PRO II Reference Manual - Vol I - Component and Thermophysical Properties

PRO/II 8.3

Component and Thermophysical Properties Reference Manual

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PRO/II Reference Manual, Volume I, Component and Thermo- physical Properties

The software described in this guide is furnished under a written agreement and may be used only in accordance with the terms and conditions of the license agreement under which you obtained it. The technical documentation is being delivered to you AS IS and Invensys Systems, Inc. makes no warranty as to its accuracy or use. Any use of the technical documentation or the information contained therein is at the risk of the user. Documentation may include technical or other inaccuracies or typographical errors. Invensys Systems, Inc. reserves the right to make changes without prior notice.

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Trademarks PRO/II and Invensys SIMSCI-ESSCOR are trademarks of Invensys plc, its subsidiaries and affiliates.AMSIM is a trademark of DBR Schlumberger Canada Limited.RATEFRAC®, BATCHFRAC®, and KOCH-GLITSCH are registered trademarks of Koch-Glitsch, LP.Visual Fortran is a trademark of Intel Corporation.Windows Vista, Windows 98, Windows ME, Windows NT, Windows 2000, Windows XP, Windows 2003, and MS-DOS are trademarks of Microsoft Corporation.Adobe, Acrobat, Exchange, and Reader are trademarks of Adobe Systems, Inc.All other trademarks noted herein are owned by their respective companies.U.S. GOVERNMENT RESTRICTED RIGHTS LEGENDThe Software and accompanying written materials are provided with restricted rights. Use, duplication, or disclosure by the Government is subject to restrictions as set forth in subparagraph (c) (1) (ii) of the Rights in Technical Data And Computer Software clause at DFARS 252.227-7013 or in subparagraphs (c) (1) and (2) of the Commercial Computer Software-Restricted Rights clause at 48 C.F.R. 52.227-19, as applicable. The Contractor/Manufacturer is: Invensys Systems, Inc. (Invensys SIMSCI-ESSCOR) 26561 Rancho Parkway South, Suite 100, Lake Forest, CA 92630, USA.

Printed in the United States of America, November 2008.

Table of Contents

Chapter 1 IntroductionGeneral Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1-1What is in This Manual? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1-1Who Should Use This Manual? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1-1Finding What you Need . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1-2

Chapter 2 Component DataDefined Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-1

Component Libraries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-1Fixed Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-3Temperature-dependent Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-3Properties From Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-4

Petroleum Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-5General Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-5Property Generation– SIMSCI Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-6Property Generation– CAVETT Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-10Property Generation– Lee-Kesler Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-14Property Generation – Heavy Method10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-15

Assay Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-17General Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-17Inter-conversion of Distillation Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-21Cutting TBP Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-26Generating Pseudocomponent Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-31Vapor Pressure Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-32Flash Point Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-36

Chapter 3 Thermodynamic MethodsBasic Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-1

General Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-1Phase Equilibria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-2Enthalpy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-5Entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-8

Application Guidelines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-10General Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-10

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Refinery and Gas Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-10Natural Gas Processing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-13Chemical Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-19

Generalized Correlation Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-22General Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-22Ideal (IDEAL) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-23Chao-Seader (CS). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-24Grayson-Streed (GS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-26Erbar Modification to Chao-Seader (CSE) and Grayson-Streed (GSE). . . . . . . . . 3-26Improved Grayson-Streed (IGS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-27Curl-Pitzer (CP) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-27Johnson-Grayson (JG) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-29Lee-Kesler (LK) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-29API . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-30Rackett . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-31COSTALD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-32

Equations of State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-34General Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-34General Cubic Equation of State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-34Alpha Formulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-36Mixing Rules (for Equations of State) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-40Soave-Redlich Kwong (SRK) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-41Peng-Robinson (PR). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-41Soave-Redlich-Kwong Kabadi-Danner (SRKKD). . . . . . . . . . . . . . . . . . . . . . . . . 3-41Soave-Redlich-Kwong Panagiotopoulos-Reid (SRKP) and Peng-Robinson Panagiotopoulos-Reid (PRP) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-42Soave-Redlich-Kwong Modified (SRKM) and Peng-Robinson Modified (PRM) 3-43Soave-Redlich-Kwong SimSci (SRKS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-44Soave-Redlich-Kwong Huron-Vidal (SRKH) and Peng-Robinson Huron-Vidal (PRH) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-45HEXAMER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-47UNIWAALS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-50Benedict-Webb-Rubin-Starling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-52Lee-Kesler-Plöcker (LKP) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-53Twu-Bluck-Coon(TBC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-55Fill Options (for Binary Interaction Coefficients) . . . . . . . . . . . . . . . . . . . . . . . . . 3-57

Free Water Decant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-60General Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-60Calculation Methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-60

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Liquid Activity Coefficient Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-62General Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-62Margules Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-66van Laar Equation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-67Regular Solution Theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-68Flory-Huggins Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-69Wilson Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-70NRTL Equation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-72UNIQUAC Equation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-73UNIFAC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-75Modifications to UNIFAC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-78Fill Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-82Henry's Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-85Heat of Mixing Calculations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-86

Vapor Phase Fugacities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-88General Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-88Equations of State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-89Truncated Virial Equation of State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-90Hayden-O'Connell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-91

Special Packages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-93General Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-93Alcohol Package (ALCOHOL) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-93Glycol Package (GLYCOL) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-96Sour Package (SOUR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-99GPA Sour Water Package (GPSWATER) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-102Amine Package (AMINE) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-104

Electrolyte Mathematical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-107Discussion of Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-107Modeling Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-109

Electrolyte Thermodynamic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-112Thermodynamic Framework. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-112Equilibrium Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-112Thermodynamic Framework in PRO/II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-113Aqueous Phase Activities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-114Vapor Phase Fugacities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-118Organic Phase Activities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-122Enthalpy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-123Aqueous Liquid Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-124

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Molar Volume and Density. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-125Solid-Liquid Equilibria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-127

General Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-127van't Hoff Equation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-127Solubility Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-128Fill Options for Solubility Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-129

Transport Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-129General Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-129PURE Methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-130Liquid Thermal Conductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-133TRAPP Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-136Special Methods for Liquid Viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-139Liquid Diffusivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-142

Index

ToC-4

Chapter 1 Introduction

General Information The PRO/II Unit Operations Reference Help provides details on the basic equations and calculation techniques used in the PRO/II simu-lation program and the PROVISION Graphical User Interface. It is intended as a reference source for the background behind the vari-ous PRO/II calculation methods.

What is in This Manual? This on-line manual contains the correlations and methods used to calculate thermodynamic and physical properties, such as the Soave-Redlich-Kwong (SRK) cubic equation of state for phase equilibria. This volume also contains information on the definition of pure components and petroleum fractions.

For each method described, the basic equations are presented, and appropriate references provided for details on their derivation. Gen-eral application guidelines are provided, and, for many of the meth-ods, hints to aid solution are supplied.

Who Should Use This Manual? For novice, average, and expert users of PRO/II, this on-line man-ual provides a good overview of the calculation modules used to simulate a single unit operation or a complete chemical process or plant. Expert users can find additional details on the theory pre-sented in the numerous references cited for each topic. For the nov-ice to average user, general references are also provided on the topics discussed, e.g., to standard textbooks.

Specific details concerning the data entry steps required for the PROVISION Graphical User Interface may be found in the main PRO/II Help. Detailed sample problems are provided in the PRO/II Application Briefs Manual, in the \USER\APPLIB\ directory, and in the PRO/II Casebooks.

PRO/II Component Reference Manual Introduction 1-1

Finding What you Need A Table of Contents is provided for this on-line manual. Cross-ref-erences and hypertext links are provided to the appropriate sections of the main PRO/II Help to assist in preparing and entering the required input data.

Introduction 1-2

Chapter 2 Component Data

PRO/II allows the user to specify pure-component physical prop-erty data for a given simulation. Pure component data are usually associated with either a predefined component in a data library, a user-defined (non-library) component, or a petroleum pseudocom-ponent.

Properties for defined components can be accessed in a variety of ways. They can be retrieved from an on-line databank or “library", estimated from structural or other data, or input by the user as ‘‘non-library’’ components. User input can be used to override properties retrieved from the libraries.

Properties for ‘‘pseudo’’ or petroleum components are derived from generalized correlations based on minimal data, usually the normal boiling point, molecular weight, and standard density. Hydrocarbon streams defined in terms of assay data (including distillation data) can be converted to discrete pseudo components by a number of assay processing methods.

Defined Components

Component LibrariesTable 2-1 lists the property data available in the built-in component libraries for predefined components. These libraries include the PROCESS library (the physical property library used as the default in PROCESS, PIPEPHASE, HEXTRAN, and early versions of PRO/II), the SIMSCI library (a fully documented physical property bank), the DIPPR (Design Institute for Physical Property Research) library from the American Institute of Chemical Engineers, and the OLILIB library of electrolyte species, which contains a subset of the library component properties listed in the following sections.

Most of the fixed properties used in a simulation can be found in the input reprint of the simulation. The coefficients of the correlations used for the temperature-dependent properties stored in the libraries are not shown because they are usually covered by contractual agreements which disallow their display in a simulation.

PRO/II Component Reference Manual Component Data 2-1

Table 2-1: PRO/II Library Component PropertiesFixed Properties and Constants

Acentric Factor Heat of Formation

Carbon Number Hydrogen Deficiency Number

Chemical Abstract Number Liquid Molar Volume

Chemical Formula Lower Heating Value

Critical Compressibility Factor Molecular Weight

Critical Pressure Normal Boiling Point

Critical Temperature Rackett Parameter

Critical Volume Radius of Gyration

Dipole Moment Solubility Parameter

Enthalpy of Combustion Specific Gravity

Enthalpy of Fusion Triple Point Temperature

Flash Point Triple Point Pressure

Free Energy of Formation UNIFAC Structure

Freezing Point (normal melting point)

van der Waals Area and Volume

Gross Heating Value

Temperature-dependent-Properties

Enthalpy of Vaporization Solid Heat Capacity

Ideal Vapor Enthalpy Solid Vapor Pressure

Liquid Density Surface Tension

Liquid Thermal Conductivity Vapor Pressure

Liquid Viscosity Vapor Thermal Conductivity

Saturated Liquid Enthalpy Vapor Viscosity

Solid Density

Reference

1 PPDS, Physical Property Data Service, jointly sponsored by the National Physical Laboratory, National Engineering Laboratory, and the Institution of Chemical Engineers in the UK.

2 DIPPR, Design Institute for Physical Property Data, spon-sored by the American Institute of Chemical Engineers.

Component Data 2-2

Fixed Properties

Specific gravities of permanent gases are often expressed as relative to air, without any annotations in the output.

Liquid molar volumes may be extrapolated from a condition very different from 77 F (25 C), if the component doesn't natu-rally exist as a liquid at 77 F.

Temperature-dependent PropertiesThe temperature-dependent correlations available for use in PRO/II are listed in Table 8-6 in volume I of the PRO/II Component and Thermodynamic Input Data Manual. The equations that are typi-cally used to represent a property are listed in Table 2-2. While tem-perature-dependent library properties are fitted and are usually very accurate at saturated, sub-critical conditions, caution must be used in the superheated or super-critical regions.Because of the form of some of the allowable temperature-dependent equations, extrapola-tion beyond the minimum and maximum temperatures is not done using the actual correlation. PRO/II has adopted the rules shown in Table 2-2, based on the property, for extrapolation of the tempera-ture-dependent correlations

Table 2-2: PRO/II Temperature-dependent Property Equations and Extrapolation Conventions

Temperature-dependent Property

Recommended Equations

Extrapolation Method

Vapor Pressure 14, 20, 21, 22 ln(Prop.) vs. 1/T

Liquid Density 1, 4, 16, 32 Prop. vs. T

Ideal Vapor Enthalpy 1, 17, 41 Prop. vs. T

Enthalpy of Vaporization

4, 15, 36, 43 Prop. vs. T

Saturated Liquid Enthalpy

1, 42, 35 Prop. vs. T

Liquid Viscosity 13, 20, 21 ln(Prop.) vs. 1/T

Vapor Viscosity 1, 19, 26, 27 Prop. vs. T

Liquid Thermal Conductivity

1, 4, 34 Prop. vs. T


Another note of caution concerns the use of equations 20 and 21 in modeling component vapor pressures. These equations are actually combinations of two or more traditionally used vapor pressure equations (e.g., Antoine). It is intended that the user apply only sub-sets of the available coefficients with these equations corresponding to the more traditional equations. Table 2-3 gives some examples of this mapping.

Table 2-3: PRO/II Vapor Pressure Equations

Common Vapor Pressure

Equation 20 / 21 Coefficients

Equations (#) C1 C2 C3 C4 C5 C6 C7

Clapeyron (20 or 21)

x x

Antoine (21) x x x

Riedel (20) x x x x

Frost-Kalkwarf (21)

x x x x

Reidel-Plank-Miller (20)

x x x x

Properties From StructureProperties for defined components, either library or non-library, may be estimated if the user supplies a component structure and invokes the FILL option in the component data category of input. This procedure primarily uses the methods of Joback and is good for components with molecular weights below 400 and components with less than 20 unique structural groups. More accurate results are obtained for components containing just one type of functional

Vapor Thermal Conductivity

1, 19, 33 Prop. vs. T

Surface Tension 1, 15, 30 Prop. vs. T

Solid Thermal Conductivity

1 Prop. vs. T

Solid Density 1 Prop. vs. T

Solid Cp or Enthalpy 1 Prop. vs. T

Solid Vapor Pressure 20 ln(Prop.) vs. 1/T

Table 2-2: PRO/II Temperature-dependent Property Equations and Extrapolation Conventions

Component Data 2-4

group. For example, amine properties would be more accurate than those predicted for an ethanol amine, which would contain func-tional groups for both an alcohol and an alcohol amine.

Petroleum Components

General InformationPetroleum components (often called pseudo-components) are either defined on a one-by-one basis on PETROLEUM statements or gen-erated from one or more streams given in terms of assay data. The processing of assays is described in Assay Processing section. Each individual pseudo-component is typically a narrow-boiling cut or fraction. Component properties are generated based on two of the following three properties:

Molecular weight.

Normal boiling point (NBP).

Standard liquid density.

If only two are supplied, the third is computed with the SIMSCI method (or with another method if requested with the MW key-word). These methods are described in the sections below.

From those three basic properties, the program estimates all other properties needed for the calculation of thermophysical properties. Several different sets of characterization methods are provided. These are known as the SIMSCI, CAVETT (API 1964), Lee-Kesler, CAV80 (API 1980) EXTAPI, and (starting with PRO/II version 8.2) the HEAVY methods. The Cavett methods developed in 1962 were the default in all versions of PRO/II up to and including the 3.5 series. The SIMSCI methods use a combination of published (Black and Twu, 1983; Twu, 1984) and proprietary methods developed by SimSci. These are the default for all PRO/II versions subsequent to the 3.5 series. The LK option accesses methods developed by Lee and Kesler in 1975 and 1976.The EXTAPI method is an extension of the method from the 1980 API technical data book with an adjustment for components that boil below 300F. The most recently added HEAVY method is an extension of the original Twu correla-tions. Also know as the constant Watson K extension, it extrapo-lates to estimate critical properties and molecular weight well beyond 1000 Kelvin.


Property Generation– SIMSCI Method

Critical Properties and Acentric FactorThe SIMSCI characterization method was developed by Twu in 1984. It expresses the critical properties (and molecular weight) of hydrocarbon components as a function of NBP and specific gravity. The correlation is expressed as a perturbation about a reference sys-tem of normal alkanes. The critical temperature (in degrees Rank-ine) is given by:

(2-1)

(2-2)

(2-3)

(2-4)

(2-5)

where:

SG =specific gravity

Tb = normal boiling point, degrees Rankine

α = 1 - Tb / Tc

ΔSG = specific gravity correction

f = correction factor

SG = specific gravity

subscript T refers to the temperature

subscript c refers to the critical conditions

superscript ° refers to the reference system

Component Data 2-6

The critical volume (in cubic feet per pound mole) and the critical pressure (in psia) are given by similar expressions:

(2-6)

(2-7)

(2-8)

(2-9)

(2-10)

(2-11)

(2-12)

(2-13)

where: V = molar volume, ft3/lb-mole

P = pressure, psia

subscripts V and P refer to the volume and pressure

The acentric factor for the SIMSCI method is estimated with the use of a generalized Frost-Kalkwarf vapor equation developed at Sim-Sci. The equation is given by:

(2-14)

where:


A1 to A7 = constants given in Table 2-4

PR = reduced pressure (P/Pc)

TR = reduced temperature (T/Tc),

ϖ = a parameter evaluated at the NBP and given by:

the NBP and given by:

(2-15)

where: subscripts R,b indicate reduced properties evaluated at the normal boiling point

Functions and are given by:

(2-16)

(2-17)

The values of the seven constants in these equations are shown in Table 2-4.

Table 2-4: Values of Constants for Equations (2-14)-(2-17)

A1 10.2005

A2 -10.6317

A3 -5.58058

A4 2.09167

A5 -2.09167

A6 -1.70214

A7 0.4312

To compute the acentric factor, the parameter ϖ is determined using equation (2-15) and the known (or already estimated) values for the critical temperature and pressure and the normal boiling point (NBP). This is then used in equation (2-14) to compute the reduced vapor pressure at a reduced temperature of 0.7, which is then used in the definition of the acentric factor.

Component Data 2-8

(2-18)

Other Fixed PropertiesThe heat of formation is computed from a proprietary correlation developed by SimSci. The solubility parameter is estimated from the following equation:

(2-19)

The molar latent heat of vaporization, ΔHV, is computed from the Kistiakowsky-Watson method described later on in this section, while VL is the liquid molar volume at 25 C.

Temperature-dependent PropertiesThe ideal-gas enthalpy (needed for equation-of-state calculations) is calculated from the method of Black and Twu developed in 1983. The method was an extension of work done by Lee and Kesler and involved fitting a wide variety of ideal-gas heat capacity data for hydrocarbons from the API 44 project and other sources. The equa-tion (which produces enthalpies in Btu/lb and uses temperatures in degrees Rankine) is as follows:

(2-20)

(2-21)

(2-22)

(2-23)

(2-24)

(2-25)

(2-26)

(2-27)

(2-28)

(2-29)


(2-30)

The Watson characterization factor, K, is defined as:

(2-31)

where:

NBP =normal boiling point in degrees Rankine

SG = specific gravity (typically at 60F/60F)

The constant A1 in equation (2-20) is determined so as to give an enthalpy of zero at the arbitrarily chosen zero for enthalpy, which is the saturated liquid at 0 C. The latent heat of vaporization as described below (to get from saturated liquid to saturated vapor) and the SRK equation of state (to get from saturated vapor to ideal gas) are used to compute the enthalpy departure between this refer-ence point and the ideal-gas state.

The vapor pressure is calculated from the reduced vapor-pressure equation (2-14) used above in the calculation of the acentric factor. The latent heat of vaporization also is calculated from equation (2-14), and then is related to the vapor pressure using the Clausius-Clapyron equation. Saturated liquid enthalpy is calculated by com-puting the departure from the ideal-gas enthalpy, as a sum of the latent heat and the enthalpy departure (computed with the SRK equation of state) for the saturated vapor. Saturated liquid density is computed by applying the Rackett equation (see Section - General-ized Correlation Methods) to saturated temperature and pressure conditions as predicted by vapor-pressure equation (2-14).

Property Generation– CAVETT Method

Critical Properties and Acentric FactorOptionally, the user may choose to compute critical properties from the methods developed in 1962 by Cavett. This option is called the CAVETT method. The equations are:

Component Data 2-10

Tc 308.47121 1.7133693 Tb( ) 0.0010834 Tb2( ) 3.8890584 7– Tb

3( )+–+=

0.0089212579 API( )Tb 5.309492 6– API( )Tb2 3.27116 8– API2( )Tb

3+ +–

log10Pc 2.8290406 9.4120109 10 4–× Tb 3.0474749 10 6–× Tb2–+=

0.2087611 10 4–× APITb– 0.15184103 10 8–× Tb3( ) …+ +

0.11047899 10 7–× APITb2

0.48271599 10 7–× API( ) Tb– 0.13949619 10 9–× API( )2Tb2+

(2-32)

(2-33)

where:

Tc = critical temperature in degrees Fahrenheit

Pc = critical pressure in psia

Tb = normal boiling point in degrees Fahrenheit

API = API gravity

When the CAVETT characterization options are chosen, the acen-tric factor is computed by a method due to Edmister (1958):

(2-34)

In equation (2-34), Pc is in atmospheres. Finally, the critical volume is estimated from the following equation:

(2-35)

Other Fixed PropertiesWhen the CAVETT characterization option is chosen, the heat of formation and solubility parameter are calculated exactly as in the SIMSCI method above.

Temperature-dependent PropertiesIdeal-gas enthalpies (in Btu/lb-mole) are computed with the follow-ing equations:

(2-36)


(2-37)

(2-38)

(2-39)

(2-40)

(2-41)

(2-42)

(2-43)

(2-44)

where:

T =temperature in degrees Rankine

MW = molecular weight

API = API gravity

K = Watson K-factor defined by equation (2-31).

The constant α0 in equation (2-37) is determined so as to be consis-tent with the arbitrary zero of enthalpy, which is the saturated liquid at 0 C.

Vapor pressures (in psia) are computed from a generalized Antoine equation:

(2-45)

(2-46)

Component Data 2-12

(2-47)

Temperatures (including the critical temperature Tc and normal boiling point Tb) are in degrees Rankine.

The saturated liquid density (in lb/ft3) is computed as follows:

(2-48)

(2-49)

(2-50)

(2-51)

where:

= liquid density at 60 F, calculated from the specific gravity and the density of water

Temperatures are in degrees Rankine

The latent heat of vaporization (in Btu/lb-mole) is calculated from a combination of the Watson equation (Watson, 1943, Thek and Stiel, 1966), for the temperature variation of the heat of vaporization, and the expression of Kistiakowsky (1923), for the heat of vaporization at the normal boiling point:

(2-52)

(2-53)

The critical temperature Tc, normal boiling point Tb, and tempera-ture T are all in degrees Rankine.

The saturated liquid enthalpy is estimated with the correlation of Johnson and Grayson. This method is discussed in Section: Gener-alized Correlation Methods. A constant is added so that the satu-rated liquid enthalpy is zero at 0 C.


Property Generation– Lee-Kesler Method

Critical Properties and Acentric FactorKesler and Lee used the following equations in 1976 to correlate critical temperatures and critical pressures of hydrocarbons:

(2-54)

(2-55)

where:

Tc, Tb = critical and normal boiling temperatures (both in degrees Rankine)

Pc = critical pressure in psia

SG = specific gravity

The acentric factor is estimated from an equation in an earlier work by Lee and Kesler (1975):

(2-56)

where: subscripts R, b indicate reduced properties evaluated at the normal boiling point

The critical volume is then estimated from the following equation:

(2-57)

Other Fixed PropertiesWhen the Lee-Kesler characterization option is chosen, the heat of formation and the solubility parameter are calculated exactly as in the SIMSCI method described previously.

Component Data 2-14

Temperature-dependent PropertiesIdeal-gas enthalpies (in Btu/lb-mole) are computed by integrating the following equation for the ideal-gas heat capacity:

(2-58)

The factor CF is given by:

(2-59)

where:

K = Watson K-factor defined by equation (2-31).

T = temperature in degrees Rankine.

ω = acentric factor as calculated by equation (2-56).

The constant of integration is determined so as to give an enthalpy of zero at the arbitrarily chosen basis for enthalpy, which is the sat-urated liquid at 0 C.

When the Lee-Kesler characterization option is chosen, the vapor pressure, saturated liquid density, saturated liquid enthalpy, and latent heat of vaporization are all calculated by the methods used for CAVETT characterization, as described in the previous section.

Property Generation – Heavy Method10

All the characterization methods discussed above apply predomi-nantly to paraffinic fluids having API gravities greater than 20 and Watson K factors in the 12.5 to 13.5 range. They have been shown to be progressively less accurate as the API gravity drops to 10 or less, and as the Watson K factor approaches 9 or 10.

The HEAVY characterization option provides a better estimation of pseudo components or petro fractions generated from an assay curve of heavy oil or bitumen. This extension of the SIMSCI method exhibits better extrapolation qualities for heavier, more naphthenic and aromatic materials typically present in heavy oils and bitumens. The method applies particularly well to the following ranges:

Normal Boiling Point: 111.111 to 1366.48 Kelvin


Specific Gravity: 0.49 to 1.2Molecular Weight: 16. to 2500.0

PRO/II issues warnings when data used with this option are outside these ranges.

Critical Properties and Acentric FactorEquations (2-1) through (2-12) for the SIMSCI method serve as the starting correlations. This method extrapolates those equations using the following algorithm (demonstrated for molecular weight.

1. Compute the watson K from the NBP and the Specific Gravity of the pseudo-component using equation (2-31).

2. Hold the Watson K constant and calculate Specific Gravity at the upper temperature limit of 1000 K (NBP1800 R):

SG1800R1800.0( )1 3⁄

KWatson-----------------------------= (2-60)

3. Compute molecular weight at NBP1800 R and SG1800 R:

MW( )ln MW0( )1 2fM+1 2fM–------------------⎝ ⎠

⎛ ⎞2

ln= (2-61)

4. compute a small change in Specific Gravity, NBP, and MW:

ΔSG SG1800R 0.001×=

SG ΔSG– KWatson SG ΔSG–( )– ][=

NBP1800R ΔNBP– KWatson SG1800R ΔSG–( )×[ ]3=

(2-62)

5. Compute slope at NBP1800 R:Slope ΔMWΔSG--------------=

6. Use the slope to extrapolate linearly to the given NBP and SG

MWtar MW1800R Slope SGtar SG1800R–( )×+= (2-63)

Reference

1 Black, C., and Twu, C.H., 1983, Correlation and Prediction of Thermodynamic Properties for Heavy Petroleum, Shale Oils, Tar Sands and Coal Liquids, paper presented at AIChE Spring Meeting, Houston, March 1983.

Component Data 2-16

2 Cavett, R.H., 1962, Physical Data for Distillation Calcula-tions - Vapor-Liquid Equilibria, 27th Mid-year Meeting of the API Division of Refining, 42[III], 351-357.

3 Edmister, W.C., 1958, Applied Hydrocarbon Thermody-namics, Part 4: Compressibility Factors and Equations of State, Petroleum Refiner, 37(4), 173.

4 Kesler, M.G., and Lee, B.I., 1976, Improve prediction of enthalpy of fractions, Hydrocarbon Proc., 53(3), 153-158.

5 Kistiakowsky, W., 1923, Z. Phys. Chem., 107, 65.

6 Lee, B.I., and Kesler, M.G., 1975, A Generalized Thermo-dynamic Correlation Based on Three-Parameter Corre-sponding States, AIChE J., 21, 510-527.

7 Thek, R.E., and Stiel, L.I., 1966, A New Reduced Vapor Pressure Equation, AIChE J., 12, 599-602.

8 Twu, C.H., 1984, An Internally Consistent Correlation for Predicting the Critical Properties and Molecular Weights of Petroleum and Coal-tar Liquids, Fluid Phase Equil., 16, 137-150.

9 Watson, K.M., 1943, Ind. Eng. Chem., 35, 398.

10 Spencer, Calvin; Nagvekar, Manoj; Watanasiri, Suphat; Twu, Chorng H.; Petroleum Fraction Characterization - A Viable Approach for Heavier, Highly Aromatic Fractions; Paper presented at AIChe Spring Meeting, New Orleans, LA, 2005

Assay Processing

General InformationHydrocarbon streams may be defined in terms of laboratory assay data. Typically, such an assay would consist of distillation data (TBP, ASTM D86, ASTM D1160, or ASTM D2887), gravity data (an average gravity and possibly a gravity curve), and perhaps data for molecular weight, light-ends components, and special refining properties such as pour point and sulfur content. This information is used by PRO/II to produce one or more sets of discrete pseudo-components which are then used to represent the composition of each assay stream.The process by which assay data are converted to pseudo-components can be analyzed in terms of several distinct


steps. Before each of these is examined in detail, it will be useful to list briefly each step of the process in order:

The user defines one or more sets of TBP cut points (or accepts the default set of cut points that PRO/II provides). These cut-points define the (atmospheric) boiling ranges that will ulti-mately correspond to each pseudo-component. Multiple cut point sets (also known as blends) may also be defined to better model different sections of a process.

Each set of user-supplied distillation data is converted to a TBP (True Boiling Point) basis at one atmosphere (760 mm Hg) pressure.

The resulting TBP data are fitted to a continuous curve and then the program "cuts" each curve to determine what percent-age of each assay goes into each pseudo-component as defined by the appropriate cut-point set. Gravity and molecular weight data are similarly processed so that each cut has a normal boil-ing point, specific gravity, and molecular weight. During this step, the lowest-boiling cuts may be eliminated or modified to account for any lightends components input by the user.

Within each cut-point set, all assay streams using that set (unless they are explicitly excluded from the blending - this is described later) are combined to get an average normal boiling point, gravity, and molecular weight for each of the pseudo-components generated from that cutpoint set. These properties are then used to generate all other properties (critical proper-ties, enthalpy data, etc.) for that pseudocomponent.

Note: Special refinery properties such as cloud point and sulfur content may also be defined within assays. The distribution of these properties into pseudo-components and their subsequent processing by the simulator is outside the scope of this chapter but will be covered in a later document.

Component Data 2-18

Cutpoint Sets (Blends)

Defining CutpointsIn any simulation, there is always a "primary" cutpoint set, which defaults as shown in Table 2-5.

Table 2-5: Primary TBP Cutpoint Set

TBP Range, F

Number of Components

Width per cut, F

100-800 28 25

800-1200 8 50

1200-1600 4 100

The primary cutpoints shown in Table 2-5 may be overridden by supplying a new set for which no name is assigned. In addition, "secondary" sets of cutpoints may be supplied by supplying a set and giving it a name. The blend with no name (primary cutpoint set) always exists (even if only named blends are specifically given); there is no limit to the number of named blends (secondary cutpoint sets) that may be defined. The user may designate one cutpoint set as the "default"; if no default is explicitly specified, the primary cut-point set will be the default. Each cutpoint set (if it is actually used by one or more streams) will produce its own set of pseudo compo-nents for use in the flowsheet.

Association of Streams With BlendsEach assay stream is associated with a particular blend. By default, an assay stream is assigned to the default cutpoint set. A stream may be associated with a specific secondary cutpoint set by explic-itly specifying the name of that cutpoint set (blend) in association with the stream. If the assay stream is associated with a blend name not given for any cutpoint set previously defined, a new blend with that name is created using the same cutpoints as the primary cut-point set. The user may also specify that a stream use a certain set of cutpoints but not contribute to the blended properties of the pseudo-components generated from that set (this might be appropriate if an estimate were being supplied for a recycle stream, for example). This is done by selecting the XBLEND option, which excludes the stream in question from the blending. The default is for the stream to be included in the blending for the purposes of pseudocomponent property generation; this is called the BLEND option. It is not allowed for the XBLEND option to be used on all streams associ-ated with a blend, since at least one stream must be blended in to


define the pseudocomponent properties. The blending logic is best illustrated by an example:

Suppose that two secondary cutpoint sets A1 and A2 were defined, and that A1 was designated as the default. This means that three sets actually exist, since the primary cutpoint set supplied by PRO/II still exists (though it is no longer the set with which streams will be associated by default). Now, suppose the following streams (where extraneous information like the initial conditions is not shown) are given:

Table 2-6: Blending Example

Stream Blend Option Blend Name

S1 none given (defaulted to BLEND)

none given (defaulted to A1)

S2 XBLEND none given (defaulted to A1)

S3 XBLEND A1

S4 BLEND A2

S5 BLEND B1

S6 XBLEND B1

S7 BLEND B2

Streams S1 and S2 will use the pseudo-components defined by sec-ondary cutpoint set A1, since it is the default. S3 will also use A1's pseudo-components since it is specified directly. The pseudo-com-ponents in blend A1 will have properties determined only by the cuts from stream S1, since the XBLEND option was used for S2 and S3. Stream S4 will use the pseudo components defined by cut-point set A2. Streams S5 and S6 will go into a new blend B1 which will use the cutpoints of the primary cutpoint set. Since XBLEND is used for stream S6, only stream S5's cuts will be used to determine the properties of the pseudo components in blend B1. Finally, stream S7 will use another new blend, B2, also with the cutpoints from the primary cutpoint set. Since it is a different blend, however, the pseudo-components from blend B2 will be completely distinct (even though they will use the same cutpoint ranges) from those of blend B1.

Application ConsiderationsThe selection of cutpoints is an important consideration in the simu-lation of hydrocarbon processing systems. Too few cuts can result in poor representation of yields and stream properties when distilla-

Component Data 2-20

tion operations are simulated; moreover, desired separations may not be possible because of component distributions. On the other hand, the indiscriminate use of cuts not needed for a simulation serves only to increase the CPU time unnecessarily. It is wise to examine the cut definition for each problem in light of simulation goals and requirements. The default primary cutpoint set in PRO/II represents, in our experience, a good selection for a wide range of refinery applications.

In some circumstances, it may be desirable to use more than one cutpoint set in a given problem. This "multiple blends" functional-ity is useful when different portions of a flow sheet are best repre-sented by different TBP cuts; for example, one part of the process may have streams that are much heavier than another and for which more cutpoints at higher temperatures would be desirable. It is also useful when hydrocarbon feeds to a flow sheet differ in character; for example, different blends might be used to represent an aromatic stream (producing pseudo-components with properties characteris-tic of aromatics) and a paraffinic stream feeding into the same flow-sheet. The extra detail and accuracy possible with this feature must be balanced against the increase in CPU time caused by the increased number of pseudocomponents.

Inter-conversion of Distillation Curves

Types of Distillation CurvesAssays of hydrocarbon streams are represented by distillation curves. A distillation curve represents the amount of a fluid sample that is vaporized as the temperature of the sample is raised. The temperature where the first vaporization takes place is referred to as the initial point (IP), and the temperature at which the last liquid vaporizes is called the end point (EP). Each data point represents a cumulative portion (usually represented as volume percent) of the sample vaporized when a certain temperature is reached.Estimation of thermophysical properties for the pseudo components requires (among other things) a distillation curve that represents the true boiling point (TBP) of each cut in the distillation. However, rigor-ous TBP distillations are difficult and not well standardized so it is common to perform some other well-defined distillation procedure; standard methods are defined by the American Society for Testing and Materials (ASTM). The ASTM procedures most commonly used for hydrocarbons are D86, D1160, and D2887.


ASTM D86 distillation is typically used for light and medium petroleum products and is carried out at atmospheric pressure. D1160 distillation is used for heavier petroleum products and is often carried out under vacuum, sometimes at absolute pressures as low as 1 mm Hg. The D2887 method uses gas chromatography to produce a simulated distillation curve; it is applicable to a wide range of petroleum systems. D2887 results are always reported by weight percent; other distillations are almost always reported on a volume percent basis. More details on these distillation procedures may be found in the API Technical Data Book; complete specifica-tions are given in volume 5 (Petroleum Products and Lubricants) of the Annual Book of ASTM Standards.

Conversion of D1160 CurvesPRO/II converts D1160 curves to TBP curves at 760 mm Hg using the three-step procedure recommended in the API Technical Data Book:

Convert to D1160 at 10 mm Hg using API procedure 3A4.1 (which in turn references procedure 5A1.13). This procedure is expressed as a way to estimate a vapor pressure at any tempera-ture given the normal boiling point, but the same equations may be solved to yield a normal boiling temperature given the boil-ing temperature at another pressure. The equations used are as follows:

(2-64)

(2-65)

(2-66)

where:

P* = vapor pressure in mm Hg at temperature T (in degrees Rank-ine)

The parameter X is defined by:

Component Data 2-22

(2-67)

where:

Tb = boiling point (in degrees Rankine) at a pressure of 760 mm Hg

For conversions where neither pressure is 760 mm Hg, the conver-sion may be made by applying the above equations twice in succes-sion, using 760 mm Hg as an intermediate point:

Convert to TBP at 10 mm Hg using API Figure 3A2.1 (which has been converted to equation form by SimSci).

Convert to TBP at 760 mm Hg using API procedure 3A4.1.

Conversion of D2887 CurvesPRO/II converts D2887 simulated distillation data to TBP curves at 760 mm Hg using the two-step procedure recommended in the API Technical Data Book:

Convert to D86 at 760 mm Hg using API procedure 3A3.1. This procedure converts D2887 Simulated Distillation (SD) points (in weight percent) to D86 points (in volume percent) using the following equation:

(2-68)

where:

D86 and SD = the ASTM D86 and ASTM D2887 temperatures in degrees Rankine at each volume percent (for D86) and the corre-sponding weight percent (for SD), and a, b, and c are constants varying with percent distilled according toTable 2-7.

Table 2-7: Values of Constants a, b, c

Percent Distilled

a

b

c

0 6.0154 0.7445 0.2879

10 4.2262 0.7944 0.2671

30 4.8882 0.7719 0.3450


The parameter F in equation (2-68) is calculated by the following equation:

(2-69)

where:

SD10% and SD50% = D2887 temperatures in degrees Rankine at the 10% and 50% points, respectively

Convert to TBP at 760 mm Hg using API procedure 3A1.1, which is described in the section Conversion of D86 Curves with New (1987) API Method below.

Conversion of D86 CurvesPRO/II has three options for the conversion of D86 curves to TBP curves at 760 mm Hg. These are the currently recommended (1987) API method, the older (1963) API method, and the Edmister-Oka-moto correlation. In addition, a correction for cracking may be applied to D86 data; this correction was recommended by the API for use with their older conversion procedure, but is not recom-mended for use with the current (1987) method. The conversion of D86 curves takes place in the following steps:

If a cracking correction is desired, correct the temperatures above 475 F as follows:

(2-70)

where:

= the corrected and observed temperatures, respec-tively, in degrees Fahrenheit.

If necessary, convert the D86 curve at pressure P to D86 at 760 mm Hg with the standard ASTM correction factor:

50 24.1357 0.5425 0.7132

70 1.0835 0.9867 0.0486

90 1.0956 0.9834 0.0354

95 1.9073 0.9007 0.0625

Table 2-7: Values of Constants a, b, c

Component Data 2-24

(2-71)

where:

TP = D86 temperature in Fahrenheit at pressure P

T760 = D86 temperature in Fahrenheit at 760 mm Hg

Convert from D86 at 760 mm Hg to TBP at 760 mm Hg using one of the three procedures below.

a) Conversion of D86 Curves with New (1987) API MethodBy default, PRO/II converts ASTM D86 distillation curves to TBP curves at 760 mm Hg using procedure 3A1.1 (developed by Riazi and Daubert in 1986) recommended in the 5th edition of the API Technical Data Book. The equation for this procedure is as follows:

(2-72)

where a and b are constants varying with percent of liquid sample distilled as given in Table 2-8.

Table 2-8: Values of Constants a, b

Percent Distilled a b

0 0.9167 1.0019

10 0.5277 1.0900

30 0.7429 1.0425

50 0.8920 1.0176

70 0.8705 1.0226

90 0.9490 1.0110

95 0.8008 1.0355

b) Conversion of D86 Curves with Old (1963) API MethodThis method, while no longer the default, is still available for users whose flow sheets may be tuned to the results using the old method. This method was recommended (and shown in graphical form) in older editions of the API Technical Data Book. The graphical corre-lation has been converted to equation form by SimSci.

c) Conversion of D86 Curves with Edmister-Okamoto MethodEdmister and Okamoto (1969) developed a method which is still widely used for converting ASTM D86 curves to TBP curves. If the


Edmister-Okamoto method is specified as the conversion method, their procedure (converted from the original graphical form to equa-tions by SimSci) is used for conversion of D86 to TBP curves.

Cutting TBP Curves

Fitting of Distillation CurvesBefore a curve is cut into pseudo-components, the distillation data must be fitted to a continuous curve. This is necessary because the supplied data points will not in general correspond to the desired cutpoints. PRO/II offers three methods for fitting distillation curves.

The default is the cubic spline method (known as the SPLINE option). A cubic spline function is used to fit all given volume per-cents between the first and last points. Beyond those bounds, points 1 and 2 and points N and N-1 are used to define a normal distribu-tion function to extrapolate to the 0.01% and 99.99% points, respec-tively. If only two points are supplied, the entire curve is defined by the distribution function fit. This extrapolation feature is particu-larly valuable when extrapolating heavy ends distillations which often terminate well below 50 volume percent. This method in gen-eral results in an excellent curve fit. The only exception is when the distillation data contain a significant step function (such a step is often the unphysical result of an error in obtaining or reporting the data); in that case, the step creates an instability that tends to propa-gate throughout the entire length of the curve. Should this happen, the input data should be checked for validity.

The quadratic fit method (known as the QUADRATIC option) pro-vides a successive quadratic approximation to the shape of the input assay curve. This method is recommended in the rare case (see above) where a cubic spline fit is unstable.

The Probability Density Function (PDF) method (known as the PDF option) is different in that it does not necessarily pass through all the points input by the user. Instead, it fits a probability density function to all points supplied. The resulting curve will maintain the probability-curve shape characteristic of petroleum distillations, while minimizing the sum of the squares of the differences between the curve and the input data. If desired, the curve may be con-strained to pass through either or both of the initial point and end point. The PDF method is recommended whenever it is suspected that the distillation data are "noisy," containing significant random errors.

Component Data 2-26

It is worth noting that the choice of curve-fitting procedure will also have a slight impact on the distillation inter-conversions described in the previous section. That is because most of the conversion pro-cedures work by doing the conversion at a fixed set of volume per-cents, which must be obtained by interpolation and sometimes extrapolation, using some curve-fitting procedure.

Division into pseudo-componentsOnce a smooth distillation curve is obtained, the volume percent distilled at each cutpoint is determined. The differences between values at adjacent cutpoints define the percent of the stream's vol-ume that is assigned to the pseudocomponent defined by the inter-val between two adjacent cutpoints. For example, using the default set of cutpoints shown in Table 2-5, the first pseudocomponent would contain all material boiling between 100 F and 125 F, the second would contain the material boiling between 125 F and 150 F, and so forth. Material boiling above the last cutpoint (1600 F) would be combined with the last (1500-1600) cut, while (with the exception of lightends as discussed below) material boiling below 100 F would be combined with the first cut. If the distillation data do not extend into all of the cut ranges (in this example, if the initial point were higher than 125 F or if the end point were lower than 1500 F), the unused cuts are omitted from the simulation.

The normal boiling point (NBP) of each cut is determined as a vol-ume-fraction average (or, in rare cases where TBP, D86, or D1160 distillations are entered on a weight basis, as a weight-fraction aver-age) by integrating across the cut range. For small cut ranges, this will closely approach other types of average boiling points. These average boiling points are used (possibly after blending with cuts from other assay streams in the flow sheet) as correlating parame-ters when calculating other thermophysical properties for each pseudocomponent.

These procedures are demonstrated in Figure 2.1 for a fictitious assay with an IP of 90 F being cut according to the default cutpoint set (Table 2-5); for simplicity only the first ten percent of the curve is shown. In addition to its range, the first cut picks up the portion boiling below 100 F, and its average boiling point (about 110 F in this case) is determined by integrating the curve from the IP to the 125 F point. The second cut is assigned the material boiling from 125 F to 150 F, which is integrated to get a NBP of approximately 138 F. The third and subsequent cuts are generated in a similar man-ner.


Figure 2.1:Cutting TBP Curves

Gravity DataPRO/II requires the user to enter an average gravity (either as a Spe-cific Gravity, API Gravity, or Watson K-factor) for each assay. If a Watson K is given, it is converted to a gravity using the TBP data for the curve. Entry of a gravity curve is recommended but not required.

If a user-supplied gravity curve does not extend to the 95% point, quadratic extrapolation is used to generate an estimate for the grav-ity at the 100% point. A gravity for each cut is determined at its mid-point, and an average gravity for the stream is computed. If this average does not agree with the specified average, the program will either normalize the gravity curve (if data are given up to 95%) or adjust the estimated 100% point gravity value to force agreement. Since the latter could in some cases result in unreasonable gravity values for the last few cuts, the user should consider providing an estimate of the 100% point gravity value and letting the program normalize the curve, particularly when gravity data are available to 80% or beyond.

If no gravity curve is given, the program will generate one from the specified average gravity. The default method for doing this is referred to as the WATSONK method. For a pure component, the Watson K-factor is defined by the following equation:

(2-73)

Component Data 2-28

where:

NBP = normal boiling point in degrees Rankine

SG = specific gravity at 60 F relative to H2O at 60 F

For a mixture (such as a petroleum cut), the NBP is traditionally replaced by a more complicated quantity called the mean average boiling point (MeABP). For this purpose, however, it is sufficient to simply use the volume-averaged boiling point computed from the distillation curve. The gravity curve is generated by assuming a constant value of the Watson K, applying equation (2-73) to each cut to get a gravity, averaging these values, and then adjusting the assumed value of the Watson K until the resulting average gravity agrees with the average gravity input by the user.

Another method (known as the PRE301 option) is available prima-rily for compatibility with older versions. It is similar to the pre-ferred method described above, except that the average Watson K is estimated from the 10, 30, 50, 70, and 90 percent points on a D86 curve (which can be obtained from the TBP curve by reversing one of the procedures in the previous section) and then applied to the NBP of each TBP cut to generate a gravity curve. This curve is then normalized to produce the specified average gravity.

The preferred method (constant Watson K applied to TBP curve) is justified by the observation that, for many petroleum crude streams, the Watson K of various petroleum cuts above light naphtha tends to remain fairly constant. For other types of petroleum streams, however, this assumption is often incorrect. Hence, for truly accu-rate simulation work, the user is advised to supply gravity curves whenever possible.

Molecular Weight DataIn addition to the NBP and specific gravity, simulation with assays requires the molecular weight of each cut. These may be omitted completely by the user, in which case they are estimated by the pro-gram.

The user may supply a molecular weight curve, which is quadrati-cally interpolated and extrapolated to cover the entire range of pseudocomponents. Optionally, the user may also supply an aver-age molecular weight. In that case, the molecular weight value for the last cut is adjusted so that the curve matches the given average, or if the 100% value is provided, the entire molecular weight curve is normalized to match the given average.


If no molecular-weight data are supplied, the molecular weights are estimated; the default method is a proprietary modification (known as the SIMSCI method) of the method developed by Twu (1984). This method is a perturbation expansion with the normal alkanes as a reference fluid.

Twu's method was originally developed to be an improvement over Figure 2B2.1 in older editions of the API Technical Data Book. That figure relates molecular weight to NBP and API gravity for NBP’s greater than 300 F. The SIMSCI method matches that data between normal boiling points of 300 F and 800 F, and better extrapolates outside that temperature range.

The unaltered old API method is (API63) is also available.

A newer 1980 API method, called CAV80, is available. This is API procedure 2B2.1, an extension of the earlier API method that better matches known pure-component data below 300 F. It has been cor-related up to 1960 F.

PRO/II additionally supports a composite method (known as EXTAPI). This option uses the older API63 method for average boiling temperatures of 300 F and lower. Above this temperature, EXTAPI uses the CAV80 correlation.

Lightends DataHydrocarbon streams often contain significant amounts of light hydrocarbons (while there is no universal definition of "light," C6 is a common upper limit). Simulation of such systems is more accu-rate if these components are considered explicitly rather than being lumped into pseudocomponents. If the distillation curve is reported on a lightends-free basis, the light components can be fed to the flow sheet in a separate stream and handled in a straightforward manner. Typically, however, the lightends make up the initial part of the reported distillation curve, and adjustment of the cut-up curves is required to avoid double-counting the lightends components.

By default, the program "matches" user-supplied lightends data to the TBP curve. The user-specified rates for all lightends compo-nents are adjusted up or down, all in the same proportion, until the NBP of the highest-boiling lightends component exactly intersects the TBP curve. All of the cuts from the TBP curve falling into the region covered by the lightends are then discarded and the lightends components are used in subsequent calculations. This procedure is illustrated in Figure 2.2 where light end component flows are adjusted until the highest-boiling light end (nC5 in this example)

Component Data 2-30

has a mid-volume percent (point "a") that exactly coincides with the point on the TBP curve where the temperature is equal to the NBP of nC5. The cumulative volume percent of lightends is represented by point "b," and the cuts below point b (and the low-boiling por-tion of the cut encompassing that point) are discarded.

Figure 2.2: Matching Lightends to TBP Curve

Alternatively, the lightends may be specified as a fraction or percent (on a weight or liquid-volume basis) of the total assay or as a fixed lightends flowrate. In these cases, the input numbers for the light-ends components can be normalized to determine the individual component flow rates. A final alternative is to specify the flow rate of each lightends component individually.

Generating Pseudocomponent PropertiesOnce each curve is cut, the program processes each blend to pro-duce average properties for the pseudo-components from each cut-point interval in that blend. All the streams in a given blend (except for those for which the XBLEND option was used) are totaled to get the weights, volumes, and moles for each cutpoint interval. Using the above totals, the average molecular weight and gravity are cal-culated for each cut range. Finally, the normal boiling point for each pseudocomponent is calculated by weight averaging the individual values from the contributing streams.Once the normal boiling point, gravity, and molecular weight are known for each pseudocompo-nent, all other properties (critical properties, enthalpies, etc.) are


determined according to the characterization method selected by the user (or defaulted by the program). These methods are described in Petroleum Components section.

Vapor Pressure CalculationsWhile not a part of the program's actual processing of assay streams, many problems involving hydrocarbon systems will involve a specification on some vapor pressure measurement. The two most common of these are the True Vapor Pressure (TVP) and the Reid Vapor Pressure (RVP). PRO/II allows specification of these quantities from several unit operations, and they may be reported in output in the Heating/Cooling Curve (HCURVE) utility or as part of a user-defined stream report.True Vapor Pressure (TVP) Calculations.

True Vapor PressureThe TVP of a stream is defined as the bubble-point pressure at a given reference temperature. By default, that reference temperature is 100 F, but this may be overridden by the user. The user may spec-ify a specific thermodynamic system to be used in performing all TVP calculations in the flow sheet; by default, the calculation for a stream is performed using the thermodynamic system used to gen-erate that stream.

Reid Vapor Pressure (RVP) CalculationsThe RVP laboratory procedure provides an inexpensive and repro-ducible measurement correlating to the vapor pressure of a fluid. The measured RVP is usually within 1 psi of the TVP of a stream. It is always reported as "psi," although the ASTM test procedures (except for D5191 which, as mentioned below, uses an evacuated sample bomb) actually read gauge pressure. Since the air in the bomb accounts for approximately 1 atm, the measured gauge pres-sure is a rough measure of the true vapor pressure. Six different cal-culation methods are available. Within each calculation method, the answer will depend somewhat on the thermodynamic system used. As with the TVP, the thermodynamic system for RVP calculations may be specified explicitly or, by default, the thermodynamic sys-tem used to generate the stream will be used.

The APINAPHTHA method calculates the RVP from Figure 5B1.1 in the API Technical Data Book, which represents the RVP as a function of the TVP and the slope of the D86 curve at the 10% point. The graphical data have been converted to equation form by Simsci. This method is the default for PRO/II's RVP calculations. It

Component Data 2-32

is useful for many gasolines and other finished petroleum products, but it should not be used for oxygenated gasoline blends.

The APICRUDE method calculates the RVP from Figure 5B1.2 in the API Technical Data Book, which represents the RVP as a func-tion of the TVP and the slope of the D86 curve at the 10% point. The graphical data have been converted to equation form by Sim-Sci. It is primarily intended for crude oils.

The ASTM D323-82 method (known as the D323 method) simu-lates a standard ASTM procedure for RVP measurement. The liquid hydrocarbon portion of the sample is saturated with air at 33 F and 1 atm pressure. This liquid is then mixed at 100 F with air in a 4:1 volume ratio. Since the test chamber is not dried in this procedure, a small amount of water is also added to simulate this mixture. The mixture is flashed at 100 F at a constant volume (corresponding to the experiment in a sealed bomb), and the gauge pressure of the resulting vapor-liquid mixture is reported as the RVP. Both air and water should be in the component list for proper use of this method.

The obsolete ASTM D323-73 method (known as the P323 method) is available for compatibility with earlier versions of the program.

The ASTM D4953-91 method (known as the D4953 method) was developed by the ASTM primarily for oxygenated gasolines. The experimental method is identical to the D323 method, except that the system is kept completely free of water. The algorithm for simu-lating this method is identical to that for D323, except that no water is added to the mixture. Air should be in the component list for proper use of this method.

The ASTM D5191-91 method (known as the D5191 method) was developed as an alternative to the D4953 method for gasolines and gasoline-oxygenate blends. In this method, the air-saturated sample is placed in an evacuated bomb with five times the volume of the sample, and then the total pressure of the sample is measured. In the simulator, this is accomplished by flashing, at constant volume, a mixture of 1 part sample (at 33 F and 1 atm) and 4 parts air (at the near-vacuum conditions of 0.01 psia and 100 F). The resulting total pressure is then converted to a dry vapor pressure equivalent (DVPE) using the following equation:

(2-74)

where:

X = the measured total pressure


A = 0.548 psi (3.78 kPa)

This number is then reported as the RVP. Air should be in the com-ponent list for proper use of this method.

Comments on RVP and TVP MethodsBecause of the sensitivity of the RVP (and the TVP) to the light components of the mixture, these components should be modeled as exactly as possible if precise values of RVP or TVP are important. This might mean treating more light hydrocarbons as defined com-ponents rather than as pseudo-components; oxygenated compounds blended into gasolines should also be represented as defined com-ponents rather than as part of an assay. It is also important to apply a thermodynamic method that is appropriate for the stream in ques-tion (see section - Application Guidelines). The thermodynamics becomes particularly important for oxygenated systems, which are not well-modeled by traditional hydrocarbon methods such as Grayson-Streed. These systems are probably best modeled by an equation of state such as SRK with the SimSci alpha formulation and one of the advanced mixing rules (see section - Equations of State). It is important to have binary interaction parameters between the oxygenates and the hydrocarbon components of the system. PRO/II's databanks contain many such parameters, but others may have to be regressed to experimental data or estimated.

One should not be too surprised if calculated values for RVP differ from an experimental measurement by as much as one psi. Part of this is due to the uncertainty in the experimental procedure, and part is due to the fact that the lightends composition inside the simula-tion may not be identical to that of the experimental sample.

One of the less appreciated effects in experimental measurements is the presence of water, not only in the sample vessel, but also in the air in the form of humidity. The difference between the D323 (a "wet" method) RVP and the D4953 (a "dry" method) RVP will be approximately the vapor pressure of water at 100 F (about 0.9 psi), with the D323 RVP being higher. Both of these calculations assume that dry air is used in the procedure. The presence of humidity in the air mixed with the sample can alter the D323 results, lowering the measured RVP because of the decreased driving force for vaporiza-tion of the liquid water. In the extreme case of 100% humidity, the D323 results will be nearly identical with the D4953 results. There-fore, a "wet" test performed with air that was not dry would be expected to give results intermediate between PRO/II's D323 and D4953 calculations. The results from the D5191 method (both in

Component Data 2-34

terms of the experimental and calculated numbers) should in gen-eral be very close to D4953 results.

The primary application guideline for which RVP calculation model to use is, of course, to choose the one that corresponds to the exper-imental procedure applied to that stream. Secondary considerations include limitations of the individual methods. The APINAPHTHA and APICRUDE methods are good only for hydrocarbon naphtha and crude streams, respectively. The D323 method (and its obsolete predecessor, P323) is intended for hydrocarbon streams; the pres-ence of water makes it less well-suited for use with streams contain-ing oxygenated compounds. The D4953 and D5191 methods are both better suited for oxygenated systems, and calculations with these methods should give similar results.

Reference

1 American Petroleum Institute, 1988, Technical Data Book - Petroleum Refining, 5th edition (also previous editions), American Petroleum Institute, Washington, DC.

2 American Society for Testing of Materials, Annual Book of ASTM Standards, section 5 (Petroleum Products, Lubri-cants, and Fossil Fuels), ASTM, Philadelphia, PA (issued annually).

3 Edmister, W.C., and Okamoto, K.K., 1959, Applied Hydro-carbon Thermodynamics, Part 12: Equilibrium Flash Vaporization Calculations for Petroleum Fractions, Petro-leum Refiner, 38(8), 117.

4 Twu, C.H., 1984, An Internally Consistent Correlation for Predicting the Critical Properties and Molecular Weights of Petroleum and Coal-tar Liquids, Fluid Phase Equil., 16, 137-150.


Flash Point CalculationsFlash point is the lowest temperature at which a liquid can form an ignitable mixture with oxygen in air near the surface of the liquid under specific test conditions. Typically, the temperature is cor-rected to 14.7 psia (1 atmosphere) at which application of a test flame causes the vapor to ignite.

At this temperature the vapor may cease to burn when the source of ignition is removed. A slightly higher temperature, the fire point, is defined at which the vapor continues to burn after being ignited. Neither of these parameters is related to the temperatures of the ignition source or of the burning liquid, which are much higher.

There are two basic types of flash point measurement - open cup and closed cup.

In open cup devices, the sample is contained in an open cup that allows free mixing with ambient air. The sample is heated, and at intervals a flame is brought over the surface. The measured flash point will actually vary with the height of the flame above the liquid surface, and at sufficient height the measured flash point tempera-ture will coincide with the fire point.

Closed cup testers are sealed with a lid through which the ignition source can be introduced periodically. The vapor above the liquid is assumed to be in reasonable equilibrium with the liquid. Closed cup testers give lower values for the flash point (typically 5-10 K) and are a better approximation to the temperature at which the vapor pressure reaches the Lower Flammable Limit (LFL). See reference (1) at the end of this section.

Index and User Mixing methodsPRO/II supports methods for calculating the flash point from user-supplied average values or sets of values at cut-point temperatures. The data may be obtained from experiments using flash point test equipment, or from any other sources available to the user. In PRO/II, these are basically mixing methods that are not further discussed here. Since the data itself determines the type of flash point, the open cup and closed cup options serve only to properly the label the values when they appear in reports. Refer to the topic “Special Property Data” in the chapter Streams with Assay Data of the PRO/II keyword Input Manual. Also see the chapter Transport and Spe-cial Properties in volume 2 of the Component and Thermodynamic Data Input Manual.

Component Data 2-36

Correlated MethodsEmpirical methods are derived equations based on the lower end boiling temperatures of distillation curves. Generally, continuous-component streams are characterized into discrete "cut-points" using the ASTM D86 method. Depending upon the correlation, the boiling temperatures ranging between the zero percent and the 10 percent cut points are used and combined using various weighting strategies to obtain a representative temperature. This temperature then is incorporated as a variable in an empirical equation that com-putes the flash point directly.

The two non-proprietary methods available in PRO/II are the SIM-SCI (or Nelson) method and a modified version of the API meth-ods. These forms have not been updated since their first appearance in PRO/II version 3.3. In these forms, both closed cup and open cup calculations use identical equations.

API CorrelationThe equation in PRO/II is an older API method that Simsci-Esscor has recast from the original Fahrenheit to Rankine temperatures to eliminate zero from the division and LOG terms. It has been super-seded by procedure 2B7.1 of the API technical Data book (2). The form used in PRO/II is shown in equation (2-75).

TFP = 1.0 / ( -0.014568 + 2.84947 / TBP10% (2-75)

+ 1.903e-03 * LOG(TBP10%) )

where

TFP = Flash point temperature, Rankine

TBP10% = Boiling temperature of the ASTM D86 10% cut point, Rankine

Range over which the equation was evaluated

Flash point, F 0 - 450

ASTM D86 TBP, F 150 - 850

API makes the following statements about the equation:

The equation may be extrapolated to a limited extent. The flash point could be more accurately correlated to the ASTM D86


5% point, but a lack of data prevented development of a corre-lation. (3)

SIMSCI CorrelationThis implements the method of Nelson (4), which is similar to the API method and is based on ASTM D86 distillation curve data. It calculates a weighted average of the 0%, 5%, and 10% cut point boiling temperatures to compute a representative boiling tempera-ture. These values then are used in the equation to compute the flash point temperature directly as shown in equation (2-76).

TFP = ((TBPinit + 2.0 * TBP5% + TBP10%) / 4.0) (2-76)

* 0.64 - 100.0

where:

TFP = Calculated flash point temperature, Fahrenheit

TBPinit = Boiling temperature of the initial cut point, typi-cally the ASTM D86 0% point, Fahrenheit

TBP5% = Boiling temperature of the ASTM D86 5% cut point, Fahrenheit

TBP10% = Boiling temperature of the ASTM D86 10% cut point, Fahrenheit

Reference

1. 51758, ASTM 93, Determination of flash point - Closed cup equilibrium method (ISO 1523:2002).

2. API Technical Data Book, vol. 1, 6 ed., 1997, pp 2-30

3. API Technical Data Book, vol. 1, 6 ed., 1997, pp 2-31

4. Petroleum Refinery Engineering, 3rd ed., pg 125, 127; Nelson, W. L; McGraw-Hill, Inc., New York, 1949

Component Data 2-38

Chapter 3 Thermodynamic Methods

PRO/II offers numerous methods for calculating thermodynamic properties such as K-values, enthalpies, entropies, densities, gas and solid solubilities in liquids, and vapor fugacities. These methods include:

Generalized correlations, such as the Chao-Seader K-value method, and the API liquid density method,

Equations of state, such as the Soave-Redlich-Kwong method for calculating K-values, enthalpies, entropies, and densities,

Liquid activity coefficient methods, such as the Non-Random Two-Liquid (NRTL) method for calculating K-values,

Vapor fugacity methods, such as the Hayden-O'Connell Method for dimerizing species,

Special methods for calculating the properties of specific sys-tems of components such as alcohols, amines, glycols, and sour water systems.

Basic Principles

General InformationWhen modeling a single chemical process, or entire chemical plant, the use of appropriate thermodynamic methods and precise data is essential in obtaining a good design. PRO/II contains numerous proven thermodynamic methods for the calculation of the following thermophysical properties:

Distribution of components between phases in equilibrium (K-values).

Liquid and vapor phase enthalpies.

Liquid and vapor phase entropies.

Liquid and vapor phase densities.

PRO/II Component Reference Manual Thermodynamic Methods 3-1

Phase EquilibriaWhen two or more phases are brought into contact, material is transferred from one to another until the phases reach equilibrium, and the compositions in each phase become constant. At equilib-rium for a multi-component system, the temperature, pressure, and chemical potential of component i is the same in every phase, i.e.:

(3-1)

(3-2)

(3-3)

where:

T = system temperature

P = system pressure

μ = the chemical potential

α, β,..., π represent the phases

The fugacity of a substance is then defined as:

(3-4)

where:

= fugacity of component i

= standard state fugacity of component i at T, P

= standard state chemical potential of component i at T, P

It follows from (3) and (4) that the fugacities in each phase must also be equal:

(3-5)

The fugacity of a substance can be visualized as a “corrected partial pressure” such that the fugacity of a component in an ideal-gas mix-ture is equal to the component partial pressure.

For vapor-liquid equilibrium calculations, the ratio of the mole frac-tion of a component in the vapor phase to that in the liquid phase is defined as the K-value:

Thermodynamic Methods 3-2

(3-6)

where:

= K-value, or equilibrium ratio

= mole fraction in the vapor phase

= mole fraction in the liquid phase

For liquid-liquid equilibria, a corresponding equilibrium ratio or distribution coefficient is defined:

(3-7)

where:

= liquid-liquid distribution coefficient

I, II represent the two liquid phases

The vapor-phase fugacity coefficient of a component, is defined as the ratio of its fugacity to its partial pressure, i.e.:

(3-8)

where:

= vapor-phase fugacity coefficient of component i

If a liquid activity coefficient method is used in the liquid phase cal-culation, then the activity coefficient of the liquid phase can be related to the liquid fugacity by the following relationship:

(3-9)

where:

= liquid-phase activity coefficient

= standard state fugacity of pure liquid i

With this definition of liquid fugacity, γiL→ 1 as xi → 1. The stan-dard state fugacity is as follows:


(3-10)

where:

= saturated vapor pressure of component i at T

R = gas constant

= liquid molar volume of component i at T and P

= fugacity coefficient of pure component i at T and Pisat

Equation (3-10) provides two correction factors for the pure liquid fugacity. The fugacity coefficient, , corrects for deviations of the saturated vapor from ideal-gas behavior. The exponential cor-rection factor, known as the Poynting correction factor, corrects for the effect of pressure on the liquid fugacity. The Poynting correc-tion factor is usually negligible for low and moderate pressures.

Combining equations (3-6), (3-8), and (3-9) yields:

(3-11)

Combining equations (3-7) and (3-9) yields:

(3-12)

If an equation of state is applied to both vapor and liquid phases, the vapor-liquid K-values can be written as:

(3-13)

The liquid-liquid equilibria can be written as:

(3-14)

Equations (3-11), (3-12), (3-13), and (3-14) are used to calculate the distribution of components between phases.


For vapor-liquid equilibria, equation-of-state methods may be used to calculate the fugacity coefficients for both liquid and vapor phases using equation (3-13). One important limitation of equation-of-state methods is that they have to be applicable over a wide range of densities, from near-zero density for gases to high liquid densi-ties, using constants obtained from pure-component data. Equations of state are not very accurate for non-ideal systems unless combined with component mixing rules and alpha formulations appropriate for those components. See “Equations of State” on page 34.

Equation (3-11) may be solved by using equation-of-state methods to calculate vapor fugacities combined with liquid activity methods to compute liquid activity coefficients. See “Liquid Activity Coeffi-cient Methods” on page 62. Liquid activity methods are most often used to describe the behavior of strongly non-ideal mixtures.

Reference

1 Prausnitz, J. M., Lichtenthaler, R. N., and Gomes de Aze-vedo, E., 1986, Molecular Thermodynamics of Fluid-Phase Equilibria, 2nd Ed., Prentice-Hall, N.Y.

2 Sandler, S. I., 1989, Chemical and Engineering Thermody-namics, 2nd ed., John Wiley & Sons, New York.

3 Smith, J. M. and Van Ness, H. C., 1987, Introduction to Chemical Engineering Thermodynamics, 4th ed., McGraw-Hill, New York.

4 Van Ness, H. C. and Abbott, M. M., 1982, Classical Ther-modynamics of Non-electrical Solutions: With Applica-tions to Phase Equilibria, McGraw-Hill, New York.

Enthalpy The enthalpy of a system, H, is defined in terms of the energy of the system, U as follows:

(3-15)

where: H = enthalpy of the system of nT moles

U = internal energy of the system of nT moles

V = total volume of the system


At constant temperature and pressure, the internal energy of the sys-tem is related to the volume by:

(3-16)

The enthalpy of the system is then given by:

The enthalpy of the system is then given by:

(3-17)

where: H* = mixture ideal gas enthalpy =

= molar enthalpy of ideal gas i at temperature T

z = compressibility factor ≡ PV/nTRT

PRO/II provides two distinct approaches to the calculation of enthalpy. For the majority of thermodynamic systems of methods, enthalpy is calculated as a departure from the ideal-gas enthalpy of the mixture. Enthalpy departure functions for both vapor and liquid phases are calculated by an equation of state or corresponding states model.

For liquid activity coefficient thermodynamic systems, however, PRO/II, by default, invokes the LIBRARY thermodynamic method for vapor and liquid enthalpy calculations.

The LIBRARY method consists of two correlations. The first corre-lates saturated-liquid enthalpy as a function of temperature and the second correlates latent heat of vaporization, also as a function of temperature. At temperatures below the critical, vapor enthalpy is calculated by adding the latent heat to the saturated liquid enthalpy at the system temperature. In other words, the vapor enthalpy is the saturated vapor enthalpy at the system temperature. For both phases, the pressure is implicitly the saturated vapor pressure at the system temperature. No other pressure correction term is applied.

For almost all library components, the correlations in use for liquid enthalpy can be used safely up to a reduced temperature, T/Tc, of


approximately 0.9. Tc is the temperature at the critical point, beyond which vapor and liquid become indistinguishable.

Note: The normal boiling point of a library component typically occurs when Tr is approximately equal to 0.7.

In general, the use of liquid activity coefficient models is not rec-ommended for system pressures above 1000 kPA. Below these con-ditions, the use of LIBRARY enthalpy methods will not introduce significant errors provided that the system temperature is below the critical temperatures of all components present in significant quan-tities. Quite often, however, we would like to use a liquid activity coefficient model when permanent gases are present in the mixture. As the system temperature is usually above the critical temperature of these gases, there is no standard-state liquid fugacity at system conditions, so we replace that term by the Henry's Law constant. However, the problem of adding the super-critical components' con-tribution to the liquid enthalpies remains. For the liquid phase con-tribution, PRO/II extrapolates the component's saturated liquid enthalpy curve linearly from the critical temperature.Above the crit-ical this extrapolation uses the slope of the library enthalpy tangent to the liquid saturation curve at the normal boiling point. At temper-atures above the critical, there is no distinction between vapor and liquid phases and the vapor enthalpy is set equal to the extrapolated liquid enthalpy. The point at which the slope for linear extrapolation is obtained is chosen quite arbitrarily; as mentioned, we use the nor-mal boiling point temperature.

Note: At temperatures near Tc, the enthalpy of the saturated vapor for a pure component exhibits a decrease with temperature. This can lead to the computation of a negative value of the constant-pressure heat capacity Cp when using the LIBRARY method for vapor enthalpies. This is entirely an artifact of the fact that the sat-uration curve is not a constant-pressure path. The printout of a negative heat capacity is therefore a sign that the temperature is too high to be using LIBRARY vapor enthalpies, and the user should switch to another method.

For low pressure and temperatures well below the lowest critical, LIBRARY enthalpies are often satisfactory. For high pressures or temperatures above the critical of a component, it will usually be better to use an equation of state for vapor and, possibly, liquid enthalpies. Beware, however, if a liquid activity coefficient method was selected for K-value; in such systems the traditional cubic equation of state may not be capable of describing the liquid phase


non-ideality, and it is therefore unlikely that the equation of state will predict the correct liquid phase enthalpy. In this situation, one of the more advanced cubic equations using an alpha formulation which correctly predicts pure component vapor pressures, is a better choice. As the contribution to the liquid enthalpy of dissolved super-critical components is usually small, the LIBRARY method can usually safely be used for liquid enthalpies. Ideal-gas based enthalpies and saturation enthalpies can be used in combination for vapor and liquid, respectively, for defined components because the ideal-gas enthalpy datum has been fixed relative to the saturated-liquid enthalpy datum (HL = 0 at T = 273.15 K). For components that are sub-critical at 273.15 K, the SRK vapor enthalpy departure function, which applied to the ideal gas enthalpy, gives the equiva-lent results as adding the latent heat to zero-liquid enthalpy. For components that are super-critical at 273.15 K, using an alpha for-mulation will give consistent results between departure-based and library enthalpies.

Entropy The entropy of a system, S, is defined in terms of the enthalpy, as follows:

(3-18)

and

(3-19)

where: φ = fugacity coefficient of mixture

= reference pressure of 1 atmosphere

S* = mixture ideal-gas entropy

= molar entropy of ideal gas i

ni = moles of component i

xi = mole fraction of component i

The ideal molar entropy is related to the ideal molar enthalpy by:


(3-20)

where:

= reference temperature, 1 degree Rankine in PRO/II

= ideal-gas heat capacity of component i

Ideal-gas entropy at the reference temperature is set equal to zero.

As for enthalpy computations, liquid and vapor entropies are calcu-lated in PRO/II using either an equation of state method such as SRKM, or a generalized correlation method such as Curl-Pitzer.

Density Cubic equation-of-state methods are generally not very accurate in predicting liquid densities. More accurate predictive methods have been developed especially for liquid mixtures. Such methods include the API and Rackett correlation methods. These methods are described in detail in Section, Generalized Correlation Methods.

Vapor densities are computed in PRO/II using the following formu-lae:

(3-21)

(3-22)

where:

= vapor density


v = molar vapor volume

z = compressibility factor

Vapor densities can be predicted quite accurately using equation of state methods, in addition to generalized correlation methods. The IDEAL vapor density method corresponds to z=1.


Application Guidelines

General InformationChoosing an appropriate thermodynamic method for a specific application is an important step in obtaining an accurate process simulation. Normally, there may be any number of thermodynamic methods suitable for a given application. The user is left to use his or her best judgement, experience, and knowledge of the available thermodynamic methods to choose the best method.

It is important to note that for most thermodynamic methods, the PRO/II databanks contain adjustable binary parameters obtained from fitting published experimental and/or plant data. The thermo-dynamic method chosen should ideally be used only in the tempera-ture and pressure ranges at which the parameters were regressed. Ideally, for each simulation, actual experimental or plant data should be regressed in order to obtain the best interaction parame-ters for the application.

There are several places where the user can find information and guidelines on using the thermodynamic methods available in PRO/II. These are:

PRO/II Case books

PRO/II Application Briefs Manual

These show how PRO/II is used to simulate many refinery, chemi-cal, and petrochemical processing applications using the thermody-namic methods appropriate to each system.

Refinery and Gas ProcessesThese processes may be subdivided into the following:

Low pressure crude systems (vacuum towers and atmospheric stills)

High pressure crude systems (including FCCU main fraction-ators, and coker fractionators)

Reformers and hydrofiners

Lube oil and solvent de-asphalting units


Low Pressure Crude UnitsLow pressure crude units generally contain less than 3 volume% light ends. Moreover, the petroleum fractions present in the feed exhibit nearly ideal behavior. For these units, the characterization of the petroleum fractions is far more important than the thermody-namic method used. The user should try different assay and charac-terization methods first if the simulation results do not match the plant data.

Since these units contain a small amount of light ends, the Braun K10 (BK10) method should be used quickly as a first attempt, and will likely give acceptable answers. The BK10 method does, how-ever, provide only gross estimates for the K-values for H2, and is not recommended for streams containing H2. For such systems, and for other systems where the BK10 results are not satisfactory, the Grayson-Streed (GS), Grayson-Streed Erbar (GSE), or Improved Grayson-Streed (IGS) methods should be chosen. These methods contain special coefficients for hydrogen and methane, and as such, provide better predictions for streams containing small amounts of H2 at low pressures. It is important to note that the pre-defined ther-modynamic systems GS, GSE, and IGS use the Curl-Pitzer (CP) method for calculating enthalpies. For systems containing heavy ends such as vacuum towers, however, the saturated vapor is often at reduced temperatures of less than 0.6. This is the lower limit of the Curl-Pitzer enthalpy method. For these units, therefore, substi-tuting the Lee-Kesler (LK) method for Curl-Pitzer enthalpies may improve the results.

In addition, the top of many of these low pressure units often con-tain significant amounts of light components such as methane. Under these conditions, an equation of state method such as Soave-Redlich-Kwong (SRK) or Peng-Robinson (PR) will provide better answers than the BK10 or Grayson-Streed methods.

Table 3-1: Methods Recommended for Low Pressure Crude Systems

BK10 Gives fast and acceptable answers.

GS/GSE/IGS Generally more accurate than BK10 especially for streams containing H2. Use LK enthalpies instead of CP enthalpies for vacuum towers.


High Pressure Crude UnitsHigh pressure crude units generally contain greater amounts of light ends than low pressure units. Still, for these units, as for the low pressure crude units, the characterization of the petroleum fractions remains far more important than the thermodynamic method used. The user should again try different assay and characterization meth-ods first if the simulation results do not match the plant data. Since these units contain larger amounts of light ends, the GS, GSE, IGS, SRK or PR methods should be used, and will likely give acceptable answers.

For FCCU main fractionators, the petroleum fractions are much more hydrogen deficient than are crude fractions. Since most char-acterization correlations are derived from crude petroleum data, it is expected that the results will be less accurate than for crude frac-tions.

Table 3-2: Methods Recommended for High Pressure Crude Systems

GS/GSE/IGS Quicker but generally less accurate than SRK or PR, especially for streams containing light ends. Use LK enthalpies instead of CP enthalpies for vacuum towers.

SRK/PR Provides better results when light ends dominate.

Reformers and HydrofinersThese units contain streams with a high hydrogen content. The Grayson-Streed method, which contains special liquid activity curves for methane and hydrogen, may be used to provide adequate answers. For the SRK and PR methods, the PRO/II databanks con-tain extensive binary interaction parameter data for component pairs involving hydrogen.

SRK/PR Provides better results when light ends dominate.

Table 3-1: Methods Recommended for Low Pressure Crude Systems

Table 3-3: Methods Recommended for Reformers and Hydrofiners

GS/GSE/IGS Quicker but generally less accurate than SRK or PR, especially for predicting the hydrogen content of the liquid phase.


These methods provide results comparable or better than the GS methods. Moreover, these methods are more accurate than GS methods in predicting the hydrogen solubility in the liquid phase. If the user wishes to obtain the most accurate prediction of hydrogen solubility in the hydrocarbon liquid phase, he/she should use the SimSci modified SRK or PR methods, SRKM or PRM.

Lube Oil and Solvent De-asphalting UnitsThese units contain streams with non-ideal components such as H2S and mercaptans. The SimSci modified SRK or PR methods, SRKM or PRM, are recommended, but only if user-supplied binary interaction data are available. If no binary interaction data specifi-cally regressed for the system are available, then the data in the PRO/II databanks can be used, and the SRK or PR methods are rec-ommended.

Table 3-4: Methods Recommended for Lube Oil and Solvent

De-asphalting Units

SRKM/PRM

Recommended when user-supplied binary interac-tion data are available

SRK/PR Recommended when no user-supplied binary interaction data are available

Natural Gas ProcessingNatural gas systems often contain inerts such as N2, acid or sour gases such as CO2, H2S, or mercaptans, and water, along with the usual light hydrocarbon components. Natural gas streams may be treated by a number of methods, e.g., to sweeten using amines, or to dehydrate using glycol.

For natural gas systems containing less than 5% N2, CO2, or H2S, but no polar components, SRK, PR, or BWRS methods provide excellent answers. The SRK and PR binary interaction parameters between these lower molecular weight molecules and other compo-nents are estimated by correlations based on the molecular weight

SRK/PR Provides better results than GS methods.

SRKM/PRM Provides better results than SRK/PR when predicting the hydrogen content of the liquid phase.

Table 3-3: Methods Recommended for Reformers and Hydrofiners


of the hydrogen molecule. For small amounts of these components, this is satisfactory. The BWRS equation of state also contains many binary interaction parameters for component pairs involving lower weight components supplied in Dechema. Unlike cubic equations of state such as SRK or PR, the BWRS equation of state does not satisfy the critical constraints, and so does not extrapolate well into the critical region.

For natural gas systems containing more than 5% N2, CO2, or H2S, but no polar components, equation-of-state methods such as SRK or PR are still recommended, although the binary parameters esti-mated by molecular weight correlations may not produce the best results. The user should provide binary interaction parameters for component pairs involving these lower molecular weight compo-nents if possible.

For natural gas systems containing water at low pressures, equa-tion-of-state methods such as SRK or PR may be used, along with the default water decant option, to predict the behavior of these sys-tems.

Table 3-5: Methods Recommended for Natural Gas Systems

SRK/PR/ BWRS

Recommended for most natural gas and low pres-sure natural gas + water systems

SRKKD Recommended for high pressure natural gas + water systems

SRKM/PRM /SRKS

Recommended for natural gas + polar components

For these systems at high pressures, where the solubility of hydro-carbon in water is significant, the default water decant option, which predicts a pure water phase, is unacceptable. In this case, equation-of-state methods containing advanced mixing rules such as SRKM, PRM or SRKS, or the Kabadi-Danner modification to SRK (SRKKD) should be used to predict the vapor-liquid-liquid behavior of these systems. These methods provide the best answers if all the relevant binary interaction parameters are available. For the SRKKD method in particular, PRO/II contains binary interac-tion parameters for component pairs involving N2, H2, CO2, CO, and H2S. For SRKM, PRM, or SRKS methods, the user should make sure that all relevant binary interaction data are entered.


For natural gas systems containing polar components such as meth-anol, the SRKM, PRM, or SRKS methods are recommended to pre-dict the vapor-liquid-liquid behavior of these systems.

The processes used to treat natural gas streams may be sub-divided into the following:

Glycol dehydration systems

Sour water systems

Amine systems.

Glycol Dehydration SystemsThe predefined thermodynamic system GLYCOL has been spe-cially created for these systems. This system uses the predefined system SRKM but invokes the GLYCOL databank. This databank contains binary interaction parameters for component pairs involv-ing glycols tri-ethylene glycol (TEG) and, to a lesser extent, dieth-ylene glycol (DEG) and ethylene glycol (EG). These data have been regressed in the temperature and pressure range normally seen in glycol dehydrators:

Temperature: 80-400 οF

Pressure: up to 2000 psia

This method is described in more detail in page 3-93, of this man-ual, Special Packages.

SourWater SystemsThe standard version of PRO/II contains two methods, SOUR and GPSWATER, for predicting the VLE behavior of sour water sys-tems. These methods are described in more detail in Special Pack-ages Section. The recommended temperature, pressure and composition ranges for each method is given in Table 3-6 below.

Table 3-6: Methods Recommended for Sour Water SystemsSOUR Recommended Ranges:

68 < T (F) < 300 P(psia) < 1500 wNH3 + wCO2 + wH2S < 0.30


Amine SystemsAmine systems used to sweeten natural gas streams may be mod-eled in PRO/II using the AMINE special package (see Section, Spe-cial Packages). Data is provided for amines MEA, DEA, DGA, DIPA, and MDEA. Results obtained for MEA and DEA are accu-rate enough for use in final design work. However, results for DIPA systems are not suitable for final design work. For MDEA or DGA systems, the results may be made to more closely fit plant data by the use of a dimensionless residence time correction.

The recommended temperature, pressure, and loading ranges (gram-moles sour gases per gram-moles amine) for each amine sys-tem available in PRO/II is given in Table 3-7.

GPSWATER

Recommended Ranges: 68 < T(F) < 600 P(psia) < 2000 wNH3 < 0.40 PCO2 + PH2S < 1200 psia

Electrolyte Version of PRO/II

Recommended when strong electrolytes such as caustic are used, or when pH control or accurate prediction of HCN or phenol phase distribution is important. Recommended Ranges: 32 < T(°F) < 400 P(psia) < 3000 x dissolved gases < 0.30

Table 3-6: Methods Recommended for Sour Water Systems

Table 3-7: Methods Recommended for Amine SystemsMEA Recommended Ranges:

25 < P(psig) < 500 T(οF) < 275 wamine ~ 0.15 - 0.25 0.5-0.6 gmole gas/gmole amine

DEA Recommended Ranges: 100 < P(psig) < 1000 T(οF) < 275 wamine ~ 0.25 - 0.35 0.45 gmole gas/gmole amine

DGA Recommended Ranges: 100 < P(psig) < 1000 T(οF) < 275 wamine ~ 0.55 - 0.65 0.50 gmole gas/gmole amine


Petrochemical Applications

Common examples of these processes are the following:

Light hydrocarbon applications

Aromatic systems

Aromatic/non-aromatic systems

Alcohol dehydration systems

Light Hydrocarbon ApplicationsMost light hydrocarbon mixtures at low pressures may be modeled well by the SRK or PR equations of state. The BWRS equation of state, which was developed for light hydrocarbon mixtures is also recommended, but not near the critical region. At high pressures, the SRKM or SRKS equation of state should be used to best predict the water solubility in the hydrocarbon phase. The COSTALD liq-uid density was developed expressly for light hydrocarbon mix-tures. This method is over 99.8% accurate in predicting the liquid densities of these mixtures, and should be requested by the user.

Table 3-8: Methods Recommended for Light HydrocarbonsSRK/PR/ BWRS

Recommended for systems of similar light hydrocarbons at low pressures

SRKM /SRKS

Recommended at higher pressures

COSTALD Recommended for liquid density

Aromatic SystemsMixtures of pure aromatic components such as aniline, and nitro benzene at low pressures less than 2 atmospheres exhibit close to

MDEA Recommended Ranges: 100 < P(psig) < 1000 T(οF) < 275 wamine ~ 0.50 0.40 gmole gas/gmole amine

DIPA Recommended Ranges: 100 < P(psig) < 1000 T(οF) < 275 wamine ~ 0.30 0.40 gmole gas/gmole amine

Table 3-7: Methods Recommended for Amine Systems


ideal behavior. Ideal methods can therefore be used to predict phase behavior, and compute enthalpies, entropies, and densities. At pres-sures above 2 atmospheres, the Grayson-Streed, or SRK, or PR methods provide good results in the prediction of phase equilibria. The SRK or PR equations of state should provide better results, but with a small CPU penalty.

Table 3-9: Methods Recommended for AromaticsIDEAL Recommended for systems at low pressures below 2

atm

GS/ SRK/ PR Recommended at pressures higher than 2 atm

IDEAL/ API/ COSTALD

Recommended for liquid density. The COSTALD method is best at high temperatures and if light components such as CH4 are present.

Aromatic/Non-aromatic SystemsSystems of mixtures of aromatic and non-aromatic components are highly non-ideal. Liquid activity methods such as NRTL or UNI-QUAC, or equation-of-state methods with advanced mixing rules such as SRKM or SRKS can be used to model these systems. Both types of methods can be used to successfully model aromatic/non-aromatic mixtures, provided that all the binary interaction data for the components in the system are provided. The PRO/II databanks contain an extensive variety of interaction data for the NRTL and UNIQUAC, and SRKM methods. One advantage to using the liquid activity methods NRTL or UNIQUAC however, is that the FILL option may be used to fill in any missing interaction parameters using UNIFAC. All library components in the PRO/II databanks have UNIFAC structures already defined. PRO/II also will estimate UNIFAC structures for petro components based on their Watson K and molecular weight values, and the user may supply UNIFAC structures for components not in the PROII databanks.

When gases such as H2, N2, or O2 are present in small quantities (up to about 5 mole %), the Henry's Law option may be used to cal-culate the gas solubilities. Once the Henry's Law option is selected by the user, PRO/II arbitrarily defines all components with critical temperatures less than 400 Kelvin as solute components, though the user may override these selections.


For large amounts of super-critical gases, an equation-of-state method with an advanced mixing rule should be used to predict the phase behavior.

Table 3-10: Methods Recommended for Aromatic/Non-aromatic Systems

SRKM/ PRM

Recommended at high pressures or when > 5 mole % super-critical gases are present

NRTL/ UNIQUAC

Recommended with the FILL option when binary interaction parameters are not available or with the HENRY option when < 5 mole % super-critical gases are present

Alcohol Dehydration SystemsThe PRO/II special package ALCOHOL is recommended for sys-tems containing alcohols with water. This package uses a special databank of NRTL parameters containing interaction parameters expressly regressed under temperature and pressure conditions commonly found in dehydration systems. The NRTL method is suggested if user-supplied interaction data are to be used.

Table 3-11: Methods Recommended for Alcohol SystemsALCOHOL Recommended for all alcohol dehydration systems.

NRTL/ UNIQUAC

Recommended when user-supplied data are provided.

Chemical Applications

Non-ionic SystemsThese systems, which typically contain oxygen, nitrogen, or halo-gen derivatives of hydrocarbons such as amides, esters, or ethers, are also similar to non-hydrocarbon systems found in petrochemical applications. For low pressure systems, a liquid activity coefficient method is recommended. For single liquid phase systems, the WIL-SON, NRTL, or UNIQUAC methods are equally good, provided all interaction parameters are provided. PRO/II databanks contain extensive parameters for NRTL and UNIQUAC, but the user must supply interaction data for the WILSON method. The WILSON method is the simplest, and requires the least CPU time.

For systems with two liquid phases, the NRTL or UNIQUAC meth-ods should be used, provided that at least some interaction data is


available. The FILL option can be used to fill in any missing inter-action data using the UNIFAC method. If no interaction data are available, the UNIFAC method should be used since the PRO/II databanks contain a large amount of group interaction data for both VLE and LLE applications. For moderate pressure systems up to 10 atmospheres, a liquid activity method can still be used, provided that the interaction parameters used are still valid in that pressure range. For example, if the system pressure were much higher than the pressure at which the interaction parameters were regressed, the vapor phase fugacity may be taken into account in modeling the phase behavior. If the PHI option is selected, the liquid-phase Poynting correction factor is automatically selected also.

It is also important to note that all the interaction parameters in the PRO/II databanks, except for dimerizing components such as car-boxylic acids, were regressed without including any vapor-phase nonideality. This means that the PHI option should be used for car-boxylic acid systems at all pressures, but should only be used for most components at high pressures. For systems containing compo-nents such as carboxylic acids that dimerize in the vapor phase, the Hayden-O'Connell fugacity method may be used to calculate all vapor-phase properties such as fugacity, enthalpy, and density. For components such as hydrogen fluoride which forms hexamers in the vapor phase, PRO/II contains an equation of state specially created for such systems, HEXAMER. This method is recommended for processes such as HF alkylation or the manufacture of refrigerants such as HFC-134a. For all other components, an equation-of-state method such as SRK or PR may be used to calculate vapor-phase fugacities.

When super-critical gases are present in small quantities (generally less than 5 mole %), the Henry's Law option should be used to com-pute gas solubilities. For high pressure systems, greater than 10 atmospheres, or for systems with large quantities of super-critical gas, an equation-of-state method using an advanced mixing rule such as SRKM or PRM should be used. The UNIWAALS equation-of-state method uses UNIFAC structure information to predict phase behavior. This method is useful when interaction data are not


available and, unlike a liquid activity method such as UNIFAC, is able to handle super-critical gases.

Table 3-12: Methods Recommended for Non-ionic Chemical Systems

WILSON Recommended for single liquid phase slightly non-ideal mixtures. If all interaction data are not available use the FILL=UNIFAC option.

NRTL/ UNIQUAC

Recommended for all non-ideal mixtures. Use with the FILL option when binary interaction parameters are not available or with the HENRY option when < 5 mole % super-critical gases are present. For moderate pressures use the PHI option for vapor phase nonidealities.

SRKS/SRKM/ PRM/ UNIWAALS

Recommended for high pressure systems or when > 5 mole % super-critical gases are present.

HOCV Recommended for vapor fugacity and enthalpy and density calculations in systems containing dimerizing components such as carboxylic acids. Use with a liquid activity method.

HEXAMER Recommended for systems containing hexamerizing components such as HF.

Ionic SystemsA special version of PRO/II expressly made for aqueous electro-lytes is recommended when modeling these systems. This version combines the PRO/II flow-sheet simulator with rigorous electrolyte thermodynamic algorithms developed by OLI Systems, Inc. Chemi-cal systems which may be modeled by this special version include amine, acid, mixed salts, sour water, caustic, and Ben-field systems. See Sections, Electrolyte Mathematical Model, and 1.2.10, Electro-lyte Thermodynamic Equations for further details.

Table 3-13: Methods Recommended for Ionic Chemical Systems

PRO/II Electrolyte Version

Environmental ApplicationsThese systems typically involve stripping dilute pollutants out of water. By themselves, liquid activity methods such as NRTL do not model these dilute systems with much accuracy. A better approach


is to use a liquid activity method in combination with Henry's Law constants at the process temperature to model these dilute aqueous systems. PRO/II contains Henry's Law constants for many compo-nents such as HCl, SO2, and ethanediol in water. Some additional Henry's Law constants for chlorofluorocarbons (CFC’s) and hydrof-luorocarbons (HFC’s) in water are also available in the PRO/II data-banks. Other sources for Henry's Law data include the U.S. Environmental Protection Agency.

Table 3-14: Methods Recommended for Environmental Applications

Liquid Activity Method + Henry's Law Option

Solid ApplicationsSolid-liquid equilibria for most systems can be represented in PRO/II by the van’t Hoff (ideal) solubility method or by using user-sup-plied solubility data. In general, for those systems where the solute and solvent components are chemically similar and form a near-ideal solution, the van’t Hoff method is appropriate. For non-ideal systems, solubility data should be supplied. For many organic crys-tallization systems, which are very near ideal in behavior, the van’t Hoff SLE method provides good results. The VLE behavior can usually be adequately represented by IDEAL or any liquid activity methods. Precipitation of solid salts and minerals from aqueous solutions can be calculated more rigorously by using the electrolyte version of PRO/II.

Table 3-15: Methods Recommended for Solid ApplicationsIdeal or Liquid Activity Method(VLE) + VANT HOFF Method (SLE)

Recommended for most solid systems involving organics.

PRO/II Electrolyte Version Recommended for solid salt and mineral precipitation from aqueous solutions.

Generalized Correlation Methods

General InformationVapor-liquid equilibria can be predicted for hydrocarbon mixtures using various general correlation methods. Examples of these are those developed by Chao and Seader, or Grayson and Streed. Vapor-liquid equilibria can also be predicted by convergence pres-sure correlations such as the K10 charts developed by Cajander et


al. Densities, enthalpies, and entropies can also be calculated using a number of correlation methods such as Lee-Kesler, and COS-TALD.

Ideal (IDEAL)Ideal K-values are generally applicable to systems which exhibit behavior close to ideality in the liquid phase. Mixtures of similar fluids often exhibit nearly ideal behavior. In an ideal solution at constant temperature and pressure, the fugacity of every component is proportional to its mole fraction. For every component i, the fol-lowing fundamental thermodynamic equilibrium relationship holds:

(3-23)

where:

superscript L refers to the liquid phase

superscript V refers to the vapor phase

= fugacity of component i

In the vapor phase, the fugacity is assumed to be equal to the partial pressure:

(3-24)

where:

= vapor mole fraction

P = system pressure

In the liquid phase for an "ideal" liquid (ignoring correction factors that are usually small):

(3-25)

where: = liquid mole fraction

= pure component i liquid fugacity

= vapor pressure of component i at the system temperature

Raoult's law thus holds:


(3-26)

The ideal K-value is therefore given by:

PPxyK isat

iii // ==(3-27)

Note that there is no compositional dependency of the K-values. They are only a function of temperature (due to the dependence of Pisat on T) and pressure.

Ideal vapor densities are obtained from the ideal gas law:

(3-28)

where: ρ = vapor density of mixture

Ideal-liquid densities are obtained from pure-component saturated-liquid density correlations.

Ideal liquid enthalpies are obtained from pure-component liquid enthalpy correlations, and the corresponding vapor enthalpies are obtained by adding in the effect of the known latent heat of vapor-ization of the component.

Ideal entropies are calculated from the ideal enthalpy data using the following equation

(3-29)

where:

= ideal entropy

= ideal component heat capacity

= ideal enthalpy

= reference temperature (1 degree Rankine)

T = temperature of mixture

Chao-Seader (CS)Chao and Seader calculated liquid K-values for the components of non-ideal mixtures using the relationship:


(3-30)

where:

= the standard-state fugacity of component i in the pure liquid phase

γi= the activity coefficient of component i in the equilibrium liq-uid mixture

= the fugacity coefficient of component i in the equilibrium vapor mixture

It was shown that γi could be calculated from molar liquid volumes and solubility parameters, using the Scatchard-Hildebrand equation, with regular liquid solution assumed. The Redlich-Kwong equation of state was used to evaluate φ. (See “Equations of State” on page 34.) Chao and Seader presented a generalized correlation for fi0L/P, the fugacity coefficient of pure liquid "I" in real and hypo-thetical states.

In the development of their correlation for their vapor-liquid K-value correlation, Chao and Seader used the framework of Pitzer's modified form of the principle of corresponding states for the pure-liquid fugacity coefficients, giving values of fi0L/P as a function of reduced temperature, reduced pressure, and acentric factor for both real and hypothetical liquids:

(3-31)

where: ω = acentric factor

The first term on the right hand side of equation (3-31) represents the fugacity coefficient of simple fluids. The second term is a cor-rection accounting for the departure of the properties of real fluids from those of simple fluids.

Limitations of the Chao-Seader method are given below:

For all hydrocarbons (except methane);

Pressure: up to 2000 psia, but not exceeding 0.8 of the critical pres-sure of the system.


Temperature: -100 oF to 500 oF, and pseudo-reduced temperature, Tr, of the equilibrium liquid mixture less than 0.93. The pseudo-reduced temperature is based on the molar average of the critical temperatures of the components.

Concentration: up to 20 mole % of other dissolved gases in the liq-uid.

This method is not suitable for other non-hydrocarbon compo-nents such as N2, H2S, CO2, etc.

Reference

Chao, K. C., and Seader, J. D., 1961, A Generalized Correlation of Vapor-Liquid Equilibria in Hydrocarbon Mixtures, AIChE J., 7(4), 598-605.

Grayson-Streed (GS) Grayson and Streed modified the Chao-Seader correlation in 1963 by fitting data over a wider range of conditions and hence deriving different constants for the equations giving the fugacity coefficients of the pure liquids. Special coefficients for hydrogen and methane are supplied because typical application temperatures are far above the critical points of these two components. Grayson and Streed's modifications have extended the application range for hydrocarbon systems up to 800 oF and 3000 psia. The lower limits imposed by Chao and Seader still apply.

Reference

Grayson, H. G., and Streed, C. W., 1963, Vapor-Liquid Equilibria for High Temperature, High Pressure Hydrocarbon-Hydrocarbon Systems, 6th World Congress, Frankfurt am Main, June 19-26.

Erbar Modification to Chao-Seader (CSE) and Grayson-Streed (GSE)In 1963, Erbar and Edmister developed a new set of constants for the Chao-Seader liquid fugacity coefficient specifically for N2, H2S, and CO2, in order to improve the prediction of the K-values of these gases. At the same time, new solubility parameter and molar volume values were found for these components.

A limitation of this modified method, however, is that the H2S cor-relation cannot be used in any cases where an azeotrope may exist (e.g., H2S/C3H8 mixtures), as the azeotrope will not be predicted.


Reference

Erbar, J. H., and Edmister, W. C., 1963, Vapor-Liquid Equilibria for High Temperature, High Pressure Hydrocarbon-Hydrocarbon Sys-tems, 6th World Congress, Frankfurt am Main, June 19-26.

Improved Grayson-Streed (IGS)For hydrocarbon-water mixtures, the Grayson-Streed and Erbar-modified Grayson-Streed methods accurately predict the phase behavior of the hydrocarbon-rich phase, but does not do as well in predicting the water-rich phase. A separate set of solubility parame-ters was used in the water-rich phase, and a new set of liquid fugac-ity coefficients developed for N2, H2O, H2S, CO, and O2. This new method is known as the Improved Grayson-Streed. It was found that the Grayson-Streed liquid fugacity coefficient for the "simple" fluid decreases rapidly as Tr increases above 2.5, and can in fact become negative. The liquid fugacity coefficient for the "simple" fluid was therefore replaced by that for hydrogen at reduced temperatures of 2.5 and above.

Curl-Pitzer (CP)This correlation may be used to predict both liquid and vapor enthalpies and entropies. It computes the enthalpy deviation using the principle of corresponding states, i.e. in terms of the reduced temperature, reduced pressure, and acentric factor. The critical tem-perature and pressure for the mixture is computed using the mixture rules of Stewart, Burkhart, and Voo. The mixture acentric factor used is the molar average value.

The Curl-Pitzer method is limited to nonpolar mixtures, and may be used for Pr up to 10, and Tr from 0.35 to 4.0 for liquids, and Tr from 0.6 to 4.0 for vapors. For systems containing heavy ends, the satu-rated vapor is sometimes at a reduced temperature of less than 0.6. In this case, the CP correlation extrapolates reasonably, producing satisfactory results.

The Curl-Pitzer method is generally useful for refinery hydrocar-bons, and in oil absorption gas plants.

Reference

5 Stewart, Burkhart, and Voo, 1959, Prediction of Pseudo-Critical Constants for Mixtures, Paper presented at AIChE Meeting, Kansas City.


6 American Petroleum Institute, 1970, Technical Data Book - Petroleum Refining, 2nd Ed., Procedure 7B3.1, 7-29 - 7-286.

7 American Petroleum Institute, 1970, Technical Data Book - Petroleum Refining, 2nd Ed., Procedure 7H2.1, 7-201 - 7-202.

Braun K10 (BK10)The K-value of each component is a function of the system temper-ature, pressure, and the composition of the vapor and liquid phases. For natural gas systems, the convergence pressure can be used as the parameter that represents the composition of the vapor and liq-uid phases in equilibrium. The convergence pressure is, in general, the critical pressure of a system at a given temperature at which the K-values of all components converge to unity (when the system pressure reaches the convergence pressure).

The Braun K10 charts developed by Cajander et al. in 1960 show the low pressure equilibrium ratio, arbitrarily taken at 10 psia sys-tem pressure and 5000 psi convergence pressure. For many hydro-carbon systems, no experimental data are available. For these cases, the equilibrium K-values may be predicted from vapor pressure:

K10 = Psat / 10 (3-32)

where:

= saturated vapor pressure in psia.

The relationship given in equation (3-32) only holds for K-values less than 2.5. For H2, the K-value is assumed to be 10 times as large as the methane value. For N2, O2, and CO, the K-values are assumed to be identical to that of methane. The K-values for CO2 and H2S are assumed to be identical to that of propylene.

For petroleum fractions in which the form of the vapor pressure curve is unknown, a rough K10 chart is developed from the normal boiling point of the fraction. The following method is used:

On the appropriate K10 chart, the point K10 = 14.7/10 = 1.27 is plotted at the atmospheric boiling point.

The whole K10 curve can then be sketched in by similitude to the known K10 curves for homologous hydrocarbons.


The K10 charts apply to mixtures that behave ideally at low pres-sures, e.g., for mixtures of one molecule type such as mixtures of paraffins and olefins. For mixtures of naphthalenes mixed with ole-fins and paraffins, the accuracy of BK10 is slightly poorer. Large errors can be expected for mixtures of aromatics with paraffins, ole-fins, or naphthalenes, which cause non-idealities and form azeo-tropes.

Reference

Cajander, B. C., Hipkin, H. G., and Lenior, J. M., 1960, Prediction of Equilibrium Ratios from Nomographs of Improved Accuracy, J. Chem. Eng. Data, 5(3), 251-259.

Johnson-Grayson (JG)This correlation may be used to predict both liquid and vapor enthalpies. It is essentially an ideal-enthalpy correlation, using satu-rated liquid at 0 C as the datum for the correlation (-200 F in ver-sions 3.5 and earlier). Vapor phase corrections are calculated using the Curl-Pitzer correlation. Pressure effects are not considered for the liquid phase.

Johnson-Grayson is useful for systems containing heavy ends between 0 F and 1200 F. However, it can be extrapolated to higher temperatures. The correlation should not be used if the mixture is C4-C5 or lighter.

Reference

Johnson, and Grayson, 1961, Enthalpy of Petroleum Fractions, Petroleum Refiner, 40(2), 123-29.

Lee-Kesler (LK)This correlation may be used to predict both liquid and vapor enthalpies, entropies, and densities. This correlation uses the three-parameter corresponding-states theory, which essentially states that all fluids having the same acentric factor must have the same prop-erties at the same reduced temperature and pressure. Special mixing rules have been used to calculate the mixture reduced properties. For most fluids, the Lee-Kesler method is 98% accurate in predict-ing the gas phase compressibility factors. The method also gives reasonable results for slightly polar mixtures. This method is not recommended for highly polar mixtures, or those which form strongly associative hydrogen bonds. However, the Lee-Kesler method provides accurate results for polar fluids at low tempera-


tures near the saturated vapor region. The Lee-Kesler method is not recommended for calculating liquid densities of hydrocarbons heavier than C8.

Reference

8 American Petroleum Institute, 1975, Technical Data Book, Petroleum Refining, 3rd Ed., 2-1 - 7-4.

9 Lee, B. I., and Kesler, M. G., 1975, A Generalized Thermo-dynamic Correlation Based on Three-Parameter Corre-sponding States, AIChE J., 21, 510-527.

10 Kesler, M. G., and Lee, B. I., 1976, Improved Prediction of Enthalpy of Fractions, Hydrocarbon Proc., 53, 153-158.

APIThis correlation may be used to predict liquid densities. An initial density is calculated at 60 F using the weight average of the compo-nents. The reduced temperature and pressure of the stream at 60 F and 14.7 psia are computed using Kay's rule, i.e., the reduced tem-perature and pressure are assumed to be a linear function of the liq-uid mole fraction. A density factor C, is then read from Figure 6A2.21 in the API Technical Data Book. A second correction factor is then determined corresponding to the reduced temperature and pressure at the actual fluid conditions. The actual liquid density is then calculated according to:

(3-33)

where:

= actual liquid density

= liquid density at 60 F

Cact = actual correction factor

C60 = correction factor at 60 F

The API method works well for most hydrocarbon systems, pro-vided that the reduced temperature is less than 1.0.


Reference

American Petroleum Institute, 1978, Technical Data Book - Petro-leum Refining, 5th Ed., 6-45 - 6-46.

RackettThis correlation may be used to predict liquid densities. The satu-rated liquid density is obtained from:

(3-34)

where:

Vsi = saturated liquid volume

Zrai = Rackett parameter for component i

Tci, Pci = critical temperature and pressure for component i

Tri = reduced temperature for component i

The PRO/II databanks contain Rackett parameters for many compo-nents. However, if Rackett parameters are not available, PRO/II will use the critical compressibility factor, zc. When the Rackett parameter is missing for a petroleum or assay component, PRO/II back-calculates the missing parameter to ensure the specific gravity of the pseudocomponent is correct.

For mixtures, there are two ways to use the Rackett equation. The most straightforward, known as the RACKETT method in PRO/II, is to use equation (3-34) for the molar volume of each pure compo-nent and then mix the volumes together linearly. A second approach is the "One-Fluid" Rackett method (known as the RCK2 method), in which mixing rules are used to determine effective critical parameters for the mixture and then equation (3-34) is used to deter-mine the mixture density. For most mixtures, the difference between these two methods will not be significant.

Reference

11 Rackett, H. G., 1970, Equation of State for Saturated Liq-uids, J. Chem. Eng. Data, 15, 514.


12 Spencer, C. F., and Danner, R. P., 1972, Improved Equation for Prediction of Saturated Liquid Density, J. Chem. Eng. Data, 17, 236-241.

13 Spencer, C. F., and Adler, S. B., 1978, A Critical Review of Equations for Predicting Saturated Liquid Density, J. Chem. Eng. Data, 23, 82-89.

COSTALDThe corresponding-states liquid density model for predicts the liq-uid densities of “LNG-like” fluids. This accurate and reliable method is over 99.8% accurate in predicting the densities of light hydrocarbon mixtures. This model uses two characteristic parame-ters for each pure component in the mixture - a characteristic vol-ume, V*, and a “tuned” acentric factor, . The acentric factor is chosen such that the SRK equation of state best matches the vapor pressure data. Typically, this “tuned” acentric factor varies little in value from the standard acentric factor. The saturated volume is given by:

(3-35)

(3-36)

(3-37)

where:

= saturated molar volume

V* = characteristic volume

= reduced volume

= COSTALD parameters

= SRK “tuned” acentric factor

For mixtures, the following mixing rules are used:


(3-38)

(3-39)

(3-40)

(3-41)

where: subscript m refers to mixture properties.

For compressed pure liquids and liquid mixtures, the original work was extended by Thomson et al. in 1982, adding a pressure correc-tion of the form:

(3-42)

where: B, C are constants, dependent on composition

= saturated vapor pressure, obtained from a generalized vapor pressure relationship.

V = molar volume

The COSTALD method is valid for aromatics and light hydrocar-bons up to reduced temperatures of 0.95. PRO/II databanks contain COSTALD characteristic volume, V* for many components. How-ever, if the characteristic volume is not available, PRO/II will use the critical volume of the pure component, Vc. For petroleum and assay components, however, PRO/II will back calculate a character-istic volume, if missing, in order to provide a correct specific grav-ity for the pseudocomponent.

Reference

14 Hankinson, R. W., and G. H. Thomson, 1979, A New Cor-relation for Saturated Densities of Liquids and Their Mix-tures, AIChE J., 25(4), 653.


15 Thomson, G. H., Brobst, K. R., and Hankinson, R. W., 1982, An Improved Correlation for Densities of Com-pressed Liquids and Liquid Mixtures, AIChE J., 28(4), 671.

Equations of State

General InformationEquations of state for phase-equilibrium calculations are applicable to wide ranges of temperature and pressure conditions. They can also be used to calculate all the related thermodynamic properties such as enthalpy and entropy. The reference state for both the vapor and liquid phase is the ideal gas, and deviations from the ideal-gas state are determined by calculating fugacity coefficients for both phases. For cubic equations of state in particular, critical and super-critical conditions can be predicted quite accurately. By using an appropriate temperature-dependent function to describe the attrac-tive forces between molecules, volume function, and mixing rule, cubic equations of state have been shown to be quite successful in predicting vapor-liquid equilibria for highly non-ideal systems.

General Cubic Equation of StateA general two-parameter cubic equation of state can be expressed by the equation:

(3-43)

where:

P = the pressure

T = the absolute temperature

v = the molar volume

u, w = constants, typically integers

The values of u and w determine the type of cubic equation of state. Table 3-16 shows three of the best known of these. The van der Waals equation developed in 1873 is obtained by setting u=w=0. By setting u=1 and w=0, the Redlich-Kwong equation (1949) is


obtained. Peng and Robinson developed their equation of state in 1976 by setting u=2 and w=-1.

Table 3-16: Some Cubic Equations of Stateu w Equation of state

0 0 van der Waals (vdW)

1 0 Redlich-Kwong (RK)

2 -1 Peng-Robinson (PR)

The parameters a and b at the critical temperature, ( and ) are found by setting the first and second derivatives of pressure with respect to volume equal to zero at the critical point. Application of these constraints at the critical point to equation (3-43) yields:

(3-44)

(3-45)

(3-46)

where:

subscript c refers to the critical point

The critical constraints result in three expressions for three unknowns, Ac, Bc, and Zc. These unknowns depend on the values of u and w. Actually, Ac and Bc are the only true unknowns appear-ing in these equations, because Pc, Tc, and Vc (and hence Zc) are properties of a substance, having numerical values independent of any equation of state. In solving these three equations, Vc is in fact treated as a third unknown. Table 3-17 lists these constants for the van der Waals, Redlich-Kwong, and Peng-Robinson equations of state.

Table 3-17: Constants for Two-Parameter Cubic Equations of State

Ac Bc Zc Equation of state


Reference

16 Abbott, M. M., 1973, Cubic Equations of State, AIChE J., 19(3), 596-601.

17 van der Waals, J. D., 1873, Over de Constinuiteit van den gas-en Vloeistoftoestand, Doctoral Dissertation, Leiden, Holland.

18 Redlich, O., and Kwong, N. S., 1949, On the Thermody-namics of Solutions. v: An Equation of State. Fugacities of Gaseous Solutions, Chem. Rev., 44, 233.

19 Peng, D. Y., and Robinson, D. B., 1976, A New Two-con-stant Equation of State for Fluids and Fluid Mixtures, Ind. Eng. Chem. Fundam., 15, 58-64.

Alpha Formulations The temperature dependent parameter a(T) can be rewritten as:

(3-47)

In equation (3-47), α(T) is a temperature-dependent function which takes into account the attractive forces between molecules. The accuracy of the equation of state for pure-component vapor pres-sures (and therefore to a large extent for mixture phase equilibria) depends on the form of the alpha formulation, α(T), from equation (3-47). The real-gas behavior approaches that of the ideal gas at high temperatures, and this requires that α goes to a finite number as the temperature becomes infinite. Three basic requirements for the temperature-dependent alpha function must therefore all be sat-isfied:

The α function must be finite and positive for all temperatures,

The α function must equal unity at the critical point, and

The α function must approach a finite value as the temperature approaches infinity.

0.42188 0.1250 0.3750 van der Waals (vdW)

0.42747 0.0866403 0.3333 Redlich-Kwong (RK)

0.45724 0.0778 0.3074 Peng-Robinson (PR)

Table 3-17: Constants for Two-Parameter Cubic Equations of State


For the Redlich-Kwong equation of state, which works well for the vapor phase at high temperatures, α(T) is given by:

(3-48)

PRO/II allows the user to utilize a choice of 11 different alpha for-mulations for cubic equations of state (SRK, PR, modified SRK or PR, or UNIWAALS). Table 3-18 shows the 11 available alpha for-mulations for α(T).

Table 3-18: a) Alpha Formulations

Form Equation Reference

01 Soave (1972)

02 Peng-Robinson (1980)

03 Soave (1979)

04 Boston-Math-ias (1980)

05 Twu (1988)

06 Twu-Bluck-Cunningham-Coon (1991) (Recom-mended by SimSci)

07 Alternative for form (04)

08 Alternative for form (06)


Some newer formulations(9) have been added for the temperature dependent alpha term. These forms do not require the user to supply values for constants (C1, C2, etc.) Instead, they perform transforms on the acentric factors of the components of interest.

Note: These forms automatically are applied to PETRO compo-nents whenever the SIMSCI alpha formulation method (equation 6 above) is in effect.

09 Mathias-Cope-man (1983)

10 Mathias (1983)

11 Melhem-Saini-Goodwin (1989)

Table 3-18: a) Alpha Formulations

Table 3-19: b Alpha Formulations

Form Equation Reference

15

where:

and

Twu-Coon-Cunning-ham (1995)


where:

= constants

= reduced temperature

= acentric factor

Reference

20 Soave, G., 1972, Equilibrium Constants from a Modified Redlich-Kwong Equation of State, Chem. Eng. Sci., 35, 1197.

21 Soave, G, 1979, Application of a Cubic Equation of State to Vapor-Liquid Equilibria of Systems Containing Polar Com-ponents, Inst. Chem. Eng. Symp. Ser., No. 56, 1

22 Boston, J. F., and Mathias, P. M., 1980, Phase Equilibria in a Third Generation Process Simulation, Proc. of the 2nd Inter. Conf. on Phase Equil. & Fluid Properties in the Chemical Process Industries, Berlin (West), March 17-21.

23 Twu, C. H, 1988, A Modified Redlich-Kwong Equation of State for Highly Polar, super-critical Systems, Inter. Symp. on Thermodynamics in Chemical Engineering and Indus-try, May 30-June 2.

24 Twu, C.H., Bluck, D., Cunningham, J.R., and Coon, J.E., 1991, A Cubic Equation of State with a New Alpha Func-tion and New Mixing Rule, Fluid Phase Equil., 69, 33-50.

16

where:

and

Twu-Coon-Cunning-ham (1995)

Table 3-19: b Alpha Formulations


25 Mathias, P. M., and Copeman, T. W., 1983, Extension of the Peng-Robinson Equation of State to Complex Mixtures, Fluid Phase Equil., 13, 91-108.

26 Mathias, P. M., 1983, A Versatile Phase Equilibrium Equa-tion of State, Ind. Eng. Chem. Proc. Des. Dev., 22, 358-391.

27 Melhem, G. A., Saini, R., and Goodwin, B. M., 1989, A Modified Peng-Robinson Equation of State, Fluid Phase Equil., 47, 189-237.

28 Twu, C.H., Coon, J.E., Cunningham, J.R., 1995, A New Generalized Alpha Function for a Cubic Equation of State; part 1: Peng-Robinson equation; part 2: Redlich-Kwong equation, Fluid Phase Equil., 105, 49-69.

Mixing Rules (for Equations of State)The accuracy of correlating vapor-liquid equilibrium data using a cubic equation of state can be improved further by choosing an appropriate mixing rule for calculating a and b in equation (3-43) for mixtures. The original mixing rule was derived from the van der Waals one-fluid approximation:

(3-49)

(3-50)

where: = mole fraction of component i.

The binary interaction parameter, kij, is introduced into the mixing rule to correct the geometric mean rule of parameter a in the general cubic equation of state (3-43):

(3-51)

where: Kij = Kji = binary interaction parameter.

The original mixing rule is capable of representing vapor-liquid equilibria for nonpolar and/or slightly polar systems using only one (possibly temperature-dependent) binary interaction parameter.


Soave-Redlich Kwong (SRK)In 1972, to improve the prediction of the vapor pressure of pure components, and thus multi-component vapor-liquid equilibria, Soave proposed the following form of a(T):

(3-52)

M 0.48 1.574ω 0.176ω2–+= (3-53)

where:

= reduced temperature, T/Tc

ω = acentric factor

The constants in (3-53) were obtained from the reduction of vapor-pressure data for a limited number of common hydrocarbons. This limits the use of the SRK equation of state to non-polar compo-nents. This equation of state does not accurately predict the behav-ior of polar components or light gases such as hydrogen. However, the simplicity of equations (3-52) and (3-53), and its accuracy for calculating vapor pressures at temperatures higher than the normal boiling point for hydrocarbons allowed it to gain widespread popu-larity in industry. PRO/II contains correlations for the kijs of hydro-carbons with N2, O2, H2, H2S, CO2, mercaptans, and other sulfur compounds.

Peng-Robinson (PR)The form of α(T) proposed by Peng and Robinson in 1976 is the same as that proposed in 1972 by Soave. The numerical values for the constants in equation (3-53) are different because the volume function is different and because a somewhat different set of data was used.

M 0.37464 1.54226ω 0.26992ω2–+= (3-54)

Soave-Redlich-Kwong Kabadi-Danner (SRKKD)While the K-values between the hydrocarbon-rich liquid phase and vapor phase can be accurately predicted by most cubic equations of state, the K-values involving the water-rich liquid phase are not. In order to apply cubic equations of state to water-hydrocarbon sys-tems, Kabadi and Danner in 1985 proposed a two-parameter mixing


rule for the SRK equation of state. This proposed mixing rule is composition dependent, and is designed expressly for water and well-defined hydrocarbon systems:

(3-55)

(3-56)

(3-57)

where:

= interaction parameter between hydrocarbons and water in the hydrocarbon-rich phase

= hydrocarbon group contribution from group j

= sum of group contributions from the different structural groups forming a hydrocarbon molecule i.

To provide estimates for water/hydrocarbon equilibria when no data are available, Kabadi and Danner developed a procedure for esti-mating the binary interaction parameters kij and Gi. Within a homologous series of hydrocarbons, kij was found to be approxi-mately constant and recommended values were given for seven hydrocarbon classes. A group contribution method was proposed for estimating Gi.

One limitation of this method, however, is that the solubility of hydrocarbon in the aqueous phase is predicted only within an order of magnitude.

Reference

Kabadi, V. N., and Danner, R. P., 1985, A Modified Soave-Redlich-Kwong Equation of State for Water-Hydrocarbon Phase Equilibria, Ind. Eng. Chem. Proc. Des. Dev., 24(3), 537-541.

Soave-Redlich-Kwong Panagiotopoulos-Reid (SRKP) and Peng-Robinson Panagiotopoulos-Reid (PRP)In 1986 Panagiotopoulos and Reid proposed an asymmetric mixing rule containing two parameters for the SRK and PR equations of


state (denoted as SRKP and PRP). The interaction parameter they proposed to be used in equation (3-49) is given by:

(3-58)

The two adjustable interaction parameters are kij and kji. This asymmetric definition of the binary interaction parameters signifi-cantly improves the accuracy in correlating binary data for polar and non-polar systems. This mixing rule has been used to test sev-eral systems, including low pressure non-ideal systems, high pres-sure systems, three-phase systems, and systems with super-critical fluids. The results in all cases reported are in good agreement with experimental data.

Reference

1 Panagiotopoulos, A. Z., and Reid, R. C., 1986, A New Mix-ing Rule for Cubic Equations of State for Highly Polar Asymmetric Systems, ACS Symp. Ser. 300, American Chemical Society, Washington, DC, 71-82.

2 The Panagiotopoulos-Reid mixing rule, however, is funda-mentally inconsistent for multi-component systems. This inconsistency is exhibited in two (related) flaws:

3 The dilution of the mixture with additional components (reducing all the mole fractions xi) nullifies the effect of the second binary parameter kij. In the limit of an infinite num-ber of components so that all the xi approach zero, the mix-ing rule reduces to the original van der Waals mixing rule, equation(3-51).

4 The mixing rule is not invariant to dividing a component into a number of identical pseudo-components. For exam-ple, if methane in a mixture is divided arbitrarily into “alpha” and “beta” methane, the calculated properties of the mixture will be slightly different.

Soave-Redlich-Kwong Modified (SRKM) and Peng-Rob-inson Modified (PRM)SimSci has modified equation (3-58) in a way that eliminates the first of the two flaws noted above. This improvement provides bet-ter predictions of properties for multi-component systems:


(3-59)

Equation (3-59) is identical to equation (3-58) for binary systems if c12 = 1. The expression for aji, which is similar to equation (3-59), can be obtained by interchanging subscripts i and j. The four adjust-able interaction parameters are kij and kji, and cij and cji. For binary nonpolar systems, where deviations from ideality are not large, or are only weakly asymmetric, only two parameters, k12 and k21 are sufficient to fit the data (i.e., c12 = c21 = 1). In this case, equation (3-59) becomes identical to the mixing rule proposed (also for the purpose of overcoming the first flaw noted above) by Har-vey and Prausnitz in 1989. For binary polar or polar-nonpolar sys-tems, where the non-ideality is large or strongly asymmetric, it may be necessary to include the additional parameters c12 and c21. In particular, for binary polar-nonpolar systems, which have the great-est deviation from ideality, c12 is not set equal to c21. For binary polar systems however, c12 can generally be set equal to c21.

Reference

Harvey, A. H., and Prausnitz, J. M., 1989, Thermodynamics of High-Pressure Aqueous Systems Containing Gases and Salts, AIChE J., 35, 635-644.

Soave-Redlich-Kwong SimSci (SRKS)In 1991, Twu et al. proposed another modified mixing rule that eliminated both of the inconsistencies of the Panagiotopoulos-Reid mixing rule noted above. For a binary system, the mixing rule can be expressed in the following form for a12:

. (3-60)

(3-61)

(3-62)

The four adjustable parameters are; k12, k21, β12, and β21. Again, as for the SRKM equation of state, for binary nonpolar systems, where deviations from ideality are not large, or are only weakly asymmetric, only two parameters, k12 and k21 are sufficient to fit the data (i.e., β12 = β21 = 1). For binary polar or polar-nonpolar systems, where the non-ideality is large or strongly asymmetric, it may be necessary to include the additional parameters β12 and β21. In particular, for binary polar-nonpolar systems, which have the


greatest deviation from ideality, β12 is not set equal to β21. For binary polar systems however, β12 can generally be set equal to β21.

Twu et al. have derived the activity coefficients from the SRKS equation of state, and have found that for a binary system, k12 or k21 are directly related to the infinite dilution activity coefficients γ1 or γ2 respectively. The values of k12 and k21 are therefore deter-mined when both values of the infinite dilution activity coefficients are known for a binary system. The physical meaning of the binary parameters k12 and k21 is that they are used to locate the infinite dilution activity coefficients in a binary system containing compo-nents 1 and 2.

After both end points of the liquid activity coefficients are found, the parameters β12 and β21 are then required to describe the shapes of the liquid activity coefficient curves for components 1 and 2 in the finite range of concentration. In general, for real systems, kij is not equal to kji, and βij and βji are not equal to zero. The conven-tional mixing rule obtained by setting k12 = k21 and β12 = β21 = 0 for a binary system either results in a compromise of the phase equi-librium representation, or fails to correlate highly asymmetric sys-tems.

For a multi-component system, (17) can be generalized as:

(3-63)

(3-64)

(3-65)

where: subscript m refers to the multi-component system mixture.

Reference

Twu, C. H., Bluck, D., Cunningham, J. R., and Coon, J. E., 1991, A Cubic Equation of State with a New Alpha Function and New Mix-ing Rule, Fluid Phase Equil., 69, 33-50.

Soave-Redlich-Kwong Huron-Vidal (SRKH) and Peng-Robinson Huron-Vidal (PRH)The previous SRK and PR mixing rule modifications include com-position-dependence for applying these equations of state to com-


plex mixtures. A more complicated way to represent the phase behavior of strongly non-ideal systems is to develop the relation-ship between the mixing rule and excess Gibbs free energy such that the infinite-pressure Gibbs free energy could be expressed by a NRTL-like method (see Section, Liquid Activity Methods). This approach was proposed by Huron and Vidal in 1979. The general equation relating excess Gibbs free energy to fugacity coefficients is given by:

(3-66)

where:

= excess Gibbs free energy per mole

φ = fugacity coefficient of the mixture

φi = fugacity coefficient of pure component i

At infinite pressure, the excess Gibbs free energy is calculated using the Redlich-Kwong equation of state and linear mixing rules for the parameter b from the general cubic equation of state. At infinite pressure, equation (3-66) then becomes:

(3-67)

where:

= the excess Gibbs free energy at infinite pressure

Equation (3-67) can be rewritten to produce a new mixing rule for the cubic equation of state parameter a:

(3-68)

The excess Gibbs free energy can be calculated by any liquid activ-ity method. Huron and Vidal chose to use the NRTL liquid activity method to calculate


(3-69)

(3-70)

(3-71)

The only difference between the classical NRTL equation and equa-tions (3-69)-(3-71) is the definition of the local composition as cor-rected volume fractions, which leads to the introduction of the volume parameter bj in the calculation of Gji. Substituting for the excess Gibbs free energy in (25) yields:

(3-72)

By regressing experimental data to obtain the parameters in the modified NRTL expression, excellent representation of vapor-liquid equilibria can be made for several systems. The Huron-Vidal mix-ing rules are highly empirical in nature. However, the prediction of equilibria at low densities is reasonable, and the equation of state can be expected to yield better results at higher pressures, because the mixing rules have been derived at the infinite pressure limit of the excess Gibbs free energy. One limitation of this model is that it cannot directly utilize parameters for the NRTL method correlated from low temperature data. This is because an excess Gibbs energy model from an equation of state at infinite pressure cannot be equated with an activity coefficient excess Gibbs energy model at low pressure.

Reference

Huron, M. J., and Vidal, J., 1979, New Mixing Rules in Simple Equations of State for Representing Vapor-Liquid Equilibria of Strongly Non-ideal Mixtures, Fluid Phase Equil., 3, 255-271.

HEXAMERHydrogen fluoride is an important chemical used in many vital pro-cesses, including HF alkylation, and in the manufacture of refriger-ants and other halogenated compounds. Unlike hydrocarbons, however, hydrogen fluoride is polar and hydrogen bonded, and therefore self-associates not only in the liquid phase, but also in the vapor phase. Experimental evidence strongly suggests that the HF vapor exists primarily as a monomer and a hexamer mixture. In


addition, evidence points to the hexamer existing in the form of a cyclic benzene-like species. This behavior results in significant departures from ideality, especially in calculating fugacity coeffi-cients, vapor compressibility factors, heat of vaporization, and enthalpies.

Twu et al. (1993), developed a cubic equation of state with a built-in chemical equilibrium model to account for HF association. The cubic equation of state incorporating association is given by:

(3-73)

(3-74)

(3-75)

where: a(T) = α(T) a(Tc) = Redlich-Kwong equation of state parameter which refers to the monomer

b = Redlich-Kwong equation of state parameter which refers to the monomer

v = molar volume

V = total volume

= extent of association

= total number of moles of monomer and hexamers

= the number of moles that would exist in the absence of asso-ciation

Note: Only 1 hexamerizing component (HF) may be present when using the HEXAMER method.

The values of a(Tc) and b can be obtained from the critical con-stants for the Redlich-Kwong equation of state (see Table 3-17), and the critical temperature and pressure for HF. The alpha func-tion, α(T), is obtained by matching the equation of state to HF vapor pressure data. Comparing equation (3-73) to the general two-parameter equation of state given by equation (3-43), it can be seen that the only difference is the term nr, which accounts for the contri-


bution of association. The value of nr is 1.0 when there is no associ-ation, and approaches 1/6 when there is complete hexamerization. As the temperature increases, the extent of hexamerization should decrease, i.e., the value of should increase.

The total number of moles of monomer and hexamer, , and the total number of moles that would exist in the absence of associa-tion, , are related by:

(3-76)

where: = the true mole fraction of species i

= number of moles of species i

The hexamerization equilibrium reaction is written as:

(3-77)

The corresponding chemical equilibrium constant for this reaction, which is a function of temperature only, is defined as:

(3-78)

where: K = equilibrium constant

= fugacity coefficient of the true monomer species

= fugacity coefficient of the true hexamer species

= true mole fraction of the monomer species

= true mole fraction of the hexamer species

P = total pressure

The fugacity coefficients in equation (3-78) are found from the cubic equation of state using classical thermodynamics. Substitut-ing equation (3-76) into equation (3-78), and using the overall material balance, reduces this to:

(3-79)

where:


= the reduced equilibrium constant

Once the equilibrium constant K is known, equation (3-79) can be solved to obtain a value for z1 and a corresponding value for z6.

The equilibrium constant for HF hexamerization can be calculated from the following relationship:

(3-80)

where: K = equilibrium constant,

T = temperature, K

Twu et al. have shown that, at the critical point, the values of z1, the true mole fraction of monomer, and nr, are given by:

(3-81)

(3-82)

So, even at the critical point, there is still a considerable amount of the hexamer species present.

Mixture properties may be computed by using the SRKS mixing rule, equation (3-63) on page 45.

Reference

Twu, C. H., Coon, J. E., and Cunningham, J. R., 1993, An Equation of State for Hydrogen Fluoride, Fluid Phase Equil., 86, 47-62.

UNIWAALSIn the UNIWAALS model proposed by Gupte et al. in 1986, the cubic equation of state is combined with the excess Gibbs free energy model. By using this approach, the same parameters of the excess Gibbs free energy model based on low pressure VLE data can be extended to apply to high pressures by using the equation of state. This is a valuable method because group interaction parame-ters from group contribution methods such as UNIFAC (see Sec-tion, Liquid Activity Methods) are readily available for numerous groups. The equations for the UNIWAALS method are developed by equating the gE derived from the van der Waals equation of state


to the gE derived from UNIFAC at the system temperature and pressure. This equality produces the following mixing rule:

(3-83)

(3-84)

(3-85)

where:

= excess volume

The mixing rule for the a/b parameter contains the mixture (v) and pure (vi) fluid volumes. The pure component volumes are obtained for the liquid phase at the given temperature and pressure condi-tions. Parameter b for the mixture is calculated using the original mixing rule developed for the RK equation of state (equation (3-50) on page 40), and UNIFAC is used to calculate gE/RT. Subsequently, the van der Waals equation of state and equation (3-85) are solved simultaneously to obtain the mixture volume, v, and a/RTb.

Several limitations to this method should be noted:

1 For the calculation of the parameter a, the mixture and pure-component liquid volumes (v and vi) are required, even if the liquid phase does not actually exist at the given temperature and pressure.

2 The mixture parameter v is volume dependent, and thus pressure and volume become related through a differential equation, rather than through a conventional algebraic equation.

3 The critical constraints of the UNIWAALS equation of state are no longer satisfied by the values of the parameters a and b at the critical temperature. The resulting equation of state is no longer a cubic equation of state, and analytical solution of the equation of state is impossible.

4 The fugacity coefficients are cumbersome to evaluate.


5 The accuracy of the UNIWAALS model is not better than that of the UNIFAC model at low temperatures, and the accuracy deteriorates with increasing temperatures.

Reference

Gupte, P. A., Rasmussen, P., and Fredenslund, A., 1986, A New Group-Contribution Equation of State for Vapor-Liquid Equilibria, Ind. Eng. Chem. Fundam., 25, 636-645.

Benedict-Webb-Rubin-StarlingThe Benedict-Webb-Rubin equation of state was first proposed in 1940 to predict liquid and vapor properties at high temperatures, and to correlate vapor-liquid equilibria for light hydrocarbon mix-tures. This original (BWR) equation of state however provided poor results at low temperatures, and around the critical point. To improve the accuracy of this equation in predicting thermodynamic properties for light hydrocarbons in the cryogenic liquid, gas, and dense fluid regions, and at high temperatures, the BWR equation was modified by Starling in 1973 to give the following form:

P ρRT B0RT A0–C0

T2------–

D0

T3------

E0

T4------–+

⎝ ⎠⎜ ⎟⎛ ⎞

ρ2

bRT a– dT---–⎝ ⎠

⎛ ⎞ ρ3 α a dT---+⎝ ⎠

⎛ ⎞ ρ6

cρ3

T2-------- 1 γρ2+( ) γρ2–( )exp

+

+ +

+

= (3-86)

The eleven parameters for pure components (B0, A0, etc.) are gen-eralized as functions of component acentric factor, critical tempera-ture, and critical density. The mixing rules for the eleven mixture parameters are analogous to the mixing rules used for the BWR equation. The single binary interaction parameter for the BWRS equation of state is built into the mixing rules. The BWRS equation of state can predict pure-component properties for light hydrocar-bons very accurately when experimental data covering entire ranges are available.

Limitations to the BWRS equation of state are given below:

1 Because the equation is generalized in terms of critical tem-peratures, critical density, and acentric factor, it has diffi-


culty predicting properties for heavy hydrocarbons and polar systems.

2 The BWRS equation does not satisfy the critical con-straints, and therefore the equation is inferior to cubic equations of state when applied to the critical and super-critical regions.

3 The BWRS equation is less predictive that cubic equations of state for mixture calculations.

4 Unlike cubic equations of state, BWRS cannot be solved analytically, and normally requires more CPU time.

Reference

1 Benedict, M, Webb, G. R., and Rubin, L. C., 1940, An Empirical Equation for Thermodynamic Properties of Light Hydrocarbons and Their Mixtures. I. Methane, Ethane, Pro-pane, and Butane, J. Chem. Phys., 8, 334-345.

2 Starling, K. E., 1973, Fluid Thermodynamic Properties for Light Petroleum Systems, Gulf Publishing Company, Houston, TX.

Lee-Kesler-Plöcker (LKP)The LKP equation is based on the Benedict-Webb-Rubin equation of state and on Pitzer's extended theory of corresponding states. Thermodynamic data are correlated as a function of critical temper-ature and pressure and the acentric factor as follows:

(3-87)

where:

Z = compressibility factor

ω = acentric factor

subscripts o, r denote Simple and Reference fluids, respectively.

The work of Plöcker et al., introduces new mixing rules which are purported by the authors to better handle mixtures of asymmetric molecules. This is accomplished by the introduction of an exponent, η into the mixing rules.


The mixing rules proposed here are:

(3-88)

(3-89)

(3-90)

where:

Vc = the molar critical volume

Tc = the critical temperature

z = mole fraction in vapor or liquid phase

ω = the acentric factor

The cross coefficients are given by:

(3-91)

(3-92)

where:

Kjk is an adjustable binary parameter, characteristic of the j-k binary, independent of temperature, density, and composition.

The pseudo-critical pressure is found by:

(3-93)

When η is zero, the mixing rules are similar to those of Prausnitz and Gunn; when η is 1.0, the mixing rules become the van der Waals mixing rules, as used by Leland et al. For symmetric mix-tures, η is zero; for strongly asymmetric mixtures, η is a positive value less than unity. Based on an analysis of experimental data, the authors suggest using a value of 0.25 when a specific determination is not available. PRO/II uses a default η value of 0.25.

Adjustable binary parameters, Kij's are also used in the mixing rules. Values reported by Plöcker et al. have been incorporated into


PRO/II. The LKP method is claimed by the authors to be superior to Starling's BWRS equation for highly asymmetric systems. The method is not accurate around the critical point because the mixture critical constants are empirical, and do not represent the true critical point. Therefore, the authors recommend that the method not be used above a reduced temperature of 0.96.

Reference

1 Lee, B.I., and Kesler, M.G., 1975, A Generalized Thermody-namic Correlation Based on Three-Parameter Corresponding States, AIChE J., 21, 510-527.

2. Leland, T.W., and Mueller, W.H., 1959, Applying the Theory of Corresponding States to multi-component Mixtures,Ind. Eng. Chem., 51, 597-600.

3. Pitzer, K.S., and Hultgren G.O., 1958, The Volumetric and Thermodynamic Properties of Fluids, V. Two Component Solu-tions, J. Am. Chem. Soc., 80, 4793-96.

4. Plöcker, U., Knapp, H., and Prausnitz, J.M., 1978, Calculation of High-Pressure Vapor-Liquid Equilibria from a Correspond-ing States Correlation with Emphasis on Asymmetric Mixtures, Ind. Eng. Chem. Proc. Des. Dev., 17, 324-332.

5. Prausnitz, J.M., and Gunn, R.D., 1958, Volumetric Properties of Nonpolar Gaseous Mixtures, AIChE J., 4, 430-35.

6. Prausnitz, J.M., and Gunn, R.D., 1958, Pseudo-critical Con-stants from Volumetric Data for Gas Mixtures, AIChE J., 4, 494.

Twu-Bluck-Coon(TBC)The previous SRK and PR mixing rule modifications included com-position-dependence for applying these equations of state to com-plex mixtures. A more rigorous way to represent the phase behavior of strongly non-ideal systems is to develop the relationship between the mixing rule and excess free energy model such that the zero-pressure Gibbs free energy could be expressed by a NRTL-like method (see Section, Liquid Activity Methods). Such approach had been extended by Twu, Bluck and Coon in 1998 with a newly developed zero-pressure-based mixing rule which would accurately reproduce the excess Gibbs model and allow the available activity coefficient models at low pressures be used directly. The general Helmholtz free-energy departure function is given by:


AE AvdwE– ΔA ΔAvdw–= (3-94)

At zero pressure, equation (3-94) may be derived as:

(3-95)

where:EA0 = excess Helmholtz free energy at zero-pressure; EvdwA0 = excess Helmholtz free energy at zero-pressure

calculated by a CEOS, such as SRK;

0vC = density function calculated from SRK;

Equation (3-95) can be written to obtain the new mixing rule:

(3-96)

and

(3-97)

At zero pressure, the value of the excess Helmholtz energy is identi-cal to the excess Gibbs energy model. Therefore, any activity model such as the NRTL equation can be used directly. For a solution of n components, the NRTL equation is expressed as,

(3-98)

where:


TAji

ji =τ and )exp( jijijiG τα−=

By regressing experimental data to obtain the parameters in the NRTL expression, excellent representation of vapor-liquid equilib-ria can be made. The prediction of equilibria at low densities is rea-sonable, and the equation of state can be expected to yield better results at higher pressures, because the mixing rules have been derived at the zero pressure limit of the excess Gibbs free energy. The TBC equation of state overcomes the limitation of infinite-pressure based models, such as Huron-Vidal (SRKH, PRH,…) that it can directly utilize parameters for the NRTL method correlated from low temperature data.

Reference

1. Twu, C. H.; Coon, J. E.; Bluck, D. “Comparison of the Peng-Robinson and Soave-Redlich-Kwong Equations of State Using a New Zero-Pressure-Based Mixing Rule for the Prediction of High-Pressure and High-Temperature Phase Equilibria”. Ind. Eng. Chem. Res. 1998, 37, 1580-1585.

Fill Options (for Binary Interaction Coefficients) The ability of equation-of state methods to accurately predict vapor-liquid equilibria and/or vapor-liquid-liquid equilibria depends to a great degree on whether or not binary interaction parameters are available for that method. Refer to the Kij term of equation (3-51).

Fill Options for Use With Cubic Equations of State

PRO/II implements a number of binary interaction prediction meth-ods for hydrocarbon/hydrocarbon mixtures. These prediction meth-ods automatically provide the optimal light/heavy kij’s for methane, ethane and propane with other hydrocarbons. They were designed specifically with an eye towards heavy petroleum fractions, to be used in conjunction with SimSci's generalized alpha forms listed in Table 3-18 and Table 3-19 on page 3-38.

GOR The GOR method was developed by Simsci to automat-ically generate kij’s between methane and ethane and other heavier hydrocarbons. It is based on correlating existing deepwater US Gulf of Mexico experimental data.


The methods listed above were selected based on their applicability and are ordered so each subsequent method in the list generates more and more kij’s. In this respect, they provide a spectrum of results that can be selected based on the goodness of fit to the spe-cific data being modeled. Applying these changes to a PRO/II input can improve the initial estimates for gas oil separations.

When a cubic equation-of-state method such as SRK or PR is selected for phase equilibrium calculations, and a FILL option is specified, PRO/II uses the following hierarchy to obtain the binary interaction data the model needs. For VLE or LLE calculations:

1 First, use any user-supplied binary interaction parameters, or mutual solubility, infinite dilution, or azeotropic data.

2 Second, search VLE and LLE databanks that contain binary interaction parameters.

3 Third, search the SimSci azeotropic databanks for appropri-ate azeotropic data, which then are regressed to provide binary interaction data.

GAO The modified Gao et al method, is a modification where only interactions for methane, ethane and propane are used with an extension to undefined fractions of the method published in Fluid Phase Equilibria. The origi-nal work was based upon the Peng-Robinson equation of state.

Gao, Guanghua; Daridon, Jean-Luc; Saint-Guirons, Henri; Xans, Pierre; Montel, Francois; A simple correla-tion to evaluate binary interaction parameters of the Peng-Robinson equation of state: binary light hydrocar-bon systems; Fluid Phase Equilibria; 74, (1992) 85-93.

CPHC The modified Chueh-Prausnitz method is an adaptation of a method reported in the AIChE Journal, 13(6), (1967), 1099-1107. It predicts interactions between all hydrocarbons present in the problem.

Cheuh, P. L.; Prausnitz, J. M.; Vapor-Liquid Equilibria at High Pressures: Calculation of Partial Molar Vol-umes in Nonpolar Liquid Mixtures; AIChE Journal, Vol. 13, no. 6, pg 1099-1107 (1967).


4 If some binary interaction parameters still are missing after completing steps 1 through 3, then the specified FILL method is employed.

5 Finally, if binary interaction parameters are still missing after completing steps 1-4, all remaining missing parame-ters are assigned a value of zero.

Figure 3-1 on page 3-83 shows the mechanism used by PRO/II to backfill missing binary parameters for VLE, or VLLE calculations.

For VLLE calculations, in order to avoid conflicts between VLE and LLE binary interaction data, PRO/II follows a number of strict rules when filling in these binary interaction data.

If no VLE or LLE interaction data are supplied by the user, PRO/II uses the following order in searching for interaction data for both VLE and LLE calculations:

1 The LLE databank

2 The VLE databank

When the user supplies VLE interaction data only, PRO/II uses the following order in searching for binary parameters for both VLE and LLE calculations:

1.User-supplied values on the KVALUE(VLE) statements

2. The LLE databank

3. The VLE databank

If the user supplies LLE interaction data only, or both VLE and LLE interaction data, for LLE calculations, the databanks are searched in the order:

1. User-supplied data on KVALUE(LLE) statements

2 The LLE databank

3 The VLE databank

If the user supplies LLE interaction data only, or both VLE and LLE interaction data, for VLE calculations, the databanks are searched in the order:

1.User-supplied data on KVALUE(VLE) statements2.The VLE databank


Free Water Decant

General InformationIn many hydrocarbon-water mixtures, including those found in refinery and gas processing plants, the water phase formed is nearly immiscible with the liquid hydrocarbon phase. For such systems, the water phase can be assumed to decant as a pure aqueous phase. This reduces the number of computations involved with rigorous VLLE methods. The water-decant method as implemented in PRO/II follows these steps:

Water vapor is assumed to form an ideal mixture with the hydrocarbon vapor phase.

The water partial pressure is calculated using one of two meth-ods.

The pressure of the system, P, is calculated on a water-free basis, by subtracting the water partial pressure.

A pure water liquid phase is formed when the partial pressure of water reaches its saturation pressure at that temperature.

The amount of water dissolved in the hydrocarbon-rich liquid phase is computed using one of a number of water solubility correlations.

Note: The free water decant option may only be used with the Soave-Redlich-Kwong, Peng-Robinson, Grayson-Streed, Chao-Seader, Improved Grayson-Streed, Erbar modifications to Gray-son-Streed and Chao-Seader, Braun K10, or Benedict-Webb-Rubin-Starling methods. Water decant is automatically activated when either one of these methods is selected.

Calculation MethodsThe amount of water dissolved in the hydrocarbon-rich liquid phase can be computed once the water K-values, , are known. These are calculated using the following relationship:

(3-99)

where:

= water partial pressure at temperature T


= solubility of water in the hydrocarbon-rich liquid phase

P = system pressure

The water partial pressure is calculated using either the ASME steam tables, or Chart 15-14 in the GPSA Data Book. The GPSA Data Book option is recommended for natural gas mixtures above 2000 psia. Three sets of steam tables can be used:

Water properties can be calculated assuming saturated vapor and liquid conditions.

Steam tables for superheated water vapor based on the Keenan and Keyes equation of state.

IF 97 Steam Tables - International Association for the Proper-ties of Water and Steam - Industrial Formulation 1997 steam tables are used for the property calculations.

Water Solubility Calculation Methods

The water solubility, , can be computed by one of several methods in PRO/II:

1. The default method developed by SimSci. In this method, water solubility is calculated for individual hydrocarbons and light gases given in Table 3-20. The SimSci method uses a cor-relation based on the number of carbon and hydrogen atoms present in the component. For pseudo-components, the water solubility is calculated as a function of the Watson (UOP) K-factor.

Table 3-20: Components Available in the SIMSCI Water Solubility Method

Paraffins Naphthenes

Unsaturated Hydrocarbons Aromatics

Methyl Mercaptan CS2

NH3 Argon

CO2 Helium

HCl H2S

N2 NO

O2 SO2

2. A second method uses Figure 9A1.2 in the API Technical Data Book to compute water solubility in kerosene. PRO/II will automatically invoke this option if the SIMSCI decant option is


chosen, and a component not included in Table 3-20 is present in the system.

3. A third method employs the equation-of-state method that is being used for calculating the K-values of the other compo-nents present in the system to compute the water K-value. Missing binary interaction parameters for the water-hydrocar-bon components pairs are estimated using the Soave-Redlich-Kwong Kabadi-Danner equation of state. This method is only valid for SRK or PR equations of state

4. The following methods are from the 1999 API Technical Data Book, Procedure 9A1.3. They calculate the solubility of water in various liquid hydrocarbon mixtures.

1999 API Technical Data Book Water Solubility MethodsLUBE lube oil Refer to the Component and

Thermodynamic Data Keyword Input Manual, Volume II, Table 1-5, “Properties of Water Solubility Fluids,” for a listing of the basic properties of these fluids.

NAPH Naphtha

APIKERO Kerosene

PARA Paraffin oil

GASO Gasoline

JP3 JP-3 fuel

JP4 JP-4 fuel

Liquid Activity Coefficient Methods

General InformationLiquid activity coefficient methods for phase equilibrium calcula-tions differ at a fundamental level from equation of state (EOS) methods. In EOS methods, fugacity coefficients (referring to an ideal-gas state) are computed for both vapor and liquid phases. In activity coefficient methods, the reference state for each component in the liquid phase is the pure liquid at the temperature and pressure of the mixture. It is often more convenient and accurate to use this approach when the liquid phase is a mixture of components which do not differ greatly in volatility; it is also often easier to describe strongly non-ideal systems with a liquid activity coefficient model than with an equation of state.

The thermodynamics of liquid mixtures within an activity coeffi-cient framework is covered in standard textbooks, a few of which


are referenced at the end of this section. The activity coefficient is introduced in the way the fugacity of component i in the liquid phase is written:

(3-100)

where:

= fugacity of component i in liquid phase

= standard-state liquid fugacity of component i

xi = mole fraction of component i in liquid γi = liquid-phase activity coefficient of component i

The standard-state fugacity is defined as that of the pure liquid i at the temperature and pressure of the mixture. With this defini-tion, gi approaches one in the limit xi 1. The standard-state fugacity may be related to the vapor pressure of component i as fol-lows:

(3-101)

where: P = system pressure

Pisat = vapor pressure of component i at system temperature

R = gas constantT = system temperature

νiL = liquid molar volume of component i at T and P

φisat = fugacity coefficient of pure component i at temperature

T and pressure Pisat .

The exponential term in Equation (3-101) is the Poynting factor which accounts for the effect of pressure on the liquid fugacity. If the pressure does not exceed a few atmospheres, this correction can generally be neglected. Since liquid volumes do not depend greatly on pressure, Equation (3-101) can be simplified to:


(3-102)

When liquid activity coefficients are used, any method may be used to compute the vapor-phase fugacity. An ideal gas is often assumed, but in general vapor fugacities may be written as:

(3-103) where:

fiV = fugacity of component i in vapor phase

yi = mole fraction of component i in vapor

φiV = fugacity coefficient of component i in vapor

For an ideal gas, the fugacity coefficient φiV is one, but it may also

be computed from an equation of state or other correlation.

Equations (3-100) and (3-103) are fundamentally different in the way they describe liquid and vapor fugacities, respectively. The two equations do not in general “match” at the vapor-liquid critical point, where vapor and liquid phases become indistinguishable. Phase equilibrium calculations near a vapor-liquid critical point must be carried out with some other method such as an equation of state.

The familiar vapor-liquid K-value is defined as the ratio of yi to xi, and can be obtained by combining Equations (3-100) and (3-103):

(3-104)

At low and moderate pressures, the Poynting correction is often ignored and Equation (3-104) becomes

(3-105)

Unless there is vapor-phase association (as is the case with carboxy-lic acids, for example), the fugacity coefficients may also be ignored at low and moderate pressures. Equation (3-104) then sim-plifies to


(3-106)

For most low-pressure systems, the regression of experimental vapor-liquid equilibrium data will produce essentially the same parameters if equation (3-105) or (3-106) is used in place of the full equation (3-104). This is not necessarily the case at higher pressures and for systems where vapor-phase non-ideality is important. Sig-nificant errors can be introduced when the regression and calcula-tions using the regressed parameters employ differing sets of simplifying assumptions. In general, calculations should be per-formed using the same assumptions about vapor fugacities and the Poynting factor as those employed in fitting the parameters. An important exception to this rule is the case where parameters were fitted at low pressure but the calculations are at a substantially higher pressure; in such a case it is best to employ non-ideal vapor-phase fugacities and the Poynting correction in the calculation even if they were not used in the original fit.

Liquid activity coefficients are derived from expressions for the excess Gibbs energy of a liquid mixture. The defining equation is:

(3-107)

where:

GE = excess Gibbs energy of liquid mixture ni = moles of component i in liquid

The following sections describe the expressions available for describing liquid-phase activity coefficients.

Reference

1 Prausnitz, J.M., Lichtenthaler, R.N. and Gomes de Aze-vedo, E., 1986, Molecular Thermodynamics of Fluid Phase Equilibria, 2nd ed., Prentice Hall, Englewood Cliffs, NJ.

2 Sandler, S.I., 1989, Chemical and Engineering Thermody-namics, 2nd ed., John Wiley & Sons, New York.


3 Smith, J.M. and Van Ness, H.C., 1987, Introduction to Chemical Engineering Thermodynamics, 4th ed., McGraw Hill, New York.

4 Van Ness, H.C. and Abbott, M.M., 1982, Classical Thermo-dynamics of Non-electrolyte Solutions: With Applications to Phase Equilibria, McGraw Hill, New York.

5 Walas, S.M., 1985, Phase Equilibria in Chemical Engineer-ing, Butterworth, Boston.

Margules EquationTable 3-21: Margules Equation

Required Pure Component Properties


Vapor pressure Temperature Use at or near temperatures where parameters were fitted

The oldest empirical correlations for liquid activity coefficients, such as the Margules equation (1895), are derived from simple polynomial expansions. The most popular form of the Margules equation was proposed by Redlich and Kister (1948). When that expansion is truncated after the quadratic term, the resulting three-parameter correlation is known as the four-suffix Margules equa-tion. The resulting expression for the activity coefficient is:

(3-108)

where:


Thus, for each ij binary pair in a multi-component system, the parameters are aij, aji, and dij. No temperature dependence is included in this implementation; one should therefore be cautious about using this equation at temperatures differing substantially from the range in which the parameters were fitted.

Reference

1 Margules, 1895, Sitzber., Akad. Wiss. Wien, Math. Nature., (2A), 104, 1234.

2 Redlich, O. and Kister, A. T., 1948, Algebraic Representa-tion of Thermodynamic Properties and the Classification of Solutions, Ind. Eng. Chem. 40, 345348.

van Laar EquationTable 3-22: van Laar Equation



Vapor pressure

Components

Use for chemically similar components

Another old correlation which is still frequently used is the van Laar equation. It may be obtained by discarding ternary and higher order terms in an alternative expansion of the excess Gibbs energy (known as Wohl's equation), though that is not how van Laar derived it originally. The resulting expression for the activity coeffi-cient is:

(3-109)

where:

Two parameters, aij and aji, are required for each binary. As with the Margules equation, no method is included for making the


parameters temperature dependent. It should also be noted that the van Laar equation, because of its functional form, is incapable of representing maxima or minima in the relationship between activity coefficient and mole fraction. In practice, however, such maxima and minima are relatively rare.

Reference

1 van Laar, J. J., 1910, The Vapor Pressure of Binary Mix-tures, Z. Phys. Chem., 72, 723-751.

2 Wohl, K., 1946, Thermodynamic Evaluation of Binary and Ternary Liquid Systems, Trans. AIChE, 42, 215-249.

Regular Solution TheoryTable 3-23: Regular Solution Theory



Vapor pressure Liquid molar volume Solubility parameter

Components Not valid for polar components and solutions containing fluorocarbons

Hildebrand defined a regular solution as one in which the excess entropy vanishes when the solution is mixed at constant tempera-ture and constant volume. This is nearly the case for most solutions of nonpolar compounds, provided the molecules do not differ greatly in size. The excess Gibbs energy is then primarily deter-mined by the attractive intermolecular forces. Scatchard and Hilde-brand made a simple assumption relating mixture interactions to those in pure fluids; the result is a simple theory in which the activ-ity coefficients are a function of pure-component properties only. The important property is the solubility parameter, which is related to the energy required to vaporize a liquid component to an ideal gas state. The activity coefficient expression is

(3-110)

where:

= liquid molar volume of component i


δi = solubility parameter of component i

There are no adjustable parameters in regular solution theory. It is useful for mixtures of nonpolar components, but it should not be used for highly non-ideal mixtures, especially if they contain polar components. Solubility parameters have been tabulated for numer-ous compounds, and these parameters are included for most compo-nents in PRO/II's library.

Reference

Hildebrand, J.H., Prausnitz, J. M. and Scott, R. L., 1970, Regular and Related Solutions, Van Nostrand Reinhold Co., New York.

Flory-Huggins TheoryTable 3-24: Flory Huggins Theory



Vapor pressure Liquid molar volume Solubility parameter

Components Best for components which are chemically similar and which differ only in size (e.g. polymer solutions)

The Flory-Huggins model may be considered a correction to the Regular Solution Theory for the entropic effects of mixing mole-cules which differ greatly in size. It is therefore suitable for poly-mer/solvent systems, especially if the molecules involved are nonpolar. In this simplest implementation of the theory, there are no binary parameters. The activity coefficient expression is:

(3-111)

where:

= activity coefficient from regular solution theory

= liquid molar volume of component i

= liquid molar volume of solution


Reference

1 Flory, P. J., 1942, Thermodynamics of Higher Polymer Solutions, J.Chem.Phys., 10, 51.

2 Huggins, M. L., 1942, Thermodynamic Properties of Solu-tions of Long Chain Compounds, Ann. N.Y. Acad. Sci., 43, 9.

3 Misovich, M. J., Grulka, E. A., and Banks, R. F., 1985, Generalized Correlation for Solvent Activities in Polymer Solutions, Ind. Eng. Chem. Proc. Des. Dev., 24, 1036.

Wilson EquationTable 3-25: Wilson Equation



Vapor pressure Liquid molar volume

Components Useful for polar or associating components in nonpolar solvents and for completely miscible liquids

The Wilson equation was the first to incorporate the concept of “local composition.” The basic idea is that, because of differences in intermolecular forces, the composition in the neighborhood of a specific molecule in solution will differ from that of the bulk liquid. The two parameters per binary are, at least in principle, associated with the degree to which each molecule can produce a change in the composition of its local environment. The expression for the activ-ity coefficient is:

where:

(when unit of aid is K)


(when unit of aij is KCAL or KJ)

(when unit of aij is NODIME)

and is the liquid molar volume of component i.

aij represents a characteristic energy of interaction between species i and j. While there is no explicit temperature dependence in the Wilson equation's parameters, the derivation is such that the equa-tion may be used with some confidence over a wider range of tem-peratures than either the Margules or van Laar equations. It is also much more successful in correlating mixtures containing polar components. The Wilson equation cannot describe local maxima or minima in the activity coefficient. Its single significant shortcom-ing, however, is that it is mathematically unable to predict the split-ting of a liquid into two partially miscible phases. It is therefore completely unsuitable for problems involving liquid-liquid equilib-ria.

Reference

1 Holmes, M. H. and van Winkle, M., 1970, Wilson Equa-tion Used to Predict Vapor Compositions, Ind. Eng. Chem., 62(1), 2231.

2 Orye, R. V. and Prausnitz, J. M., 1965, multi-component Equilibria with the Wilson Equation, Ind. Eng.Chem., 57(5), 1826.

3 Wilson, G. M., 1964, Vapor-Liquid Equilibrium XI. A New Expression for the Excess Free Energy of Mixing, J. Amer. Chem. Soc., 86, 127.


NRTL EquationTable 3-26: NRTL Equation



Vapor pressure Components Useful for strongly non-ideal mixtures and for partially immiscible systems.

The NRTL (non-random two-liquid) equation was developed by Renon and Prausnitz to make use of the local composition concept, while avoiding the Wilson equation's inability to predict liquid-liq-uid phase separation. The resulting equation has been quite success-ful in correlating a wide variety of systems. The expression for the activity coefficient is:

(3-112)where:

(when unit is K)

(when unit is KCAL or KJ)

Three parameters, τij, τji, and αij = αji are required for each binary. These parameters may be made temperature dependent as described above. If tij is to be represented with only one constant, it has been found empirically that better results over a range of tem-peratures are obtained if only bij is used and aij = cij = 0. The α parameter does not vary greatly from binary to binary, and it is often satisfactory to fix it at 0.3 for vapor-liquid systems and 0.2 for liquid-liquid systems.

Reference1 Renon, H. and Prausnitz, J. M., 1968, Local Composition

in Thermodynamic Excess Functions for Liquid Mixtures, AIChE J., 14, 135144.


2 Harris, R. E., 1972, Chem. Eng. Prog., 68(10), 57.

UNIQUAC EquationTable 3-27: UNIQUAC Equation



Vapor pressure van der Waals area and volume

Components Useful for non-electrolyte mixtures containing polar or nonpolar components and for partially miscible systems

The UNIQUAC (universal quasi-chemical) equation was developed by Abrams and Prausnitz based on statistical-mechanical consider-ations and the lattice-based quasi chemical model of Guggenheim. As in the Wilson and NRTL equations, local compositions are used. However, local surface-area fractions are the primary composition variables instead of volume fractions. Each molecule i is character-ized by a volume parameter ri and a surface-area parameter qi.

The excess Gibbs energy (and therefore the logarithm of the activity coefficient) is divided into a combinatorial and a residual part. The combinatorial part depends only on the sizes and shapes of the indi-vidual molecules; it contains no binary parameters. The residual part, which accounts for the energetic interactions, has two adjust-able binary parameters. The UNIQUAC equation has, like the NRTL equation, been quite successful in correlating a wide variety of systems. The expression for the activity coefficient is:

(3-113)

(3-114)

(3-115)

where:


(when unit is K)

(when unit is KCAL or KJ)

Awi = van der Waals area of molecule iVwi = van der Waals volume of molecule i

Two parameters, Uij and Uji, are required for each binary; they may be made temperature dependent as described above. If no tempera-ture dependence is used for Uij, better results over a range of tem-peratures are normally obtained by using aij and setting bij = 0.

Reference1 Abrams, D. S. and Prausnitz, J. M., 1975, Statistical Thermody-

namics of Mixtures: A New Expression for the Excess Gibbs Free Energy of Partly or Completely Miscible Systems, AIChE J., 21, 116-128.

2. Anderson, T. F. and Prausnitz, J. M., 1978, Application of the UNIQUAC Equation to Calculation of multi-component Phase Equilibria. 1. Vapor-Liquid Equilibria, Ind. Eng. Chem. Proc. Des. Dev., 17, 552-561.

3. Anderson, T. F. and Prausnitz, J. M., 1978, Application of the UNIQUAC Equation to Calculation of multi-component Phase Equilibria. 2. Liquid Liquid Equilibria, Ind. Eng. Chem. Proc. Des. Dev., 17, 561-567.


4. Maurer, G. and Prausnitz, J. M., 1978, On the Derivation and Extension of the UNIQUAC Equation, Fluid Phase Equilibria, 2, 91-99.

UNIFACTable 3-28: UNIQUAC Equation



Vapor Pressure Pressure up to 100 atmospheres

van der Waals area and volume

Temperature 32 300F

Components All components well below their critical points

The UNIFAC (universal functional activity coefficient) method was developed in 1975 by Fredenslund, Jones, and Prausnitz. This method estimates activity coefficients based on the group contribu-tion concept following the Analytical Solution of Groups (ASOG) model proposed by Derr and Deal in 1969. Interactions between two molecules are assumed to be a function of group-group interac-tions. Whereas there are thousands of chemical compounds of inter-est in chemical processing, the number of functional groups is much smaller. Group-group interaction data are obtained from reduction of experimental data for binary component pairs.

The UNIFAC method is based on the UNIQUAC model which rep-resents the excess Gibbs energy (and logarithm of the activity coef-ficient) as a combination of two effects. Equation (3-112) on page 72 is therefore used:

The combinational term, γiCln , is computed directly from the

UNIQUAC equation (3-113) on page 73 using the van der Waals area and volume parameter calculated from the individual structural groups:


where:

where:NOC = number of componentsNOG = number of different groups in the mixturez = lattice coordination number = 10

νki = number of functional groups of type k in molecule i

Rk = volume parameter of functional group k

Qk = area parameter of functional group k

xi = mole fraction of component i in the liquid phase

The group volume and area parameters are obtained from the atomic and molecular structure.


(3-116)

(3-117)

where: Vwk = van der Waals volume of group k

Awk = van der Waals area of group k

The residual term, , is given by:

(3-118)

where:

= residual activity coefficient of group k in the mixture

= residual activity coefficient of group k in a reference solution containing only molecules of group type i. This quantity is

required so that as xi 1

The residual activity coefficient is given by:

(3-119)

where: m, n = 1, 2, ... NOG

The parameter tmk is given by

(3-120)

where: amk = binary interaction parameter for groups m and k

The binary energy interaction parameter amk is assumed to be a constant and not a function of temperature. A large number of inter-


action parameters between structural groups, as well as group size and shape parameters have been incorporated into PRO/II.

Reference

1 Derr, E.L., and Deal, C.H., 1969, Inst. Chem. Eng. Symp. Ser., 32(3), 40.

2 Fredenslund, Aa., Jones, R.L., and Prausnitz, J.M., 1975, Group Contribution Estimation of Activity Coefficients in non-ideal Liquid Mixtures, AIChE J., 27, 1086-1099.

3 Skjold-Jørgensen, S., Kolbe, B., Groehling, J., and Rasmus-sen, P., 1979, Vapor-Liquid Equilibria by UNIFAC Group Contribution. Revision and Extension, Ind. Eng. Chem. Proc. Des. Dev., 18(4), 714-722.

4 Gmehling, J., Rasmussen, P., and Fredenslund, Aa., 1983, Vapor-Liquid Equilibria by UNIFAC Group Contribution. Revision and Extension, Ind. Eng. Chem. Proc. Des. Dev., 22(10), 676-678.

5 Hansen, H.K., Rasmussen, P., Fredenslund, Aa., Schiller, M., and Gmehling, J., 1991, Vapor-Liquid Equilibria by UNIFAC Group Contribution. 5. Revision and Extension, Ind. Eng. Chem. Res., 30(10), 2352-2355.

Modifications to UNIFACThe UNIFAC method provides good order-of-magnitude estimates. The accuracy of the method can be improved by incorporating a temperature-dependent form for the binary group energy interaction parameter.

UFT1 Lyngby modified UNIFACResearchers at Lyngby developed a three-parameter temperature dependent form for the binary interaction parameter. The parameter τmk is now given by:

(3-121)


(3-122)

where: amk, bmk, cmk = binary interaction parameters

To = 298.15 K

The combinatorial part of the logarithm of the activity coefficient is given by:

(3-123)

(3-124)

Reference

Larsen, B.L., Rasmussen, P., and Fredenslund, Aa., 1987, A Modi-fied UNIFAC Group Contribution Model for Prediction of Phase Equilibria and Heats of Mixing, Ind. Eng. Chem. Res., 26(11), 2274-2286.

UFT2 Dortmund modified UNIFACFor this modified method, the temperature-dependent form of Amk is given by:

(3-125)

The combinational part of the logarithm of the activity coefficient is given by:

(3-126)

(3-127)

where:


z = lattice coordination number = 10

Reference

1 Weidlich, V., and Gmehling, J., 1987, A Modified UNIFAC Model. 1. Prediction of VLE, hE, and γ, Ind. Eng. Chem. Res., 26, 1372-1381.

2 Gmehling, J., Li, J., and Schiller, M., 1993, "A Modified UNIFAC Model. 2. Present Parameter Matrix and Results for Different Thermodynamic Properties,” Ind. Eng. Chem Res., 32(1) 178.

3 Gmehling, J., Lohmann, J., Jakob, A., Li, J., Joh, R., 1998, “A Modified UNIFAC Model. 3. Revision and Extension,” Ind. Eng. Chem Res., 37,4876.

UFT3For this modified UNIFAC method, the temperature-dependent form of Amk is given by:

(3-128)

The combinatorial and residual parts of the activity coefficient are identical to those described previously for the UNIFAC method.

Reference

Torres-Marchal, C., and Cantalino, A.L., 1986, Industrial Applica-tions of UNIFAC, Fluid Phase Equil., 29, 69-76.

UNFV - Free volume modification to UNIFACThis method was developed for modeling polymer systems. The liquid activity coefficient is given by a combination of the same combinatorial and residual terms as UNIFAC, plus a free volume effect term:

(3-129)


(3-130)

where:

b=1.28

where: Vi = volume per gram of solvent i

Mi = molecular weight of solvent i

wi = weight fraction of component i

Ci = number of effective degrees of freedom per molecule of sol-vent i = 3.3

Reference

Oishi, T., and Prausnitz, J.M., 1978, Estimation of Solvent Activi-ties in Polymer Solutions Using a Group Contribution Method, Ind. Eng. Chem. Proc. Des. Dev., 17(3), 333-339.


Fill Options The ability of a liquid activity method to accurately predict vapor-liquid equilibria and/or vapor-liquid-liquid equilibria depends to a great degree on whether or not binary interaction parameters are available for that method. PRO/II contains a proven mechanism for filling in missing binary interaction parameters for liquid activity methods. When a liquid activity method such as NRTL is selected for phase equilibrium calculations, and the FILL option is selected, PRO/II uses the following mechanism in order to obtain the binary interaction data the model needs:

1 Any user-supplied binary interaction parameters, or mutual solubility, infinite dilution, or azeotropic data are used in preference to any other data.

2 The VLE and LLE databanks which contain binary interac-tion parameters are then searched for data.

3 The SimSci azeotropic databank is searched for appropriate azeotropic data, which are then regressed to provide binary interaction data.

4 For VLE calculations, if steps 1 through 3 do not supply the required parameters, then the group contribution methods UNIFAC or its modification UFT1, or the regular solution method, or the Flory-Huggins method may be used to pro-vide estimates for the interaction parameters. For LLE cal-culations, UNIFAC or the modified UNIFAC method UFT1 is used to supply the parameter estimates.

5 Finally, if binary interaction parameters are still missing after steps 1-4 are followed, then all missing parameters are set equal to zero.

Figure 3-1 shows the mechanism used by PRO/II to backfill miss-ing binary parameters for VLE, or VLLE calculations.


Figure 3-1: Flowchart for FILL Methods


For VLLE calculations, in order to avoid conflicts between VLE and LLE binary interaction data, PRO/II follows a number of strict rules when filling in these binary interaction data.

If no VLE or LLE interaction data are supplied by the user, PRO/II uses the following order in searching for interaction data for both VLE and LLE calculations:

1 The LLE databank

2 The VLE databank

If the user supplies VLE interaction data only, then PRO/II uses the following order in searching for binary parameters for both VLE and LLE calculations:

1.The user-supplied values given on the KVALUE(VLE) state-ment

2. The LLE databank

3. The VLE databank

If the user supplies LLE interaction data only, or both VLE and LLE interaction data, for LLE calculations, the databanks are searched in the order:

1.The user-supplied data given on the KVALUE(LLE) state-ment

2 The LLE databank

3 The VLE databank

If the user supplies LLE interaction data only, or both VLE and LLE interaction data, for VLE calculations, the databanks are searched in the order:

1.The user-supplied data given on the KVALUE(VLE) state-ment

2 The VLE databank


Henry's LawWhen liquid activity methods are used, the standard-state fugacity for a component is the fugacity of the pure liquid. This standard state is not convenient, however, for dissolved gases, especially if the temperature is above the critical temperature of the solute in question. For super-critical gases, and also for trace solutes such as organic pollutants in water, it is more convenient to use a standard state defined at infinite dilution. This standard-state fugacity is the Henry's constant.

Thermodynamically, the Henry's constant of a solute i in a solvent j is defined as the infinite-dilution limit of the ratio of the fugacity to the mole fraction:

(3-131)

Unless the pressure is high or there is vapor-phase association, the fugacity fi can be replaced by the partial pressure yiP. The K-value can then be expressed as:

(3-132)

This relationship is strictly true only in the infinite-dilution limit, but K-values from Henry's law generally remain accurate at solute mole fractions up to approximately five percent.

PRO/II correlates Henry's constants to the following functional form:

(3-133)

The temperature dependence in equation (3-131) is that expected from a thermodynamic analysis provided the solvent's critical point is not approached too closely. Thermodynamics also predicts that the effect of pressure on the effective Henry's constant at conditions beyond infinite dilution is linear in pressure (with C4 proportional to the solute's partial molar volume). The pressure correction is neg-ligible at low and moderate pressures; if the pressure is sufficiently high for that term to become important it is likely that better results could be obtained by an equation of state with an advanced mixing rule.


When the HENRY option is specified, components with critical temperatures below 400 K are automatically designated as solute components by PRO/II. The user may, however, override these des-ignations as desired. PRO/II has an extensive databank of Henry's constants for super-critical gases in various solvents and also for many organic compounds in water. Henry's constants may also be input by the user. If no Henry's constant is given for a solute, PRO/II substitutes the solute's vapor pressure (extrapolated if necessary). This substitution is good only for nearly ideal solutions. In particu-lar if no Henry's constant is available for an organic solute in water it is better to remove the organic from the list of solutes and allow the liquid activity method (with interaction parameters filled in via UNIFAC if necessary) to compute the K-value.

Note: The temperature dependence of Henry's constants is very important. Especially for organic solutes in water, often only a single value at 25 C is reported. Calculations using this input value at significantly different temperatures (for example, steam stripping near 100 C) are likely to produce unrealistic answers (for example, drastically overestimating the amount of steam required). In such cases, the user can obtain a better answer by assuming that the temperature dependence of the solute's Henry's constant is the same as for its vapor pressure. The slope of ln Psat versus 1/T becomes C2 in equation (3-131), and (with C3=C4=0) the 25 C point can then be used to solve for C1.

The Henry's constant of a solute in a mixture of solvents is com-puted from the following mixing rule:

(3-134)

where the sum is taken over all solute species j, and the mole frac-tions xj used in the sum are computed on a solute-free basis.

Reference

Prausnitz, J.M., Lichtenthaler, R.N., and Gomes de Azevedo, E., 1986, Molecular Thermodynamics of Fluid Phase Equilibria, 2nd edition, Prentice Hall, Englewood Cliffs, NJ, Chapter 8.

Heat of Mixing CalculationsFor many liquid mixtures, the enthalpy may be accurately approxi-mately as a mole fraction sum of pure-component enthalpies (see


Ideal in Section, Generalized Correlations). For some systems, however, the excess enthalpy, or heat of mixing, is not negligible and should be accounted for if accurate prediction of the liquid enthalpy is important. It should be noted that SimSci's equations of state and generalized correlations produce a heat of mixing as a nat-ural part of their calculations. Therefore, explicit calculation of the heat of mixing is only used in conjunction with the IDEAL method for liquid enthalpy, which is normally used with liquid activity coefficient K-value methods.

Gamma MethodThermodynamics allows the excess enthalpy to be computed directly from the activity coefficients in a mixture and their temper-ature dependence. This is known as the GAMMA option, and the equation is:

(3-135)

where:

= excess heat of mixing

Despite the attractiveness of this direct thermodynamic computa-tion, experience has shown that the activity-coefficient parameters which correlate phase equilibria do not in general produce very accurate values for excess enthalpies. GAMMA is a viable option when no other method is available, but the resulting heats of mixing may only be accurate to within a factor of two.

Redlich-KisterExpansionExperimental data for heats of mixing for binary systems are most often represented by an expansion about an equi-molar mixture:

(3-136)

where:

In equation (3-136), known as the Redlich-Kister expansion, α12 represents the excess enthalpy of a 50-50 binary mixture. Higher-order terms correlate asymmetry in the curve of excess enthalpy versus composition.


SimSci's databanks contain regressed values of the coefficients in equation (3-136) for approximately 2200 binary mixtures. In addi-tion, these parameters may be regressed to heat-of-mixing data with SimSci's REGRESS program (now available through the Thermo Data Manager) and then entered through input by the user.

The empirical nature of the Redlich-Kister expansion means that there is some degree of arbitrariness in the way it is extended to mixtures. SimSci offers two options, known as RK1 and RK2. Both have the same basic form:

(3-137)

where:

X xi xj–= (form RK1)

Xxi xj–xi xj+--------------= (form RK2)

Note: Which mixture rule is better for a multi-component system (they are equivalent for binaries) depends upon the system, and there are no general guidelines. RK2 is, however, somewhat pref-erable from the standpoint of theoretical consistency.

Vapor Phase Fugacities

General InformationIn vapor-liquid equilibrium calculations, it becomes necessary to calculate separately the fugacity of each component in the vapor and liquid phases. Each of the two phases usually requires different techniques. For example, liquid-phase non-idealities may be described by activity coefficients, while deviations from ideal gas behavior in the vapor phase are described by fugacity coefficients. The vapor phase fugacity coefficients may be obtained through the use of an equation of state. The fugacity coefficients are obtained from classical thermodynamics as follows:


(3-138)

(3-139)

where: φi = fugacity coefficient of component i

fi = fugacity of component i

R = gas constant

T = system temperature

P = system pressure

ni = number of moles of component i

yi = mole fraction of component i in the vapor phase

V = volume of system

z = compressibility factor of the mixture

In equation (3-138), the partial derivatives of P with respect to ni must be evaluated using an appropriate equation of state. Therefore, the problem of calculating fugacities of components in a gaseous mixture is equivalent to the problem of establishing a reliable equa-tion of state for such a mixture. Once such an equation is found, the fugacities can be computed from equations (3-138) and (3-139).

Equations of StateEquations of state are powerful methods for calculating vapor-phase fugacities at low and high densities. The analytical expres-sion of the fugacity coefficient can be derived from a cubic equation of state. The derivation of the fugacity coefficient from a cubic equation of state is straightforward because the cubic equation of state in pressure is volume-explicit. Cubic equations of state are usually applied to systems comprising mixtures of nonpolar or weakly polar components. The usefulness of a cubic equation of state can be greatly enhanced by using an advanced alpha function, and an advanced mixing rule. Modified cubic equations of state can be suitable for systems containing polar components. See “Equa-tions of State” on page 34.


Additionally, a cubic equation of state (incorporated with a chemi-cal theory of association) is suitable for systems containing polar and hydrogen-bonding molecules. These include carboxylic acids which form monomer-dimer pairs and hydrogen fluoride. Such methods include the Associating Equation of State and the Hayden O'Connell method. See “Hayden-O'Connell” on page 91..

The equation-of-state methods are generally more reliable for cal-culating vapor phase fugacity coefficients than any other method, except for dimerizing components where the Hayden-O'Connell method should be used.

Truncated Virial Equation of StateMany equations of state have been proposed for calculating vapor fugacities, as mentioned in the previous section, but almost all of them are empirical in nature. The virial equation of state for gases has a sound theoretical foundation, and is free of arbitrary assump-tions. The virial equation gives the compressibility factor as a power series in the reciprocal molar volume:

(3-140)

where:

v = molar volume

B, C, D, .. = second, third, fourth etc. virial coefficients

The virial coefficients are a function of temperature and composi-tion only. For low or moderate vapor densities, the virial equation can be truncated after the second virial coefficient and converted to a pressure-explicit form:

(3-141)

The compositional dependence of B for a mixture containing N components is given by:

(3-142)

where:

Bii = second virial coefficient for pure component i Bij = second virial cross coefficient


The cross coefficients characterize on interaction using between one molecule of component i and one of component j. They may be obtained from mixture data, though often they are estimated from the pure component coefficients.

O'Connell and Prausnitz developed a correlation for the reduced second virial coefficient (both pure component and cross coeffi-cients) which consists of three generalized functions:

1. One for nonpolar contributions to the second virial coefficient,2. One for polar interactions based on the dipole moment, and,

3. An association function for substances which exhibit specific forces such as hydrogen bonds.

Use of this correlation requires the critical temperature, critical pressure, critical volume, acentric factor, dipole moment, and asso-ciation constant for each component present. Missing dipole moments and association constants are assumed to be zero. One limitation of this method is that as the virial equation of state is an expansion about the compressibility factor of an ideal gas, higher-order terms cannot be neglected in high density regions. The virial equation of state can provide reliable estimates of vapor-phase fugacity coefficients at low pressures or high temperatures only.

Reference

O'Connell, J. P., and Prausnitz, J. M., 1967, Empirical Correlation of Second Virial Coefficients for Vapor-Liquid Equilibrium Calcu-lations, Ind. Eng. Chem. Proc. Des. Dev., 6(2), 245-250.

Hayden-O'ConnellThe truncated virial equation of state described above is useful for predicting deviations from ideality in those systems where moder-ate attractive forces yield fugacity coefficients not far removed from unity. However, in systems containing carboxylic acids, two acid molecules tend to form a dimer, resulting in large negative deviations from vapor ideality even at very low pressures.

To account for dimerization, Hayden and O'Connell in 1975, devel-oped an expression of fugacity coefficient based on the chemical theory of vapor imperfection. The “chemical theory” assumes that there are dimerization equilibria for a binary mixture of components A and B:


(3-143)

(3-144)

where:

A1, B1 = monomers

A2, B2 = dimers

AB = cross dimer

Hayden and O'Connell related second virial coefficients to the dimerization equilibrium constants, KA2, KB2, and KAB, and developed generalized second virial coefficients for simple and complex systems. Properties required to use this correlation are; the critical temperature, critical pressure, mean radius of gyration, dipole moment, association parameter, and solvation parameter. Association and solution parameters for common associating com-ponents are available in PRO/II's databanks.

This method is a reliable generalized method for calculating vapor phase fugacities up to moderate pressures, especially for systems where no data are available.

Reference

Hayden, J. G., and, O'Connell, J. P., 1975, A Generalized Method for Predicting Second Virial Coefficients, Ind. Eng. Chem. Proc. Des. Dev., 14(3), 209-216.


Special Packages

General InformationPRO/II contains a number of thermodynamic methods specifi-cally developed for special industrial applications. Data pack-ages are available for the following applications:

Alcohol systems

Glycol systems

Sour water systems

Amine systems

For many applications, databanks containing binary interactions specifically regressed for components commonly found in the application have been developed and incorporated into PRO/II. For example, for alcohol systems, a special alcohol databank, in combi-nation with the NRTL K-value method is used to calculate the K-values. For other applications, such as the SOUR or GPSWAT method for sour systems containing NH3, H2S, CO2, and H2O, a K-value method has been specifically developed for phase equilib-rium calculations.

Alcohol Package (ALCOHOL)The alcohol data package uses the NRTL liquid activity method to calculate phase equilibria (see Section, Liquid Activity Methods). This system uses a special set of NRTL binary interaction data for systems containing alcohols, water, and other polar components. The binary parameters have been obtained by the regression of experimental data for alcohol systems. The recommended tempera-ture and pressure ranges for the ALCOHOL data package are as fol-lows:

Temperature:

122-230 oF for H2O-alcohol systems

150-230 oF for all other systems


The vapor enthalpy and density and the vapor and liquid entropies are calculated using the SRKM equation of state (see Section, Equations of State), while the liquid enthalpy and density are calcu-


lated using ideal methods (see Section, Generalized Correlation Methods).

Table 3-29 shows the components present in the ALCOHOL data-bank for which there are binary interaction parameters available.

Figure 3-2 on page 3-96 shows the availability of binary interaction data in the Alcohol data bank.


.

Table 3-29: Components Available for ALCOHOL Package

Components Formula LIBIDMiscellaneous AcetaldehydeSulfolane Light Gases HydrogenNitrogenOxygenCarbon Dioxide Hydrocarbons IsopentaneN-pentaneCyclopentane2 Methylpentane1-HexeneN-HexaneMethylcyclopentaneBenzeneCyclohexane2-4 Dimethylpentane3-Methylhexane1-Trans-2-Dimethylcyclopentanen-heptaneMethylcyclohexaneToluene2-4 Dimethylhexane

1-Trans-2-Cis-4-Tri- methylcyclopentane

C2H4OC4H8O2SH2S H2N2O2CO2 C5H12C5H12C5H10C6H14C6H12C6H14C6H12C6H6C6H12C7H16C7H16C7H14

C7H16C7H14C7H8C8H10

C8H10

ACHSULFLN H2N2O2CO2 IC5NC5CP2MP1HEXENENC6MCPC6H6CH24DMP3MHX1T2MCP

NC7MCHTOLU24DMHX

1T2C4MCP


Figure 3-2: Binary Interaction Data in the Alcohol Databank

Glycol Package (GLYCOL)The glycol data package uses the SRKM equation of state to calcu-late phase equilibria for glycol dehydration applications (see Sec-tion, Equations of State). This system uses a special set of SRKM binary interaction data and alpha parameters for systems containing glycols, water, and other components. The binary parameters and alpha parameters have been obtained by the regression of experi-mental data for glycol systems. The recommended temperature and pressure ranges for the GLYCOL package are:

Temperature: 80-400 F



Other thermodynamic properties such as the vapor and liquid enthalpy, entropy, and vapor density are calculated using the SRKM equation of state, while the liquid density is calculated using the API method (see Section, Generalized Correlation Methods).

Table 3-30 shows the components present in the GLYCOL databank for which there are binary interaction parameters available.

Table 3-30: Components Available for GLYCOL PackageComponents Formula LIBID

Hydrogen Nitrogen Oxygen Carbon Dioxide Hydrogen Sulfide Methane Ethane Propane Isobutane N-butane Isopentane Pentane Hexane Heptane Cyclohexane Methylcyclohexane Ethylcyclohexane Benzene Toluene O-xylene M-xylene P-xylene Ethylbenzene Ethylene Glycol Diethylene Glycol Triethylene Glycol Water

H2 N2 O2 CO2 H2S CH4 C2H6 C3H8 C4H10 C4H10 C5H12 C5H12 C6H14 C7H16 C6H12 C7H14 C8H16 C6H6 C7H8 C8H10 C8H10 C8H10 C8H10 C2H6O2 C4H10O3 C6H14O4 H2O

H2 N2 O2 CO2 H2S C1 C2 C3 IC4 NC4 IC5 NC5 NC6 NC7 CH MCH ECH BNZN TOLU OXYL MXYL PXYL EBZN EG DEG TEG H2O

Figure 3-3 shows the binary interaction parameters, denoted by "x", present in the glycol databank. Interaction parameters denoted by "o" are supplied from the SRK databank. It should be noted that for all pairs not denoted by "x" or "o", the missing binary interaction


parameters are estimated using a molecular weight correlation, or are set equal to 0.0.

Figure 3-3: Binary Interaction Data in the Glycol Databank


Sour Package (SOUR)This sour water package uses the SWEQ (Sour Water EQuilibrium) method developed by Wilson for a joint API/EPA project. Phase equilibria for sour water components NH3, H2S, CO2, and H2O are modeled using a modified van Krevelen approach. The van Krev-elen model assumes that H2S and CO2 only exist in solution as ion-ized species. This is only true for solutions containing an excess of NH3 or other basic gas. This limitation has been removed in the SWEQ method by considering the chemical equilibrium between ionic species of H2S or CO2 and their undissociated molecules in the liquid phase.

In the SWEQ model, the partial pressure in the vapor phase for H2S or CO2 is given by:

pH2S HH2S C×H2S

= (3-145)

pCO2HCO2

C×CO2

= (3-146)

where: = partial pressure of component i

= Henry's Law constant for component i in water

= concentration of component i in the liquid phase, gmoles/kg solution

The SWEQ model uses Henry's Law constants for each component in solution as a function of temperature and composition of the undissociated molecular species in the liquid phase. The Henry's constants for H2S and CO2 were obtained from data published by Kent and Eisenberg who developed a model for predicting H2S-CO2-MEA-H2O and H2S-CO2-DEA-H2O systems. The Henry's Law constants used in the SWEQ model for equations (3-144) and (3-145) are:

(3-147)

(3-148)


where: T = system temperature, degrees Rankine

The Henry's Law constant for water was obtained by correlating H2O vapor pressure data from the A.S.M.E. steam tables over the range 25 C to 150 C:

(3-149)

The Henry's Law constant for NH3 was taken from data published by Edwards et al.:

(3-150)

The chemical equilibria of all the main reactions in the liquid phase due to the dissociation of the sour gas molecules are considered in the model. The reaction equilibrium constants, Ki, are correlated as functions of temperature, composition of undissociated sour gas molecules in the liquid phase, and ionic strength.

(3-151)

where:

= equilibrium constant of reaction i

= equilibrium constant at infinite dilution for all species

a,b,c = constants

I = ionic strength =

= ionic charge of species j

The reaction equilibrium constants at infinite dilution, , are given in the form first proposed by Kent and Eisenberg:

(3-152)

where:

A,B,C,D,E = constants

The constants used in the SWEQ model for equations (3-151) and (3-152), obtained by the regression of experimental data, are given


in the original EPA report. The original SWEQ method was devel-oped for pressures less than 50 psia where non-idealities in the vapor phase are not important. Corrections for vapor-phase non-ide-alities using SRKM have been incorporated PRO/II, thus extending the applicable pressure range to 1500 psia.

The phase behavior of all other components present in the system is modeled using the SRKM equation of state (see Section, Equations of State). The following limits apply to the SOUR method as imple-mented in PRO/II:



Composition:

where: = weight fraction of component i

Note: NH3 and water must be present when using the SOUR method.

Other thermodynamic properties such as the vapor enthalpy, vapor and liquid entropy, and vapor density are calculated using the SRKM equation of state, while the liquid enthalpy and density are calculated using ideal methods (see Section, Generalized Correla-tion Methods).

Reference

1 Wilson, G. M., 1980, A New Correlation for NH3, CO2, H2S Volatility Data from Aqueous Sour Water Systems, EPA Report EPA-600/2-80-067.

2 van Krevelen, D. W., Hoftijzer, P. J., and Huntjens, F. J., 1949, Rec. Trav. Chim., 68, 191-216.

3 Black, C., 1958, Vapor Phase Imperfections in Vapor-Liq-uid Equilibria, Ind. Eng. Chem., 50(3), 391-402.

4 Kent, R. L., and Eisenberg, B., 1976, Better Data for Amine Treating, Hydrocarbon Processing, Feb., 87-90.

5 Handbook of Chemistry and Physics, 1971, 51st Edition, The Chemical Rubber Co.


6 Edwards, T. J., Newman, J., and Prausnitz, J. M., 1975, Thermodynamics of Aqueous Solutions Containing Vola-tile Weak Electrolytes, AIChE J., 21, 248-259.

GPA Sour Water Package (GPSWATER)This sour water package uses the method developed by the Gas Pro-cessors Association in 1990 for sour water systems containing com-ponents NH3, H2S, CO2, CO, CS2, MeSH, EtSH, and H2O. This model uses the SWEQ model (see above) as a precursor, extending the temperature range of applicability to 600 F. The total pressure limit is increased to 2000 psia by allowing for vapor phase non-ide-alities, and accounting for pressure effects in the liquid phase using a Poynting correction factor.

As in the SWEQ model, the chemical equilibria for all the reactions involving the NH3, H2S, CO2, CO, methyl mercaptan (MeSH), and ethyl mercaptan (EtSH) in water are considered. The components CO, methyl mercaptan (MeSH), and ethyl mercaptan (EtSH) are treated as Henry's Law components (see Section, Liquid Activity Methods) Reactions considered include:

Water:

(3-153)

Ammonia:

) (3-154)

Hydrogen Sulfide:

(3-155)

Bisulfide:

(3-156)

Carbon Dioxide:

(3-157)

Bicarbonate:


(3-158)

Carbon Dioxide and Ammonia:

(3-159)

(3-160)

(3-161)

The chemical equilibrium constants, Ki, are correlated as functions of temperature and composition. In addition, the effect of inert gases such as N2 and H2 on phase equilibria is also considered. In the liquid phase, pressure effects are accounted for by the use of a Poynting correction factor, and electrostatic effects are incorporated into the calculated liquid activity coefficients.

Vapor-phase non-idealities are computed using a truncated virial equation of state. The virial equation used is truncated after the third virial coefficient as follows:

(3-162)

where:

B, C are the second and third virial coefficients

v = molar volume

z = compressibility factor

Phase equilibria for all other components present in the system are modeled using the SRKM equation of state (see Section, Equations of State).

The following limits apply to the GPSWATER method:



Composition: wNH3 < 0.40

where:


= weight fraction of component i

= partial pressure of component i in the vapor phase

Note: NH3, CO2, H2S, and water must be present when using the GPSWATER method.

Other thermodynamic properties such as the vapor enthalpy, vapor and liquid entropy, and vapor density are calculated using the SRKM equation of state, while the liquid enthalpy and density are calculated using ideal methods (see Section, Generalized Correla-tion Methods).

Reference

Wilson, G. M., and Eng, W. W. Y., 1990, GPSWAT: GPA Sour Water Equilibria Correlation and Computer Program, GPA Research Report RR-118, Gas Processors Association.

Amine Package (AMINE)The PRO/II simulation program contains a method to model the removal of H2S and CO2 from natural gas feeds using alkanola-mines. Alkanolamines are formed by ammonia reacting with an alcohol. Amines are considered to be either primary, secondary, or tertiary, depending on whether 1 or 2 or 3 of the hydrogen atoms have been replaced on the ammonia molecule. PRO/II provides data for the primary amines monoethanolamine (MEA), secondary amines diethanolamine (DEA), diglycolamine (DGA), and diiso-propanolamine (DIPA), and the tertiary amine methyldiethanola-mine (MDEA). MEA and DEA are the most frequently used amines in industry.

In aqueous solutions, H2S and CO2 react in an acid-base buffer mechanism with alkanolamines. The acid-base equilibrium reac-tions are written as chemical dissociations following the approach taken by Kent and Eisenberg:

Water:

(3-163)

Hydrogen Sulfide:

(3-164)


Bisulfide:

(3-165)

Carbon Dioxide:

(3-166)

Bicarbonate:

(3-167)

Alkanolamine:

(3-168)

where:

= equilibrium constant for reaction i

= alkanolamine

R represents an alkyl group, alkanol, or hydrogen

In addition to the acid-base reactions above, CO2 also reacts directly with primary and secondary alkanolamines to form a stable carbamate, which can revert to form bicarbonate ions.

Carbamate Reversion to Bicarbonate:

(3-169)

Tertiary amines such as MDEA are not known to form stable car-bamates. In an aqueous solution with MDEA, CO2 forms bicarbon-ate ions by reaction (22) only.

Note: CO2, H2O, and H2S must be present when using the AMINE method.

The chemical equilibrium constants, Ki, are represented by the fol-lowing equation:


(3-170)

The equilibrium constant for the protonated amine dissociation reaction given in reaction (24) is corrected to the pure amine refer-ence state. This is done by relating the constant to the infinite-dilu-tion activity coefficient of the amine in water estimated from experimental data for the system amine-water.

The liquid enthalpy is calculated using ideal methods and adding a correction for the heat of reaction as follows using either a modified Clausius-Clapeyron equation or fits of data from the Gas Processors Association:

(3-171)

where:

ΔHr = heat of reaction

R = gas constant

KT1, KT2 = K-values at temperatures T1 and T2

The vapor phase enthalpy and density, and liquid and vapor phase entropy are calculated using the SRKM equation of state (see Sec-tion, Equations of State). Ideal methods are used to calculate the liq-uid-phase density (see Section, Generalized Correlation Methods).

For MEA and DEA systems, data have been regressed from a large number of sources, resulting in good prediction of phase equilibria for these systems. For systems containing DIPA, a limited amount of experimental data was available, and so the DIPA results are not recommended for final design purposes. For MDEA and DGA sys-tems, the user is allowed to input a residence time correction to allow the simulation results to more closely match plant data. The following application ranges are suggested for amine systems:

Table 3-31: Application Guidelines for Amine SystemsMEA DEA DGA MDEA DIPA

Pressure, psig

25-500 100-1000 100-1000 100-1000

100-1000

Temperature, F

<275 <275 <275 <275 <275


Reference

1 Kent, R. L., and Eisenberg, B., 1976, Better Data for Amine Treating, Hydrocarbon Processing, Feb., 87-90.

2 Maddox, R. N., Vaz, R. N., and Mains, G. J., 1981, Ethano-lamine Process Simulated by Rigorous Calculation, Hydro-carbon Processing, 60, 139-142.

Electrolyte Mathematical Model

Discussion of EquationsThe mathematical model employed in PRO/II Electrolytes is a deterministic set of nonlinear algebraic equations. The equation set is composed of:

Equilibrium Expressions

For each vapor-liquid, liquid-liquid, solid-liquid, and liquid intra-phase equilibrium, there is an equation of the form:

(3-172)

where:

K = thermodynamic equilibrium constant: a function of tempera-ture and pressure

= activity coefficient or, for vapors, fugacity coefficient of the ith product and reactant, respectively; a function of temperature, pressure, and composition

Concentration, wt % amine

~15-25 ~25-35 ~55-65 ~50 ~30

Acid gas loading, gmole gas/gmole amine

0.5-0.6 0.45 0.50 0.4 0.4

Table 3-31: Application Guidelines for Amine Systems


= stoichiometric coefficient of the ith product and reac-tant, respectively

= molality or, for vapors, partial pressure of the ith product and reactant, respectively..

Note: When H2O (the solvent) appears in the equilibrium expres-sion, its contribution is expressed as aH2O, the activity of water. All pure solid component activities are assumed to be one. The fugacity coefficient, φi is defined as fi/yiP or fi/Pi, where f denotes fugacity, P represents total pressure, and Pi stands for partial pressure. The adopted convention is that φi approaches one as total pressure approaches zero. The activity ai is given by γimi, where γi approaches one as the molality of all solutes approaches zero.Note: Equilibrium constants often are written entirely in terms of fugacities, in which case thermodynamics requires that K is a function of temperature only. When activities are used instead of fugacities, as in the present treatment, then K is affected by the choice of standard state. Since the standard state for solutes is infinite dilution in H2O, a pressure dependence is introduced from the pressure dependence of the water properties. This effect is negligible except at conditions approaching water's critical point. Consequently, over the temperature and pressure validity range for the electrolyte thermodynamic methods (0-200 C; 0-200 atm), K is treated only as a function of temperature.

An electro-neutrality equation

(3-173)

where:

Zi = species charge

NC, NA = number of cations and anions, respectively

Equations For Solutions Involving a Second Liquid Phase, (liquid-liquid equilibrium)

(3-174)

where:


ai = activity of ith species

A, O = represent aqueous and organic phases, respectively

NM = number of molecular species distributing between phases

Note: The required number of material balances, i.e. NB, com-pletes the model and assures that the number of equations and the number of unknowns are equal. Normally these balances include an overall, a vapor phase, an organic phase, and several compo-nent balances.

Thus, assuming NK equilibrium equations, the model has NK + NB + NM + 1 equations. The customary unknowns are:

The moles of H2O in the aqueous liquid phase plus all ionic and molecular species molalities.

The vapor phase: species mole fractions plus overall vapor fraction.

The organic liquid phase: species mole fractions plus overall organic phase fraction (if second liquid phase is present).

The solid phase composition: moles precipitated for all solid species.

As noted above, the number of NB equations required is that num-ber which assures that the number of equations equals the overall number of unknowns. This is a natural consequence of the phase rule.

Modeling ExampleTo better understand this modeling concept, consider the aqueous system represented by H2O-CO2-NACL. The reactions considered will be:

(3-175)

(3-176)

(3-177)

(3-178)

(3-179)

(3-180)


Based upon the general model described earlier, this leads to:

Equilibrium Expressions

(3-181)

(3-182)

(3-183)

(3-184)

(3-185)

(3-186)

Electro-neutrality Equation

(3-187)

Liquid-liquid Equilibrium Equations

There are none in this example.

Material Balance Equations

Overall material balance:

(3-188)

where:

in = inflow or feed component in units of moles

V = overall vapor fraction on a mole basis


In equation (3-188), the products H2O and NACLppt are in units of moles.

3 Vapor balance

(3-189)

where:

y = mole fraction for vapor species

Sodium balance

(3-190)

Chlorine balance

(3-191)

Carbon balance

(3-192)

Equations (3-181) – (3-192) are the required 12 equations. Assum-ing that the temperature and pressure are known, and further assum-ing that deterministic formulations are available for the equilibrium constants, activity coefficients, fugacity coefficients, and the activ-ity of water, then the corresponding 12 unknowns (calculated vari-ables) are:

and moles of water.


Electrolyte Thermodynamic Equations

Thermodynamic FrameworkThe mathematical model described in the previous section utilizes several thermodynamic quantities. Specifically these are:

Equilibrium constants - normally strong functions of tempera-ture and weaker functions of pressure.

Aqueous-phase activity coefficients - normally strong functions of temperature and composition and weaker functions of pres-sure.

Vapor-phase fugacity coefficients - normally significant func-tions of temperature, pressure and composition, particularly at elevated pressures.

Organic liquid-phase activities - normally strong functions of temperature and composition and weaker functions of pressure.

The formulations used by PRO/II Electrolytes for each of these quantities are described below. In addition, the thermodynamic framework includes formulations for the calculation of enthalpies and densities for aqueous liquid, organic liquid, vapor, and solid phases. These latter formulations are also presented below.

Equilibrium ConstantsBy considering basic thermodynamic relationships and assuming a constant heat capacity of reaction, the following general equation can be derived:

(3-193)

where:

T = temperature in Kelvins

Tr = reference temperature, 298.15 K

ΔG° = free energy of the reaction in the standard state at the reference temperature (and pressure, 1 bar). This is derived from the standard-state Gibbs free energies of formation, ΔG°f, by first, summing the product of the reaction coefficient times ΔG°f over all reactants and


then, over all products. Next, the sum for the reactants is subtracted from the sum for the products to obtain ΔG°.

ΔH° = corresponding standard state heat of reaction at the ref-erence conditions. Obtained from the standard-state enthalpy of formation, ΔH°f, using the same general procedure as used for ΔG°.

ΔCp°= corresponding standard state heat capacity of reaction at the reference conditions. Obtained from the stan-dard state heat capacity, Cp°, using the same general procedure as used in ΔG°.

R = gas constant

The derivation of the relationship given in equation (3-193) can be found in the Handbook of Aqueous Electrolyte Thermodynam-ics(Ref. 1). Values of ΔG°f, ΔΗ°f, and Cp° for reaction species are usually available in the critically evaluated data compilations of the National Bureau of Standards (Ref. 2) or the Russian Academy of Sciences (Ref. 3).

The chosen standard states for the thermodynamic framework are as follows:

Aqueous solutes - hypothetical, infinitely dilute solution at unit molality;

Solvent - pure fluid; Gaseous species - hypothetical 1 bar ideal gas; Solid species - pure solid.

These are the same standard states as used by the NBS2.

Thermodynamic Framework in PRO/IIThe original implementation in PRO/II now is referred to as the “Old Framework”. For some reactions, where sufficient measure-ments are available, it uses empirically fitted functions for K values as a function of temperature instead of equation (3-193). The “Old Framework” is used for all models supplied by SIMSCI and by the PUBLIC library.

A new framework was introduced in the PUBNEW library starting with PRO/II 5.11. This form uses an equation of state to predict K values as a function of both temperature and pressure.


Version 7.0 of PRO/II replaced the Electrolyte Utility Package (EUP) with the newer Chemistry Wizard from OLI Systems, Inc. A newer version of the Chemistry Wizard became available starting with PRO/II version 8.0. Contact your OLI Systems representative for the most appropriate information.

Note: The older EUP no longer is supported by Invensys Simsci-Esscor or OLI Systems, Inc. Documentation of the Chemistry Wiz-ard is available separately from OLI Systems, Inc.

Aqueous Phase ActivitiesThe key to successful simulation of aqueous systems is to accu-rately predict the reaction equilibria described in the previous sec-tion. Greater precision is added by a good description of the following correction factors:

Activity coefficients of ions in solution.

Activity coefficients of molecules in solution.

Activity of water.

In PRO/II Electrolytes, these quantities can be represented in terms of a number of alternative as well as complementary formulations. The common element of all of these formulations is that they involve the interaction of pairs of species in solution. Two general assumptions are made:

Interactions between like-charged ions are not significant.

Higher-level interactions (involving more than two species) are not significant.

IonsFor ions the formulation used is:

(3-194)

DHi = Debye-Huckel term for long-range, ion-ion interactions,

defined as:

(3-195)

where:


A = Debye-Hückel constant, a known function of temperature and solvent density (Ref. 1)

I = ionic strength =

where m = molality

Zi = charge on ion i

The Debye-Hckel term predicts the long-range or electrostatic effects. For dilute solutions of ionic strength less than 0.1, this is the only term needed.

BZi = Bromley-Zemaitis (Refs. 4,5) term for short-range, ion-ion

interactions, defined as:

(3-196)

where:

(3-197)

NO = number of ions with charge opposite to that of the ion being represented.

Bij,Cij, Dij = three interaction coefficients for each cation-anion interaction. These are each made 3-parameter func-tions of temperature. Thus, for each cation-anion interac-tion, there are 9 coefficients that must be established.

Pi = Pitzer (Refs. 6,7) term for short-range, ion-molecular interactions, defined as:

(3-198)


where:

(3-199)

and

(3-200)

and

(3-201)

where:

NM = number of molecular species in solution

NS = number of species in solution

= two interaction coefficients for each ion-molecule or molecule-molecule interaction.

Note: Each of the ij interaction coefficients is a 3-parameter func-tion of temperature. Thus, for each interaction, there are 6 coeffi-cients that must be established.

Molecules Other Than WaterFor molecules other than water, the Setschenow equation is used. Where ij(0) and ij(1) parameters are available, the preferred formu-lation is from Pitzer (Refs 6,7). The Setschenow and Pitzer relations are:

(3-202)

where:

bi = Setschenow coefficient for the neutral species

bj = "Salting-out" coefficient particular to each ion


NI = the number of ionic species in solution

and

(3-203)

BPij is defined by equation (3-199) above.

Water ActivityThe water activity for multi-component systems is obtained from an integrated form of the Gibbs-Duhem equation, together with a mix-ing rule suggested by Meissner and Kusik (Ref. 8). The formulation can be represented as:

(3-204)

where:

(3-205)

(3-206)

NC = the number of cation species in solution

NA = the number of anion species in solution

The above formulations are, in cases where the necessary interac-tion coefficients have been fit to cover the conditions being simu-lated, quite adequate for predicting systems in which water is the principal solvent.


Vapor Phase FugacitiesFour alternative methods are provided:

Ideal, all fugacity coefficients are assumed to be 1.0.

Nothnagel method, generally valid up to 20 atmospheres.

Nakamura method, generally valid up to 200 atmospheres.

Soave-Redlich-Kwong (SRK) method, valid over a wide range of conditions and generally recommended when vapor-phase non-ideality is important.

Nothnagel MethodNothnagel et al.(Ref. 9) developed a method for calculating fugac-ity coefficients in mixtures at moderate pressures. The main feature of the method is the inclusion of dimerization effects on the second virial coefficient.

The equation of state is written as:

(3-207)

where:

bm = size parameter for mixture, cm3 / mole

nT = number of moles of true species

P = pressure, atmospheres

R = gas constant, 82.056 cm3 atm / mole K

T = temperature, Kelvins

V = total volume, cm3

nT is obtained from the solution of the dimerization equilibria described below. bm is given by a sum over all true species:

(3-208)

where:

bi = size parameter for true species i, cm3 / mole

ni = number of moles of true species i


If i is a dimer formed by monomers A and B, bi is given by:

(3-209)

Values of b for monomers are tabulated in the original reference.

For component j, the fugacity coefficient is given by:

(3-210)

where:

bj = size parameter for monomer j, cm3 / mole

yj = apparent mole fraction of component j

zj = true mole fraction of component j monomer

The true mole fractions zj are computed from the dimerization equi-libria. Each dimerization is described by an equilibrium constant Kij:

(3-211)

(3-212)

The dimerization equilibrium constants are related to the enthalpy and entropy of dimerization:

(3-213)

where:

D Hij = enthalpy of dimerization, cal/mole

D Sij = entropy of dimerization, cal/mole

R = gas constant, 82.056 cm3 atm/mole K (left side of equa-tion (3-213)), 1.987 cal/mole K (right side of equation (3-213)).


The correlations for ΔHij and ΔSij, along with the necessary param-eters for 178 components, may be found in the original paper (Ref. 9).

Nakamura MethodNakamura et al. (Ref. 10) proposed the following perturbed-hard-sphere equation of state for gas mixtures:

(3-214)

where:

P = pressure, atmospheres

R = gas constant, 0.082056 liter atm/mole K

T = temperature, Kelvins

v = molar volume, liter / mole

ε = reduced density, b/4v

b = parameter signifying the hard-core size of the molecule, liter / mole

a = parameter signifying the attractive force strength, atm/mole

In addition to equations for the reduced enthalpy difference and entropy difference, the following equation was presented for calcu-lating the fugacity coefficient of a species k in the gas mixture:

(3-215)

With the P, R, T, v, and ε terms defined earlier, the following defini-tions and calculations apply:

n = number of species


(3-216)

where:

g = pure-component parameter

δ =pure-component parameter

(3-217)

where:

yi = vapor mole fraction of i

ck = pure-component parameter

(3-218)

z = compressibility factor = (3-219)

(3-220)

(3-221)

where:

α = pure-component parameter

αij = interaction parameter

(3-222)


(3-223)

(3-224)

(3-225)

(3-226)

for non polar gas

where:

βi = pure component parameter

βij = interaction parameter

Values for the pure-component and interaction parameters used in equations (3-213) through (3-226) are given in the original paper by Nakamura et al. for the following components: Ar, CH4, C2H4, C2H6, C3H6, C3H8, CO, CO2, H2, H2O, H2S, N2, NH3, and SO2.

SRK MethodCalculation of fugacity coefficients from the Soave-Redlich-Kwong equation of state is described in “General Cubic Equation of State” on page 34.

Note: For both the Nothnagel and Nakamura options, if an elec-trolyte model contains a volatile species not covered in the origi-nal paper by Nakamura et al. for the method (MEA and HCl are examples of such species) the fugacity coefficients all default to 1.0 (ideal gas). The SRK option does not suffer from this limita-tion.

Organic Phase ActivitiesActivities of components in an organic liquid phase (if one exists) are obtained from the Kabadi-Danner modification to the SRK equation of state. This method is described in Section, Equations of State, of this manual.


EnthalpyThe pressure dependence of the enthalpy for vapor, liquid, and solid phases is neglected in this thermodynamic framework. However, this does not introduce significant uncertainties in enthalpy calcula-tions over the stated model validity ranges for temperature (0 to 200 C) and pressure (up to 200 bars). Because enthalpy is treated as pressure-independent, PRO/II Electrolytes users will receive a warning about potential failure of the flash when pressure is varied to meet a duty specification.

Vapor and Solid PhasesThe enthalpy of the vapor or solid phase at the temperature and solution composition of interest is evaluated using:

(3-227)where: Hio, yi = the standard state molar enthalpy and the mole frac-

tion, respectively, of the ith vapor or solid component NC = the total number of components present in the vapor or

solid phase. At the temperature of interest, Hio is evaluated using:

(3-228)where:

, = the standard state, isobaric, molar heat capacity, and the standard state molar enthalpy of forma-tion for the ith vapor or solid component

Tr = the reference temperature of 298K.

Values of for vapor and solid species are obtained from empir-ical functions of temperature, which are given by:

(for vapor) (3-229)

(for solid) (3-230)

where: Ai, Bi, Ci = temperature-independent, but phase-dependent constants of the ith vapor or solid component.


Aqueous Liquid PhaseThe enthalpy of the aqueous solution, Haq, at the temperature and solution composition of interest is evaluated using:

(3-231)

where:

Hw = the molar enthalpy of pure water at the temperature of inter-est and at the vapor/liquid saturation pressure of H2O

xi = the mole fraction of the ith solute species

NM, NI = the total number of molecular and ionic solute species, respectively

The enthalpy of pure water may be obtained from the equation of state for H2O given by Haar, Gallagher, and Kell (Ref. 11). At the temperature and solution composition of interest, Hi is evaluated using:

(3-232)

where:

γi = the activity coefficient of the ith solute species

R = the gas constant

Values of γi and are obtained from equations (3-194) on page 114 through(3-201) for ionic species. Equations (3-202) and (3-203) on page 117 are used for molecular solutes.

Values of Hi° are obtained from equation (36), using values of

Cpi° and ΔHfi Tr,° for aqueous species and using the following

relations to represent for ionic and molecular solutes:

(for ionic solutes) (3-233)

(for molecular solutes) (3-234)


where: Ai, Bi, and Ci = temperature-independent, but phase-independent constants of the ith molecular solute.

Molar Volume and Density

Vapor PhaseThe density of the vapor phase is evaluated using the equation of state which corresponds to the chosen vapor fugacity method.

Aqueous Liquid PhaseThe molar volume of the aqueous solution, vaq, at the temperature, pressure, and solution composition of interest is evaluated using:

(3-235)

where: vw = the molar volume of pure water at the temperature and

pressure of interest, as given by the HGK (Ref. 11) equa-tion of state.

= the standard-state molar volume of the ith molecular or ionic aqueous solute species, at the reference temperature.

Organic Liquid PhaseThe density of an organic liquid phase is calculated using the Rack-ett method for liquid density. This method is described in Section, Generalized Correlations, of this manual.

Solid PhaseThe molar volume of the solid phase, vsol, at the temperature of interest is evaluated using:

where: (3-236)

= the standard state molar volume of the ith pure solid component at the reference temperature.


References

1 Zemaitis, J.F. Jr., Clark, D.M., Rafal, M., and Scrivner, N.C., 1986, Handbook of Aqueous Electrolyte Thermodynamics, AIChE.

2 Wagman, D.D., et al., 1968-1973, Selected Values of Chemical Thermodynamic Properties, NBS Tech Note, 270-3 to 8.

3 Chase, M.W. Jr., Davies, C.A., Downey, J.R. Jr., Frurip, D.J., McDonald, R.A., and Syverud, A.N., 1985, JANAF Thermody-namic Tables, 3rd edn., J. Phys. Chem. Ref. Data, 14, Supplement no. 1, 1856 pp.

4 Wagman. D. D., et al., 1982, The NBS Tables of Chemical Ther-modynamic Properties, J. Phys. Chem. Ref. Data, 11, Supplement no. 2, 392 pp.

5 Glushko, V.P., editor, 1965-1981, Thermal Constants of Com-pounds, Russian Academy of Sciences, Vols. I-X.

6 Zemaitis, J.F., Jr., 1980, Predicting Vapor-Liquid-Solid Equilibria in multi-component Aqueous Solutions of Electrolytes, Thermo-dynamics of Aqueous Systems with Industrial Applications, S.A. Newman, ed., ACS Symposium Series, 133, 227-246.

7 Bromley, L.A., 1973, Thermodynamic Properties of Strong Elec-trolytes in Aqueous Solutions, AIChE J., 19, 313-320.

8 Pitzer, K.S., 1979, Theory: Ion Interaction Approach, Activity Coefficients in Electrolyte Solutions, 1, 157-208, R.M. Pytkow-icz, ed., CRC Press, Boca Raton, FL.

9 Pitzer, K.S., 1980, Thermodynamics of Aqueous Electrolytes at Various Temperatures, Pressures and Compositions, Thermody-namics of Aqueous Systems with Industrial Applications, S.A. Newman, ed., ACS Symposium Series, 133, 451-466.

10 Meissner, H.P., and Kusik, C.L., 1973, Aqueous Solutions of Two or More Strong Electrolytes - Vapor Pressures and Solubilities, Ind. Eng. Chem. Proc. Des. Dev., 12, 205-208.

11 Nothnagel, K.H., Abrams, D.S., and Prausnitz, J.M., 1973, Gen-eralized Correlation of Fugacity Coefficients in Mixtures at Mod-erate Pressures, Ind. Eng. Chem. Proc. Des. Dev., 12, 25-35.

12 Nakamura, R., Breedveld, G.J.F., and Prausnitz, J.M., 1976, Ther-modynamic Properties of Gas Mixtures Containing Polar and Nonpolar Components, Ind. Eng. Chem. Proc. Des. Dev., 15, 557-564.


13 Haar, L., Gallagher, J.S., and Kell, G.S., 1984, NBS/NRC Steam Tables, Hemisphere Press, Washington D.C., 320 pp.

Solid-Liquid Equilibria

General InformationThe solubility of solids in liquids can be described by the van't Hoff (ideal-solubility) equation. This is sufficient for many systems where non-idealities are small. Alternatively, solubility data, corre-lated as a function of temperature, may be entered directly. Precipi-tation of solid salts and minerals from aqueous solutions may be calculated rigorously using PRO/II Electrolytes. This capability is described separately in Sections, Electrolyte Mathematical Model, and 1.2.10, Electrolyte Thermodynamic Equations, of this manual.

van't Hoff EquationThe simplest description of the solubility of a solid in a liquid phase is obtained by assuming that the activity coefficient of the solute in the liquid phase is one. The solubility is then entirely determined by the ratio of the pure solid's fugacity to its standard-state fugacity in the liquid phase, which is that of a pure sub-college liquid. This ratio is one at the solute's triple point where the solubility also becomes one. At lower temperatures, it can be calculated with fair accuracy using the heat of melting; a more accurate estimate results if the heat capacity change of melting is known. A full derivation of the ideal solubility (or van't Hoff, after the Dutch chemist who first proposed it) equation is given by Prausnitz et al. The result is:

(3-237)

where:

ΔHm = enthalpy change of melting

ΔCp = heat capacity change of melting

Tt = triple-point temperature

In practice, the more easily accessible melting temperature is usu-ally used instead of the triple-point temperature. The difference is almost always negligible. The ideal-solubility equation predicts the same solubility for a given solute regardless of solvent composition.


It is therefore primarily useful for systems where the solute and sol-vent are of a similar chemical nature and form a nearly ideal solu-tion. For example, the solubility of aromatic hydrocarbons in benzene is well described by equation (3-237)

Table 3-32: van't Hoff

Required pure component properties


Triple-point temperature (Tt)

(or melting tempera-ture if Tt is not avail-able)

Compo-nents

Solute and sol-vent should be of a similar chemi-cal nature (i.e. form a near-ideal solution).

Enthalpy of melting

.

Solubility DataFor systems where sufficient data exist, solid solubilities may be entered by the user in the form of a correlation of solubility versus temperature. This correlation has the same functional form as the van't Hoff equation:

(3-238)

where:

xij = the equilibrium solubility of solute i in solvent j at tempera-ture

For solubility of a solid solute i in a mixed solvent, theory dictates that the mixing rule should have the following form:

(3-239)

In equation (3-239) the sum is over all solvent species, and Zj is the mole fraction of solvent component j normalized to a solute-free basis. If the “normal” liquid mole fractions are denoted by z, this is written as:

(3-240)


Fill Options for Solubility DataIn a multi-component mixture, data may be missing for one or more of the i,j pairs appearing in the sum in equation (3-239). Three options are provided for filling in missing values of xij. The default option is to fill in missing values with xij as calculated by equation (3-237), the van't Hoff equation.

Note: When the van't Hoff equation is used as a FILL option, the ΔCp terms are ignored.

The FILL = ONE option uses values of one (complete miscibility) for the solute's solubility in the missing solvents. The FILL = FREE option causes the missing solvent or solvents to be ignored in the solubility calculation. In other words, if a solvent k is missing solu-bility data for the solute, the sum in equation (3-239) is only taken over those solvents for which data exist, and the mole fractions in that sum are re-normalized to a k-free (as well as solute-free) basis:

(3-241)

In equation (3-241) the sum is over all solvents k for which there are no solubility data. Note that equation (3-241) is meaningless if no solvent in the mixture has solubility data. If FILL = FREE is specified in such a case, the calculations are defaulted to the van't Hoff equation.

Reference

Prausnitz, J.M., Lichtenthaler, R.N., and Gomes de Azevedo, E., 1986, Molecular Thermodynamics of Fluid-Phase Equilibria, 2nd edition, Prentice-Hall, Englewood Cliffs, NJ, Chapter 9.

Transport Properties

General InformationThe following transport properties are calculated and/or used by PRO/II:

Table 3-33: Transport PropertiesLiquids Vapors

Viscosity Viscosity


In addition, PRO/II will calculate the vapor-liquid surface tension for a stream. Most library components include saturated vapor and liquid values for viscosity, thermal conductivity, and surface ten-sion as part of the stored physical property data. Several correla-tions have also been included in PRO/II which predict the above properties for hydrocarbon mixtures. Liquid diffusivity is used by some of the unit operations but is not stored in the component library. The transport methods are described in the sections that fol-low.With the exception of the PURE and TRAPP methods, there are no special provisions to characterize the hydrocarbon type (paraf-finic, olefinic, etc.). While these non-characterizing methods may be used for all hydrocarbon types, or petroleum fractions, the best accuracy is to be expected for paraffins, with a degradation in accu-racy for olefins or aromatics. Non-hydrocarbon transport properties are best represented by the properties from structure methods dis-cussed in Section, Component Data.

PURE MethodsThe user may choose to compute transport properties as a weighted average of pure-component values. These PURE methods (also known as LIBRARY methods) require that the property in question be available for each component in the mixture with the exception of petroleum pseudocomponents. For a pseudocomponent, the property (if not supplied by the user) is calculated using the PETRO method below. The pure-component properties at the temperature of interest are combined to calculate stream average properties according to the following mixing rules:

Thermal Conductivity Thermal Conductivity

Diffusivity

Table 3-33: Transport Properties

Table 3-34: Stream Average PropertiesStream Property Additive Basis

Liquid Thermal Conductivity


The user may also provide individual component values as a func-tion of temperature either in tabular or equation forms.

PETRO Methods

Liquid ViscosityThe method selected for liquid viscosity is dependent on the reduced temperature, which is in turn calculated by Kay's rule. When the system is near the critical point (0.98<Tr<1.0), the method developed by Letsou and Steil is used. For the range 0.76<Tr<0.98, equations relating viscosity to reduced temperature and acentric factors developed by Letsou and Steil (as cited in sec-tion 9-12 in Reid, Prausnitz and Poling) are used. These methods were developed from data on simple liquid hydrocarbons.

For low temperatures in which the temperature is below the normal boiling point, a method based on the Arrhenius relation and the Thomas equation was developed by SimSci. This method relates liquid density at the normal boiling point, the critical temperature,

wi = Weight fraction (1)

Vapor Thermal Conductivity

yi = Mole fraction (2)

Liquid Viscosity

xi = Mole fraction (3)

Vapor Viscosity

yi = Mole fraction (4)

Surface Tension

xi = Mole fraction (5)

Table 3-34: Stream Average Properties


and the system temperature. The density at the normal boiling point is estimated using the equation of Gunn and Yamada.

For intermediate ranges (Tb<T<0.76<Tc), the Andrade equation is used to determine the viscosity, based on reference values at the normal boiling point and a reduced temperature of 0.76. The refer-ence values are computed by the methods described above.

After the mixture viscosity has been estimated using one of the above methods, it is corrected for the effects of pressure using the method of Kouzel (also given in the API Technical Data Book, pp. 11-47, 2nd edition). The vapor pressure, needed for this method, is estimated with the Reidel equation.

If water decant is active for the thermodynamic method, water vis-cosities are taken from the component data library. A “wet” viscos-ity is then calculated for water/hydrocarbon streams by combining the hydrocarbon and water viscosities with the following mixing rule:

(3-242)

where:

μ = viscosity

x = mole fraction

subscripts aq and hc refer to the aqueous and hydrocarbon portions of the stream

Reference

1 Andrade, E. N., 1930, The Viscosity of Liquids, Nature, 125, 309-310.

2 Gunn, R. D., and Yamada, T., 1971, A Corresponding States Correlation of Saturated Liquid Volume, AIChE J., 17, 1341-1345.

3 Kendall, J., and Monroe, K. P., 1917, The Viscosity of Liq-uids, II, The Viscosity - Composition Curve for Ideal Liq-uid Mixtures, J. Amer. Chem. Soc., 39, 1787-1802.

4 Kouzel, 1965, Hydrocarbon Proc., 44, 120.


5 Letsou, A. and Stiel, L. I., 1973, Viscosity of Saturated Nonpolar Liquids at Elevated Pressures, AIChE J., 19, 409-411.

6 Partington, J. R., 1949, An Advanced Treatise in Physical Chemistry, 2, Longmans, London.

7 Reid, R. C., Prausnitz, J. M., and Poling, B. E., 1987, The Properties of Gases and Liquids, 4th edition, McGraw-Hill, New York.

8 Reidel, L., 1954, Eine Neue Universelle Dampfdrukformel, Chem. Ing. Tech., 26, 83.

9 Thomas, L. H., 1946, The Dependence of Viscosities of Liquids on Reduced Temperature and a Relation Between Viscosity, Density, and Chemical Constitution, J. Chem. Soc., Part II, 573-579.

Liquid Thermal ConductivityThe method of Sato and Reidel is used to calculate liquid thermal conductivities. Figure 12A4.1 (Page 12-11) in the API Technical Data Book is used to correct thermal conductivities for pressure effects.

If water decant is active for the thermodynamic method, water ther-mal conductivities are taken from the component data library. A “wet” thermal conductivity is then calculated for water/hydrocar-bon streams by combining the hydrocarbon and water viscosities with the following mixing rule:

(3-243)

where:

λ = thermal conductivity

w = weight fraction in the liquid phase

subscripts aq and hc refer to the aqueous (water) and hydrocarbon portions of the stream


Reference

10 American Petroleum Institute, 1978, Data Book, 5th edi-tion.

11 Reidel, L., 1950, The Determination of the Thermal Con-ductivity and the Specific Heat of Various Mineral Oils, Chem. Ing. Tech., 21, 349.

Surface TensionThe surface tension for hydrocarbon liquids is estimated with pro-cedure 10A3.1 (Page 10-17) in the API Technical Data Book (3rd edition). Surface tension for water is extracted from the component data library. “Wet” surface tension values for decant hydrocarbon systems are computed with the formula:

(3-244)

where:

σ = surface tension

x = mole fraction in the liquid phase


Vapor ViscosityVapor viscosities at low pressures are computed by the method of Thodos et al. They are then corrected for pressure effects using the equation of Dean and Stiel. Water vapor viscosities are taken from the component library. “Wet” vapor viscosities for decant systems are calculated by the following combinatorial formula:

(3-245)

where:

μ = mole fraction in the vapor phase




Reference

1 Thodos, G., and Yoon, 1970, Viscosity of Nonpolar Gas-eous Mixtures at Normal Pressures, AIChE J., 16, 300-304.

2 Dean, D.G., and Stiel, L.S., 1965, The Viscosity of Nonpo-lar Gas Mixtures at Moderate and High Pressures, AIChE J., 11, 526-532.

3 Herning, F., and Zipperer, L., 1936, Calculation of the Vis-cosity of Technical Gas Mixtures from the Viscosities of the Individual Gases, Gas-U. Wasserfach., 79, 69.

Vapor Thermal ConductivityThe Roy-Thodos method is used to determine vapor thermal con-ductivities. The function of temperature used is the one that is pre-sented by the authors for saturated hydrocarbons. This method is corrected for pressure effects using the equations of Stiel and Tho-dos.

Data for water are retrieved from the component data library. “Wet” conductivities are predicted for water/hydrocarbon systems as fol-lows:

(3-246)

where:

y = mole fraction in the vapor phase


subscripts aq and hc refer to the aqueous and hydrocarbon portions of the stream.

Reference

1 Perry, R.H., and Green, D., 1984, Perry's Chemical Engi-neers Handbook, 6th edition, McGraw-Hill, New York.

2 Roy, D., and Thodos, G., 1979, Thermal Conductivity of Gases, Ind. Eng.Chem.Fundam., 9, 71-79.


3 Stiel, L.I., and Thodos, G., 1964, The Thermal Conductivity of Nonpolar Substances in the Dense Gaseous and Liquid Regions., AIChE J., 10, 26.

TRAPP CorrelationThe TRAPP method predicts viscosities and thermal conductivities for pure hydrocarbon components and mixtures of hydrocarbons and light inorganics for both vapor and liquid phases.

Note: Since this method does not predict surface tension, this property is computed from the PETRO correlation described ear-lier in this section

A brief description of the method is presented here. For additional details, see the Ely and Hanley reference paper.

The TRAPP method uses a one-fluid conformal model coupled with the extended corresponding-states approach developed by Leland and his co-workers. Mathematically, the viscosity of a fluid mixture or component is given by:

(3-247)

and the thermal conductivity is represented by:

(3-248)

where:

μ = viscosity

λ = thermal conductivity

F = a dimensional factor

ρ = the fluid density

subscripts x and o denote unknown and reference fluids

superscript ' refers to the potential or translational contribution

superscript " refers to the contribution due to internal degrees of freedom

This method is applicable to the full range of densities and tempera-tures, from the dilute gas to the dense liquid. The required constants


for each component are the critical constants (Tc, Pc and Vc) and the acentric factor.

Note: The method originally was developed for, and was restricted to, the list of components given in Table 3-35. Complete parameters are available in the component libraries for these com-ponents. However, in the current versions of PRO/II, correlations have been added to generate any required parameters that are not supplied by the user. Currently, the TRAPP method applies to all library, petro, and non-library components. It may not be suitable for use with electrolyte or polymer components.

Note: The authors of the TRAPP method recommend it not be used when water is present. It should also be used with care at reduced temperatures above 0.925.

Table 3-35: TRAPP Components (3.3 versions)Component Name ID Name Component Name ID

Name

METHANE METHANE

PROPYLENE PRLN

ETHANE ETHANE 1-BUTENE BUT1

PROPANE PROPANE cis-2-BUTENE BTC2

ISOBUTANE IC4 trans-2-BUTENE BTT2

n-BUTANE BUTANE ISOBUTENE IBTE

ISOPENTANE 2MB 1,3-BUTADIENE 13BD

n-PENTANE PENTANE 1-PENTENE PNT1

NEOPENTANE 22PR cis-2-PENTENE PTC2

n-HEXANE HEXANE trans-2-PENTENE PTT2

2-METHYLPENTANE

2MP 2-METHYL-1-BUTENE

2BT1

3-METHYLPENTANE

3MP 3-METHYL-1-BUTENE

3BT1

2,2-DIMETHYLBUTANE

22MB 2-METHYL-2-BUTENE

2BT2


1 Leland, T. W., Robinson, J. S., and Suther G.A., 1968, Sta-tistical Thermodynamics of Mixtures of Molecules of Dif-ferent Sizes, Trans. Farad. Soc., 64, 1447-1460.

2 Ely, J. F., and Hanley, H. J. M., 1981, Prediction of Viscos-ity and Thermal Conductivity in Hydrocarbon Mixtures-Computer Program TRAPP, Proceedings of 60th Annual Convention, Gas Processors Association.

2,3-DIMETHYLBUTANE

23MB 1-HEXENE HXE1

n-HEPTANE HEPTANE 1-HEPTENE HPT1

n-OCTANE OCTANE PROPADIENE ALEN

n-NONANE NONANE 1,2-BUTADIENE 12BD

n-DECANE DECA BENZENE BNZN

n-UNDECANE UNDC TOLUENE TOLU

n-DODECANE DDEC m-XYLENE MXYL

n-TRIDECANE TRDC o-XYLENE OXYL

n-TETRADECANE TDCN p-XYLENE PXYL

n-PENTADECANE PNDC ETHYLBENZENE EBZN

n-HEXADECANE HXDC CARBON DIOXIDE

CO2

n-HEPTADECANE HPDC CARBON MONOXIDE

CO

CYCLOPENTANE CP HYDROGEN H2

METHYLCYCLOPENTANE

MCP HYDROGEN SULFIDE

H2S

CYCLOHEXANE CH OXYGEN O2

METHYLCYCLOHEXANE

MCH NITROGEN N2

ETHYLCYCLOPENTANE

ECP SULFUR DIOXIDE

SO2

ETHYLCYCLOHEXANE

ECH WATER H2O

ETHYLENE ETLN

Table 3-35: TRAPP Components (3.3 versions)


Special Methods for Liquid Viscosity

SIMSCI (Twu) CorrelationFor petroleum fractions, viscosity prediction methods are usually based on boiling point and specific gravity. The API Technical Data Book (1978) expresses the Watson correlation in a nomograph form. However, the graphical form is unsuitable for simulation pur-poses and cannot be extrapolated. Abbott et. al., (1970, 1971) give a correlation which agrees with the API data quite well but breaks down when extrapolated.The SimSci or Twu correlation is based on a perturbation expansion method. Here, the properties of a real sys-tem (petroleum fractions, in this case) are expanded about the val-ues of a reference system (chosen to be n-alkanes). The kinematic viscosity of a petroleum fraction at 210 F is expressed in the follow-ing manner:

(3-249)

(3-250)

(3-251)

(3-252)

Similar equations for kinematic viscosity at 100 F are given below:

(3-253)

(3-254)

You can then determine the relationship between viscosities at any two temperatures, given the kinematic viscosity at the 2 tempera-tures, using equations (3-249)-(3-254) above with the generalized relationship developed by Wright (and modified by Twu), given in equations (3-255) through (3-258) below.


(3-255)

(3-256)

(3-257)

(3-258)

where: υ = kinematic viscosity

Reference

1 Abbott, M.M., Kaufman, T.G., and Domash, L., 1971, A Correlation for Predicting Liquid Viscosities of Petroleum Fractions, Can. J. Chem. Eng., 49, 379.

2 Twu, C.H., 1985, Internally Consistent Correlation for Pre-dicting Liquid Viscosities of Petroleum Fractions, Ind. Eng. Chem. Proc. Des. Dev., 24, 1287.

3 Wright, W.A., 1969, An Improved Viscosity-temperature Chart for Hydrocarbons, J. of Materials, 4, 19.

Heavy Oil1 Correlation for Liquid ViscosityMost earlier liquid viscosity methods produce poor predictions when applied to heavy fractions. This is especially true at lower temperatures where liquid viscosity may change dramatically with small temperature changes. Simulation Sciences developed a corre-lation that is now recommended for temperatures heavy oils and bitumens. Viscosity is estimated at two reference (100F and 210F) temperatures, then the viscosity-temperature relationship is extrap-olated or interpolated, as required.

The HEAVY oils liquid viscosity method is a hybrid between the LIBRARY and SIMSCI methods. Library components are treated as individual components with viscosity contributions derived from the saturated liquid (LIBRARY) viscosity correlations. In contrast, individual petro component constants (Tc, Pc, etc.) are mixed according to the SIMSCI method to represent a single lumped (typ-ically heavy) component. This composite petro component is treated mainly as in the SIMSCI method. An exception is that the NBP is determined as the mean average of the lumped component. The SIMSCI method would compute the NBP by mole averaging.


The viscosities of the library components and of the single lumped component are combined using the Mehrotra2 mixing rule:

Mm μ( m 0.7+ ) xi Mi μ( i 0.7+ )lni

∑=ln

i defined lumped+=

(3-259)

where:

M, molecular weightm (subscript) represents the mixture and i (subscript) sums over all defined (library) component and the

single (lumped) petro component.μ is dynamic viscosity, mPa S

Reference

1 Gray, Murray R., Dekker, Marcel; Upgrading Petroleum Residues and Heavy Oils; New York (1994).

2 Mehrotra, A.K.; Eastick, R.R; Svreck, W.Y; “Viscosity of Cold Lake Bitumen and its Fractions”, Can. J. Chem. Eng., 67: 1004-1009 (1989).

API MethodThe API method used in PRO/II is very similar to the SIMSCI cor-relation discussed above. Instead of using one reference fluid, two reference fluids are used. Watson plots show that the logarithmic function of viscosity at the same boiling point temperature is a lin-ear function of API gravity. Hence, this relationship is extended as follows:

(3-260)

where:

υ = kinematic viscosity of the petroleum fraction

API = API gravity

superscripts r1,r2 refer to reference fluids 1 and 2

Since all the calculations are made at the same boiling point, equa-tion (3-260) can be simplified based on the definition of Watson characterization factor and of API gravity as:


(3-261)

where:

K = the Watson Characterization factor.

The viscosity of the reference fluid (either fluid 1 or fluid 2) can be expressed as:

(3-262)

where: C1, C2, C3, C4, C5, C6 = empirical constants.

Reference

Twu, C. H., 1986, A Generalized Method for Predicting Viscosities of Petroleum Fractions, AIChE J., 32, 2091-2094.

Liquid DiffusivityPRO/II's Dissolver unit requires the diffusivity of the solute in the solvent liquid if the user does not supply mass transfer data. PRO/II can calculate these diffusivities based on user-input data or can esti-mate them from the Wilke-Chang correlation.

User-supplied Diffusivity DataWhen the user supplies diffusivity data, the user must specify which component (or components) is to be considered the solute. Diffusiv-ity data can then be supplied for each solute in each solvent in the following form:

(3-263)

where:

Dij = diffusivity (in m2/sec) of solute i in solvent j


c1, c2, c3 = constants


For the diffusivity of a solute in a mixture of solvents, the following mixing rule is used:

(3-264)

where:

Di, m = diffusivity (in m2/sec) of solute i in solvent mixture

Xj = mole fraction of solvent component j on a solute-free basis

In equation (27) the sum is over all solvent components j.

Wilke-Chang CorrelationWilke and Chang (1955) developed a method for estimating the dif-fusivity of a solute at infinite dilution in a binary mixture. SimSci has adapted this method slightly and put it in multi-component form. The Wilke-Chang correlation is of limited accuracy, but it will generally provide a diffusivity that is good to within 50%. The correlation should not be used in cases where the solute is water or where the solute is electrolytic. The equation is as follows:

(3-265)

where:

Di, m = diffusivity (in m2/sec) of solute i in solvent mixture

Xj = mole fraction of solvent component j on a solute-free basis

Mj = molecular weight of solvent component j


μm = viscosity of solvent mixture in centipoise


Index

Numerics

1-BUTENE, 3-1371-HEPTENE, 3-1381-HEXENE, 3-95, 3-1381HEXENE, 3-951-PENTENE, 3-1371T2C4MCP, 3-951T2MCP, 3-951-Trans-2, 3-931-Trans-2-Cis-4-Tri, 3-932-DIMETHYLBUTANE, 3-1372-METHYL-2-BUTENE, 3-1372-METHYLPENTANE, 3-1373-BUTADIENE, 3-1373-DIMETHYLBUTANE, 3-1383-METHYL-1-BUTENE, 3-1373-Methylhexane, 3-953-METHYLPENTANE, 3-1376th World Congress, 3-26, 3-27

A

A.S.M.E., 3-100Acad, 3-70According, 2-23, 2-31

characterization, 2-31Account, 3-91

dimerization, 3-91, 3-92Acentric, 3-38, 3-39, 3-131Acentric factor, 2-2, 2-7, 2-8, 2-10, 2-11, 2-14, 2-15,

3-25, 3-27, 3-29, 3-32, 3-39, 3-41, 3-52, 3-53, 3-54, 3-91, 3-137

ACH, 3-95ACS Symp, 3-43ACS Symposium Series, 3-126Activity Coefficients, 3-75, 3-126

Group Contribution Estimation, 3-75Activity-coefficient, 3-87

Additive Basis, 3-130Adler, 3-32Advanced Treatise, 3-133AH2O, 3-108Ai, 3-108, 3-109, 3-123, 3-125AIChE, 3-68, 3-126AIChE J, 3-26, 3-30, 3-33, 3-34, 3-36, 3-44, 3-55, 3-72,

3-74, 3-78, 3-102, 3-142AIChE Meeting, 3-27Aij, 3-67, 3-70, 3-71, 3-72, 3-74, 3-120Aji, 3-44, 3-67, 3-72Akad, 3-67Al.Ref, 3-118, 3-120ALCOHOL, 3-17, 3-19, 3-93, 3-94, 3-95Alcohol data package, 3-93Alcohol data package uses, 3-93ALCOHOL databank, 3-94Alcohol Dehydration Systems, 3-17, 3-19Alcohol Package

Table 1.2.8-1 Components Available, 3-95ALEN, 3-138Algebraic Representation, 3-66

Thermodynamic Properties, 3-67Alkanes, 2-6, 2-30Alkanol, 3-105Alkanolamine, 3-105Alkanolamines, 3-104, 3-105Alpha formulation, 3-8, 3-36, 3-38Alter, 2-34Amer, 3-71, 3-132American Chemical Society, 3-43American Petroleum Institute, 3-28, 3-30, 3-31American Society, 2-21, 2-35

Testing, 2-21AMINE, 3-15, 3-16, 3-17, 3-105, 3-106, 3-107Amine data package, 3-104Amine Package, 3-104Amine Systems, 3-13

Methods Recommended, 3-13Amine Treating, 3-101, 3-107

Index-1

Better Data, 3-101, 3-107Amines, 3-1, 3-13, 3-16, 3-104, 3-105Amines diethanolamine, 3-104Amines MEA, 3-13Amines monoethanolamine, 3-104Amk, 3-77, 3-79, 3-80Ammonia, 3-102Analytical Solution, 3-75

following, 3-75And/or, 3-40, 3-129And/or vapor-liquid-liquid, 3-82Anderson, 3-74Andrade, 3-132Ann, 3-70Annual Book, 2-22

ASTM Standards, 2-21, 2-35Antoine, 2-4, 2-12API, 2-9, 2-11, 2-12, 2-14, 2-16, 2-17, 2-22, 2-23, 2-24,

2-25, 2-28, 2-30, 3-1, 3-9, 3-30, 3-61, 3-97, 3-132, 3-133, 3-134, 3-139, 3-141Flash point correlation, 2-37

API gravity, 2-11, 2-12, 2-28, 2-30, 3-141API liquid density, 3-1, 3-2, 3-30API Method, 2-24, 3-141API Technical Data Book, 2-22, 2-25, 2-30, 2-32, 2-33,

3-30, 3-60, 3-132, 3-133, 3-134, 3-139API/EPA, 3-99API63, 2-26APINAPHTHA, 2-32, 2-35Application Guidelines, 2-32, 3-24, 3-26, 3-27, 3-29,

3-30, 3-31, 3-32application ranges, 3-26, 3-85Applications, 3-2

Phase Equilibria, 3-5, 3-66Applied Hydrocarbon Thermodynamics, 2-17, 2-35Applying, 2-6

Rackett, 2-10Aqueous Electrolyte Thermodynamics, 3-112

Handbook, 3-113Aqueous Liquid Phase, 3-109, 3-124, 3-125Aqueous Phase Activities, 3-114, 3-116, 3-117Aqueous Solutions, 3-125

Two, 3-126Aqueous Solutions Containing Volatile Weak

Electrolytes, 3-102Aqueous Sour Water Systems, 3-101

Aromatic Systems, 3-17ASME, 3-61ASOG, 3-75Assay Processing, 2-17, 2-19, 2-21, 2-26, 2-31, 2-32Assay streams, 2-19Associating equation of state, 3-47Association, 3-48, 3-49

extent, 3-48, 3-49ASTM, 2-21, 2-22, 2-23, 2-24, 2-25ASTM D1160, 2-17ASTM D2887, 2-17ASTM D323-73, 2-33ASTM D49, 2-32ASTM D5191-91, 2-33ASTM D86, 2-17, 2-21, 2-37

converting, 2-25ASTM Standards, 2-22

Annual Book, 2-21Azeotrope, 3-26Azeotropes, 3-29azeotropic data, 3-82Azevedo, 3-5, 3-65, 3-86, 3-129

B

Backfill, 3-82PRO/II, 3-82, 3-84

Banks, 3-70Benedict-Webb-Rubin, 3-52, 3-53Benedict-Webb-Rubin-Starling, 3-52, 3-60BENZENE, 3-138Bicarbonate, 3-104

Carbamate Reversion, 3-105Bii, 3-90Bij, 3-44, 3-72, 3-74, 3-90, 3-114, 3-120

setting, 3-74Binary, 3-67

Thermodynamic Evaluation, 3-68Binary Fill options, 3-82binary interaction databank, 3-93, 3-96Binary Mixtures, 3-68Bisulfide, 3-102, 3-104BK10, 3-11, 3-29Black, 2-9Blending, 2-19, 2-20

PRO/II Component Reference Manual Index-2

Example, 2-20, 2-21Bluck, 3-45Boston, 3-39, 3-66Boston-Mathias, 3-37Braun K10, 3-11, 3-28, 3-60Brobst, 3-34Bromley-Zemaitis, 3-114Burkhart, 3-27Butane, 3-53Butterworth, 3-66BWR, 3-52BWRS, 3-13, 3-14, 3-17, 3-52, 3-53, 3-55

C

C.A. Downey, 3-125C2H4, 3-122C2H4O, 3-95C2H6, 3-97, 3-122C2H6O2, 3-97C3, 2-4, 3-85, 3-97, 3-142C3H6, 3-122C3H8, 3-97, 3-122C4, 2-4, 3-85, 3-142C4-C5, 3-29C4H10, 3-97C4H10O3, 3-97C4H8O2SH2S, 3-95C5, 2-4, 3-142C5H10, 3-95C5H12, 3-95, 3-97C6, 2-4, 2-30, 3-142C6H12, 3-95, 3-97C6H14, 3-95, 3-97C6H14O4, 3-97C6H6, 3-95, 3-97C7, 2-4C7H14, 3-95, 3-97C7H16, 3-95, 3-97C7H8, 3-95, 3-97C8, 3-30C8H10, 3-95, 3-97C8H16, 3-97

Calculate, 2-32, 3-2, 3-34, 3-47, 3-88, 3-118, 3-120fugacities, 3-89fugacity, 3-2, 3-3, 3-4, 3-5, 3-34, 3-48, 3-49, 3-118,

3-119, 3-120Calculation, 3-73

Multicomponent Phase Equilibria, 3-74Calculation Methods, 3-60Calculations

Flash Point, 2-36Cantalino, 3-80Carbamate, 3-105Carbamate Reversion, 3-104

Bicarbonate, 3-105Carbamates, 3-105CARBON DIOXIDE, 3-95, 3-97, 3-103, 3-104, 3-138Carbon Number, 2-2CAVETT, 2-5, 2-10CFCs, 3-19CH, 3-95, 3-97, 3-138CH4, 3-18, 3-97, 3-122Chang, 3-143Chao-Seader, 3-1, 3-24, 3-26, 3-60

Erbar Modification, 3-26Chao-Seader K-value, 3-1characteristic volume, 3-32, 3-33Characterization, 2-5, 2-32, 3-11, 3-12

according, 2-32sets, 2-5

Characterization-Lee-Kesler, 2-14, 2-16Chemical Abstract Number, 2-2Chemical Applications, 3-19Chemical Engineering Thermodynamics, 3-2, 3-66Chemical Engineers, 3-36Chemical Thermodynamic Properties

NBS Tables, 3-125Chim, 3-101Chlorofluorocarbons, 3-22choice, 3-37Cis-2-PENTENE, 3-137Clapeyron, 2-4Classical Thermodynamics, 3-5, 3-66

Nonelectrolyte Solutions, 3-2Clausius-Clapeyron, 3-106Clausius-Clapyron, 2-10CO, 3-13, 3-27, 3-28, 3-102, 3-120

Index-3

CO2, 3-13, 3-14, 3-26, 3-28, 3-41, 3-61, 3-93, 3-95, 3-97, 3-99, 3-101, 3-102, 3-104, 3-105, 3-122, 3-138

Coal-tar Liquids, 2-17, 2-35Coker fractionators, 3-10Complex Mixtures, 3-40Component Data, 2-1, 2-4, 3-132, 3-133, 3-134, 3-135Component Libraries, 2-1, 3-129, 3-131Component Name, 3-137Component properties-extrapolation

conventions, 2-3Component properties-temperature correlation

equations, 2-3Component Solutions, 3-55Components Available, 3-61components in databank, 3-93, 3-96Composition Curve

Ideal Liquid Mixtures, 3-132Composition-dependence, 3-45Compressed Liquids, 3-34Compressibility, 3-5, 3-9, 3-29, 3-47, 3-53, 3-88, 3-90,

3-102, 3-120Compressibility Factors, 2-17Contents, 1-2, 2-17, 3-10

Table, 1-2Convert

ASTM D86, 2-21D86, 2-21TBP, 2-21

Coon, 3-39, 3-40, 3-45, 3-50Copeman, 3-40Correlation, 2-38

API Flash Point, 2-37SIMSCI flash point, 2-38

Correlations, 3-139Predicting Liquid Viscosities, 3-139

Corresponding States, 3-53Multicomponent Mixtures, 3-53

Corresponding States Correlation, 3-55Saturated Liquid Volume, 3-132

Corresponding-states, 3-32COSTALD, 3-17, 3-18, 3-23, 3-32, 3-33COSTALD liquid density, 3-17, 3-32Critical compressibility factor, 2-2, 3-31Critical pressure, 2-2, 2-7, 2-11, 2-14, 3-25, 3-28, 3-91,

3-92Critical Properties, 2-6, 2-10Critical Review, 3-32

Equations, 3-32Critical temperature, 2-2, 2-6, 2-8, 2-11, 2-13, 2-14,

2-16, 3-7, 3-27, 3-31, 3-35, 3-48, 3-51, 3-52, 3-53, 3-54, 3-85, 3-91, 3-92, 3-131

Critical volume, 2-2, 2-7, 2-11, 2-14, 3-33, 3-54, 3-91Cross-references, 1-2Cubic, 3-36, 3-42, 3-44

New Generalized Alpha Function, 3-36cubic equation forms, 3-34Cubic equation-of-state, 3-9Cunningham, 3-39, 3-40, 3-45, 3-50Cup

Closed cup, 2-36Open Cup, 2-36

Curl-Pitzer, 3-9, 3-10, 3-27, 3-29Curves, 2-21

TBP, 2-21Cutpoint, 2-18, 2-19, 2-20, 2-21, 2-31Cutpoint Sets, 2-20Cutpoints, 2-18, 2-19, 2-26, 2-27

Defining, 2-19set, 2-18, 2-19, 2-20, 2-21, 2-27use, 2-20, 2-21

Cutpoints-application guidelines, 2-19Cutpoints-multiple sets, 2-19Cutpoints-secondary set, 2-19Cutting TBP Curves, 2-26CYCLOHEXANE, 3-95, 3-97, 3-138CYCLOPENTANE, 3-95, 3-138

D

D.M. Rafal, 3-125D1160 Curves, 2-21D2887, 2-21, 2-22, 2-23, 2-24D2887 Curves, 2-21D2887 Simulated Distillation, 2-23D323, 2-32D323 RVP, 2-34D4953, 2-33, 2-34, 2-35D5191, 2-32, 2-34, 2-35D86 Curves, 2-21Danner, 3-32, 3-41, 3-42data estimation

FILL, 3-83


Databank, 2-1, 3-13, 3-85, 3-93, 3-96Henry s, 3-85NRTL, 3-18, 3-19

databank components, 3-93, 3-96, 3-99, 3-102, 3-104Databanks, 3-82, 3-84, 3-93Daubert, 2-25DEA, 3-16, 3-104, 3-106Deal, 3-75, 3-78De-asphalting, 3-10, 3-13Debye-Hckel, 3-114, 3-115Debye-Hückel, 3-115Dechema, 3-14Defined Components, 2-3, 2-4Defining, 2-19

Cutpoints, 2-19pseudocomponent, 2-19

Density, 2-1, 2-3, 2-5, 2-6, 2-10, 2-14, 2-16, 2-26, 3-1, 3-2, 3-9, 3-19, 3-22, 3-23, 3-29, 3-30, 3-31, 3-32, 3-45, 3-52, 3-53, 3-90, 3-93, 3-96, 3-99, 3-102, 3-104, 3-112, 3-114, 3-120, 3-125, 3-131, 3-136Improved Correlation, 3-32

Density model, 3-32Departure-based, 3-8Derr, 3-75, 3-78Des, 3-40, 3-42, 3-55, 3-70, 3-74, 3-78, 3-91, 3-92, 3-140Design Institute

Physical Property Data, 2-2deviations, 3-44

equation, 3-44parameters, 3-44

DGA, 3-16, 3-106Diethylene, 3-15Diethylene Glycol, 3-97Diffusivities, 3-142Diffusivity, 3-130, 3-142

estimating, 3-143provide, 3-143requires, 3-142

Diglycolamine, 3-104Diisopropanolamine, 3-104Dimer, 3-91, 3-92, 3-119Dimerization, 3-91, 3-118Dimerize, 3-20Dimerizing, 3-1, 3-90

except, 3-20, 3-90Hayden-O Connell Method, 3-1

Dimethylcyclopentane, 3-95

Dimethylhexane, 3-95Dimethylpentane, 3-95DIPA, 3-16, 3-17, 3-106

containing, 3-106results, 3-14, 3-16

Dipole moment, 2-2, 3-91, 3-92Dissociations, 3-104Dissolver, 3-142Distillation Calculations, 2-17

Physical Data, 2-17Distillation Curves

Fitting, 2-26Interconversion, 2-21Types, 2-21

Distillation data-API 1963 method, 2-21Distillation data-API 1987 method, 2-21Distillation data-ASTM D1160, 2-21Distillation data-ASTM D2887, 2-21Distillation data-ASTM D86, 2-21Distillation data-Edmister-Okamoto method, 2-21Domash, 3-140Dortmund modified UNIFAC

UFT2, 3-79DSG, 2-6

E

EBZN, 3-97, 3-138ECH, 3-97, 3-138Edmister, 2-11, 2-17, 2-25, 2-35, 3-26, 3-27Edmister-Okamoto, 2-24, 2-25, 2-26Edwards, 3-100, 3-102Eisenberg, 3-99, 3-101, 3-107El, 3-125Electrolyte Mathematical Model, 3-107, 3-109Electrolyte Solutions, 3-126Electrolyte Thermodynamic Equations, 3-112, 3-114,

3-116, 3-117, 3-118, 3-120, 3-122, 3-123, 3-124, 3-125

Electrolytes, 3-126Electroneutrality Equation, 3-108, 3-110Empirical Correlation, 3-90

Second Virial Coefficients, 3-91Empirical Equation, 3-53

Thermodynamic Properties, 3-52Englewood Cliffs, 3-65, 3-86, 3-129

Index-5

Enthalpy, 2-3, 2-6, 2-10, 2-17, 2-31, 3-1, 3-2, 3-5, 3-8, 3-10, 3-22, 3-23, 3-27, 3-29, 3-34, 3-47, 3-86, 3-93, 3-96, 3-99, 3-102, 3-104, 3-112, 3-118, 3-120, 3-123, 3-124, 3-127Improved Prediction, 3-29

Enthalpy-ideal-gas, 2-14, 2-16Entropic, 3-69Entropy, 3-1, 3-2, 3-8, 3-22, 3-23, 3-27, 3-29, 3-34,

3-68, 3-93, 3-96, 3-99, 3-102, 3-104, 3-118, 3-120Environmental Applications, 3-19Equation

API flash point, 2-37Nelson flash point, 2-38SIMSCI flash point, 2-38

Equation of state incorporating, 3-48equation of state water solubility method, 3-60Equation-of-state, 2-9, 3-5, 3-14, 3-18, 3-19, 3-20,

3-62, 3-90Equations For Solutions Involving, 3-108

Second Liquid Phase, 3-107Equations of State, 1-1, 2-6, 2-17, 3-1, 3-2, 3-5, 3-8,

3-9, 3-10, 3-13, 3-19, 3-24, 3-31, 3-32, 3-34, 3-36, 3-40, 3-41, 3-42, 3-43, 3-44, 3-45, 3-47, 3-50, 3-52, 3-53, 3-60, 3-85, 3-86, 3-88, 3-90, 3-91, 3-93, 3-96, 3-99, 3-102, 3-104, 3-112, 3-118, 3-120, 3-122, 3-124, 3-125Fill options, 3-57

Equilibrium constant K, 3-50Equilibrium constant Kij, 3-118Equilibrium Constants, 3-39, 3-47, 3-100, 3-105,

3-108, 3-112, 3-119Equilibrium Expressions, 3-107, 3-110Equilibrium Flash Vaporization Calculations, 2-32Equilibrium Ratios, 3-29equilibrium reactions, 3-91, 3-104Equimolar, 3-87Equlibrium, 3-106Erbar, 3-26, 3-27, 3-60Erbar Modification, 3-26

Chao-Seader, 3-26Erbar modification to Chao-Seader, 3-26Erbar modification to Grayson-Streed, 3-26Erbar-modified Grayson-Streed, 3-27Estimates, 3-42, 3-142

diffusivity, 3-142, 3-143Gi, 3-42water/hydrocarbon, 3-42

Ethanediol, 3-22

Ethanolamine Process Simulated, 3-107Ethylbenzene, 3-97ETHYLCYCLOHEXANE, 3-97ETHYLCYCLOPENTANE, 3-138ETHYLENE, 3-138Ethylene Glycol, 3-97ETLN, 3-138EtSH, 3-102Excess Free Energy, 3-71

New Expression, 3-70Excess Gibbs Free Energy, 3-74

New Expression, 3-74Extent, 3-47

association, 3-47extent of association, 3-47Extrapolation Conventions, 2-3

F

FCCU, 3-10, 3-12including, 3-10

Feeds, 2-19flowsheet, 2-19, 2-21

FILL, 2-4, 3-19, 3-129Fill

Equations of state, 3-57Liquid Activity methods, 3-82

Fill Options for _Solubility Data, 3-129Fitting, 2-26

Distillation Curves, 2-26Fixed Properties, 2-3Flash, 2-36Flash Point

API Correlation, 2-37Calculations, 2-36Correlated Methods, 2-37Definition, 2-36Empirical methods, 2-37Index and User Mixing methods, 2-36Library component Properties, 2-2Nelson Correlation, 2-38open cup, 2-36SIMSCI Correlation, 2-38SIMSCI Method, 2-37

FloryHuggins Theory, 3-69Flowrate, 2-31Flowsheet, 2-19, 2-26, 2-32


feeds, 2-21Flowsheets, 2-25Fluid Mixtures, 3-36Fluid Phase Equil, 3-39, 3-40, 3-45, 3-47, 3-50, 3-80Fluid Phase Equilibria, 3-75Fluid Properties, 3-39Fluid Thermodynamic Properties, 3-52

Light Petroleum Systems, 3-52Fluid-Phase Equilibria, 3-2, 3-129FluidPhase Equilibria, 3-85

Molecular Thermodynamics, 3-65, 3-86Fluids, 3-36, 3-53, 3-55

Thermodynamic Properties, 3-53Formation, 2-9, 2-11

Heat, 2-9, 2-10, 2-11, 2-13Fractionators, 3-10, 3-12Fredenslund, 3-52, 3-75, 3-78, 3-79FREE, 3-129Free volume modification, 3-78

UNIFAC, 3-78Free volume modification to UNIFAC

UNFV, 3-78free volume modified UNIFAC

UNFV, 3-78Free Water Decant, 3-60Frost-Kalkwarf, 2-4, 2-7Fugacities, 3-1, 3-2, 3-5, 3-20, 3-34, 3-64, 3-65, 3-88,

3-89, 3-90, 3-107calculating, 3-89Gaseous Solutions, 3-34intead, 3-108terms, 3-108

Fugacity, 3-2, 3-5, 3-8, 3-19, 3-23, 3-24, 3-26, 3-27, 3-34, 3-45, 3-47, 3-50, 3-85, 3-88, 3-90, 3-91, 3-107, 3-109, 3-118, 3-120, 3-122, 3-125, 3-127calculate, 3-4, 3-5, 3-34, 3-47, 3-118, 3-120giving, 3-26represents, 3-25

Fugacity Coefficients, 3-126Generalized Correlation, 3-126

Fugacity fi, 3-85Fundam, 3-36, 3-52Fusion, 2-2

G

Gallagher, 3-124

GAMMA, 3-87Gamma Method, 3-87Gas Mixtures, 3-53

Volumetric Data, 3-55Gas Mixtures Containing Polar, 3-126

Thermodynamic Properties, 3-126Gas Processes, 3-10Gas Processors Association, 3-102, 3-104Gaseous, 3-113Gaseous Solutions, 3-34

Fugacities, 3-36Gases, 3-133, 3-135

Properties, 3-133Thermal Conductivity, 3-131

Gasoline-oxygenate, 2-33General Cubic Equation, 3-34, 3-40, 3-45

State, 3-34, 3-40, 3-45general cubic equation of state, 3-34, 3-40, 3-45GeneralInformation, 1-1, 3-1, 3-22, 3-34, 3-60, 3-88,

3-93, 3-127, 3-129Generalized Correlation, 3-24, 3-70

Solvent Activities, 3-70Vapor-Liquid Equilibria, 3-26

Generalized Correlation Methods, 3-8, 3-23, 3-24, 3-26, 3-27, 3-28, 3-29, 3-30, 3-31, 3-32

Generalized Information, 3-22Generalized Method, 3-91, 3-139

Predicting Second Virial Coefficients, 3-91Predicting Viscosities, 3-139

Generalized Thermodynamic Correlation Based on Three-Parameter Corresponding States, 2-17, 3-30, 3-53

Generating, 2-31Pseudocomponent Properties, 2-31

Generating Pseudocomponent Properties, 2-31Gibbs, 3-45, 3-50, 3-67, 3-68, 3-73, 3-75, 3-112Gibbs-Duhem, 3-117

form, 3-117Gimi, 3-107Glushko, 3-126GLYCOL, 3-13, 3-15, 3-96, 3-97Glycol data package, 3-96Glycol data package uses, 3-96GLYCOL databank, 3-15, 3-97Glycol Dehydration Systems, 3-15Glycol Package, 3-96Glycols, 3-1, 3-96

Index-7

Glycols tri-ethylene, 3-15involving, 3-14, 3-15

Gmehling, 3-78, 3-80Gomes, 3-5, 3-65, 3-86, 3-129Goodwin, 3-40GPA Research Report RR-118, 3-104GPA Sour Water Equilibria Correlation, 3-104GPA Sour Water Package, 3-102GPSA Data Book, 3-60GPSWAT, 3-93, 3-102GPSWATER, 3-15, 3-16, 3-103, 3-104GPSWATER data package, 3-102Gravity data, 2-17, 2-28Grayson, 2-13, 3-22, 3-26, 3-29Grayson-Steeed, 3-60Grayson-Streed, 3-11, 3-12, 3-18, 3-26, 3-27, 3-60Grayson-Streed Erbar, 3-11Groehling, 3-78Gross heating value, 2-2Group Contribution Estimation, 3-78

Activity Coefficients, 3-75, 3-78Group interaction data, 3-20, 3-75, 3-78GroupContribution Method

Polymer Solutions Using, 3-78Groups, 3-75, 3-76, 3-77, 3-78Grulka, 3-70GS, 3-11, 3-12, 3-13, 3-26GS/GSE/IGS, 3-11, 3-12GSE, 3-11, 3-12, 3-26Guggenheim, 3-73Guidelines, 3-66, 3-67, 3-68, 3-69, 3-70, 3-72, 3-73,

3-75, 3-128Gunn, 3-54, 3-55Gupte, 3-50, 3-52Gyration, 3-92

Radius, 3-92

H

H.K. Rasmussen, 3-75H.P., 3-126H2O, 3-27, 3-93, 3-97, 3-99, 3-100, 3-102, 3-105, 3-108,

3-109, 3-111, 3-122, 3-124correlating, 3-100pressure, 3-124

H2O-alcohol, 3-93oF, 3-93

H2O-CO2-NACL, 3-109H2S, 3-13, 3-14, 3-26, 3-27, 3-28, 3-41, 3-61, 3-93, 3-97,

3-99, 3-101, 3-102, 3-104, 3-105, 3-122, 3-138H2S Volatility Data, 3-101H2S/C3H8, 3-26H2S-CO2-DEA-H2O, 3-99H2S-CO2-MEA-H2O, 3-99Haar, 3-124, 3-127Halogenated, 3-47Handbook, 3-112

Aqueous Electrolyte Thermodynamics, 3-112Hankinson, 3-33, 3-34Hanley, 3-136, 3-138Hansen, 3-78Harris, 3-73Harvey, 3-44Hayden-O'Connell, 3-1, 3-20, 3-90, 3-91Hayden-O'Connell fu, 3-19Hayden-O'Connell fugacity, 3-91HCl, 3-22, 3-61HClO, 3-122HCN, 3-16Heat, 2-6, 2-10, 3-78, 3-86, 3-104, 3-112

Formation, 2-6, 2-10Mixing, 3-79Mixing Calculations, 3-86reaction, 3-105, 3-106, 3-112, 3-113

Heat of formation, 2-6, 2-10, 2-14Heat of Mixing Calculations, 3-86Heat of Reaction, 3-106, 3-113heat of reaction correction, 3-104Heavy Petroleum, 2-16HENRY, 3-19, 3-21, 3-86Henry s, 3-85, 3-99

databank, 3-86Henry s Law Option, 3-19Henry's constants, 3-85, 3-86Henry's Law, 3-7, 3-18, 3-20, 3-22, 3-85, 3-99, 3-100,

3-102Henry's Law constants, 3-5, 3-99Henry's law gas solubility, 3-85HEPTANE, 3-97Herning, 3-135HEXAMER, 3-21, 3-47, 3-48, 3-49, 3-50


Hexamers, 3-20, 3-48HF, 3-47HF alkylation, 3-47HF hexamerization, 3-50High Pressure Crude Systems, 3-10

Methods Recommended, 3-10High Pressure Crude Units, 3-12High Pressure Hydrocarbon-Hydrocarbon

Systems, 3-26, 3-27High Pressures, 3-135High Temperature, 3-26, 3-27

Vapor-Liquid Equilibria, 3-26Higher Polymer Solutions, 3-70Highest-boiling

lightend, 2-26Highly Polar, 3-39Highly Polar Asymmetric Systems, 3-43High-Pressure Aqueous Systems Containing

Gases, 3-44High-Pressure Vapor-Liquid Equilibria, 3-55Hildebrand, 3-68, 3-69Hipkin, 3-29HOCV, 3-21Hoftijzer, 3-101Holland, 3-36Holmes, 3-71HPDC, 3-138HPT1, 3-138Huggins, 3-70Hultgren G.O. 1958, 3-53Huntjens, 3-101Huron, 3-46, 3-47Huron-Vidal, 3-47Huron-Vidal SRK and PR, 3-45Hydrocarbon Mixtures, 3-26Hydrocarbon Mixtures-Computer Program

TRAPP, 3-138Hydrocarbon Proc, 3-30Hydrocarbon Processing, 3-101, 3-107Hydrocarbon-rich, 3-27, 3-41, 3-42, 3-60, 3-61Hydrocarbons, 3-139

Improved Viscosity-temperature Chart, 3-139Hydrocarbon-water, 3-27, 3-60Hydrofiners, 3-10, 3-12Hydrofluorocarbons, 3-22HYDROGEN, 3-138

Hydrogen deficiency number, 2-2Hydrogen Fluoride, 3-47, 3-50HYDROGEN SULFIDE, 3-97, 3-102, 3-104, 3-138

I

IC4, 3-97, 3-137IC5, 3-95, 3-97ID Name, 3-137IDEAL, 3-9, 3-18, 3-22, 3-23, 3-24, 3-87IDEAL and LIBRARY, 3-2, 3-23Ideal Liquid Mixtures

Composition Curve, 3-132Ideal Vapor Enthalpy, 2-3Ideal-solubility, 3-127IGS, 3-11, 3-12, 3-27IGS use, 3-11

Curl-Pitzer, 3-11Immiscible, 3-60, 3-72Improved Accuracy, 3-29

Nomographs, 3-29Improved Correlation, 3-34

Densities, 3-32, 3-34Improved Equation, 3-32

Prediction, 3-32Improved Grayson-Streed, 3-10, 3-27, 3-60Improved Prediction, 3-30

Enthalpy, 3-30Improved Viscosity-temperature Chart, 3-140

Hydrocarbons, 3-140Industrial Applications, 3-80, 3-126Industry, 3-39Infinite-dilution, 3-85, 3-106Infinite-pressure Gibbs, 3-46Intead, 3-107

fugacities, 3-108Interaction Coefficients

binary Fill options, 3-57, 3-82Interconversion, 2-21, 2-26Interconversion of Distillation Curves, 2-21Internally Consistent Correlation, 3-140

Predicting, 2-17, 2-35Predicting Liquid Viscosities, 3-140

Intraphase, 3-107Introduction, 1-1, 3-5, 3-47, 3-53, 3-66

Index-9

Ion Interaction Approach, 3-126Ionic Chemical Systems, 3-19

Methods Recommended, 3-21, 3-22Ions, 3-105, 3-114, 3-115, 3-116, 3-125Isobutane, 3-97ISOPENTANE, 3-95, 3-97

J

J.Chem.Phys, 3-70J.E. Cunningham, 3-36J.H. Prausnitz, 3-68J.M. Lichtenthaler, 3-85, 3-129JANAF Thermochemical Tables, 3-126Joback, 2-4John Wiley, 3-5, 3-65Johnson, 2-13, 3-29Johnson-Grayson, 3-29Jones, 3-75, 3-78

K

K.H. Abrams, 3-125Kabadi, 3-41, 3-42Kabadi-Danner, 3-14, 3-122Kabadi-Danner SRK, 3-41Kansas City, 3-27Kay s, 3-30Keenan, 3-61Kell, 3-124, 3-127Kelvin, 3-18Kelvins, 3-112, 3-118, 3-120, 3-142, 3-143Kendall, 3-132kerosene water solubility method, 3-60Kesler, 2-5, 2-9, 3-30, 3-55Keyes, 3-61K-factor, 3-61K-free, 3-129Kinematic, 3-139, 3-140, 3-141Kister, 3-66, 3-67Kistiakowsky, 2-13Kistiakowsky-Watson, 2-9Knapp, 3-55

Kolbe, 3-78Krevelen, 3-99, 3-101Kusik, 3-117, 3-126K-value, 3-2, 3-5, 3-23, 3-24, 3-28, 3-60, 3-85, 3-86,

3-93compute, 3-86selected, 3-7

K-values, 3-1, 3-4, 3-11, 3-23, 3-24, 3-26, 3-28, 3-41, 3-60, 3-62, 3-85, 3-93, 3-106

Kwong, 3-36

L

Larsen, 3-79Latent heat of vaporization, 2-6, 2-10, 2-15, 3-5, 3-23Lee, 2-5, 2-9, 2-14, 2-17, 3-30Lee-Kesler, 2-5, 3-11, 3-23, 3-29, 3-30Lee-Kesler characterization, 2-14, 2-15Lee-Kesler-Plöcker, 3-53Leiden, 3-36Leland, 3-54, 3-55, 3-136, 3-138Lenior, 3-29LIBID, 3-95, 3-97LIBRARY, 3-5, 3-130

use, 3-6, 3-7LIBRARY enthalpies, 3-7, 3-8Lichtenthaler, 3-5Light Gases, 3-93Light Hydrocarbon Applications, 3-17Light Hydrocarbons, 3-17, 3-52, 3-53Light Petroleum Systems, 3-53

Fluid Thermodynamic Properties, 3-53Lightend, 2-26Lightends, 2-17, 2-26, 2-32

Matching, 2-31number, 2-26

Lightends data, 2-30Lightends data-matching, 2-26Lightends-free, 2-30Liquid

vapor, 3-1Liquid Activity Coefficient Methods, 3-2, 3-5, 3-19,

3-62, 3-66, 3-67, 3-68, 3-69, 3-70, 3-72, 3-73, 3-75, 3-78, 3-85, 3-86

Liquid Activity MethodsFill options, 3-82


Liquid activity methods, 3-21, 3-22, 3-45, 3-78, 3-82, 3-85, 3-93

Liquid Diffusivity, 3-130, 3-142Liquid Mixtures, 3-33, 3-34, 3-72

Thermodynamic Excess Functions, 3-72Liquid molar volume, 2-2, 2-9, 3-4, 3-63, 3-68, 3-69,

3-71Liquid Regions, 3-136Liquid Thermal Conductivity, 2-3, 3-130Liquid Viscosity, 2-3, 3-131, 3-139

Special Methods, 3-139LiquidLiquid Equilibria, 3-74Liquid-Liquid Equilibrium Equations, 3-110Liquids, 3-32Liquids on Reduced Temperature, 3-133LK, 2-5, 3-11, 3-12, 3-29LKP, 3-53, 3-55LLE, 3-19LLE databank, 3-84Local Composition, 3-72LongChain Compounds, 3-70Low Pressure Crude Systems, 3-10

Methods Recommended, 3-10Low Pressure Crude Units, 3-11, 3-12Lube Oil, 3-10

Methods Recommended, 3-10Lubricants, 2-21Lyngby, 3-78Lyngby modified UNIFAC

UFT1, 3-78

M

Maddox, 3-107Main, 3-26, 3-27, 3-104Margules, 3-66, 3-67, 3-71Margules Equation, 3-66, 3-67Material Balance Equations, 3-110Materials, 2-21, 3-140Mathematical Models, 3-107, 3-112Mathias, 3-38, 3-39, 3-40Mathias-Copeman, 3-38Maurer, 3-75MCH, 3-95, 3-97MCP, 3-95, 3-138

MDEA, 3-16, 3-17, 3-105, 3-106MEA, 3-16, 3-104, 3-106, 3-122MeABP, 2-26Meissner, 3-117Melhem, 3-40Melhem-Saini-Goodwin, 3-38Melting temperature, 3-127, 3-128Mercaptan, 3-102Mercaptans, 3-13, 3-41MESH, 3-102METHANE, 3-137Methods Recommended, 3-11, 3-12, 3-13, 3-17, 3-18,

3-19Amine Systems, 3-15, 3-16Aromatic/Non-aromatic Systems, 3-17, 3-18Environmental Applications, 3-21, 3-22High Pressure Crude Systems, 3-10Ionic Chemical Systems, 3-19Low Pressure Crude Systems, 3-10Lube Oil, 3-10, 3-13Natural Gas Systems, 3-13, 3-14, 3-15Reformers, 3-10Solid Applications, 3-22Sour Water Systems, 3-13

METHY, 3-136Methyl Mercaptan, 3-61METHYLCYCLOHEXANE, 3-95, 3-97METHYLCYCLOPENTANE, 3-95, 3-138Methyldiethanolamine, 3-104Methylpentane, 3-95Misovich, 3-70Mixing, 3-40, 3-70, 3-78

Heats, 3-79Rules, 3-40

Mixing Calculations, 3-86Heat, 3-87

mixing rules, 3-18, 3-19, 3-34, 3-36, 3-40, 3-41, 3-42, 3-43, 3-44, 3-46, 3-47, 3-50, 3-85, 3-117, 3-128, 3-131, 3-142

Mixtures, 3-27, 3-73, 3-126, 3-136Pseudo-Critical Constants, 3-27Statistical Thermodynamics, 3-136

Model, 3-110Example, 3-110

modeling, 3-1Modifications, 3-78

UNIFAC, 3-78, 3-79, 3-80Modifications to UNIFAC, 3-78

Index-11

Modified, 3-37, 3-39, 3-40, 3-42modified UNIFAC, 3-78

UFT3, 3-78Modified UNIFAC Group Contribution Model, 3-79

Prediction, 3-79, 3-80Modified UNIFAC Model, 3-80Molalities, 3-109Molality, 3-108, 3-113, 3-115Molar Volume and Density, 3-125Molecular Thermodynamics, 3-5, 3-85, 3-129

Fluid-Phase Equilibria, 3-5, 3-129FluidPhase Equilibria, 3-65, 3-86

Molecular weight, 2-1, 2-5, 2-6, 2-10, 2-17, 2-31, 3-9, 3-13, 3-78, 3-96, 3-142

Molecular weight data, 2-18, 2-29Molecular weight data-API method, 2-26Molecular weight data-extended API

(EXTAPI), 2-26Molecular weight data-SimSci method, 2-26Molecular weight value, 2-29Molecular-weight, 2-30Molecule-molecule, 3-116Molecules, 3-136

Different Sizes, 3-138Monomer-dimer, 3-90Mueller, 3-55Multicomponent, 3-2, 3-41, 3-42, 3-43, 3-44, 3-66,

3-86, 3-117, 3-129, 3-142Multicomponent Aqueous Solutions, 3-126Multicomponent Equilibria, 3-71Multicomponent Mixtures, 3-55

Corresponding States, 3-53, 3-55Multicomponent Phase Equilibria, 3-73

Calculation, 3-74Multiple cutpoint, 2-18M-XYLENE, 3-97, 3-138

N

NACLppt, 3-111Nakamura, 3-120, 3-122Nakamura Method, 3-118, 3-120N-alkanes, 3-139Naphthalenes, 3-29Naphthenes, 3-61

Natural Gas Processing, 3-13Natural Gas Systems, 3-13

Methods Recommended, 3-13NBP, 2-5, 2-6, 2-8, 2-10, 2-27, 2-29, 2-30, 2-31

equal, 2-31function, 2-6

NBS Tables, 3-126Chemical Thermodynamic Properties, 3-125

NBS Tech Note, 3-125NBS2, 3-113N-butane, 3-97NC4, 3-97NC5, 3-95, 3-97NC6, 3-95, 3-97NC7, 3-95, 3-97N-DECANE, 3-138N-DODECANE, 3-138Nelson flash point, 2-38NEOPENTANE, 3-137New Alpha Function, 3-39, 3-45New Correlation, 3-33, 3-101

NH3, 3-99, 3-100, 3-101Saturated Densities, 3-33

New Expression, 3-71, 3-73Excess Free Energy, 3-70Excess Gibbs Free Energy, 3-73

New Generalized Alpha Function, 3-40Cubic, 3-37, 3-39, 3-40

New Group-Contribution, 3-52New Mixing Rules, 3-45New Two-constant, 3-36Newman, 3-102, 3-126NH3, 3-61, 3-93, 3-99, 3-102, 3-104, 3-122

containing, 3-93involving, 3-102New Correlation, 3-99

N-HEPTADECANE, 3-138N-HEPTANE, 3-95, 3-138N-HEXADECANE, 3-138N-HEXANE, 3-95, 3-137Ni, 3-8, 3-65, 3-89, 3-117, 3-118, 3-124N-NONANE, 3-138NOC, 3-76N-OCTANE, 3-138NODIME, 3-70NOG, 3-76, 3-77


Nomograph, 3-139Nomographs, 3-28

Improved Accuracy, 3-28Nonelectrolyte Solutions, 3-2

Classical Thermodynamics, 3-2Non-hydrocarbon, 3-19, 3-26, 3-130Nonideal Liquid Mixtures, 3-78Nonidealities, 3-21, 3-29, 3-88, 3-101, 3-102Nonideality, 3-8, 3-20, 3-44, 3-65Non-ionic Chemical Systems, 3-19Nonpolar Gas Mixtures, 3-135Nonpolar Gaseous Mixtures, 3-55, 3-135Nonpolar Substances, 3-136

Thermal Conductivity, 3-131Non-Random Two-Liquid, 3-1Normal boiling point, 2-2Normal Pressures, 3-135Nothnagel, 3-118, 3-122Nothnagel Method, 3-118N-PENTADECANE, 3-138N-PENTANE, 3-95, 3-137NRTL, 3-1, 3-19, 3-45, 3-72, 3-73, 3-93

databank, 3-19NRTL K-value, 3-93N-TETRADECANE, 3-138N-TRIDECANE, 3-138Number, 2-26, 3-108, 3-109

NB, 3-109N-UNDECANE, 3-138

O

O2, 3-18, 3-27, 3-28, 3-41, 3-61, 3-95, 3-97, 3-138OCTANE, 3-138Oishi, 3-81Okamoto, 2-25Old Framework, 3-112Olefinic, 3-130Order-of-magnitude, 3-78Organic Liquid Phase, 3-107, 3-122, 3-125Organic Phase Activities, 3-122Orye, 3-71OXYGEN, 3-138OXYL, 3-97

O-XYLENE, 3-97, 3-138

P

Panagiotopoulos-Reid, 3-42, 3-44Panagiotopoulos-Reid SRK and PR, 3-42Partington, 3-133Peng, 3-35, 3-36, 3-41Peng-Robinson, 3-11, 3-35, 3-36, 3-37, 3-40, 3-41,

3-42, 3-43, 3-45, 3-60Peng-Robinson Huron-Vidal, 3-45Peng-Robinson modified, 3-43Peng-Robinson Panagiotopoulos-Reid, 3-42PENTANE, 3-137Percent Distilled, 2-23, 2-25Perturbed-hard-sphere, 3-120

following, 3-120, 3-122Petro, 3-36

UNIFAC structures, 3-18PETRO Methods, 3-130, 3-131PETROLEUM, 2-5Petroleum Components, 2-5, 2-6, 2-10, 2-14, 2-16Petroleum components-acentric factor, 2-6, 2-10,

2-14, 2-16Petroleum components-critical properties, 2-6, 2-10,

2-14, 2-16Petroleum Fractions, 3-29, 3-139, 3-140, 3-142

Equilibrium Flash Vaporization Calculations, 2-35

Petroleum Products, 2-22, 2-33Petroleum Refiner, 2-17, 2-35, 3-29Petroleum Refining, 3-28, 3-30, 3-31Phase Equil, 3-36Phase Equilibria, 3-2, 3-39, 3-79

Applications, 3-5, 3-66Phase-dependent, 3-123Phase-equilibrium, 3-34Phase-independent, 3-125Physical Property Data Service, 2-2Physics, 3-101Pi, 3-108Pitzer, 3-55, 3-114, 3-116, 3-126Pitzer term, 3-114Plöcker, 3-53, 3-54, 3-55

work, 3-53

Index-13

Poling, 3-133Polymer Solutions, 3-69Polymer Solutions Using, 3-81Polymer/solvent, 3-69Poynting, 3-63, 3-64, 3-65Poynting correction, 3-4, 3-20, 3-64, 3-65, 3-102,

3-103PR, 2-8, 3-12, 3-13, 3-14, 3-18, 3-19, 3-27, 3-34, 3-36,

3-41, 3-42, 3-45, 3-60Prausnitz, 3-5, 3-44, 3-54, 3-55, 3-65, 3-71, 3-72, 3-73,

3-74, 3-75, 3-78, 3-81, 3-86, 3-91, 3-102, 3-126, 3-127, 3-129, 3-131, 3-133

Predicting, 2-14, 2-16, 2-32, 3-13, 3-125, 3-131Internally Consistent Correlation, 2-17, 2-35vapor-liquid-liquid, 3-14, 3-15Vapor-Liquid-Solid Equilibria, 3-125

Predicting Liquid Viscosities, 3-139Correlation, 3-139, 3-140, 3-141Internally Consistent Correlation, 3-139

Predicting Saturated Liquid Density, 3-31Predicting Second Virial Coefficients, 3-92

Generalized Method, 3-92Predicting Viscosities, 3-142

Generalized Method, 3-142Prediction, 2-16, 2-17, 3-31, 3-78

Improved Equation, 3-31Modified UNIFAC Group Contribution

Model, 3-78Thermodynamic Properties, 2-16

Pressure, 2-21, 3-47, 3-107, 3-124760, 2-22, 2-23, 2-24, 2-25H2O, 3-124HF, 3-47, 3-48, 3-50

Pressure-explicit, 3-90Pressure-independent, 3-123PRH, 3-45Primary TBP Cutpoint Set, 2-19PRLN, 3-137PRM, 3-13, 3-14, 3-15, 3-19, 3-20, 3-43PRO/II Application Briefs Manual, 1-1PRO/II back-calculates, 3-31PRO/II Casebooks, 1-1PRO/II databanks, 3-12, 3-13, 3-18, 3-31, 3-33PRO/II Electrolytes, 3-107, 3-112, 3-114, 3-123, 3-127PRO/II flowsheet, 3-21PRO/II Help, 1-2PRO/II Keyword Input Manual, 2-3

PRO/II s databanks, 2-32, 3-91PRO/II Temperature-dependent Property

Equations, 2-3PRO/II Unit Operations Reference Help, 1-1Probability-curve, 2-26

maintain, 2-26PROII databanks, 3-18PROPADIENE, 3-138PROPANE, 3-137Properties, 3-131Properties From Structure, 2-4, 3-130Property Generation– CAVETT Method, 2-10Property Generation– SIMSCI Method, 2-6Property Generation–Lee-Kesler Method, 2-14, 2-16PROVISION Graphical User Interface, 1-1PRP, 3-42Pseudocomponent, 2-1, 2-5, 2-17, 2-19, 2-26, 2-31,

3-31, 3-32, 3-130define, 2-19

Pseudocomponent Properties, 2-31Generating, 2-31

Pseudo-components, 3-61Pseudocomponents, 2-1, 2-5, 2-17, 2-18, 2-19, 2-20,

2-21, 2-26, 2-27, 2-29, 2-30, 2-31, 3-43, 3-130Pseudo-critical, 3-54Pseudo-Critical Constants, 3-27

Mixtures, 3-27Pseudocritical Constants, 3-55Pseudoreduced, 3-26Pseuodoreduced, 3-26Pure, 3-129PURE Methods, 3-130P-XYLENE, 3-97, 3-138Pytkowicz, 3-126

Q

QUADRATIC, 2-26, 2-28Quasichemical, 3-73

R

RACKETT, 2-6, 3-9, 3-31, 3-125applying, 2-10use, 3-31


Rackett liquid density, 3-31Rackett parameter, 2-2, 3-31Radius, 3-91

Gyration, 3-91Radius of gyration, 2-2, 3-91Rankine, 2-6, 2-10, 2-12, 2-13, 2-15, 2-23, 2-24, 2-29,

3-9, 3-23, 3-100Raoult s, 3-23Rasmussen, 3-52, 3-78Reached.Estimation, 2-21

thermophysical, 2-21Reaction, 3-104, 3-112

heat, 3-106, 3-112, 3-113recommended ranges, 3-13, 3-24, 3-27, 3-29, 3-30,

3-31, 3-32, 3-93, 3-96, 3-99, 3-102, 3-104Redlich, 3-36, 3-66, 3-67Redlich-Kister, 3-87, 3-88Redlich-Kister Expansion, 3-87, 3-88Redlich-Kwong, 3-25, 3-34, 3-35, 3-36, 3-37, 3-39,

3-40, 3-46, 3-48Reference, 3-53Refinery, 3-10Reformers, 3-10, 3-12

Methods Recommended, 3-10Regular Solution Theory, 3-68, 3-69Reid, 3-42, 3-43Reid vapor pressure (RVP), 2-32Reid vapor pressure (RVP)-APICRIDE method, 2-32Reid vapor pressure (RVP)-APINAPHTHA

method, 2-32Reid vapor pressure (RVP)-ASTM D323-73




method, 2-32Reidel, 3-132, 3-133, 3-134Reidel-Plank-Miller, 2-4Renon, 3-72Renormalized, 3-129

k-free, 3-129required components, 3-91, 3-104Required Pure Component Properties, 3-66, 3-67,

3-68, 3-69, 3-70, 3-72, 3-73, 3-75Riazi, 2-25

Riedel, 2-4Rigorous Calculation, 3-107Robinson, 3-35, 3-36, 3-41, 3-138Roy, 3-135Roy-Thodos, 3-135Rubin, 3-53Rules, 3-27, 3-40

Mixing, 3-40Stewart, 3-27

RVPrepresents, 2-32, 2-33

S

Saini, 3-40Salts, 3-44Sandler, 3-5, 3-65Sato, 3-133Satu, 3-131Saturated Densities, 3-32

New Correlation, 3-32Saturated Liquid Density, 3-32Saturated Liquid Enthalpy, 2-3Saturated Liquids, 3-31Saturated Nonpolar Liquids, 3-133Saturated-liquid density, 3-24Saturated-liquid enthalpy, 3-6, 3-8Scatchard, 3-68Scatchard-Hildebrand, 3-25Schiller, 3-78Scott, 3-69Scrivner, 3-126Seader, 3-22, 3-24, 3-25, 3-26Second Liquid Phase, 3-109

Equations For Solutions Involving, 3-107Second Virial Coefficients, 3-90

Empirical Correlation, 3-91Setschenow, 3-116Shale Oils, 2-16Should Use This Manual, 1-1SimSci azeotropic databank, 3-82SIMSCI characterization, 2-6SIMSCI library, 2-1Sitzber, 3-67

Index-15

Skjold-Jørgensen, 3-78SLE, 3-22SO2, 3-22, 3-61, 3-122, 3-138Soave, 3-37, 3-39, 3-41Soave-Redlich Kwong, 3-41Soave-Redlich-Kwong, 1-1, 3-1, 3-11, 3-41, 3-42,

3-43, 3-44, 3-45, 3-60, 3-62, 3-118, 3-122Soave-Redlich-Kwong Huron-Vidal, 3-45Soave-Redlich-Kwong Kabadi-Danner, 3-41, 3-62Soave-Redlich-Kwong modified, 3-43Soave-Redlich-Kwong Panagiotopoulos-Reid, 3-42Soave-Redlich-Kwong Panagiotoupolos-Reid, 3-42Soave-Redlich-Kwong SimSci, 3-44Solid, 3-113Solid Applications

Methods Recommended, 3-19Solid Cp, 2-4Solid Phase, 3-109, 3-123, 3-125Solid Thermal Conductivity, 2-4Solid-Liquid Equilibria, 3-127, 3-128, 3-129Solubility Data, 3-127, 3-128, 3-129Solubility Parameter, 2-2Solubility parameter (Hildebrand), 2-6, 2-14, 2-16,

3-69solute components, 3-86Solutions, 3-34, 3-67, 3-70

Classification, 3-67Thermodynamic Properties, 3-70Thermodynamics, 3-36

Solvation, 3-92Solve, 3-86

C1, 3-86Solvent, 3-10, 3-13, 3-113Solvent Activities, 3-69, 3-81

Generalized Correlation, 3-69Solvent De-asphalting Units, 3-10, 3-13SOUR, 3-13, 3-15, 3-16, 3-93, 3-99, 3-100, 3-101Sour Package, 3-99Sour water data package, 3-99Sour Water EQuilibrium, 3-99Sour Water Systems, 3-15

Methods Recommended, 3-14, 3-15, 3-16Special Methods, 3-139

Liquid Viscosity, 3-139Special Methods for LiquidViscosity, 3-139Special Packages, 3-13, 3-93, 3-96, 3-99, 3-102, 3-104

Specific gravity, 2-2, 2-6, 2-10, 2-13, 2-18, 2-28, 2-29, 3-31, 3-33, 3-139

Specific Heat, 3-131Specific heat capacity, 2-14, 2-16Spencer, 3-32Spline, 2-26SRK, 1-1, 2-10, 3-8, 3-12, 3-13, 3-14, 3-17, 3-18, 3-20,

3-32, 3-37, 3-41, 3-42, 3-45, 3-62, 3-97, 3-122SRK databank, 3-97SRK HEXAMER, 3-47SRK Method, 3-122SRK/PR, 3-12, 3-13SRKH, 3-45SRKKD, 3-14, 3-41SRKM, 3-9, 3-13, 3-14, 3-15, 3-17, 3-18, 3-20, 3-43,

3-44, 3-93, 3-96, 3-97, 3-101, 3-103, 3-104, 3-106SRKM/PRM, 3-13, 3-14SRKP, 3-43SRKS, 3-14, 3-15, 3-17, 3-18, 3-19, 3-45, 3-50SRKS/SRKM, 3-19Starling, 3-52, 3-53Starling s BWRS, 3-53State, 1-1, 2-10, 3-1, 3-2, 3-3, 3-4, 3-5, 3-6, 3-7, 3-8,

3-9, 3-11, 3-14, 3-17, 3-18, 3-25, 3-31, 3-32, 3-34, 3-35, 3-36, 3-37, 3-39, 3-40, 3-41, 3-42, 3-43, 3-44, 3-45, 3-46, 3-47, 3-48, 3-49, 3-50, 3-51, 3-52, 3-53, 3-61, 3-62, 3-64, 3-85, 3-87, 3-88, 3-89, 3-90, 3-91, 3-93, 3-96, 3-97, 3-101, 3-103, 3-104, 3-106, 3-112, 3-113, 3-118, 3-120, 3-122, 3-124, 3-125Associating Equation, 3-90equation, 1-1, 2-7, 2-8, 2-10, 2-14, 2-15, 2-17, 2-32,

2-33, 2-34, 3-1, 3-4, 3-5, 3-6, 3-7, 3-8, 3-9, 3-11, 3-14, 3-20, 3-25, 3-31, 3-32, 3-34, 3-35, 3-36, 3-37, 3-38, 3-39, 3-40, 3-41, 3-42, 3-43, 3-44, 3-45, 3-46, 3-47, 3-48, 3-49, 3-50, 3-51, 3-52, 3-53, 3-55, 3-61, 3-62, 3-63, 3-64, 3-65, 3-85, 3-86, 3-87, 3-88, 3-89, 3-90, 3-91, 3-93, 3-96, 3-97, 3-101, 3-103, 3-104, 3-106, 3-112, 3-113, 3-118, 3-119, 3-120, 3-122, 3-124, 3-125

General Cubic Equation, 3-34, 3-40, 3-45Statistical Thermodynamics, 3-74, 3-138

Mixtures, 3-136, 3-138Statistical-mechanical, 3-73Steil, 3-131Stewart, 3-27Stiel, 2-13Stoichiometric, 3-107Straightforward, 2-30, 3-31, 3-89Stream Average Properties, 3-130


Stream Property, 3-130Streed, 3-22, 3-26Streed s, 3-26Strong Electrolytes

Thermodynamic Properties, 3-125Strongly Non-ideal Mixtures, 3-47

Representing Vapor-Liquid Equilibria, 3-47Subcooled, 3-127Subcritical, 2-3SULFLN, 3-95Sulfolane, 3-95SULFUR DIOXIDE, 3-138Supercritical Systems, 3-39Surface Tension, 2-4, 3-131Suther G.A. 1968, 3-136SWEQ, 3-99, 3-100, 3-101, 3-102

uses, 3-99, 3-102Systems Containing Polar Components, 3-36

Vapor-Liquid Equilibria, 3-39

T

TBP, 2-17, 2-19, 2-21, 2-22, 2-23, 2-24, 2-25, 2-26Convert, 2-22, 2-23, 2-24, 2-25curves, 2-22, 2-23, 2-24, 2-25, 2-26D86, 2-21, 2-22, 2-23, 2-24, 2-25, 2-26Hg, 2-22, 2-23, 2-24, 2-25resulting, 2-18

TBP Curves, 2-28TBP cutpoints, 2-18

sets, 2-17, 2-18TBP Range, 2-19Tc, 2-6, 2-11, 2-13, 3-7, 3-35, 3-47, 3-54TDCN, 3-138Technical Data Book, 3-28, 3-30, 3-31Technical Gas Mixtures, 3-131TEG, 3-13, 3-97Temperature- dependent Properties, 2-3Temperature-dependent, 2-3, 3-34, 3-36, 3-40, 3-78

incorporating, 3-78Temperaturedependent, 3-72Temperature-dependent Properties, 2-3, 2-9, 2-11Temperature-independent, 3-123, 3-125Terms, 3-107

fugacities, 3-107

Ternary Liquid Systems, 3-68Tertiary amines, 3-104Theory, 1-1, 3-29, 3-53, 3-55, 3-68, 3-69, 3-90, 3-91,

3-125, 3-128Thermal Conductivity, 3-130, 3-133, 3-134, 3-135,

3-136, 3-138Determination, 3-134

Thermal Constants, 3-126Thermodynamic, 3-34, 3-36

Solutions, 3-36Thermodynamic Evaluation, 3-67

Binary, 3-67, 3-68Thermodynamic Excess Functions, 3-72

Liquid Mixtures, 3-72Thermodynamic Framework, 3-112, 3-123Thermodynamic Methods, 3-5, 3-10Thermodynamic Methods-Chemical

Applications, 3-19Thermodynamic Methods-Density, 3-9Thermodynamic Methods-Enthalpy, 3-5Thermodynamic Methods-Entropy, 3-8Thermodynamic Methods-General Information, 3-1Thermodynamic Methods-Natural Gas

Processes, 3-13Thermodynamic Methods-Phase Equilibria, 3-2Thermodynamic Methods-Refinery & Gas

Processes, 3-10Thermodynamic Properties, 2-14, 2-16, 3-52, 3-53,

3-55, 3-66, 3-69, 3-125Algebraic Representation, 3-67Empirical Equation, 3-52Fluids, 3-53Gas Mixtures Containing Polar, 3-125Prediction, 2-14, 2-16Solutions, 3-69Strong Electrolytes, 3-125

Thermophysical, 2-5, 2-21, 3-1reached.Estimation, 2-21

Third Generation Process Simulation, 3-39Thomas, 3-131, 3-133Thomson, 3-33, 3-34Three-parameter, 3-66, 3-78Three-parameter corresponding-states, 3-29TOLU, 3-95, 3-97, 3-138Torres-Marchal, 3-80TR, 2-8, 3-7, 3-26, 3-27, 3-112, 3-123Trans-2-BUTENE, 3-137Trans-2-PENTENE, 3-137

Index-17

Transport Properties, 3-129, 3-130, 3-131, 3-136, 3-139, 3-142

Transport properties-API method, 3-139Transport properties-thermal conductivity, 3-136Transport properties-TWU method, 3-139Transport properties-viscosity, 3-131Transport properties-Wilke-Chang method, 3-142TRAPP, 3-130Triethylene Glycol, 3-97Triple Point Pressure, 2-2Triple-point temperature, 3-127, 3-128True Boiling Point, 2-17True boiling point (TBP) data-cubic spline, 2-26True boiling point (TBP) data-cutting into

pseudocomponents, 2-26True boiling point (TBP) data-probability density

function (PDF), 2-26True boiling point (TBP) data-quadratic fit, 2-26True vapor pressure (TVP), 2-32True vapor pressure (TVP)-application

guidelines, 2-32Truncated Virial, 3-90, 3-91, 3-102TVIRIAL, 3-90TVP

function, 2-32, 2-33TVP Methods, 2-34Two-Parameter Cubic, 3-34, 3-35Twu, 2-5, 2-6, 2-9, 3-37, 3-39, 3-40, 3-44, 3-45, 3-48,

3-50, 3-139, 3-140, 3-142Twu-Bluck-Coon, 3-55Twu-Bluck-Cunningham-Coon, 3-37Twu-Coon-Cunningham, 3-38, 3-39Type, 2-21

Distillation Curves, 2-21, 2-25

U

UFT1, 3-82UFT1 Lyngby, 3-78UFT2 Dortmund, 3-79UFT3, 3-80UNDC, 3-138UNFV, 3-80UNIFAC, 3-19, 3-50, 3-75, 3-78, 3-85

Free volume modification, 3-80

UNIFAC Group Contribution, 3-78UNIFAC Structure

petro, 3-18UNIQUAC, 3-18, 3-19, 3-21, 3-73, 3-74, 3-75UNIQUAC Equation, 3-73, 3-74, 3-75UNIWAALS, 3-20, 3-21, 3-36, 3-50, 3-51, 3-52UNIWAALS equation-of-state, 3-20Unsaturated Hydrocarbons, 3-61Use, 2-19, 2-29, 3-5, 3-11, 3-12, 3-21, 3-22, 3-29, 3-31,

3-99, 3-103cutpoints, 2-19, 2-20, 2-21LIBRARY, 3-6, 3-7, 3-8PHI, 3-20, 3-21Rackett, 3-31SimSci, 3-13SWEQ, 3-99, 3-102three-parameter corresponding-states, 3-29

USER, 1-1User-supplied Diffusivity Data, 3-142Utilities, 3-112

V

van der Waals, 3-34, 3-35, 3-36, 3-40, 3-43, 3-50, 3-51, 3-54, 3-73, 3-74, 3-75, 3-77

van der Waals area and volume, 2-2, 3-73, 3-75Van der Waals mixing, 3-54van Laar, 3-67, 3-68, 3-71Van Laar Equation, 3-67, 3-68Van Ness, 3-5, 3-66Van Nostrand Reinhold Co, 3-69Van t Hoff, 3-19, 3-127Van t Hoff SLE, 3-19van't HoffEquation, 3-127, 3-128, 3-129VANT HOFF Method, 3-22VAPOR, 3-123Vapor and Solid Phases, 3-123Vapor fugacity, 3-1Vapor Phase, 3-125Vapor Phase Fugacities, 3-90, 3-92, 3-118, 3-120,

3-122Vapor Phase Imperfections, 3-101Vapor pressure, 2-2, 2-3, 2-4, 2-8, 2-10, 2-22, 3-4, 3-6,

3-23, 3-28, 3-32, 3-33, 3-41, 3-48, 3-63, 3-66, 3-67, 3-68, 3-69, 3-70, 3-72, 3-73, 3-86, 3-100

Vapor Pressure Calculations, 2-32


Vapor Pressure Equations, 2-4, 2-14, 2-16Vapor pressure-Antoine equation, 2-10Vapor Thermal Conductivity, 2-4, 3-131, 3-135Vapor Viscosity, 2-2, 2-3, 3-131Vapor/liquid, 3-124Vaporization, 2-3, 2-9, 2-10, 2-13, 3-6, 3-24

latent heat, 2-6, 2-10, 2-15, 3-6, 3-8, 3-24Vapor-Liquid Equilibria, 2-17, 3-24, 3-26, 3-27, 3-36,

3-52, 3-75, 3-101Generalized Correlation, 3-25, 3-26High Temperature, 3-26Systems Containing Polar Components, 3-39

VaporLiquid Equilibria, 3-74, 3-78Vapor-Liquid Equilibrium Calculations, 3-91VaporLiquid Equilibrium XI, 3-71Vapor-liquid-liquid, 3-13

predict, 3-14, 3-15Vapor-Liquid-Solid Equilibria, 3-126

Predicting, 3-126Vapor-phase fugacity, 3-112Vapor-phase nonidealities, 3-103Various Mineral Oils

Specific Heat, 3-134Versatile Phase Equilibrium, 3-40Vidal, 3-46, 3-47Virial, 3-90, 3-91, 3-92, 3-103, 3-118Viscosity, 3-131, 3-132, 3-133, 3-134, 3-135, 3-136,

3-138Nonpolar Gas Mixtures, 3-131Technical Gas Mixtures, 3-135

VL, 2-9VLE, 3-13, 3-19, 3-50, 3-78VLE databank, 3-84VLLE, 3-60Vloeistoftoestand, 3-36Volume-averaged, 2-29Volume-explicit, 3-89Volume-fraction, 2-27Volumetric, 3-55Volumetric Data, 3-53

Gas Mixtures, 3-55Volumetric Properties, 3-55

W

Walas, 3-66

Wamine, 3-16, 3-17Wasserfach, 3-135WATER, 3-137, 3-138Water Activity, 3-117Water decant, 3-14, 3-60water partial pressure, 3-60, 3-61Water/hydrocarbon, 3-41

estimates, 3-41Water-hydrocarbon, 3-41, 3-42, 3-62Water-Hydrocarbon Phase Equilibria, 3-42Watson, 2-10, 2-14, 2-16, 3-60, 3-139

expresses, 3-139function, 3-61

Watson characterization, 2-10, 3-141, 3-142Watson K, 2-29, 3-18Watson K-factor, 2-12, 2-28WATSONK, 2-28WCO2, 3-15Webb, 3-53Weidlich, 3-80Weight-fraction, 2-27WH2S, 3-15Wien, 3-67Wilke, 3-143Wilke-Chang, 3-142, 3-143Wilke-Chang Correlation, 3-142, 3-143Wilke-Chang method, 3-142WILSON, 3-19, 3-70, 3-72, 3-73, 3-99, 3-102Wilson Equation, 3-70, 3-71Wilson Equation Used, 3-71

Predict Vapor Compositions, 3-71Winkle, 3-71Wiss, 3-67WNH3, 3-15, 3-16, 3-103Wohl, 3-68Wohl s, 3-67Work, 3-53

Plöcker, 3-53Wright, 3-139, 3-140

Y

Yamada, 3-132Yoon, 3-135

Index-19

Z

Zipperer, 3-135


PRO II Reference Manual - Vol I - Component and Thermophysical Properties

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