlbrum data regresson, (for example, VLE data). Parameter Name/Element Symbol Default MDS Upper Lmt Lower Lmt Unts TCPR T c TC x TEMPERATURE PCPR p c PC x PRESSURE OMGPR ω OMEGA x PRKIJ k j 0 x Bnary nteracton parameters PRKIJ are avalable for a large number of components n ASPEN PLUS. Physcal Property Methods and Models 3-25 Verson 10

158 Property Model Descrptons References D.-Y. Peng and D. B. Robnson, "A New Two-Constant Equaton-of-state," Ind Eng. Chem. Fundam., Vol. 15, (1976), pp Peng-Robnson-MHV2 Ths model uses the Peng-Robnson equaton-of-state for pure compounds. The mxng rules are the predctve MHV2 rules. Several alpha functons can be used n the Peng-Robnson-MHV2 equaton-of-state model. For a more accurate descrpton of the pure component behavor. The pure component behavor and parameter requrements are descrbed n Standard Peng-Robnson on page 3-34, or n Peng-Robnson Alpha Functons on page The MHV2 mxng rules are an example of modfed Huron-Vdal mxng rules. A bref ntroducton s provded n Huron-Vdal Mxng Rules on page For more detals, see MHV2 Mxng Rules, ths chapter. Predctve SRK (PSRK) Ths model uses the Redlch-Kwong-Soave equaton-of-state for pure compounds. The mxng rules are the predctve Holderbaum rules, or PSRK method. Several alpha functons can be used n the PSRK equaton-of-state model. For a more accurate descrpton of the pure component behavor. The pure component behavor and parameter requrements are descrbed n Standard Redlch-Kwong- Soave on page 3-35 and n Soave Alpha Functons on page The PSRK method s an example of modfed Huron-Vdal mxng rules. A bref ntroducton s provded n Huron-Vdal Mxng Rules on page For more detals, see Predctve Soave-Redlch-Kwong-Gmehlng Mxng Rules, ths chapter. Peng-Robnson-Wong-Sandler Ths model uses the Peng-Robnson equaton-of-state for pure compounds. The mxng rules are the predctve Wong-Sandler rules. Several alpha functons can be used n the Peng-Robnson-Wong-Sandler equaton-of-state model. For a more accurate descrpton of the pure component behavor. The pure component behavor and parameter requrements are descrbed n Peng-Robnson, and n Peng-Robnson Alpha Functons on page The Wong-Sandler mxng rules are an example of modfed Huron-Vdal mxng rules. A bref ntroducton s provded n Huron-Vdal Mxng Rules on page For more detals see Wong-Sandler Mxng Rules, ths chapter Physcal Property Methods and Models Verson 10

159 Chapter 3 Redlch-Kwong The Redlch-Kwong equaton-of-state can calculate vapor phase thermodynamc propertes for the followng property methods: NRTL-RK, UNIFAC, UNIF-LL, UNIQ-RK, VANL-RK, and WILS-RK. It s applcable for systems at low to moderate pressures (maxmum pressure 10 atm) for whch the vapor-phase nondealty s small. The Hayden-O Connell model s recommended for a more nondeal vapor phase, such as n systems contanng organc acds. It s not recommended for calculatng lqud phase propertes. The equaton for the model s: p = a RT T V b 05. V ( V + b) m m m Where: a = x a b = xb a = RT c p c b = RT c p c Parameter Name/Element Symbol Default MDS Upper Lmt Lower Lmt Unts TC T c TEMPERATURE PC p c PRESSURE References O. Redlch and J.N.S. Kwong, "On the Thermodynamcs of Solutons V. An Equaton-of-state. Fugactes of Gaseous Solutons," Chem. Rev., Vol. 44, (1979), pp Physcal Property Methods and Models 3-27 Verson 10

160 Property Model Descrptons Redlch-Kwong-Aspen The Redlch-Kwong-Aspen equaton-of-state s the bass for the RK-ASPEN property method. It can be used for hydrocarbon processng applcatons. It s also used for more polar components and mxtures of hydrocarbons, and for lght gases at medum to hgh pressures. The equaton s the same as Redlch-Kwong-Soave: p = RT a V b V ( V + b) m m m A quadratc mxng rule s mantaned for: a = xx ( aa ) 05. ( 1 k ) j j j a, j An nteracton parameter s ntroduced n the mxng rule for: b = j xx j ( bb j) ( 1 kbj, ) 2 For a an extra polar parameter s used: a = fcn( T, T, p, ω, η ) b = fcn( T, p ) c c c c The nteracton parameters are temperature-dependent: k aj, = k bj, = k k + k 0 1 aj, aj, + k 0 1 bj, bj, T 1000 T 1000 For best results, bnary parameters k j must be determned from phaseequlbrum data regresson, such as VLE data. Parameter Name/Element Symbol Default MDS Upper Lmt Lower Lmt Unts TCRKS T c TC x TEMPERATURE PCRKA p c PC x PRESSURE contnued 3-28 Physcal Property Methods and Models Verson 10

161 Chapter 3 Parameter Name/Element Symbol Default MDS Upper Lmt Lower Lmt Unts OMGRKA ω OMEGA x RKAPOL η 0 x RKAKA0 RKAKA1 RKAKB0 RKAKB1 0 k 0 x aj, 1 k 0 x TEMPERATURE aj, 0 k 0 x bj, 1 k 0 x TEMPERATURE bj, Absolute temperature unts are assumed. See the ASPEN PLUS User Gude. References Mathas, P.M., "A Versatle Phase Equlbrum Equaton-of-state", Ind. Eng. Chem. Process Des. Dev., Vol. 22, (1983), pp Redlch-Kwong-Soave-Boston-Mathas The Redlch-Kwong-Soave-Boston-Mathas equaton-of-state s the bass for the RKS-BM property method. It s the Redlch-Kwong-Soave equaton-of-state wth the Boston-Mathas alpha functon (see Soave Alpha Functons on page 3-40). It s recommended for hydrocarbon processng applcatons, such as gas-processng, refnery, and petrochemcal processes. Its results are comparable to those of the Peng-Robnson-Boston-Mathas equaton-of-state. The equaton s: p = RT a V b V ( V + b) m m m Where: a = xx ( aa ) 05. ( 1 k ) b = xb j j j j a = fcn( T, T, p, ω ) c c b = fcn( T, p ) c c Physcal Property Methods and Models 3-29 Verson 10

162 Property Model Descrptons k j = k j The parameter a s calculated by the standard Soave formulaton at supercrtcal temperatures. If the component s supercrtcal, the Boston-Mathas extrapolaton s used (see Soave Alpha Functons on page 3-40). For best results, bnary parameters k j must be determned from phaseequlbrum data regresson (for example, VLE data). Parameter Name/Element Symbol Default MDS Upper Lmt Lower Lmt Unts TCRKS T c TC x TEMPERATURE PCRKS p c PC x PRESSURE OMGRKS ω OMEGA x RKSKIJ k j 0 x Bnary nteracton parameters RKSKIJ are avalable for a large number of components n ASPEN PLUS. References G. Soave, "Equlbrum Constants for Modfed Redlch-Kwong Equaton-ofstate," Chem. Eng. Sc., Vol. 27, (1972), pp Redlch-Kwong-Soave-Wong-Sandler Ths equaton-of-state model uses the Redlch-Kwong-Soave equaton-of-state for pure compounds. The predctve Wong-Sandler mxng rules are used. Several alpha functons can be used n the Redlch-Kwong-Soave-Wong-Sandler equatonof-state model for a more accurate descrpton of the pure component behavor. The pure component behavor and parameter requrements are descrbed n Standard Redlch-Kwong-Soave on page 3-35, and n Soave Alpha Functons on page The Wong-Sandler mxng rules are an example of modfed Huron-Vdal mxng rules. A bref ntroducton s provded n Huron-Vdal Mxng Rules on page For more detals, see Wong-Sandler Mxng Rules, ths chapter Physcal Property Methods and Models Verson 10

163 Chapter 3 Redlch-Kwong-Soave-MHV2 Ths equaton-of-state model uses the Redlch-Kwong-Soave equaton-of-state for pure compounds. The predctve MHV2 mxng rules are used. Several alpha functons can be used n the RK-Soave-MHV2 equaton-of-state model. For a more accurate descrpton of the pure component behavor. The pure component behavor and ts parameter requrements are descrbed n Standard Redlch- Kwong-Soave on page 3-35, and n Soave Alpha Functons on page The MHV2 mxng rules are an example of modfed Huron-Vdal mxng rules. A bref ntroducton s provded n Huron-Vdal Mxng Rules on page For more detals, see MHV2 Mxng Rules, ths chapter. Schwartzentruber-Renon The Schwartzentruber-Renon equaton-of-state s the bass for the SR-POLAR property method. It can be used to model chemcally nondeal systems wth the same accuracy as actvty coeffcent property methods, such as the WILSON property method. Ths equaton-of-state s recommended for hghly non-deal systems at hgh temperatures and pressures, such as n methanol synthess and supercrtcal extracton applcatons. The equaton for the model s: p = RT a V + c b ( V + c)( V + c+ b) Where: M m m a = xx j( aa j) 0.5 [ 1 ka, j lj( x xj)] j b = j xx b b + j j ( 1 kbj, ) 2 c = xc a = fcn( T, T, p,, q, q, q ) b = fcn( T, p ) c c c ω c c = fcn T, T c, c, c c Physcal Property Methods and Models 3-31 Verson 10

164 Property Model Descrptons k aj, = k + k T + k T aj, aj, aj, l j = l + l T + l T k bj j j j, = k + k T + k T bj, bj, bj, k aj, = k aj, l j = l j k bj, = k bj, The bnary parameters k aj,, k bj,, and l j are temperature-dependent. In most 0 cases, k aj, and l 0 j are suffcent to represent the system of nterest. VLE calculatons are ndependent of c. However, c does nfluence the fugacty values and can be adjusted to (lqud) molar volumes. For a wde temperature range, adjust c o to the molar volume at K or at bolng temperature. Parameter Name/Element Symbol Default MDS Upper Lmt Lower Lmt Unts TCRKU T c TC x TEMPERATURE PCRKU p c PC x PRESSURE OMGRKU ω OMEGA x RKUPP0 RKUPP1 RKUPP2 RKUC0 RKUC1 RKUC2 q x 0 q 0 x 1 q 0 x 2 c 0 x 0 c 0 x 1 c 0 x 2 For polar components (dpole moment >> 0), f you do not enter q 0, the system estmates q 0, q 1, q 2 from vapor pressures usng the Antone vapor pressure model. contnued 3-32 Physcal Property Methods and Models Verson 10

165 Chapter 3 Parameter Name/Element Symbol Default MDS Upper Lmt Lower Lmt Unts RKUKA0 RKUKA1 RKUKA2 0 k 0 x aj, 1 k 0 x TEMPERATURE aj, 2 k 0 x TEMPERATURE aj, RKULA0 l j 0 0 x RKULA1 l j 1 0 x TEMPERATURE RKULA2 l j 2 0 x TEMPERATURE RKUKB0 RKUKB1 RKUKB2 0 k 0 x bj, 1 k 0 x TEMPERATURE bj, 2 k 0 x TEMPERATURE bj, For polar components (dpole moment >> 0), f you do not enter q 0, the system estmates q 0, q 1, q 2 from vapor pressures usng the Antone vapor pressure model. 0 If you do not enter at least one of the bnary parameters k aj, 0 estmates k aj, 2 0 2, k aj,, l j, and l j, from the UNIFAC model. 2, k aj, 0 2 0, l j, l j, k bj, 2, or k bj, the system Absolute temperature unts are assumed. References G. Soave, "Equlbrum Constants for Modfed Redlch-Kwong Equaton-ofstate," Chem. Eng. Sc., Vol. 27, (1972), pp J. Schwartzentruber and H. Renon, "Extenson of UNIFAC to Hgh Pressures and Temperatures by the Use of a Cubc Equaton-of-State," Ind. Eng. Chem. Res., Vol. 28, (1989), pp A. Peneloux, E. Rauzy, and R. Freze, "A Consstent Correcton For Redlch- Kwong-Soave Volumes", Flud Phase Eq., Vol. 8, (1982), pp Physcal Property Methods and Models 3-33 Verson 10

166 Property Model Descrptons Standard Peng-Robnson The Standard Peng-Robnson equaton-of-state s the bass for the PENG-ROB property method. It s the Peng-Robnson equaton-of-state wth the Boston- Mathas alpha functon (see Peng-Robnson Alpha Functons on page 3-36). It s recommended for hydrocarbon processng applcatons such as gas processng, refnery, and petrochemcal processes. Its results are comparable to those of the Standard Redlch-Kwong-Soave equaton-of-state. The equaton for the BM model s: RT a p = V b V ( V + b) + b( V b) Where: m m m m b = xb a = xx ( aa ) 05. ( 1 k ) b = fcn( T, p ) j c j j j a = fcn( T, T, p, ω ) c c c k j = k j The parameter a s calculated accordng to the standard Peng-Robnson formulaton (see Peng-Robnson Alpha Functons on page 36, equatons 1 through 5). For best results, the bnary parameter k j must be determned from phase equlbrum data regresson, (for example, VLE data). ASPEN PLUS also has bult-n k j for alarge number of component pars. These parameters are used automatcally wth the PENG-ROB property method. Parameter Name/Element Symbol Default MDS Upper Lmt Lower Lmt Unts TCPR T c TC x TEMPERATURE PCPR p c PC x PRESSURE OMGPR ω OMEGA x PRKIJ k j 0 x Physcal Property Methods and Models Verson 10

167 Chapter 3 References D.-Y. Peng and D. B. Robnson, "A New Two-Constant Equaton-of-state," Ind. Eng. Chem. Fundam., Vol. 15, (1976), pp Standard Redlch-Kwong-Soave The Standard Redlch-Kwong-Soave-Boston-Mathas equaton-of-state s the bass for the RK-SOAVE property method. It s It s recommended for hydrocarbon processng applcatons, such as gas-processng, refnery, and petrochemcal processes. Its results are comparable to those of the Peng- Robnson equaton-of-state. The equaton s: RT a p = V b V ( V + b) Where: m m m RT a p = V b V ( V + b) + b( V b) Where: m m m m a = xx ( aa ) 05. ( 1 k ) b = xb j j j j a = fcn( T, T, p, ω ) b = fcn( T, p ) c c c c k j = k j The parameter a s calculated accordng to the standard Soave formulaton (see Soave Alpha Functons on page 3-40, equatons 1, 2, 3, 5, and 6). For best results, bnary parameters k j must be determned from phaseequlbrum data regresson (for example, VLE data). ASPEN PLUS also has bult-n k j for a large number of component pars. These bnary parameters are used automatcally wth the RK-SOAVE property method. Physcal Property Methods and Models 3-35 Verson 10

168 Property Model Descrptons Parameter Name/Element Symbol Default MDS Upper Lmt Lower Lmt Unts TCRKS T c TC x TEMPERATURE PCRKS p c PC x PRESSURE OMGRKS ω OMEGA x RKSKIJ k j 0 x Bnary nteracton parameters RKSKIJ are avalable for a large number of components n ASPEN PLUS. References G. Soave, "Equlbrum Constants for Modfed Redlch-Kwong Equaton-ofstate," Chem. Eng. Sc., Vol. 27, (1972), pp J. Schwartzentruber and H. Renon, "Extenson of UNIFAC to Hgh Pressures and Temperatures by the Use of a Cubc Equaton-of-state," Ind. Eng. Chem. Res., Vol. 28, (1989), pp A. Peneloux, E. Rauzy, and R. Freze, "A Consstent Correcton For Redlch- Kwong-Soave Volumes", Flud Phase Eq., Vol. 8, (1982), pp Peng-Robnson Alpha Functons The pure component parameters for the Peng-Robnson equaton-of-state are calculated as follows: a b RT =α p = RT p c c 2 2 c c (1) (2) These expressons are derved by applyng the crtcal constrants to the equaton-of-state under these condtons: α ( ) =10. T c (3) The parameter α s a temperature functon. It was orgnally ntroduced by Soave n the Redlch-Kwong equaton-of-state. Ths parameter mproves the correlaton of the pure component vapor pressure. Ths approach was also adopted by Peng and Robnson: 1 α ( T) = [ 1+ m ( 1 T 2 2 r )] (4) 3-36 Physcal Property Methods and Models Verson 10

169 Chapter 3 Equaton 3 s stll represented. The parameter m can be correlated wth the acentrc factor: m = ω ω (5) Equatons 1 through 5 are the standard Peng-Robnson formulaton. Parameter Name/Element Symbol Default MDS Upper Lmt Lower Lmt Unts TCPR T c TC X TEMPERATURE PCPR p c PC X PRESSURE OMGPR ω OMEGA X Boston-Mathas Extrapolaton For lght gases at hgh reduced temperatures (> 5), equaton 4 gves unrealstc results. The boundary condtons are that attracton between molecules should vansh for extremely hgh temperatures, and α reduces asymptotcally to zero. Boston and Mathas derved an alternatve functon for temperatures hgher than crtcal: d α T = c 1 T r ( ) [exp[ ( )]] 2 (6) Wth d = c = 1 + m d Where m s computed by equaton 5. and equaton 4 s used for subcrtcal temperatures. Addtonal parameters are not needed. Mathas-Copeman Alpha Functon m s a constant for each component n equaton 4. For very hgh accuracy or strongly curved vapor pressure behavor as a functon of temperature, the Mathas-Copeman functon s hghly flexble α ( T ) = [ 1+ c, ( 1 T 2 r ) + c, ( 1 T r ) + c3, ( 1 T 2 r ) ] (7) Physcal Property Methods and Models 3-37 Verson 10

170 Property Model Descrptons For c 2, =0 and ths expresson reduces to the standard Peng-Robnson formulaton f c1, = m. You can use vapor pressure data f the temperature s subcrtcal to regress the constants. If the temperature s supercrtcal, c 2, and c 3, are set to 0. Parameter Name/Element Symbol Default MDS Upper Lmt Lower Lmt Unts TCPR T c TC X TEMPERATURE PCPR p c PC X PRESSURE PRMCP/1 PRMCP/2 PRMCP/3 c X 1, c 0 X 2, c 0 X 3, Schwartzentruber-Renon-Watanasr Alpha Functon Ths method combnes the flexblty of the Mathas-Copeman approach and the correcton for hghly reduced temperatures by Boston and Mathas: 1 1 α ( T) = [ 1+ m ( 1 T 2 r ) ( 1 T r )( p1, + p2, T r + p31, T r )] (8) Where m s computed by equaton 5. The polar parameters p 1,, p 2, and p 3, are comparable wth the c parameters of the Mathas-Copeman expresson. Equaton 8 reduces to the standard Peng-Robnson formulaton f the polar parameters are zero. You can use vapor pressure data to regress the constants f the temperature s subcrtcal. Equaton 8 s used only for below-crtcal temperatures. For abovecrtcal temperatures, the Boston-Mathas extrapolaton s used. Use equaton 6 wth: d = + m ( p + p + p ) , 2, 3, (9) c = 1 1 d (10) 3-38 Physcal Property Methods and Models Verson 10

171 Chapter 3 Parameter Name/Element Symbol Default MDS Upper Lmt Lower Lmt Unts TCPR T c TC X TEMPERATURE PCPR p c C X PRESSURE OMGPR ω OMEGA X PRSRP/1 PRSRP/2 PRSRP/3 p X 1, p 0 X 2, p 0 X 3, Use of Alpha Functons The alpha functons n Peng-Robnson-based equaton-of-state models s provded n the followng table. You can verfy and change the value of possble opton codes on the Propertes Property Method Model form. Alpha functon Model name Frst Opton code Standard Peng Robnson ESPRSTD0, ESPRSTD Standard PR/Boston-Mathas Mathas-Copeman Schwartzentruber-Renon-Watanasr ESPR0, ESPR ESPRWS0, ESPRWS ESPRV20, ESPRV2 ESPRWS0, ESPRWS ESPRV20, ESPRV2 ESPRWS0, ESPRWS ESPRV20, ESPRV (default) 3 (default) References J. F. Boston and P.M. Mathas, "Phase Equlbra n a Thrd-Generaton Process Smulator" n Proceedngs of the 2nd Internatonal Conference on Phase Equlbra and Flud Propertes n the Chemcal Process Industres, West Berln, (17-21 March 1980) pp D.-Y. Peng and D.B. Robnson, "A New Two-Constant Equaton-of-state," Ind. Eng. Chem. Fundam., Vol. 15, (1976), pp P.M. Mathas and T.W. Copeman, "Extenson of the Peng-Robnson Equaton-ofstate To Complex Mxtures: Evaluaton of the Varous Forms of the Local Composton Concept",Flud Phase Eq., Vol. 13, (1983), p. 91. Physcal Property Methods and Models 3-39 Verson 10

172 Property Model Descrptons J. Schwartzentruber, H. Renon, and S. Watanasr, "K-values for Non-Ideal Systems:An Easer Way," Chem. Eng., March 1990, pp G. Soave, "Equlbrum Constants for a Modfed Redlch-Kwong Equaton-ofstate," Chem Eng. Sc., Vol. 27, (1972), pp Soave Alpha Functons The pure component parameters for the Redlch-Kwong equaton-of-state are calculated as: a b RT =α p = RT p c c 2 2 c c (1) (2) These expressons are derved by applyng the crtcal constrant to the equatonof-state under these condtons: α ( ) =10. T c (3) In the Redlch-Kwong equaton-of-state, alpha s: α = 1 1 T 2 r (4) It was not referred to as alpha but equaton 4 was ncorporated nto equaton 1. Parameter Name/Element Symbol Default MDS Upper Lmt Lower Lmt Unts TC T c TEMPERATURE PC p c PRESSURE Soave Modfcaton The parameter α s a temperature functon ntroduced by Soave n the Redlch- Kwong equaton-of-state to mprove the correlaton of the pure component vapor pressure: 1 α ( T) = [ 1+ m ( 1 T 2 2 r )] (5) Equaton 3 stll holds. The parameter m can be correlated wth the acentrc factor: 3-40 Physcal Property Methods and Models Verson 10

173 Chapter 3 m = ω ω (6) Equatons 1, 2, 3, 5 and 6 are the standard Redlch-Kwong-Soave formulaton. Parameter Name/Element Symbol Default MDS Upper Lmt Lower Lmt Unts TCRKS T c TC X TEMPERATURE PCRKS p c PC X PRESSURE OMGRKS ω OMEGA X Boston-Mathas Extrapolaton For lght gases at hgh reduced temperatures (> 5), equaton 4 gves unrealstc results. The boundary condtons are that attracton between molecules should vansh for extremely hgh temperatures, and α reduces asymptotcally to zero. Boston and Mathas derved an alternatve functon for temperatures hgher than crtcal: d α T = c 1 T r ( ) [exp[ ( )]] 2 (7) Wth d = c = 1 + m d Where: m = Computed by equaton 6 Equaton 5 = Used for subcrtcal temperatures Addtonal parameters are not needed. Mathas Alpha Functon In equaton 4, m s a constant for each component. For hgh accuracy or for hghly curved vapor pressure behavor as a functon of temperature, such as wth polar compounds, the Mathas functon s more flexble: Physcal Property Methods and Models 3-41 Verson 10

174 Property Model Descrptons α ( T) = [ 1+ m( 1 T ) η ( 1 T )( 07. T )] ro r r (8) For η = 0, equaton 8 reduces to the standard Redlch-Kwong-Soave formulaton, ncludng equaton 6 for m. For temperatures above crtcal, the Boston-Mathas extrapolaton s used, that s, equaton 6 wth: d c m = η 2 = 1 1 d (9) (10) Parameter Name/ Element Symbol Default MDS Upper Lmt Lower Lmt Unts TCRKA T c TC X TEMPERATURE PCRKA p c PC X PRESSURE OMGRKA ω OMEGA X RKAPOL η X Extended Mathas Alpha Functon An extenson of the Mathas approach s: ( ) α T = [ 1 + m ( 1 T 1 r ) p ( 1 T 1 r )( p T + p Tr )] 1, 2, 3, (11) Where m s computed by equaton 6. If the polar parameters p 1,, p 2, and p 3, are zero, equaton 11 reduces to the standard Redlch-Kwong-Soave formulaton. You can use vapor pressure data to regress the constants f the temperature s subcrtcal. Equaton 11 s used only for temperatures below crtcal. The Boston- Mathas extrapolaton s used for temperatures above crtcal, that s, wth: ( 1 ) d = 1 2 m p 1, + p 2, + p 3, (12) c = 1 1 d (13) 3-42 Physcal Property Methods and Models Verson 10

175 Chapter 3 Parameter Name/Element Symbol Default MDS Upper Lmt Lower Lmt Unts TCRKU T c TC X TEMPERATURE PCRKU p c PC X PRESSURE OMGRKU ω OMEGA X RKUPP0 RKUPP1 RKUPP2 p X 1, p 0 X 2, p 0 X 3, Mathas-Copeman Alpha Functon The Mathas-Copeman Alpha Functon approach s another extenson of the Mathas approach. For hgh accuracy or strongly curved vapor pressure behavor as a functon of temperature, the Mathas-Copeman functon s hghly flexble: α ( T) = [ 1+ m ( 1 T 1 r ) + c, ( 1 T 1 2 r ) + c, ( 1 T r ) ] (14) For c, = and c, = ths expresson reduces to the standard Redlch-Kwong- Soave formulaton f c1, = m. If the temperature s subcrtcal, use vapor pressure data to regress the constants. If the temperature s supercrtcal, set c 2, and c 3, to Parameter Name/Element Symbol Default MDS Upper Lmt Lower Lmt Unts TCRKS T c TC X TEMPERATURE PCRKS p c PC X PRESSURE RKSMCP/1 RKSMCP/2 RKSMCP/3 c X 1, c 0 X 2, c 0 X 3, Schwartzentruber-Renon-Watanasr Alpha Functon Ths method combnes the flexblty of the Mathas-Copeman approach and the correcton for hgh reduced temperatures by Boston and Mathas: 1 α ( T) = [ 1+ m ( 1 T r ) ( 1 T r )( p1, + p2, T r + p3, T r )] (15) Physcal Property Methods and Models 3-43 Verson 10

176 Property Model Descrptons Where m s computed by equaton 6 and the polar parameters p 1,, p 2, and p 3, are comparable wth the c parameters of the Mathas-Copeman expresson. Equaton 15 reduces to the standard Redlch-Kwong-Soave formulaton f the polar parameters are zero. Use vapor pressure data to regress the constants f the temperature s subcrtcal. Equaton 15 s very smlar to the extended Mathas equaton, but t s easer to use n data regresson. It s used only for temperatures below crtcal. The Boston-Mathas extrapolaton s used for temperatures above crtcal, that s, use equaton 6 wth: d m = 1+ ( p1, + p2, + p3, ) (16) 2 c = 1 1 d (17) Parameter Name/Element Symbol Default MDS Upper Lmt Lower Lmt Unts TCPR T c TC X TEMPERATURE PCPR p c PC X PRESSURE OMGPR ω OMEGA X RKSSRP/1 RKSSRP/2 RKSSRP/3 p X 1, p 0 X 2, p 0 X 3, Use of Alpha Functons The use of alpha functons n Soave-Redlch-Kwong based equaton-of-state models s gven n the followng table. You can verfy and change the value of possble opton codes on the Propertes Property Method Model form. Alpha Functon Model Name Frst Opton Code orgnal RK ESRK0, ESRK standard RKS ESRKSTD0, ESRKSTD standard RKS/Boston-Mathas ESRKS0, ESRKS0 ESRKSWS0, ESRKSWS ESRKSV10, ESRKV1 ESRKSV20, ESRKSV contnued 3-44 Physcal Property Methods and Models Verson 10

177 Chapter 3 Alpha Functon Model Name Frst Opton Code Mathas/Boston-Mathas ESRKA0, ESRKA Extended Mathas/Boston-Mathas ESRKU0, ESRKU Mathas-Copeman Schwartzentruber-Renon-Watanasr ESRKSW0, ESRKSW ESRKSV10, ESRKSV1 ESRKSV20, ESRKSV2 ESPRWS0, ESPRWS ESRKSV10, ESRKSV1 ESRKSV20, ESRKSV (default) 3 (default) 3 (default) References J. F. Boston and P.M. Mathas, "Phase Equlbra n a Thrd-Generaton Process Smulator" n Proceedngs of the 2nd Internatonal Conference on Phase Equlbra and Flud Propertes n the Chemcal Process Industres, West Berln, (17-21 March 1980), pp P. M. Mathas, "A Versatle Phase Equlbrum Equaton-of-state", Ind. Eng. Chem. Process Des. Dev., Vol. 22, (1983), pp P.M. Mathas and T.W. Copeman, "Extenson of the Peng-Robnson Equaton-ofstate To Complex Mxtures: Evaluaton of the Varous Forms of the Local Composton Concept", Flud Phase Eq., Vol. 13, (1983), p. 91. O. Redlch and J. N. S. Kwong, "On the Thermodynamcs of Solutons V. An Equaton-of-state. Fugactes of Gaseous Solutons," Chem. Rev., Vol. 44, (1949), pp J. Schwartzentruber and H. Renon, "Extenson of UNIFAC to Hgh Pressures and Temperatures by the Use of a Cubc Equaton-of-state," Ind. Eng. Chem. Res., Vol. 28, (1989), pp J. Schwartzentruber, H. Renon, and S. Watanasr, "K-values for Non-Ideal Systems:An Easer Way," Chem. Eng., March 1990, pp G. Soave, "Equlbrum Constants for a Modfed Redlch-Kwong Equaton-ofstate," Chem Eng. Sc., Vol. 27, (1972), pp Physcal Property Methods and Models 3-45 Verson 10

178 Property Model Descrptons Huron-Vdal Mxng Rules Huron and Vdal (1979) used a smple thermodynamc relatonshp to equate the excess Gbbs energy to expressons for the fugacty coeffcent as computed by equatons of state: E G RT ln ϕ x RT ln ϕ * (1) m = Equaton 1 s vald at any pressure, but cannot be evaluated unless some assumptons are made. If Equaton 1 s evaluated at nfnte pressure, the mxture must be lqud-lke and extremely dense. It can be assumed that: V( p = ) = b V E ( p = ) =0 (2) (3) Usng equatons 2 and 3 n equaton 1 results n an expresson for a/b that contans the excess Gbbs energy at an nfnte pressure: a b x a 1 E = Gm( p = ) (4) b Λ Where: Λ= λ 1 1+ λ 1 ln (5) λ 1+ λ The parameters λ 1 and λ 2 depend on the equaton-of-state used. In general a cubc equaton-of-state can be wrtten as: RT a p = ( V b) ( V + λ b)( V + λ b) m 1 m 2 (6) Values for λ 1 and λ 2 for the Peng-Robnson and the Soave-Redlch-Kwong equatons of state are: Equaton-of-state λ 1 λ 2 Peng-Robnson Redlch-Kwong-Soave Physcal Property Methods and Models Verson 10

179 Chapter 3 Ths expresson can be used at any pressure as a mxng rule for the parameter. The mxng rule for b s fxed by equaton 3. Even when used at other pressures, ths expresson contans the excess Gbbs energy at nfnte pressure. You can use any actvty coeffecent model to evaluate the excess Gbbs energy at nfnte pressure. Bnary nteracton coeffcents must be regressed. The mxng rule used contans as many bnary parameters as the actvty coeffcent model chosen. Ths mxng rule has been used successfully for polar mxtures at hgh pressures, such as systems contanng lght gases. In theory, any actvty coeffcent model can be used. But the NRTL equaton (as modfed by Huron and Vdal) has demonstrated better performance. The Huron-Vdal mxng rules combne extreme flexblty wth thermodynamc consstency, unlke many other mole-fracton-dependent equaton-of-state mxng rules. The Huron-Vdal mxng rules do not allow flexblty n the descrpton of the excess molar volume, but always predct reasonable excess volumes. The Huron-Vdal mxng rules are theoretcally ncorrect for low pressure, because quadratc mole fracton dependence of the second vral coeffcent (f derved from the equaton-of-state) s not preserved. Snce equatons of state are prmarly used at hgh pressure, the practcal consequences of ths drawback are mnmal. The Gbbs energy at nfnte pressure and the Gbbs energy at an arbtrary hgh pressure are smlar. But the correspondence s not close enough to make the mxng rule predctve. There are several methods for modfyng the Huron-Vdal mxng rule to make t more predctve. The followng three methods are used n ASPEN PLUS equaton-of-state models: The modfed Huron-Vdal mxng rule, second order approxmaton (MHV2) The Predctve SRK Method (PSRK) The Wong-Sandler modfed Huron-Vdal mxng rule (WS) These mxng rules are dscussed separately n the followng sectons. They have major advantages over other composton-dependent equaton-of-state mxng rules. References M.- J. Huron and J. Vdal,"New Mxng Rules n Smple Equatons of State for representng Vapour-lqud equlbra of strongly non-deal mxtures," Flud Phase Eq., Vol. 3, (1979), pp Physcal Property Methods and Models 3-47 Verson 10

180 Property Model Descrptons MHV2 Mxng Rules Dahl and Mchelsen (1990) use a thermodynamc relatonshp between excess Gbbs energy and the fugacty computed by equatons of state. Ths relatonshp s equvalent to the one used by Huron and Vdal: E Gm RT f f = x ln RT ln (1) RT The advantage s that the expressons for mxture and pure component fugactes do not contan the pressure. They are functons of compacty V/b and α : * * f ln ln b Q V + =, RT α (2) b Where: α = a brt (3) and f ln ln b Q V m + =, RT α (4) b wth α= a brt (5) The constants λ 1 and λ 2,whch depend only on the equaton-of-state (see Huron- Vdal Mxng Rules, ths chapter) occur n equatons 2 and 4. Instead of usng nfnte pressure for smplfcaton of equaton 1, the condton of zero pressure s used. At p= 0 an exact relatonshp between the compacty and α can be derved. By substtuton the smplfed equaton q( α ) s obtaned, and equaton 1 becomes: G E m ( p = 0) RT + x b ln = q( α) xq( ) b α (6) However, q( α ) can only be wrtten explctly for α=58.. Only an approxmaton s possble below that threshold. Dahl and Mchelsen use a second order polynomal ftted to the analytcal soluton for 10 < α < 13 that can be extrapolated to low alpha: 2 q( α) = qα+ q 2 α (7) 3-48 Physcal Property Methods and Models Verson 10

181 Chapter 3 Snce q( α) s a unversal functon (for each equaton-of-state), the combnaton of equatons 6 and 7 form the MHV2 mxng rule. Excess Gbbs energes, from any actvty coeffcent model wth parameters optmzed at low pressures, can be used to determne α, f α, b, and b are known. To compute b, a lnear mxng rule s assumed as n the orgnal Huron-Vdal mxng rules: b = x b Ths equaton s equvalent to the assumpton of zero excess molar volume. The MHV2 mxng rule was the frst successful predctve mxng rule for equatons of state. Ths mxng rule uses prevously determned actvty coeffcent parameters for predctons at hgh pressures. UNIFAC was chosen as a default for ts predctve character. The Lyngby modfed UNIFAC formulaton was chosen for optmum performance (see UNIFAC (Lyngby Modfed) on page 3-72). However, any actvty coeffcent model can be used when ts bnary nteracton parameters are known. Lke the Huron-Vdal mxng rules, the MHV2 mxng rules are not flexble n the descrpton of the excess molar volume. The MHV2 mxng rules are theoretcally ncorrect at the low pressure lmt. But the practcal consequences of ths drawback are mnmal (see Huron-Vdal Mxng Rules, ths chapter). References S. Dahl and M.L. Mchelsen, "Hgh-Pressure Vapor-Lqud Equlbrum wth a UNIFAC-based Equaton-of-state," AIChE J., Vol. 36, (1990), pp (8) Predctve Soave-Redlch-Kwong-Gmehlng Mxng Rules These mxng rules by Holderbaum and Gmehlng (1991) use a relatonshp between the excess Helmholtz energy and equaton-of-state. They do not use a relatonshp between equaton-of-state propertes and excess Gbbs energy, as n the Huron-Vdal mxng rules. The pressure-explct expresson for the equatonof-state s substtuted n the thermodynamc equaton: A p = V T (1) The Helmholtz energy s calculated by ntegraton. A E s obtaned by: E Am = Am xa * RT x ln x (2) I Where both A * and A m are calculated by usng equaton 1. A * and A m are wrtten n terms of equaton-of-state parameters. Physcal Property Methods and Models 3-49 Verson 10

182 Property Model Descrptons The smplfcaton of constant packng fracton ( Vm / b) s used: V b *, l l Vm = b (3) Wth: b = x b (4) Therefore: V E ( p = ) =0 m (5) The mxng rule s: a b x a 1 = A b Λ E m ( p) (6) Where Λ s slghtly dfferent from Λ for the Huron-Vdal mxng rule: Vm + λl 1 1 Λ = ln b λ1 λ2 Vm + λ 2 b (7) Where λ 1 and λ 2, depend on the equaton-of-state (see Huron-Vdal Mxng Rules, ths chapter). If equaton 6 s appled at nfnte pressure, the packng fracton goes to 1. The excess Helmholtz energy s equal to the excess Gbbs energy. The Huron-Vdal mxng rules are recovered. The goal of these mxng rules s to be able to use bnary nteracton parameters for actvty coeffcent models at any pressure. These parameters have been optmzed at low pressures. UNIFAC s chosen for ts predctve character. Two ssues exst: the packng fracton s not equal to one, and the excess Gbbs and Helmholtz energy are not equal at the low pressure where the UNIFAC parameters have been derved. Fscher (1993) determned that bolng pont, the average packng fracton for about 80 dfferent lquds wth dfferent chemcal natures was 1.1. Adoptng ths value, the dfference between lqud excess Gbbs energy and lqud excess Helmholtz energy can be computed as: l Vm l *, = b V = b,, *, l m m m V b l m l *, = 11. V = 11. b El El l A ( p) = G ( p = 1atm) + pdv x pdv (8) 3-50 Physcal Property Methods and Models Verson 10

183 Chapter 3 The result s a predctve mxng rule for cubc equatons of state. But the orgnal UNIFAC formulaton gves the best performance for any bnary par wth nteractons avalable from UNIFAC. Gas-solvent nteractons are unavalable. At the Unversty of Oldenburg n Germany, the UNIFAC groups were extended wth often-occurrng gases. New group nteractons were determned from gassolvent data, specfc to the Redlch-Kwong-Soave equaton-of-state. The new bult-n parameters to ASPEN PLUS are actvated when usng the PSRK equaton-of-state model. The PSRK method has a lot n common wth the Huron-Vdal mxng rules. The mole fracton s dependent on the second vral coeffcent and excess volume s predcted. These are mnor dsadvantages. References T. Holderbaum and J. Gmehlng, "PSRK: A Group Contrbuton Equaton-of-state based on UNIFAC," Flud Phase Eq., Vol. 70, (1991), pp K. Fscher, "De PSRK-Methode: Ene Zustandsglechung unter Verwendung des UNIFAC-Gruppenbetragsmodells," (Düsseldorf: VDI Fortschrttberchte, Rehe 3: Verfahrenstechnk, Nr. 324, VDI Verlag GmbH, 1993). Wong-Sandler Mxng Rules These mxng rules use a relatonshp between the excess Helmholtz energy and equaton-of-state. They do not use a relatonshp between equaton-of-state propertes and excess Gbbs energy, as n the Huron-Vdal mxng rules. The pressure-explct expresson for the equaton-of-state s substtuted n the thermodynamc equaton: A p = V T (1) The Helmholtz energy s obtaned by ntegraton, A E s obtaned by: E Am = Am xa * RT x ln x (2) Where both A * and A m are calculated by usng equaton 1. A * and A m are wrtten n terms of equaton-of-state parameters. Lke Huron and Vdal, the lmtng case of nfnte pressure s used. Ths smplfes the expressons for A * and A m. Equaton 2 becomes: a b x a 1 E = Am( p = ) (3) b Λ Physcal Property Methods and Models 3-51 Verson 10

184 Property Model Descrptons Where Λ depends on the equaton-of-state (see Huron-Vdal Mxng Rules, ths chapter). Equaton 3 s completely analogous to the Huron-Vdal mxng rule for the excess Gbbs energy at nfnte pressure. (See equaton 4, Huron-Vdal Mxng Rules, ths chapter.) The excess Helmholtz energy can be approxmated by the excess Gbbs energy at low pressure from any lqud actvty coeffcent model. Usng the Helmholtz energy permts another mxng rule for b than the lnear mxng rule. The mxng rule for b s derved as follows. The second vral coeffcent must depend quadratcally on the mole fracton: BT ( )= Wth: j xxb j j (4) B j B Bjj = ( + ) ( 1 k ) j 2 (5) The relatonshp between the equaton-of-state at low pressure and the vral coeffcent s: B = b a RT (6) B = b a RT (7) Wong and Sandler dscovered the followng mxng rule to satsfy equaton 4 (usng equatons 6 and 7): b = A 1 E m j xx B j j ( p = ) ΛRT xb j The excess Helmholtz energy s almost ndependent of pressure. It can be approxmated by the Gbbs energy at low pressure. The dfference between the two functons s corrected by fttng k j untl the excess Gbbs energy from the equaton-of-state (usng the mxng rules 3 and 8) s equal to the excess Gbbs energy computed by an actvty coeffecent model. Ths s done at a specfc mole fracton and temperature. Ths mxng rule accurately predcts the VLE of polar mxtures at hgh pressures. UNIFAC or other actvty coeffecent models and parameters from the lterature are used. Gas solubltes are not predcted. They must be regressed from expermental data Physcal Property Methods and Models Verson 10

185 Chapter 3 Unlke other (modfed) Huron-Vdal mxng rules, the Wong and Sandler mxng rule meets the theoretcal lmt at low pressure. The use of k j does nfluence excess molar volume behavor. For calculatons where denstes are mportant, check whether they are realstc. References D. S. Wong and S. I. Sandler, "A Theoretcally Correct New Mxng Rule for Cubc Equatons of State for Both Hghly and Slghtly Non-deal Mxtures," AIChE J., Vol. 38, (1992), pp D. S. Wong, H. Orbey, and S. I. Sandler, "Equaton-of-state Mxng Rule for Nondeal Mxtures Usng Avalable Actvty Coeffcent Model Parameters and That Allows Extrapolaton over Large Ranges of Temperature and Pressure", Ind Eng Chem. Res., Vol. 31, (1992), pp H. Orbey, S. I. Sandler and D. S. Wong, "Accurate Equaton-of-state Predctons at Hgh Temperatures and Pressures Usng the Exstng UNIFAC Model," Flud Phase Eq., Vol. 85, (1993), pp Actvty Coeffcent Models ASPEN PLUS has 18 bult-n actvty coeffcent models. Ths secton descrbes the actvty coeffcent models avalable. Model Bromley-Ptzer Chen-Null Constant Actvty Coeffcent Electrolyte NRTL Ideal Lqud NRTL (Non-Random-Two-Lqud) Ptzer Polynomal Actvty Coeffcent Redlch-Kster Type Electrolyte Regular soluton, local composton Arthmetc Electrolyte Ideal Local composton Electrolyte Arthmetc Arthmetc contnued Physcal Property Methods and Models 3-53 Verson 10

186 Property Model Descrptons Model Scatchard-Hldebrand Three-Suffx Margules UNIFAC UNIFAC (Lyngby modfed) UNIFAC (Dortmund modfed) UNIQUAC Van Laar Wagner nteracton parameter Wlson Wlson wth Lqud Molar Volume Type Regular soluton Arthmetc Group contrbuton Group contrbuton Group contrbuton Local composton Regular soluton Arthmetc Local composton Local composton Bromley-Ptzer Actvty Coeffcent Model The Bromley-Ptzer actvty coeffcent model s a smplfed Ptzer actvty coeffcent model wth Bromley correlatons for the nteracton parameters. See Appendx A for a detaled descrpton. Ths model has predctve capabltes. It can be used up to 6M onc strength, but s less accurate than the Ptzer model f the parameter correlatons are used. The Bromley-Ptzer model n ASPEN PLUS nvolves user-suppled parameters, used n the calculaton of bnary parameters for the electrolyte system. Parameters β ( 0 ), β ( 1 ), β ( 2 ), β ( 3) and θ have fve elements to account for temperature dependences. Elements P1 through P5 follow the temperature dependency relaton: ref 1 1 T 2 ref 2 f( T) = P1 + P2( T T ) + P3 P ln P( T ( T ) ) T T ref + 4 ref + 5 T Where: T ref = K. The user must: Supply these elements usng a Propertes Parameters Bnary.T-Dependent form. Specfy Comp ID and Comp ID j on ths form, usng the same order that appears on the Components.Man form Physcal Property Methods and Models Verson 10

187 Chapter 3 Parameter Name Symbol No. of Elements Default Unts Ionc Unary Parameters GMBPB β on 1 0 GMBPD δ on Caton-Anon Parameters GMBPB0 β ( 0) 5 0 GMBPB1 β ( 1) 5 0 GMBPB2 β ( 2) 5 0 GMBPB3 β ( 3) 5 0 Caton-Caton Parameters GMBPTH θ cc 5 0 Anon-Anon Parameters GMBPTH θ aa 5 0 Molecule-IonParameters Molecule-Molecule Parameters GMBPB0 β ( 0) 5 0 GMBPB1 β ( 1) 5 0 Chen-Null The Chen-Null model calculates lqud actvty coeffcents and t can be used for hghly non-deal systems. The generalzed expresson used n ts dervaton can be adapted to represent other well known formalsms for the actvty coeffcent by properly defnng ts bnary terms. Ths characterstc allows the model the use of already avalable bnary parameters regressed for those other lqud actvty models wth thermodynamc consstency. The equaton for the Chen-Null lqud actvty coefcent s: lnγ Aj x Rj xj A x R x 1 j j = + xk + 2 Sj xj Vj xj k j j jk jk j j j Ak Rk Sk Vk Sjk xj Vjk x j Ajk xj Rjk xj Sjk xj V jk j j j j j j x j Physcal Property Methods and Models 3-55 Verson 10

188 Property Model Descrptons Where: R j = A A j j A = 0 A A A j j j = 1 bj = aj + T Subscrpts and j are component ndces. The choce of model and parameters can be set for each bnary par consttutng the process mxture by assgnng the approprate value to the ICHNUL parameter. The Regular Soluton and Scatchard-Hamer models are reganed by substtutng n the general expresson (ICHNUL = 1 or 2). V j V = S j = V *, l j *, l Where: *, l V j = Lqud molar volume of component The Chen-Null actvty coeffcent model collapses to the Margules lqud actvty coeffcent expresson by settng (ICHNUL = 3): V j = S =1 j The Van Laar Lqud actvty coeffcent model s the obtaned when the V and S parameters n the Chen-Null models are set to the rato of the cross terms of A (ICHNUL = 4:) V j = S = j A A j j Fnally, the Renon or NRTL model s obtaned when we make the followng susbsttutons n the Chen-Null expresson for the lqud actvty (ICHNUL = 5). S R A j = j A j j 3-56 Physcal Property Methods and Models Verson 10

189 Chapter 3 A = 2τ G j j j V j = G j The followng are defned for the Non-Random Two-Lqud actvty coeffcent model. Where: G j ( τ ) = e C j j b j τ j = a j + T C = c + d ( T K) j j j c d j j = c j = d j The bnary parameters CHNULL/1, CHNULL/2, and CHNULL/3 can be determned from regresson of VLE and/or LLE data. Also, f you have parameters for many of the mxture pars for the Margules, Van Laar, Scatchard- Hldebrand, and NRTL (Non-Random-Two-Lqud) actvty models, you can use them drectly wth the Chen-Null actvty model after selectng the proper code (ICHNUL) to dentfy the source model and enterng the approprate actvty model parameters. Parameter Name/Element Symbol Default Upper Lmt Lower Lmt Unts ICHNUL CHNULL/1 a j 0 CHNULL/2 b j 0 CHNULL/3 Vj 0 The parameter ICHNUL s used to dentfy the actvty model parameters avalable for each bnary par of nterest. The followng values are allowed for ICHNUL: ICHNUL = 1 or 2, sets the model to the Scatchard-Hamer or regular s oluton model for the assocated bnary; ICHNUL = 3, sets the model to the Three-Suffx Margules actvty model for the assocated bnary; ICHNUL = 4, sets the model to the Van Laar formalsm for the actvty model for the assocated bnary; ICHNUL = 5, sets the model to the NRTL (Renon) formalsm for the actvty model for the assocated bnary. Physcal Property Methods and Models 3-57 Verson 10

190 Property Model Descrptons ICHNUL = 6, sets the model to the full Chen-Null formalsm for the actvty model for the assocated bnary. When you specfy a value for the ICHNUL parameter that s dfferent than the default, you must enter the approprate bnary model parameters for the chosen actvty model drectly. The routne wll automatcally convert the expressons and parameters to conform to the Chen-Null formulaton. Constant Actvty Coeffcent Ths approach s used exclusvely n metallurgcal applcatons where multple lqud and sold phases can coexst. You can assgn any value to the actvty coeffcent of component. Use the Propertes Parameters Unary.Scalar form. The equaton s: γ = a Parameter Name/Element Symbol Default MDS Upper Lmt Lower Lmt Unts GMCONS a 1.0 x Electrolyte NRTL Actvty Coeffcent Model ASPEN PLUS uses the electrolyte NRTL model to calculate actvty coeffcents, enthalpes, and Gbbs energes for electrolyte systems. Model development and workng equatons are provded n Appendx B. The adjustable parameters for the electrolyte NRTL model nclude the: Pure component delectrc constant coeffcent of nonaqueous solvents Born radus of onc speces NRTL parameters for molecule-molecule, molecule-electrolyte, and electrolyte-electrolyte pars The pure component delectrc constant coeffcents of nonaqueous solvents and Born radus of onc speces are requred only for mxed-solvent electrolyte systems. The temperature dependency of the delectrc constant of solvent B s: 1 1 ε B ( T)= A B + B B T C B Each type of electrolyte NRTL parameter conssts of both the nonrandomness factor, α, and energy parameters, τ. The temperature dependency relatons of the electrolyte NRTL parameters are: Molecule-Molecule Bnary Parameters: B = + + FBB ln( T) + GBB T T BB τ BB A BB 3-58 Physcal Property Methods and Models Verson 10

191 Chapter 3 Electrolyte-Molecule Par Parameters: D = + + E T ca, B τ ca, B C ca, B D = + + E T Bca, τ Bca, C Bca, ca, B Bca, ref ( ) T T T ref ( ) T T T T + ln ref T T + ln ref T Electrolyte-Electrolyte Par Parameters: For the electrolyte-electrolyte par parameters, the two electrolytes must share ether one common caton or one common anon: D = + + E T ca, c a τ ca, c a C ca, c a D = + + E T ca, ca τ ca, ca C ca, ca Where: T ref = K ca, c a ca, ca ref ( ) T T T ref ( ) T T T T + ln ref T T + ln ref T Many parameter pars are ncluded n the electrolyte NRTL model parameter databank (see ASPEN PLUS Physcal Property Data, Chapter 1). Parameter Name Symbol No. of Elements Default MDS Unts Delectrc Constant Unary Parameters CPDIEC A B 1 B B 1 0 C B TEMPERATURE Ionc Born Radus Unary Parameters RADIUS r 1 3x10-10 LENGTH Molecule-Molecule Bnary Parameters If delectrc constant parameters are mssng for a solvent, the delectrc constant of water s automatcally assgned. Absolute temperature unts are assumed (ASPEN PLUS User Gude). contnued Physcal Property Methods and Models 3-59 Verson 10

192 Property Model Descrptons Parameter Name Symbol No. of Elements Default MDS Unts NRTL/1 A BB 0 x A 0 x BB NRTL/2 B BB 0 x TEMPERATURE NRTL/3 α α B 0 x BB TEMPERATURE =.3 x BB B B NRTL/4 0 x TEMPERATURE NRTL/5 F BB 0 x TEMPERATURE F 0 x TEMPERATURE BB NRTL/6 G BB 0 x TEMPERATURE Electrolyte-Molecule Par Parameters G 0 x TEMPERATURE BB GMELCC C 1 0 x ca, B C 1 0 x Bca, GMELCD D 1 0 x ca, B TEMPERATURE D 1 0 x Bca, TEMPERATURE GMELCE E 1 0 x ca, B GMELCN α α E 1 0 x Bca, ca, B = 1.2 x B, ca Absolute temperature unts are assumed (ASPEN PLUS User Gude). If an electrolyte-molecule parameter s mssng, the followng defaults are used: Electrolyte-water -4 Water-electrolyte 8 Electolyte-solvent -2 Solvent-electrolyte 10 Electrolyte-solute -2 Solute-electrolyte 10 contnued 3-60 Physcal Property Methods and Models Verson 10

193 Chapter 3 Parameter Name Symbol No. of Elements Default MDS Unts Electrolyte-Electrolyte Par Parameters GMELCC C 1 0 x ca, ca C 1 0 x ca, ca C 1 0 x ca, c a C 1 0 x caca, GMELCD D 1 0 x ca, ca TEMPERATURE D 1 0 x ca, ca TEMPERATURE D 1 0 x ca, c a TEMPERATURE D 1 0 x caca, TEMPERATURE GMELCE E 1 0 x ca, ca GMELCN α α E 1 0 x ca, ca E 1 0 x ca, c a E 1 0 x caca, α ca, ca = 1.2 x ca, ca = α 1.2 x ca, c a c a, ca If delectrc constant parameters are mssng for a solvent, the delectrc constant of water s automatcally assgned. Absolute temperature unts are assumed (ASPEN PLUS User Gude). If an electrolyte-molecule parameter s mssng, the followng defaults are used: Electrolyte-water -4 Water-electrolyte 8 Electolyte-solvent -2 Solvent-electrolyte 10 Electrolyte-solute -2 Solute-electrolyte 10 Physcal Property Methods and Models 3-61 Verson 10

194 Property Model Descrptons Ideal Lqud Ths model s used n Raoult s law. It represents dealty of the lqud phase. Ths model can be used for mxtures of hydrocarbons of smlar carbon number. It can be used as a reference to compare the results of other actvty coeffcent models. The equaton s: ln γ = 0 NRTL (Non-Random Two-Lqud) The NRTL model calculates lqud actvty coeffcents for the followng property methods: NRTL, NRTL-2, NRTL-HOC, NRTL-NTH, and NRTL-RK. It s recommended for hghly non-deal chemcal systems, and can be used for VLE and LLE applcatons. The model can also be used n the advanced equaton-ofstate mxng rules, such as Wong-Sandler and MHV2. The equaton for the NRTL model s: xjτ jgj j xg j j lnγ = + τj xg k k j xg k kj Where: k G j = exp ( α τ ) τ j = a j j j bj + T + ej ln T + fjt α j = c + d ( T K) τ = 0 G = 1 j j k x m k τ m mj mj xg k G kj a j a j b j b j c j c j d j d j 3-62 Physcal Property Methods and Models Verson 10

195 Chapter 3 Recommended c j Values for Dfferent Types of Mxtures c j Mxtures 0.30 Nonpolar substances; nonpolar wth polar non-assocated lquds; small devatons from dealty 0.20 Saturated hydrocarbons wth polar non-assocated lquds and systems that exhbt lqud-lqud mmscblty 0.47 Strongly self-assocated substances wth nonpolar substances The bnary parameters a j, b j, c j, d j, e j, and f j can be determned from VLE and/or LLE data regresson. ASPEN PLUS has a large number of bult-n bnary parameters for the NRTL model. The bnary parameters have been regressed usng VLE and LLE data from the Dortmund Databank. The bnary parameters for the VLE applcatons were regressed usng the deal gas, Redlch-Kwong, and Hayden O Connell equatons of state. See ASPEN PLUS Physcal Property Data, Chapter 1 for detals. Parameter Name/Element Symbol Default MDS Upper Lmt Lower Lmt Unts NRTL/1 a j 0 x NRTL/2 b j 0 x TEMPERATURE NRTL/3 c j 0.30 x NRTL/4 d j 0 x TEMPERATURE NRTL/5 e j 0 x TEMPERATURE NRTL/6 f j 0 x TEMPERATURE Absolute temperature unts are assumed. References H. Renon and J.M. Prausntz, "Local Compostons n Thermodynamc Excess Functons for Lqud Mxtures," AIChE J., Vol. 14, No. 1, (1968), pp Ptzer Actvty Coeffcent Model The Ptzer model s commonly used n the calculaton of actvty coeffcents for aqueous electrolytes up to 6 molal onc strength. Do not use ths model f a nonaqueous solvent exsts. The model development and workng equatons are provded n Appendx C. Parameter converson between the Ptzer notaton and our notaton s also provded. Physcal Property Methods and Models 3-63 Verson 10

196 Property Model Descrptons The Ptzer model n ASPEN PLUS nvolves user-suppled parameters that are used n the calculaton of bnary and ternary parameters for the electrolyte system. Fve elements (P1 through P5) account for the temperature dependences of () parameters β 0 (), β 1 (), β 2 (), β 3, c ϕ, and θ. These parameters follow the temperature dependency relaton: ref 1 1 T f( T) = P + P ( T T ) + P + P ln T T T Where: Tref = K ref 4 ref 5 2 ref 2 ( ( ) ) + P T T The user must: Supply these elements usng a Propertes Parameters Bnary.T-Dependent form. Specfy Comp ID and Comp ID j on ths form, usng the same order that appears on the Components.Man form. The parameters are summarzed n the followng table. There s a Ptzer parameter databank n ASPEN PLUS (see ASPEN PLUS Physcal Property Data, Chapter 1). Parameter Name Symbol No. of Elements Default MDS Unts Caton-Anon Parameters GMPTB0 β ( 0) 5 0 x GMPTB1 β ( 1) 5 0 x GMPTB2 β ( 2) 5 0 x GMPTB3 β ( 3) 5 0 x GMPTC C θ 5 0 x Caton-Caton Parameters GMPTTH θ cc 5 0 x Anon-Anon Parameters GMPTTH θ aa 5 0 x Caton1-Caton 2-Common Anon Parameters GMPTPS Ψ 1 0 x cc a contnued 3-64 Physcal Property Methods and Models Verson 10

197 Chapter 3 Parameter Name Symbol No. of Elements Default MDS Unts Anon1-Anon2-Common Caton Parameters GMPTPS Ψ ca a 1 0 x Molecule-Ion and Molecule-Molecule Parameters GMPTB0 β ( 0) 5 0 x GMPTB1 β ( 1) 5 0 x GMPTC C θ 5 0 x Polynomal Actvty Coeffcent Ths model represents actvty coefcent as an emprcal functon of composton and temperature. It s used frequently n metallurgcal applcatons where multple lqud and sold soluton phases can exst. The equaton s: ln γ = A + Bx + Cx + D x + E x Where: A = a T + a + a ln( T) B = b T + b + b ln( T) C = c T + c + c ln( T) D = d T + d + d ln( T) E = e T + e + e ln( T) For any component, the value of the actvty coeffcent can be fxed: γ = f Parameter Name/Element Symbol Default MDS Upper Lmt Lower Lmt Unts GMPLYP/1 a 1 0 x GMPLYP/2 a 2 0 x GMPLYP/3 a 3 0 x GMPLYP/4 b 1 0 x contnued Physcal Property Methods and Models 3-65 Verson 10

198 Property Model Descrptons Parameter Name/Element Symbol Default MDS Upper Lmt Lower Lmt Unts GMPLYP/5 b 2 0 x GMPLYP/6 b 3 0 x GMPLYP/7 c 1 0 x GMPLYP/8 c 2 0 x GMPLYP/9 c 3 0 x GMPLYP/10 d 1 0 x GMPLYP/11 d 2 0 x GMPLYP/12 d 3 0 x GMPLYP/13 e 1 0 x GMPLYP/14 e 2 0 x GMPLYP/15 e 3 0 x GMPLYO f x Redlch-Kster Ths model calculates actvty coeffcents. It s a polynomal n the dfference between mole fractons n the mxture. It can be used for lqud and sold mxtures (mxed crystals). The equaton s: ( ) ( ) nc 5 2 ( ) ( ) ( n 2 ) 1 j 2 j k n jk j k [( 2 1) j k] = xa x x nx x xxa x x n x x nc 5 n ln γ j n, j j, j= 1 n= 1 k= 1 n= 1 Where: nc = Number of components A j 1, = aj T + b A j 2, = cj T + d 3, = ej T + f A j A j 4, = gj T + h j j j j 3-66 Physcal Property Methods and Models Verson 10

199 Chapter 3 A j 5, = mj T + n j For any component, the value of the actvty coeffcent can be fxed: γ = v Parameter Name/ Element Symbol Default MDS Upper Lmt Lower Lmt Unts GMRKTB/1 a j 0 x GMRKTB/2 b j 0 x GMRKTB/3 c j 0 x GMRKTB/4 d j 0 x GMRKTB/5 e j 0 x GMRKTB/6 f j 0 x GMRKTB/7 g j 0 x GMRKTB/8 h j 0 x GMRKTB/9 m j 0 x GMRKTB/10 n j 0 x GMRKTO v x Scatchard-Hldebrand The Scatchard-Hldebrand model calculates lqud actvty coeffcents. It s used n the CHAO-SEA property method and the GRAYSON property method. The equaton for the Scatchard-Hldebrand model s: *, l V ln γ = ϕ jϕk ( Aj 12Ajk ) RT Where: A j = 2( δ δ j) j k 2 ϕ = xv l V *, l m Physcal Property Methods and Models 3-67 Verson 10

200 Property Model Descrptons *, L V m = xv *, l The Scatchard-Hldebrand model does not requre bnary parameters. Parameter Name/Element Symbol Default MDS Upper Lmt Lower Lmt Unts TC T c x TEMPERATURE DELTA δ x SOLUPARAM VLCVT1 *, CVT V x MOLE-VOLUME GMSHVL *, I I V V = V *, *, CVT T c x MOLE-VOLUME Three-Suffx Margules Ths model can be used to descrbe the excess propertes of lqud and sold solutons. It does not fnd much use n chemcal engneerng applcatons, but s stll wdely used n metallurgcal applcatons. Note that the bnary parameters for ths model do not have physcal sgnfcance. The equaton s: nc nc nc nc nc nc ( ) ( ) ( 2 ) ( ) ln γ = 1 k j + k j x j k jl x j x l + k j k jl x j x j x k jl k ljj x l x 2 2 j j Where k j s a bnary parameter: ( ) k = a T + b + c ln T j j j j j l j For any component, the value of the actvty coeffcent can be fxed: γ = d j l Parameter Name/ Element Symbol Default MDS Upper Lmt Lower Lmt Unts GMMRGB/1 a j 0 x TEMPERATURE GMMRGB/2 b j 0 x GMMRGB/3 c j 0 x GMMRGO d x 3-68 Physcal Property Methods and Models Verson 10

201 Chapter 3 References M. Margules, "Über de Zusammensetzung der gesättgten Dämpfe von Mschungen," Stzungsber. Akad. Wss. Venna, Vol. 104, (1895), p D.A. Gaskell, Introducton to Metallurgcal Thermodyancs, 2nd ed., (New York: Hemsphere Publshng Corp., 1981), p R.C. Red, J.M. Prausntz, and B.E. Polng, The Propertes of Gases and Lquds, 4th ed., (New York: McGraw-Hll, 1987). UNIFAC The UNIFAC model calculates lqud actvty coeffcents for the followng property methods: UNIFAC, UNIF-HOC, and UNIF-LL. Because the UNIFAC model s a group-contrbuton model, t s predctve. All publshed group parameters and group bnary parameters are stored n ASPEN PLUS. The equaton for the orgnal UNIFAC lqud actvty coeffcent model s made up of a combnatoral and resdual term: c r ln γ = lnγ + lnγ ln γ c Φ Φ Z Φ Φ = ln + 1 ln + 1 x x 2 θ θ Where the molecular volume and surface fractons are: Φ = nc j xr xr j j x z q and θ = 2 nc x z j q 2 j j Where nc s the number of components n the mxture. The coordnaton number z s set to 10. The parameters r and q are calculated from the group volume and area parameters: r ng = v R and q = v Q k k k ng k k k Where ν k s the number of groups of type k n molecule, and ng s the number of groups n the mxture. The resdual term s: ng [ ] r ln γ = νk ln Γk ln Γk k Physcal Property Methods and Models 3-69 Verson 10

202 Property Model Descrptons Γ k s the actvty coeffcent of a group at mxture composton, and Γ k s the actvty coeffcent of group k n a mxture of groups correspondng to pure. The parameters Γ k and Γ k are defned by: ng ng m km ln Γ k = Q k ln m mk θ τ 1 θ τ ng m m θτ n Wth: n nm k k θ k = 2 ng And: m X X m bmn T τ mn = e / z Q z Q 2 m The parameter X k s the group mole fracton of group k n the lqud: X k = j nc m ν kj j nc ng ν x mj j x j Parameter Name/Element SymbolT Default MDS Lower Lmt Upper Lmt Unts UFGRP ( νk νm...) GMUFQ Q k GMUFR R k GMUFB b kn TEMPERATURE The parameter UFGRP stores the UNIFAC functonal group number and number of occurrences of each group. UFGRP s stored n the ASPEN PLUS pure component databank for most components. For nondatabank components, enter UFGRP on the Propertes Molecular Structure Functonal Group sheet. See ASPEN PLUS Physcal Property Data, Chapter 3, for a lst of the UNIFAC functonal groups Physcal Property Methods and Models Verson 10

203 Chapter 3 References Aa. Fredenslund, R.L. Jones and J.M. Prausntz, AIChE J., Vol. 21, (1975), p Aa. Fredenslund, J. Gmehlng and P. Rasmussen, "Vapor-Lqud Equlbra usng UNIFAC," (Amsterdam: Elsever, 1977). H.K. Hansen, P. Rasmussen, Aa. Fredenslund, M. Schller, and J. Gmehlng, "Vapor-Lqud Equlbra by UNIFAC Group Contrbuton. 5 Revson and Extenson", Ind. Eng. Chem. Res., Vol. 30, (1991), pp UNIFAC (Dortmund Modfed) The UNIFAC modfcaton by Gmehlng and coworkers (Wedlch and Gmehlng, 1987; Gmehlng et al., 1993), s slghtly dfferent n the combnatoral part. It s otherwse unchanged compared to the orgnal UNIFAC: c Φ z ln γ = ln q ln x + Φ x Φ θ + Φ θ Wth: Φ 3 r 4 = x xr j j 3 4 j The temperature dependency of the nteracton parameters s: a = a + a T + a T mn mn, 1 mn, 2 mn, 3 2 Parameter Name/Element SymbolT Default MDS Lower Lmt Upper Lmt Unts UFGRPD ( k m ) ν ν... k m GMUFDQ Q k GMUFDR R k UNIFDM/1 a mn,1 0 TEMPERATURE UINFDM/2 a mn,2 0 TEMPERATURE UNIFDM/3 a mn,3 0 TEMPERATURE Physcal Property Methods and Models 3-71 Verson 10

204 Property Model Descrptons The parameter UFGRPD stores the group number and the number of occurrences of each group. UFGRPD s stored n the ASPEN PLUS pure component databank. For nondatabank components, enter UFGRPD on the Propertes Molecular Structure Functonal Group sheet. See ASPEN PLUS Physcal Property Data, Chapter 3, for a lst of the Dortmund modfed UNIFAC functonal groups. References U. Wedlch and J. Gmehlng, "A Modfed UNIFAC Model 1. Predcton of VLE, h E and γ," Ind. Eng. Chem. Res., Vol. 26, (1987), pp J. Gmehlng, J. L, and M. Schller, "A Modfed UNIFAC Model. 2. Present Parameter Matrx and Results for Dfferent Thermodynamc Propertes," Ind. Eng. Chem. Res., Vol. 32, (1993), pp UNIFAC (Lyngby Modfed) The equatons for the "temperature-dependent UNIFAC" (Larsen et al., 1987) are smlar to the orgnal UNIFAC: c r ln γ = ln γ + ln γ, ln γ c ω ω = ln + 1 x x Volume fractons are modfed: ω = nc j xr 2 3 xr j j 2 3 Wth: r ng = ν R k k k ng ( ) r ln γ = νk ln Γk ln Γk k 3-72 Physcal Property Methods and Models Verson 10

205 Chapter 3 Where Γ k and Γ k defned as: have the same meanng as n the orgnal UNIFAC, but ng z ln Γ k = Qk 1 ln θ m τ mk + 2 m Wth: ng m m ng n θ τ n km θτ nm k k θ k = 2 ng m X X z Q m a T τ mn = e mn z Q 2 m The temperature dependency of a s descrbed by a functon nstead of a constant: amn = amn, 1 + amn, 2( T ) + amn, 3 T ln + T T Parameter Name/Element Symbol T Default MDS Lower Lmt Upper Lmt Unts UFGRPL ( νk νm...) GMUFLQ Q k GMUFLR R k UNIFLB/1 a mn,1 0 TEMPERATURE UNIFLB/2 a mn,2 0 TEMPERATURE UNIFLB/3 a mn,3 0 TEMPERATURE The parameter UFGRPL stores the modfed UNIFAC functonal group number and the number of occurrences of each group. UFGRPL s stored n the ASPEN PLUS pure component databank. For nondatabank components, enter UFGRP on the Propertes Molec-Struct.Func Group form. See ASPEN PLUS Physcal Property Data, Chapter 3, for a lst of the Larsen modfed UNIFAC functonal groups. Physcal Property Methods and Models 3-73 Verson 10

206 Property Model Descrptons References B. Larsen, P. Rasmussen, and Aa. Fredenslund, "A Modfed UNIFAC Group- Contrbuton Model for Predcton of Phase Equlbra and Heats of Mxng," Ind. Eng. Chem. Res., Vol. 26, (1987), pp UNIQUAC The UNIQUAC model calculates lqud actvty coeffcents for these property methods: UNIQUAC, UNIQ-2, UNIQ-HOC, UNIQ-NTH, and UNIQ-RK. It s recommended for hghly non-deal chemcal systems, and can be used for VLE and LLE applcatons. Ths model can also be used n the advanced equatons of state mxng rules, such as Wong-Sandler and MHV2. The equaton for the UNIQUAC model s: Φ z θ Φ lnγ = ln + q ln q ln t q θτ j j t + j l + q xl x 2 Φ x Where: ; = θ = qx q q q x T T k k k θ = qx q ; q = q x T T k k k Φ = Φ rx r T ; r T r k x k k l = ( ) t = = = z r q r θτ k k k τ j = exp( a + b T + C ln T + d T z = 10 j j j j j j j j a j a j b j b j c j c j 3-74 Physcal Property Methods and Models Verson 10

207 Chapter 3 d j d j The bnary parameters a j, b j, c j, and d j can be determned from VLE and/or LLE data regresson. ASPEN PLUS has a large number of bult-n parameters for the UNIQUAC model. The bnary parameters have been regressed usng VLE and LLE data from the Dortmund Databank. The bnary parameters for VLE applcatons were regressed usng the deal gas, Redlch-Kwong, and Hayden- O Connell equatons of state. See Chapter 1, ASPEN PLUS Physcal Property Data, for detals. Parameter Name/Element Symbol Default MDS Lower Lmt Upper Lmt Unts GMUQR r x GMUQQ q x GMUQQ1 q q x UNIQ/1 a j 0 x UNIQ/2 b j 0 x TEMPERATURE UNIQ/3 c j 0 x TEMPERATURE UNIQ/4 d j 0 x TEMPERATURE Absolute temperature unts are assumed. References D.S. Abrams and J.M. Prausntz, "Statstcal Thermodynamcs of lqud mxtures: A new expresson for the Excess Gbbs Energy of Partly or Completely Mscble Systems," AIChE J., Vol. 21, (1975), p A. Bond, "Physcal Propertes of Molecular Crystals, Lquds and Gases," (New York: Wley, 1960). Smonetty, Yee and Tassos, "Predcton and Correlaton of LLE," Ind. Eng. Chem., Process Des. Dev., Vol. 21, (1982), p Van Laar The Van Laar model (Van Laar 1910) calculates lqud actvty coeffcents for the property methods: VANLAAR, VANL-2, VANL-HOC, VANL-NTH, and VANL- RK. It can be used for hghly nondeal systems. [ ] 2 ( 1 ) ( 1) ln = A z + C z ( z ) + z AB AB γ Physcal Property Methods and Models 3-75 Verson 10

208 Property Model Descrptons Where: Ax z = Ax+ B x ( 1 ) A = xa j j ( 1 x) j B = xa j j ( 1 x) j C = xc ( 1 x) j j j A j = a + b T C j = c + d T j j j j C j = C j A = B = C = 0 a j a j b j b j Parameters Name/Element Symbol Default MDS Lower Lmt Upper Lmt Unts VANL/1 a j 0 x VANL/2 b j 0 x TEMPERATURE VANL/3 c j 0 x VANL/4 d j 0 x TEMPERATURE Absolute temperature unts are assumed. References J.J. Van Laar, "The Vapor Pressure of Bnary Mxtures," Z. Phys. Chem., Vol. 72, (1910), p R.C. Red, J.M. Prausntz, and B.E. Polng, The Propertes of Gases and Lquds, 4th ed. (New York: McGraw-Hll, 1987) Physcal Property Methods and Models Verson 10

209 Chapter 3 Wagner Interacton Parameter The Wagner Interacton Parameter model calculates actvty coeffcents. Ths model s used for dlute solutons n metallurgcal applcatons. The relatve actvty coeffcent wth respect tothe reference actvty coeffcent of a solute (n a mxture of solutes, j, and l and solvent A) s: ln ref ( ) γ γ = ln γ + kx j A Where: nc nc nc A j j= 1 ln γ A = 1 2 k jl x j x l jand l A j l The parameter γ ref s the reference actvty coeffcent of solute : ref ln γ = a T + b + c ln( T) k j s a bnary parameter: ( ) k = d T + e + f ln T j j j j For any component, the value of the actvty coeffcent can be fxed: γ = g Ths model s recommended for dlute solutons. Parameter Name/ Element Symbol Default MDS Lower Lmt Upper Lmt Unts GMWIPR/1 a 0 x TEMPERATURE GMWIPR/2 b 0 x GMWIPR/3 c 0 x GMWIPB/1 d j 0 x TEMPERATURE GMWIPB/2 e j 0 x GMWIPB/3 f j 0 x GMWIPO g x GMWIPS 0 x GMWIPS s used to dentfy the solvent component. You must set GMWIPS to 1.0 for the solvent component. Ths model allows only one solvent. Physcal Property Methods and Models 3-77 Verson 10

210 Property Model Descrptons References A.D. Pelton and C. W. Ball, "A Modfed Interacton Parameter Formalsm for Non-Dlute Solutons," Metallurgcal Transactons A, Vol. 17A, (July 1986), p Wlson The Wlson model calculates lqud actvty coeffcents for the property methods: WILSON, WILS2, WILS-HOC, WILS-NTH, WILS-RK, and WILS-HF. It s recommended for hghly nondeal systems, especally alcohol-water systems. It can also be used n the advanced equaton-of-state mxng rules, such as Wong- Sandler and MHV2. Ths model cannot be used for lqud-lqud equlbrum calculatons. The equaton for the Wlson model s: ln γ = ln Ax j j 1 Where: j j k Ax j j A x ln A j = a + b T + c ln T + d T j j j j jk k a j a j b j b j c j c j d j d j The bnary parameters a j, b j, c j, and d j must be determned from VLE data regresson. ASPEN PLUS has a large number of bult-n bnary parameters for the Wlson model. The bnary parameters have been regressed usng VLE data from the Dortmund Databank. The bnary parameters were regressed usng the deal gas, Redlch-Kwong, and Hayden-O Connell equatons of state. See Chapter 1, ASPEN PLUS Physcal Property Data, for detals. Parameter Name/Element Symbol Default MDS Lower Lmt Upper Lmt Unts WILSON/1 a j 0 x WILSON/2 b j 0 x TEMPERATURE WILSON/3 c j 0 x - TEMPERATURE WILSON/4 d j 0 x TEMPERATURE Absolute temperature unts are assumed Physcal Property Methods and Models Verson 10

211 Chapter 3 References G.M. Wlson, J. Am. Chem. Soc., Vol. 86, (1964), p Wlson Model wth Lqud Molar Volume Ths Wlson model calculates lqud actvty coeffcents usng the orgnal formulaton of Wlson (Wlson 1964) except that lqud molar volume s calculated at system temperature, nstead of at 25 C. It s recommended for hghly nondeal systems, especally alcohol-water systems. It can be used n any actvty coeffcent property method or n the advanced equaton-of-state mxng rules, such as Wong-Sandler and MHV2. Ths model cannot be used for lqud-lqud equlbrum calculatons. The equaton for the Wlson model s: ln γ = ln Ax j j 1 j Where: j ln A j ln V j bj = V + T k Ax j j A x jk k b j b j V and V j are lqud molar volume at the system temperature calculated usng the Rackett model. The bnary parameters b j and b j must be determned from VLE data regresson. There are no bult-n bnary parameters for ths model. Parameter Name/Element Symbol Default MDS Lower Lmt Upper Lmt Unts WSNVOL/1 b j 0 x TEMPERATURE Absolute temperature unts are assumed. Pure component parameters for the Rackett model are also requred. References G.M. Wlson, J. Am. Chem. Soc., Vol. 86, (1964), p Physcal Property Methods and Models 3-79 Verson 10

212 Property Model Descrptons Vapor Pressure and Lqud Fugacty Models ASPEN PLUS has 4 bult-n vapor pressure and lqud fugacty models. Ths secton descrbes the vapor pressure and lqud fugacty models avalable. Model Extended Antone/Wagner Chao-Seader Grayson-Streed Kent-Esenberg Type Vapor pressure Fugacty Fugacty Fugacty Extended Antone/Wagner The vapor pressure of a lqud can be calculated usng the extended Antone equaton or the Wagner equaton. Extended Antone Equaton Many parameters are avalable for the extended Antone equaton from the ASPEN PLUS pure component databank. Ths equaton s used whenever the parameter PLXANT s avalable. The equaton for the extended Antone vapor pressure model s: ln p *, l C2 = C1 + T + C 3 C7 + C T + C ln T + C t forc C Extrapolaton of ln p *, l versus 1/T occurs outsde of temperature bounds. Parameter Name/Element Symbol Default MDS Lower Lmt Upper Lmt Unts PLXANT/1 PLXANT/2 PLXANT/3,..., 7 C C C x PRESSURE, 1 TEMPERATURE C x 2 TEMPERATURE,..., 0 x TEMPERATURE 3 7 PLXANT/8 PLXANT/9 C 0 x TEMPERATURE 8 C 1000 x TEMPERATURE 9 If elements 5, 6, or 7 are non-zero, absolute temperature unts are assumed for elements 1 through Physcal Property Methods and Models Verson 10

213 Chapter 3 Wagner Vapor Pressure Equaton The Wagner vapor pressure equaton s the best equaton for correlaton. However, ts results are senstve to the values of Tc and pc. The equaton s used f the parameter WAGNER s avalable: [ 1( 1 ) 2 ( 1 ) 3 ( 1 ) 4 ( 1 ) ] ln *, l. pr = C Tr + C Tr + C Tr + C Tr Tr Where: T r = T T c *, l *, l p = p p r c Parameter Name/ElementSymbol Default MDS Lower Lmt Upper Lmt Unts WAGNER/1 WAGNER/2 WAGNER/3 WAGNER/4 C x 1 C 0 x 2 C 0 x 3 C 0 x 4 TC T c TEMPERATURE PC p c PRESSURE References Red, Prausntz, and Polng, The Propertes of Gases and Lquds, 4th ed., (New York: McGraw-Hll, 1987). Harlacher and Braun, "A Four-Parameter Extenson of the Theorem of Correspondng States," Ind. Eng. Chem. Process Des. Dev., Vol. 9, (1970), p W. Wagner, Cryogencs, Vol. 13, (1973), pp Chao-Seader The Chao-Seader model calculates pure component fugacty coeffcent, for lquds. It s used n the CHAO-SEA property method. Ths s an emprcal model wth the Curl-Ptzer form. The general form of the model s: () 0 () 1 *, l ln ϕ = ln ν + ω ln ν Where: ν () 0 () 1, ν = fcn( T, T, p, p ) c c Physcal Property Methods and Models 3-81 Verson 10

214 Property Model Descrptons Parameter Name/Element Symbol Default MDS Lower Lmt Upper Lmt Unts TC T c TEMPERATURE PC p c PRESSURE OMEGA ω References K.C. Chao and J.D. Seader, "A General Correlaton of Vapor-Lqud Equlbra n Hydrocarbon Mxtures," AIChE J., Vol. 7, (1961), p Grayson-Streed The Grayson-Streed model calculates pure component fugacty coeffcents for lquds, and s used n the GRAYSON property method. It s an emprcal model wth the Curl-Ptzer form. The general form of the model s: ( 0) ( 1) *, l ln ϕ = ln ν + ω ln ν Where: ν ( 0) ( 1), ν = fcn( T, T, p, p ) c c Parameter Name/Element Symbol Default MDS Lower Lmt Upper Lmt Unts TC T c TEMPERATURE PC p c PRESSURE OMEGA ω References H.G. Grayson and C.W. Streed, Paper 20-PO7, Sxth World Petroleum Conference, Frankfurt, June Kent-Esenberg The Kent-Esenberg model calculates lqud mxture component fugacty coeffcents and lqud enthalpy for the AMINES property method Physcal Property Methods and Models Verson 10

215 Chapter 3 The chemcal equlbra n HS 2 + CO2 +amne systems are descrbed usng these chemcal reactons: RR NH K H = + RR NH RR NCOO H O K + 2 RR NH + HCO = 2 3 HO CO K H + HCO = HO K 2 H + OH = HCO K H + CO3 = HS 2 K = H + HS HS K Where: = H + S R and R = Alcohol substtuted alkyl groups The equlbrum constants are gven by: 2 3 ln K = A + A T + A T + A T + A T The chemcal equlbrum equatons are solved smultaneously wth the balance equatons. Ths obtans the mole fractons of free HS 2 and CO 2 n soluton. The equlbrum partal pressures of HS 2 and CO 2 are related to the respectve free concentratons by Henry s constants: ln H = B + B T 1 2 The apparent fugactes and partal molar enthalpes, Gbbs energes and entropes of HS 2 and CO 2 are calculated by standard thermodynamc relatonshps. The chemcal reactons are always consdered. 4 Physcal Property Methods and Models 3-83 Verson 10

216 Property Model Descrptons The values of the coeffcents for the seven equlbrum constants ( A A ),..., and 1 5 for the two Henry s constants B 1 and B 2 are bult nto ASPEN PLUS. The coeffcents for the equlbrum constants were determned by regresson. All avalable data for the four amnes were used: monoethanolamne, dethanolamne, dsopropanolamne and dglycolamne. You are not requred to enter any parameters for ths model. References R.L. Kent and B. Esenberg, Hydrocarbon Processng, (February 1976), pp Physcal Property Methods and Models Verson 10

217 Chapter 3 Heat of Vaporzaton Model ASPEN PLUS uses two models to calculate pure component heat of vaporzaton: the Watson/DIPPR model and the Clausus-Clapeyron model. For the Watson/DIPPR model, the DIPPR equaton s the prmary equaton used for all components. The Watson equaton s used n PCES. DIPPR Equaton The equaton for the DIPPR heat of vaporzaton model s: ( ) ( 2 3 ) r + 4 r + 5 r 1 C C T C T C T vap H * = C T r C T 1 for 6 C7 Where: T r = T T c Extrapolaton of vap H * versus T occurs outsde of temperature bounds. Parameter Name/Element Symbol Default MDS Lower Lmt Upper Lmt Unts DHVLDP/1 DHVLDP/2,., 5 C C C x MOLE-ENTHALPY 1,..., 0 x 2 5 DHVLDP/6 DHVLDP/7 C 0 x TEMPERATURE 6 C 1000 x TEMPERATURE 7 TC T c TEMPERATURE Watson Equaton The equaton for the Watson model s: ( ) = ( ) H T H T * * vap vap Where: 1 1 TT 1 T T 1 c c ( 11 ) a + b T T c for T > T mn vap H * ( T) 1 = Heat of vaporzaton at temperature T 1 Physcal Property Methods and Models 3-85 Verson 10

218 Property Model Descrptons Parameter Name/Element Symbol Default Lower Lmt Upper Lmt Unts TC T c TEMPERATURE DHVLWT/1 * H ( T ) vap 1 5X10 4 5X10 8 MOLE-ENTHALPY DHVLWT/2 T TEMPERATURE DHVLWT/3 a DHVLWT/4 b DHVLWT/5 T mn TEMPERATURE Clausus-Clapeyron Equaton ASPEN PLUS can calculate heat of vaporzaton usng the Clausus-Clapeyron equaton: dp *, l * vap H = dt TV V Where: *, v *, l ( ) *, l dp = Slope of the vapor pressure curve calculated from the Extended Antone equaton dt *, v V = Vapor molar volume calculated from the Redlch-Kwong equaton-of-state *, l V = Lqud molar volume calculated from the Rackett equaton For parameter requrements, see Extended Antone/Wagner, the Rackett model, and Redlch-Kwong, all n ths chapter. Molar Volume and Densty Models ASPEN PLUS has 10 bult-n molar volume and densty models avalable. Ths secton descrbes the molar volume and densty models. Model API Lqud Volume Brelv-O'Connell Type Lqud volume Partal molar lqud volume of gases contnued 3-86 Physcal Property Methods and Models Verson 10

219 Chapter 3 Model Clarke Aqueous Electrolyte Volume Costald Lqud Volume Debje-Hückel Volume Rackett/DIPPR Pure Component Lqud Volume Rackett Mxture Lqud Volume Modfed Rackett Solds Volume Polynomal Type Lqud volume Lqud volume Electrolyte lqud volume Lqud volume/lqud densty Lqud volume Lqud volume Sold volume API Lqud Volume Ths model calculates lqud molar volume for a mxture, usng the API procedure and the Rackett model. Ideal mxng s assumed: l l V = x V + xv m p Where: p r l r x p = Mole fracton of pseudocomponents x r = Mole fracton of real components For pseudocomponents, the API procedure s used: V l p ( ) = fcn T, T, API Where: b fcn = A correlaton based on API Fgure 6A3.5 (API Techncal Data Book, Petroleum Refnng, 4th edton) For real components, the mxture Rackett model s used: 27 RA[ 1+ ( 1 Tr ) ] RT Z l c Vr = p c See the Rackett model for descrptons. Parameter Name/Element Symbol Default MDS Lower Lmt Upper Lmt Unts TB T b TEMPERATURE API API Physcal Property Methods and Models 3-87 Verson 10

220 Property Model Descrptons Parameter Name/Element Symbol Default MDS Lower Lmt Upper Lmt Unts TB T b TEMPERATURE API API TC T c TEMPERATURE PC p c PRESSURE RKTZRA Z RA r ZC Brelv-O Connell The Brelv-O Connell model calculates partal molar volume of a supercrtcal component at nfnte dluton n pure solvent A. Partal molar volume at nfnte dluton s requred to compute the effect of pressure on Henry s constant. (See Henry s Constant on page ) The general form of the Brelv-O Connell model s: BO BO * ( l A A ) V = fcn V, V, V A Where: = Solute or dssolved-gas component A = Solvent component The lqud molar volume of solvent s obtaned from the Rackett model: 27 RA[ 1+ ( 1 TrA ) ] V = RT Z *, l ca A pca Parameter Name/Element Symbol Default MDS Lower Lmt Upper Lmt Unts TC T ca TEMPERATURE PC p ca PRESSURE contnued 3-88 Physcal Property Methods and Models Verson 10

221 Chapter 3 Parameter Name/Element Symbol Default MDS Lower Lmt Upper Lmt Unts RKTZRA Z A RA ZC x VLBROC/1 V BO VC x MOLE-VOLUME VLBROC/2 0 x TEMPERATURE References S.W. Brelv and J.P. O Connell, AIChE J., Vol. 18, (1972), p S.W. Brelv and J.P. O Connell, AIChE J., Vol. 21, (1975), p Clarke Aqueous Electrolyte Volume The Clarke model calculates lqud molar volume for electrolytes solutons. The model s applcable to mxed solvents and s based on: Amagat s law (equaton 1) The relatonshp between the partal molar volume of an electrolyte and ts mole fracton n the solvent (equaton 2) All quanttes are expressed n terms of apparent components. Apparent Component Approach Amagat s law s: V l m = xv (1) For water and molecular solutes, V = V * and s computed from the Rackett equaton. If water s the only molecular component, the ASME steam table s used to compute V * for water. For electrolytes: V = V + A ca ca ca 1+ x ca x ca (2) Where: x ca = Apparent electrolyte mole fracton The mole fractons x ca are reconsttuted arbtrarly from the true onc concentratons, even f you use the apparent component approach. Ths technque s explaned n Electrolyte Smulaton, Chapter 5. Physcal Property Methods and Models 3-89 Verson 10

222 Property Model Descrptons The result s that electrolytes are generated from all possble combnatons of ons n soluton. For example: gven an aqueous soluton of CA 2+, Na +, SO 4 2, Cl four electrolytes are found: CaCl 2, Na2SO, CaSO 4 4 and NaCl. The Clarke parameters of all four electrolytes are used. You can rely on the default, whch calculates the Clarke parameters from onc parameters. Otherwse, you must enter parameters for any electrolytes that may not exst n the components lst. If you do not want to use the default, the frst step n usng the Clarke model s to enter any needed component ID s for electrolytes not n the components lst. The mole fractons of apparent electrolytes used n the calculaton are all nonzero, but are arbtrary values. For a gven onc soluton, the Clarke model always yelds the same volume, ndependent of the mole fractons of the electrolytes. Constrants between the Clarke parameters result: V + V = V + V CaCl Na SO CaSO NaCl A smlar equaton exsts for A ca You can consder these constrants n smple parameter nput and n data regresson. True Component Approach The true molar volume s obtaned from the apparent molar volume: V V n lt, la, m = m n Where: a t lt, V m = Lqud volume per number of true speces la, V m = l Lqud volume per number of apparent speces, V m n a = Number of apparent speces n t = Number of true speces of equaton 1 The apparent molar volume s calculated as explaned n the precedng subsecton. Temperature Dependence The temperature dependence of the molar volume of the soluton s approxmately equal to the temperature dependence of the molar volume of the solvent mxture: () = m( ) 298 l V T V K m xv B *, l xv l B B B B B *, l( T) ( 298K) 3-90 Physcal Property Methods and Models Verson 10

223 Chapter 3 Where: B = Any solvent Parameter Name/Element Applcable Components Symbol Default Unts VLCLK/1 Caton-Anon V ca MOLE-VOLUME VLCLK/2 Caton-Anon A ca MOLE-VOLUME If VLCLK/1 s mssng, t s calculated based on VLBROC and CHARGE. If VLBROC s mssng, the default value of 012. x 10 2 s used. COSTALD Lqud Volume The equaton for the COSTALD lqud volume model s: R δ ( m ) sat CTD R V = V V 0 1 ωv m Where: m,, m V R,0 m and V R,5 m are functons or T r for 025. < 095. For 095. < T r 10., there s a lnear nterpolaton between the lqud densty at T r = 0.95 and the vapor densty at T r = Ths model can be used to calculate saturated and compressed lqud molar volume. The compresed lqud molar volume s calculated usng the Tat equaton. Mxng Rules: CTD CTD CTD Vm = xv + 3 xv xv I CTD 1 *. *. *, 4 CTD CTD Vm Tc = xxv j j T ω = x ω Where: j cj *, CTD *, CTD ( c j cj) CTD V T = V T V T j cj 1 2 T r Physcal Property Methods and Models 3-91 Verson 10

224 Property Model Descrptons Parameter Name/Element Symbol Default MDS Lower Lmt Upper Lmt Unts TC T c TEMPERATURE VSTCTD *, CTD V VC X MOLE-VOLUME OMGCTD ω OMEGA X References R.W. Hanknson and G.H. Thomson, AIChE J., Vol. 25, (1979), p G.H. Thomson, K.R. Brobst, and R.W. Hanknson, AIChE J., Vol. 28, (1982), p. 4, p Debje-Hückel Volume The Debje-Hückel model calculates lqud molar volume for aqueous electrolyte solutons. The equaton for the Debje-Hückel volume model s: * V x V x V = + k m w w k k Where: V k s the molar volume for water and s calculated from the ASME steam table. V k s calculated from the Debje-Hückel lmtng law for onc speces. It s assumed to be the nfnte dluton partal volume for molecular solutes. V = V + z 10 k k k Where: AV ln + 3b ( 1 bi ) V k = Partal molar onc volume at nfnte dluton z k = Charge number of on k A V = Debje-Hückel constant for volume b = Physcal Property Methods and Models Verson 10

225 Chapter 3 I = mz, the onc strength, wth m k = Molarty of on k A V s computed as follows: k k k A V 6 lln εw = 2x10 Aϕ R 3 + p 1 p w ρ w p Where: A ϕ = Debje-Hückel constant for the osmotc coeffcents (Ptzer, 1979) ( 2π( 10 ρw) NA) Q ε kt e ρ w = Densty of water (kg / m -3 ) w B ε w = Delectrc constant of water ( Fm 1 ), a functon of pressure and temperature (Bradley and Ptzer, 1979) Parameter Name Applcable Components Symbol Default Unts VLBROC Ions, molecular Solutes V k 0 MOLE-VOLUME References H.C. Helgeson and D.H. Krkham, "Theoretcal predcton of the thermodynamc behavor of aqueous electrolytes at hgh pressure and temperature. I. Thermodynamc/electrostatc propertes of the solvent", Am. J. Sc., 274, 1089 (1974). Rackett/DIPPR Pure Component Lqud Volume Two equatons are avalable for pure component lqud molar volume: the Rackett equaton and the DIPPR equaton. The DIPPR equaton s used f the parameter DNLDIP s avalable for a gven component. The Rackett equaton s used f the parameter RKTZRA s avalable. For lqud molar volume of mxtures, the Rackett mxture equaton s always used. Ths s not necessarly consstent wth the pure component molar volume or densty. Physcal Property Methods and Models 3-93 Verson 10

226 Property Model Descrptons DIPPR The DIPPR equaton s: C / ( TC = C C ) for C T C ρ *, l ( / ) Ths equaton s smlar to the Rackett equaton. It returns lqud molar volume for pure components. Parameter Name/Element Symbol Default MDS Lower Lmt Upper Lmt Unts /1 C x MOLE-DENSITY 1 DNLDIP/2 DNLDIP/3 DNLDIP/4 DNLDIP/5 DNLDIP/6 DNLDIP/7 C 0 x 2 C 3 T x c TEMPERATURE C 0 x 4 C 0 x 5 C 0 x TEMPERATURE 6 C 1000 x TEMPERATURE 7 If element 3 s non-zero, absolute temperature unts are assumed for element 3. (See Chapter 5.) Rackett The equaton for the Rackett model s: V l 27 [ ( ) RT *, RA 1+ 1 Tr Z ] c = p Where: c T r = T T c Parameter Name/ Element Symbol Default MDS Lower Lmt Upper Lmt Unts TC T c TEMPERATURE PC p c PRESSURE RKTZRA *, RA Z ZC x Physcal Property Methods and Models Verson 10

227 Chapter 3 References H.G. Rackett, J.Chem, Eng. Data., Vol. 15, (1970), p C.F. Spencer and R.P. Danner, J. Chem. Eng. Data, Vol. 17, (1972), p Rackett Mxture Lqud Volume The Rackett equaton calculates lqud molar volume for all actvty coeffcent-based and petroleum-tuned equaton-of-state based property methods. In the last category of property methods, the equaton s used n conjuncton wth the API model. The API model s used for pseudocomponents, whle the Rackett model s used for real components. (See API Lqud Volume on page 3-87.) The equaton for the Rackett model s: V RT Z P RA ( ) l c m m = c Where: 2 1+ ( 1 T r ) 7 T c = j 1 ( ) 2 ( 1 ) xxvv TT k V j c cj c cj j 2 cm Tc P c = x T P Z m RA = xz V cm = xv T r = T T c c c *, RA c Physcal Property Methods and Models 3-95 Verson 10

228 Property Model Descrptons Parameter Name/Element Symbol Default MDS Lower Lmt Upper Lmt Unts TC T c TEMPERATURE PC p c PRESSURE VCRKT V c VC x MOLE-VOLUME RKTZRA *, RA Z ZC x RKTKIJ k j 8( VV c cj) ( Vc + Vcj ) x References H.G. Rackett, J.Chem, Eng. Data., Vol. 15, (1970), p C.F. Spencer and R.P. Danner, J. Chem. Eng. Data, Vol. 17, (1972), p Modfed Rackett The Modfed Rackett equaton mproves the accuracy of lqud mxture molar volume calculaton by ntroducng addtonal parameters to compute the pure component parameter RKTZRA and the bnary parameter k j. The equaton for the Modfed Rackett model s: V RT Z P RA ( ) l c m m = c Where: ( ) 2 + T r T c = j 1 ( ) 2 ( 1 ) xxvv TT k V j c cj c cj j 2 cm k j = 2 Aj + BjT+ CjT Tc P c = x T P Z m RA = xz c c *, RA 3-96 Physcal Property Methods and Models Verson 10

229 Chapter 3 V cm = xv T r = T T c c Parameter Name/Element Symbol Default MDS Lower Lmt Upper Lmt Unts MRKZRA/1 a RKTZRA x MRKZRA/2 b 0 x MRKZRA/3 c 0 x MRKKIJ/1 A j 0 x MRKKIJ/2 B j 0 x MRKKIJ/3 C j 0 x References H.G. Rackett, J.Chem, Eng. Data., Vol. 15, (1970), p C.F. Spencer and R.P. Danner, J. Chem. Eng. Data, Vol. 17, (1972), p Solds Volume Polynomal The equaton for the solds volume polynomal s: ( ) *, s V T = C + C T + C T + C T + C T for C T C Parameter Name Applcable Components Symbol MDS Default Unts VSPOLY/1 Salts, CI solds C x 1 VSPOLY/2,..., 5 Salts, CI solds C,..., C x VSPOLY/6 Salts, CI solds C x 0 6 VSPOLY/7 Salts, CI solds C x The unts are TEMPERATURE and MOLE-VOLUME. Physcal Property Methods and Models 3-97 Verson 10

230 Property Model Descrptons Heat Capacty Models ASPEN PLUS has fve bult-n heat capacty models. Ths secton descrbes the heat capacty models avalable. Model Aqueous Infnte Dluton Heat Capacty Polynomal Crss-Cobble Aqueous Infnte Dluton Ionc Heat Capacty DIPPR Lqud Heat Capacty Ideal Gas Heat Capacty/DIPPR Solds Heat Capacty Polynomal Type Electrolyte lqud Electrolyte lqud Lqud Ideal gas Sold Aqueous Infnte Dluton Heat Capacty The aqueous phase nfnte dluton enthalpes, entropes, and Gbbs energes are calculated from the heat capacty polynomal. The values are used n the calculaton of aqueous and mxed solvent propertes of electrolyte solutons:, aq 2 C4 C5 C6 Cp, = C1 + C2T + C3T for C T C 2 T T T, aq C p, 7 8 s lnearly extrapolated usng the slope at C for T < C 7 7, aq C p, s lnearly extrapolated usng the slope at C for T > C 8 8 Parameter Name/Element Applcable Components Symbol Default Unts CPAQ0 Ions, molecular solutes C 1 CPAQ0 Ions, molecular solutes C,..., C CPAQ0 Ions, molecular solutes C 0 6 CPAQ0 Ions, molecular solutes C The unts are TEMPERATURE and HEAT CAPACITY. Crss-Cobble Aqueous Infnte Dluton Ionc Heat Capacty The Crss-Cobble correlaton for aqueous nfnte dluton onc heat capacty s used f no parameters are avalable for the aqueous nfnte dluton heat capacty polynomal. From the calculated heat capacty, the thermodynamc propertes entropy, enthalpy and Gbbs energy at nfnte dluton n water are derved: 3-98 Physcal Property Methods and Models Verson 10

231 Chapter 3 aq aq ( a ( 298) or c ( 298),, )) C, aq f S, T S, = = T = ontype T p, Parameter Name Applcable Components Symbol Default Unts IONTYP Ions Ion Type 0 SO25C Anons S a aq Catons,, aq ( ), aq H T 298 G ( T = 298 ) S a aq f a f ,, aq ( ), aq H T 298 G ( T = 298 ) f a f a a MOLE-ENTROPY MOLE-ENTROPY IONTYP = 1 for catons = 2 for smple anons and hydroxde ons = 3 for oxy anons = 4 for acd oxy anons = 5 for hydrogen on DIPPR Lqud Heat Capacty The DIPPR lqud heat capacty model s used for the calculaton of pure component lqud heat capacty and pure component lqud enthalpy. To use ths model, two condtons must exst: The parameter CPLDIP s avalable. The component s not supercrtcal (HENRY-COMP). The model uses a specfc method (see Chapter 4): l ref ( ) ( ) *, l *, *, l H T H T = Cp, dt H ( T ) *,l ref T T ref s calculated as: ref g v g ( ) ( ) l H T = H + H H H T ref *, *, *, *, *,l vap s the reference temperature; t defaults to K. You can enter a dfferent value for the reference temperature. Ths s useful when you want to use ths model for very lght components or for components that are solds at K. Actvate ths method by specfyng the route DHL09 for the property DHL on the Propertes Property Methods Routes sheet. For equaton-of-state property method, you must also modfy the route for the property DHLMX to use a route wth method 2 or 3, nstead of method 1. For example, you can use the route DHLMX00 or DHLMX30. You must ascertan that the route for DHLMX that you select contans the approprate vapor phase model and heat of mxng calculatons. Clck the Vew button on the form to see detals of the route. Physcal Property Methods and Models 3-99 Verson 10

232 Property Model Descrptons Optonally, you can specfy that ths model s used for only certan components. The propertes for the remanng components are then calculated by the standard model. Use the parameter COMPHL to specfy the components for whch ths model s used. By default, all components wth the CPLDIP parameters use ths model. The equaton s: *, l C = C + C T + C T + C T + C T for C T C p, *, l Lnear extrapolaton occurs for C p versus T outsde of bounds. Parameter Name/Element Symbol Default MDS Lower Lmt Upper Lmt Unts CPLDIP/1 C 1 T CPLDIP/2,...,5 C C 2 5 x MOLE-HEAT-CAPACITY, TEMPERATURE,..., 0 x MOLE-HEAT-CAPACITY, TEMPERATURE CPLDIP/6 CPLDIP/7 C 0 x TEMPERATURE 6 C 1000 x TEMPERATURE 7 TREFHL T ref TEMPERATURE COMPHL TEMPERATURE To specfy that the model s used for a component, enter a value of 1.0 for ths component parameter. Ideal Gas Heat Capacty/DIPPR The DIPPR deal gas heat capacty equaton s used for most components n the ASPEN PLUS pure components databank. It s used when the parameter CPIGDP s avalable for a gven component. DIPPR The equaton for the DIPPR deal gas heat capacty model by Al and Lee 1981 s: *, g C = C + C p 1 2 C snh 3 T + C C 4 ( C T) cosh( C T) T 5 2 for C T C 6 7 Ths model s also used to calculate deal gas enthalpes, entropes, and Gbbs energes Physcal Property Methods and Models Verson 10

233 Chapter 3 Parameter Name/Element Symbol Default MDS Lower Lmt Upper Lmt Unts CPIGDP/1 CPIGDP/2 CPIGDP/3 CPIGDP/4 CPIGDP/5 CPIGDP/6 CPIGDP/7 C x MOLE-HEAT-CAPACITY 1 C 0 x MOLE-HEAT-CAPACITY 2 C 0 x 3 TEMPERATURE C 0 x MOLE-HEAT-CAPACITY 4 C 0 x 5 TEMPERATURE C 0 x TEMPERATURE 6 C 1000 x TEMPERATURE 7 If elements 3 or 5 are non-zero, absolute temperature unts are assumed. Ideal Gas Heat Capacty Polynomal The deal gas heat capacty polynomal s used for components stored n ASPENPCD, AQUEOUS, and SOLIDS databanks. Ths model s also used n PCES. *, g C = C + C T + C T + C T + C T + C T for C T C p *, g C11 C = C + C T for T < C p *, g C p s lnearly extrapolated usng slope at C for T > C 8 8 Ths model s also used to calculate deal gas enthalpes, entropes, and Gbbs energes. Parameter Name/Element Symbol Default MDS Lower Lmt Upper Lmt Unts CPIG/1 CPIG/2,..., 6 C C C MOLE-HEAT-CAPACITY, 1 TEMPERATURE,..., 0 MOLE-HEAT-CAPACITY, TEMPERATURE 2 6 CPIG/7 C 0 TEMPERATURE 7 CPIG/8 C 1000 TEMPERATURE 8 CPIG/9, 10, 11 C 9, C10, C11 MOLE-HEAT-CAPACITY, TEMPERATURE If elements 10 or 11 are non-zero, absolute temperature unts are assumed for elements 9 through 11. Physcal Property Methods and Models Verson 10

234 Property Model Descrptons References Data for the Ideal Gas Heat Capacty Polynomal: Red, Prausntz and Polng, The Propertes of Gases and Lquds, 4th ed., (New York: McGraw-Hll, 1987). ASPEN PLUS combuston data bank, JANAF Thermochemcal Data, Compled and calculated by the Thermal Research Laboratory of Dow Chemcal Company. F. A. Aly and L. L. Lee, "Self-Consstent Equatons for Calculatng the Ideal Gas Heat Capacty, Enthalpy, and Entropy, Flud Phase Eq., Vol. 6, (1981), p Solds Heat Capacty Polynomal The enthalpy, entropy, and Gbbs energy of solds are calculated from the heat capacty polynomal: *, s 2 C4 C5 C6 Cp, = C1 + C2T + C3T for C T C 2 T T T 7 8 C *,8 p, lnearly extrapolated usng the slope at C 7 for T < C 7 and C *,8 p, lnearly extrapolated usng the slope at C 8 for T > C 8 Parameter Name Applcable Components Symbol MDS Default Unts CPSPO1/1 Solds, Salts C x 1 CPSPO1/2,..., 6 Solds, Salts C,..., C x CPSPO1/7 Solds, Salts C x 0 7 CPSPO1/8 Solds, Salts C x If elements 4, 5, or 6 are non-zero, absolute temperature unts are assumed for elements 1 through 6. The unts are TEMPERATURE and HEAT CAPACITY. Solublty Correlatons ASPEN PLUS has two bult-n solublty correlaton models. Ths secton descrbes the solublty correlaton models avalable. Model Henry s constant Water solublty Type Gas solublty n lqud Water solublty n organc lqud Physcal Property Methods and Models Verson 10

235 Chapter 3 Henry s Constant The Henry s constant model s used when Henry s Law s appled to calculate K- values for dssolved gas components n a mxture. Henry s Law s avalable n all actvty coeffcent property methods, such as the WILSON property method. The model calculates Henry s constant for a dssolved gas component () n one or more solvents (A or B): ln ( H ) w ln( H γ = A A γ A) Where: w A = ln H, H A xa x B A 2 ( V ) 3 ca ( V ) B *, l ( T pa ) cb 2 3 = a + b T + c ln T + d T for T T T *, l A ( T, P) = HA( T pa ) A A A A L H, exp RT p VA dp p 1 *, a l The parameter V *, l A s obtaned from the Brelv-O Connell model. p A s obtaned from the Antone model. γ s obtaned from the approprate actvty coeffcent model. The Henry s constants a A, b A, c A, and d A are specfc to a solute-solvent par. They can be obtaned from regresson of gas solublty data. ASPEN PLUS has a large number of bult-n Henry s constants for many solutes n solvents. These parameters were obtaned usng data from the Dortmund Databank. See ASPEN PLUS Physcal Property Data, Chapter 1, for detals. Physcal Property Methods and Models Verson 10

236 Property Model Descrptons Parameter Name/Element Symbol Default MDS Lower Lmt Upper Lmt Unts VC V ca MOLE-VOLUME HENRY/1 a A x PRESSURE, TEMPERATURE HENRY/2 b A 0 x TEMPERATURE HENRY/3 c A 0 x TEMPERATURE HENRY/4 d A 0 x TEMPERATURE HENRY/5 T L 0 x TEMPERATURE HENRY/6 T H 2000 x TEMPERATURE If a A s mssng, ln H A γ A s set to zero and the weghtng factor w A s renormalzed. If elements 2 or 3 are non-zero, absolute temperature unts are assumed for elements 1 through 4. Water Solublty Ths model calculates solublty of water n a hydrocarbon-rch lqud phase. The model s used automatcally when you model a hydrocarbon-water system wth the free-water opton. See Chapter 6 for detals. The expresson for the lqud mole fracton of water n the th hydrocarbon speces s: ln x w C2 = C1 + + CTfor C T C T The parameters for 60 hydrocarbon components are stored n the ASPEN PLUS pure component databank. Parameter Name/Element Symbol Default MDS Lower Lmt Upper Lmt Unts WATSOL/1 C 1 fcn( Tb ASG M ),, TEMPERATURE WATSOL/2 C 2 fcn( Tb ASG M ),, TEMPERATURE WATSOL/3 C TEMPERATURE Absolute temperature unts are assumed contnued Physcal Property Methods and Models Verson 10

237 Chapter 3 Parameter Name/Element Symbol Default MDS Lower Lmt Upper Lmt Unts WATSOL/4 WATSOL/5 C TEMPERATURE C TEMPERATURE 5 Absolute temperature unts are assumed Other Thermodynamc Property Models ASPEN PLUS has four bult-n addtonal thermodynamc property models that do not ft n any other category. Ths secton descrbes these models: Cavett Lqud Enthalpy Departure BARIN Equatons for Gbbs Energy, Enthalpy, Entropy and Heat Capacty Electrolyte NRTL Enthalpy Electrolyte NRTL Gbbs Energy Lqud Enthalpy from Lqud Heat Capacty Correlaton Enthalpes Based on Dfferent Reference States Cavett The general form for the Cavett model s: *, l *, g * ( H H ) = fcn( T, Tc, p, pc, Zλ ) l g *, l *, g ( Hm Hm) = x( H H ) Parameter Name/Element Symbol Default MDS Lower Lmt Upper Lmt Unts TC T c TEMPERATURE PC p c PRESSURE DHLCVT Z ZC X λ, Physcal Property Methods and Models Verson 10

238 Property Model Descrptons BARIN Equatons for Gbbs Energy, Enthalpy, Entropy, and Heat Capacty The followng equatons are used when parmeters from the ASPEN PLUS norganc databank are retreved. Gbbs energy: ( ln ) *, α α α α α α α α α G = a + b T + c T T + d T + e T + f T + g T + h T n, n, n, n, n, n, n, n, Enthalpy: *, α α α α 2 α 3 α 4 α 1 α 2 H = a c T d T + 2e T + ef T + 2 g T + eh T (2) n, n, n, n, n, n, n, Entropy: ( ln ) *, α α α α α α α α S = b c 1+ T 2d T 3e T 4f T + g T + 2h T n, n, n, n, n, n, n, Heat capacty: *, α α α α α α α C = c 2d T 6e T 12f T 2g T 6h T p, n, n, n, n, n, n, α refers to an arbtrary phase whch can be sold, lqud, or deal gas. For each phase, multple sets of parameters from 1 to n are present to cover multple temperature ranges. The value of the parameter n depends on the phase. (See tables that follow.) The four propertes C p, H, S, and G are nterrelated as a result of the thermodynamc relatonshps: ref ( ) ( ) *, α *, α *, α H T H T = Cp, dt T T ref (1) (3) (4) α ref ( ) ( ) α S T S T C T *, α *, *, p, = T ref T dt G = H TS *, α *, α *, α There are analytcal relatonshps between the expressons descrbng the propertes C p, H, S, and G (equatons 1 to 4). The parameters a n, to h n, can occur n more than one equaton. Sold Phase The parameters n range n s are vald for temperature: T < T < T s nl, nh, Physcal Property Methods and Models Verson 10

239 Chapter 3 Parameter Name /Element Symbol Default MDS Lower Lmt Upper Lmt Unts CPSXPn/1 CPSXPn/2 s T nl, s T nh, x TEMPERATURE x TEMPERATURE CPSXPn/3 s a n, x CPSXPn/4 s b n, 0 x CPSXPn/5 s c n, 0 x CPSXPn/6 s d n, 0 x CPSXPn/7 s e n, 0 x CPSXPn/8 s f n, 0 x CPSXPn/9 s g n, 0 x CPSXPn/10 s h n, 0 x n s 1 through 7.CPSXP1 vector stores sold parameters for the frst temperature range. CPSXP2 vector stores sold parameters for the second temperature range, and so on. TEMPERATURE, ENTHALPY, ENTROPY Lqud Phase The parameters n range n l are vald for temperature: T < T < T l nl, nh, Parameter Name /Element Symbol Default MDS Lower Lmt Upper Lmt Unts CPLXPn/1 CPLXPn/2 l T nl, l T nh, x TEMPERATURE x TEMPERATURE CPLXPn/3 l a n, x CPLXPn/4 l b n, 0 x CPLXPn/5 l c n, 0 x n s 1 through 2. CPLXP1 stores lqud parameters for the frst temperature range. CPLXP2 stores lqud parameters for the second temperature range. TEMPERATURE, ENTHALPY, ENTROPY contnued Physcal Property Methods and Models Verson 10

240 Property Model Descrptons Parameter Name /Element Symbol Default MDS Lower Lmt Upper Lmt Unts CPLXPn/6 l d n, 0 x CPLXPn/7 l e n, 0 x CPLXPn/8 l f n, 0 x CPLXPn/9 l g n, 0 x CPLXPn/10 l h n, 0 x n s 1 through 2. CPLXP1 stores lqud parameters for the frst temperature range. CPLXP2 stores lqud parameters for the second temperature range. TEMPERATURE, ENTHALPY, ENTROPY Ideal Gas Phase The parameters n range n g are vald for temperature: T < T < T g nl, nh, Parameter Name /Element Symbol Default MDS Lower Lmt Upper Lmt Unts CPIXPn/1 CPIXPn/2 g T nl, g T nl, x TEMPERATURE x TEMPERATURE CPIXPn/3 g a n, x CPIXPn/4 g b n, 0 x CPIXPn/5 g c n, 0 x CPIXPn/6 g d n, 0 x CPIXPn/7 g e n, 0 x CPIXPn/8 g f n, 0 x CPIXPn/9 g g n, 0 x CPIXPn/10 g h n, 0 x n s 1 through 3. CPIXP1 vector stores deal gas parameters for the frst temperature range. CPIXP2 vector stores deal gas parameters for the second temperature range, and so on. TEMPERATURE, ENTHALPY, ENTROPY Physcal Property Methods and Models Verson 10

241 Chapter 3 Electrolyte NRTL Enthalpy The equaton for the electrolyte NRTL enthalpy model s: H = x H + x H + H * * * E m w w k k k m The molar enthalpy H * * E m and the molar excess enthalpy H m are defned wth the asymmetrcal reference state: the pure solvent water and nfnte dluton of molecular solutes and ons. (here * refers to the asymmetrcal reference state.) H w * s the pure water molar enthalpy, calculated from the Ideal Gas model and the ASME Steam Table equaton-of-state. (here * refers to pure component.) ( ( )) T g g (. ) pk, w, ) w(, ) H * H *, g = T = C dt + H T p H T p w f The property H k s calculated from the nfnte dluton aqueous phase heat capacty polynomal model, by default. If polynomal model parameters are not avalable, t s calculated from the Crss-Cobble model for ons and from Henry s law for molecular solutes. The subscrpt k can refer to a molecular solute (), to a caton (c), or an anon (a): T, aq k = f k + pk, , aq H H C * E H m s excess enthalpy and s calculated from the electrolyte NRTL actvty coeffcent model. See Crss-Cobble model and Henry s law model, ths chapter, for more nformaton Parameter Name Applcable Components Symbol Default Unts IONTYP Ions Ion 0 SO25C Catons, aq S ( T = ) c 298 MOLE-ENTROPY Anons, aq S ( T = ) a 298 MOLE-ENTROPY DHAQFM Ions, Molecular Solutes aq f H, MOLE-ENTHALPY k CPAQ0 Ions, Molecular Solutes, aq C HEAT-CAPACITY pk, Not needed f CPAQ0 s gven for ons contnued Physcal Property Methods and Models Verson 10

242 Property Model Descrptons Parameter Name Applcable Components Symbol Default Unts DHFORM Molecular Solutes g f H *, MOLE-EHTHALPY Water g f H *, MOLE-ENTHALPY w CPIG Molecular Solutes *, g C p, Water *, g C pw, Not needed f CPAQ0 s gven for ons Not needed f DHAQFM and CPAQ0 are gven for molecular solutes The unt keywords for CPIG are TEMPERATURE and HEAT-CAPACITY. If elements 10 or 11 of CPIG are non-zero, absolute temperature unts are assumed for all elements. (See ASPEN PLUS User Gude.) Electrolyte NRTL Gbbs Energy The equaton for the NRTL Gbbs energy model s: G = x µ + x µ + x ln x + G * * * E m w w k k k j j j m The molar Gbbs energy and the molar excess Gbbs energy G * * E m and G m are defned wth the asymmetrcal reference state: as pure water and nfnte dluton of molecular solutes and ons. (* refers to the asymmetrcal reference state.) The deal mxng term s calculated normally, where j refers to any component. The molar Gbbs energy of pure water (or thermodynamc potental) µ * w s calculated from the deal gas contrbuton. Ths s a functon of the deal gas heat capacty and the departure functon. (here * refers to the pure component.) ( w w ) g µ = µ + µ µ * *, * *,g w w The departure functon s obtaned from the ASME steam tables. The aqueous nfnte dluton thermodynamc potental µ k s calculated from the nfnte dluton aqueous phase heat capacty polynomal model, by default. k refers to any on or molecular solute. If polynomal model parameters are not avalable, t s calculated from the Crss-Cobble model for ons and from Henry s law for molecular solutes:,, (, aq pk ) aq µ k = fcn f G k C G * E s calculated from the electrolyte NRTL actvty coeffcent model Physcal Property Methods and Models Verson 10

243 Chapter 3 See the Crss-Cobble model and Henry s law model, ths chapter, for more nformaton. Parameter Name Applcable Components Symbol Default Unts IONTYP Ions Ion 0 SO25C Catons, aq S ( T = ) c 298 MOLE-ENTROPY Anons, aq S ( T = ) a 298 MOLE-ENTROPY DGAQFM Ions, molecular solutes aq f G, MOLE-ENTHALPY k CPAQ0 Ions, molecular solutes, aq C HEAT-CAPACITY pk, DGFORM Molecular solutes f G MOLE-ENTHALPY Water f G MOLE-ENTHALPY w CPIG Molecular solutes *, g C p, Water *, g C pw, Not needed f CPAQ0 s gven for ons Not needed f DHAQFM and CPAQ0 are gven for molecular solutes The unt keywords for CPIG are TEMPERATURE and HEAT-CAPACITY. If elements 10 or 11 of CPIG are non-zero, absolute temperature unts are assumed for all elements. (See ASPEN PLUS User Gude.) Lqud Enthalpy from Lqud Heat Capacty Correlaton Lqud enthalpy s drectly calculated by ntegraton of lqud heat capacty: l ref ( ) = ( ) + *, l *, *, l H T H T C dt T T ref p, The reference enthalpy s calculated at T ref ref g v g ( ) ( ) l H T = H + H H H *, *, *, *, *, l vap as: Physcal Property Methods and Models Verson 10

244 Property Model Descrptons Where: *, g H = Ideal gas enthalpy H g H = Vapor enthalpy departure from equaton-of-state *, v *, l vap H *, = Heat of vaporzaton from Watson/DIPPR model T ref = Reference temperature, specfed by user. Defaults to K See DIPPR Lqud Heat Capacty on page 3-99 for parameter requrement and addtonal detals. Enthalpes Based on Dfferent Reference States Two property methods, WILS-LR and WILS-GLR, are avalable to calculate enthalpes based on dfferent reference states. The WILS-LR property method s based on saturated lqud reference state for all components. The WILS-GLR property method allows both deal gas and saturated lqud reference states. These property methods use an enthalpy method that optmzes the accuracy tradeoff between lqud heat capacty, heat of vaporzaton, and vapor heat capacty at actual process condtons. Ths hghly recommended method elmnates many of the problems assocated wth accurate thermal propertes for both phases, especally the lqud phase. The lqud enthalpy of mxture s calculated by the followng equaton (see the table labeled Lqud Enthalpy Methods n Chapter 4): l g ( ) l g H = H + H H m Where: m m m H m g = Enthalpy of deal gas mxture = xh *, g *, g H = Ideal gas enthalpy of pure component l g ( H H ) m = Enthalpy departure of mxture m Physcal Property Methods and Models Verson 10

245 Chapter 3 For supercrtcal components, declared as Henry s components, the enthalpy departure s calculated as follows: l g Hm Hm = RT x 2 δ l ln Φ δt For subcrtcal components: H l m g H = l g m xa( HA HA ) + H A *, *, E, l m E, l H m = 2 δ ln γ B RT xb δt B H g H = Enthalpy departure of pure component A *, l *, A A H *, g and H *, l can be calculated based on ether saturated lqud or deal gas as reference state. Saturated Lqud as Reference State The saturated lqud enthalpy at temperature T s calculated as follows: *, l ref, l *, l H H C dt Where: T = + T ref, l p, ref, l H = ref, l Reference enthalpy for lqud state at T = ref, l 0 at T of K by default *, l C p = Lqud heat capacty of component, The deal gas enthalpy at temperature T s calculated from lqud enthalpy as follows: con l * con, l *, l ( ) (, ) *, g ref, l *, l *, *, g H = H + C dt + H T H T p + C dt Where: T con, l T ref, l p, vap con, l T = Temperature of converson from lqud to vapor enthalpy for component v, T T con, l p, ( T ) * con, l vap H = Heat of vaporzaton of component at temperature of T con, l Physcal Property Methods and Models Verson 10

246 Property Model Descrptons con l l ( ) *, *, Hv, T, p = Vapor enthalpy departure of component at the *, l converson temperature and vapor pressure p *, l p = Lqud vapor pressure of component *, g C p = Ideal gas heat capacty of component, con, l T s the temperature at whch one crosses from lqud state to the vapor state. Ths s a user-defned temperature that defaults to the system temperature con, l T. T may be selected such that heat of vaporzaton for component at the temperature s most accurate. The vapor enthalpy s calculated from deal gas enthalpy as follows: (, ) *, v *, g * H = H + H T P Where: H * v, ( T P) v,, = Vapor enthalpy departure of pure component at the system temperature and pressure The lqud heat capacty and the deal gas heat capacty can be calculated from the ASPEN, DIPPR, or BARIN models. The heat of vaporzaton can be calculated from the Watson/DIPPR model. The enthalpy departure s obtaned from an equaton-of-state. Parameter Name/Element Symbol Default MDS Lower Lmt Upper Lmt Unts RSTATE 2 TREFHL ref, l T TEMPERATURE DHLFRM TCONHL ref, l H O MOLE-ENTHALPY con, l T T TEMPERATURE Enthalpy reference state, RSTATE=2 denotes saturated lqud as reference state. For WILS-LR property method TREFHL defaults to K. For WILS-GLR property method, TREFHL defaults to K. Lqud heat capacty s requred for all components Physcal Property Methods and Models Verson 10

247 Chapter 3 Ideal Gas as Reference State The saturated lqud enthalpy s calculated as follows: con g l con g l (, ) (, ) *, l ref, g *, g *, *, *, *, *, l H = H + C dt + H T p H T p + C dt Where: con, g T T ref, g p, v, vap T con, g T p, ref, g H = ref, g Reference state enthalpy for deal gas at T = Heat of formaton of deal gas at K by default ref, g T = ref, g Reference temperature correspondng to H. Defaults to K con, g T = The temperature at whch one crosses from vapor state to lqud state. Ths s a user-defned temperature that defaults to the con, g system temperature T. T may be selected such that heat of vaporzaton of component at the temperature s most accurate. The deal gas enthalpy s calculated as follows: *, g ref, g *, g H H C dt T = + T ref, g p, The vapor enthalpy s calculated as follows: ( ) *, v *, g H = H + H T P v,, The lqud heat capacty and the deal gas heat capacty can be calculated from the ASPEN, DIPPR or BARIN models. The heat of vaporzaton can be calculated from the Watson/DIPPR model. The enthalpy departure s obtaned from an equaton-of-state. Physcal Property Methods and Models Verson 10

248 Property Model Descrptons Parameter Name/Element Symbol Default MDS Lower Lmt Upper Lmt Unts RSTATE 1 or 2 TREFHI ref, g T TEMPERATURE DHFORM TCONHI ref, g H MOLE-ENTHALPY con, l T T TEMPERATURE Enthalpy reference state. RSTATE can be 1 (for deal gas) or 2 (for lqud) For components wth TB << K, RSTATE defaults to 1 (deal gas). TREFHI defaults to K. For components wth TB >> K, RSTATE defaults to 2 (lqud). TREFHL defaults to K Physcal Property Methods and Models Verson 10

249 Chapter 3 Helgeson Equatons of State The Helgeson equatons of state for standard volume V o, heat capacty C p o, entropy S o, enthalpy of formaton H o, and Gbbs energy of formaton G o at nfnte dluton n aqueous phase are: V o Q p + p + T + 1 ω ω 1 ψ ψ θ ε p a a a a = T C o p c = + 1 c2 2T ( T θ) ( T θ) 1 T 1 2 ε ω 2 T a ( p p ) + a r 4 p ln p + ψ ω + ωtx + 2TY pr + ψ T p S o o = S + Tr Pr c 1 c T Tr ln + ln Tr θ T θ Tr θ θ T T ( T θ) ( θ) 2 1 p + ψ + ( ) ω ω T θ a p pr a ln Y pr ψ ε T r p ω Y Tr Pr Tr Pr o o H = H f + c ( T Tr) c + a ( p pr) + a ( T θ) 1 1 T θ T θ r + 2T θ p + ψ 1 2 a ( p pr) + a ln + ω 1 + ωty 3 4 pr + ψ ε 1 T Tr ω 1 1 ω Pr 1 ω ε T ε p Tr Pr TY Tr Pr r Tr Pr ln p + ψ p + ψ r o o o T G = G f STr Pr( T Tr) c1 Tln T + Tr + 1( p pr) + 2 T a a ln r c 1 1 θ T T Tr T ln T θ Tr θ θ θ T Tr T θ ω Tr Pr a 3 1 ε Tr Pr ( p p ) + r 1 + ω a 4 ( ) Tr Pr Tr Pr r ( θ) ( θ) p + ψ 1 ln + ω 1 pr + ψ ε Y T T p + ψ p + ψ r Physcal Property Methods and Models Verson 10

250 Property Model Descrptons Where: 1 Q = lnε ε P T 2 1 lnε X = T lnε 2 ε T P 1 Y = lnε ε T P 2 P Where: ψ = Pressure constant for a solvent (2600 bar for water) θ = Temperature constant for a solvent (228 K for water) ω = Born coeffcent ε = Delectrc constant of a solvent T r = Reference temperature ( K) P r = Reference pressure (1 bar) Parameter Name/Element Symbol Default MDS Lower Lmt Upper Lmt Unts a a AHGPAR/1,., 4 1,..., 0 4 CHGPAR/1,., 2 c1, c x 2 DHAQHG DGAQHG H f o 0-0.5*10 10 G f o 0-0.5* *10 10 MOLE-ENTHALPY 0.5*10 10 MOLE-ENTHALPY S25HG o S Tr Pr 0-0.5* *10 10 MOLE-ENTROPY OMEGHG ω Tr Pr 0-0.5* *10 10 MOLE-ENTHALPY If pressure s under 200 bar, AHGPAR may not be requred Physcal Property Methods and Models Verson 10

251 Chapter 3 References Tanger J.C. IV and H.C. Helgeson, Calculaton of the thermodynamc and transport propertes of aqueous speces at hgh pressures and temperatures: Revsed equaton of state for the standard partal propertes of ons and electrolytes, Amercan Journal of Scence, Vol. 288, (1988), p Shock E.L. and H.C. Helgeson, Calculaton of the thermodynamc and transport propertes of aqueous speces at hgh pressures and temperatures: Correlaton algorthms for onc speces and equaton of state predctons to 5 kb and 1000 C, Geochmca et Cosmochmca Acta, Vol. 52, p Shock E.L. H.C. Helgeson and D.A. Sverjensky, Calculaton of the thermodynamc and transport propertes of aqueous speces at hgh pressures and temperatures: Standard partal molal propertes of norganc neutral speces, Geochmca et Cosmochmca Acta, Vol. 53, p Physcal Property Methods and Models Verson 10

252 Property Model Descrptons Transport Property Models Ths secton descrbes the transport property models avalable n ASPEN PLUS. The followng table provdes an overvew of the avalable models. Ths table lsts the ASPEN PLUS model names, and ther possble use n dfferent phase types, for pure components and mxtures. Transport Property Models Vscosty models Model name Phase(s) Pure Mxture Andrade / DIPPR MUL0ANDR, MUL2ANDR L X X API Lqud Vscosty MUL2API L X Chapman-Enskog-Brokaw /DIPPR Chapman-Enskog-Brokaw-Wlke Mxng Rule MUV0CEB V X MUV2BROK, MUV2WILK V X Chung-Lee-Starlng Low Pressure MUL0CLSL, MUL2CLSL V X X Chung-Lee-Starlng MUV0CLS2, MUV0CLS2, MUL0CLS2, MUL2CLS2 V L X X Dean-Stel Pressure Correcton MUV0DSPC, MUV2DSPC V X X IAPS Vscosty MUV0H2O MUL0H2O V L X X Jones-Dole Electrolyte Correcton MUL2JONS L X Letsou-Stel MUL0LEST, MUL2LEST L X X Lucas MUV0LUC, MUV2LUC V X X Thermal conductvty models Vscosty models Model name Phase(s) Pure Mxture Chung-Lee-StarlngThermal Conductvtty KV0CLS2, KV2CLS2, KL0CLS2, KL2CLS2 V L X X IAPS Thermal Conductvty KV0H2O KL0H2O V L X X L Mxng Rule KL2LI L X X Redel Electrolyte Correcton KL2RDL L X Sato-Redel / DIPPR KL0SR, KL2SRVR L X X Stel-Thodos / DIPPR KV0STLP V X contnued Physcal Property Methods and Models Verson 10

253 Chapter 3 Thermal conductvty models (contnued) Vscosty models Model name Phase(s) Pure Mxture Stel-Thodos Pressure Correcton KV0STPC, KV2STPC V X X TRAPP Thermal Conductvty KV0TRAP, KV2TRAP, KL0TRAP, KL2TRAP V L X X Vredeveld Mxng Rule KL2SRVR L X X Dffusvty models Model name Phase(s) Pure Mxture Chapman-Enskog-Wlke-Lee Bnary Chapman-Enskog-Wlke-Lee Mxture Dawson-Khoury-Kobayash Bnary Dawson-Khoury-Kobayash Mxture DV0CEWL V X DV1CEWL V X DV1DKK V X DV1DKK V X Nernst-Hartley Electrolytes DL0NST, DL1NST L X Wlke-Chang Bnary DL0WC2 L X Surface tenson models Vscosty models Model name Phase(s) Pure Mxture API Surface Tenson SIG2API L X Hakm-Stenberg-Stel / DIPPR SIG0HSS, SIG2HSS L X IAPS thermal conductvty SIG0H2O L X Onsager-Samaras Electrolyte Correcton SIG2ONSG L X Vscosty Models ASPEN PLUS has 12 bult-n vscosty models. Model Andrade/DIPPR API lqud vscosty Chapman-Enskog-Brokaw/DIPPR Chapman-Enskog-Brokaw-Wlke Mxng Rule Type Lqud Lqud Low pressure vapor, pure components Low pressure vapor, mxture contnued Physcal Property Methods and Models Verson 10

254 Property Model Descrptons Model Chung-Lee-Starlng Low Pressure Chung-Lee-Starlng Dean-Stel Pressure correcton IAPS vscosty Jones-Dole Electrolyte Correcton Letsou-Stel Lucas TRAPP vscosty Type Low pressure vapor Lqud or vapor Vapor Water or steam Electrolyte Hgh temperature lqud Vapor Vapor or lqud Andrade/DIPPR The lqud mxture vscosty s calculated by the equaton: ( kxx j j mxx j j ) 2 2 ln η l = + j Where: k j = m j = a c j j bj + T dj + T *, l The pure component lqud vscosty η can be calculated by two equatons: Andrade DIPPR lqud vscosty The bnary parameters k j and m j allow accurate representaton of complex lqud mxture vscosty. Both bnary parameters default to zero. Parameter Name/Element Symbol Default MDS Lower Lmt Upper Lmt Unts ANDKIJ/1 a j 0 ANDKIJ/2 b j 0 ANDMIJ/1 c j 0 ANDMIJ/2 d j Physcal Property Methods and Models Verson 10

255 Chapter 3 Andrade The Andrade equaton s: ln *, l η B = A + + C lnt for T T T T l h Parameter Name/Element Symbol Default MDS Lower Lmt Upper Lmt Unts MULAND/1 A X VISCOSITY, TEMPERATURE MULAND/2 B X TEMPERATURE MULAND/3 C X TEMPERATURE MULAND/4 T l 0.0 X TEMPERATURE MULAND/5 T h X TEMPERATURE If elements 2 or 3 are non-zero, absolute temperature unts are assumed for elements 1 to 3. DIPPR Lqud Vscosty The equaton for the DIPPR lqud vscosty model s: ln *, l η C5 = C + C T + C ln T + C T for C T C If the MULDIP parameters for a gven component are avalable, the DIPPR equaton s used nstead of the Andrade model. The Andrade model s also used by PCES. Parameter Name/Element Symbol Default MDS Lower Lmt Upper Lmt Unts MULDIP/1 MULDIP/2,..., 5 C C C X VISCOSITY, 1 TEMPERATURE,..., 0 X TEMPERATURE 2 5 MULDIP/6 MULDIP/7 C 0 X TEMPERATURE 6 C 1000 X TEMPERATURE 7 If elements 3, 4, or 5 are non-zero, absolute temperature unts are assumed for elements 1 to 5. References R.C. Red, J.M. Prausntz, and B.E. Polng, The Propertes of Gases and Lquds, 4th ed., (New York: McGraw-Hll, 1987), p Physcal Property Methods and Models Verson 10

256 Property Model Descrptons API Lqud Vscosty The lqud mxture vscosty s calculated usng a combnaton of the API and Andrade/DIPPR equatons. Ths model s recommended for petroleum and petrochemcal applcatons. It s used n the CHAO-SEA, GRAYSON, LK-PLOCK, PENG-ROB, and RK-SOAVE opton sets. For pseudocomponents, the API model s used: l ( API V ) η l = fcn T, x, Tb,, m Where: fcn = A correlaton based on API Procedures and Fgures 11A4.1, 11A4.2, and 11A4.3 (API Techncal Data Book, Petroleum Refnng, 4th edton) V m l s obtaned from the API lqud volume model. For real components, the Andrade/DIPPR model s used. Parameter Name/Element Symbol Default MDS Lower Lmt Upper Lmt Unts TB T b TEMPERATURE API API Chapman-Enskog-Brokaw/DIPPR *, The pure component low pressure vapor vscosty η ν usng two equatons: Chapman-Enskog DIPPR vapor vscosty (p = 0) can be calculated Chapman-Enskog-Brokaw The equaton for the Chapman-Enskog model s: η *, ν MT = 0 = x10 26 σ 2 Ω ( p ) Where: Ω η = fcn( T k),ε η Physcal Property Methods and Models Verson 10

257 Chapter 3 Polar parameter δ s used to determne whether to use the Stockmayer or Lennard-Jones potental parameters: ε k (energy parameter) and σ (collson dameter). To calculate δ, the dpole moment p and ether the Stockmayer parameters or the dpole moment T b and V bm are needed. The polarty correcton s from Brokaw. Parameter Name/Element Symbol Default MDS Lower Lmt Upper Lmt Unts MW M MUP p 0.0 5x10-24 DIPOLEMOMENT STKPAR/1 ( ) ε ST k fcn( Tb Vb ),,p X TEMPERATURE STKPAR/2 ST σ fcn( T V ) LJPAR/1 ( ) ε,,p X LENGTH b b LJ k fcn( T c,ω ) X TEMPERATURE LJPAR/2 LJ σ fcn( T p ),,ω X LENGTH c c DIPPR Vapor Vscosty The equaton for the DIPPR vapor vscosty model s: *, η ν C 2 ( 0) ( 1 / ) 2 p= = C T + C T+ C T for C T C If the MUVDIP parameters for a gven component are avalable, the DIPPR equaton s used nstead of the Chapman-Enskog-Brokaw model. PCES uses the DIPPR vapor vscosty model. Parameter Name/Element Symbol Default MDS LoweLmt Upper Lmt Unts MUVDIP/1 C X VISCOSITY 1 MUVDIP/2 MUVDIP/3, 4 C C C 0 X 2, 0 X TEMPERATURE 3 4 MUVDIP/5 MUVDIP/6 MUVDIP/7 C 0 X 5 C 0 X TEMPERATURE 6 C 1000 X TEMPERATURE 7 If elements 2, 3, or 4 are non-zero, absolute temperature unts are assumed for elements 1 through 4. Physcal Property Methods and Models Verson 10

258 Property Model Descrptons References R.C. Red, J.M. Prausntz, and B.E. Polng. The Propertes of Gases and Lquds, 4th ed., (New York: McGraw-Hll, 1987), p Chapman-Enskog-Brokaw-Wlke Mxng Rule The low pressure vapor mxture vscosty s calculated by the Wlke approxmaton of the Chapman-Enskog equaton: ν η ( p 0) = = y *, ν η ( p= 0) yjφj j For Φ j,the formulaton by Brokaw s used: Φ j η = *, ν ( p = 0) η *, ν j Where: A j = fcn( M M j ) Sj = δ ( ε ),, and the correcton factor for polar gases (, ) ST, fcn k T Polar parameter δ s used to determne whether to use the Stockmayer or Lennard-Jones potental parameters: ε k (energy parameter ) and σ (collson dameter). To calculate δ, the dpole moment p, and ether the Stockmayer parameters or T b and V bm are needed. *, The pure component vapor vscosty η ν (p = 0) can be calculated usng the Chapman- Enskog-Brokaw/DIPPR (or another) low pressure vapor vscosty model. *, Ensure that you supply parameters for η ν (p = 0) Physcal Property Methods and Models Verson 10

259 Chapter 3 Parameter Name/Element Symbol Default MDS Lower Lmt Upper Lmt Unts MW M MUP p 0.0 5x10-24 DIPOLEMOMENT STKPAR/1 ( ) ε ST k fcn( Tb Vb ),,p X TEMPERATURE STKPAR/2 ST σ fcn( T V ),,p X LENGTH b b References R.C. Red, J.M. Prausntz, and T.K. Sherwood, The Propertes of Gases and Lquds, 3rd ed., (New York: McGraw-Hll, 1977), pp Chung-Lee-Starlng Low-Pressure Vapor Vscosty The low-pressure vapor vscosty by Chung, Lee, and Starlng s: η ν ( p 0) = = V ( MT) 2 3 cm Ω η 1 2 F C Where the vscosty collson ntegral s: Ω η = fcn( T r ) The shape and polarty correcton s: F = fcn( Ω, p, κ ) c r The parameter p r s the reduced dpolemoment: p r p = ( VcmTc ) The polar parameter κ s tabulated for certan alcohols and carboxylc acds. The prevous equatons can be used for mxtures when applyng these mxng rules: V T = y y V cm j j cj c = j yyt V V j cj cj cm Physcal Property Methods and Models Verson 10

260 Property Model Descrptons M = xxω V j ω = V p p r 4 p = V T 2 cm c 2 2 xxt j cjv 3 cj M j j 2 TV 3 c cm j j cj cm xx p 2 p 2 jv j = V κ = xx Where: j j c cj κ j j V cj = ( ξ j )( VV c cj ) ξ j = 0 (n almost all cases) T cj = ( 1 ζj )( TT c cj ) ζ j = 0 (n almost all cases) ω j = ( ω + ω j) M j = 2 2MM ( M + M j) 1 κ j = ( κκ j ) 2 j Physcal Property Methods and Models Verson 10

261 Chapter 3 Parameter Name/Element Symbol Default MDS Lower Lmt Upper Lmt Unts TCCLS T c TC x TEMPERATURE VCCLS V c VC x MOLE-VOLUME MW M MUP p 0.0 5x10 24 DIPOLEMOMENT OMGCLS ω OMEGA x CLSK κ 0.0 x CLSKV ξ j 0.0 x CLSKT ζ j 0.0 x The model specfc parameters also affect the Chung-Lee-Starlng Vscosty and the Chung-Lee-Starlng Thermal Conductvty models. References R.C. Red, J.M. Prausntz, and B.E. Polng, The Propertes of Gases and Lquds, 4th ed., (New York: McGraw-Hll, 1987), p. 396, p Chung-Lee-Starlng Vscosty The Chung-Lee-Starlng vscosty equaton for vapor and lqud, hgh and low pressure s: η ν 1 ( MT) 2 F ( MT ) C = 2 f + V 3 Ω V cm η 1 2 c cm f Wth: f 1 = fcn( ρ, V, ω, p, κ) m cm r f 2 = fcn( ω, p, κ) F 2 = fcn( ω, p, κ) r r The molar densty can be calculated usng an equaton-of-state model (for example, the Benedct-Webb-Rubn). The parameter p r s the reduced dpolemoment: p r p = ( VcmTc ) Physcal Property Methods and Models Verson 10

262 Property Model Descrptons The polar parameter κ s tabulated for certan alcohols and carboxylc acds. For low pressures, f 1 s reduced to 1.0 and f 2 becomes neglgble. The equaton reduces to the low pressure vapor vscosty model by Chung-Lee and Starlng. The prevous equatons can be used for mxtures when applyng these mxng rules: V T = y y V cm j j cj c = M = j yyt V V j cj cj cm xxω V j ω = V p p r 4 p = V T 2 cm c 2 2 xxt j cjv 3 cj M j j 2 TV 3 c cm j j cj cm xx p 2 p 2 jv j = V κ = xx Where: j j c cj κ j j V cj = ( ξ j )( VV c cj ) ξ j = 0 (n almost all cases) T cj = ( 1 ζj )( TT c cj ) ζ j = 0 (n almost all cases) ω j = ( ω + ω j) Physcal Property Methods and Models Verson 10

263 Chapter 3 M j = 2MM ( M + M j) 1 κ j = ( κκ j ) 2 j 1 2 Parameter Name/Element Symbol Default MDS Lower Lmt Upper Lmt Unts TCCLS T c TC x TEMPERATURE VCCLS V c VC x MOLE-VOLUME MW M MUP p 0.0 5x10 24 DIPOLEMOMENT OMGCLS ω OMEGA x CLSK κ 0.0 x CLSKV ξ j 0.0 x CLSKT ζ j 0.0 x The model specfc parameters affect the results of the Chung-Lee-Starlng Thermal Conductvty and Low Pressure Vscosty models as well. References R.C. Red, J.M. Prausntz, and B.E. Polng, The Propertes of Gases and Lquds, 4th ed., (New York: McGraw-Hll, 1987), p Dean-Stel Pressure Correcton The pressure correcton to low pressure vapor vscosty or the resdual vapor vscosty by Dean and Stel s: η 108 m p p ( rm = = ) ξ () η ( 0) ν ν ρ ρ Where η ν (p = 0) s obtaned from a low pressure vscosty model (for example, Chapman-Enskog-Brokaw). The dmensonless-makng factor ξ s: ξ = N 2 A 1 T 6 c M p c Physcal Property Methods and Models Verson 10

264 Property Model Descrptons T c = yt c M = p c = ym ZcmRT V cm c V cm = yv Z cm = yz c c ρ rm = V Vcm ν m The parameter <$EV sub m sup {^v}> s obtaned from Redlch-Kwong equatonof-state. Parameter Name/Element Symbol Default MDS Lower Lmt Upper Lmt Unts MW M VC V c MOLE-VOLUME IAPS Vscosty for Water The IAPS vscosty models, developed by the Internatonal Assocaton for Propertes of Steam, calculate vapor and lqud vscosty for water and steam. These models are used n opton sets STEAMNBS and STEAM-TA. The general form of the equaton for the IAPS vscosty models s: η w ( ) = fcn T, p Where: fcn = Correlaton developed by IAPS The models are only applcable to water. There are no parameters requred for the models Physcal Property Methods and Models Verson 10

265 Chapter 3 Jones-Dole Electrolyte Correcton The Jones-Dole model calculates the correcton to the lqud mxture vscosty of a solvent mxture, due to the presence of electrolytes: η l l = ηsolv 1+ η ca (1) ca Where: η solv = Vscosty of the lqud solvent mxture, calculated by the Andrade/DIPPR model l η ca = Contrbuton to the vscosty correcton due to apparent electrolyte ca l The parameter η ca can be calculated by three dfferent equatons. If these parameters are avalable IONMOB and IONMUB IONMUB Use ths equaton Dole-Jones Breslau-Mller Carbonell Jones-Dole The Jones-Dole equaton s: l η ca = A c + B c 2) ca a ca ca a ca Where: c a ca x = V a ca l m = Concentraton of apparent electrolyte ca (3) a x ca = Mole fracton of apparent electrolyte ca A ca = η l solv 145. L c + L a ( c a c a ) ( 2εT) 1 2 4LL c a 3+ 2LL( L + L) L c L a (4) L a = l + l T (5) a, 1 a, 2 L c = l + l T (6) c, 1 c, 2 Physcal Property Methods and Models Verson 10

266 Property Model Descrptons B ca = ( bc, 1 bc, 2T) ( ba, 1 ba, 2T) (7) Breslau-Mller The Breslau-Mller equaton s: l η ca e a ca ( c a ca ) 2 = 2. 5Vc V e (8) Where the effectve volume V c s gven by: V V e e = = ( B ) ca 260. ( B ) ca 506. Carbonell for salts nvolvng unvalent ons (9) for other salts The Carbonell equaton s: (9a) l η ca a a c ca = exp Mx k k 10. (10) k T Where: M k = Molecular weght of an apparent electrolyte component k You must provde parameters for the Andrade model, used for the calculaton of the lqud mxture vscosty of the solvent mxture. Parameter Name/Element Symbol Default Lower Lmt Upper Lmt Unts CHARGE z 0.0 MW M IONMOB/1 I 1 AREA, MOLES IONMOB/2 I AREA, MOLES, TEMPERATURE IONMUB/1 b 1 MOLE-VOLUME IONMUB/2 b 2 0,0 MOLE-VOLUME, TEMPERATURE References A. L. Horvath, Handbook of Aqueous Elecrolyte Solutons, (Chchester: Ells Horwood, 1985) Physcal Property Methods and Models Verson 10

267 Chapter 3 Letsou-Stel The Letsou-Stel model calculates lqud vscosty at hgh temperatures for Ths model s used n PCES. T r The general form for the model s: ( ) ( ) 0 1 l l l ηε= ηε + ω ηε Where: ( ηε) l 0 = fcn( T, x, T ) ( ηε) l 1 = fcn( T, x, T ) ε = fcn( x, M, T, p,ω ) ω = x ω c c c c Parameter Name/Element Symbol Default MDS Lower Lmt Upper Lmt Unts MW M TC T c TEMPERATURE PC p c PRESSURE OMEGA ω References R.C. Red, J.M. Pransntz, and B.E. Polng, The Propertes of Gases and Lquds, 4th ed., (New York: McGraw-Hll, 1987), p Lucas Vapor Vscosty The equaton for the Lucas vapor vscosty model s: ν ( ( p 0) ) ν η = η = ξ YF p F Q ξ Where the dmensonless low pressure vscosty s gven by: ( η ν ( p= 0) ξ) = fcn( Tr) FP( p= 0) FQ( p= 0) Physcal Property Methods and Models Verson 10

268 Property Model Descrptons The dmensonless-makng group s: ξ=n 2 A 1 T 6 c M p c The pressure correcton factor Y s: ( ) Y = fcn p, T r r The polar and quantum correcton factors at hgh and low pressure are: ( P ) F P = fcn Y, F ( p = 0) ( Q ) F Q = fcn Y, F ( p = 0) F F P ( p = 0 ) = fcn( T, p, Z, p ) Q ( p= 0 ) = ( ) r c c = 2 2 fcn T r, but s only nonunty for the quantum gates H, E and He. The Lucas mxng rules are: T c = yt p c = M = F F RT V c c c yz yv RZcT = p ym P ( p=0 ) = yf ( p ) c c c c P = 0 Q = 0, Q ( p=0 ) = A y F ( p ) Where A dffers from unty only for certan mxtures., Physcal Property Methods and Models Verson 10

269 Chapter 3 Parameter Name/Element Symbol Default MDS Lower Lmt Upper Lmt Unts TCLUC T c TC x TEMPERATURE PCLUC p c PC x PRESSURE ZCLUC Z c ZC x MW M MUP p 0.0 5x10 24 DIPOLEMOMENT References R.C. Red, J.M. Prausntz, and B.E. Polng, The Propertes of Gases and Lquds, 4th ed., (New York: McGraw-Hll, 1987), p. 421, 431. TRAPP Vscosty Model The general form for the TRAPP vscosty model s: (,,,,,,,, ω ) η= fcn t p x M T p V Z Where: c c c c The parameter x s the mole fracton vector; fcn s a correspondng states correlaton based on the model for vapor and lqud vscosty TRAPP, by the Natonal Bureau of Standards (NBS, currently NIST). The model can be used for both pure components and mxtures. The model should be used for nonpolar components only. Parameter Name/Element Symbol Default MDS Lower Lmt Upper Lmt Unts MW M TCTRAP T c TC x TEMPERATURE PCTRAP p c PC x PRESSURE VCTRAP V c VC x MOLE-VOLUME ZCTRAP Z c ZC x OMGRAP ω OMEGA x References J.F. Ely and H.J.M. Hanley, "Predcton of Transport Propertes. 1. Vscostes of Fluds and Mxtures," Ind. Eng. Chem. Fundam., Vol. 20, (1981), pp Physcal Property Methods and Models Verson 10

270 Property Model Descrptons Thermal Conductvty Models ASPEN PLUS has eght bult-n thermal conductvty models. Ths secton descrbes the thermal conductvty models avalable. Model Chung-Lee-Starlng IAPS L Mxng Rule Redel Electrolyte Correcton Sato-Redel/DIPPR Stel-Thodos/DIPPR Stel-Thodos Pressure Correcton TRAPP Thermal Conductvty Vredeveld Mxng Rule Wassljewa-Mason-Saxena Mxng Rule Type Vapor or lqud Water or stream Lqud mxture Electrolyte Lqud Low pressure vapor Vapor Vapor or lqud Lqud mxture Low pressure vapor Chung-Lee-Starlng Thermal Conductvty The man equaton for the Chung-Lee-Starlng thermal conductvty model s: ( = ) 312. η p 0 Ψ λ = f M Where: + f 1 2 f 1 = ( ρ, ω, p, κ) fcn m r f 2 = fcn( T, M, V, ρ, ω, p, κ) Ψ = fcn( C,, ) c cm rm r ν ω T r η( p = 0 ) can be calcuated by the low pressure Chung-Lee-Starlng model. The molar densty can be calculated usng an equaton-of-state model (for example, the Benedct-Webb-Rubn equaton-of-state). The parameter p r s the reduced dpolemoment: p r p = ( VcmTc ) The polar parameter κ s tabulated for certan alcohols and carboxylc acds Physcal Property Methods and Models Verson 10

271 Chapter 3 For low pressures, f 1 s reduced to 1.0 and f 2 s reduced to zero. Ths gves the Chung-Lee-Starlng expresson for thermal conductvty of low pressure gases. The same expressons are used for mxtures. The mxture expresson for η( p = 0) must be used. (See Chung-Lee-Starlng Low-Pressure Vapor Vscosty on page ) C ν = x Cν, M = xxω V j ω = V p p r 4 p = V T 2 cm c 2 2 xxt j cjv 3 cj M j j 2 TV 3 c cm j j cj cm xx p 2 p 2 jv j = V κ = xx Where: j j c cj κ j j V cj = ( ξ j )( VV c cj ) ξ j = 0 (n almost all cases) T cj = ( 1 ζj )( TT c cj ) ζ j = 0 (n almost all cases) ω j = M j = ( ω + ω j) 2 2MM ( M + M j) 1 κ j = ( κκ j ) 2 j Physcal Property Methods and Models Verson 10

272 Property Model Descrptons Parameter Name/Element Symbol Default MDS Lower Lmt Upper Lmt Unts TCCLS T c TC x TEMPERATURE VCCLS V c VC x MOLE-VOLUME MW M MUP p 0.0 5x10 24 DIPOLEMOMENT OMGCLS ω OMEGA x CLSK κ 0.0 x CLSKV ξ j 0.0 x CLSKT ζ j 0.0 x The model-specfc parameters also affect the results of the Chung-Lee-Starlng vscosty models. References R.C. Red, J.M. Prausntz, and B.E. Polng, The Propertes of Gases and Lquds, 4th ed., (New York: McGraw-Hll, 1987), p. 505, 523. IAPS Thermal Conductvty for Water The IAPS thermal conductvty models were developed by the Internatonal Assocaton for Propertes of Steam. These models can calculate vapor and lqud thermal conductvty for water and steam. They are used n opton sets STEAMNBS and STEAM-TA. The general form of the equaton for the IAPS thermal conductvty models s: λ w ( ) = fcn T, p Where: fcn = Correlaton developed by IAPS The models are only applcable to water. No parameters are requred. L Mxng Rule Lqud mxture thermal conductvty s calculated usng L equaton (Red et.al., 1987): l λ = ΦΦλ j j j Physcal Property Methods and Models Verson 10

273 Chapter 3 Where: *, l *, l ( ) ( j ) λj = 2 λ + λ *, xv = l Φ *, l j xv j The pure component lqud molar volume V model. *, l s calculated from the Rackett *, l The pure component thermal conductvty λ can be calculated by two equatons: Sato-Redel DIPPR See the Sato-Redel/DIPPR model for descrptons. Redel Electrolyte Correcton The Redel model can calculate the correcton to the lqud mxture thermal conductvty of a solvent mxture, due to the presence of electrolytes: l λ l ( T) = λsolv( T = 293) + ( ac + aa) Where: ca x V a ca l m l solv( T) ( T 293) λ λ l solv = l λ solv = Thermal conductvty of the lqud solvent mxture, calculated by the Sato-Redel model a x ca = Mole fracton of the apparent electrolyte ca a c, a = Redel onc coeffcent a V m l = Apparent molar volume computed by the Clarke densty model Apparent electrolyte mole fractons are computed from the true on mole-fractons and onc charge number. They can also be computed f you use the apparent component approach. A more detaled dscusson of ths method s found n Chapter 5. You must provde parameters for the Sato-Redel model. Ths model s used for the calculaton of the thermal conductvty of solvent mxtures. Physcal Property Methods and Models Verson 10

274 Property Model Descrptons Parameter Name/Element Symbol Default Lower Lmt Upper Lmt Unts CHARGE z 0.0 IONRDL a 0.0 THERMAL CONDUCTIVITY, MOLE-VOLUME Sato-Redel/DIPPR The pure component thermal conductvty can be calculated by two equatons: Sato-Redel DIPPR Sato-Redel The Sato-Redel equaton s (Red et al., 1987): *, l. λ = Where: ( Tr) ( T ) M T br = Tb Tc T r = TT c br Parameter Name/Element Symbol Default MDS Lower Lmt Upper Lmt Unts MW M TC T c TEMPERATURE TB T b TEMPERATURE DIPPR The DIPPR equaton s: *, l λ = C + C T + C T + C T + C T for C T C Lnear extrapolaton of λ *,l versus T occurs outsde of bounds. If the KLDIP parameters for a gven component are avalable, the DIPPR model s used nstead of the Sato-Redel model. The DIPPR model s also used by PCES Physcal Property Methods and Models Verson 10

275 Chapter 3 Parameter Name/Element Symbol Default MDS Lower Lmt Upper Lmt Unts KLDIP/1 KLDIP/2,, 5 C C C x THERMAL- 1 CONDUCTIVITY, TEMPERATURE,..., 0 x THERMAL- 2 5 CONDUCTIVITY, TEMPERATURE KLDIP/6 C 0 x TEMPERATURE 6 KLDIP/7 C x TEMPERATURE Vredeveld Mxng Rule Lqud mxture thermal conductvty s calculated usng the Vredeveld equaton (Red et al., 1977): l λ = *, ( λ l ) xm 2 j x M j j 1 2 *, l Pure component thermal conductvty λ can be calcualted by two equatons: Sato-Redel DIPPR See the Sato-Redel/DIPPR model for descrptons. References R.C. Red, J.M. Prausntz, and T.K. Sherwood, The Propertes of Gases and Lquds, 4th ed., (New York: McGraw-Hll, 1977), p R.C. Red, J.M. Prausntz, and B.E. Polng, The Propertes of Gases and Lquds, 4th ed., (New York: McGraw-Hll, 1987), p Stel-Thodos/DIPPR The pure component thermal conductvty for low pressure gasses can be calculated by two equatons: Stel-Thodos DIPPR vapor thermal conductvty Physcal Property Methods and Models Verson 10

276 Property Model Descrptons Stel-Thodos The Stel-Thodos equaton s: λ g ( 115. ( ) 169. x10 ) 4 ν = η C R + M *, ν *, *, p Where: *, η ν ( p ) = 0 can be obtaned from the Chapman-Enskog-Brokaw model. *, g C p s obtaned from the Ideal Gas Heat Capacty model. R s the unversal gas constant. Parameter Name/Element Symbol Default MDS Lower Lmt Upper Lmt Unts MW M DIPPR Vapor Thermal Conductvty The DIPPR equaton for vapor thermal conductvty s: *, l λ 2 ( ) 2 = CT 1+ C T+ CT for C T C C * Lnear extrapolaton of λ ν versus T occurs outsde of bounds. If the KVDIP parameters for a gven component are avalable, the DIPPR equaton s used nstead of the Stel-Thodos equaton. The DIPPR equaton s also used n PCES. Parameter Name/Element Symbol Default MDS Lower Lmt Upper Lmt Unts KVDIP/1 C x THERMAL 1 CONDUCTIVITY KVDIP/2 KVDIP/3, 4 C C C 0 x 2, 0 x TEMPERATURE 3 4 KVDIP/5 0 x KVDIP/6 KVDIP/7 C 0 x TEMPERATURE 6 C 1000 x TEMPERATURE 7 If elements 2, 3, or 4 are non-zero, absolute temperature unts are assumed for elements 1 through Physcal Property Methods and Models Verson 10

277 Chapter 3 References R.C. Red, J.M. Prauntz, and B.E. Polng, The Propertes of Gases and Lqud, 4th ed., (New York: McGraw-Hll, 1987), p Stel-Thodos Pressure Correcton Model The pressure correcton to a pure component or mxture thermal conductvty at low pressure s gven by: n ( ( 0, ) rm,,, c, c, c ) λ ν = fcn λ p = ρ y M T V Z Where: c ν m ρ rm = y V V The parameter V ν m can be obtaned from Redlch-Kwong. λ ν ( ) p = 0 can be obtaned from the low pressure Stel-Thodos Thermal Conductvty model (Stel-Thodos/DIPPR). Ths model should not be used for polar substances, hydrogen, or helum. Parameter Name/Element Symbol Default MDS Lower Lmt Upper Lmt Unts MW M TC T c TEMPERATURE PC PRESSURE VC V c MOLE-VOLUME ZC Z c References R.C. Red, J.M. Prauntz, and B.E. Polng, The Propertes of Gases and Lquds, 4th ed., (New York: McGraw-Hll, 1987), p TRAPP Thermal Conductvty Model The general form for the TRAPP thermal conductvty model s: *, g (,,,, c, c, c, c, ω, p ) λ = fcn T P x M T p V Z C Physcal Property Methods and Models Verson 10

278 Property Model Descrptons Where: x = Mole fracton vector *, g C p = Ideal gas heat capacty calculated usng the ASPEN PLUS or DIPPR deal gas heat capacty equatons fcn = Correspondng states correlaton based on the model for vapor and lqud thermal conductvty made by the Natonal Bureau of standards (NBS, currently NIST) The model can be used for both pure components and mxtures. The model should be used for nonpolar components only. Parameter Name/Element Symbol Default MDS Lower Lmt Upper Lmt Unts MW M TCTRAP T c TC x TEMPERATURE PCTRAP p c PC x PRESSURE VCTRAP V c VC x MOLE-VOLUME ZCTRAP Z c ZC x OMGRAP ω OMEGA x References J.F. Ely and H.J. M. Hanley, "Predcton of Transport Propertes. 2. Thermal Conductvty of Pure Fluds and Mxtures," Ind. Eng. Chem. Fundam., Vol. 22, (1983), pp Wassljewa-Mason-Saxena Mxng Rule The vapor mxture thermal conductvty at low pressures s calculated from the pure component values, usng the Wassljewa-Mason-Saxena equaton: λ ν ( p 0) = = y λ *, ν j ( p = 0) ya j j A j n = 1+ n *, ν *, ν j ( p = 0) ( p = 0) [ ] 4 ( M M ) j 81 ( + M M j) Physcal Property Methods and Models Verson 10

279 Chapter 3 Where: *, λ ν = Calculated by the Stel-Thodos model or the DIPPR thermal conductvty model (Stel-Thodos/DIPPR) *, η ν ( p ) = 0 = Obtaned from the Chapman-Enskog-Brokaw model *, g C p = Obtaned from the Ideal Gas Heat Capacty model R = Unversal gas constant *, You must supply parameters for η ν ( p ) *., = 0 and λ ν. Parameter Name/Element Symbol Default MDS Lower Lmt Upper Lmt Unts MW M References R.C. Red, J.M. Prausntz, and B.E. Polng, The Propertes of Gases and Lquds, 4th ed., (New York: McGraw-Hll, 1987), pp Physcal Property Methods and Models Verson 10

280 Property Model Descrptons Dffusvty Models ASPEN PLUS has seven bult-n dffusvty models. Ths secton descrbes the dffusvty models avalable. Model Chapman-Enskog-Wlke-Lee (Bnary) Chapman-Enskog-Wlke-Lee (Mxture) Dawson-Khoury-Kobayash (Bnary) Dawson-Khoury-Kobayash (Mxture) Nernst-Hartley Wlke-Chang (Bnary) Wlke-Chang (Mxture) Type Low pressure vapor Low pressure vapor Vapor Vapor Electrolyte Lqud Lqud Chapman-Enskog-Wlke-Lee (Bnary) ν The bnary dffuson coeffcent at low pressures D ( p ) the Chapman-Enskog-Wlke-Lee model: 2 3 [ ] 2 [ pσokωd] ( = ) = x x10 3 ( ) j ( ) D p f M T f M ν j Where: [ ] ( ) = ( + j) ( j) f M M M M M The collson ntegral for dffuson s: Ω D = fcn( T, ε j k) The bnary sze and energy parameters are defned as: σ j = ( σ + σ j) 2 1 ε j = ( εε j ) = 0 s calculated usng Polar parameter δ s used to determne whether to use the Stockmayer or Lennard-Jones potental parameters: ε k (energy parameter ) and σ (collson dameter). To calculate δ, the dpole moment p, and ether the Stockmayer parameters or T b and V bm are needed Physcal Property Methods and Models Verson 10

281 Chapter 3 Parameter Name/Element Symbol Default MDS Lower Lmt Upper Lmt Unts MW M MUP p 0.0 5X10 24 DIPOLEMOMENT STKPAR/1 ( ε k) ST fcn( T V ) p,, x TEMPERATURE b b STKPAR/2 σ ST fcn( T V ) p,, x LENGTH b b LJPAR/1 ( ε k) LJ ( ) fcn T c,ω x TEMPERATURE LJPAR/2 σ LJ fcn( T c,p,ω ) x LENGTH References R.C. Red, J.M. Prauntz, and B.E. Polng, The Propertes of Gases and Lquds, 4th ed., (New York: McGraw-Hll, 1987), p Chapman-Enskog-Wlke-Lee (Mxture) The dffuson coeffcent of a gas nto a gas mxture at low pressures s calculated usng Blanc s law: ν D ( p= 0) = y j j j D ν j ( p= 0) ν The bnary dffuson coeffcent D ( p ) y j j = 0 at low pressures s calculated usng the Chapman-Enskog-Wlke-Lee model. (See Chapman-Enskog-Wlke-Lee (Bnary) on page ) You must provde parameters for ths model. Physcal Property Methods and Models Verson 10

282 Property Model Descrptons Parameter Name/Element Symbol Default MDS Lower Lmt Upper Lmt Unts DVBLNC 1 x DVBLNC s set to 1 for a dffusng component and 0 for a non-dffusng component. References R.C. Red, J.M. Prausntz, and B.E. Polng, The Propertes of Gases and Lquds, 4th ed., (New York: McGraw-Hll, 1987), p Dawson-Khoury-Kobayash (Bnary) The bnary dffuson coeffcent D ν j at hgh pressures s calculated from the Dawson-Khoury-Kobayash model: 2 3 [ 1 1 2( ) 3( ) ] ( 0) ( 1 ) D ν ν a ν a p ν a p ν D ν ρ = + ρ + + p = ρ p = atm j m rm rm rm g m ρ ν ν rm =Vcm Vm ρ ν m =1 V ν m V cm = yv y + yv * * c j cj + y j ( p ) ν Dj = 0 s the low-pressure bnary dffuson coeffcent obtaned from the Chapman-Enskog-Wlke-Lee model. are obtaned from the Redlch-Kwong equaton-of- The parameters ρ ν and V ν m m state model. You must supply parameters for these two models. Subscrpt denotes a dffusng component. j denotes a solvent. Parameter Name/Element Symbol Default MDS Lower Lmt Upper Lmt Unts VC V c x MOLE-VOLUME References R.C. Red, J.M. Prausntz, and T.K. Sherwood. The Propertes of Gases and Lquds, 3rd ed., (New York: McGraw-Hll, 1977), pp Physcal Property Methods and Models Verson 10

283 Chapter 3 Dawson-Khoury-Kobayash (Mxture) The dffuson coeffcent of a gas nto a gas mxture at hgh pressure s calculated usng Blanc s law: D ν = j y j j D y ν j j The bnary dffuson coeffcent D ν j at hgh pressures s calculated from the Dawson-Khoury-Kobayash model. (See Dawson-Khoury-Kobayash (Bnary) on page ) You must provde parameters for ths model. Parameter Name/Element Symbol Default MDS Lower Lmt Upper Lmt Unts DVBLNC 1 DVBLNC s set to 1 for a dffusng component and 0 for a nondffusng component. References R.C. Red, J.M. Prausntz, and B.E. Polng, The Propertes of Gases and Lquds, 4th ed., (New York: McGraw-Hll, 1987), p Nernst-Hartley The effectve dffusvty of an on n a lqud mxture wth electrolytes can be calculated usng the Nernst-Hartley model: D RT = ( l l T) x + zf 2 1, e, k (1) k Where: F = 965. x 10 7 C/kmole (Faraday s number) x k = Mole fracton of any molecular speces k z = Charge number of speces The bnary dffuson coeffcent of the on wth respect to a molecular speces s set equal to the effectve dffusvty of the on n the lqud mxture: D k D (2) Physcal Property Methods and Models Verson 10

284 Property Model Descrptons The bnary dffuson coeffcent of an on wth respect to an on j s set to the mean of the effectve dffusvtes of the two ons: D j = ( D + Dj) 2 Parameter Name/Element Symbol Default Lower Lmt Upper Lmt Unts CHARGE z 0.0 IONMOB/1 I 1 AREA, MOLES IONMOB/2 I AREA, MOLES, TEMPERATURE References A. L. Horvath, Handbook of Aqueous Electrolyte Solutons, (Chchester: Ells Horwood, Ltd, 1985). Wlke-Chang (Bnary) The Wlke-Chang model calculates the lqud dffuson coeffcent of component n a mxture at fnte concentratons:, l x j, l ( j ) ( j ) l D = D D j x The equaton for the Wlke-Chang model at nfnte dluton s: D ( ϕ M ) l *, l nj( Vb ), l j j j =. x Where s the dffusng solute and j the solvent: ϕ j = Assocaton factor of solvent 1 2. T n j l = Lqud vscosty of the solvent smulaton. Ths can be obtaned from the Andrade/DIPPR model. You must provde parameters for one of these models Physcal Property Methods and Models Verson 10

285 Chapter 3 Parameter Name/Element Symbol Default Lower Lmt Upper Lmt Unts MW M j VB *, l V MOLE-VOLUME b References R.C. Red, J.M. Prausntz, and B.E. Polng, The Propertes of Gases and Lquds, 4th ed., (New York: McGraw-Hll, 1987), p Wlke-Chang (Mxture) The Wlke-Chang model calculates the lqud dffuson coeffcent of component n a mxture. The equaton for the Wlke-Chang model s: D l ( ϕ M) T = x10 16 l 06. n V 1 2 *, l ( b ) Wth: ϕm j = Where: x j ϕ x M j j j j ϕ j = Assocaton factor of solvent n l = Mxture lqud vscosty of all nondffusng components. Ths can be obtaned from the Andrade/DIPPR or another lqud mxture vscosty model. You must provde parameters for one of these models. Parameter Name/Element Symbol Default Lower Lmt Upper Lmt Unts MW M j VB *, l V MOLE-VOLUME b DLWC 1 Physcal Property Methods and Models Verson 10

286 Property Model Descrptons References R.C. Red, J.M. Praunsntz, and B.E. Polng, The Propertes of Gases and Lquds, 4th ed., (New York: McGraw-Hll, 1987), p Surface Tenson Models ASPEN PLUS has four bult-n surface tenson models.ths secton descrbes the surface tenson models avalable. Model API IAPS Hakm-Stenberg-Stel/DIPPR Onsager-Samaras Electrolyte Correcton Type Lqud-vapor Water-stream Lqud-vapor Electrolyte lqud-vapor API Surface Tenson The lqud mxture surface tenson for hydrocarbons s calculated usng the API model. Ths model s recommended for petroleum and petrochemcal applcatons. It s used n the CHAO-SEA, GRAYSON, LK-PLOCK, PENG-ROB, and RK- SOAVE opton sets. The general form of the model s: ( SG T ) σ l = fcn T, x, Tb,, c Where: fcn = A correlaton based on API Procedure 10A32 (API Techncal Data Book, Petroleum Refnng, 4th edton) Parameter Name/Element Symbol Default MDS Lower Lmt Upper Lmt Unts TB T b TEMPERATURE SG SG TC T c TEMPERATURE Physcal Property Methods and Models Verson 10

287 Chapter 3 IAPS Surface Tenson for Water The IAPS surface tenson model was developed by the Internatonal Assocaton for Propertes of Steam. It calculates lqud surface tenson for water and steam. Ths model s used n opton sets STEAMNBS and STEAM-TA. The general form of the equaton for the IAPS surface tenson model s: σ w ( ) = fcn T, p Where: fcn = Correlaton developed by IAPS The model s only applcable to water. No parameters are requred. Hakm-Stenberg-Stel/DIPPR The lqud mxture surface tenson s calculated usng the equaton: σ l l = x σ *, The pure component lqud surface tenson can be calculated by two equatons: Hakm-Stenberg-Stel DIPPR lqud surface tenson Hakm-Stenberg-Stel The Hakm-Stenberg-Stel equaton s: *, l σ = x10 p T Q c c p 1 T 04. r m Where: Q p = ω χ χ ω ω χ m = ω χ χ ω ω χ The parameter χ s the Stel polar factor. Physcal Property Methods and Models Verson 10

288 Property Model Descrptons Parameter Name/Element Symbol Default Lower Lmt Upper Lmt Unts TC T c TEMPERATURE PC p c PRESSURE OMEGA ω CHI χ 0 DIPPR Lqud Surface Tenson The DIPPR equaton for lqud surface tenson s: *, l σ Where: ( ) ( 2 3 C C T C T C T ) r + 4 r + 5 r 1 = C T for C T C 1 r 6 7 T r = TT c If the SIGDIP parameters for a gven component are avalable, use the DIPPR equaton. The DIPPR model s used by PCES. Parameter Name/Element Symbol Default Lower Lmt Upper Lmt Unts SIGDIP/1 C SURFACE-TENSION 1 SIGDIP/2,..., 5 C,..., C SIGDIP/6 SIGDIP/7 C 0 TEMPERATURE 6 C 1000 TEMPERATURE 7 References R.C. Red, J.M. Prausntz, and B.E. Polng, The Propertes of Gases and Lquds, 4th. ed., (New York: McGraw-Hll, 1987), p Onsager-Samaras The Onsager-Samaras model calculates the correcton to the lqud mxture surface tenson ofa solvent mxture, due to the presence of electrolytes: a σ = σsolv + xca σ ca (1) ca Physcal Property Methods and Models Verson 10

289 Chapter 3 Where: σ solv = Surface tenson of the solvent mxture calculated by the Hakm- Stenberg-Stel model a x ca = Mole fracton of the apparent electrolyte ca σ ca = Contrbuton to the surface tenson correcton due to apparent electrolyte ca For each apparent electrolyte ca, the contrbuton to the surface tenson correcton s calculated as: σ ca ( ε T) 80 0 a solv = cca log. x a ε solv cca (2) Where: ε solv = Delectrc constant of the solvent mxture c ca a = x V a ca l m V m l = Lqud molar volume calculated by the Clarke model Apparent electrolyte mole fractons are computed from the true on mole-fractons and onc charge number. They are also computed f you use the apparent component approach. See Chapter 5 for a more detaled dscusson of ths method. You must provde parameters for the Hakm-Stenberg-Stel model, used for the calculaton of the surface tenson of the solvent mxture. Parameter Name/Element Symbol Default Lower Lmt Upper Lmt Unts CHARGE z 0.0 References A. L. Horvath, Handbook of Aqueous Electrolyte Solutons, (Chchester: Ells, Ltd. 1985). Physcal Property Methods and Models Verson 10

290 Property Model Descrptons Nonconventonal Sold Property Models Ths secton descrbes the nonconventonal sold densty and enthalpy models avalable n ASPEN PLUS. The followng table lsts the avalable models and ther model names. Nonconventonal components are sold components that cannot be characterzed by a molecular formula. These components are treated as pure components for process smulaton, though they are complex mxtures. Nonconventonal Sold Property Models General Enthalpy and Densty Models Model name Phase(s) General densty polynomal DNSTYGEN S General heat capacty polynomal ENTHGEN S Enthalpy and Densty Models for Coal and Char General coal enthalpy model HCOALGEN S IGT coal densty model DCOALIGT S IGT char densty model DCHARIGT S General Enthalpy and Densty Models ASPEN PLUS has two bult-n general enthalpy and densty models. Ths secton descrbes the general enthalpy and densty models avalable. Model General Densty Polynomal Heat Capacty Polynomal General Densty Polynomal DNSTYGEN s a general model that gves the densty of any nonconventonal sold component. It uses a smple mass fracton weghted average for the recprocal temperature-dependent specfc denstes of ts ndvdual consttuents. There may be up to twenty consttuents wth mass percentages. You must defne these consttuents, usng the general component attrbute GENANAL. The equatons are: ρ s = 1 w ρ j j Physcal Property Methods and Models Verson 10

291 Chapter 3 s 2 ρ, j =, j1 +, j2 +, j3 +, j4 Where: a a T a T a T w j = Mass fracton of the jth consttuent n component s ρ, j = Densty of the jth constuent n component 3 Parameter Name/Element Symbol Default MDS Lower Lmt Upper Lmt Unts DENGEN/1+4 (J-1) DENGEN/2+4 (J-1) DENGEN/3+4 (J-1) DENGEN/4+4 (J-1) a x, j1 a x 0, j2 a x 0, j3 a x 0, j4 The unts are MASS-DENSITY and TEMPERATURE. Use the elements of GENANAL to nput the mass percentages of the consttuents. The structure of DENGEN s: four coeffcents for the frst consttuent, four coeffcents for the second consttuent, and so on. General Heat Capacty Polynomal ENTHGEN s a general model that gves the specfc enthalpy of any nonconventonal component as a smple mass-fracton-weghted-average for the enthalpes of ts ndvdual consttuents. You may defne up to twenty consttuents wth mass percentages, usng the general component attrbute GENANAL. The specfc enthalpy of each consttuent at any temperature s calculated by combnng specfc enthalpy of formaton of the sold wth a sensble heat change. (See Chapter 1.) The equatons are: h s s = w, jh, j s s s h h C dt = +, j f j p, j T s 2 C = a + a T + a T + a T p, j, j1, j2, j3, j4 3 Where: w j = Mass fracton of the jth consttuent n component Physcal Property Methods and Models Verson 10

292 Property Model Descrptons h s = Specfc enthalpy of sold component f s h j = Specfc enthalpy of formaton of consttuent j C P s, j = Heat capacty of the jth consttuent n component Parameter Name/Element Symbol Default MDS Lower Lmt Upper Lmt Unts DHFGEN/J s f h x 0 MASS-ENTHALPY j HCGEN/1+4 (J-1) HCGEN/2+4 HCGEN/3+4 (J-1) HCGEN/4+4 (J-1) a x, j1 a x 0, j2 a x 0, j3 a x 0, j4 The unts are MASS-ENTHALPY and TEMPERATURE. The elements of GENANAL are used to nput the mass percentages of the consttuents. The structure for HCGEN s: four coeffcents for the frst consttuent, four coeffcents for the second consttuent, and so on. Enthalpy and Densty Models for Coal and Char Coal s modeled n ASPEN PLUS as a nonconventonal sold. Coal models are emprcal correlatons, whch requre sold materal characterzaton nformaton. Component attrbutes are derved from consttuent analyses. Defntons of coal component attrbutes are gven n the ASPEN PLUS User Gude, Chapter 6. Enthalpy and densty are the only propertes calculated for nonconventonal solds. Ths secton descrbes the specal models avalable n ASPEN PLUS for the enthalpy and densty of coal and char. The component attrbutes requred by each model are ncluded. The coal models are: General coal enthalpy IGT coal densty IGT char densty Physcal Property Methods and Models Verson 10

293 Chapter 3 Notaton Most correlatons for the calculaton of coal propertes requre proxmate, ultmate, and other analyses. These are converted to a dry, mneral-matter-free bass. Only the organc porton of the coal s consdered. Mosture correctons are made for all analyses except hydrogen, accordng to the formula: w d = w w 1 H2O Where: w = The value determned for weght fracton w d = The value on a dry bass w HO 2 = The mosture weght fracton For hydrogen, the formula ncludes a correcton for free-mosture hydrogen: w w = w 1 w d H H 2 O H HO 2 The mneral matter content s calculated usng the modfed Parr formula: w = 113. w w + w MM A Sp Cl The ash term corrects for water lost by decomposton of clays n the ash determnaton. The average water consttuton of clays s assumed to be 11.2 percent. The sulfur term allows for loss n weght of pyrtc sulfur when pyrte s burned to ferrc oxde. The orgnal Parr formula assumed that all sulfur s pyrtc sulfur. Ths formula ncluded sulfatc and organc sulfur n the mneralmatter calculaton. When nformaton regardng the forms of sulfur s avalable, use the modfed Parr formula to gve a better approxmaton of the percent of norganc materal present. Because chlorne s usually small for Unted States coals, you can omt chlorne from the calculaton. Correct analyses from a dry bass to a dry, mneral-matter-free bass, usng the formula: w dm = d w w 1 w MM d Physcal Property Methods and Models Verson 10

294 Property Model Descrptons Where: w d = Correcton factor for other losses, such as the loss of carbon n carbonates and the loss of hydrogen present n the water consttuton of clays d d w = W W C d d w = w 0. 02w H A A d Sp d sp The oxygen and organc sulfur contents are usually calculated by dfference as: dm dm dm dm W = 1 W W W W O dm dm dm w = w w w S Where: St C Sp H dm Ss So dm N C p = Heat capacty / (J/kgK) c p = Heat capacty / (cal/gc) h = Specfc enthalpy c h = Specfc heat of combuston f h = Specfc heat of formaton R O = Mean-maxmum relectance n ol T = Temperature/K t = Temperature/C w = Weght fracton ρ = Specfc densty Subscrpts: A = Ash C = Carbon Cl = Chlorne FC = Fxed carbon H = Hydrogen Physcal Property Methods and Models Verson 10

295 Chapter 3 HO 2 = Mosture MM = Mneral matter N = Ntrogen O = Oxygen So = Organc sulfur Sp = Pyrtc sulfur St = Total sulfur S = Other sulfur VM = Volatle matter Superscrpts: d = Dry bass m = Mneral-matter-free bass General Coal Enthalpy Model The general coal model for computng enthalpy n ASPEN PLUS s HCOALGEN. Ths model ncludes a number of dfferent correlatons for the followng: Heat of combuston Heat of formaton Heat capacty You can select one of these correlatons usng an opton code n the Propertes Advanced NC-Props form. (See the ASPEN PLUS User Gude, Chapter 6). Use opton codes to specfy a calculaton method for propertes. Each element n the opton code vector s used n the calculaton of a dfferent property. The table labeled HCOALGEN Opton Codes lsts model opton codes for HCLOALGEN. The table s followed by a detaled descrpton of the calculatons used for each correlaton. The correlatons are descrbed nthe followng secton. The component attrbutes are defned n ASPEN PLUS User Gude, Chapter 6. Heat of Combuston Correlatons The heat of combuston of coal n the HCOALGEN model s a gross calorfc value. It s expressed n Btu/lb of coal on a dry mneral-matter-free bass. ASTM Standard D-2015 defnes standard condtons for measurng gross calorfc value. Intal oxygen pressure s 20 to 40 atmospheres. Products are n the form of ash; lqud water; and gaseous CO 2, SO 2, and NO 2. Physcal Property Methods and Models Verson 10

296 Property Model Descrptons You can calculate net calorfc value from gross calorfc value by makng a deducton for the latent heat of vaporzaton of water. Heat of combuston values are converted back to a dry, mneral-mattercontanng bass wth a correcton for the heat of combuston of pyrte. The formula s: c ( ) d dm h = 1 wmm ch w sp, The heat of combuston correlatons were evaluated by the Insttute of Gas Technology (IGT). They used data for 121 samples of coal from the Penn State Data Base (IGT, 1976) and 457 samples from a USGS report (Swanson, et al., 1976). These samples ncluded a wde range of Unted States coal felds. The constant terms n the HCOALGEN correlatons are bas correctons obtaned from the IGT study. Boe Correlaton: c dm [ dm dm dm dm dm 1 C, 2 H, 3 St, 4 O, 5 N, ] 2 h = a w + a w + a w + a w + a w 10 + a 6 Parameter Name/Element Symbol Default BOIEC/1 a BOIEC/2 a BOIEC/3 a contnued Physcal Property Methods and Models Verson 10

297 Chapter 3 Parameter Name/Element Symbol Default BOIEC/4 a BOIEC/5 a BOIEC/6 a Dulong Correlaton: c dm [ dm dm dm dm dm 1 C, 2 H, 3 S, 4 O, 5 N, ] 2 h = a w + a w + a w + a w + a w 10 + a Parameter Name/Element Symbol Default DLNGC/1 a DLNGC/2 a DLNGC/3 a DLNGC/4 a DLNGC/5 a Grummel and Davs Correlaton: dm ( a5 + a2 w, ) dm d ( C H ) ( A) dm dm dm 1, 2, 3 S, 4 O, 1 w, dm H c h = 2 a w + a w + a w + a w 10 + a 6 Parameter Name/Element Symbol Default GMLDC/1 a GMLDC/2 a GMLDC/3 a GMLDC/4 a GMLDC/5 a GMLDC/6 a Physcal Property Methods and Models Verson 10

298 Property Model Descrptons Mott and Spooner Correlaton: c c dm [ dm dm dm dm 1 C 2 H 3 S 4 O ] h = a w + a w + a w a w 10 + a w dm,,,, 7 for O,. dm h = a w + a w + a w a dm dm dm 1 C, 2 H, 3 S, 6 a w dm 5 O, dm 2 dm w d O, + a7 for wo,. wa, Parameter Name/Element Symbol Default MTSPC/1 a MTSPC/2 a MTSPC/3 a MTSPC/4 a MTSPC/5 a MTSPC/6 a MTSPC/7 a IGT Correlaton: c dm [ d d d d 1 C, 2 H, 3 S, 4 A, ] 2 h = a w + a w + a w + a w 10 + a Parameter Name/Element Symbol Default CIGTC/1 a CIGTC/2 a CIGTC/3 a CIGTC/4 a CIGTC/5 a User Input Value of Heat Combuston Parameter Name/Element Symbol Default HCOMB d c h Physcal Property Methods and Models Verson 10

299 Chapter 3 Standard Heat of Formaton Correlatons There are two standard heat of formaton correlatons for the HCOALGEN model: Heat of combuston-based Drect Heat of Combuston-Based Correlaton Ths s based on the assumpton that combuston results n complete oxdaton of all elements except sulfatc sulfur and ash, whch are consdered nert. The numercal coeffcents are combnatons of stochometrc coeffcents and heat of formaton for CO 2, HO 2, HCl, and NO 2.at K: f d d 6 d 5 d 4 h = h (. 1418x 10 w x 10 w x10 w c x 10 w x 10 w ) 10 d H, C, S, 6 d 4 d 2 N, Cl, Drect Correlaton Normally small, relatve to ts heat of combuston. An error of 1% n the heat of a combuston-based correlaton produces about a 50% error when t s used to calculate the heat of formaton. For ths reason, the followng drect correlaton was developed, usng data from the Penn State Data Base. It has a standard devaton of Btu/lb, whch s close to the lmt, due to measurement n the heat of combuston: f d [ dm dm d d d 2 1 c, 2 H, 3 H, 4 Sp 5 Ss] 10 d [ ( ) ] d d 2 + a6ro, + a7 wc, + wfc, + a8wvm 10 dm 2 dm 2 d d 2 d + a9( wc, ) + a10( wst, ) + a11 ( wc, wfc, ) + a12( wvm, ) 2 d + a ( Ro ) + a ( wvm )( w d d 4 13, 14, C, wfc, ) 10 + a15 h = a w + a w + a w + a w + a w Where: 2 [ ] 10 4 Parameter Name/Element Symbol Default HFC/1 a HFC/2 a HFC/3 a HFC/4 a HFC/5 a HFC/6 a HFC/7 a contnued Physcal Property Methods and Models Verson 10

300 Property Model Descrptons Parameter Name/Element Symbol Default HFC/8 a HFC/9 a HFC/10 a HFC/11 a HFC/12 a HFC/13 a HFC/14 a HFC/15 a Heat Capacty Krov Correlatons The Krov correlaton (1965) consdered coal to be a mxure of mosture, ash, fxed carbon, and prmary and secondary volatle matter. Prmary volatle matter s any volatle matter equal to the total volatle matter content, up to 10%. The correlaton developed by Krov treats the heat capacty as a weghted sum of the heat capactes of the consttuents: C ncn d p, = wjcp, j j= 1 2 C = a + a T + a T + a T pj,, j1, j2, j3, j4 Where: = Component ndex j = Consttuent ndex j = 1, 2,..., ncn 1 = Mosture 2 = Fxed carbon 3 = Prmary volatle matter 4 = Secondary volatle matter 5 = Ash w j = Mass fracton of jth consttuent on dry bass Physcal Property Methods and Models Verson 10

301 Chapter 3 Parameter Name/Element Symbol Default CP1C/1 a, CP1C/2 a,12 0 CP1C/3 a,13 0 CP1C/4 a,14 0 CP1C/5 a, CP1C/6 a 68. x10 4,22 CP1C/7 a 42. x10 7,23 CP1C/8 a,24 0 CP1C/9 a, CP1C/10 a,32 81.x10 4 CP1C/11 a,33 0 CP1C/12 a,34 0 CP1C/13 a, CP1C/14 a,42 61.x10 4 CP1C/15 a,43 0 CP1C/16 a,44 0 CP1C/17 a, CP1C/18 a, x10 4 CP1C/19 a,53 0 CP1C/20 a,54 0 Physcal Property Methods and Models Verson 10

302 Property Model Descrptons Cubc Temperature Equaton The cubc temperature equaton s: d 2 c = a + a t + a t + a t p Parameter Name/Element Symbol Default CP2C/1 a CP2C/2 a x10 3 CP2C/3 a x10 5 CP2C/4 a x10 7 The default values of the parameters were developed by Gomez, Gayle, and Taylor (1965). They used selected data from three lgntes and a subbtumnous B coal, over a temperature range from 32.7 to C. HCOALGEN Opton Codes Opton Code Number Opton Code Value Calculaton Method Parameter Names Component Attrbutes 1 Heat of Combuston 1 Boe correlaton BOIEC ULTANAL SULFANAL PROXANAL 2 Dulong correlaton DLNGC ULTANAL SULFANAL PROXANAL 3 Grummel and Davs correlaton 4 Mott and Spooner correlaton GMLDC MTSPC ULTANAL SULFANAL PROXANAL ULTANAL ULFANAL ROXANAL 5 IGT correlaton CIGTC ULTANAL ROXANAL 6 User nput value HCOMB ULTANAL ROXANAL contnue Physcal Property Methods and Models Verson 10

303 Chapter 3 HCOALGEN Opton Codes (contnued) Opton Code Number Opton Code Value Calculaton Method Parameter Names Component Attrbutes 2 Standard Heat of Formaton 1 Heat-of-combusonbased correlaton ULTANAL ULFANAL 2 Drect correlaton HFC ULTANAL SULFANAL PROXANAL 3 Heat Capacty 1 Krov correlaton CP1C PROXANAL 2 Cubc temperature equaton CP2C 4 Enthalpy Bass 1 Elements n ther standard states at K and 1 atm 2 Component at K IGT Coal Densty Model The DCOALIGT model gves the true (skeletal or sold-phase) densty of coal on a dry bass. It uses ultmate and sulfur analyses. The model s based on equatons from IGT (1976): ρ ρ dm W = dm H, ρ dm dm [ ρ ( 0. 42wA ) ] d d d d, 015. wsp, wa, wSp, 1 = a + a w + a ww + a w dm ( dm, H ) ( dm,, H, ) d d d ( WH,. wa, +. wsp, ) d d ( wa, wSp, ) 1 2 H = The equaton for ρ dm s good for a wde range of hydrogen contents, ncludng anthractes and hgh temperature cokes. The standard devaton of ths correlaton for a set of 190 ponts collected by IGT from the lterature was 3 Physcal Property Methods and Models Verson 10

304 Property Model Descrptons 12 x m kg. The ponts are essentally unform over the whole range. Ths s equvalent to a standard devaton of about 1.6% for a coal havng a hydrogen content of 5%. It ncreases to about 2.2% for a coke or anthracte havng a hydrogen content of 1% Physcal Property Methods and Models Verson 10

305 Chapter 3 Parameter Name/Element Symbol Default DENIGT/1 a DENIGT/2 a DENIGT/3 a DENIGT/4 a IGT Char Densty Model The DGHARIGT model gves the true (skeletal or sold-phase) densty of char or coke on a dry bass. It uses ultmate and sulfur analyses. Ths model s based on equatons from IGT (1976): ρ d = w 3ρ dm d dm A, ρ + 31, ( w d A) ρ d 1 = a + a w + a w + a w dm 1 2 H, 2, ( dm, 2 H ) ( dm 3 H, ) 3 w dm H, = w d H, d ( 1 wa, ) Parameter Name/Element Symbol Default DENIGT/1 a DENIGT/2 a DENIGT/3 a DENIGT/4 a The denstes of graphtc hgh-temperature carbons (ncludng cokes) range from 22. x10 3 to 226. x10 3 kg m 3. Denstes of nongraphtc hgh-temperature carbons (derved from chars) range from 20. x10 3 to 22. x10 3 kg m 3. Most of the data used n developng ths correlaton were for carbonzed cokng coals. Although data on a few chars (carbonzed non-cokng coals) were ncluded, none has a hydrogen content less than 2%. The correlaton s probably not accurate for hgh temperature chars. Physcal Property Methods and Models Verson 10

306 Property Model Descrptons References I.M. Chang, B.S. Thess, Massachusetts Insttute of Technology, M. Gomez, J.B. Gayle, and A.R. Taylor, Jr., Heat Content and Specfc Heat of Coals and Related Products, U.S. Bureau of Mnes, R.I. 6607, IGT (Insttute of Gas Technology), Coal Converson Systems Techncal Data Book, Secton PMa. 44.1, N.Y. Krov, "Specfc Heats and Total Heat Contents of Coals and Related Materals are Elevated Temperatures," BCURA Monthly Bulletn, (1965), pp. 29, 33. V.E. Swanson et al., Collecton, Chemcal Analyss and Evaluaton of Coal Samples n 1975, U.S. Geologcal Survey, Open-Fle Report (1976), pp Physcal Property Methods and Models Verson 10

307 Chapter 4 4 Property Calculaton Methods and Routes In ASPEN PLUS the methods and models used to calculate thermodynamc and transport propertes are packaged n property methods. Each property method contans all the methods and models needed for a smulaton. A unque combnaton of methods and models for calculatng a property s called a route. The ASPEN PLUS User Gude, Chapter 7, descrbes the property methods avalable n ASPEN PLUS, provdes gudelnes for choosng an approprate property method for your smulaton, and descrbes how to modfy property methods to sut your smulaton needs by replacng property models. Ths chapter dscusses: Major, subordnate, and ntermedate propertes n ASPEN PLUS Calculaton methods avalable Routng concepts Property models avalable Tracng routes Modfyng and creatng property methods Modfyng and creatng routes Physcal Property Methods and Models 4-1 Verson 10

308 Property Calculaton Methods and Routes Introducton Most propertes are calculated n several steps. An example s the calculaton of the fugacty coeffcent of a component n a lqud mxture: ϕ l = γ ϕ *, l (1) Where: *, l ϕ *, = ϕ ν p p *, l (2) Equatons 1 and 2 are both derved from thermodynamcs. The equatons relate the l *, l l ϕ, ϕ γ, ϕ *,, p *, and state varables l propertes of nterest ( ) to other propertes ( ) ( x p). In general, ths type of equaton s derved from unversal scentfc prncples. These equatons are called methods., In the computaton of the lqud mxture fugacty, you need to calculate: Actvty coeffcent ( ) γ *, l Vapor pressure ( p ) Pure component vapor fugacty coeffcent Ths type of property s usually calculated usng equatons that depend on unversal parameters lke T c and p c ; state varables, such as T and p; and correlaton parameters. The use of correlaton parameters makes these equatons much less unversal and more subjectve than methods. For dstncton, we call them models. Often several models exst to calculate one property. For example, to calculate γ you can use the NRTL, UNIQUAC, or UNIFAC model. The reason for treatng models and methods separately s to allow for maxmum flexblty n property calculatons. Therefore the descrptons provded should help show the flexblty of the ASPEN PLUS property system, rather than consttute defntons. For detaled descrptons and lsts of avalable methods and models, see Methods and Routes and Models, ths chapter. A complete calculaton route conssts of a combnaton of methods and models. A number of frequently used routes have been defned n ASPEN PLUS. Routes that belong logcally together have been grouped to form property methods. For more about property methods, see Chapter 2. Routes are dscussed n detal n Routes and Models, ths chapter. To choose a dfferent calculaton route for a gven property route than what s defned n a property method, you can exchange routes or models n property methods (see Modfyng and Creatng Property Methods, ths chapter). 4-2 Physcal Property Methods and Models Verson 10

309 Chapter 4 For a specfc property, there are many choces of models and methods used to buld a route. Therefore ASPEN PLUS does not contan all possble routes as predefned routes. However you can freely construct calculaton routes accordng to your needs. Ths s a unque feature of ASPEN PLUS. Modfyng and creatng new routes from exstng methods, routes and models, and usng them n modfed or new property methods s explaned n Modfyng and Creatng Routes, ths chapter. Physcal Propertes n ASPEN PLUS The followng propertes may be requred by unt operatons n ASPEN PLUS smulatons: Thermodynamc Propertes Fugacty coeffcents (for K-values) Enthalpy Entropy Gbbs energy Molar volume Transport Propertes Vscosty Thermal conductvty Dffuson coeffcent Surface tenson The propertes requred by unt operaton models n ASPEN PLUS are called major propertes and are lsted n the table labeled Major Propertes n ASPEN PLUS on page 4-4. A major property may depend on other major propertes. In addton, a major property may depend on other propertes that are not major propertes. These other propertes can be dvded nto two categores: subordnate propertes and ntermedate propertes. Subordnate propertes may depend on other major, subordnate or ntermedate propertes, but are not drectly requred for unt operaton model calculatons. Examples of subordnate propertes are enthalpy departure and excess enthalpy. The table labeled Subordnate Propertes n ASPEN PLUS on page 4-6 lsts the subordnate propertes. Intermedate propertes are calculated drectly by property models, rather than as fundamental combnatons of other propertes. Common examples of ntermedate propertes are vapor pressure and actvty coeffcents. The table labeled Intermedate Propertes n ASPEN PLUS on page 4-8 lsts the ntermedate propertes. Major and subordnate propertes are obtaned by a method evaluaton. Intermedate propertes are obtaned by a model evaluaton. Physcal Property Methods and Models 4-3 Verson 10

310 Property Calculaton Methods and Routes Major Propertes n ASPEN PLUS Property Name Symbol Descrpton PHlV PHIL PHlS *, v ϕ Vapor pure component fugacty coeffcent *, l ϕ Lqud pure component fugacty coeffcent *, s ϕ Sold pure component fugacty coeffcent PHlV ϕ v Vapor fugacty coeffcent of a component n a mxture PHlLMX ϕ l Lqud fugacty coeffcent of a component n a mxture PHlSMX ϕ s Sold fugacty coeffcent of a component n a mxture HV HL HS *, v H Vapor pure component molar enthalpy *, l H Lqud pure component molar enthalpy *, s H Sold pure component molar enthalpy HVMX H v Vapor mxture molar enthalpy HLMX H l Lqud mxture molar enthalpy HSMX H s Sold mxture molar enthalpy GV GL GS *, v µ Vapor pure component molar Gbbs free energy *, l µ Lqud pure component molar Gbbs free energy *, s µ Sold pure component molar Gbbs free energy GVMX G v Vapor mxture molar Gbbs free energy GLMX G l Lqud mxture molar Gbbs free energy GSMX G s Sold mxture molar Gbbs free energy SV SL SS *, v S Vapor pure component molar entropy *, l S Lqud pure component molar entropy *, s S Sold pure component molar entropy SVMX S v Vapor mxture molar entropy contnued 4-4 Physcal Property Methods and Models Verson 10

311 Chapter 4 Major Propertes n ASPEN PLUS SLMX S l Lqud mxture molar entropy SSMX S s Sold mxture molar entropy VV *, v V Vapor pure component molar volume VL *, l V Lqud pure component molar volume VS *, s V Sold pure component molar volume VVMX V v Vapor mxture molar volume VLMX V l Lqud mxture molar volume VSMX V s Sold mxture molar volume<f20mi> MUV MUL *, v η Vapor pure component vscosty *, l η Lqud pure component vscosty MUVMX η v Vapor mxture vscosty MULMX η l Lqud mxture vscosty KV KL KS *, v λ Vapor pure component thermal conductvty *, l λ Lqud pure component thermal conductvty *, s λ Sold pure component thermal conductvty KVMX λ v Vapor mxture thermal conductvty KLMX KSMX l λ s λ Lqud mxture thermal conductvty Sold mxture thermal conductvty DV D j v Vapor bnary dffuson coeffcent DL D j l Lqud bnary dffuson coeffcent DVMX D v Vapor dffuson coeffcent of a component n a mxture DLMX D l Lqud dffuson coeffcent of a component n a mxture SIGL *, l σ Pure component surface tenson SIGLMX σ l Mxture surface tenson Physcal Property Methods and Models 4-5 Verson 10

312 Property Calculaton Methods and Routes Subordnate Propertes n ASPEN PLUS Property Name Symbol Descrpton DHV v H H *, *,g DHL l H H *, *,g DHS s H H *, *,g DHVMX v H H DHLMX l H H DHSMX s H H m m m g m g m g m DHVPC *, v *, v * H ( p) H ( p ) DHLPC *, l *, l * H ( p) H ( p ) DHSPC *, s *, s * H ( p) H ( p ) DGV v µ µ *, *,g DGL l µ µ *, *,g DGS s µ µ *, *,g DGVMX v G G DGLMX l G G DGSMX s G G DGVPC µ v v ( p) µ *, ( p ) DGLPC µ l l ( p) µ *, ( p ) DGSPC µ s s ( p) µ *, ( p ) DSV v S S m m m g m g m g m *, *,g DSL l S S *, *,g Vapor pure component molar enthalpy departure Lqud pure component molar enthalpy departure Sold pure component molar enthalpy departure Vapor mxture molar enthalpy departure Lqud mxture molar enthalpy departure Sold mxture molar enthalpy departure Vapor pure component molar enthalpy departure pressure correcton Lqud pure component molar enthalpy departure pressure correcton Sold pure component molar enthalpy departure pressure correcton Vapor pure component molar Gbbs energy departure Lqud pure component molar Gbbs energy departure Sold pure component molar Gbbs energy departure Vapor mxture molar Gbbs energy departure Lqud mxture molar Gbbs energy departure Sold mxture molar Gbbs energy departure Vapor pure component molar Gbbs energy departure pressure correcton Lqud pure component molar Gbbs energy departure pressure correcton Sold pure component molar Gbbs energy departure pressure correcton Vapor pure component molar entropy departure Lqud pure component molar entropy departure contnued 4-6 Physcal Property Methods and Models Verson 10

313 Chapter 4 Subordnate Propertes n ASPEN PLUS Property Name Symbol Descrpton DSS s S S *, *,g DSVMX v S S DSLMX l S S DSSMX s S S m m m g m g m g m Sold pure component molar entropy departure Vapor mxture molar entropy departure Lqud mxture molar entropy departure Sold mxture molar entropy departure HNRY H A Henry s constant of supercrtcal component n subcrtcal component A HLXS HSXS GLXS GSXS El, H Lqud mxture molar excess enthalpy m Es, H Sold mxture molar excess enthalpy m El, G Lqud mxture molar excess Gbbs energy m Es, G Sold mxture molar excess Gbbs energy m PHILPC θ *,l Pure component lqud fugacty coeffcent pressure correcton PHISPC θ *,s Pure component sold fugacty coeffcent pressure correcton GAMPC θ E Lqud actvty coeffcent pressure correcton, symmetrc conventon GAMPC1 θ *E Lqud actvty coeffcent pressure correcton, asymmetrc conventon HNRYPC θ A Henry s constant pressure correcton for supercrtcal component n subcrtcal component A XTRUE x true True composton MUVLP *, v η ( p = 0) Pure component low pressure vapor vscosty MUVPC *, v *, v η ( p) η ( p=0) Pure component vapor vscosty pressure correcton MUVMXLP η v ( p =0) Low pressure vapor mxture vscosty MUVMXPC v v η ( p) η ( p=0) Vapor mxture vscosty pressure correcton KVLP *, v λ ( p ) =0 Pure component low pressure vapor thermal conductvty contnued Physcal Property Methods and Models 4-7 Verson 10

314 Property Calculaton Methods and Routes Subordnate Propertes n ASPEN PLUS Property Name Symbol Descrpton KVLP *, v *, v λ ( p= 0) λ ( p= 0) Pure component vapor thermal conductvty pressure correcton KVMXLP λ v ( p =0) Low pressure, vapor mxture thermal conductvty KVMXPC v v λ ( p) λ ( p=0) Vapor mxture thermal conductvty pressure correcton Intermedate Propertes n ASPEN PLUS Property Name Symbol Descrpton GAMMA γ Lqud phase actvty coeffcent GAMUS γ * Lqud phase actvty coeffcent, unsymmetrc conventon GAMMAS γ s Sold phase actvty coeffcent WHNRY w Henry s constant mxng rule weghtng factor PL PS *, l p Lqud pure component vapor pressure *, s p Sold pure component vapor pressure DHVL vap H * DHLS fus H * DHVS sub H * Pure component enthalpy of vaporzaton Pure component enthalpy of fuson Pure component enthalpy of sublmaton VLPM V l Partal molar lqud volume 4-8 Physcal Property Methods and Models Verson 10

315 Chapter 4 Methods Ths secton descrbes the methods avalable for calculatng the major and subordnate propertes n ASPEN PLUS. A method s an equaton used to calculate physcal propertes based on unversal scentfc prncples only, such as thermodynamcs. Ths equaton may contan assumptons, such as the vapor can be treated as deal gas or the pressure s low enough to neglect the pressure correcton. The equaton may need propertes and state varables but not correlaton parameters to calculate a specfc property. Appled thermodynamcs ndcate that there usually s more than one method for calculatng a partcular property. For example, the enthalpy departure of a *, l *,g component n the lqud phase, H H can be calculated from ts fugacty coeffcent n the lqud phase: *, l *, g 2 ln ϕ H H = RT T *, l Ths method s often used for supercrtcal solutes n lqud soluton. Alternatvely, the lqud departure functon can be calculated from the vapor enthalpy departure and the heat of vaporzaton: *, l *, g *, ν *, g H H = H H H vap Both methods are equally vald. There s another possblty, whch s to calculate the departure functon drectly by an equaton of state. Equatons of state use correlaton parameters and are therefore classfed as models, so: (,, ) *, l *,g H H = f p T correlaton parameters Ths s not a method but rather a vald alternatve to calculate the enthalpy departure. To make the model avalable to the lst of methods, a smple method s used that refers to a model: (,, ) *, l *,g H H = f p T specfed model In general, a lst of methods avalable for a property wll be smlar to the lst presented here for the enthalpy departure. Compare the tables on pages 4-11 through Physcal Property Methods and Models 4-9 Verson 10

316 Property Calculaton Methods and Routes In a method you can have any number of major propertes, subordnate propertes, or models. Usually there s a method that can be used wth an equaton-of-state approach and an alternatve that s used wth the actvty coeffcent approach (see Chapter 1). There s always a method that refers to a model. Although there are a lmted number of thermodynamc methods, n general, all the exstng thermodynamc methods for each property are present. Transport property methods are not as unversal as thermodynamc methods. Therefore the transport property methods offered n ASPEN PLUS mght not be exhaustve, but multple methods for one property also exst. All physcal property methods avalable for calculatng major and subordnate propertes n ASPEN PLUS are provded n the tables on pages 4-11 through For each major or subordnate property, these tables lst: Property symbol and name Property type: major or subordnate Methods avalable for calculatng the property For each method the fundamental equaton s gven. The table also lsts whch nformaton s needed to specfy each step n the method (see Routes and Models, ths chapter). Example 1 Methods for calculatng lqud mxture enthalpy From the table labeled Lqud Enthalpy Methods on page 4-18, there are four methods for calculatng HLMX: Method 1 HLMX s calculated drectly by an emprcal model. The model may depend on temperature T, pressure p, lqud composton, and certan model-specfc parameters. ( ) l l H = f T, p, x, parameters Method 2 HLMX s calculated from the deal lqud mxture enthalpy and excess enthalpy. l l H = x H + H m *, El, m ( HLMX = x HL + HLXS) The major property HLMX depends on the lqud pure component enthalpy, HL, and the lqud mxture excess enthalpy, HLXS. HL s also a major property, whle HLXS s a subordnate property Physcal Property Methods and Models Verson 10

317 Chapter 4 Method 3 HLMX s calculated from the deal gas mxture enthalpy, HIGMX, and the lqud mxture enthalpy departure, DHLMX. l g ( m m ) l g H = H + H H m m ( HLMX = HIGMX + DHLMX) The subordnate property DHLMX can be calculated by one of two methods as lsted n the table labeled Lqud Enthalpy Methods on page In all the equaton-of-state property methods, DHLMX s calculated drectly by an equaton of state (that s, method 1 s used for DHLMX). Method 4 HLMX s calculated drectly by the Electrolyte model. H l m = Where: t ( ) f x x t = The component true mole fractons ( x t s also the symbol for the subordnate property XTRUE: HLMX = f (XTRUE)). Vapor Fugacty Coeffcent Methods Property Symbol and Name Property Type Method Code Method Route Structure Informaton Requred *, v ϕ PHIV ϕ v PHIVMX Major 1 Specfed model *, v ϕ Model name Major 1 Specfed model ϕ v Model name (Default: ϕ v = 1) 2 v *, v ϕ = f( y, ϕ ) 3 v ϕ f( γ ) *, v ϕ Route ID ϕ v Model name = γ Model name ϕ v Model name Physcal Property Methods and Models 4-11 Verson 10

318 Property Calculaton Methods and Routes Lqud Fugacty Coeffcent Methods Property Symbol and Name Property Type Method Code Method Route Structure Informaton Requred *, l ϕ PHIL Major 1 Specfed model *, l ϕ 2 v l ϕ ( T p ) Model name l l, p θ p *, l Model name *, v p ϕ Model name (Default: ϕ *,v = 1 ) *, *, *, *, θ *,l Route ID *, l (Default: θ = 1) 3 Specfed model for supercrtcal components For subcrtcal components: *, v ϕ ( *, l T p ) *, l p p 1, exp V *, p RT p l *, l dp *, l ϕ Model name p *, l Model name *, l ϕ Model name *, l V Model Name *, l θ PHILPC Subord. 1 1 exp RT *, l p p V *, l dp p *, l Model name *, l V Model Name Integraton opton code (Default:1 pont) ϕ l PHILMX 2 Specfed model *, l θ Major 1 Specfed model ϕ l Model name Model name 2 l γϕ θ *, E γ Model name 3 Unsymmetrc Conventon (Default: γ = 1 ) *, l ϕ Route ID θ E Route ID (Default: θ E = 1 ) For subcrtcal components (A or B): *, l ϕ A Route ID contnued 4-12 Physcal Property Methods and Models Verson 10

319 Chapter 4 Lqud Fugacty Coeffcent Methods (contnued) Property Symbol and Name Property Type Method Code Method Route Structure Informaton Requred ϕ l A = δ γ ϕ *, l γ A A A A Model name (Default: γ A = 1 ) For supercrtcal components (I or j) ϕ l Where: = γ H pγ w H H A A j lnδa = x j ln ln x A j γ ja γ j H ja Route ID H ln = γ 4 l γϕ θ B H wb ln γ ( γ ) ln γ lm ln B B w B Model name = w B Model opton code (see jx j 0 Chapter 3) w B = 1 Method Opton code B Where: γ 0: Do not calculate H 1: Calculate H (Default = 0 ) *, E γ Model name t ( ) (Default: γ = 1 ) *, l ϕ Route ID θ E Route ID (Default: θ E = 1 ) = f x (Default: θ E = 1 ) 5 Unsymmetrc Conventon For subcrtcal components (A or B): x t Route ID *, l ϕ Route ID contnued Physcal Property Methods and Models 4-13 Verson 10

320 Property Calculaton Methods and Routes Lqud Fugacty Coeffcent Methods (contnued) Property Symbol and Name Property Type Method Code Method Route Structure Informaton Requred ϕ l A = δ γ ϕ *, l γ A A A A Model name (Default: γ A = 1 ) Where: γ A t ( ) = f x x t Route ID For supercrtcal components ( or j) ϕ l Where: = γ H pγ W H H A A j lnδa = x j ln ln X A j γ ja γ j H ja Route ID H H B ln = wb ln γ B γ B ( γ ) ln γ lm ln w B Model name = w B Model opton code (see jx j 0 Chapter 3) w B = 1 Method Opton code B 0: Do not calculate H 1: Calculate H (Default = 0 ) x t XTRUE 6 l ϕ = f( γ ) γ Model name Subord. 1 t x = f( T, x,, ) l ϕ Model name γ Chemstry γ Model name θ E GAMPC Subord. 1 1 exp RT V V dp l *, l ( ) p p ref V l Model name *, l V Model name Integraton opton code contnued 4-14 Physcal Property Methods and Models Verson 10

321 Chapter 4 Lqud Fugacty Coeffcent Methods (contnued) Property Symbol and Name Property Type Method Code Method Route Structure Informaton Requred (Default: 1 pont) 2 Specfed model θ E Model name *, E θ GAMPC1 Subord. 1 exp 1 RT p p Vdp l ref V l Model name Integraton opton code (Default: 1 pont) 2 Specfed model *, E θ Model name H A HNRY Subord. 1 Specfed model H A Model name 2 ref HA( p T), θ H A Model name A θ A Route ID (Default: θ A = 1) p ref defned by the p ref opton code of HNRYPC θ A HNRYPC Subord. 1 exp 1 RT p p Vdp l ref *, l p A Model name (f needed for p ref ) p ref Opton code 1: p ref = 0 2: p ref = 1 atm 3: p ref *, l = p A (T) (Default = 2) V Model name Integraton code (Default: 1 pont) 2 Specfed model θ A Model name Physcal Property Methods and Models 4-15 Verson 10

322 Property Calculaton Methods and Routes Sold Fugacty Coeffcent Methods Property Symbol and Name Property Type Method Code Method Route Structure Informaton Requred *, s ϕ PHIS Major 1 Specfed Model *, s ϕ 2 ϕ s ( T, p ) p *, v *, *, s *, θ p s *, s p Model name Model name *, v ϕ Model name *, v (Default: ϕ = 1) *, s θ Route ID *, s (Default: θ = 1) 3 s ϕ ϕ *, *,l *, s ϕ *, l ϕ Model name Route ID *, s θ PHISPC Subord. 1 p 1 *, exp RT V s dp s *, p *, s p Model name *, s V Model name Integraton opton code (Default: 1 pont) 2 Specfed model *, s θ Model name ϕ s PHISMX Major 1 Specfed model ϕ s Model name 2 s s s ϕ = f( x, ϕ ) *, *, s ϕ Route ID ϕ s Model name 3 γϕ s *,s γ s Model name *, s ϕ Route ID 4-16 Physcal Property Methods and Models Verson 10

323 Chapter 4 Vapor Enthalpy Methods Property Symbol and Name Property Type Method Code Method Route Structure Informaton Requred H *,ν HV Major 1 Specfed model H *,ν Model name 2 *, g *, *,g H + ( H ν H ) ( *, *,g H H ) ν Route ID *, (Default: H ν *,g H = 0) *, H ν *,g H DHV 3 *, l * *, l H + H H vap Route ID vap H * Model name Subord. 1 Specfed model *, *,g ( H H ) ν Model name 2 v 2 ln ϕ *, *, v ϕ RT T Model name ν H m HVMX H ν m DHVMX H g m Major 1 Specfed model H m ν Model name 2 yh *,ν H *,ν Route ID 3 g g Hm + ( H ν m Hm ) ( g H H ) m m ν Route ID (Default: H ν g m Hm =0 ) Subord. 1 Specfed model g ( Hm Hm ) ν Model name 2 v 2 lnϕ RT y T ϕ v Model name Physcal Property Methods and Models 4-17 Verson 10

324 Property Calculaton Methods and Routes Lqud Enthalpy Methods Property Symbol and Name Property Type Method Code Method Route Structure Informaton Requred *, l H HL H DHL H *, l *,g Major 1 Specfed model *, l H Subor d. Model name 2 *, g *, l *,g *, l *,g H + ( H H ) ( H H ) ID Route 1 Specfed model *, l *,g ( H H ) name Model 2 l 2 ln ϕ *, *, l ϕ RT T Model name H H *, l ( T, p) l ( T, p ) *, l *, DHLPC Subor d. *, *, *, * ( H T p H T ) H ( T) vap ( ) 3 v l g ( ) ( ), *, l *, l *, l + H ( T, p) H ( T, p ) ( ) *, l *, l *, g H ( T, pp ) H ( T) 1 *, l *, g H ( T, p) H ( T) ( ) l p Model name *, v *,g ( H H ) Route ID *, v *,g (Default: H H = 0 ) l vap H Model name *, l *, l *,l ( H ( T, p) H ( T p )), Route ID (Default: l l H T, p H T, p = 0) ( ) ( ) *, *, *,l *, l p Model name *, l *,g ( H H ) ID Route 2 p p V *, l *, l V T T p dp *, l p Model name 3 Specfed model *, l V Model name Integraton opton code (Default: 1 pont ) *, l *, l *,l ( H ( T, p) H ( T p )), Model name contnued 4-18 Physcal Property Methods and Models Verson 10

325 Chapter 4 Lqud Enthalpy Methods (contnued) Property Symbol and Name Property Type Method Code Method Route Structure Informaton Requred l H m HLMX H l m DHLMX H g m Major 1 Specfed model H m l Subor d. 2 l xh + H *, El, m *, l H Model name Route ID El, H Route ID El, (Default: H =0) 3 g H ( H l g l g m + m Hm ) ( Hm Hm ) 4 Electrolyte model ( x t ) H m l Route ID Model name x t Route ID 1 Specfed model l g ( Hm Hm ) name Model 2 x ( H *, l H *, g ) H EI, *, l *,g + m ( H H ) Route ID El, H m Route ID El, (Default: H m = 0 ) contnued Physcal Property Methods and Models 4-19 Verson 10

326 Property Calculaton Methods and Routes Lqud Enthalpy Methods (contnued) Property Symbol and Name Property Type Method Code Method 3 Unsymmetrc conventon For subcrtcal components A or B: I g ( A A ) x H H + H A *, *, EI, m EI, ln Hm = RT xb δ γ 2 γt For supercrtcal component or j: δln ϕ 2 RT x j j δt where: ϕ Ι ι = γ ι H pγ H ln = Βω γ ln = lm ln x 0 w B = 1 B B B ( ) γ ι I j H ln γ B ιβ B Route Structure Informaton Requred *, ( H I *,g A HA ) ID where: γ B Model name H B Route ID Route w B Model name w B Model opton code (see Chapter 3) El, H m HLXS Subor d. 1 Specfed model El, H m 2 El, 2 ln γ Hm = RT x T Model name γ Model name 4-20 Physcal Property Methods and Models Verson 10

327 Chapter 4 Sold Enthalpy Methods Property Symbol and Name Property Type Method Code Method Route Structure Informaton Requred *, s H HL H H *, s *,g Major 1 Specfed model *, s H Model name 2 *, g *, s *,g *, s *,g H + ( H H ) ( H H ) Route ID Subord. 1 Specfed model *, s *,g ( H H ) Model name DHS s (, ) (, ) *, s H T p HSubord. *, *,s T p 1 DHSPC *, ( H *, T p *, H T ) * subh ( T) ( ) 2 v s g (, ) ( ) *, s *, s *, s + H ( T, p) H ( T, p ) p p V *, s *, s V T dp T *, s p Model name *, v *,g ( H H ) Route ID *, v *,g (Default: H H = 0 ) sub * H () T Model name s (, ) (, ) *, s *, *,s ( H T p H T p ) Route ID (Default: *, s H T, p *, s *,s H T, p = 0 ) *, s p ( ) ( ) Model name *, s V Model name Integraton opton code (Default: 1 pont) H m s HSMX Major 1 Specfed model Model name 2 s s xh + H *, Es, m H m s Route ID *, s H Es, H m Route ID Es, (Default: H m 3 g H ( H s g s g m + m Hm ) ( Hm Hm ) = 0 ) Route ID contnued Physcal Property Methods and Models 4-21 Verson 10

328 Property Calculaton Methods and Routes Sold Enthalpy Methods (contnued) Property Symbol and Name H s m H DHSMX Es, H m HSXS g m Property Type Method Code Method Subord. 1 Specfed model s g ( Hm Hm ) Route Structure Informaton Requred Model name 2 x s *, s *, g Es, *, s *,g ( H H ) + Hm ( H H ) Subord. 1 Specfed model Es, H m Route ID Es, H m Route ID Es, (Default: H m = 0 ) Model name 2 Es, s ln Hm = RT x γ 2 T s γ Model name Vapor Gbbs Energy Methods Property Symbol and Name Property Type Method Code Method Route Structure Informaton Requred *, v µ GV v µ µ *, *,g DGV Major 1 Specfed model *, v µ Model name 2 *, g *, v *,g *, v *,g µ + ( µ µ ) ( µ µ ) Route ID *, *,g = 0 ) v (Default: µ µ Subord. 1 Specfed model *, v *,g ( µ µ ) Model name 2 *, v p RT ln ϕ + RT ln p ref *, v ϕ Route ID G m v GVMX Major 1 Specfed model G m v Model name contnued 4-22 Physcal Property Methods and Models Verson 10

329 Chapter 4 Vapor Gbbs Energy Methods (contnued) Property Symbol and Name G G v m DGVMX g m Property Type Method Code Method 2 v yµ *, + RT y ln y Route Structure Informaton Requred *, v µ Route ID 3 g G ( G v g v g m + m Gm ) ( Gm Gm ) Route ID v g (Default: Gm Gm = 0 ) Subord. 1 Specfed model v g ( Gm Gm ) Model name 2 v p RT yln ϕ + RT ln p ref *, v ϕ Route ID *, v (Default: ϕ = 1 ) Lqud Gbbs Energy Methods Property SymbolProperty and Name Type Method Code Method Route Structure Informaton Requred *, l µ GL l µ µ *, *,g Major 1 Specfed model *, l µ Model name 2 *, g *, l *,g *, l *,g µ + ( µ µ ) ( µ µ ) Route ID Subord. 1 Specfed model *, l *,g ( µ µ ) Model name DGL 2 3 *, l p RT ln ϕ + RT ln p ref *, l *, l *, g ( µ ( T, p ) µ ( T) ) *, l *, l *, l µ ( T, p) µ ( T, p ) + ( ) *, l ϕ *, l p Route ID Model name Route ID *, *,g = 0) *, l *,g ( µ µ ) l (Default: µ µ ( µ ( ) µ ( )) *, l l l T, p *, T, p *, oute ID (Default: l l ( T, p) ( T, p ) l µ µ 0 ) = *, *, *, R contnued Physcal Property Methods and Models 4-23 Verson 10

330 Property Calculaton Methods and Routes Lqud Gbbs Energy Methods (contnued) Property SymbolProperty and Name Type µ µ *, l ( T, p) l ( T, p ) *, l *, DGLPC Method Code Method ( ) *, l *, l *, g µ ( T, p ) µ ( T) Subord. 1 *, l *, g µ ( T, p) µ ( T) ( ) Route Structure Informaton Requred *, l p Model name *, l *,g ( µ µ ) Route ID 2 p *, p l V *, l dp *, l p Model name *, l V Model Name Integraton opton code (Default: 1 pont) l G m GLMX G l m DGLMX G g m Major 1 Specfed model G m l 2 l x + RT x ln x + G El µ *,, m 3 g l g Gm + ( Gm Gm ) 4 Electrolyte model ( x t ) *, l µ El, G m Model name Route ID Route ID El, (Default: G m Model name x t Route ID Subord. 1 Specfed model l g ( Gm Gm ) = 0 ) Model name 2 l g El x( µ *, µ *, ) G, *, l *,g + m ( µ µ ) Route ID El, G m Route ID El, (Default: G m = 0 ) El, G m GLXS Subord. 1 Specfed model El, G m Model name 2 RT x lnγ γ Model name 4-24 Physcal Property Methods and Models Verson 10

331 Chapter 4 Sold Gbbs Energy Methods Property Symbol and Name Property Type Method Code Method Route Structure Informaton Requred *, s µ GL s µ µ *, *,g DGL Major 1 Specfed model *, s µ Model name 2 *, g *, s *,g *, s *,g µ + ( µ µ ) ( µ µ ) Route ID Subord. 1 Specfed model *, s *,g ( µ µ ) Model name µ µ *, s ( T, p) s ( T, p ) *, s *, DGLPC 2 3 Subord. 1 *, s p RT ln ϕ + RT ln p ref *, s *, s *, g ( µ ( T, p ) µ ( T) ) *, s *, s *, s µ ( T, p) µ ( T, p ) + ( ) p *, p l V *, l dp *, s ϕ *, s p Route ID Model name ( µ *, s *, s ( ) µ *, g T, p ( )) T Route ID (Default: s g ( T p ) () T *, l *, *, µ, µ = 0) ( µ ( ) µ ( )) *, s s s T, p *, T, p *, R oute ID (Default: µ *, s s s ( T, p) µ *, ( T, p *, ) = 0 ) *, l p Model name *, l V Model Name Integraton opton code (Default: 1 pont) G m s GLMX Major 1 Specfed model G m s 2 s s Es s xµ *, + G, m + RT x ln x s *, s µ Es, G m Model name Route ID Route ID 3 g s g Gm + ( Gm Gm ) Es, (Default: G m = 0 ) contnued Physcal Property Methods and Models 4-25 Verson 10

332 Property Calculaton Methods and Routes Sold Gbbs Energy Methods Property Symbol and Name G s m DGLMX G g m Property Type Method Code Method Subord. 1 Specfed model s g ( Gm Gm ) Route Structure Informaton Requred Model name 2 x s s g Es ( µ *, µ *, ) G, *, s *,g + m ( µ µ ) Route ID Es, G m Route ID Es, (Default: G m = 0 ) Es, G m GLXS Subord. 1 Specfed model Es, G m Model name 2 s RT x s lnγ γ Model name Vapor Entropy Methods Property Symbol and Name *, v S SV Property Type Major 1 Method Code Method 1 T H *, v *,v ( µ ) Route Structure Informaton Requred *, v H Route ID 2 *, g *, v *,g *, v *,g S + ( S S ) ( S S ) Route ID *, v *,g (Default: S S = 0 ) S *, v *,g S Subord. 1 DSV S m v Major 1 3 Specfed model *, v S 2 H T H T T *, v *, g *, v *,g Model name *, v *,g µ µ ( H H ) Route ID *, v *,g (Default: H H = 0 ) *, v *,g ( µ µ ) Route ID *, v *,g (Default: µ µ = 0) ( µ *, v µ *, g ) ( *, v *,g µ µ ) ( v G v m m) 1 T H H m v Route ID G m v Route ID Model name contnued 4-26 Physcal Property Methods and Models Verson 10

333 Chapter 4 Vapor Entropy Methods (contnued) Property Symbol and Name Property Type Method Code Method 2 g S ( S v g v g m + m Sm ) ( Sm Sm ) Route Structure Informaton Requred Route ID v g (Default: Sm Sm = 0 ) 3 Specfed model S m v Model name S v m S DSVMX g m Subord. 1 Specfed model v g ( Sm Sm ) 2 v Hm H T 3 T G g m G v m G T g m Model name v g ( Hm Hm ) Route ID v g (Default: Hm Hm = 0 ) v g G G Route ID ( m m ) v g (Default Gm Gm = 0) ( v G v g g m m ) ( Gm Gm ) Model name Lqud Entropy Methods Property Symbol and Name *, l S SL Property Type Major 1 Method Code Method *, l *,l ( µ ) 1 T H Route Structure Informaton Requred *, l H *, l µ Route ID Route ID 2 *, g *, v *,g *, l *,g S + ( S S ) ( S S ) Route ID S *, l *,g S Subord. 1 DSL 3 Specfed model *, l S H H T T *, l *, g *, l *,g Model name *, l *,g µ µ ( H H ) Route ID 2 T ( µ *, l µ *, g ) ( *, l *,g µ µ ) *, l *,g ( µ µ ) Route ID Model name contnued Physcal Property Methods and Models 4-27 Verson 10

334 Property Calculaton Methods and Routes Lqud Entropy Methods (contnued) Property Symbol and Name Property Type Method Code Method Route Structure Informaton Requred 3 Specfed Model *, l *,g ( S S ) Model name S m l SLMX Major 1 1 T H ( l G l m m) l H m Route ID l G m Route ID 2 g S ( S l g l g m + m Sm ) ( Sm Sm ) Route ID 3 Specfed model l S m Model name 4 l l l t Sm f( Hm Gm x ) =,, H m l model l G m model S l m S DSLMX g m x t Route ID Subord. 1 Specfed model l g ( Sm Sm ) 2 l Hm H T 3 T G g m G l m G T g m Model name l g ( Hm Hm ) l g ( Gm Gm ) Route ID Route ID ( l G l g g m m ) ( Gm Gm ) Model name Sold Entropy Methods Property Symbol and Name Property Type Method Code Method Route Structure Informaton Requred *, s S SS Major 1 Specfed model *, s S 2 1 T H *, s *,s ( µ ) *, s H *, s µ Model name Route ID Route ID contnued 4-28 Physcal Property Methods and Models Verson 10

335 Chapter 4 Sold Entropy Methods (contnued) Property Symbol and Name S Property Type *, s *,g S Subord. 1 DSS Method Code Method H H T *, s *, g *, s *,g Route Structure Informaton Requred *, s *,g µ µ ( H H ) T *, s *,g ( µ µ ) Route ID Route ID 2 Specfed model *, s *,g ( S S ) Model name s S m SSMX S s m S DSSMX g m Major 1 1 T H ( s G s m m) s H m Route ID s G m Route ID 2 g S ( S s g s g m + m Sm ) ( Sm Sm ) Route ID Subord. 1 Specfed model s g ( Sm Sm ) 2 s Hm H T 3 T G g m G s m G T g m Model name s g ( Hm Hm ) s g ( Gm Gm ) Route ID Route ID ( s G s g g m m ) ( Gm Gm ) Model name Molar Volume Methods Property Symbol and Name Property Type Method Code Method Route Structure Informaton Requred *, v V VV Major 1 Specfed model *, v V Model name V m v VVMX Major 1 Specfed model V m v Model name 2 v v Vm = f( y, V ) *, *, v V Route ID V m v Model name contnued Physcal Property Methods and Models 4-29 Verson 10

336 Property Calculaton Methods and Routes Molar Volume Methods (contnued) Property Symbol and Name Property Type Method Code Method 3 v V f( ) m = γ γ Model name Route Structure Informaton Requred V m v Model name (eos only) *, l V VL Major 1 Specfed model *, l V Model name l V m VLMX *, s V VS s V m VSMX Major 1 Specfed model V m l 2 l l Vm = f( x, V ) 3 Model name *, *, l V Route ID V m l Electrolyte model ( x t *, l ) V 4 l V f( ) m Model name Model name x t Route ID = γ γ Model name Major 1 Specfed model *, s V V m l Model name (eos only) Model name Major 1 Specfed model V m s Model name 2 s s s Vm = f( x, V ) *, *, s V Route ID s V m Model name 4-30 Physcal Property Methods and Models Verson 10

337 Chapter 4 Vscosty Methods Property Symbol and Name Property Type Method Code Method Route Structure Informaton Requred *, v n MUV Major 1 Specfed model *, v η Model name ( ) 2 *, v *, v *, v η = η ( p=0 ) η ( p ) 3 *, v *, v η f( V ) *, v = V *, v *, v 4 η = η ( p= 0) *, v *, v + η ( p) η ( p= 0) ( ) *, v η Route ID = 0 Route ID Model name *, v ( η ( p )) = 0 Route ID *, v *, v ( η () p η ( p )) *, η v ( p= 0) Subord. 1 Specfed model *, v η ( p ) MUVLP η η *, v *, v () p ( p= 0) ID ( ) = 0 Route = 0 Model name ( o ) Subord. 1 Specfed model *, v *, v η ( p) η ( p ) odel name = 0 M MUVPC n v MUVMX *, *, *, v ( p o p= ) = f( V ) 2 v v η ( ) η ( ) *, v 0 V Route ID Model name Major 1 Specfed model η v Model name 2 v v η = f( y, η ) *, *, v η Route ID η v Model name ( ) 3 v v η = η ( p=0 ) ( ) 4 η v v f( Vm) η v p=0 Route ID = V m v Route ID 5 v v η = η( p= 0) + v v η () p η ( p= 0) ( ) η v Model name ( η v ( p=0 )) Route ID v v η () p η ( p=0) ( ) Route ID contnued Physcal Property Methods and Models 4-31 Verson 10

338 Property Calculaton Methods and Routes Vscosty Methods (contnued) Property Symbol and Name ( η v ( p=0) ) MUVMXLP η η v v ( p) ( p= 0) Property Type Method Code Method Route Structure Informaton Requred Subord. 1 Specfed model ( η v ( p=0 )) Model name v ( p= 0 ) = f( y, η ( p= 0) ) 2 v η ( ) ( ) ( ) *, *, v η ( p ) ( ) = 0 Route ID η v p=0 Model name ( ) Subord. 1 Specfed model v v η () p η ( p ) name =0 Model MUVMXP C *, l η MUL η l MULMX ( p p= ) = f( V v m) 2 v v η () η ( ) 0 V m v Route ID v v ( η () p η ( p )) name Major 1 Specfed model *, l η 2 *, l *, l η fv ( ) *, l = V *, l η =0 Model Model name Route ID Model Name Major 1 Specfed model η l Model name 2 l l η = f( x, η ) 3 η l l fv ( m) *, *, l η Route ID = V m l η l Model name Route ID η l Model name 4-32 Physcal Property Methods and Models Verson 10

339 Chapter 4 Thermal Conductvty Methods Property Symbol and Name Property Type Method Code Method Route Structure Informaton Requred *, v λ MUV Major 1 Specfed model *, v λ ( ) Model name 2 *, v *, λ λ v *, v = ( p=0 ) λ ( p ) *, v *, v 3 λ = λ ( p= 0) *, λ v *, + ( p) λ v ( p= 0) ( ) ( ) 4 *, v *, v *, v λ fv, η ( p ) *, v = =0 V ( ) *, v ( λ ( p )) = 0 Route ID = 0 Route ID *, ( λ v *, ( p) λ v ( p )) *, v η = 0 Route ID Route ID ( p ) = 0 Model name *, v λ *, v λ Model Name ( p= 0) Subord. 1 Specfed model *, v λ ( p ) = 0 Model name KVLP λ λ *, v *, v KVPC λ v KVMX () p ( p= 0) ( ) 2 *, v *, v *, v λ ( p= 0) = f η ( p= 0 ) η ( p ) *, v λ = 0 Route ID Model name ( ) Subord. 1 Specfed model *, λ v *, ( p) λ v ( p=0) *, *, *, v ( p p= ) = f( V ) 2 λ v ( ) λ v ( ) Model name *, v 0 V Route ID *, ( λ v *, ( p) λ v ( p=0) ) Model name Major 1 Specfed model λ v Model name 2 v v λ = f( y, λ ) *, *, v λ Route ID λ v Model name ( ) 3 v v λ = λ ( p = 0 ) ( ) λ v p = 0 Route ID contnued Physcal Property Methods and Models 4-33 Verson 10

340 Property Calculaton Methods and Routes Thermal Conductvty Methods (contnued) Property Symbol and Name λ v ( p=0) KVMXLP λ v v () p λ ( p= 0) KVMXPC Property Type Method Code Method 4 v λ v = λ ( p= 0) + v v λ () p λ ( p= 0) ( ) ( m ) 5 v λ v v = f V η ( p= ), 0 V m v Route ID Route Structure Informaton Requred ( λ v ( p = 0 )) Route ID v v λ () p λ ( p ) ( ) ID ( ( )) =0 Route η v p=0 Route ID λ v Model name ( ) Subord. 1 Specfed model ( ) v 2 λ ( p= 0) = *, λ v *, v f y, ( p= 0), η ( p= 0) ( ) λ v p = 0 Model name *, v λ Route ID *, η v ( p ) ( ) ( ) = 0 Route ID λ v p = 0 Model name ( ) Subord. 1 Specfed model v v λ () p λ ( p=0) ( p p= ) = f( V v m) 2 v v λ () λ ( 0) Model name Route ID v v v v λ p λ p= 0 λ p λ p= 0 ( ( ) ( )) () ( ) Model name ( ) *, l λ KL λ l KLMX Major 1 Specfed model *, l λ ( ) 2 *, l *, l *, v λ fv, η ( p ) *, l = =0 V Model name Route ID *, v ( η ( p )) *, l λ = 0 Route ID Model name Major 1 Specfed model λ l Model name 2 l l λ = f( x, λ ) *, *, l λ Route ID λ l Model name contnued 4-34 Physcal Property Methods and Models Verson 10

341 Chapter 4 Thermal Conductvty Methods (contnued) Property Symbol and Name Property Type Method Code Method ( m ) 3 l λ l v = fv η ( p= ), 0 V m l Route Structure Informaton Requred Route ID ( ( )) η v p= 0 Route ID λ l Model name *, s λ KS λ s KSMX Major 1 Specfed model *, s λ Model name Major 1 Specfed model λ s Model name 2 s s s λ = f( x, λ ) *, *, s λ Route ID λ s Model name Dffuson Coeffcent Methods Property Symbol and Name Property Type Method Code Method Route Structure Informaton Requred v D j DV v D DVMX l D j DL l D DLMX Major 1 Specfed model v D j Model name Major 1 Specfed model v D Model name 2 v v D f( y Dj) =, D j v Route ID y Model name Major 1 Specfed model Model name Major 1 Specfed model Model name 2 l l D f( x Dj) =, D j l Route ID l D Model name Physcal Property Methods and Models 4-35 Verson 10

342 Property Calculaton Methods and Routes Surface Tenson Methods Property Symbol and Name Property Type Method Code Method Route Structure Informaton Requred *, l σ SIGL σ l SIGLMX Major 1 Specfed model Model name Major 1 Specfed model Model name 2 l l σ = f( x, σ ) *, *, l σ Route ID σ l Model name Routes And Models Ths secton explans the structure of physcal property calculatons by showng the relatonshp between models and routes, and between routes on dfferent levels. It also explans how to trace a calculaton route. Concept of Routes Each property value needed for a method evaluaton s obtaned from ether another method evaluaton or a model evaluaton. Propertes obtaned by method evaluaton are major or subordnate propertes. Propertes obtaned by a model evaluaton are ntermedate propertes. The calculaton of the top-level property s dctated by: Property name Method Sub-level route for each major or subordnate property Model name for each ntermedate property (sometmes wth a model opton code) Ths nformaton s called a route. There s not necessarly a major or subordnate property n each method, but f one occurs n the method of the property of nterest, then the route depends on sub-level routes. There can be any number of levels n a route. Each level needs the nformaton lsted prevously to be completely specfed. Ths way a tree of nformaton s formed. Snce a model does not depend on lower-level nformaton, you can thnk of t as an end-pont of a tree branch. Model opton codes are dscussed n Models, ths chapter. (Example 1 dscusses a route that does not depend on other routes.) 4-36 Physcal Property Methods and Models Verson 10

343 Chapter 4 Each bult-n route n ASPEN PLUS has a unque route ID, whch s composed of the property name (see the tables labeled Major Propertes n ASPEN PLUS, Subordnate Propertes n ASPEN PLUS, and Intermedate Propertes n ASPEN PLUS, all earler n ths chapter) and a number, for example HLMX10. Therefore the route ID can be used to represent the route nformaton. (See example 2 for a route whch depends on a secondary route.) Route IDs assocated wth the route nformaton represent a unque combnaton of sub-level routes and models. Therefore, a top-level route ID specfes the full calculaton tree. Because of the unqueness of route IDs, you can use them for documentng your smulaton. A property method can calculate a fxed lst of propertes (see Physcal Propertes n ASPEN PLUS, ths chapter). The calculaton procedure of each property consttutes a route and has a route ID. Therefore, a property method conssts of a collecton of the route IDs of the propertes t can calculate. The Property Methods Routes sheet shows the routes used n a property method. If you want to see all of the bult-n routes used for calculatng the property specfed n the Property feld, use the lst box n a Route ID feld (see the fgure labeled Propertes Property Methods Routes Sheet. Propertes Property Methods Routes Sheet Physcal Property Methods and Models 4-37 Verson 10

344 Property Calculaton Methods and Routes Example 1 Route nformaton for PHILMX, method 1 The frst method from the table labeled Lqud Fugacty Coeffcent Methods on page 4-12 for the calculaton of the fugacty coeffcent of component n a lqud mxture s specfed model. The model can be an equaton-of-state model, that calculates the fugacty coeffcent as a functon of state varables and correlaton parameters: ϕ l ( ) = f p, T, x,correlaton parameters There are many models that can be used to calculate ϕ l, such as the Redlch-Kwong-Soave model, the Peng-Robnson model, or the Hayden-O Connell model. It s suffcent to select a model name n order to completely specfy a route accordng to ths method. Example 2 Route nformaton for HLMX, method 3 The thrd method for calculatng the lqud mxture enthalpy H m l (see the table labeled Lqud Enthalpy Methods on page 4-18): l g ( m ) m H l g = H + H H m m In ths method, H m l depends on the deal gas enthalpy and the enthalpy departure H l m H g m, a subordnate property. The table labeled Lqud Enthalpy Methods on page 4-18 ndcates n the rghtmost column that the requred nformaton s the route ID for the subordnate property. The top-level route now refers to a sub-level route ID. For all methods that use both an deal gas contrbuton and a departure functon, ASPEN PLUS automatcally flls n the deal gas calculaton. You need to specfy only the departure functon. To specfy the sub-level route for the enthalpy departure, you must choose a method. For example, method 1: specfed model (see the table labeled Lqud Enthalpy Methods on page 4-18). For ths method, the requred nformaton s the model name, such as the Redlch-Kwong-Soave equaton-of-state model Physcal Property Methods and Models Verson 10

345 Chapter 4 Models A model conssts of one or more equatons to evaluate a property, and has state varables, unversal parameters, and correlaton parameters as nput varables. Propertes obtaned by model evaluaton are called ntermedate propertes. They never depend on major or subordnate propertes, whch need a method evaluaton. In contrast to methods whch are based on unversal scentfc prncples only, models are much more arbtrary n nature, and have constants whch need to be determned by data fttng. An example of a model s the Extended Antone vapor pressure equaton (see Chapter 3). Equatons of state have bult-n correlaton parameters and are also models. Models are sometmes used n multple routes of a property method. For example, an equaton-of-state model can be used to calculate all vapor and lqud departure functons of an equaton-of-state-based property method. The Rackett model can be used to calculate the pure component and mxture lqud molar *, volumes, (V l and V m l ), and t can also be used n the calculaton of the Poyntng correcton factor, as part of the calculaton of the pure component lqud fugacty coeffcent. The Propertes Property Methods Models sheet dsplays the models that are globally used n the routes of the current property method (see the fgure labeled Propertes Property Methods Models Sheet). In specfc routes, exceptons to the global usage may occur. Modfyng and Creatng Routes, ths chapter, dscusses how to dentfy these exceptons. For a gven model, clck on the Affected Propertes button to dsplay a lst of propertes whch are affected by the model calculatons. Use the lst box on the Model Name feld to dsplay a lst of all avalable models for a specfc property. You can also use the tables labeled Thermodynamc Physcal Property Models on page 4-41, Transport Property Models on page 4-43, and Nonconventonal Sold Property Models on page If you need to use a propretary model or a new model from the lterature, you can nterface these to ASPEN PLUS (See ASPEN PLUS User Models.) Physcal Property Methods and Models 4-39 Verson 10

346 Property Calculaton Methods and Routes Propertes Property Methods Models Sheet Some models have model opton codes to specfy dfferent possble calculaton optons. For example, the model WHNRY has three optons to calculate the weghtng factor from the crtcal molar volume. The calculaton opton s dentfed by the model opton code. On the Property Methods Models sheet, frst select the model, then clck the Opton Codes button to dsplay a lst of opton code values for the model. Use Help for descrptons of the opton codes Physcal Property Methods and Models Verson 10