Pro-II (Components & Thermodynamics)

7/26/2019 Pro-II (Components & Thermodynamics)

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PRO/II Componentand ThermophysicalPropertiesReference Manual

The software described in this manual is furnished under a licenseagreement and may be used only in accordance with the terms of thatagreement.

Information in this document is subject to change without notice.Simulation Sciences Inc. assumes no liability for any damage to anyhardware or software component or any loss of data that may occur asa result of the use of the information contained in this manual.

Copyright Notice Copyright 1994 Simulation Sciences Inc. All Rights Reserved. Nopart of this publication may be copied and/or distributed without theexpress written permission of Simulation Sciences Inc., 601 S. ValenciaAvenue, Brea, CA 92621, USA.

Trademarks PRO/II is a registered mark of Simulation Sciences Inc.SIMSCI is a service mark of Simulation Sciences Inc.

Printed in the United States of America.

Credi ts Contributors:Althea Champagnie, Ph.D.J ohn CunninghamAllan Harvey, Ph.D.J ohn Tanger, Ph.D.

C.H. Twu, Ph.D.

Layout:Kris Oca

On-line Document Conversion:Mark NortonPeter StepmanAlthea Champagnie, Ph.D.


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Table of Contents

List of Tables TOC-5List of Figures TOC-6

Introduction Int-1

General Information Int-1

What is in This Manual? Int-1

Who Should Use This Manual? Int-1

Finding What you Need Int-1

1.1 Component Data I-3

1.1.1 Defined Components I-4

Component Libraries I-4

Using DATAPREPTM I-6Fixed Properties I-6

Temperature-dependent Properties I-6

Properties From Structure I-8

1.1.2 Petroleum Components I-9

General Information I-9

Property Generation--SIMSCI Method I-9

Property Generation--CAVETT Method I-13

Property Generation--Lee-Kesler Method I-16

1.1.3 Assay Processing I-18


Cutpoint Sets (Blends) I-19

Interconversion of Distillation Curves I-21

Cutting TBP Curves I-25

Generating Pseudocomponent Properties I-30

Vapor Pressure Calculations I-30

1.2 Thermodynamic Methods I-37

1.2.1 Basic Principles I-38


Phase Equilibria I-38

Enthalpy I-41

Entropy I-43

Density I-44

1.2.2 Appl ication Guidel ines I-45


Thermodynamic Expert System (TES) I-45

Refinery and Gas Processes I-46

Natural Gas Processing I-49

Petrochemical Applications I-52

Chemical Applications I-54

PRO/II Component and Thermophysical Properties Table of Contents TOC-1Reference M anual


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1.2.3 General ized Correlation Methods I-58


Ideal (IDEAL) I-58

Chao-Seader (CS) I-60

Grayson-Streed (GS) I-61

Erbar Modification to Chao-Seader (CSE) andGrayson-Streed (GSE) I-61

Improved Grayson-Streed (IGS) I-62

Curl-Pitzer (CP) I-62

Braun K10(BK10) I-63

J ohnson-Grayson (J G) I-64

Lee-Kesler (LK) I-64

API I-65

Rackett I-65

COSTALD I-66

1.2.4 Equations of State I-69


General Cubic Equation of State I-69

Alpha Formulations I-71Mixing Rules I-73

Soave-Redlich Kwong (SRK) I-74

Peng-Robinson (PR) I-74

Soave-Redlich-Kwong Kabadi-Danner (SRKKD) I-75

Soave-Redlich-KwongPanagiotopoulos-Reid(SRKP) and Peng-Robinson Panagiotopoulos-Reid (PRP) I-76

Soave-Redlich-Kwong Modified Panagiotopoulos-Reid (SRKM) and Peng-Robinson ModifiedPanagiotopoulos-Reid (PRM) I-77

Soave-Redlich-Kwong SimSci (SRKS) I-77

Soave-Redlich-Kwong Huron-Vidal (SRKH) andPeng-Robinson Huron-Vidal (PRH) I-79

HEXAMER I-80

UNIWAALS I-83

Benedict-Webb-Rubin-Starling I-84

Lee-Kesler-Plcker (LKP) I-85

1.2.5 Free Water Decant I-88


Calculation Methods I-88

1.2.6 Liquid Activi ty Coeffi cient Methods I-90


Margules Equation I-93

van Laar Equation I-94Regular Solution Theory I-95

Flory-Huggins Theory I-96

Wilson Equation I-97

NRTL Equation I-98

UNIQUAC Equation I-99

UNIFAC I-101

Modifications to UNIFAC I-104

Fill Methods I-107

TOC-2 Table of Contents May 1994


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Henrys Law I-110

Heat of Mixing Calculations I-111

1.2.7 Vapor Phase Fugaci ties I-113


Equations of State I-114

Truncated Virial Equation of State I-114

Hayden-OConnell I-116

1.2.8 Special Packages I-117


Alcohol Package (ALCOHOL) I-117

Glycol Package (GLYCOL) I-120

Sour Package (SOUR) I-122

GPA Sour Water Package (GPSWATER) I-125

Amine Package (AMINE) I-127

1.2.9 Electrolyte Mathematical Model I-131

Discussion of Equations I-131

Modeling Example I-133

1. 2.10 Electrolyte Thermodynamic Equations I-135

Thermodynamic Framework I-135Equilibrium Constants I-135

Aqueous Phase Activities I-136

Vapor Phase Fugacities I-139

Organic Phase Activities I-143

Enthalpy I-143

Aqueous Liquid Phase I-144

Molar Volume and Density I-144

1.2.11 Sol id-Liquid Equi l ibria I-147


vant Hoff Equation I-147

Solubility Data I-148Fill Options for Solubility Data I-148

1.2.12 Transport Properties I-150


PURE Methods I-150

PETRO Methods I-151

TRAPP Correlation I-155

Special Methods for Liquid Viscosity I-157

Liquid Diffusivity I-159

Index Idx-1



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List of Tables

1.1.1-1 PRO/II Library Component Properties . . . . . . . . . . . . . I-5

1.1.1-2 PRO/II Temperature-dependent Property Equations andExtrapolation Conventions . . . . . . . . . . . . . . . . . . . I-7

1.1.1-3 PRO/II Vapor Pressure Equations . . . . . . . . . . . . . . . . I-7

1.1.2-1 Values of Constants for Equations (14)-(17) . . . . . . . . . . I-11

1.1.3-1 Primary TBP Cutpoint Set . . . . . . . . . . . . . . . . . . . . I-19

1.1.3-2 Blending Example . . . . . . . . . . . . . . . . . . . . . . . . I-20

1.1.3-3 Values of Constants a, b, c . . . . . . . . . . . . . . . . . . . I-23

1.1.3-4 Values of Constants a, b . . . . . . . . . . . . . . . . . . . . . I-25

1.2.2-1 Methods Recommended for Low Pressure Crude Systems . . I-47

1.2.2-2 Methods Recommended for High Pressure Crude Systems . . I-47

1.2.2-3 Methods Recommended for Reformers and Hydrofiners . . . . I-48

1.2.2-4 Methods Recommended for Lube Oil and SolventDe-asphalting Units . . . . . . . . . . . . . . . . . . . . . . . I-48

1.2.2-5 Methods Recommended for Natural Gas Systems . . . . . . . I-50

1.2.2-6 Methods Recommended for Sour Water Systems . . . . . . . I-51

1.2.2-7 Recommended Ranges for Amine Systems . . . . . . . . . . . I-52

1.2.2-8 Methods Recommended for Light Hydrocarbons . . . . . . . . I-52

1.2.2-9 Methods Recommended for Aromatics . . . . . . . . . . . . . I-53

1.2.2-10 Methods Recommended for Aromatic/Non-aromaticSystems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-54

1.2.2-11 Methods Recommended for Alcohol Systems . . . . . . . . . I-54

1.2.2-12 Methods Recommended for Non-ionic Chemical Systems . . . I-56

1.2.2-13 Methods Recommended for Ionic Chemical Systems . . . . . I-56

1.2.2-14 Methods Recommended for Environmental Applications . . . I-57

1.2.2-15 Methods Recommended for Solid Applications . . . . . . . . I-57

1.2.4-1 Some Cubic Equations of State . . . . . . . . . . . . . . . . . I-69

1.2.4-2 Constants for Two-parameter Cubic Equations of State . . . . I-70

1.2.4-3 Alpha Formulations . . . . . . . . . . . . . . . . . . . . . . . I-72

1.2.5-1 Components Available in the SIMSCI Water Solubility Method . I-89

1.2.6-1 Margules Equation . . . . . . . . . . . . . . . . . . . . . . . I-93

1.2.6-2 van Laar Equation . . . . . . . . . . . . . . . . . . . . . . . . I-94

1.2.6-3 Regular Solution Theory . . . . . . . . . . . . . . . . . . . . I-95

1.2.6-4 Flory-Huggins Theory . . . . . . . . . . . . . . . . . . . . . . I-96

1.2.6-5 Wilson Equation . . . . . . . . . . . . . . . . . . . . . . . . . I-97



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1.2.65 Wilson Equation . . . . . . . . . . . . . . . . . . . . . . . . . I-97

1.2.6-6 NRTL Equation . . . . . . . . . . . . . . . . . . . . . . . . . . I-98

1.2.6-7 UNIQUAC Equation . . . . . . . . . . . . . . . . . . . . . . . I-99

1.2.6-8 UNIFAC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-101

1.2.8-1 Components Available for ALCOHOL Package . . . . . . . . . I-118

1.2.8-2 Components Available for GLYCOL Package . . . . . . . . . . I-120

1.2.8-3 Application Guidelines for Amine Systems . . . . . . . . . . . I-129

1.2.11-1 vant Hoff . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-148

1.2.12-1 Transport Properties . . . . . . . . . . . . . . . . . . . . . . . I-150

1.2.12-2 Stream Average Properties . . . . . . . . . . . . . . . . . . . I-151

1.2.12-3 TRAPP Components (3.3 versions) . . . . . . . . . . . . . . . I-156

List of Figures1.1.3-1 Cutting TBP Curves . . . . . . . . . . . . . . . . . . . . . . . I-27

1.1.3-2 Matching Lightends to TBP Curve . . . . . . . . . . . . . . . . I-30

1.2.6-1 Flowchart for FILL Methods . . . . . . . . . . . . . . . . . . . I-109

1.2.8-1 Binary Interaction Data in the Alcohol Databank . . . . . . . . I-119

1.2.8-2 Binary Interaction Data in the Glycol Databank . . . . . . . . . I-121



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Introduction

GeneralInformation

The PRO/II Component and Thermophysical Properties Reference Manual

provides details on the basic equations and calculation techniques used in the

PRO/II simulation program. It is intended as a complement to the PRO/II

Keyword Input Manual, providing a reference source for the background behindthe various PRO/II calculation methods.

What is inThis Manual?

This manual contains the correlations and methods used to calculate thermo-

dynamic and physical properties, such as the Soave-Redlich-Kwong (SRK)

cubic equation of state for phase equilibria. This manual also contains infor-

mation on the definition of pure components and petroleum fractions.

For each method described, the basic equations are presented, and appropri-

ate references provided for details on their derivation. General application

guidelines are provided, and, for many of the methods, hints to aid solution

are supplied.

Who Should UseThis Manual?

For novice, average, and expert users of PRO/II, this manual provides a good

overview of the property calculation methods used to simulate a single unit

operation or a complete chemical process or plant. Expert users can find

additional details on the theory presented in the numerous references cited

for each method. For the novice to average user, general references are also

provided on the topics discussed, e.g., to standard textbooks.

Specific details concerning the coding of the keywords required for the

PRO/II input file can be found in the PRO/II Keyword Input Manual.

Detailed sample problems are provided in the PRO/II Application Briefs

Manual and in thePRO/II Casebooks.

Finding Whatyou Need

A Table of Contents and an Index are provided for this manual. Cross-

references are provided to the appropriate section(s) of the PRO/II Keyword

Input Manual for help in writing the input files.

PRO/II Component and Thermophysical Properties Introduction Int-1Reference M anual


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Symbols Used in This Manual

Symbol Meaning

Indicates a PRO/II input coding note. The number beside the

symbol indicates the section in the PRO/II Keyword Input

Manualto refer to for more information on coding the

input file.

Indicates an important note.

Indicates a list of references.

Int-2 Introduction May 1994


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Component Data

PRO/II allows the user to specify pure-component physical property data for agiven simulation. Pure component data are usually associated with either a prede-

fined component in a data library, a user-defined (non-library) component, or a

petroleum pseudocomponent.

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 pseudocomponents by a

number of assay processing methods.

1. 1

Section 1.1 Component Data

PRO/II Component and Thermophysical Properties I-3Reference M anual


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Defined Components

ComponentLibraries

Table 1.1.1-1 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 prop-

erty 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 be-

cause they are usually covered by contractual agreements which disallowtheir display in a simulation.

References

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, sponsored by the

American Institute of Chemical Engineers.

1.1.1

Component Data Section 1.1

I-4 Defined Components May 1994


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Table 1.1.1-1: PRO/II Library Component Properties

Fi xed Pr operti es and Constants Tem peratur e-dependent Pr operti es

Acentric Factor Enthalpy of Vaporization

Carbon Number Ideal Vapor Enthalpy

Chemical Abstract Number Liquid Density

Chemical Formula Liquid Thermal ConductivityCritical Compressibility Factor Liquid Viscosity

Critical Pressure Saturated Liquid Enthalpy

Critical Temperature Solid Density

Critical Volume Solid Heat Capacity

Dipole Moment Solid Vapor Pressure

Enthalpy of Combustion Surface Tension

Enthalpy of Fusion Vapor Pressure

Flash Point Vapor Thermal Conductivity

Free Energy of Formation Vapor Viscosity

Freezing Point (normal melting point)

Gross Heating Value

Heat of Formation

Hydrogen Deficiency Number

Liquid Molar Volume

Lower Heating Value

Molecular Weight

Normal Boiling Point

Rackett Parameter

Radius of Gyration

Solubility Parameter

Specific Gravity

Triple Point Temperature

Triple Point Pressure

UNIFAC Structure

van der Waals Area and Volume


PRO/II Component and Thermophysical Properties Defined Components I-5Reference M anual


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Using DATAPREPTM SimSci provides an interactive program, DATAPREP, for review and ma-nipulation of the pure component fixed and temperature-dependent proper-

ties available for defined components in libraries. DATAPREP is PC based.

Detailed descriptions for both the fixed and temperature-dependent library

properties mentioned above are contained in Appendix A of theDATAPREP

User Guide.

A comprehensive summary of the available data for each component, for any

release of the libraries, can also be generated by using DATAPREP.

DATAPREPs functionality also includes the ability to generate keyword

input file inserts containing component properties for non-library compo-

nents. Private pure component libraries can also be made using DATAPREP.

In addition to the USER.LB1 and USER.LB2 files that can be used directly

by PRO/II on a PC, ASCII input files are generated for input to the library

manager program for use on other platforms. Please refer to theDATAPREP

User Guidefor further information about its capabilities.

ReferenceDATAPREP User Guide, 1991, Simulation Sciences Inc.

Fixed Properties As explained in the above section, these properties are described in Appen-dix A of theDATAPREP User Guide. Some things to be aware of are that

the specific gravities of permanent gases are often given relative to air, with-

out any annotations in the output, and liquid molar volumes can be

extrapolated from a condition very different from 77F (25 C), if thecomponent doesnt naturally exist as a liquid at 77 F.

Temperature-

dependentProperties

The temperature-dependent correlations available for use in PRO/II are listed

in Section 17, Component Properties, of the PRO/II Keyword Input Manual.The equations that are typically used to represent a property are listed in Ta-

ble 1.1.1-2. While temperature-dependent library properties are fitted and are

usually very accurate at saturated, subcritical conditions, caution must be

used in the superheated or supercritical regions.

Because of the form of some of the allowable temperature-dependent equations,

extrapolation beyond the minimum and maximum temperatures is not done using

the actual correlation. PRO/II has adopted the rules shown in Table 1.1.1-2, based

on the property, for extrapolation of the temperature-dependent correlations.




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Table 1.1.1-2: PRO/II Temperature-dependent Property Equations andExtrapolation Conventions

Temperature-dependentProperty

RecommendedEquations

ExtrapolationMethod

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

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

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 subsets of the available coefficients with

these equations corresponding to the more traditional equations. Table

1.1.1-3 gives some examples of this mapping.

Table 1.1.1-3: PRO/II Vapor Pressure Equations

Equation 20 / 21 Coefficients

Common VP 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


PRO/II Component and Thermophysical Properties Defined Components I-7Reference M anual


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Properties FromStructure

Properties 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 group. For example, amine properties would be moreaccurate than those predicted for an ethanol amine, which would contain

functional groups for both an alcohol and an alcohol amine. This feature is

available in DATAPREP and in PRO/II for all versions subsequent to v3.3.

Complete documentation of the estimation techniques used is contained in

Section 3.7, Prediction,of theDATAPREP User Guide.




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Petrol eum Components

GeneralInformation

Petroleum components (often called pseudocomponents) are either defined

on a one-by-one basis on PETROLEUM statements or generated from one or

more streams given in terms of assay data. The processing of assays is de-

scribed in Section 1.1.3,Assay Processing. Each individual pseudocompo-

nent 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 keyword). 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. Three different sets of

characterization methods are provided. These are known as the CAVETT, SIM-

SCI, and Lee-Kesler methods. The Cavett methods developed in 1962 have been

the default in all versions of PRO/II up to and including the 3.5 series. The SIM-

SCI 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.

PropertyGeneration--

SIMSCI MethodCriti cal Properties and Acentric Factor

The SIMSCI characterization method was developed by Twu in 1984. It

expresses the critical properties (and molecular weight) of hydrocarbon com-

ponents as a function of NBP and specific gravity. The correlation is ex-

pressed as a perturbation about a reference system of normal alkanes. The

critical temperature (in degrees Rankine) is given by:

(1 )Tc=Tc

1 +2fT

1 2fT

2

(2 )fT=SGT0.362456

Tb12+0.03982850.948125

Tb12

SGT

1.1.2


PRO/II Component and Thermophysical Properties Petroleum Components I-9Reference M anual


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(3 )SGT=exp5

SG

SG

1

(4 )Tc=Tb(0.533272 +0.19101710

3Tb+0.77968110

7Tb

2

0.2843761010Tb3+0.9594681028Tb13)1

(5 )SG

=0.843593 0.1286243.36159

3

13749.512

where:

SG = specific gravity

Tb= normal boiling point, degrees Rankine

= 1 - Tb/ Tc

SG = specific gravity correctionf = correction factor


subscript Trefers to the temperature

subscript crefers to the critical conditions

superscript refers to the reference system

The critical volume (in cubic feet per pound mole) and the critical pressure

(in psia) are given by similar expressions:

(6 )V

c=V

c

1+2f

V

1 2f

V

2

(7 )fV=SGV

0.466590

Tb12+0.182421+3.01721

Tb12

SGV

(8 )SGV=exp 4

SG

2SG2

1

(9 )Vc

=

1

0.419869 0.5058391.5643639481.7014

8

(10)Pc=Pc

Tc

TcVc

Vc

1+2fP

12fP

2

(11)f

P=SG

P[2.5326246.1955

Tb120.00127885T

b

+11.4277 +252.140Tb

12+0.00230535TbSGP]

(12)SGP=exp0.5

SG

SG

1

(13)Pc

=3.83354+1.19629

12+34.8888+36.19522+104.19342

where:

V = molar volume, ft3/lbmole

P = pressure, psia

subscripts Vand Prefer to the volume and pressure


I-10 Petroleum Components May 1994


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The acentric factor for the SIMSCI method is estimated with the use of a gen-

eralized Frost-Kalkwarf vapor equation developed at SimSci. The equation is

given by:

(14)lnPR=A1+A4

+A2+A5

TR+A3+A6

lnTR+A7PRTR2

where:

A1toA7= constants given in Table 1.1.2-1

PR= reduced pressure (P/Pc)

TR= reduced temperature (T/Tc),

= a parameter evaluated at the NBP and given by:

(15)

=lnPR,bA7PR,b

TR,b2f

TR,bf

TR,b

where:

subscriptsR,bindicate reduced properties evaluated at the

normal boiling point

Functionsfandfare given by:

(16)f(TR)=A1+A2TR+A3lnTR

(17)f(TR)=A4+A5

TR+A6lnTR

The values of the seven constants in these equations are shown in Table 1.1.2-1.

Table 1.1.2- 1: Values ofConstants for Equations (14)-(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 is determined using equation(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

(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:

(18)=log10PR,TR=0.71




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Other Fixed Properties

The heat of formation is computed from a proprietary correlation developed by

SimSci. The solubility parameter is estimated from the following equation:

(19)=

HVRT

VL

12

The molar latent heat of vaporization, HV, is computed from the Kistiakowsky-Watson method described later on in this section, while VLis the liquid molar

volume at 25 C.

Temperature-dependent Properties

The ideal-gas enthalpy (needed for equation-of-state calculations) is calcu-

lated 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 vari-

ety of ideal-gas heat capacity data for hydrocarbons from the API 44 project

and other sources. The equation (which produces enthalpies in Btu/lb and

uses temperatures in degrees Rankine) is as follows:

(20)H

=A1+A2T+

A32

T2+

A4

3T

3

(21)A2=C1+C7C4

(22)A3=C2+C7C5

(23)A4=C3+C7C6

(24)C1=0.33886 +0.02827K

(25)C2=(0.9291 1.1543K+0.0368K

2)104

(26)C3=1.665810

7

(27)C4=(0.26105 0.59332K)

(28)C5=4.9210

4

(29)C6=(0.536 0.6828K)107

(30)C7=[(12.8 K)(10 K)

10K]2

The Watson characterization factor, K, is defined as:

(31)K=NBP

13

SG

where:

NBP = normal boiling point in degrees Rankine





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The constantA1in equation (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 liq-

uid 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

reference point and the ideal-gas state.

The vapor pressure is calculated from the reduced vapor-pressure equation(14) used above in the calculation of the acentric factor. The latent heat of

vaporization is also calculated from equation (14). The saturated liquid en-

thalpy is calculated by computing 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. The saturated liquid density is

computed by applying the Rackett equation (see Section 1.2.3, Generalized

Correlation Methods) to saturated temperature and pressure conditions as

predicted from the vapor-pressure equation (14).

PropertyGeneration--

CAVETT Method

Critical Properties and Acentric Factor

Optionally, the user may choose to compute critical properties from the meth-

ods developed in 1962 by Cavett. This option is called the CAVETT method.

The equations are:

(32)Tc=768.07121 +1.7133693Tb0.0010834003Tb20.0089212579(API)Tb

+0.38890584106Tb3+0.5309492(API)Tb

2+0.327116107(API)2Tb

2

(33)log10Pc=2.8290406 +0.94120109103

Tb0.30474749105

Tb2

0.2087611104(API)Tb+0.15184103108T

b

3+0.11047899107(API)T

b

2

0.48271599107

(API)2

Tb+0.13949619109

(API)2

Tb2

where:

Tc= critical temperature in degrees Rankine

Pc= critical pressure in psia

Tb= normal boiling point in degrees Fahrenheit

API = API gravity

When the CAVETT characterization options are chosen, the acentric factor is

computed by a method due to Edmister (1958):

(34)=3

7

log10Pc

(Tc

Tb

)1

1




21/171

In equation (34), Pcis in atmospheres. Finally, the critical volume is esti-

mated from the following equation:

(35)Zc=

PcVcRTc

=0.291 0.08

15 PRO/II Note: For more information on using the CAVETT characterizationmethod, see Section 15, Petroleum Component Properties, of the PRO/IIKeyword Input Manual.


When the CAVETT characterization option is chosen, the heat of formation

and solubility parameter are calculated exactly as in the SIMSCI method

above.


Ideal-gas enthalpies (in Btu/lb-mole) are computed with the following equations:

(36)H=A+BT+CT2+DT3

(37)A=a5MWa4+a0

(38)B=459.67 (1379.01a12a2)+a3

(39)C=a21379.01a1

(40)D=a1=9.17510

11API5.633108MW

(41)a2=3.10710

45.832108APIMW

(42)a3=

1.702510

6

1.489106

APIAPI2.85710

5API

+4.29310

33.084104KK+0.088)K0.819

MW

(43)a4=459.67

459.67

459.67a1a2

+a3

(44)a5=(0.351K8.953)K+43.402

K+188.25

+3.53510

4API0.053API5.95610

3K+3.544

API

where:

T = temperature in degrees Rankine

MW = molecular weight

API = API gravityK = Watson K-factor defined by equation (31)

The constant a0in equation (37) is determined so as to be consistent with the

arbitrary zero of enthalpy, which is the saturated liquid at 0 C.




22/171

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

(45)ln P=A+ B

T80.0

(46)A=ln(14.696) B

Tb80.0

(47)B=

ln Pcln(14.696)1

Tc80.0 1

Tb80.0

Temperatures (including the critical temperatureTcand normal boiling point

Tb) are in degrees Rankine.

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

(48)L

=A+BT+CT2

(49)A=1.328 L,60

(50)B=

0.3076 L,60Tc

(51)C=

0.3989 L,60Tc

2

where:

L,60

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

Temperatures are in degrees Rankine

The latent heat of vaporization (in Btu/lb-mole) is calculated from a combina-

tion of the Watson equation (Watson, 1943, Thek and Stiel, 1966), for the tem-perature variation of the heat of vaporization, and the expression of

Kistiakowsky (1923), for the heat of vaporization at the normal boiling point:

(52)

Hvap

=H0

TcT

TcTb

0.38

(53)H0=Tb7.58 +4.571 lnTb

The critical temperature Tc, normal boiling point Tb, and temperature Tare

all in degrees Rankine.

The saturated liquid enthalpy is estimated with the correlation of Johnson

and Grayson. This method is discussed in Section 1.2.3, Generalized Correla-tion Methods. A constant is added so that the saturated liquid enthalpy is

zero at 0 C.




23/171

PropertyGeneration--Lee-

Kesler Method

Criti cal Properties and Acentric Factor

Kesler and Lee used the following equations in 1976 to correlate critical tem-

peratures and critical pressures of hydrocarbons:

(54)

Tc

=341.7

+811SG

+

(0.4244

+0.1174 SG

)T

b

+

(0.4669

3.2623 SG

)10

5

T

b

(55)

lnPc=8.3634 0.0566SG0.24244 +2.2898SG+0.11857SG

210

3Tb+

1.4685 +3.648

SG+0.47227 SG210

7Tb

20.42019 +1.6977

SG210

10Tb

3

where:

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

Rankine)

Pc= critical pressure in psia


The acentric factor is estimated from an equation in an earlier work by Lee

and Kesler (1975):

(56)=

lnPR,b5.92714 +6.09648TR,b+1.28862lnTR,b0.169347TR,b6

15.251815.6875TR,b13.4721 lnTR,b+0.43577TR,b6

where:

subscriptsR,bindicate reduced properties evaluated at the normal

boiling point

The critical volume is then estimated from the following equation:

(57)Zc=

PcVcRTc

=0.29050.085


When 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.


Ideal-gas enthalpies (in Btu/lb-mole) are computed by integrating the follow-

ing equation for the ideal-gas heat capacity:

(58)

Cp

=0.33886 +0.02827K0.9291 1.1543K+0.0368K2

104

T1.6658107

T

2

(CF)0.26105 0.59332(4.56 9.48)104

T(0.536 0.6828)107T2




24/171

The factor CFis given by:

(59)CF=[(12.8 K)(10 K)(10)]

2

where:

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

T = temperature in degrees Rankine

= acentric factor as calculated by equation (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 saturated 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 vaporiza-

tion are all calculated by the methods used for CAVETT characterization, as

described in the previous section.

References

1. Black, C., and Twu, C.H., 1983, Correlation and Prediction ofThermodynamic Properties for Heavy Petroleum, Shale Oils, Tar Sands

and Coal Liquids, paper presented at AIChE Spring Meeting, Houston,

March 1983.

2. Cavett, R.H., 1962, Physical Data for Distillation Calculations -

Vapor-Liquid Equilibria, 27th Mid-year Meeting of the API Division of

Refining, 42[III], 351-357.

3. Edmister, W.C., 1958, Applied Hydrocarbon Thermodynamics, 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 Thermodynamic

Correlation Based on Three-Parameter Corresponding 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.




25/171

Assay Processing

GeneralInformation

Hydrocarbon streams may be defined in terms of laboratory assay data. Typi-

cally, such an assay would consist of distillation data (TBP, ASTM D86,

ASTM D1160, or ASTM D2887), gravity data (an average gravity and possi-

bly a gravity curve), and perhaps data for molecular weight, lightends compo-

nents, 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

pseudocomponents which are then used to represent the composition of each

assay stream.

The process by which assay data are converted to pseudocomponents can be ana-

lyzed in terms of several distinct steps. Before each of these is examined in de-

tail, it will be useful to list briefly each step of the process in order:

The user defines one or more sets of TBP cutpoints (or accepts the de-fault set of cutpoints that PRO/II provides). These cutpoints define the

(atmospheric) boiling ranges that will ultimately correspond to each

pseudocomponent. Multiple cutpoint 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 pro-

gram cuts each curve to determine what percentage of each assay

goes into each pseudocomponent as defined by the appropriate cutpoint

set. Gravity and molecular weight data are similarly processed so that

each cut has a normal boiling point, specific gravity, and molecular

weight. During this step, the lowest-boiling cuts may be eliminated ormodified to account for any lightends components input by the user.

Within each cutpoint set, all assay streams using that set (unless they are

explicitly excluded from the blending - this is described later) are com-

bined to get an average normal boiling point, gravity, and molecular

weight for each of the pseudocomponents generated from that cutpoint

set. These properties are then used to generate all other properties (criti-

cal properties, enthalpy data, etc.) for that pseudocomponent.

Note: Special refinery properties such as cloud point and sulfur content mayalso be defined within assays. The distribution of these properties into pseudo-

components and their subsequent processing by the simulator is outside thescope of this chapter but will be covered in a later document.

1.1.3


I-18 Assay Processing May 1994


26/171

Cutpoint Sets(Blends)

Defining Cutpoints

In any simulation, there is always a primary cutpoint set, which defaults

as shown in Table 1.1.3-1.

Table 1.1.3-1: Prim ary TBP Cutpoint Set

TBP Range, oF Number ofComponents Width, oF

100-800 28 25

800-1200 8 50

1200-1600 4 100

The primary cutpoints shown in Table 1.1.3-1 may be overridden by supply-

ing 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 pri-mary cutpoint set will be the default. Each cutpoint set (if it is actually used

by one or more streams) will produce its own set of pseudocomponents for

use in the flowsheet.

15 PRO/II Note: For more information on specifying TBP cutpoint sets, see Section15, Petroleum Component Properties, of thePRO/II Keyword Input Manual.

Association of Streams With Blends

Each 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 explicitly 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 de-

fined, a new blend with that name is created using the same cutpoints as the

primary cutpoint set. The user may also specify that a stream use a certain set

of cutpoints but not contribute to the blended properties of the pseudocompo-

nents 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 blend-

ing. The default is for the stream to be included in the blending for the pur-

poses of pseudocomponent property generation; this is called the BLEND

option. It is not allowed for the XBLEND option to be used on all streams as-

sociated 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:


PRO/II Component and Thermophysical Properties Assay Processing I-19Reference M anual


27/171

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, sup-

pose the following streams (where extraneous information like the initial con-

ditions is not shown) are given:

Table 1.1.3-2: Blending Example

Stream Blend Option Blend Name

S1 none given(defaulted toBLEND)

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 pseudocomponents defined by secondary cut-

point set A1, since it is the default. S3 will also use A1s pseudocomponents

since it is specified directly. The pseudocomponents 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 pseudocomponents de-

fined by cutpoint 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 S5s cuts will be used to determine the prop-

erties of the pseudocomponents in blend B1. Finally, stream S7 will use an-

other new blend, B2, also with the cutpoints from the primary cutpoint set.

Since it is a different blend, however, the pseudocomponents from blend B2

will be completely distinct (even though they will use the same cutpointranges) from those of blend B1.

15 PRO/II Note: For more information on blending options for assay streams, seeSection 15, Petroleum Component Properties, of the PRO/II Keyword Input

Manual.




28/171

Application Considerations

The selection of cutpoints is an important consideration in the simulation of

hydrocarbon processing systems. Too few cuts can result in poor repre-

sentation of yields and stream properties when distillation 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 unnecessar-

ily. It is wise to examine the cut definition for each problem in light of simu-

lation 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 functionality is useful when dif-

ferent portions of a flowsheet are best represented 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 flowsheet differ in

character; for example, different blends might be used to represent an aro-

matic stream (producing pseudocomponents with properties characteristic of

aromatics) and a paraffinic stream feeding into the same flowsheet. The extra

detail and accuracy possible with this feature must be balanced against the in-

crease in CPU time caused by the increased number of pseudocomponents.

Interconversion ofDistillation Curves

Types of Distil lati on Curves

Assays of hydrocarbon streams are represented by distillation curves. A dis-

tillation curve represents the amount of a fluid sample that is vaporized as

the temperature of the sample is raised. The temperature where the first va-

porization takes place is referred to as the initial point (IP), and the tempera-

ture at which the last liquid vaporizes is called the end point (EP). Each data

point represents a cumulative portion (usually represented as volume per-

cent) of the sample vaporized when a certain temperature is reached.

Estimation of thermophysical properties for the pseudocomponents requires

(among other things) a distillation curve that represents the true boiling point

(TBP) of each cut in the distillation. However, rigorous 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.




29/171

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 intheAPI Technical Data Book; complete specifications are given in volume 5

(Petroleum Products and Lubricants) of theAnnual Book of ASTM Standards.

Conversion of D1160 Curves

PRO/II converts D1160 curves to TBP curves at 760 mm Hg using the three-

step procedure recommended in theAPI 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 temperature given the normal boiling

point, but the same equations may be solved to yield a normal boiling

temperature given the boiling temperature at another pressure. The equa-

tions used are as follows:

(1 )

(2 )log

10P=2663.129X5.994296

95.76X0.972546 0.0013X0.0022

(2P760 mmHg)

(3 )

where:

P* = vapor pressure in mm Hg at temperature T (in degrees

Rankine)

The parameterXis defined by:

(4 )

X=

Tb

T0.0002867Tb

748.1 0.2145Tb

where:

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

Hg

log10P=3000.538X6.76156

43X0.987672 forX>0.0022 (P


30/171

For conversions where neither pressure is 760 mm Hg, the conversion may

be made by applying the above equations twice in succession, 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.


PRO/II converts D2887 simulated distillation data to TBP curves at 760 mm Hg

using the two-step procedure recommended in theAPI 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:

(5 )D86 =a(SD)bFc

where:

D86 and SD = the ASTM D86 and ASTM D2887 temperatures in de-

grees Rankine at each volume percent (for D86) and thecorresponding weight percent (for SD), and a, b, and c

are constants varying with percent distilled according

to Table 1.1.3-3.

Table 1.1.3-3: Values of Constants a, b, c

PercentDistilled a b c

0 6.0154 0.7445 0.2879

10 4.2262 0.7944 0.2671

30 4.8882 0.7719 0.3450

50 24.1357 0.5425 0.713270 1.0835 0.9867 0.0486

90 1.0956 0.9834 0.0354

100 1.9073 0.9007 0.0625

The parameterFin equation (5) is calculated by the following equation:

(6 )F=0.009524(SD10%)0.05434(SD50%)0.6147

where:

SD10% and SD50% = D2887 temperatures in degrees Rankine at the 10% and

50% points, respectively




31/171

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

Methodbelow.


PRO/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-Okamoto correlation. In addition, a correc-

tion 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 asfollows:

(7 )Tcorr=Tobs+D; log10D= 1.587 +0.00473Tobs

where:

Tcorr, Tobs= the corrected and observed temperatures, respectively,

in degrees Fahrenheit.If necessary, convert the D86 curve at pressure Pto D86 at 760 mm Hg

with the standard ASTM correction factor:

(8 )T760=TP+0.00012(760 P)(460 +TP)

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 theAPI Technical Data Book.

The equation for this procedure is as follows:

(9 )TBP=a(D86)b

where aand bare constants varying with percent of liquid sample distilled

as given in Table 1.1.3-4:




32/171

Table 1.1.3-4: 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

100 0.8008 1.0355

b) Conversion of D86 Curves with Old (1963) API Method

This method, while no longer the default, is still available for users whose

flowsheets 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 correlation has been converted to

equation form by SimSci.

c) Conversion of D86 Curves with Edmister-Okamoto Method

Edmister and Okamoto (1959) developed a method which is still widelyused 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 equations by SimSci) is

used for conversion of D86 to TBP curves.

Cutting TBP Curves Fitting of Distill ation Curves

Before a curve is cut into pseudocomponents, the distillation data must be fit-

ted 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 cu-

bic spline function is used to fit all given volume percents 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 distribution function to extrapolate to the 0.01%

and 99.99% points, respectively. If only two points are supplied, the entire

curve is defined by the distribution function fit. This extrapolation feature is

particularly valuable when extrapolating heavy ends distillations which often

terminate well below 50 volume percent. This method in general 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 propagate throughout the entire length of the curve. Should this

happen, the input data should be checked for validity.




33/171

The quadratic fit method (known as the QUADRATIC option) provides a suc-

cessive 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 dif-

ferences between the curve and the input data. If desired, the curve may be

constrained to pass through either or both of the initial point and end point.

The PDF method is recommended whenever it is suspected that the distilla-

tion data are noisy, containing significant random errors.

It is worth noting that the choice of curve-fitting procedure will also have a

slight impact on the distillation interconversions described in the previous sec-

tion. That is because most of the conversion procedures work by doing the

conversion at a fixed set of volume percents, which must be obtained by interpo-

lation and sometimes extrapolation, using some curve-fitting procedure.

Division into Pseudocomponents

Once a smooth distillation curve is obtained, the volume percent distilled at each

cutpoint is determined. The differences between values at adjacent cutpoints de-

fine the percent of the streams volume that is assigned to the pseudocomponent

defined by the interval between two adjacent cutpoints. For example, using the

default set of cutpoints shown in Table 1.1.3-1, the first pseudocomponent would

contain all material boiling between 100 F and 125 F, the second would con-tain the material boiling between 125 F and 150 F, and so forth. Material boil-ing 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 distil-lation 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), theunused cuts are omitted from the simulation.

The normal boiling point (NBP) of each cut is determined as a volume-frac-

tion average (or, in rare cases where TBP, D86, or D1160 distillations are

entered on a weight basis, as a weight-fraction average) 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 flowsheet) as correlating

parameters when calculating other thermophysical properties for each

pseudocomponent.




34/171

These procedures are demonstrated in Figure 1.1.3-1 for a fictitious assay

with an IP of 90 F being cut according to the default cutpoint set (Table1.1.3-1); for simplicity only the first ten percent of the curve is shown. In ad-

dition to its range, the first cut picks up the portion boiling below 100 F, andits average boiling point (about 110 F in this case) is determined by integrat-ing the curve from the IP to the 125 F point. The second cut is assigned thematerial boiling from 125 F to 150 F, which is integrated to get a NBP ofapproximately 138 F. The third and subsequent cuts are generated in a simi-lar manner.

Figure 1.1.3-1 :Cutting TBP Curves

Gravity Data

PRO/II requires the user to enter an average gravity (either as a Specific

Gravity, API Gravity, or Watson K-factor) for each assay. If a Watson K isgiven, 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 gravity 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 es-

timate of the 100% point gravity value and letting the program normalize the

curve, particularly when gravity data are available to 80% or beyond.




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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 WAT-

SONK method. For a pure component, the Watson K-factor is defined by the

following equation:

(10)K=

NBP13

SG

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 boil-

ing point computed from the distillation curve. The gravity curve is gener-

ated by assuming a constant value of the Watson K, applying equation (10)

to each cut to get a gravity, averaging these values, and then adjusting the as-

sumed 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 primarily for com-patibility with older versions. It is similar to the preferred 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 incor-

rect. Hence, for truly accurate simulation work, the user is advised to supply

gravity curves whenever possible.

Molecular Weight Data

In 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 program.

The user may supply a molecular weight curve, which is quadratically inter-

polated and extrapolated to cover the entire range of pseudocomponents. Op-

tionally, the user may also supply an average 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 mo-

lecular weight curve is normalized to match the given average.




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If no molecular-weight data are supplied, the molecular weights are esti-

mated; the default method is a proprietary modification (known as the SIM-

SCI method) of the method developed by Twu (1984). This method is a

perturbation expansion with the normal alkanes as a reference fluid. Twus

method was originally developed to be an improvement over Figure 2B2.1 in

older editions of theAPI Technical Data Book. That figure relates molecular

weight to NBP and API gravity for NBPs greater than 300 F. The SIMSCI

method matches that data between normal boiling points of 300 F and 800F, and better extrapolates outside that temperature range.

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

A newer API method, called the extended API method (known as the EXTAPI

option), is also available. This is API procedure 2B2.1, and it is an extension of

the earlier API method which better matches known pure-component data below

300 F. The equation is as follows:

(11)

MW=20.486 exp(1.16510

4Tb7.78712 SG+1.158210

3TbSG)

Tb

1.26007SG

4.98308

where:

SG = specific gravity of the pseudocomponent

Tb= normal boiling point in degrees Rankine

Lightends Data

Hydrocarbon 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 accurate 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 flowsheet in a separate stream and handled in a straightforward manner. Typi-

cally, 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 components 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 1.1.3-2,

where lightend component flows are adjusted until the highest-boiling lightend

(nC5 in this example) 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 portion of the cut encompassing that point)

are discarded.




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Figure 1.1.3-2 :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 lightends components can be normal-

ized to determine the individual component flowrates. A final alternative is to

specify the flowrate of each lightends component individually.

GeneratingPseudocomponent

Properties

Once each curve is cut, the program processes each blend to produce average

properties for the pseudocomponents from each cutpoint 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 molecu-

lar weight and gravity are calculated 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 pseudocomponent, 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 Section

1.1.2,Petroleum Components.

Vapor PressureCalculations

While not a part of the programs 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 al-

lows specification of these quantities from several unit operations, and they

may be reported in output in the Heating/Cooling Curve (HCURVE) utilityor as part of a user-defined stream report.




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True Vapor Pressure (TVP) Calculati ons

The TVP of a stream is defined as the bubble-point pressure at a given refer-

ence temperature. By default, that reference temperature is 100 F, but thismay be overridden by the user. The user may specify a specific thermody-

namic system to be used in performing all TVP calculations in the flowsheet;

by default, the calculation for a stream is performed using the thermody-

namic system used to generate that stream.

Reid Vapor Pressure (RVP) Calculations

The RVP laboratory procedure provides an inexpensive and reproducible meas-

urement correlating to the vapor pressure of a fluid. The measured RVP is usu-

ally 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 pressure is a rough

measure of the true vapor pressure. Six different calculation methods are avail-

able. 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

system used to generate the stream will be used.

The APINAPHTHA method calculates the RVP from Figure 5B1.1 in theAPI

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 con-

verted to equation form by Simsci. This method is the default for PRO/IIs RVP

calculations. It is useful for many gasolines and other finished petroleum prod-

ucts, but it should not be used for oxygenated gasoline blends.

The APICRUDE method calculates the RVP from Figure 5B1.2 in theAPI

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. It is primarily intended for crude oils.

The ASTM D323-82 method (known as the D323 method) simulates a stand-ard 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 isthen mixed at 100 F with air in a 4:1 volume ratio. Since the test chamber isnot 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 (corre-sponding 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 avail-

able for compatibility with earlier versions of the program.




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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 simulating this method is identical to that for

D323, except that no water is added to the mixture. Air should be in the com-

ponent 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 meas-

ured. In the simulator, this is accomplished by flashing, at constant volume, a mix-

ture of 1 part sample (at 33 F and 1 atm) and 4 parts air (at the near-vacuumconditions of 0.01 psia and 100 F). The resulting total pressure is then con-verted to a dry vapor pressure equivalent (DVPE) using the following equation:

(12)DVPE=0.965XA

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 component list

for proper use of this method.

Comments on RVP and TVP Methods

Because 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 components rather than as pseudocomponents;

oxygenated compounds blended into gasolines should also be represented as

defined components rather than as part of an assay. It is also important to ap-

ply a thermodynamic method that is appropriate for the stream in question

(see Section 1.2.2,Application Guidelines). The thermodynamics becomesparticularly 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 Sim-

Sci alpha formulation and one of the advanced mixing rules (see Section

1.2.4,Equations of State). It is important to have binary interaction parame-

ters between the oxygenates and the hydrocarbon components of the system.

PRO/IIs 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 simulation may not be identical to that ofthe experimental sample.




40/171

One of the less appreciated effects in experimental measurements is the pres-

ence 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 ofthese 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, low-

ering 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. Therefore, a wet

test performed with air that was not dry would be expected to give results in-

termediate between PRO/IIs D323 and D4953 calculations. The results from

the D5191 method (both in terms of the experimental and calculated num-

bers) should in general be very close to D4953 results.

The primary application guideline for which RVP calculational model to use

is, of course, to choose the one that corresponds to the experimental proce-

dure 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 hydrocar-bon streams; the presence of water makes it less well-suited for use with

streams containing oxygenated compounds. The D4953 and D5191 methods

are both better suited for oxygenated systems, and calculations with these

methods should give similar results.

References

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, Lubricants, and Fossil Fuels),ASTM, Philadelphia, PA (issued annually).

3. Edmister, W.C., and Okamoto, K.K., 1959, Applied Hydrocarbon

Thermodynamics, Part 12: Equilibrium Flash Vaporization Calculations

for Petroleum Fractions, Petroleum 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.




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42/171

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-OConnell method for dimerizing

species.Special methods for calculating the properties of specific systems of compo-

nents such as alcohols, glycols, and sour water systems.

Solid-liquid equilibria methods such as the vant Hoff method for calculating

the solubility of a solid in a liquid.

In addition, the electrolyte version of PRO/II contains a number of thermody-

namic methods to handle systems containing aqueous ionic species.

1. 2

Section 1.2 Thermodynamic Methods

PRO/II Component and Thermophysical Properties I-37Reference M anual


43/171

Basic Principl es

GeneralInformation

When modeling a single chemical process or an 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-phase and vapor-phase enthalpies.

Liquid-phase and vapor-phase entropies.

Liquid-phase and vapor-phase densities.

PhaseEquilibria When two or more phases are brought into contact, material is transferredfrom one to another until the phases reach equilibrium, and the compositionsin each phase become constant. At equilibrium for a multicomponent system,

the temperature, pressure, and chemical potential of component iis the same

in every phase, i.e.:

(1 )T=T==T

(2 )P

=P==P

(3 )i

=i

==i

where:

T = system temperature

P = system pressure

= the chemical potential

,, ..., represent the phasesThe fugacity of a substance is then defined as:

(4 )ii

0=RTln

f

i/fi

0

where:

fi= fugacity of component i

fi0= standard-state fugacity of component iat T, P

i0= standard-state chemical potential of component iat T,P

1.2.1

Thermodynamic Methods Section 1.2

I-38 Basic Pri nciples May 1994


44/171

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

(5 )fi

=fi

==f

i

, i=1,2, n

The fugacity of a substance can be visualized as a corrected partial pres-

sure such that the fugacity of a component in an ideal-gas mixture is equal

to the component partial pressure.

For vapor-liquid equilibrium calculations, the ratio of the mole fraction of a com-

ponent in the vapor phase to that in the liquid phase is defined as the K-value:

(6 )Kiyi/xi

where:

Ki= K-value, or equilibrium ratio

yi= mole fraction in the vapor phase

xi= mole fraction in the liquid phase

For liquid-liquid equilibria, a corresponding equilibrium ratio or distribution

coefficient is defined:

(7 )KDi

xi

I/xi

II

where:

KDi= liquid-liquid distribution coefficient

I,IIrepresent the two liquid phases

The vapor-phase fugacity coefficient of a component, iV, is defined as the

ratio of its fugacity to its partial pressure, i.e.:

(8 )iVfi

V/yiP

where:

iV= vapor-phase fugacity coefficient of component i

If a liquid activity coefficient method is used in the liquid phase calculation,

then the activity coefficient of the liquid phase can be related to the liquid

fugacity by the following relationship:

(9 )fiL

=iL

xifiOL

where:

i

L= liquid-phase activity coefficient

fi0L

= standard-state fugacity of pure liquidi

Section 1.2 Thermodynamic Methods

PRO/II Component and Thermophysical Properties Basic Principl es I-39Reference M anual


45/171

With this definition of liquid fugacity, iL1 asxi1. The standard-statefugacity is as follows:

(10)f

i

0L=P

i

sat

i

satexp

Pi

sat

P

vi

L/RTdP

where:

Pisat= saturated vapor pressure of component iat T

R = gas constant

viL

= liquid molar volume of component iat Tand P

isat= fugacity coefficient of pure componentiat Tand Pi

sat

Equation (10) provides two correction factors for the pure liquid fugacity. The

fugacity coefficient, isat, corrects for deviations of the saturated vapor fromideal-gas behavior. The exponential correction factor, known as the Poynting cor-

rection factor, corrects for the effect of pressure on the liquid fugacity. The

Poynting correction factor is usually negligible for low and moderate pressures.

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

(11)Ki=

i

Lf

i

OL/Pi

V

Combining equations (7) and (9) yields:

(12)KDi

=i

LII/i

LI

If an equation of state is applied to both vapor and liquid phases, the vapor-

liquid K-values can be written as:

(13)Ki=iL

/iV

The liquid-liquid equilibria can be written as:

(14)K

Di=

i

LII

iL

I

Equations (11), (12), (13), and (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 (13).

One important limitation of equation-of-state methods is that they have to be ap-

plicable over a wide range of densities, from near-zero density for gases to high

liquid densities, using constants obtained from pure-component data. Equations

of state are not very accurate for nonideal systems unless combined with compo-nent mixing rules and alpha formulations (see Section 1.2.4,Equations of State)

appropriate for those components.

Thermodynamic Methods Section 1.2

I-40 Basic Pri nciples May 1994


46/171

Equation (11) may be solved by using equation-of-state methods to calculate va-

por fugacities combined with liquid activity methods to compute liquid activity

coefficients (see Section 1.2.6,Liquid Activity Methods). Liquid activity met

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