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ThTechnical Support13
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The doTable of Contents
Technical Support................................................... 13
Online Technical Support Center ...........................14
Phone and E-mail................................................15
1  Introducing Aspen HYSYS Thermodynamics COM 
Interface1-1
1.1 Introduction .................................................... 1-2
2  Thermodynamic Principles ...................................2-1
2.1 Introduction .................................................... 2-3
2.2 Chemical Potential & Fugacity ............................ 2-6
2.3 Chemical Potential for Ideal Gas......................... 2-7
2.4 Chemical Potential & Fugacity for a Real Gas........ 2-8
2.5 Fugacity & Activity Coefficients .......................... 2-9
2.6 Henry’s Law ...................................................2-12
2.7 Gibbs-Duhem Equation ....................................2-16
2.8 Association in Vapour Phase - Ideal Gas .............2-20
2.9 Equilibrium Calculations ...................................2-24
2.10 Basic Models for VLE & LLE ...............................2-26
2.11 Phase Stability................................................2-33
2.12 Enthalpy/Cp Departure Functions ......................2-38
3  Thermodynamic Calculation Models......................3-1
3.1 Equations of State............................................ 3-2
3.2 Activity Models ...............................................3-98
3.3 Chao-Seader Model .......................................3-191
3.4 Grayson-Streed Model ...................................3-192
4   Physical Property Calculation Methods ................4-1
4.1 Cavett Method ................................................. 4-2
4.2 Rackett Method................................................ 4-8iii
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The do4.3 COSTALD Method............................................4-11
4.4 Viscosity ........................................................4-14
4.5 Thermal Conductivity.......................................4-18
4.6 Surface Tension ..............................................4-21
4.7 Insoluble Solids ..............................................4-22
5  References & Standard States ..............................5-1
5.1 Enthalpy Reference States................................. 5-2
5.2 Entropy Reference States .................................. 5-4
5.3 Ideal Gas Cp ................................................... 5-5
5.4 Standard State Fugacity.................................... 5-6
6  Flash Calculations.................................................6-1
6.1 Introduction .................................................... 6-2
6.2 T-P Flash Calculation ........................................ 6-3
6.3 Vapour Fraction Flash ....................................... 6-4
6.4 Flash Control Settings....................................... 6-7
7  Property Packages................................................7-1
7.1 Introduction .................................................... 7-2
7.2 Vapour Phase Models........................................ 7-2
7.3 Liquid Phase Models ........................................7-13
8  Utilities.................................................................8-1
8.1 Introduction .................................................... 8-2
8.2 Envelope Utility................................................ 8-2
9  References ...........................................................9-1
 Index.................................................................... I-1iv
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Introducing Aspen HYSYS Thermodynamics COM Interface 1-1
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Th1  Introducing Aspen HYSYS 
Thermodynamics COM Interface1-1
1.1  Introduction................................................................................... 2
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1-2 Introduction
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Th1.1 Introduction
The use of process simulation has expanded from its origins in 
engineering design to applications in real time optimization, 
dynamic simulation and control studies, performance 
monitoring, operator training systems and others. At every 
stage of the lifecycle there is a need for consistent results such 
that the modeling efforts can be leveraged in those many 
applications.
Accurate thermophysical properties of fluids are essential for 
design and operation in the chemical process industries. The 
need of having a good thermophysical model is widely 
recognized in this context. All process models rely on physical 
properties to represent the behavior of unit operations, and the 
transformations that process streams undergo in a process. 
Properties are calculated from models created and fine-tuned to 
mimic the behaviour of the process substances at the operating 
conditions
Aspen HYSYS Thermodynamics COM Interface is a complete 
thermodynamics package that encompasses property methods, 
flash calculations, property databases, and property estimation. 
The package is fully componentized, and therefore fully 
extensible to the level of detail that allows the user to utilize, 
supplement, or replace any of the components. The objective of 
this package is to improve the engineering workflow by 
providing an open structure that can be used in many different 
software applications and obtain consistent results.1-2
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Introducing Aspen HYSYS Thermodynamics COM 
ww
ThThe main benefit of Aspen HYSYS Thermodynamics COM 
Interface is delivered via consistent and rigorous 
thermodynamic calculations across engineering applications.
Aspen HYSYS Thermodynamics COM Interface enables the 
provision of specialized thermodynamic capabilities to the 
HYSYS Environment and to other third party applications 
including internal legacy tools. It also allows the user to support 
development of internal thermo capabilities. Aspen HYSYS 
Thermodynamics COM Interface is written to specifically support 
thermodynamics. 
The Aspen HYSYS Thermodynamics COM Interface reference 
guide details information on relevant equations, models, and the 
thermodynamic calculation engine. The calculation engine 
encompasses a wide variety of thermodynamic property 
calculations, flash methods, and databases used in the Aspen 
HYSYS Thermodynamics COM Interface framework.1-3
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1-4 Introduction
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Th1-4
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Thermodynamic Principles 2-1
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Th2  Thermodynamic 
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e document is for study 2.1  Introduction................................................................................... 3
2.2  Chemical Potential & Fugacity........................................................ 8
2.3  Chemical Potential for Ideal Gas .................................................... 9
2.4  Chemical Potential & Fugacity for a Real Gas ............................... 11
2.5  Fugacity & Activity Coefficients.................................................... 12
2.6  Henry’s Law ................................................................................. 15
2.6.1  Non-Condensable Components................................................. 17
2.6.2  Estimation of Henry’s constants................................................ 18
2.7  Gibbs-Duhem Equation ................................................................ 19
2.7.1  Simplifications on Liquid Fugacity using Activity Coeff.................. 21
2.8  Association in Vapour Phase - Ideal Gas ...................................... 24
2.9  Equilibrium Calculations............................................................... 28
2.10  Basic Models for VLE & LLE ........................................................ 30
2.10.1  Symmetric Phase Representation............................................ 30
2.10.2  Asymmetric Phase Representation .......................................... 30
2.10.3  Interaction Parameters.......................................................... 31
2.10.4  Selecting Property Methods.................................................... 32
2.10.5  Vapour Phase Options for Activity Models................................. 35
2.11  Phase Stability ........................................................................... 37
2.11.1  Gibbs Free Energy for Binary Systems ..................................... 382-1
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2-2 
2-2
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The document is for study 2.12  Enthalpy/Cp Departure Functions...............................................42
2.12.1  Alternative Formulation for Low Pressure Systems .....................47il:cadserv21@hotmail.com
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Thermodynamic Principles 
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Th2.1 Introduction
To determine the actual state of a mixture defined by its 
components and two intensive variables (usually pressure and 
temperature), a unique set of conditions and equations defining 
equilibrium is required.
Consider a closed, multi-component and multi-phase system 
whose phases are in thermal, mechanical, and mass transfer 
equilibrium. At this state, the internal energy of the system is at 
a minimum, and any variation in U at constant entropy and 
volume vanishes (1Prausnitz et al, 1986):
The total differential for the internal energy is:
where:  j = Phase (from 1 to π)
 i = Component (from 1 to nc)
 μi
j = Chemical potential of component i in phase j, defined as
(2.1)
(2.2)
(2.3)
(2.4)
dU TdS PdV–=
dU( )S V, 0=
dU T j Sd
j
P j Vd
j
μi
jdni
j
i 1=
nc
∑
j 1=
π
∑+
j 1=
π
∑–
j 1=
π
∑=
μi
j
ni∂
∂U
⎝ ⎠
⎜ ⎟
⎛ ⎞
S V nk 1≠
j
, ,
=
2-3
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2-4 Introduction
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ThSince the system is closed, the differentials in number of moles, 
volume and entropy are not all independent, but are instead 
constrained as follows:
Therefore, a system of equations with π(nc+2) variables and nc 
+ 2 constraints (Equations (2.5), (2.6) and (2.7)) is defined. 
The constraints can be used to eliminate some variables and 
reduce the system to a set of (π - 1)(nc + 2) independent 
equations.
(2.5)
(2.6)
(2.7)
dS Sd j
j 1=
π
∑ 0= =
dV Vd j
j 1=
π
∑ 0= =
dni
j 0=
j 1=
π
∑ i 1, ..., nc=2-4
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Thermodynamic Principles 
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ThThe variables can be eliminated in the following way:
(2.8)
(2.9)
(2.10)
dS1 Sd j
j 2=
π
∑–=
dV1 Vd j
j 2=
π
∑–=
dni
1 dni
j
j 2=
π
∑=2-5
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2-6 Introduction
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ThThe result is as follows:
where: the differentials on the right side of Equation (2.11) are 
independent.
Setting all of the independent variables constant except one, at 
equilibrium you have:
Therefore:
Repeating the same argument for all of the independent 
variables, the general conditions necessary for thermodynamic 
equilibrium between heterogeneous phases are established (for 
all i):
From now on, it is assumed that Equations (2.14) and (2.15) 
are always satisfied. The equilibrium condition established in 
Equation (2.16) will be discussed in more detail. Note that the 
description of equilibrium according to Equations (2.13), 
(2.14), (2.15), and (2.16) is at best incomplete, since other 
intensive variables could be important in the process being 
analysed. For example, the electric or magnetic fields in the 
(2.11)
(2.12)
(2.13)
T1 = T 2 
=...=T π
Thermal Equilibrium - no heat flux across phases (2.14)
P1 = P 2 
=...=P π
Mechanical Equilibrium - no phase displacement (2.15)
μi
1 = μi
2 =...= 
μi
π
Mass Transfer Equilibrium - no mass transfer for 
component i between phases (2.16)
dU T j T 1–( ) Sd
j
P j P1–( ) Vd
j
μi
j μi
1–( )dni
j
i 1=
nc
∑
j 1>
π
∑+
j 1>
π
∑–
j 1>
π
∑=
U∂
S∂
------ 0= U∂
V∂
------ 0= U∂
ni∂
------ 0= U2∂
S2∂
--------- 0=
T1 T j= j 2, ..., π=2-6
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Thermodynamic Principles 
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Thequations, or area affects are not being considered.2-7
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2-8 Chemical Potential & Fugacity
ww
ThNevertheless, Equations (2.13), (2.14), (2.15) and (2.16) 
are important in chemical engineering thermodynamic 
calculations, and will be assumed to always apply. Provided that 
a reasonable physical model is available for the property 
calculations, virtually all chemical engineering problems that 
involve phase equilibria can be represented by the above 
equations and constraints.
The following will relate the chemical potential in Equation 
(2.16) with measurable system properties.
2.2 Chemical Potential & 
Fugacity
The concept of chemical potential was introduced by J. Willard 
Gibbs to explain phase and chemical equilibria. Since chemical 
potential cannot be directly related with any directly measured 
property, G.N. Lewis introduced the concept of fugacity in 1902. 
Using a series of elegant transformations, Lewis found a way to 
change the representation using chemical potential by 
representing the equilibrium conditions with an equivalent 
property directly related to composition, temperature and 
pressure. He named this property "fugacity." It can be seen as a 
"thermodynamic pressure" or, in simpler terms, the effective 
partial pressure that one compound exerts in a mixture.2-8
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Thermodynamic Principles 
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Th2.3 Chemical Potential for 
Ideal Gas
You start by finding an equivalent to Equation (2.5) which 
allows us to work with a better set of independent variables, 
namely pressure and temperature. This brings us to the Gibbs 
free energy, which is expressed as a function of P and T:
where:
The chemical potential is the partial molar Gibbs free energy, 
since partial molar properties are defined at constant P and T. 
Note that the chemical potential is not the partial molar internal 
energy, enthalpy or Helmholtz energy. Since a partial molar 
property is used, the following holds:
(2.17)
(2.18)
(2.19)
dG SdT– VdP μi nid
i 1=
nc
∑+ +=
μi ni∂
∂G
⎝ ⎠
⎛ ⎞
T P nk 1≠, ,
=
dGi SidT– VidP+=2-9
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2-10 Chemical Potential for Ideal Gas
ww
Thwhere:
Now assuming the system to be at constant temperature:
(2.20)
(2.21)
Gi
G∂
ni∂
------⎝ ⎠
⎛ ⎞
T P nk 1≠, ,
=
dμi dGi VidP= =2-10
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Thermodynamic Principles 
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Th2.4 Chemical Potential & 
Fugacity for a Real Gas
Although Equation (2.21) has only limited interest, its basic 
form can still be used. Pressure, P, can be replaced by another 
thermodynamic quantity which represents a real gas. This 
quantity is called fugacity, and it is a function of pressure, 
temperature and composition:
It is interesting to note that the combination of Equations 
(2.22) and (2.16) results in a simple set of equations for the 
multi-phase, multi-component phase equilibria:
Assuming again that the system is at constant temperature, 
Equations (2.21) and (2.22) can be combined, resulting in a 
working definition for fugacity:
In principle, if the behaviour of the partial molar volume is 
known, the fugacity can be computed, and the phase equilibria 
is defined. In reality, the engineering solution to this problem 
lies in the creation of models for the fluid’s equation of state—
from those models, the fugacity is calculated.
(2.22)
(2.23)
(2.24)
μi Ci RT filn+=
fi
1 fi
2 … fi
π= = =
P∂
∂ filn( )⎝ ⎠
⎛ ⎞
T
Vi
RT
------=2-11
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2-12 Fugacity & Activity Coefficients
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Th2.5 Fugacity & Activity 
Coefficients
Writing the fugacity expressions for a real and ideal gas:
Subtracting and rearranging Equation (2.26) from Equation 
(2.25) yields:
You integrate from 0 to P, noting that the behaviour of any real 
gas approaches the behaviour of an ideal gas at sufficiently low 
pressures (the limit of f/P as P 0 = 1):
Using the definition of compressibility factor (PV = ZRT), 
Equation (2.28) can be expressed in a more familiar format:
(2.25)
(2.26)
(2.27)
(2.28)
(2.29)
RTd fln VdP=
RTd Pln VidealdP=
RTd f
P
---ln V V– ideal( )dP=
f
P
---ln V
RT
------ V
RT
------–
ideal
⎝ ⎠
⎛ ⎞
0
P
∫ dP=
f
P
--ln Z 1–( )
P
----------------
0
P
∫ dP=2-12
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Thermodynamic Principles 
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ThThe ratio f/P measures the deviation of a real gas from ideal gas 
behaviour, and is called the fugacity coefficient:
These results are easily generalized for multi-component 
mixtures:
The partial molar compressibility factor is calculated:
substituting Equation (2.32) into Equation (2.31) and 
rearranging:
The quantity fi /Pxi measures the deviation behaviour of 
component i in a mixture as a real gas from the behaviour of an 
ideal gas, and is called the fugacity coefficient of component i in 
the mixture:
(2.30)
(2.31)
(2.32)
(2.33)
(2.34)
φ f
P
--=
fi
Pxi
-------ln
Zi 1–( )
P
------------------
0
P
∫ dP=
Zi ni∂
∂Z
⎝ ⎠
⎛ ⎞
T P nk i≠
j, ,
P
RT
------
ni∂
∂V
⎝ ⎠
⎛ ⎞
T P nk i≠
j, ,
PVi
RT
--------= = =
fi
Pxi
-------ln 1
RT
------ Vi
RT
P
------–⎝ ⎠
⎛ ⎞
0
P
∫ dP=
φi
fi
Pxi
-------=2-13
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2-14 Fugacity & Activity Coefficients
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ThFor mixtures in the liquid state, an ideal mixing condition can be 
defined. Usually this is done using the Lewis-Randall concept of 
ideal solution, in which an ideal solution is defined as:
where:  fi
,pure refers to the fugacity of pure component i in the vapour 
or liquid phase, at the mixture pressure and 
temperature. 
The definition used by Lewis and Randall defines an ideal 
solution, not the ideal gas behaviour for the fugacities. 
Therefore, the fugacities of each pure component may be given 
by an accurate equation of state, while the mixture assumes 
that different molecules do not interact. Although very few 
mixtures actually obey ideal solution behaviour, approximate 
equilibrium charts (nomographs) using the Lewis-Randall rule 
were calculated in the 1940s and 50s, and were successfully 
used in the design of hydrocarbon distillation towers.
Generalizing Equation (2.36) for an arbitrary standard state, 
the activity coefficient for component i can written as:
It is important to properly define the normalization condition 
(the way in which ideal solution behaviour is defined (i.e., when 
the activity coefficient approaches one), so that supercritical 
components are handled correctly, and the Gibbs-Duhem 
equation is satisfied.
(2.35)
(2.36)
(2.37)
fi
V yi fi
V pure,=
fi
L xi fi
L pure,=
γi
fi
L
fi
L pure, xi
--------------------=2-14
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Thermodynamic Principles 
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Th2.6 Henry’s Law
The normalized condition is the state where the activity 
coefficient is equal to 1. For ordinary mixtures of condensable 
components (i.e., components at a temperature below the 
critical temperature), the normalization condition is defined as 
(2Prausnitz et al, 1980):
However, the definition does not apply for components that 
cannot exist as pure liquids at the conditions of the system. 
Sometimes, for components like carbon dioxide at near ambient 
conditions, a reasonably correct hypothetical liquid fugacity can 
be extrapolated. But for components like hydrogen and 
nitrogen, this extrapolated liquid behaviour has little physical 
significance.
For solutions of light gases in condensable solvents, a different 
normalization convention can be defined than the (other than 
the one in Equation (2.38)):
(2.38)
(2.39)
fi
L
fi
L pure, xi
--------------------
xi 1→
lim γixi 1→
lim 1= =
fi
L
fi
refxi
-----------
xi 0→
lim γi∗xi 0→
lim 1= =2-15
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2-16 Henry’s Law
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ThThis equation implies that the fugacity of component i in a multi-
component mixture approaches the product of the mole fraction 
and standard state fugacity in very dilute solutions of 
component i. Using the definition of γi* it can be shown that:
where: Hij is called Henry’s Constant of component i in solvent j.
Therefore, the Henry’s constant is the standard state fugacity 
for a non-condensable component in a specific solvent. Usually 
the Henry’s constant is a rather strong function of temperature, 
but a weak function of the pressure and composition. The 
extension of Henry’s law into more concentrated solutions and 
at higher pressures is represented by the Kritchevsky-Ilinskaya 
equation:
where:  Pj
sat = Solvent saturation pressure at mixture temperature
Hij
sat = Henry’s law calculated at the saturation pressure of 
the solvent
Aij = Margules interaction parameter for molecular 
interactions between the solute and solvent
= Infinite dilution partial molar volume of solute i in 
solvent j
(2.40)
(2.41)
fi
ref fi
L
xi
---
xi 0→
lim Hij= =
Hijln Hij
Pj
Sat Aij
RT
------ xj
2 1–( )
Vi
∞ P Pj
sat–( )
RT
-------------------------------+ +ln=
Vi
∞
2-16
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Th2.6.1 Non-Condensable 
Components
Non-condensable components are treated using Henry’s 
constants as defined by Equation (2.40). The temperature 
dependency of the Henry’s law for a binary pair ij is represented 
by an Antoine-type of equation with four parameters per binary 
pair:
A mixing rule for the Henry’s constant of a non-condensable 
component in a mixture of condensable components must be 
defined. There are several alternatives, but the following 
formulation works reasonably well:
(2.42)
(2.43)
Hijln Aij
Bij
T------ Cij Tln DijT+ + +=
The Henry’s constant of 
component i in a multi-
component mixture is 
estimated neglecting the 
solvent-solvent 
interactions.
Hi mixture,ln
HijxjVc j,
2
3
--
ln
j 1 j i≠,=
nc
∑
xjVc j,
2
3
--
j 1 j i≠,=
nc
∑
----------------------------------------------=2-17
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2-18 Henry’s Law
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Th2.6.2 Estimation of Henry’s 
constants
A rigorous estimation of gas solubilities in condensable solvents 
depends on the existence of a rigorous theory of solutions, 
which currently does not exist. On the other hand, 
corresponding states and regular solution theory give us a 
correlative tool which allows us to estimate gas solubilities. The 
use of regular solution theory assumes that there is no volume 
change on mixing. Therefore consider a process in which the 
pure gas, i, is condensed to a liquid-like state, corresponding to 
the partial molar volume of the gas in the solvent. At this point, 
“liquid” gas is dissolved in the solvent (Prausnitz et al, 1986):
Since the gas dissolved in the liquid is in equilibrium with the 
gas in the gas phase:
and therefore:
Using regular solution theory to estimate the activity coefficient 
of the gas in the solvent:
(2.44)
(2.45)
(2.46)
(2.47)
(2.48)
(2.49)
Δg ΔgI ΔgII+=
ΔgI RT
fi
L pure,
fi
G
---------------ln=
ΔgII RT γixiln=
fi
G γixifi
L pure,=
Δg 0=
RT γiln νi
L δj δi–( )2φj
2=2-18
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Thand finally the expression for the Henry’s constant is:
Since regular solution theory assumes that the activity 
coefficient is proportional to the inverse of temperature, the 
term νi
L(δj - δi)φj
2 is temperature independent, and any 
convenient temperature (usually 25 oC) can be used for the 
calculation of νi
L, νj
L, δi, and δj. Note also that as a first 
approximation, φj is very close to 1, and Equation (2.50) 
simplifies to:
This is the equation used when estimating Henry’s constants. 
The Henry’s constants are calculated constants at 270.0, 300.0, 
330.0, 360.0, 390.0, 420.0, 450.0 K and fits the results using 
Equation (2.42), for each non-condensable/condensable pair 
present in the fluid package.   
2.7 Gibbs-Duhem 
Equation 
At constant temperature and pressure, the Gibbs-Duhem 
(2.50)
(2.51)
The interaction between two non-condensable components 
are not taken into account.
Hij
fi
G
xi
---- fi
L pure, νi
L δj δi–( )2φj
2
RT
----------------------------------exp= =
Hij
fi
G
xi
---- fi
L pure, νi
L δi δj–( )2
RT
----------------------------exp= =2-19
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2-20 Gibbs-Duhem Equation
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Thequation states that:
This equation applies to condensable and non-condensable 
components and only when integrating the Gibbs-Duhem 
equation should normalization conditions be considered. A more 
general form of the Gibbs-Duhem is also available, which is 
applicable to non-isothermal and non-isobaric cases. These 
forms are difficult to integrate, and do little to help in the 
definition of the standard state fugacity.
If the liquid composition of a binary mixture was varied from xi 
= 0 to   xi = 1 at constant temperature, the equilibrium pressure 
would change. Therefore, if the integrated form of Equation 
(2.52) is used to correlate isothermal activity coefficients, all of 
the activity coefficients will have to be corrected to some 
constant reference pressure. This is easily done if the 
dependency of fugacity on pressure is known:
Now if the fugacity equation is written using activity coefficients:
The definition of the standard state fugacity now comes directly 
(2.52)
(2.53)
(2.54)
xid γiln 0=
i 1=
nc
∑
γi
Pref
γi
P Vi
RT
------ Pd
P
Pref
∫
⎝ ⎠
⎜ ⎟
⎜ ⎟
⎛ ⎞
exp=
fi
L γi
Pxi fi
ref= or fi
L γi
Pref
xi fi
ref Vi
RT
------ Pd
Pref
P
∫
⎝ ⎠
⎜ ⎟
⎜ ⎟
⎛ ⎞
exp=2-20
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Thfrom the Gibbs-Duhem equation using the normalization 
condition for a condensable component; i.e., fi
ref is the fugacity 
of component i in the pure state at the mixture temperature and 
reference pressure preference. The standard state fugacity can 
be conveniently represented as a departure from the saturated 
conditions:
Combining Equations (2.54) and (2.55):
This equation is the basis for practically all low to moderate 
pressure engineering equilibrium calculations using activity 
coefficients. The exponential correction in Equations (2.54) 
and (2.55) is often called the Poynting correction, and takes 
into account the fact that the liquid is at a different pressure 
than the saturation pressure. The Poynting correction at low to 
moderate pressures is very close to unity.
2.7.1 Simplifications on Liquid 
Fugacity using Activity 
Coeff
There are many traditional simplifications involving Equation 
(2.56) which are currently used in engineering applications.
(2.55)
(2.56)
fi
ref Pi
vapφi
sat Vi
RT
------ Pd
Pi
vap
Pref
∫
⎝ ⎠
⎜ ⎟
⎜ ⎟
⎜ ⎟
⎛ ⎞
exp=
fi
L Pi
vapφi
sat Vi
RT
------
Vi
RT
------+ Pd
Pi
vap
Pref
∫exp=2-21
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2-22 Gibbs-Duhem Equation
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ThIdeal Gas
When ideal gas behaviour is assumed, this usually implies that 
the Poynting correction is dropped. Also, since the gas is ideal, 
φi
sat = 1:
Low Pressures & Conditions Away 
from the Critical Point
For conditions away from the critical point and at low to 
moderate pressures, the activity coefficients are virtually 
independent of pressure. For these conditions, it is common to 
set Pref = Pi
vap giving us the familiar equation:
It is common to assume that the partial molar volume is 
approximately the same as the molar volume of the pure liquid i 
at P and T, and equation simplifies even further:
Since fluids are usually incompressible at conditions removed 
from the critical point, Vi can be considered constant and the 
(2.57)
(2.58)
(2.59)
(2.60)
fi
L γixi Pi
vap=
fi
ref Pi
vap=
fi
L γixiPi
vapφi
sat Vi
RT
------⎝ ⎠
⎛ ⎞ Pd
Pi
vap
P
∫exp=
fi
L γixiPi
vapφi
sat Vi
RT
------⎝ ⎠
⎛ ⎞ Pd
Pi
vap
P
∫exp=2-22
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Thintegration of Equation (2.60) leads to:
(2.61)
(2.62)
fi
L γixiPi
vapφi
sat Vi P Pi
vap–( )
RT
------------------------------exp=
fi
ref Pi
vapφi
sat Vi P Pi
vap–( )
RT
------------------------------exp=2-23
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2-24 Association in Vapour Phase - Ideal Gas
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ThThis is the equation used when taking into account vapour 
phase non-ideality. Sometimes, Equation (2.60) is simplified 
even further, assuming that the Poynting correction is equal to 
1:
Equations (2.57), (2.60) and (2.61) form the basis used to 
name several of the activity coefficient based property 
packages.
2.8 Association in Vapour 
Phase - Ideal Gas
For some types of mixtures (especially carboxylic acids), there is 
a strong tendency for association in the vapour phase, where 
the associating component can dimerize, forming a reasonably 
stable “associated” component. Effectively, a simple chemical 
reaction in the vapour phase takes place, and even at modest 
pressures a strong deviation from the vapour phase behaviour 
predicted by the ideal gas law may be observed. This happens 
because an additional “component” is present in the mixture 
(Walas, 1985).
where: A is the associating component in the mixture (assumed 
binary for simplicity).
the equilibrium constant for the chemical reaction can be written 
(2.63)
(2.64)
(2.65)
fi
L γixiPi
vapφi
sat=
fi
ref Pi
vapφi
sat=
2A A2↔2-24
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Thas:
Assuming that the species in the vapour phase behave like ideal 
gases:
where: Pd is the dimer partial pressure
Pm is the monomer partial pressure
At equilibrium, the molar concentrations of monomer and dimer 
are:
where: e is the extent of dimerization
The expression for the dimerization extent in terms of the 
equilibrium constant can be written as follows:
Solving for e the following:
(2.66)
(2.67)
(2.68)
(2.69)
(2.70)
(2.71)
K
A2[ ]
A[ ]2
----------=
K
Pd[ ]
Pm[ ]2
--------------=
ym
2 2– e
2 e–
-----------=
yd
e
2 e–
-----------=
K
Pd
Pm
2
------
PA
vapyd
PA
vapym( )
2
------------------------ e 2 e–( )
2 2e–( )2PA
vap
--------------------------------- e 2 e–( )
4PA
vap 1 e–( )
2
---------------------------------= = = =
e 1
1 4KPA
vap+
---------------------------=2-25
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2-26 Association in Vapour Phase - Ideal Gas
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ThThe vapour pressure of the associating substance at a given 
temperature is the sum of the monomer and dimer partial 
pressures:
The hypothetical monomer vapour pressure P om can be solved 
for:
The partial pressure of the monomer can be written as a 
function of a hypothetical monomer vapour pressure and the 
activity coefficient of the associated substance in the liquid 
mixture:
Note that in the working equations the mole fraction of dimer is 
not included. The associating substance is used when calculating 
the number of moles in the vapour phase:
where:  wA = Weight of associating substance
 nm, nd = Number of moles of monomer and dimer
Mm = Molecular weight of monomer
Dividing by Mm:
(2.72)
(2.73)
(2.74)
(2.75)
(2.76)
PA
vap Pm° Pd+ Pm° K Pm°[ ]2+= =
Pm°
1 4KPA
vap+ 1–
2K
-----------------------------------------=
Pm γAxAPm°=
wA nmMm 2ndMm+=
nA nm 2nd+=2-26
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ThSince there are nt total number of moles in the vapour phase, 
the mass balance is expressed as:
where: the index 2 represents the non-associating component in the 
mixture. 
Since it is assumed that the components in the mixture behave 
like an ideal gas:
where:  PA is the total pressure using Equation (2.77).
Knowing that:
You have:
The usage of Equations (2.80) and (2.81) can be easily 
accomodated by defining a new standard state fugacity for 
systems with dimerization:
(2.77)
(2.78)
(2.79)
(2.80)
(2.81)
(2.82)
xm 2xd x2+ + 1=
PA Pm 2Pd P2+ +=
P Pm Pd P2+ +=
yA
Pm 2Pd+
Pm 2Pd P2+ +
-----------------------------------
Pm 2Pd+
P Pd+
----------------------= =
y2
P2
Pm 2Pd P2+ +
-----------------------------------
P2
P Pd+
---------------
γ2x2P2
vap
P Pd+
---------------------= = =
fdimerizing
L P
P Pd+
---------------⎝ ⎠
⎛ ⎞ Pm° 1 2KPm+( )=2-27
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2-28 Equilibrium Calculations
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ThSeveral property packages in DISTIL support ideal gas 
dimerization. The standard nomenclature is:
[Activity Coefficient Model] + [Dimer] = Property Package 
Name
For example, NRTL-Dimer is the property package which uses 
NRTL for the activity coefficient calculations and the carboxylic 
acid dimer assuming ideal gas phase behaviour. The following 
carboxylic acids are supported:
• Formic Acid
• Acetic Acid
• Acrylic Acid
• Propionic Acid
• Butyric Acid
• IsoButyric Acid
• Valeric Acid
• Hexanoic Acid
2.9 Equilibrium 
Calculations
When performing flash calculations, K-values are usually 
calculated. K-values are defined as follows:
where: yi is the composition of one phase (usually the vapour)
xi is the composition of another phase (usually the liquid)
(2.83)
(2.84)
fnon d– imerizing
L P
P Pd+
---------------⎝ ⎠
⎛ ⎞ Pvap
non dimerizing–=
Ki
yi
xi
---=2-28
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ThWhen using equations of state to represent the vapour and 
liquid behaviour, you have:
and therefore:
Activity coefficient based models can easily be expressed in this 
format:
and therefore:
where the standard state reference fugacity is calculated by 
Equations (2.58), (2.62) or (2.64) depending on the desired 
property package.
(2.85)
(2.86)
(2.87)
(2.88)
(2.89)
fi
V φi
VyiP=
fi
L φi
LxiP=
Ki
φi
L
φi
V
-----=
f L
i φL
i xiP γixi f ref
i= =
φi
L γi fi
ref
P
-----------=2-29
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2-30 Basic Models for VLE & LLE
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Th2.10 Basic Models for VLE 
& LLE
2.10.1 Symmetric Phase 
Representation
Symmetric phase representation is the use of only one 
thermodynamic model to represent the behaviour of the vapour 
and liquid phases. Examples are the Peng-Robinson and SRK 
models.
The advantages of symmetric phase representation are as 
follows:
• Consistent representation for both liquid and vapour 
phases.
• Other thermodynamic properties like enthalpies, 
entropies and densities can be readily obtained.
The disadvantages of symmetric phase representation are as 
follows:
• It is not always accurate enough to represent the 
behaviour of the liquid and vapour phase for polar 
components. Unless empirical modifications are made on 
the equations, the representation of the vapour 
pressures for polar components is not accurate.
• The simple composition dependence usually shown by 
standard cubic equations of state is inadequate to 
represent the phase behaviour of polar mixtures.
2.10.2 Asymmetric Phase 
Representation
Asymmetric phase representation is the use of one model to 
represent the behaviour of the vapour phase and a separate 
model to represent the behaviour of the liquid phase (such as 
Ideal Gas/UNIQUAC, or RK/Van Laar).2-30
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ThThe advantages of asymmetric phase representation are:
• The vapour pressure representation is limited only by the 
accuracy of the vapour pressure correlation.
• There are more adjustable parameters to represent the 
liquid mixture behaviour.
• There is the possibility of reasonable liquid-liquid 
representation.
The disadvantages of asymmetric phase representation are:
• The necessity of an arbitrary reference state.
• There are potential problems representing supercritical 
components.
• There are problems when approaching the mixture 
critical point.
• Enthalpies, entropies and densities must be computed 
using a separate model.
2.10.3 Interaction Parameters
The phase behaviour of mixtures is generally not well 
represented using only pure component properties. When 
working with either the symmetric or asymmetric approach, it 
will often be necessary to use some experimental data to "help" 
the semi-theoretical equations represent reality. If you are 
using an equation of state, this experimental parameter is 
usually called "kij", and is commonly used to correct the 
quadratic mixture term in cubic equations of state, roughly 
representing the energies of interaction between components 
present in the mixture. 
If you are using an activity model, the experimental parameters 
are usually called “aij” and “aji”. Several different approaches 
create different equations with different interpretations of what 
interaction parameters are. As a rough comparison, the 
Margules and Van Laar equations are polynomial expansions of 
the Gibbs free energy of mixture, and the Wilson, NRTL and 
UNIQUAC methods are statistical mechanics equations based on 
the Local Composition Concept.2-31
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2-32 Basic Models for VLE & LLE
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Th2.10.4 Selecting Property 
Methods
The various property packages available allow you to predict 
properties of mixtures ranging from well defined light 
hydrocarbon systems to highly non-ideal (non-electrolyte) 
chemical systems. Enhanced equations of state (PR and PRSV) 
are provided for rigorous treatment of hydrocarbon systems and 
activity coefficient models for chemical systems. All of these 
equations have their own inherent limitations and you are 
encouraged to become more familiar with the application of 
each equation. This section contains a description of each 
property package as well as listings of referenced literature.
For oil, gas and petrochemical applications, the Peng-Robinson 
EOS (PR) is generally the recommended property package. The 
enhancements to this equation of state enable it to be accurate 
for a variety of systems over a wide range of conditions. It 
rigorously solves any single, two-phase or three-phase system 
with a high degree of efficiency and reliability, and is applicable 
over a wide range of conditions, as shown in the following table.
The PR equation of state has been enhanced to yield accurate 
phase equilibrium calculations for systems ranging from low 
temperature cryogenic systems to high temperature, high 
pressure reservoir systems. The same equation of state 
satisfactorily predicts component distributions for heavy oil 
systems, aqueous glycol and methanol systems, and acid gas/
sour water systems.
The range of applicability in many cases is more indicative of 
the availability of good data rather than on the actual 
limitations of the Equation of State.
Method
Temperature
, F
Pressure, psia 
PR > -456 (-271 
C)
< 15,000 (100,000 
kPa)
SRK > -225 (-143 
C)
< 5,000 (35,000 
kPa)2-32
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ThAlthough the Soave-Redlich-Kwong (SRK) equation will also 
provide comparable results to the PR in many cases, it has been 
observed that its range of application is significantly more 
limited and this method is not as reliable for non-ideal systems. 
For example, it should not be used for systems with methanol or 
glycols.
As an alternative, the PRSV equation of state should be 
considered. It can handle the same systems as the PR equation 
with equivalent, or better accuracy, plus it is more suitable for 
handling non-ideal systems.
The advantage of the PRSV equation is that not only does it 
have the potential to more accurately predict the phase 
behaviour of hydrocarbon systems, particularly for systems 
composed of dissimilar components, but it can also be extended 
to handle non-ideal systems with accuracies that rival traditional 
activity coefficient models. The only compromise is increased 
computational time and an additional interaction parameter 
which is required for the equation.
The PR and PRSV equations of state can be used to perform 
rigorous three-phase flash calculations for aqueous systems 
containing water, methanol or glycols, as well as systems 
containing other hydrocarbons or non-hydrocarbons in the 
second liquid phase. The same is true for SRK, but only for 
aqueous systems.
The PR can also be used for crude systems, which have 
traditionally been modeled with dual model thermodynamic 
packages (an activity model representing the liquid phase 
behaviour, and an equation of state or the ideal gas law for the 
vapour phase properties). These earlier models become less 
accurate for systems with large amounts of light ends or when 
approaching critical regions. Also, the dual model system leads 
to internal inconsistencies. The proprietary enhancements to the 
PR and SRK methods allow these Equations of State to correctly 
represent vacuum conditions and heavy components (a problem 
with traditional EOS methods), and handle the light-end 
components and high-pressure systems.2-33
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2-34 Basic Models for VLE & LLE
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ThThe table below lists some typical systems and the 
recommended correlations. However, when in doubt of the 
accuracy or application of one of the property packages, call 
Technical Support. They will try to either provide you with 
additional validation material or give the best estimate of its 
accuracy.
The Property Package methods are divided into eight basic 
categories, as shown in the following table. Listed with each of 
the property methods are the available methods for VLE and 
Enthalpy/Entropy calculations.
Type of System
Recommended Property 
Method
TEG Dehydration PR
Cryogenic Gas Processing PR, PRSV
Air Separation PR, PRSV
Reservoir Systems PR, PR Options
Highly Polar and non-hydrocarbon 
systems
Activity Models, PRSV
Hydrocarbon systems where H2O 
solubility in HC is important
Kabadi Danner
Property Method VLE Calculation
Enthalpy/Entropy 
Calculation
Equations of State
PR PR PR
SRK SRK SRK
Equation of State Options
PRSV PRSV PRSV
Kabadi Danner Kabadi Danner SRK
RK-Zudekevitch-Joffee RK-Zudekevitch-Joffee RK-Zudekevitch-Joffee
Activity Models
Liquid
Margules Margules Cavett
Van Laar Van Laar Cavett
Wilson Wilson Cavett
NRTL NRTL Cavett
UNIQUAC UNIQUAC Cavett
Chien Null Chien Null Cavett
Vapour
Ideal Gas Ideal Gas Ideal Gas2-34
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Th2.10.5 Vapour Phase Options 
for Activity Models
There are several models available for calculating the vapour 
phase in conjunction with the selected activity model. The 
choice will depend on specific considerations of your system. 
However, in cases when you are operating at moderate 
pressures (less than 5 atm), choosing Ideal Gas should be 
satisfactory.
Ideal
The ideal gas law will be used to model the vapour phase. This 
model is appropriate for low pressures and for a vapour phase 
with little intermolecular interaction.
Peng Robinson and SRK
These two options have been provided to allow for better 
representation of unit operations (such as compressor loops).
Henry’s Law
For systems containing non-condensable components, you can 
supply Henry’s law information via the extended Henry’s law 
equations. 
Ideal Gas/Dimer Ideal Gas/Dimer Ideal Gas
RK RK RK
Peng Robinson Peng Robinson Peng Robinson
Virial Virial Virial
Property Method VLE Calculation
Enthalpy/Entropy 
Calculation2-35
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2-36 Basic Models for VLE & LLE
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ThThe program considers the following components as “non-
condensable”:
This information is used to model dilute solute/solvent 
interactions. Non-condensable components are defined as those 
components that have critical temperatures below the system 
temperature you are modeling. 
The equation has the following form:
where: i = Solute or non-condensable component
j = Solvent or condensable component
Hij = Henry’s constant between i and j in kPa, Temperature in 
degrees K
 A = A coefficient entered as aij in the parameter matrix 
B = B coefficient entered as aji in the parameter matrix 
C = C coefficient entered as bij in the parameter matrix 
D = D coefficient entered as bji in the parameter matrix 
T = temperature in degrees K
Component Simulation Name
C1 Methane
C2 Ethane
C2= Ethylene
C2# Acetylene
H2 Hydrogen
He Helium
Argon Argon
N2 Nitrogen
O2 Oxygen
NitricOxide Nitric Oxide
CO Carbon Monoxide
CO2 Carbon Dioxide
H2S Hydrogen Sulfide
(2.90)
Refer to Section 2.6.1 - 
Non-Condensable 
Components and Section 
2.6 - Henry’s Law for the 
use of Henry’s Law.
Hijln A B
T
--- C T( ) DT+ln+ +=2-36
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ThOnly components listed in the table will be treated as Henry’s 
Law components. If the program does not contain pre-fitted 
Henry’s coefficients, it will estimate the missing coefficients. To 
supply your own coefficients, you must enter them directly into 
the aij and bij matrices according to Equation (2.90).
No interaction between "non-condensable" component pairs is 
taken into account in the VLE calculations.
2.11 Phase Stability
So far, the equality of fugacities on the phases for each 
individual component has been used as the criteria for phase 
equilibria. Although the equality of fugacities is a necessary 
criteria, it is not sufficient to ensure that the system is at 
equilibrium. A necessary and sufficient criteria for 
thermodynamic equilibrium is that the fugacities of the 
individual components are the same and the Gibbs Free Energy 
of the system is at its minimum.
Mathematically:
and Gsystem = minimum.
The problem of phase stability is not a trivial one, since the 
number of phases that constitute a system is not known initially, 
and the creation (or deletion) of new phases during the search 
for the minimum is a blend of physics, empiricism and art.
(2.91)fi
I fi
II fi
III…= =2-37
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2-38 Phase Stability
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Th2.11.1 Gibbs Free Energy for 
Binary Systems
According to the definitions, the excess Gibbs energy is given 
by:
From the previous discussion on partial molar properties, 
; thus, if you find a condition such that:
is smaller than:
where: np = number of phases
(2.92)
(2.93)
(2.94)
GE G GID– RT xi γiln
i 1=
nc
∑ RT xi
fi
xi fi
ref
-------------ln∑= = =
GE xiGE
i∑=
GE xi
PGi
P E,
i
nc
∑
j 1=
np
∑=
GE xi
PGi
P E,
i
nc
∑
j 1=
np 1–
∑=2-38
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ThThe former condition is more stable than the latter one. If GE for 
two phases is smaller than GE for one phase, then a solution 
with two phases is more stable than the solution with one. This 
is represented graphically as shown in the following figures. 
  
 Figure 2.1
 Figure 2.2
xi0.5
1
G1
xi
0.50
dG1
dx2-39
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2-40 Phase Stability
ww
ThIf you have a binary mixture of bulk composition xi, the Gibbs 
Free Energy of the mixture will be G1 = Gixi + Gjxj. If you 
consider that two phases can exist, the mass and energy 
balance tells us that:
where: β is the phase fraction
Therefore, (G2, xi), (G
I, xi
I) and (GII, xi
II) are co-linear points 
and you can calculate G2 = βGI + (1-β)GII.
where:
Thus, the conditions for phase splitting can be mathematically 
expressed as requiring that the function G1 has a local 
maximum and is convex. This is conveniently expressed using 
derivatives:
If you use
(2.95)
(2.96)
(2.97)
(2.98)
β
xi xi
I–
xi
II xi
I–
----------------= and β G2 GI–
GII GI–
-------------------=
GI GI xi
I xj
I P T, , ,( )= GII GII xi
II xj
II P T, , ,( )=
xi∂
∂G1
⎝ ⎠
⎜ ⎟
⎛ ⎞
T P,
0= and
xi
2
2
∂
∂ G1
⎝ ⎠
⎜ ⎟
⎛ ⎞
T P,
0=
GE G GID– RT xi γiln
i 1=
nc
∑= =2-40
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Thermodynamic Principles 
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Thand you use the simple Margules one-parameter expression, 
you have:
 and
And you want to verify the condition:
The minimum of  is at xi = xj = 0.5 and is equal to 4RT. 
Thus, the minimum value of A for which phase splitting occurs is 
. A similar analysis can be performed for the other activity 
coefficient models for the binary case. The multi-component 
problem is more complex and useful discussions can be found in 
the book by 3Modell and Reid (1983) and in the works of 
4Michelsen (1982) and 5Seider (1979).
(2.99)
(2.100)
(2.101)
G GID GE+ GID Axixj+= =
GID xiGi∑ RTxi xi RTxj xjln+ln+=
G xiGi∑ RT xi xi xj xjln+ln( ) Axixj+ +=
xi∂
∂G
⎝ ⎠
⎛ ⎞
T P,
A 2Axi– RT
xi
xj
--- Gi Gj–+ln+=
xi
2
∂
∂ G
⎝ ⎠
⎜ ⎟
⎛ ⎞
T P,
2A– R T
xjxi
--------+=
xi
2
∂
∂ G
⎝ ⎠
⎜ ⎟
⎛ ⎞
T P,
2A– RT
xjxi
-------- 0<+=
RT
xjxi
--------
A
RT
------ 2>2-41
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2-42 Enthalpy/Cp Departure Functions
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Th2.12 Enthalpy/Cp 
Departure Functions
Let Prop be any thermodynamic property. If you define the 
difference of Prop-Propo to be the residual of that property (its 
value minus the value it would have at a reference state) and 
call this reference state the ideal gas at the system temperature 
and composition, you have:
where: P is an arbitrary pressure, usually 1 atm.
If you have an equation of state defined in terms of V and T 
(explicit in pressure), the Helmholtz free energy is the most 
convenient to work with (dA = -SdT -PdV).
(2.102)
 Figure 2.3
P°V° RT= or V° RT
P°
------=
Pr
e
ss
ur
e
Id
e
a
l
G
a
s
Enthalpy
A
B
C D
Isobar 1
Isobar 2
Isotherm 2
Isotherm 12-42
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Thermodynamic Principles 
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ThAt constant temperature you have dA = -PdV and if you 
integrate from the reference state, you have:
You can divide the integral into two parts:
The second integral refers to the ideal gas, and can be 
immediately evaluated:
It is interesting to note that A-Ao for an ideal gas is not zero. The 
A-Ao
(2.103)
(2.104)
(2.105)
A A°– P Vd
V°
V
∫–=
A A°– P Vd
∞
V
∫– P Vd
V°
∞
∫–=
P RT
V
------= and P Vd
V°
∞
∫
RT
V
------ Vd
V°
∞
∫=2-43
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2-44 Enthalpy/Cp Departure Functions
ww
Thterm can be rearranged by adding and subtracting and the 
final result is:
(Notice that (P-RT/V) goes to zero when the limit V  is 
approached).
(2.106)
RT
V
------ Vd
∞
V
∫
A A°– P RT
V
------–⎝ ⎠
⎛ ⎞ Vd
∞
V
∫– RT V
V°
-----ln–=
∞→2-44
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Thermodynamic Principles 
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ThThe other energy-related thermodynamic functions are 
immediately derived from the Helmholtz energy:
By the definition of Cp, you have:
and integrating at constant temperature you have:
A more complete table of thermodynamic relations and a very 
convenient derivation for cubic equations of state is given by 
6Reid, Prausnitz and Poling (1987). The only missing derivations 
are the ideal gas properties. Recalling the previous section, if 
(2.107)
(2.108)
(2.109)
S S°– T∂
∂ A A°–( )V– T∂
∂P
⎝ ⎠
⎛ ⎞
V
R
V
---– V R V
V°
-----ln+d
∞
V
∫= =
H H°– A A°–( ) T S S°–( ) RT Z 1–( )+ +=
Cp T∂
∂H
⎝ ⎠
⎛ ⎞
P
= and P∂
∂Cp
⎝ ⎠
⎛ ⎞
T
T
T2
2
∂
∂ V
⎝ ⎠
⎜ ⎟
⎛ ⎞
P
–=
dCp T
T2
2
∂
∂ V
⎝ ⎠
⎜ ⎟
⎛ ⎞
P
dP–=
Cp Cp°– T
T2
2
∂
∂ V
⎝ ⎠
⎜ ⎟
⎛ ⎞
P
Pd
P°
P
∫–=
or
Cp Cp°– T
T2
2
∂
∂ P
⎝ ⎠
⎜ ⎟
⎛ ⎞
V
Vd
∞
V
∫
T P∂
T∂
-----⎝ ⎠
⎛ ⎞
V
2
P∂
T∂
-----⎝ ⎠
⎛ ⎞
T
------------------ R––=2-45
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2-46 Enthalpy/Cp Departure Functions
ww
Thyou were to call I an ideal gas property:
(2.110)I mix xiIi
i 1=
nc
∑=2-46
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Thermodynamic Principles 
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Th2.12.1 Alternative Formulation 
for Low Pressure Systems
For chemical systems, where the non-idealities in the liquid 
phase may be severe even at relatively low pressures, alternate 
formulations for the thermal properties are as follows:
The vapour properties can be calculated as:
where: ΔHV is the enthalpy of vapourization of the mixture at the 
system pressure
Usually the  term is ignored (although it can be computed 
in a fairly straight forward way for systems where association in 
the vapour phase is important (2Prausnitz et al., (1980)).
The term  is the contribution to the enthalpy due to 
compression or expansion, and is zero for an ideal gas. The 
calculation of this term depends on what model was selected for 
the vapour phase—Ideal Gas, Redlich Kwong or Virial.
(2.111)
(2.112)
Hi
L Cpi Td
T ref,
T
∫= and HL xiHi
L ΔHmix
L+
i 1=
nc
∑=
Hmix
V Hmix
L ΔHV ΔHP
V ΔHmix
V+ + +=
It is assumed that Hi
L at 
the reference temperature 
is zero.
ΔHmix
V
ΔHP
V
2-47
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2-48 Enthalpy/Cp Departure Functions
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ThAll contribution to the enthalpy at constant temperature can be 
summarized as follows (7Henley and Seader, 1981):
 Figure 2.4
A
B
C
D
T Tc
Critical Temperature
P = 0 (Ideal Gas)
Vapour at Zero Pressure
P = System P
M
o
la
r
En
th
a
lp
y
H
Absolute Temperature T
{Heat of
Vapourization
pressure correction to bring
the vapour to saturation
pressure to
compress the
liquid2-48
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Thermodynamic Calculation Models 3-1
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Th3  Thermodynamic 
Calculation Models3-1
3.1  Equations of State.......................................................................... 2
3.1.1  Ideal Gas Equation of State ....................................................... 3
3.1.2  Peng-Robinson Equation of State................................................ 7
3.1.3  HysysPR Equation of State....................................................... 17
3.1.4  Peng-Robinson Stryjek-Vera..................................................... 25
3.1.5  Soave-Redlich-Kwong Equation of State .................................... 36
3.1.6  Redlich-Kwong Equation of State .............................................. 46
3.1.7  Zudkevitch-Joffee Equation of State .......................................... 56
3.1.8  Kabadi-Danner Equation of State.............................................. 65
3.1.9  The Virial Equation of State ..................................................... 77
3.1.10  Lee-Kesler Equation of State .................................................. 92
3.1.11  Lee-Kesler-Plöcker ................................................................ 96
3.2  Activity Models............................................................................. 98
3.2.1  Ideal Solution Model ..............................................................101
3.2.2  Regular Solution Model ..........................................................106
3.2.3  van Laar Model .....................................................................111
3.2.4  Margules Model.....................................................................123
3.2.5  Wilson Model ........................................................................130
3.2.6  NRTL Model ..........................................................................141
3.2.7  HypNRTL Model.....................................................................154
3.2.8  The General NRTL Model ........................................................155
3.2.9  HYSYS - General NRTL ...........................................................157
3.2.10  UNIQUAC Model ..................................................................158
3.2.11  UNIFAC Model .....................................................................170
3.2.12  Chien-Null Model .................................................................182
3.3  Chao-Seader Model .................................................................... 191
3.4  Grayson-Streed Model................................................................ 192
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3-2 Equations of State
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Th3.1 Equations of State
The program currently offers the enhanced Peng-Robinson (PR), 
and Soave-Redlich-Kwong (SRK) equations of state. In addition, 
several methods are offered which are modifications of these 
property packages, including PRSV, Zudkevitch Joffee and 
Kabadi Danner. Of these, the Peng-Robinson equation of state 
supports the widest range of operating conditions and the 
greatest variety of systems. The Peng-Robinson and Soave-
Redlich-Kwong equations of state (EOS) generate all required 
equilibrium and thermodynamic properties directly. Although the 
forms of these EOS methods are common with other commercial 
simulators, they have been significantly enhanced to extend 
their range of applicability.
The PR and SRK packages contain enhanced binary interaction 
parameters for all library hydrocarbon-hydrocarbon pairs (a 
combination of fitted and generated interaction parameters), as 
well as for most hydrocarbon-non-hydrocarbon binaries.   
For non-library or hydrocarbon hypocomponents, HC-HC 
interaction parameters can be generated automatically for 
improved VLE property predictions.
The PR equation of state applies a functionality to some specific 
component-component interaction parameters. Key components 
receiving special treatment include He, H2, N2, CO2, H2S, H2O, 
CH3OH, EG and TEG.
The PR or SRK EOS should not be used for non-ideal 
chemicals such as alcohols, acids or other components. 
These systems are more accurately handled by the Activity 
Models or the PRSV EOS.3-2
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Thermodynamic Calculation Models 
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Th3.1.1 Ideal Gas Equation of 
State
To use the fugacity coefficient approach, a functional form 
relating P, V, and T is required. These functional relationships 
are called equations of state, and their development dates from 
the 17th century when Boyle first discovered the functionality 
between pressure and volume. The experimental results 
obtained from Boyle, Charles, Gay-Lussac, Dalton and Avogadro 
can be summarized in the Ideal Gas law:
The Ideal Gas equation, while very useful in some applications 
and as a limiting case, is restricted from the practical point of 
view. The primary drawbacks of the ideal gas equation stem 
from the fact that in its derivation two major simplifications are 
assumed:
1. The molecules do not have a physical dimension; they are 
points in a geometrical sense. 
2. There are no electrostatic interactions between molecules.
                                 PV = RT (3.1)
 Figure 3.1
V
P
3-3
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3-4 Equations of State
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ThFor further information on the derivation of the Ideal Gas law 
from first principles, see 8Feynman (1966).
Property Methods
A quick reference of calculation methods is shown in the table 
below for Ideal Gas.
The calculation methods from the table are described in the 
following sections.
IG Molar Volume
The following relation calculates the Molar Volume for a specific 
phase.
Property Class Name and Applicable Phases
Calculation Method
Applicable 
Phase
Property Class Name
Molar Volume Vapour COTHIGVolume Class
Enthalpy Vapour COTHIGEnthalpy Class
Entropy Vapour COTHIGEntropy Class
Isobaric heat capacity Vapour COTHIGCp Class
Fugacity coefficient 
calculation 
Vapour COTHIGLnFugacityCoeff 
Class
Fugacity calculation Vapour COTHIGLnFugacity Class
(3.2)
Property Class Name Applicable Phase
COTHIGVolume Class Vapour
Usually the Ideal Gas 
equation is adequate when 
working with distillation 
systems without 
association at low 
V RT
P
------=3-4
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ThIG Enthalpy
The following relation calculates enthalpy.
where: Hi
IG is the pure compound ideal gas enthalpy
Property Class Name and Applicable Phases
IG Entropy
The following relation calculates entropy.
where: Si
IG is the pure compound ideal gas entropy
Property Class Name and Applicable Phases
(3.3)
Property Class Name Applicable Phase
COTHIGEnthalpy Class Vapour
(3.4)
Property Class Name Applicable Phase
COTHIGEntropy Class Vapour
H xiHi
IG
∑=
S xiSi
IG R xi xiln∑–∑=3-5
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ThIG Cp (Heat Capacity)
The following relation calculates the isobaric heat capacity.
where: Cpi
IG is the pure compound ideal gas Cp
Property Class Name and Applicable Phases
IG Fugacity Coefficient
The following relation calculates the fugacity coefficient.
Property Class Name and Applicable Phases
(3.5)
Property Class Name Applicable Phase
COTHIGCp Class Vapour
(3.6)
Property Class Name Applicable Phase
COTHIGLnFugacityCoeff 
Class
Vapour
Cp xiCpi
IG
∑=
φiln 0=3-6
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ThIG Fugacity
The following relation calculates the fugacity for a specific 
phase.
Property Class Name and Applicable Phases
3.1.2 Peng-Robinson Equation 
of State
The 9Peng Robinson (1976) equation of state (EOS) is a 
modification of the RK equation to better represent VLE 
calculations. The densities for the liquid phase in the SRK did 
not accurately represent the experimental values due to a high 
universal critical compressibility factor of 0.3333. The PR is a 
modification of the RK equation of state which corresponds to a 
lower critical compressibility of about 0.307 thus representing 
the VLE of natural gas systems accurately. The PR equation is 
represented by:
(3.7)
Property Class Name Applicable Phase
COTHIGLnFugacity Class Vapour
(3.8)
fi yiP=
P RT
V b–
------------ a
V V b+( ) b V b–( )+
------------------------------------------------–=3-7
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3-8 Equations of State
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Thwhere:
The functional dependency of the “a” term is shown in the 
following relation.
The accuracy of the PR and SRK equations of state are 
approximately the same. However, the PR EOS represents the 
density of the liquid phase more accurately due to the lower 
critical compressibility factor.
These equations were originally developed for pure components. 
To apply the PR EOS to mixtures, mixing rules are required for 
the “a” and “b” terms in Equation (3.2). Refer to the Mixing 
Rules section on the mixing rules available.
Property Methods
A quick reference of calculation methods is shown in the table 
below for the PR EOS.
(3.9)
(3.10)
Calculation Method
Applicable 
Phase
Property Class Name
Z Factor Vapour and 
Liquid
COTHPRZFactor Class
Molar Volume Vapour and 
Liquid
COTHPRVolume Class
Enthalpy Vapour and 
Liquid
COTHPREnthalpy Class
Entropy Vapour and 
Liquid
COTHPREntropy Class
a acα=
ac 0.45724
R2Tc
2
Pc
-----------=
b 0.07780
RTc
Pc
--------=
α 1 κ 1 Tr
0.5–( )+=
κ 0.37464 1.5422ω 0.26992ω2–+=
Equations of state in 
general - attractive and 
repulsion parts
Simplest cubic EOS - van 
der Waals
Principle of corresponding 
states
First successful 
modification for 
engineering - RK
The property that is usually 
required for engineering 
calculations is vapour 
pressure.
The SRK and RK EOS 
propose modifications 
which improve the vapour 
pressure calculations for 
relatively simple gases and 
hydrocarbons.3-8
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ThThe calculation methods from the table are described in the 
following sections.
PR Z Factor
The compressibility factor, Z, is calculated as the root for the 
following equation:
There are three roots for the above equation. It is considered 
that the smallest root is for the liquid phase and the largest root 
is for the vapour phase. The third root has no physical meaning.
Isobaric heat capacity Vapour and 
Liquid
COTHPRCp Class
Fugacity coefficient 
calculation 
Vapour and 
Liquid
COTHPRLnFugacityCoeff 
Class
Fugacity calculation Vapour and 
Liquid
COTHPRLnFugacity Class
Isochoric heat capacity Vapour and 
Liquid
COTHPRCv Class
Mixing Rule 1 Vapour and 
Liquid
COTHPRab_1 Class
Mixing Rule 2 Vapour and 
Liquid
COTHPRab_2 Class
Mixing Rule 3 Vapour and 
Liquid
COTHPRab_3 Class
Mixing Rule 4 Vapour and 
Liquid
COTHPRab_4 Class
Mixing Rule 5 Vapour and 
Liquid
COTHPRab_5 Class
Mixing Rule 6 Vapour and 
Liquid
COTHPRab_6 Class
(3.11)
(3.12)
(3.13)
Calculation Method
Applicable 
Phase
Property Class Name
Z3 1 B–( )Z2– Z A 3B2– 2B–( ) AB B2– B3–( )–+ 0=
A aP
R2T 2
-----------=
B bP
RT
------=3-9
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ThPR Molar Volume
The following relation calculates the molar volume for a specific 
phase.
Property Class Name and Applicable Phases
PR Enthalpy
The following relation calculates the enthalpy.
(3.14)
Property Class Name Applicable Phase
COTHPRVolume Class Vapour and Liquid
The compressibility factor, Z, is calculated using PR Z Factor. 
For consistency, the PR molar volume always calls the PR Z 
Factor for the calculation of Z.
(3.15)
V ZRT
P
----------=
H HIG PV RT a da
dT
------⎝ ⎠
⎛ ⎞ T–⎝ ⎠
⎛ ⎞– 1
2 2b
------------- V b 1 2+( )+
V b 1 2–( )+
----------------------------------ln–=–3-10
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Thwhere: HIG is the ideal gas enthalpy calculated at temperature, T
Property Class Name and Applicable Phases
PR Entropy
The following relation calculates the entropy.
where: SIG is the ideal gas entropy calculated at temperature, T
Property Class Name Applicable Phase
COTHPREnthalpy Class Vapour and Liquid
The volume, V, is calculated using PR Molar Volume. For 
consistency, the PR Enthalpy always calls the PR Volume for 
the calculation of V.
(3.16)S SIG R V b–
RT
------------⎝ ⎠
⎛ ⎞ 1
2b 2
------------- V b 1 2+( )+
V b 1 2–( )+
----------------------------------⎝ ⎠
⎛ ⎞ da
dT
------ln–ln=–3-11
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3-12 Equations of State
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ThProperty Class Name and Applicable Phases 
   
 
PR Cp (Heat Capacity)
The following relation calculates the isobaric heat capacity.
where: CpIG is the ideal gas heat capacity calculated at temperature, 
T
Property Class Name and Applicable Phases
Property Class Name Applicable Phase
COTHPREntropy Class Vapour and Liquid
The volume, V, is calculated using PR Molar Volume. For 
consistency, the PR Entropy always calls the PR Volume for 
the calculation of V.
(3.17)
Property Class Name Applicable Phase
COTHPRCp Class Vapour and Liquid
The volume, V, is calculated using PR Molar Volume. For 
consistency, the PR Entropy always calls the PR Volume for 
the calculation of V.
Cp Cp
IG T ∂2P
∂T2
--------
⎝ ⎠
⎜ ⎟
⎛ ⎞
V
V R
T ∂V
∂T
------⎝ ⎠
⎛ ⎞
P
2
∂V
∂P
------⎝ ⎠
⎛ ⎞
T
------------------+ +d
∞
V
∫–=–3-12
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ThPR Fugacity Coefficient
The following relation calculates the fugacity coefficient.
Property Class Name and Applicable Phases
PR Fugacity
The following relation calculates the fugacity for a specific 
phase.
(3.18)
(3.19)
(3.20)
Property Class Name Applicable Phase
COTHPRLnFugacityCoeff 
Class
Vapour and Liquid
The volume, V, is calculated using PR Molar Volume. For 
consistency, the PR Fugacity Coefficient always calls the PR 
Volume for the calculation of V. The parameters a and b are 
calculated from the Mixing Rules.
(3.21)
φiln V b–( ) b
V b–
------------ a
2 2b
------------- V b 1 2+( )+
V b 1 2–( )+
----------------------------------⎝ ⎠
⎛ ⎞ 1– a
a
-- b
b
--++⎝ ⎠
⎛ ⎞ln+ +ln–=
a ∂n2a
∂n
-----------=
b ∂nb
∂n
---------=
fi φiyiP=3-13
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ThProperty Class Name and Applicable Phase
PR Cv (isochoric)
The following relation calculates the isochoric heat capacity.
Property Class Name and Applicable Phases
Mixing Rules
The mixing rules available for the PR EOS state are shown 
below.
Property Class Name Applicable Phase
COTHPRLnFugacity Class Vapour and Liquid
(3.22)
Property Class Name Applicable Phase
COTHPRCv Class Vapour and Liquid
(3.23)
(3.24)
(3.25)
(3.26)
Cv Cp
T ∂P
∂T
------⎝ ⎠
⎛ ⎞ 2
V
∂P
∂V
------⎝ ⎠
⎛ ⎞
T
---------------------+=
a xixjaij( )
j 1=
nc
∑
i 1=
nc
∑=
b bixi
i 1=
nc
∑=
aij ξi j aciacjαiαj=
αi 1 κi–( ) 1 Tri
0.5–( )=3-14
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ThMixing Rule 1
The definition of terms a and b are the same for all Mixing 
Rules. The only difference between the mixing rules is the 
temperature dependent binary interaction parameter, ξij, which is 
defined as:
where: Aij, Bij, and Cij are asymmetric binary interaction parameters
Mixing Rule 2
The definition of terms a and b are the same for all Mixing 
Rules. The only difference between the mixing rules is the 
temperature dependent binary interaction parameter, ξij, which is 
defined as:
where: Aij, Bij, and Cij are asymmetric binary interaction parameters
(3.27)
(3.28)
(3.29)
(3.30)
(3.31)
aci
0.45724R2Tci
2
Pci
---------------------------------=
bi
0.07780RTci
Pci
------------------------------=
κi 0.37464 1.54226ωi 0.26992ωi
2–+= ωi 0.49<
ξij 1 Aij– BijT CijT
2+ +=
ξij 1 Aij– BijT
Cij
T
------+ +=3-15
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ThMixing Rule 3
The definition of terms a and b are the same for all Mixing 
Rules. The only difference between the mixing rules is the 
temperature dependent binary interaction parameter, ξij, which is 
defined as
Mixing Rule 4
The definition of terms a and b are the same for all Mixing 
Rules. The only difference between the mixing rules is the 
temperature dependent binary interaction parameter, ξij, which is 
defined as:
where: Aij, Bij, and Cij are asymmetric binary interaction parameters
Mixing Rule 5
The definition of terms a and b are the same for all Mixing 
Rules. The only difference between mixing rules is the 
temperature dependent binary interaction parameter, ξij, which is 
defined as:
where: Aij, Bij, and Cij are asymmetric binary interaction parameters
(3.32)
(3.33)
(3.34)
ξij 1 xi Aij Bij CijT
2+ +( )– xj Aji BjiT CjiT
2+ +( )–=
ξij 1 xi Aij BijT
Cij
T
------+ +⎝ ⎠
⎛ ⎞– xj Aji Bji
Cji
T
------+ +⎝ ⎠
⎛ ⎞–=
ξi j 1
Aij BijT CijT
2+ +( ) Aji BjiT CijT
2+ +( )
xi Aij BijT CijT
2+ +( ) xj Aji BjiT CjiT
2+ +( )+
---------------------------------------------------------------------------------------------------------------–=3-16
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ThMixing Rule 6
The definition of terms a and b are the same for all Mixing 
Rules. The only difference between mixing rules is the 
temperature dependent binary interaction parameter, ξij, which is 
defined as:
where: Aij, Bij, and Cij are asymmetric binary interaction parameters
3.1.3 HysysPR Equation of 
State
The HysysPR EOS is similar to the PR EOS with several 
enhancements to the original PR equation. It extends its range 
of applicability and better represents the VLE of complex 
systems. The HysysPR equation is represented by:
where:
(3.35)
(3.36)
(3.37)
ξij 1
Aij BijT
Cij
T
------+ +⎝ ⎠
⎛ ⎞ Aji BjiT
Cij
T
------+ +⎝ ⎠
⎛ ⎞
xi Aij BijT
Cij
T
------+ +⎝ ⎠
⎛ ⎞ xj Aji BjiT
Cji
T
------+ +⎝ ⎠
⎛ ⎞+
----------------------------------------------------------------------------------------------------–=
P RT
V b–
------------ a
V V b+( ) b V b–( )+
------------------------------------------------–=
a acα=
ac 0.45724
R2Tc
2
Pc
-----------=
b 0.077480
RTc
Pc
---------=3-17
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ThThe functional dependency of the “a” term is shown in the 
following relation as Soave:
Property Methods
A quick reference of calculation methods is shown in the table 
below for the HysysPR EOS.
The calculation methods from the table are described in the 
following sections.
(3.38)
Calculation 
Method
Applicable 
Phase
Property Class Name
Z Factor Vapour and 
Liquid
COTH_HYSYS_ZFactor Class
Molar Volume Vapour and 
Liquid
COTH_HYSYS_Volume Class
Enthalpy Vapour and 
Liquid
COTH_HYSYS_PREnthalpy Class
Entropy Vapour and 
Liquid
COTH_HYSYS_Entropy Class
Isobaric heat 
capacity
Vapour and 
Liquid
COTH_HYSYS_Cp Class
Fugacity coefficient 
calculation 
Vapour and 
Liquid
COTH_HYSYS_LnFugacityCoeff 
Class
Fugacity calculation Vapour and 
Liquid
COTH_HYSYS_LnFugacity Class
Isochoric heat 
capacity
Vapour and 
Liquid
COTH_HYSYS_Cv Class
α 1 S 1 Tr
0.5–( )+=
S 0.37464 1.5422ω 0.26992ω2–+=3-18
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ThHysysPR Z Factor
The compressibility factor, Z, is calculated as the root for the 
following equation:
There are three roots for the above equation. It is considered 
that the smallest root is for the liquid phase and the largest root 
is for the vapour phase. The third root has no physical meaning.
HysysPR Molar Volume
The following relation calculates the molar volume for a specific 
phase.
Property Class Name and Applicable Phases
(3.39)
(3.40)
(3.41)
(3.42)
Property Class Name Applicable Phase
COTH_HYSYS_Volume Class Vapour and Liquid
The compressibility factor, Z, is calculated using HysysPR Z 
Factor. For consistency, the HysysPR molar volume always 
calls the HysysPR Z Factor for the calculation of Z.
Z3 1 B–( )Z2– Z A 3B2– 2B–( ) AB B2– B3–( )–+ 0=
A aP
R2T 2
-----------=
B bP
RT
------=
V ZRT
P
----------=3-19
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ThHysysPR Enthalpy
The following relation calculates the enthalpy.
where: HIG is the ideal gas enthalpy calculated at temperature, T
Property Class Name and Applicable Phases
(3.43)
Property Class Name Applicable Phase
COTH_HYSYS_Enthalpy 
Class
Vapour and Liquid
The volume, V, is calculated using HysysPR Molar Volume. 
For consistency, the PR Enthalpy always calls the PR Volume 
for the calculation of V.
H HIG PV RT a da
dT
------⎝ ⎠
⎛ ⎞ T–⎝ ⎠
⎛ ⎞– 1
2 2b
------------- V b 1 2+( )+
V b 1 2–( )+
----------------------------------ln–=–3-20
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ThHysysPR Entropy
The following relation calculates the entropy.
where: SIG is the ideal gas entropy calculated at temperature, T
Property Class Name and Applicable Phases
(3.44)
Property Class Name Applicable Phase
COTH_HYSYS_Entropy Class Vapour and Liquid
The volume, V, is calculated using HysysPR Molar Volume. 
For consistency, the HysysPR Entropy always calls the 
HysysPR Volume for the calculation of V.
S SIG R V b–
RT
------------⎝ ⎠
⎛ ⎞ 1
2b 2
------------- V b 1 2+( )+
V b 1 2–( )+
----------------------------------⎝ ⎠
⎛ ⎞ da
dT
------ln–ln=–3-21
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ThHysysPR Cp (Heat Capacity)
The following relation calculates the isobaric heat capacity.
where: CpIG is the ideal gas heat capacity calculated at temperature, 
T
Property Class Name and Applicable Phases
HysysPR Fugacity Coefficient
The following relation calculates the fugacity coefficient.
(3.45)
Property Class Name Applicable Phase
COTH_HYSYS_Cp Class Vapour and Liquid
(3.46)
(3.47)
(3.48)
Cp Cp
IG T ∂2P
∂T2
--------
⎝ ⎠
⎜ ⎟
⎛ ⎞
V
V R
T ∂V
∂T
------⎝ ⎠
⎛ ⎞
P
2
∂V
∂P
------⎝ ⎠
⎛ ⎞
T
------------------+ +d
∞
V
∫–=–
φiln V b–( ) b
V b–
------------ a
2 2b
------------- V b 1 2+( )+
V b 1 2–( )+
----------------------------------⎝ ⎠
⎛ ⎞ 1– a
a
-- b
b
--++⎝ ⎠
⎛ ⎞ln+ +ln–=
a ∂n2a
∂n
-----------=
b ∂nb
∂n
---------=3-22
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ThProperty Class Name and Applicable Phases
HysysPR Fugacity
The following relation calculates the fugacity for a specific 
phase.
Property Class Name and Applicable Phases
HysysPR Cv (isochoric)
The following relation calculates the isochoric heat capacity.
Property Class Name Applicable Phase
COTH_HYSYS_LnFugacityCoeff 
Class
Vapour and Liquid
The volume, V, is calculated using HysysPR Molar Volume. 
For consistency, the HysysPR Fugacity Coefficient always 
calls the HysysPR Volume for the calculation of V. The 
parameters a and b are calculated from the Mixing Rules.
(3.49)
Property Class Name Applicable Phase
COTH_HYSYS_LnFugacity 
Class
Vapour and Liquid
(3.50)
fi φiyiP=
Cv Cp
T ∂P
∂T
------⎝ ⎠
⎛ ⎞ 2
V
∂P
∂V
------⎝ ⎠
⎛ ⎞
T
---------------------+=3-23
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ThProperty Class Name and Applicable Phases
Mixing Rules
The mixing rules available for the HysysPR EOS state are shown 
below.
where: κij = asymmetric binary interaction parameter
Property Class Name Applicable Phase
COTH_HYSYS_Cv Class Vapour and Liquid
(3.51)
(3.52)
(3.53)
(3.54)
(3.55)
(3.56)
(3.57)
a xixjaij( )
j 1=
nc
∑
i 1=
nc
∑=
b bixi
i 1=
nc
∑=
aij 1 kij–( ) aciacjαiαj=
αi 1 κi–( ) 1 Tri
0.5–( )=
aci
0.45724R2Tci
2
Pci
---------------------------------=
bi
0.07780RTci
Pci
------------------------------=
κi
0.37464 1.54226ωi 0.26992ωi
2–+
0.37964 1.48503ωi 0.16442ωi
2– 0.016666ωi
3+ +
⎩
⎪
⎨
⎪
⎧
=
ωi 0.49<
ωi 0.49≥3-24
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Th3.1.4 Peng-Robinson Stryjek-
Vera
The Peng-Robinson 10Stryjek-Vera PRSV, 1986) equation of state 
is a two-fold modification of the PR equation of state that 
extends the application of the original PR method for highly non-
ideal systems. It has been shown to match vapour pressures 
curves of pure components and mixtures more accurately, 
especially at low vapour pressures.
It has been extended to handle non-ideal systems providing 
results similar to those obtained using excess Gibbs energy 
functions like the Wilson, NRTL or UNIQUAC equations.
The PRSV equation of state is defined as:
where:
(3.58)
(3.59)
P RT
V b–
------------ a
V V b+( ) b V b–( )+
------------------------------------------------–=
a acα=
ac 0.45724
R2Tc
2
Pc
-----------=
b 0.077480
RTc
Pc
---------=3-25
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ThOne of the proposed modifications to the PR equation of state by 
Stryjek and Vera was an expanded alpha, "α", term that became 
a function of acentricity and an empirical parameter, κi, used for 
fitting pure component vapour pressures.
where:  κ1 = Characteristic pure component parameter
 ωi = Acentric factor
The adjustable κ1 parameter allows for a much better fit of the 
pure component vapour pressure curves. This parameter has 
been regressed against the pure component vapour pressure for 
all library components.
For hypocomponents that have been generated to represent oil 
fractions, the κ1 term for each hypocomponent will be 
automatically regressed against the Lee-Kesler vapour pressure 
curves. For individual user-added hypothetical components, κ1 
terms can either be entered or they will automatically be 
regressed against the Lee-Kesler, Gomez-Thodos or Reidel 
correlations.
The second modification consists of a new set of mixing rules for 
mixtures. To apply the PRSV EOS to mixtures, mixing rules are 
required for the “a” and “b” terms in Equation (3.46). Refer to 
the Mixing Rules section for the set of mixing rules applicable.
(3.60)
αi 1 κi 1 Tr
0.5–( )+[ ]
2
=
κi κ0i κ1 1 Tri
0.5+( ) 0.7 Tri–( )+=
κ0i 0.378893 1.4897153ωi 0.17131848ωi
2– 0.0196554ωi
3+ +=3-26
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ThProperty Methods
A quick reference of calculation methods is shown in the table 
below for the PRSV EOS.
The calculation methods from the table are described in the 
following sections. 
Calculation Method
Applicable 
Phase
Property Class Name
Z Factor Vapour and 
Liquid
COTHPRSVZFactor Class
Molar Volume Vapour and 
Liquid
COTHPRSVVolume Class
Enthalpy Vapour and 
Liquid
COTHPRSVEnthalpy Class
Entropy Vapour and 
Liquid
COTHPRSVEntropy Class
Isobaric heat capacity Vapour and 
Liquid
COTHPRSVCp Class
Fugacity coefficient 
calculation 
Vapour and 
Liquid
COTHPRSVLnFugacityCoeff 
Class
Fugacity calculation Vapour and 
Liquid
COTHPRSVLnFugacity Class
Isochoric heat capacity Vapour and 
Liquid
COTHPRSVCv Class
Mixing Rule 1 Vapour and 
Liquid
COTHPRSVab_1 Class
Mixing Rule 2 Vapour and 
Liquid
COTHPRSVab_2 Class
Mixing Rule 3 Vapour and 
Liquid
COTHPRSVab_3 Class
Mixing Rule 4 Vapour and 
Liquid
COTHPRSVab_4 Class
Mixing Rule 5 Vapour and 
Liquid
COTHPRSVab_5 Class
Mixing Rule 6 Vapour and 
Liquid
COTHPRSVab_6 Class3-27
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ThPRSV Z Factor
The compressibility factor, Z, is calculated as the root for the 
following equation:
There are three roots for the above equation. It is considered 
that the smallest root is for the liquid phase and the largest root 
is for the vapour phase. The third root has no physical meaning.
PRSV Molar Volume
The following relation calculates the molar volume for a specific 
phase.
Property Class Name and Applicable Phases
(3.61)
(3.62)
(3.63)
(3.64)
Property Class Name Applicable Phase
COTHPRSVVolume Class Vapour and Liquid
The compressibility factor, Z, is calculated using PRSV Z 
Factor. For consistency, the PRSV molar volume always calls 
the PRSV Z factor for the calculation of Z.
Z3 1 B–( )Z2– Z A 3B2– 2B–( ) AB B2– B3–( )–+ 0=
A aP
R2T 2
-----------=
B bP
RT
------=
V ZRT
P
----------=3-28
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ThPRSV Enthalpy
The following relation calculates the enthalpy
where: HIG is the ideal gas enthalpy calculated at temperature, T
Property Class Name and Applicable Phases
(3.65)
Property Class Name Applicable Phase
COTHPRSVEnthalpy Class Vapour and Liquid
The volume, V, is calculated using PRSV Molar Volume. For 
consistency, the PRSV Enthalpy always calls the PRSV 
Volume for the calculation of V.
H HIG PV RT a da
dT
------⎝ ⎠
⎛ ⎞ T–⎝ ⎠
⎛ ⎞– 1
2 2b
------------- V b 1 2+( )+
V b 1 2–( )+
----------------------------------ln–=–3-29
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ThPRSV Entropy
The following relation calculates the entropy.
where: SIG is the ideal gas entropy calculated at temperature, T
Property Class Name and Applicable Phases
(3.66)
Property Class Name Applicable Phase
COTHPRSVEntropy Class Vapour and Liquid
The volume, V, is calculated using PRSV Molar Volume. For 
consistency, the PRSV Entropy always calls the PRSV Volume 
for the calculation of V.
S SIG R V b–
RT
------------⎝ ⎠
⎛ ⎞ 1
2b 2
------------- V b 1 2+( )+
V b 1 2–( )+
----------------------------------⎝ ⎠
⎛ ⎞ da
dT
------ln–ln=–3-30
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ThPRSV Cp (Heat Capacity)
The following relation calculates the isobaric heat capacity.
Property Class Name and Applicable Phases
PRSV Fugacity Coefficient
The following relation calculates the fugacity Coefficient.
(3.67)
Property Class Name Applicable Phase
COTHPRSVCp Class Vapour and Liquid
(3.68)
(3.69)
(3.70)
Cp Cp
IG T ∂2P
∂T2
--------
⎝ ⎠
⎜ ⎟
⎛ ⎞
V
V R
T ∂V
∂T
------⎝ ⎠
⎛ ⎞
P
2
∂V
∂P
------⎝ ⎠
⎛ ⎞
T
------------------+ +d
∞
V
∫–=–
φiln V b–( ) b
V b–
------------ a
2 2b
------------- V b 1 2+( )+
V b 1 2–( )+
----------------------------------⎝ ⎠
⎛ ⎞ 1– a
a
-- b
b
--++⎝ ⎠
⎛ ⎞ln+ +ln–=
a ∂n2a
∂n
-----------=
b ∂nb
∂n
---------=3-31
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ThProperty Class Name and Applicable Phases
PRSV Fugacity
The following relation calculates the fugacity for a specific 
phase.
Property Class Name and Applicable Phases
PRSV Cv (isochoric)
The following relation calculates the isochoric heat capacity.
Property Class Name Applicable Phase
COTHPRSVLnFugacityCoeff 
Class
Vapour and Liquid
The volume, V, is calculated using PRSV Molar Volume. For 
consistency, the PRSV Fugacity Coefficient always calls the 
PRSV Volume for the calculation of V. The parameters a and 
b are calculated from the Mixing Rules.
(3.71)
Property Class Name Applicable Phase
COTHPRSVLnFugacity Class Vapour and Liquid
(3.72)
fi φiyiP=
Cv Cp
T ∂P
∂T
------⎝ ⎠
⎛ ⎞ 2
V
∂P
∂V
------⎝ ⎠
⎛ ⎞
T
---------------------+=3-32
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ThProperty Class Name and Applicable Phases
Mixing Rules
The mixing rules available for the PRSV equation are shown 
below.
Property Class Name Applicable Phase
COTHPRSVCv Class Vapour and Liquid
(3.73)
(3.74)
(3.75)
(3.76)
(3.77)
(3.78)
(3.79)
(3.80)
a xixjaij( )
j 1=
nc
∑
i 1=
nc
∑=
b bixi
i 1=
nc
∑=
aij aiiajj( )0.5ξij=
αi 1 κi–( ) 1 Tri
0.5–( )=
ai
0.45724R2Tci
2
Pci
---------------------------------=
bi
0.07780RTci
Pci
------------------------------=
κi κi0 κi1 1 Tri
0.5+( ) 0.7 Tri–( )+=
κi0 0.378893 1.4897153ωi 0.17131848ωi
2– 0.0196554ωi
3+ +=3-33
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ThMixing Rule 1
The definition of terms a and b are the same for all Mixing 
Rules. The only difference between the mixing rules is the 
temperature dependent binary interaction parameter, ξij, which is 
defined as:
where: Aij, Bij, and Cij are asymmetric binary interaction parameters
Mixing Rule 2
The definition of terms a and b are the same for all Mixing 
Rules. The only difference between the mixing rules is the 
temperature dependent binary interaction parameter, ξij, which is 
defined as:
where: Aij, Bij, and Cij are asymmetric binary interaction parameters
Mixing Rule 3
The definition of terms a and b are the same for all Mixing 
Rules. The only difference between the mixing rules is the 
temperature dependent binary interaction parameter, ξij, which is 
defined as:  
(3.81)
(3.82)
(3.83)
ξij 1 Aij– BijT CijT
2+ +=
ξij 1 Aij– BijT
Cij
T
------+ +=
ξij 1 xi Aij Bij CijT
2+ +( )– xj Aji BjiT CjiT
2+ +( )–=3-34
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ThMixing Rule 4
The definition of terms a and b are the same for all Mixing 
Rules. The only difference between the mixing rules is the 
temperature dependent binary interaction parameter, ξij, which is 
defined as:
where: Aij, Bij, and Cij are asymmetric binary interaction parameters
Mixing Rule 5
The definition of terms a and b are the same for all Mixing 
Rules. The only difference between the mixing rules is the 
temperature dependent binary interaction parameter, ξij, which is 
defined as:
where: Aij, Bij, and Cij are asymmetric binary interaction parameters
Mixing Rule 6
The definition of terms a and b are the same for all Mixing 
Rules. The only difference between the mixing rules is the 
temperature dependent binary interaction parameter, ξij:
where: Aij, Bij, and Cij are asymmetric binary interaction parameters
(3.84)
(3.85)
(3.86)
ξij 1 xi Aij BijT
Cij
T
------+ +⎝ ⎠
⎛ ⎞– xj Aji Bji
Cji
T
------+ +⎝ ⎠
⎛ ⎞–=
ξi j 1
Aij BijT CijT
2+ +( ) Aji BjiT CijT
2+ +( )
xi Aij BijT CijT
2+ +( ) xj Aji BjiT CjiT
2+ +( )+
---------------------------------------------------------------------------------------------------------------–=
ξij 1
Aij BijT
Cij
T
------+ +⎝ ⎠
⎛ ⎞ Aji BjiT
Cij
T
------+ +⎝ ⎠
⎛ ⎞
xi Aij BijT
Cij
T
------+ +⎝ ⎠
⎛ ⎞ xj Aji BjiT
Cji
T
------+ +⎝ ⎠
⎛ ⎞+
----------------------------------------------------------------------------------------------------–=3-35
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Th3.1.5 Soave-Redlich-Kwong 
Equation of State
Wilson (1965, 1966) noted that the main drawback of the RK 
equation of state was its inability of accurately reproducing the 
vapour pressures of pure component constituents of a given 
mixture. He proposed a modification to the RK equation of state 
using the acentricity as a correlating parameter, but this 
approach was widely ignored until 1972, when 11Soave (1972) 
proposed a modification of the RK equation of this form:
The “a” term was fitted to reproduce the vapour pressure of 
hydrocarbons using the acentric factor as a correlating 
parameter. This led to the following development:
Empirical modifications for the “a” term for specific substances 
like hydrogen were proposed by 12Graboski and Daubert (1976), 
and different, substance specific forms for the “a” term with 
several adjusted parameters are proposed up to the present, 
varying from 1 to 3 adjustable parameters. The SRK equation of 
state can represent the behaviour of hydrocarbon systems for 
separation operations with accuracy. Since, it is readily 
converted into computer code, its usage has been intense in the 
last twenty years. Other derived thermodynamic properties, like 
enthalpies and entropies, are reasonably accurate for 
engineering work, and the SRK equation has wide acceptance in 
the engineering community today.
(3.87)
(3.88)
P RT
V b–
------------
a T Tc ω, ,( )
V V b+( )
--------------------------–=
P RT
V b–
------------
acα
V V b+( )
---------------------–=
ac Ωa
R2Tc
2
Pc
-----------=
α 1 S 1 Tr
0.5–( )+=
S 0.480 1.574ω 0.176ω2–+=3-36
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ThTo apply the SRK EOS to mixtures, mixing rules are required for 
the “a” and “b” terms in Equation (3.270). 
Property Methods
A quick reference of calculation methods is shown in the table 
below for the SRK EOS.
The calculation methods from the table are described in the 
following sections.
Calculation Method
Applicable 
Phase
Property Class Name
Z Factor Vapour and 
Liquid
COTHSRKZFactor Class
Molar Volume Vapour and 
Liquid
COTHSRKVolume Class
Enthalpy Vapour and 
Liquid
COTHSRKEnthalpy Class
Entropy Vapour and 
Liquid
COTHSRKEntropy Class
Isobaric heat capacity Vapour and 
Liquid
COTHSRKCp Class
Fugacity coefficient 
calculation
Vapour and 
Liquid
COTHSRKLnFugacityCoeff 
Class
Fugacity calculation Vapour and 
Liquid
COTHSRKLnFugacity Class
Isochoric heat capacity Vapour and 
Liquid
COTHSRKCv Class
Mixing Rule 1 Vapour and 
Liquid
COTHSRKab_1 Class
Mixing Rule 2 Vapour and 
Liquid
COTHSRKab_2 Class
Mixing Rule 3 Vapour and 
Liquid
COTHSRKab_3 Class
Mixing Rule 4 Vapour and 
Liquid
COTHSRKab_4 Class
Mixing Rule 5 Vapour and 
Liquid
COTHSRKab_5 Class
Mixing Rule 6 Vapour and 
Liquid
COTHSRKab_6 Class
Refer to the Mixing 
Rules section for the 
applicable set of mixing 3-37
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ThSRK Z Factor
The compressibility factor is calculated as the root for the 
following equation:
There are three roots for the above equation. 
It is considered that the smallest root is for the liquid phase and 
the largest root is for the vapour phase. The third root has no 
physical meaning.
SRK Molar Volume
The following relation calculates the molar volume for a specific 
phase.
(3.89)
(3.90)
(3.91)
(3.92)
Z3 Z 2– Z A B– B2–( ) AB–+ 0=
A aP
R2T 2
-----------=
B bP
RT
------=
V ZRT
P
----------=3-38
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ThProperty Class Name and Applicable Phases 
SRK Enthalpy
The following relation calculates the enthalpy.
where: HIG is the ideal gas enthalpy calculated at temperature, T
Property Class Name and Applicable Phases
Property Class Name Applicable Phase
COTHSRKVolume Class Vapour and Liquid
The compressibility factor, Z, is calculated using SRK Z 
Factor. For consistency, the SRK molar volume always calls 
the SRK Z Factor for the calculation of Z
(3.93)
Property Class Name Applicable Phase
COTHSRKEnthalpy Class Vapour and Liquid
The volume, V, is calculated using SRK Molar Volume. For 
consistency, the SRK Enthalpy always calls the SRK Volume 
for the calculation of V.
H HIG PV RT– 1
b
-- a T∂a
∂T
------–⎝ ⎠
⎛ ⎞ V
V b+
------------ln+=–3-39
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ThSRK Entropy
The following relation calculates the entropy.
where: SIG is the ideal gas entropy calculated at temperature, T.
Property Class Name and Applicable Phases
SRK Cp (Heat Capacity)
The following relation calculates the isobaric heat capacity.
(3.94)
Property Class Name Applicable Phase
COTHSRKEntropy Class Vapour and Liquid
The volume, V, is calculated using SRK Molar Volume. For 
consistency, the SRK Entropy always calls the SRK Volume 
for the calculation of V.
(3.95)
S SIG R V b–
RT
------------⎝ ⎠
⎛ ⎞ 1
b
-- ∂a
∂T
-----⎝ ⎠
⎛ ⎞ V b+
V
------------⎝ ⎠
⎛ ⎞ln–ln=–
Cp Cp
IG T ∂2P
∂T2
--------
⎝ ⎠
⎜ ⎟
⎛ ⎞
V
V R
T ∂V
∂T
------⎝ ⎠
⎛ ⎞
P
2
∂V
∂P
------⎝ ⎠
⎛ ⎞
T
------------------+ +d
∞
V
∫–=–3-40
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ThProperty Class Name and Applicable Phases
SRK Fugacity Coefficient
The following relation calculates the fugacity coefficient.
Property Class Name and Applicable Phases
Property Class Name Applicable Phase
COTHSRKCp Class Vapour and Liquid
(3.96)
(3.97)
(3.98)
Property Class Name Applicable Phase
COTHSRKLnFugacityCoeff 
Class
Vapour and Liquid
The volume, V, is calculated using SRK Molar Volume. For 
consistency, the SRK Fugacity Coefficient always calls the 
SRK Volume for the calculation of V. The parameters a and b 
are calculated from the Mixing Rules.
φiln V b–( ) b
V b–
------------ a
RTb
---------- b
b
-- a
a
--– 1–⎝ ⎠
⎛ ⎞ V b+
V
------------⎝ ⎠
⎛ ⎞ln+ +ln=
a ∂n2a
∂n
-----------=
b ∂nb
∂ni
---------=3-41
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ThSRK Fugacity
The following relation calculates the fugacity for a specific 
phase.
Property Class Name and Applicable Phases
SRK Cv (isochoric)
The following relation calculates the isochoric heat capacity.
Property Class Name and Applicable Phases
(3.99)
Property Class Name Applicable Phase
COTHSRKLnFugacity Class Vapour and Liquid
(3.100)
Property Class Name Applicable Phase
COTHSRKCv Class Vapour and Liquid
fi φiyiP=
Cv Cp
T ∂P
∂T
------⎝ ⎠
⎛ ⎞ 2
V
∂P
∂V
------⎝ ⎠
⎛ ⎞
T
---------------------+=3-42
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ThMixing Rules
The mixing rules available for the SRK EOS state are shown 
below.
Mixing Rule 1
The definition of terms a and b are the same for all Mixing 
Rules. The only difference between the mixing rules is the 
temperature dependent binary interaction parameter, ξij, which is 
defined as:
where: Aij, Bij, and Cij are asymmetric binary interaction parameters
(3.101)
(3.102)
(3.103)
(3.104)
(3.105)
(3.106)
(3.107)
(3.108)
a xixjaij( )
j 1=
nc
∑
i 1=
nc
∑=
b bixi
i 1=
nc
∑=
aij ξi j aciacjαiαj=
αi 1 κi j– 1 Tri
0.5–( )=
aci
0.42748R2Tci
2
Pci
---------------------------------=
bi
0.08664RTci
Pci
------------------------------=
κi 0.48 1.574ωi 0.176ωi
2–+=
ξij 1 Aij– BijT CijT
2+ +=3-43
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ThMixing Rule 2
The definition of terms a and b are the same for all Mixing 
Rules. The only difference between the mixing rules is the 
temperature dependent binary interaction parameter, ξij, which is 
defined as:
where: Aij, Bij, and Cij are asymmetric binary interaction parameters
Mixing Rule 3
The definition of terms a and b are the same for all Mixing 
Rules. The only difference between the mixing rules is the 
temperature dependent binary interaction parameter, ξij, which is 
defined as:
Mixing Rule 4
The definition of terms a and b are the same for all Mixing 
Rules. The only difference between the mixing rules is the 
temperature dependent binary interaction parameter, ξij, which is 
defined as:
where: Aij, Bij, and Cij are asymmetric binary interaction parameters
(3.109)
(3.110)
(3.111)
ξij 1 Aij– BijT
Cij
T
------+ +=
ξij 1 xi Aij Bij CijT
2+ +( )– xj Aji BjiT CjiT
2+ +( )–=
ξij 1 xi Aij BijT
Cij
T
------+ +⎝ ⎠
⎛ ⎞– xj Aji Bji
Cji
T
------+ +⎝ ⎠
⎛ ⎞–=3-44
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ThMixing Rule 5
The definition of terms a and b are the same for all Mixing 
Rules. The only difference between the mixing rules is the 
temperature dependent binary interaction parameter, ξij, which is 
defined as:
where: Aij, Bij, and Cij are asymmetric binary interaction parameters
Mixing Rule 6
The definition of terms a and b are the same for all Mixing 
Rules. The only difference between the mixing rules is the 
temperature dependent binary interaction parameter, ξij, which is 
defined as:
where: Aij, Bij, and Cij are asymmetric binary interaction parameters
(3.112)
(3.113)
ξi j 1
Aij BijT CijT
2+ +( ) Aji BjiT CijT
2+ +( )
xi Aij BijT CijT
2+ +( ) xj Aji BjiT CjiT
2+ +( )+
---------------------------------------------------------------------------------------------------------------–=
ξij 1
Aij BijT
Cij
T
------+ +⎝ ⎠
⎛ ⎞ Aji BjiT
Cij
T
------+ +⎝ ⎠
⎛ ⎞
xi Aij BijT
Cij
T
------+ +⎝ ⎠
⎛ ⎞ xj Aji BjiT
Cji
T
------+ +⎝ ⎠
⎛ ⎞+
----------------------------------------------------------------------------------------------------–=3-45
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Th3.1.6 Redlich-Kwong Equation 
of State
In 1949, Redlich and Kwong proposed a modification of the van 
der Waals equation where the universal critical compressibility 
was reduced to a more reasonable number (i.e., 0.3333). This 
modification, known as the Redlich-Kwong (RK) equation of 
state, was very successful, and for the first time, a simple cubic 
equation of state would be used for engineering calculations 
with acceptable accuracy. Previous equations used for 
engineering calculations were modifications of the virial 
equation of state, notably the Beatie-Bridgeman and the 
Benedict-Webb-Rubin (BWR).
These other equations, although capable of accurately 
representing the behaviour of pure fluids, had many adjustable 
constants to be determined through empirical fitting of PVT 
properties, and received limited use. On the other hand, the RK 
equation required only Tc and Pc, and (fortunately) the 
principles of corresponding states using Tc and Pc applies with 
fair accuracy for simple hydrocarbon systems. This combination 
of simplicity and relative accuracy made the RK equation of 
state a very useful tool for engineering calculations in 
hydrocarbon systems. The Redlich-Kwong equation of state is 
represented by the following equation:
(3.114)P RT
V b–
------------ a
V V b+( )
--------------------- 1
T
------–=3-46
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Thand the reduced form is represented by:
Although simple systems approximately obey the corresponding 
states law as expressed by the RK equation, further 
improvements were required, especially when using the 
equation to predict the vapour pressure of pure substances. It 
was noted by several researchers, notably Pitzer, that the 
corresponding states principle could be extended by the use of a 
third corresponding state parameter, in addition to Tc and Pc. 
The two most widely used third parameters are the critical 
compressibility (Zc) and the acentric factor (ω). The acentric 
factor has a special appeal for equations of state based on the 
van der Waals ideas, since it is related to the lack of sphericity of 
a given substance. Pitzer defined the acentric factor as:
In this way, one may consider developing an equation of state 
using Tc, Pc, and ω as correlating parameters.
To apply the RK EOS to mixtures, mixing rules are required for 
the “a” and “b” terms in Equation (3.64). Refer to the Mixing 
Rules section for the set of mixing rules applicable.
(3.115)
 
(3.116)
Pr
3Tr
Vr 3Ωb–
---------------------
9Ωa
Tr
0.5Vr Vr 3Ωb+( )
------------------------------------------–=
Ωa 0.42748=
Ωb 0.08664=
a ΩaR2Tc
2.5
Pc
--------=
b ΩbR
Tc
Pc
-----=
Pitzer's definition is based 
on an empirical study in 
which it was verified that 
noble gases have a 
reduced pressure of about 
0.1 at Tr = 0.7.
ω 1– Prlog–= when Tr 0.7=3-47
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ThProperty Methods
A quick reference of calculation methods is shown in the table 
below for the RK EOS.
The calculation methods from the table are described in the 
following sections.
Calculation Method
Applicable 
Phase
Property Class Name
Z Factor Vapour and 
Liquid
COTHRKZFactor Class
Molar Volume Vapour and 
Liquid
COTHRKVolume Class
Enthalpy Vapour and 
Liquid
COTHRKEnthalpy Class
Entropy Vapour and 
Liquid
COTHRKEntropy Class
Isobaric heat capacity Vapour and 
Liquid
COTHRKCp Class
Fugacity coefficient 
calculation 
Vapour and 
Liquid
COTHRKLnFugacityCoeff 
Class
Fugacity calculation Vapour and 
Liquid
COTHRKLnFugacity Class
Isochoric heat capacity Vapour and 
Liquid
COTHRKCv Class
Mixing Rule 1 Vapour and 
Liquid
COTHRKab_1 Class
Mixing Rule 2 Vapour and 
Liquid
COTHRKab_2 Class
Mixing Rule 3 Vapour and 
Liquid
COTHRKab_3 Class
Mixing Rule 4 Vapour and 
Liquid
COTHRKab_4 Class
Mixing Rule 5 Vapour and 
Liquid
COTHRKab_5 Class
Mixing Rule 6 Vapour and 
Liquid
COTHRKab_6 Class3-48
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ThRK Z Factor
The compressibility factor is calculated as the root for the 
following equation:
There are three roots for the above equation. It is considered 
that the smallest root is for the liquid phase and the largest root 
is for the vapour phase. The third root has no physical meaning.
RK Molar Volume
The following relation calculates the molar volume for a specific 
phase.
(3.117)
(3.118)
(3.119)
(3.120)
Z3 Z2– Z A B– B2–( ) AB–+ 0=
A aP
R2T 2
-----------=
B bP
RT
------=
V ZRT
P
----------=3-49
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ThProperty Class Name and Applicable Phases
RK Enthalpy
The following relation calculates the enthalpy. 
where: HIG is the ideal gas enthalpy calculated at temperature, T
Property Class Name and Applicable Phases
Property Class Name Applicable Phase
COTHRKVolume Class Vapour and Liquid
The compressibility factor, Z, is calculated using RK Z Factor. 
For consistency, the RK molar volume always calls the RK Z 
Factor for the calculation of Z
(3.121)
Property Class Name Applicable Phase
COTHRKEnthalpy Class Vapour and Liquid
The volume, V, is calculated using RK Molar Volume. For 
consistency, the RK Enthalpy always calls the RK Volume for 
the calculation of V.
H HIG PV RT– 1
b
-- a T∂a
∂T
------–⎝ ⎠
⎛ ⎞ V
V b+
------------ln+=–3-50
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ThRK Entropy
The following relation calculates the entropy.
where: SIG is the ideal gas entropy calculated at temperature, T
Property Class Name and Applicable Phases
RK Cp (Heat Capacity)
The following relation calculates the isobaric heat capacity.
Property Class Name and Applicable Phases
(3.122)
Property Class Name Applicable Phase
COTHRKEntropy Class Vapour and Liquid
The volume, V, is calculated using RK Molar Volume. For 
consistency, the RK Entropy always calls the RK Volume for 
the calculation of V.
(3.123)
Property Class Name Applicable Phase
COTHRKCp Class Vapour and Liquid
S SIG R V b–
RT
------------⎝ ⎠
⎛ ⎞ 1
b
-- ∂a
∂T
-----⎝ ⎠
⎛ ⎞ V b+
V
------------⎝ ⎠
⎛ ⎞ln–ln=–
Cp Cp
IG T ∂2P
∂T2
--------
⎝ ⎠
⎜ ⎟
⎛ ⎞
V
V R
T ∂V
∂T
------⎝ ⎠
⎛ ⎞
P
2
∂V
∂P
------⎝ ⎠
⎛ ⎞
T
------------------+ +d
∞
V
∫–=–3-51
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ThRK Fugacity Coefficient
The following relation calculates the fugacity coefficient.
Property Class Name and Applicable Phases
RK Fugacity
The following relation calculates the fugacity for a specific 
phase.
Property Class Name and Applicable Phases
(3.124)
(3.125)
(3.126)
Property Class Name Applicable Phase
COTHRKLnFugacityCoeff Class Vapour and Liquid
The volume, V, is calculated using RK Molar Volume. For 
consistency, the RK Fugacity Coefficient always calls the RK 
Volume for the calculation of V. The parameters a and b are 
calculated from the Mixing Rules.
(3.127)
Property Class Name Applicable Phase
COTHRKLnFugacity Class Vapour and Liquid
φiln V b–( ) b
V b–
------------ a
RTb
---------- b
b
-- a
a
--– 1–⎝ ⎠
⎛ ⎞ V b+
V
------------⎝ ⎠
⎛ ⎞ln+ +ln=
a ∂n2a
∂n
-----------=
b ∂nb
∂ni
---------=
fi φiyiP=3-52
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ThRK Cv (isochoric)
The following relation calculates the isochoric heat capacity.
Property Class Name and Applicable Phases
Mixing Rules
The mixing rules available for the RK EOS state are shown 
below.
(3.128)
Property Class Name Applicable Phase
COTHRKCv Class Vapour and Liquid
(3.129)
(3.130)
(3.131)
(3.132)
(3.133)
Cv Cp
T ∂P
∂T
------⎝ ⎠
⎛ ⎞ 2
V
∂P
∂V
------⎝ ⎠
⎛ ⎞
T
---------------------+=
a xixjaij( )
j 1=
nc
∑
i 1=
nc
∑=
b bixi
i 1=
nc
∑=
aij ξij aiaj=
ai
0.42748R2Tci
2.5
Pci T
-----------------------------------=
bi
0.08664RTci
Pci
------------------------------=3-53
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ThMixing Rule 1
The definition of terms a and b are the same for all Mixing 
Rules. The only difference between the mixing rules is the 
temperature dependent binary interaction parameter, ξij, which is 
defined as:
where: Aij, Bij, and Cij are asymmetric binary interaction parameters.
Mixing Rule 2
The definition of terms a and b are the same for all Mixing 
Rules. The only difference between the mixing rules is the 
temperature dependent binary interaction parameter, ξij, which is 
defined as:
where: Aij, Bij, and Cij are asymmetric binary interaction parameters
Mixing Rule 3
The definition of terms a and b are the same for all Mixing 
Rules. The only difference between the mixing rules is the 
temperature dependent binary interaction parameter, ξij, which is 
defined as:
(3.134)
(3.135)
(3.136)
ξij 1 Aij– BijT CijT
2+ +=
ξij 1 Aij– BijT
Cij
T
------+ +=
ξij 1 xi Aij Bij CijT
2+ +( )– xj Aji BjiT CjiT
2+ +( )–=3-54
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ThMixing Rule 4
The definition of terms a and b are the same for all Mixing 
Rules. The only difference between the mixing rules is the 
temperature dependent binary interaction parameter, ξij:
where: Aij, Bij, and Cij are asymmetric binary interaction parameters
Mixing Rule 5
The definition of terms a and b are the same for all Mixing 
Rules. The only difference between the mixing rules is the 
temperature dependent binary interaction parameter, ξij, which is 
defined as:
where: Aij, Bij, and Cij are asymmetric binary interaction parameters
Mixing Rule 6
The definition of terms a and b are the same for all Mixing 
Rules. The only difference between the mixing rules is the 
temperature dependent binary interaction parameter, ξij, which is 
defined as:
where: Aij, Bij, and Cij are asymmetric binary interaction parameters
(3.137)
(3.138)
(3.139)
ξij 1 xi Aij BijT
Cij
T
------+ +⎝ ⎠
⎛ ⎞– xj Aji Bji
Cji
T
------+ +⎝ ⎠
⎛ ⎞–=
ξi j 1
Aij BijT CijT
2+ +( ) Aji BjiT CijT
2+ +( )
xi Aij BijT CijT
2+ +( ) xj Aji BjiT CjiT
2+ +( )+
---------------------------------------------------------------------------------------------------------------–=
ξij 1
Aij BijT
Cij
T
------+ +⎝ ⎠
⎛ ⎞ Aji BjiT
Cij
T
------+ +⎝ ⎠
⎛ ⎞
xi Aij BijT
Cij
T
------+ +⎝ ⎠
⎛ ⎞ xj Aji BjiT
Cji
T
------+ +⎝ ⎠
⎛ ⎞+
----------------------------------------------------------------------------------------------------–=3-55
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Th3.1.7 Zudkevitch-Joffee 
Equation of State
The 13Zudkevitch-Joffee (ZJ, 1970) model is a modification of the 
Redlich- Kwong equation of state. This model has been 
enhanced for better prediction of vapour-liquid equilibria for 
hydrocarbon systems, and systems containing Hydrogen. The 
major advantage of this model over previous versions of the RK 
equation is the improved capability of predicting pure compound 
vapour pressure and the simplification of the method for 
determining the required coefficients for the equation.
Enthalpy calculations for this model are performed using the 
Lee-Kesler method.
The Zudkevitch-Joffe EOS is represented by the following 
equation:
To apply the ZJ EOS to mixtures, mixing rules are required for 
the “a” and “b” terms in Equation (3.84). Refer to the Mixing 
Rules section for the set of mixing rules applicable.
(3.140)P RT
V b–
------------ a
V V b+( )
---------------------–=3-56
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ThProperty Methods
Calculation methods for ZJ EOS are shown in the following table.
The calculation methods from the table are described in the 
following sections. 
ZJ Z Factor
The compressibility factor is calculated as the root for the 
following equation:
There are three roots for the above equation. It is considered 
that the smallest root is for the liquid phase and the largest root 
is for the vapour phase. The third root has no physical meaning.
Calculation Method
Applicable 
Phase
Property Class Name
Z Factor Vapour and Liquid COTHZJZFactor Class
Molar Volume Vapour and Liquid COTHZJVolume Class
Enthalpy Vapour and Liquid COTHZJEnthalpy Class
Entropy Vapour and Liquid COTHZJEntropy Class
Isobaric heat capacity Vapour and Liquid COTHZJCp Class
Fugacity coefficient 
calculation 
Vapour and Liquid COTHZJLnFugacityCoeff 
Class
Fugacity calculation Vapour and Liquid COTHZJLnFugacity Class
Isochoric heat capacity Vapour and Liquid COTHZJCv Class
Mixing Rule 1 Vapour and Liquid COTHZJab_1 Class
Mixing Rule 2 Vapour and Liquid COTHZJab_2 Class
Mixing Rule 3 Vapour and Liquid COTHZJab_3 Class
Mixing Rule 4 Vapour and Liquid COTHZJab_4 Class
Mixing Rule 5 Vapour and Liquid COTHZJab_5 Class
Mixing Rule 6 Vapour and Liquid COTHZJab_6 Class
(3.141)
(3.142)
(3.143)
Z3 Z2– Z A B– B2–( ) AB–+ 0=
A aP
R2T2
-----------=
B bP
RT
------=3-57
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ThZJ Molar Volume
The following relation calculates the molar volume for a specific 
phase.
Property Class Name and Applicable Phases
ZJ Enthalpy
The following relation calculates the enthalpy. 
where: HIG is the ideal gas enthalpy calculated at temperature, T
(3.144)
Property Class Name Applicable Phase
COTHZJVolume Class Vapour and Liquid
The compressibility factor, Z, is calculated using ZJ Z Factor. 
For consistency, the ZJ molar volume always calls the ZJ Z 
Factor for the calculation of Z.
(3.145)
V ZRT
P
----------=
H HIG PV RT– 1
b
-- a T∂a
∂T
------–⎝ ⎠
⎛ ⎞ V
V b+
------------ln+=–3-58
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ThProperty Class Name and Applicable Phases  
ZJ Entropy
The following relation calculates the entropy.
where: SIG is the ideal gas entropy calculated at temperature, T
Property Class Name and Applicable Phases
Property Class Name Applicable Phase
COTHLeeKeslerEnthalpy 
Class
Vapour and Liquid
The volume, V, is calculated using ZJ Molar Volume. For 
consistency, the ZJ Enthalpy always calls the ZJ Volume for 
the calculation of V.
(3.146)
Property Class Name Applicable Phase
COTHLeeKeslerEntropy 
Class
Vapour and Liquid
The volume, V, is calculated using ZJ Molar Volume. For 
consistency, the ZJ Entropy always calls the ZJ Volume for 
the calculation of V.
S SIG R V b–
RT
------------⎝ ⎠
⎛ ⎞ 1
b
-- ∂a
∂T
-----⎝ ⎠
⎛ ⎞ V b+
V
------------⎝ ⎠
⎛ ⎞ln–ln=–3-59
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ThZJ Cp (Heat Capacity)
The following relation calculates the isobaric heat capacity.
Property Class Name and Applicable Phases
ZJ Fugacity Coefficient
The following relation calculates the fugacity coefficient:
(3.147)
Property Class Name Applicable Phase
COTHLeeKeslerCp Class Vapour and Liquid
(3.148)
(3.149)
(3.150)
Cp Cp
IG T ∂2P
∂T2
--------
⎝ ⎠
⎜ ⎟
⎛ ⎞
V
V R
T ∂V
∂T
------⎝ ⎠
⎛ ⎞
P
2
∂V
∂P
------⎝ ⎠
⎛ ⎞
T
------------------+ +d
∞
V
∫–=–
φiln V b–( ) b
V b–
------------ a
RTb
---------- b
b
-- a
a
--– 1–⎝ ⎠
⎛ ⎞ V b+
V
------------⎝ ⎠
⎛ ⎞ln+ +ln=
a ∂n2a
∂n
-----------=
b ∂nb
∂ni
---------=3-60
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ThProperty Class Name and Applicable Phases
ZJ Fugacity
The following relation calculates the fugacity for a specific 
phase.
Property Class Name and Applicable Phases
ZJ Cv (isochoric)
The following relation calculates the isochoric heat capacity.
Property Class Name Applicable Phase
COTHZJLnFugacityCoeff Class Vapour and Liquid
The volume, V, is calculated using ZJ Molar Volume. For 
consistency, the ZJ Fugacity Coefficient always calls the ZJ 
Volume for the calculation of V. The parameters a and b are 
calculated from the Mixing Rules.
(3.151)
Property Class Name Applicable Phase
COTHZJLnFugacity Class Vapour and Liquid
(3.152)
fi φiyiP=
Cv Cp
T ∂P
∂T
------⎝ ⎠
⎛ ⎞ 2
V
∂P
∂V
------⎝ ⎠
⎛ ⎞
T
---------------------+=3-61
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ThProperty Class Name and Applicable Phases
Mixing Rules
The mixing rules available for the ZJ EOS state are shown below.
(for Tr < 0.9) (41Soave, 1986)
With M1 and M2 determined at 0.9Tc to match the value and 
slope of the vapour pressure curve (14Mathias, 1983):
Property Class Name Applicable Phase
COTHZJCv Class Vapour and Liquid
(3.153)
(3.154)
(3.155)
(3.156)
(3.157)
(3.158)
(3.159)
a xixjaij( )
j 1=
nc
∑
i 1=
nc
∑=
b bixi
i 1=
nc
∑=
aij ξij aiajαiαj=
αisub c– ritical
1 Dk
Pr
Tr
----- 10ln–ln–
k 1+
2
-----------
Dk
Pr
Tr
----- 10ln–ln–
k 1–
k 3=
10
∑+
k 1=
2
∑+=
Pr Pi
sat Pci⁄=
α super critical–ln 2M1 1 Tr
M2–( )=
M1M2
1
2
-- dα
dTr
--------⎝ ⎠
⎛ ⎞
0.9Tc
–=3-62
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ThMixing Rule 1
The definition of terms a and b are the same for all Mixing 
Rules. The only difference between the mixing rules is the 
temperature dependent binary interaction parameter, ξij, which is 
defined as:
where: Aij, Bij, and Cij are asymmetric binary interaction parameters
Mixing Rule 2
The definition of terms a and b are the same for all Mixing 
Rules. The only difference between the mixing rules is the 
temperature dependent binary interaction parameter, ξij, which is 
defined as:
where: Aij, Bij, and Cij are asymmetric binary interaction parameters
(3.160)
(3.161)
(3.162)
(3.163)
(3.164)
(3.165)
M2
M1 1–
M1
---------------=
aci
0.42748R2Tci
2
Pci
---------------------------------=
bi
0.08664RTci
Pci
------------------------------=
κi 0.48 1.574ωi 0.176ωi
2–+=
ξij 1 Aij– BijT CijT
2+ +=
ξij 1 Aij– BijT
Cij
T
------+ +=3-63
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ThMixing Rule 3
The definition of terms a and b are the same for all Mixing 
Rules. The only difference between the mixing rules is the 
temperature dependent binary interaction parameter, ξij, which is 
defined as:
Mixing Rule 4
The definition of terms a and b are the same for all Mixing 
Rules. The only difference between the mixing rules is the 
temperature dependent binary interaction parameter, ξij, which is 
defined as:
where: Aij, Bij, and Cij are asymmetric binary interaction parameters
Mixing Rule 5
The definition of terms a and b are the same for all Mixing 
Rules. The only difference between the mixing rules is the 
temperature dependent binary interaction parameter, ξij, which is 
defined as:
where: Aij, Bij, and Cij are asymmetric binary interaction parameters
(3.166)
(3.167)
(3.168)
ξij 1 xi Aij Bij CijT
2+ +( )– xj Aji BjiT CjiT
2+ +( )–=
ξij 1 xi Aij BijT
Cij
T
------+ +⎝ ⎠
⎛ ⎞– xj Aji Bji
Cji
T
------+ +⎝ ⎠
⎛ ⎞–=
ξi j 1
Aij BijT CijT
2+ +( ) Aji BjiT CijT
2+ +( )
xi Aij BijT CijT
2+ +( ) xj Aji BjiT CjiT
2+ +( )+
---------------------------------------------------------------------------------------------------------------–=3-64
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ThMixing Rule 6
The definition of terms a and b are the same for all Mixing 
Rules. The only difference between the mixing rules is the 
temperature dependent binary interaction parameter, ξij, which is 
defined as:
where: Aij, Bij, and Cij are asymmetric binary interaction parameters
3.1.8 Kabadi-Danner Equation 
of State
The 16Kabadi-Danner (KD, 1985) model is a modification of the 
SRK equation of State. It is enhanced to improve the vapour-
liquid-liquid equilibria calculations for water-hydrocarbon 
systems, particularly in the dilute regions.
The model is an improvement over previous attempts which 
were limited in the region of validity. The modification is based 
on an asymmetric mixing rule, whereby the interaction in the 
water phase (with its strong hydrogen bonding) is calculated. It 
is based on both the interaction between the hydrocarbon and 
the water, and on the perturbation by the hydrocarbon on the 
water-water interaction due to its structure.
The Kabadi-Danner equation of state is written as:
(3.169)
(3.170)
ξij 1
Aij BijT
Cij
T
------+ +⎝ ⎠
⎛ ⎞ Aji BjiT
Cij
T
------+ +⎝ ⎠
⎛ ⎞
xi Aij BijT
Cij
T
------+ +⎝ ⎠
⎛ ⎞ xj Aji BjiT
Cji
T
------+ +⎝ ⎠
⎛ ⎞+
----------------------------------------------------------------------------------------------------–=
P RT
V b–
------------ a
V V b+( )
---------------------–=3-65
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ThThe KD equation of state is similar to the SRK equation of state, 
with the following modifications:
• Inclusion of a second energy parameter. The ai’ 
secondary energy parameter is a function of the 
hydrocarbon structure expressed as a group factor Gi. 
The Gi factor is assumed to be zero for all non-
hydrocarbons, including water.
• Different alpha function for water (16Kabadi and Danner, 
1985).
The interaction parameters between water and hydrocarbon 
were generalized by Twu and Bluck, based on the kij values 
given by Kabadi and Danner:
where: Watson is the hydrocarbon characterization factor, defined 
as:
The group factors Gi are expressed as a perturbation from 
normal alcane values as generalized by 17Twu and Bluck (1988):
(3.171)
(3.172)
(3.173)
(3.174)
(3.175)
(3.176)
(3.177)
kiw
0.315 Watson 10.5<
0.3325– 0.061667Watson+ 10.5 Watson 13.5≤≤
0.5 Watson 13.5>⎩
⎪
⎨
⎪
⎧
=
Watson
Tb3
SG
---------=
Gln G° 1 2f+
1 2f–
-------------⎝ ⎠
⎛ ⎞ 2
ln=
f f1 SG f2 SG2Δ+Δ=
f1 C1 C2 Tbln⁄ R( )+=
f2 C3 C4 Tbln⁄ R( )+=
SGΔ e5 SG° SG–( ) 1–=3-66
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ThThe alcane group factor Go is calculated as:
To apply the KD EOS to mixtures, mixing rules are required for 
the “a” and “b” terms in Equation (3.170). Refer to the 
Mixing Rules section for the applicable set of mixing rules.
(3.178)
(3.179)
(3.180)
(3.181)
Coefficients
a1 = 
0.405040
a6 = -
0.958481
a2 = 1.99638 c1 = -
0.178530
a3 = 34.9349 c2 = 1.41110
a4 = 
0.507059
c3 = 
0.237806
a5 = 1.2589 c4 = -
1.97726
G° 1.358–
426 1.358–
---------------------------⎝ ⎠
⎛ ⎞
a5 1
a4
----
Ngv a6F°+
Ngv F°–
---------------------------⎝ ⎠
⎛ ⎞ln=
Ngv
1 a6e a4–+
1 e a4––
-------------------------=
F°
1 a3e
a1–
+
1 e
a1–
–
------------------------ 1 e
a1τ–
–
1 a3e
a1– τ
+
--------------------------=
τ
Tb 200.99–
2000 200.99–
---------------------------------⎝ ⎠
⎛ ⎞
a2
=
(3.182)
(3.183)
(3.184)
SG° 0.843593 0.128624β– 3.36159β3– 13749.5β12–=
β 1
Tb
Tc
-----–=
Tb
Tc°
------- 0.533272 0.191017 3–×10 Tb 0.779681 7–×10 Tb
2 0.284376 10–×10 Tb
3– 95.9468
Tb
100
--------⎝ ⎠
⎛ ⎞
13–
+ + +=3-67
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ThProperty Methods
A quick reference of calculation methods is shown in the table 
below for the KD EOS.
The calculation methods from the table are described in the 
following sections.
Calculation Method
Applicable 
Phase
Property Class Name
Z Factor Vapour and Liquid COTHKDZFactor Class
Molar Volume Vapour and Liquid COTHKDVolume Class
Enthalpy Vapour and Liquid COTHKDEnthalpy Class
Entropy Vapour and Liquid COTHKDEntropy Class
Isobaric heat capacity Vapour and Liquid COTHKDCp Class
Fugacity coefficient 
calculation 
Vapour and Liquid COTHKDLnFugacityCoeff 
Class
Fugacity calculation Vapour and Liquid COTHKDLnFugacity Class
Isochoric heat capacity Vapour and Liquid COTHKDCv Class
Mixing Rule 1 Vapour and Liquid COTHKDab_1 Class
Mixing Rule 2 Vapour and Liquid COTHKDab_2 Class
Mixing Rule 3 Vapour and Liquid COTHKDab_3 Class
Mixing Rule 4 Vapour and Liquid COTHKDab_4 Class
Mixing Rule 5 Vapour and Liquid COTHKDab_5 Class
Mixing Rule 6 Vapour and Liquid COTHKDab_6 Class3-68
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ThKD Z Factor
The compressibility factor is calculated as the root for the 
following equation:
There are three roots for the above equation. It is considered 
that the smallest root is for the liquid phase and the largest root 
is for the vapour phase. The third root has no physical meaning.
KD Molar Volume
The following relation calculates the molar volume for a specific 
phase.
Property Class Name and Applicable Phases
(3.185)
(3.186)
(3.187)
(3.188)
Property Class Name Applicable Phase
COTHKDVolume Class Vapour and Liquid
The compressibility factor, Z, is calculated using KD Z Factor. 
For consistency, the KD molar volume always calls the KD Z 
Factor for the calculation of Z.
Z3 Z2– Z A B– B2–( ) AB–+ 0=
A aP
R2T 2
-----------=
B bP
RT
------=
V ZRT
P
----------=3-69
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ThKD Enthalpy
The following relation calculates the enthalpy. 
where: HIG is the ideal gas enthalpy calculated at temperature, T
Property Class Name and Applicable Phases
KD Entropy
The following relation calculates the entropy.
where: SIG is the ideal gas entropy calculated at temperature, T
Property Class Name and Applicable Phases
(3.189)
Property Class Name Applicable Phase
COTHKDEnthalpy Class Vapour and Liquid
The volume, V, is calculated using KD Molar Volume. For 
consistency, the KD Enthalpy always calls the KD Volume for 
the calculation of V.
(3.190)
Property Class Name Applicable Phase
COTHKDEntropy Class Vapour and Liquid
The volume, V, is calculated using KD Molar Volume. For 
consistency, the KD Entropy always calls the KD Volume for 
the calculation of V.
H HIG PV RT– 1
b
-- a T∂a
∂T
------–⎝ ⎠
⎛ ⎞ V
V b+
------------ln+=–
S SIG R V b–
RT
------------⎝ ⎠
⎛ ⎞ 1
b
-- ∂a
∂T
-----⎝ ⎠
⎛ ⎞ V b+
V
------------⎝ ⎠
⎛ ⎞ln–ln=–3-70
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ThKD Cp (Heat Capacity)
The following relation calculates the isobaric heat capacity.
Property Class Name and Applicable Phases
KD Fugacity Coefficient
The following relation calculates the Fugacity Coefficient:
(3.191)
Property Class Name Applicable Phase
COTHKDCp Class Vapour and Liquid
(3.192)
(3.193)
(3.194)
Cp Cp
IG T ∂2P
∂T2
--------
⎝ ⎠
⎜ ⎟
⎛ ⎞
V
V R
T ∂V
∂T
------⎝ ⎠
⎛ ⎞
P
2
∂V
∂P
------⎝ ⎠
⎛ ⎞
T
------------------+ +d
∞
V
∫–=–
φiln V b–( ) b
V b–
------------ a
RTb
---------- b
b
-- a
a
--– 1–⎝ ⎠
⎛ ⎞ V b+
V
------------⎝ ⎠
⎛ ⎞ln+ +ln=
a ∂n2a
∂n
-----------=
b ∂nb
∂ni
---------=3-71
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ThProperty Class Name and Applicable Phases
KD Fugacity
The following relation calculates the fugacity for a specific 
phase.
Property Class Name and Applicable Phases
Property Class Name Applicable Phase
COTHKDLnFugacityCoeff Class Vapour and Liquid
The volume, V, is calculated using KD Molar Volume. For 
consistency, the KD Fugacity Coefficient always calls the KD 
Volume for the calculation of V.
(3.195)
Property Class Name Applicable Phase
COTHKDLnFugacity Class Vapour and Liquid
fi φiyiP=3-72
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ThKD Cv (isochoric)
The following relation calculates the isochoric heat capacity.
Property Class Name and Applicable Phases
(3.196)
Property Class Name Applicable Phase
COTHKDCv Class Vapour and Liquid
Cv Cp
T ∂P
∂T
------⎝ ⎠
⎛ ⎞ 2
V
∂P
∂V
------⎝ ⎠
⎛ ⎞
T
---------------------+=3-73
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ThMixing Rules
The mixing rules available for the KD EOS state are shown 
below.
(3.197)
(3.198)
(3.199)
(3.200)
(3.201)
(3.202)
(3.203)
(3.204)
a xixjaij( ) xixw
2 ai'( )
i 1=
nc
∑+
j 1=
nc
∑
i 1=
nc
∑=
b bixi
i 1=
nc
∑=
aij ξij aiajαiαj=
αi
1 κi+( ) 1 Tri
0.5–( ) i w≠
1 0.662 1 Trw
0.8–( )+ i w=
⎩
⎪
⎨
⎪
⎧
=
ai
0.42747R2Tci
2
Pci
---------------------------------=
bi
0.08664RTci
Pci
------------------------------=
κi 0.480 1.57ωi 0.176ωi
2–+=
ai'
Gi1 Trw
0.8– T Tcw<
0.0 T Tcw≥⎩
⎨
⎧
=
3-74
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ThMixing Rule 1
The definition of terms a and b are the same for all Mixing 
Rules. The only difference between the mixing rules is the 
temperature dependent binary interaction parameter, ξij, which is 
defined as:
where: Aij, Bij, and Cij are asymmetric binary interaction parameters
Mixing Rule 2
The definition of terms a and b are the same for all Mixing 
Rules. The only difference between the mixing rules is the 
temperature dependent binary interaction parameter, ξij, which is 
defined as:
where: Aij, Bij, and Cij are asymmetric binary interaction parameters
Mixing Rule 3
The definition of terms a and b are the same for all Mixing 
Rules. The only difference between the mixing rules is the 
temperature dependent binary interaction parameter, ξij, which is 
defined as:
(3.205)
(3.206)
(3.207)
ξij 1 Aij– BijT CijT
2+ +=
ξij 1 Aij– BijT
Cij
T
------+ +=
ξij 1 xi Aij Bij CijT
2+ +( )– xj Aji BjiT CjiT
2+ +( )–=3-75
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ThMixing Rule 4
The definition of terms a and b are the same for all Mixing 
Rules. The only difference between the mixing rules is the 
temperature dependent binary interaction parameter, ξij, which is 
defined as:
where: Aij, Bij, and Cij are asymmetric binary interaction parameters
Mixing Rule 5
The definition of terms a and b are the same for all Mixing 
Rules. The only difference between the mixing rules is the 
temperature dependent binary interaction parameter, ξij:
where: Aij, Bij, and Cij are asymmetric binary interaction parameters
Mixing Rule 6
The definition of terms a and b are the same for all Mixing 
Rules. The only difference between the mixing rules is the 
temperature dependent binary interaction parameter, ξij:
where: Aij, Bij, and Cij are asymmetric binary interaction parameters
(3.208)
(3.209)
(3.210)
ξij 1 xi Aij BijT
Cij
T
------+ +⎝ ⎠
⎛ ⎞– xj Aji Bji
Cji
T
------+ +⎝ ⎠
⎛ ⎞–=
ξi j 1
Aij BijT CijT
2+ +( ) Aji BjiT CijT
2+ +( )
xi Aij BijT CijT
2+ +( ) xj Aji BjiT CjiT
2+ +( )+
---------------------------------------------------------------------------------------------------------------–=
ξij 1
Aij BijT
Cij
T
------+ +⎝ ⎠
⎛ ⎞ Aji BjiT
Cij
T
------+ +⎝ ⎠
⎛ ⎞
xi Aij BijT
Cij
T
------+ +⎝ ⎠
⎛ ⎞ xj Aji BjiT
Cji
T
------+ +⎝ ⎠
⎛ ⎞+
----------------------------------------------------------------------------------------------------–=3-76
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Th3.1.9 The Virial Equation of 
State
The Virial equation of state has theoretical importance since it 
can be derived from rigorous statistical mechanical arguments. 
It is represented as an infinite sum of power series in the 
inverse of the molar volume:
where: B is the second virial coefficient, C the third, etc.
The above equation may be rewritten as a series in molar 
density:
and pressure:
The last format is not widely used since it gives an inferior 
representation of Z over a range of densities or pressures (6Reid, 
Prausnitz and Poling, 1987). It is clear that B can be calculated 
as:
(3.211)
(3.212)
(3.213)
(3.214)
(3.215)
The term Virial comes 
from the Latin vis (force) 
and refers to the 
interaction forces between 
2, 3 or more molecules.
Z PV
RT
------- 1 B
V
--- C
V 2----- D
V 3----- …+ + + += =
Z 1 Bρ Cρ2 Dρ3 …+ + + +=
Z 1 B'P C'P2 D'P3 …+ + + +=
Z 1 Bρ Cρ2 Dρ3 …+ + + +=
ρ∂
∂Z
⎝ ⎠
⎛ ⎞
T
B 2Cρ 3Dρ2 …+ + +=3-77
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Thand taking the limit where ρ -> 0, B can be expressed as:
Similarly, the following can be obtained:
This approach can easily be extended to higher terms.
It is experimentally verified that the Virial equation, when 
truncated after the second Virial coefficient, gives reasonable 
vapour phase density predictions provided that the density is 
smaller than half of the critical density. The Virial EOS truncated 
after the second Virial coefficient is:
Calculating the Second Virial 
Coefficient
There are several ways of estimating the second virial coefficient 
for pure components and mixtures. If accurate volumetric data 
is available, the procedure is straightforward, but tedious. In 
your applications, it is better to estimate the second virial 
coefficient similar to the way in which the cubic equation of state 
parameters were determined. That is, it is desired to express 
the second virial coefficient as a function of Tc, Pc and the 
acentric factor. Pitzer attempted to do this, proposing a simple 
corresponding states approach:
(3.216)
(3.217)
(3.218)
(3.219)
B
ρ∂
∂Z
⎝ ⎠
⎛ ⎞
Tρ 0→
lim=
C
ρ2
2
∂
∂ Z
⎝ ⎠
⎜ ⎟
⎛ ⎞
Tρ 0→
lim= D
ρ3
3
∂
∂ Z
⎝ ⎠
⎜ ⎟
⎛ ⎞
Tρ 0→
lim=
Z PV
RT
------- 1 B
V
--+= =
B B 0( ) ωB 1( )+=3-78
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Thwhere: B(0) is a simple fluid term depending only on Tc 
B(1) is a correction term for the real fluid, which is a function 
of Tc and Pc
Note that this three-parameter corresponding states relation 
displays in many different forms, such as in the Soave, Peng-
Robinson, Lee-Kesler and BWR-Starling equations of state.
Pitzer proposed several modifications to this simple form. Pitzer 
was motivated mainly because polar fluids do not obey a simple 
three-parameter corresponding states theory. 18Tsonopoulos 
(1974) suggested that the problem can (at least partially) be 
solved by the inclusion of a third term in the previous 
expression:
where: B(2) is a function of Tc and one (or more) empirical constants
It was found that this empirical function can sometimes be 
generalized in terms of the reduced dipole moment:
where: Pc is in bar and μR is in debyes
The method of 19Hayden and O'Connell (1975) is used, where 
they define:
where: Bij
F, non-polar = Second virial coefficient contribution from    
the non-polar part due to physical interactions
Bij
F, polar = Second virial coefficient contribution from the 
polar part due to physical interactions
(3.220)
(3.221)
(3.222)
B B 0( ) ωB 1( ) B 2( )+ +=
μR
105μ2Pc
Tc
-------------------- 0.9869×=
Bij Bij
F Bij
D+=
Bij
F Bij
F
non polar–,( ) Bij
F
polar,( )+=
Bij
D Bij
D
metastable,( ) Bij
D
bound,( ) Bij
D
chemical,( )+ +=3-79
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ThBij
D, metastable = Second virial coefficient contribution due 
to the formation of metastable compounds due to the 
"chemical" (dimerization) reaction
Bij
D, bound = Second virial coefficient contribution due to the 
formation of chemical bonds
Bij
D, chemical = Second virial coefficient contribution due to 
the chemical reaction
The several contributions to the second Virial coefficient are 
calculated as follows:
(3.223)
(3.224)
(3.225)
(3.226)
Bij
F
non polar–, bij
0 0.94 1.47
Tij
*'
---------– 0.85
Tij
*'2
--------- 1.015
Tij
*'3
------------–+
⎝ ⎠
⎜ ⎟
⎛ ⎞
=
Bij
F
polar, b– ij
0 μij
*' 0.74 3.0
Tij
*'
------– 2.1
Tij
*'2
-------- 2.1
Tij
*'3
--------+ +
⎝ ⎠
⎜ ⎟
⎛ ⎞
=
Bij
D
metastable,( ) Bij
D
bound,( )+ bij
0 Aij
HijΔ
Tij
∗
----------
⎝ ⎠
⎜ ⎟
⎛ ⎞
exp=
Bij
D
chemical,( ) bij
0 Eij 1
1500ηij
T
------------------⎝ ⎠
⎛ ⎞exp–⎝ ⎠
⎛ ⎞=3-80
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Thwhere:
For pure components:
(3.227)
1
Tij
*'
------ 1
Tij
*
----- 1.6ωij–=
Tij
* T
εi j k⁄( )
----------------=
bij
0 1.26184σij
3= cm3 gmol⁄( )
μi j
*' μij
*= if μij
* 0.04<
μij
*' 0= if 0.04 μi j
*≤ 0.25<
μij
*' μi j
* 0.25–= if μij
* 0.25≥
Aij 0.3– 0.05μi j
*–=
HijΔ 1.99 0.2μij
*2+=
μij
* 7243.8μiμj
εij
k
-----⎝ ⎠
⎛ ⎞ σij
3
--------------------------=
Eij ηij
650
εi j
k
-----⎝ ⎠
⎛ ⎞ 300+
-------------------------- 4.27–
⎝ ⎠
⎜ ⎟
⎜ ⎟
⎜ ⎟
⎛ ⎞
⎩ ⎭
⎪ ⎪
⎨ ⎬
⎪ ⎪
⎧ ⎫
exp= if ηij 4.5<
Eij ηij
42800
εi j
k
-----⎝ ⎠
⎛ ⎞ 22400+
-------------------------------- 4.27–
⎝ ⎠
⎜ ⎟
⎜ ⎟
⎜ ⎟
⎛ ⎞
⎩ ⎭
⎪ ⎪
⎨ ⎬
⎪ ⎪
⎧ ⎫
exp= if ηi j 4.5≥
ωi 0.006026RDi 0.02096RDi
2 0.001366RDi
3–+=
εij
k
-----
εi j
k
-----⎝ ⎠
⎛ ⎞
′
1 ξC1 1 ξ 1
C1
2
-----+⎝ ⎠
⎛ ⎞–⎝ ⎠
⎛ ⎞–⎝ ⎠
⎛ ⎞=
σi σi' 1 ξC2+( )1 3⁄=
εi
k
---⎝ ⎠
⎛ ⎞
′
Tc i, 0.748 0.91ωi 0.4
ηi
2 20ωi+
--------------------–+⎝ ⎠
⎛ ⎞=3-81
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Thand
For the cross parameters:
(3.228)
(3.229)
(3.230)
(3.231)
σi' 2.44 ωi–( ) 1.0133
Tc i,
Pc i,
--------⎝ ⎠
⎛ ⎞
1 3⁄
=
 
ξ 0= if μi 1.45    <
or
ξ
1.7941 7×10 μi
4
2.882
1.882ωi
0.03 ωi+
---------------------–⎝ ⎠
⎛ ⎞ Tc i, σi'
6 εi
k
---⎝ ⎠
⎛ ⎞′
----------------------------------------------------------------------------------
⎝ ⎠
⎜ ⎟
⎜ ⎟
⎜ ⎟
⎜ ⎟
⎜ ⎟
⎛ ⎞
   if μi 1.45≥=
C1
16 400ωi+
10 400ωi+
--------------------------    and  C2
3
10 400ωi+
--------------------------==
ωij
1
2
-- ωi ωj+( )=
εi j
k
-----⎝ ⎠
⎛ ⎞ εij
k
-----⎝ ⎠
⎛ ⎞′ 1 ξ′C1′+( )=
σij σij′ 1 ξ– ′C2′( )=
εi j
k
-----⎝ ⎠
⎛ ⎞
′
0.7
εii
k
-----⎝ ⎠
⎛ ⎞ εj j
k
-----⎝ ⎠
⎛ ⎞
1
2
--
0.6
1
εii k⁄
----------- 1
εjj k⁄
-----------+
------------------------------------+=
σij σiiσjj( )
1
2
--
=
ξ′
ui
2 εjj
k
-----⎝ ⎠
⎛ ⎞
2 3⁄
σj j
4
εij
k
-----⎝ ⎠
⎛ ⎞′ σi j
6
---------------------------------= if  μi 2 and μj≥ 0=
ξ′
u2 εii
k
-----⎝ ⎠
⎛ ⎞
2
σi i
4
εij
k
-----⎝ ⎠
⎛ ⎞′ σ′ij
6
--------------------------= if  μj 2 and μi≥ 0=
ξ′ 0 for all other values of  μi and μj=3-82
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ThThus, Hayden-O'Connell models the behaviour of a mixture 
subject to physical (polarity) and chemical (associative and 
solvation) forces as a function of Tc, Pc, RD (radius of gyration), 
μ (dipole moment) and two empirical constants that describe the 
"chemical" behaviour of the gas:
This is discussed in more detail in the next section.
Mixing Rules
For a multi-component mixture, it can be shown that Bmix is 
rigorously calculated by:
and the fugacity coefficient for a component i in the mixture 
comes from:
(3.232)
(3.233)
(3.234)
C1
′ 16 400ωi j+
10 400ωi j+
----------------------------   and  C2
′ 3
10 400ωij+
----------------------------==
   ηii association parameter=
ηij solvation parameter=
Bmix yi yj Bij
j
∑
i
∑=
φiln 2 yi Bij Bmix–
j
∑⎝ ⎠
⎜ ⎟
⎛ ⎞ P
RT
------=3-83
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ThVapour Phase Chemical Association 
using the Virial Equation
Although it was suggested many years ago that the non-ideality 
in mixtures could be explained by pseudo-chemical reactions 
and formation of complexes, there is evidence that this is true 
only in a few special cases. Of special practical importance are 
mixtures which contain carboxylic acids. Carboxylic acids tend to 
dimerize through strong hydrogen bonding.
This is not limited to carboxylic acids alone; hydrofluoric acid 
forms polymers (usually hexamers) and the hydrogen bonding 
can happen with dissimilar molecules.
Usually, hydrogen bonding between similar molecules is called 
association, while bonding between dissimilar molecules is 
called solvation.
The hydrogen bonding process can be observed as a chemical 
reaction: 
where: i and j are monomer molecules and ij is the complex formed 
by hydrogen bonding
The following may be written to describe the chemical reaction:
where: Z is the true mole fraction of the species in equilibrium
 is the fugacity coefficient of the true species
P is the system pressure
kij is the reaction equilibrium constant
(3.235)
(3.236)
i j ij↔+
kij
fij
fi fj
------
Zijφ
#
ij
ZiZjφi
#φ#
jP
---------------------------= =
φ#3-84
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ThIf yi is defined as the mole fraction of component i in the vapour 
phase, disregarding dimerization, it can be shown that:
where:  denotes the apparent fugacity coefficient of component i
If it is assumed that the vapour solution behaves like an ideal 
solution (Lewis), the following may be written:
where: Bi
F is the contribution to the second virial coefficient from 
physical forces
If the Lewis ideal solution is carried all the way:
The chemical equilibrium constant is found from the relation:
where: Bij
D is the contribution of dimerization to the second virial 
coefficient
(3.237)
(3.238)
(3.239)
(3.240)
(3.241)
φ#
iZi φiyi= or φi
φi
#Zi
yi
----------=
φi
φln i
# Bi
FP
RT
----------=
kij
φijZijP
φiZiPφjZjP
---------------------------=
kij
Zij
ZiZj
--------- 1
P
---
Bij
F P
RT
------⎝ ⎠
⎛ ⎞exp
Bii
F P
RT
------⎝ ⎠
⎛ ⎞ Bjj
F P
RT
------⎝ ⎠
⎛ ⎞expexp
-----------------------------------------------------------×=
kij
Bij
D– 2 δi j–( )
RT
------------------------------=
δi j
0 i j≠
1 i j=⎩
⎨
⎧
=
3-85
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ThTherefore:
The calculation of the fugacity coefficient for species i and j is 
accomplished by solving the previous chemical equilibrium 
constant equation combined with the restriction that the sum of 
Zi, Zj and Zij is equal to 1.
Application of the Virial Equation
The equation enables you to better model vapour phase 
fugacities of systems displaying strong vapour phase 
interactions. Typically this occurs in systems containing 
carboxylic acids, or compounds that have the tendency to form 
stable hydrogen bonds in the vapour phase. In these cases, the 
fugacity coefficient shows large deviations from ideality, even at 
low or moderate pressures. 
The regression module contains temperature dependent 
coefficients for carboxylic acids. You can overwrite these by 
changing the Association (ij) or Solvation (ii) coefficients from 
the default values.
If the virial coefficients need to be calculated, the software 
contains correlations utilizing the following pure component 
properties:
• critical temperature
• critical pressure
• dipole moment
• mean radius of gyration
• association parameter
• association parameter for each binary pair
(3.242)
kij
Zij
ZiZj
--------- 1
P
---
Bij
F P
RT
------⎝ ⎠
⎛ ⎞exp
Bii
F P
RT
------⎝ ⎠
⎛ ⎞ Bjj
F P
RT
------⎝ ⎠
⎛ ⎞expexp
-----------------------------------------------------------×=
    
Bij
D– 2 δi j–( )
RT
------------------------------=3-86
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ThThe equation is restricted to systems where the density is 
moderate, typically less than one-half the critical density. The 
Virial equation used is valid for the following range:
Property Methods
A quick reference of calculation methods is shown in the table 
below for the Virial EOS.
The calculation methods from the table are described in the 
following sections. 
(3.243)
Calculation Method
Applicable 
Phase
Property Class Name
Molar Volume Vapour COTHVirial_Volume Class
Enthalpy Vapour COTHVirial_Enthalpy Class
Entropy Vapour COTHVirial_Entropy Class
Isobaric heat capacity Vapour COTHVirial_Cp Class
Fugacity coefficient 
calculation 
Vapour COTHVirial_LnFugacityCoeff 
Class
Fugacity calculation Vapour COTHVirial_LnFugacity Class
Density Vapour COTHVirial_Density Class
Isochoric Heat 
Capacity
Vapour COTHVirial_Cv Class
Gibbs Energy Vapour COTHVirial_GibbsEnergy Class
Helmholtz Energy Vapour COTHVirial_HelmholtzEnergy 
Class
Z Factor Vapour COTHVirial_ZFactor Class
P T
2
--
yiPci
i 1=
m
∑
yiTci
i 1=
m
∑
--------------------≤3-87
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ThVirial Molar Volume
The following relation calculates the molar volume for a specific 
phase.
Property Class Name and Applicable Phases
Virial Enthalpy
The following relation calculates the enthalpy.
Property Class Name and Applicable Phases
Virial Entropy
The following relation calculates the entropy.
(3.244)
Property Class Name Applicable Phase
COTHVirial_Volume Class Vapour 
(3.245)
Property Class Name Applicable Phase
COTHVirial_Enthalpy Class Vapour 
(3.246)
V B
Z 1–
-----------=
H H°– A A°– T S S°–( ) RT Z 1–( )+ +=
S So RT dB dT⁄( )
V B–
--------------------- R V
V B–
------------ln R V
Vo
-----ln+––=–3-88
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ThProperty Class Name and Applicable Phases
Virial Cp (Heat Capacity)
The following relation calculates the isobaric heat capacity.
Property Class Name and Applicable Phases
Virial Fugacity Coefficient
The following relation calculates the fugacity coefficient:
Property Class Name and Applicable Phases
Property Class Name Applicable Phase
COTHVirial_Entropy Class Vapour
(3.247)
Property Class Name Applicable Phase
COTHVirial_Cp Class Vapour 
(3.248)
Property Class Name Applicable Phase
COTHVirial_LnFugacityCoeff 
Class
Vapour
Cp Cp°– T
T2
2
∂
∂ P
⎝ ⎠
⎜ ⎟
⎛ ⎞
Vd
∞
V
∫ T T∂
∂P
⎝ ⎠
⎛ ⎞
V
2
T∂
∂P
⎝ ⎠
⎛ ⎞
T
-----------------– R–=
φiln 2 yi Bij Bmix–
j
∑⎝ ⎠
⎜ ⎟
⎛ ⎞ P
RT
------=3-89
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ThVirial Fugacity
The following relation calculates the fugacity for a specific 
phase.
Property Class Name and Applicable Phases
Virial Density
The following relation calculates the molar density for a specific 
phase.
Property Class Name and Applicable Phases
Virial Cv (isochoric)
The following relation calculates the isochoric heat capacity.
(3.249)
Property Class Name Applicable Phase
COTHVirial_LnFugacity 
Class
Vapour and Liquid
(3.250)
Property Class Name Applicable Phase
COTHVirial_Density Class Vapour and Liquid
(3.251)
fi φiyiP=
ρ P
ZRT
----------=
Cv Cv°– T
T2
2
∂
∂ P
⎝ ⎠
⎜ ⎟
⎛ ⎞
Vd
∞
V
∫=3-90
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ThProperty Class Name and Applicable Phases
Virial Gibbs Energy
The following relation calculates the Gibbs energy.
Property Class Name and Applicable Phases
Virial Helmholtz Energy
The following relation calculates the Helmholtz energy.
Property Class Name and Applicable Phases
Property Class Name Applicable Phase
COTHVirial_Cv Class Vapour and Liquid
(3.252)
Property Class Name Applicable Phase
COTHVirial_GibbsEnergy 
Class
Vapour
(3.253)
Property Class Name Applicable Phase
COTHVirial_HelmholtzEnergy 
Class
Vapour
G A RT Z 1–( )+=
A Ao RT V
V B–
------------ln RT V
Vo
-----ln–=–3-91
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ThVirial Z Factor
The following relation calculates the Z Factor.
Property Class Name and Applicable Phases
3.1.10 Lee-Kesler Equation of 
State
The 50Lee-Kesler (LK, 1975) method is an effort to extend the 
method originally proposed by Pitzer to temperatures lower than 
0.8 Tr. Lee and Kesler expanded Pitzer's method expressing the 
compressibility factor as:
where:  Z o = the compressibility factor of a simple fluid
Z r = the compressibility factor of a reference fluid
They chose the reduced form of the BWR EOS to represent both 
Z o and Z r:
(3.254)
Property Class Name Applicable Phase
COTHVirial_ZFactor Class Vapour
(3.255)
(3.256)
Z 1 B
V
--+=
Z Z° ω
ωr
----- Zr Z°–( )+=
Z 1 B
Vr
----- C
Vr
2
----- D
Vr
5
----- D
Tr
3
Vr
3
----------- β γ
Vr
2
-----–
⎝ ⎠
⎜ ⎟
⎛ ⎞
e
γ
Vr
2
-----
⎝ ⎠
⎛ ⎞–
+ + + +=3-92
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Thwhere:
The constants in these equations were determined using 
experimental compressibility and enthalpy data. Two sets of 
constants, one for the simple fluid (ωo = 0) and one for the 
reference fluid (ωr=0.3978, n-C8) were determined. 
Property Methods
A quick reference of calculation methods is shown in the table 
below for the LK EOS.
The calculation methods from the table are described in the 
following sections.
Calculation 
Method
Applicable Phase Property Class Name
Enthalpy Vapour and Liquid COTHLeeKeslerEnthalpy Class
Entropy Vapour and Liquid COTHLeeKeslerEntropy Class
Isobaric heat 
capacity
Vapour and Liquid COTHLeeKeslerCp Class
Vr
VPc
RTc
---------=
B b1
b2
Tr
----–
b3
Tr
2
-----–
b4
Tr
4
-----–=
C c1
c2
Tr
----–
c3
Tr
3
-----+=
D d1
d2
Tr
----+=3-93
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ThLK Enthalpy
The following relation calculates the enthalpy departure.
where:
Property Class Name and Applicable Phases
LK Entropy
The following relation calculates the entropy departure.
(3.257)
(3.258)
(3.259)
Property Class Name Applicable Phase
COTHLeeKeslerEnthalpy 
Class
Vapour and Liquid
The values of Tc and Vc are calculated from the Mixing Rules.
(3.260)
H HIG–
RTc
------------------- Tr Z 1–
b2 2
b3
Tr
---- 3
b4
Tr
2
-----+ +
TrVr
------------------------------------–
c2 3
c3
Tr
2
-----–
2TrVr
2
--------------------–
d2
5TrVr
5
--------------– 3E+
⎩ ⎭
⎪ ⎪
⎪ ⎪
⎨ ⎬
⎪ ⎪
⎪ ⎪
⎧ ⎫
=
Tr
T
Tc
----=
Vr
V
Vc
-----=
S S°
IG–
R
------------------ Zln P
P°
-----⎝ ⎠
⎛ ⎞ln–
b1
b3
Tr
2
----- 2
b4
Tr
3
-----+ +
Vr
---------------------------------–
c1 3
c3
Tr
2
-----–
2Vr
2
--------------------–
d1
5Vr
2
--------– 2E+=3-94
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Thwhere:
Property Class Name and Applicable Phases
LK Cp (Heat Capacity)
The following relation calculates the isobaric heat capacity.
Property Class Name and Applicable Phases
(3.261)
(3.262)
Property Class Name Applicable Phase
COTHLeeKeslerEntropy 
Class
Vapour and Liquid
The values of Tc and Vc are calculated from the Mixing Rules.
(3.263)
Property Class Name Applicable Phase
COTHLeeKeslerCp Class Vapour and Liquid
Tr
T
Tc
----=
Vr
V
Vc
-----=
Cp Cp
IG T ∂2P
∂T2
--------
⎝ ⎠
⎜ ⎟
⎛ ⎞
V
V R
T ∂V
∂T
------⎝ ⎠
⎛ ⎞
P
2
∂V
∂P
------⎝ ⎠
⎛ ⎞
T
------------------+ +d
∞
V
∫–=–3-95
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3-96 Equations of State
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ThMixing Rules
For mixtures, the Critical properties for the LK EOS state are 
defined as follows.
3.1.11 Lee-Kesler-Plöcker
The Lee-Kesler-Plöcker equation is an accurate general method 
for non-polar substances and mixtures. 3Plöcker et al, applied 
the Lee-Kesler equation to mixtures, which itself was modified 
from the BWR equation.
The compressibility factors are determined as follows:
(3.264)
(3.265)
ω xiωi
i 1=
N
∑=
zci
0.2905 0.0851ωi–=
Vci
Zci
RTci
Pci
-----------------=
Vc
1
8
-- xixj Vci
1
3
--
Vcj
1
3
--
+
⎝ ⎠
⎜ ⎟
⎛ ⎞
3
j 1=
N
∑
i 1=
N
∑=
Tc
1
8Vc
-------- xixj Vci
1
3
--
Vcj
1
3
--
+
⎝ ⎠
⎜ ⎟
⎛ ⎞
3
Tci
Tcj
( )0.5
j 1=
N
∑
i 1=
N
∑=
Pc 0.2905 0.085ω–( )
RTc
Vc
---------=
The Lee-Kesler-Plöcker 
equation does not use the 
COSTALD correlation in 
computing liquid density. 
This may result in 
differences when 
comparing results 
z z o( ) ω
ω r( )
--------- z r( ) z o( )–( )+=
z pv
RT
------
prvr
Tr
--------- z Tr vr Ak, ,( )= = =3-96
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Thwhere:  
Mixing rules for pseudocritical properties are as follows:
where:
(3.266)
(3.267)
z 1 B
vr
---- C
vr
2
---- D
vr
5
---- C4
Tr
3vr
2
---------- β γ
vr
2
----+ γ–
vr
2
-----exp+ + + +=
vr
pcv
RTc
---------=
C c1
c2
Tr
----–
c3
Tr
2
-----+=
ω o( ) 0=
B b1
b2
Tr
----–
b3
Tr
2
-----–
b4
Tr
3
-----–=
D d1
d2
Tr
----–=
ω r( ) 0.3978=
Tcm
1
Vcm
η
---------
⎝ ⎠
⎜ ⎟
⎛ ⎞
xixjvcij
j
∑
i
∑=
Tcij
Tci
Tcj
( )1 2⁄= Tcii
Tci
= Tcjj
Tcj
=
vcm
xixjvcij
j
∑
i
∑= vcij
1
8
-- vci
1 3⁄ vcj
1 3⁄+( )
3
=
vci
zci
RTci
pci
----------= zci
0.2905 0.085ωi–=
pcm
zcm
RTcm
vcm
-----------= zcm
0.2905 0.085ωm–=
ωm xiωi
i
∑=3-97
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Th3.2 Activity Models
Although equation of state models have proven to be very 
reliable in predicting properties of most hydrocarbon-based 
fluids over a large range of operating conditions, their 
application has been limited to primarily non-polar or slightly 
polar components. Polar or non-ideal chemical systems have 
traditionally been handled using dual model approaches. In this 
approach, an equation of state is used for predicting the vapour 
fugacity coefficients (normally ideal gas or the Redlich-Kwong, 
Peng-Robinson or SRK equations of state) and an activity 
coefficient model is used for the liquid phase. Although there is 
considerable research being conducted to extend equation of 
state applications into the chemical arena (e.g., the PRSV 
equation), the state of the art of property predictions for 
chemical systems is still governed mainly by activity models.
Activity models are much more empirical in nature when 
compared to the property predictions in the hydrocarbon 
industry. For this reason, they cannot be used as reliably as the 
equations of state for generalized application or extrapolated 
into untested operating conditions. Their adjustable parameters 
should be fitted against a representative sample of experimental 
data and their application should be limited to moderate 
pressures. Consequently, caution should be exercised when 
selecting these models for your simulation.
The phase separation or equilibrium ratio Ki for component i 
(defined in terms of the vapour phase fugacity coefficient and 
the liquid phase activity coefficient), is calculated from the 
following expression:
where:  γi = Liquid phase activity coefficient of component i
fi
o= Standard state fugacity of component i
P = System pressure
fi = Vapour phase fugacity coefficient of component i
(3.268)
Activity models generate 
the best results when they 
are applied in the 
operating region in which 
the interaction parameters 
were generated.
Ki
yi
xi
---
γi fi°
Pφi
---------= =3-98
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ThAlthough for ideal solutions the activity coefficient is unity, for 
most chemical (non-ideal) systems this approximation is 
incorrect. Dissimilar chemicals normally exhibit not only large 
deviations from an ideal solution, but the deviation is also found 
to be a strong function of the composition. To account for this 
non-ideality, activity models were developed to predict the 
activity coefficients of the components in the liquid phase. The 
derived correlations were based on the excess Gibbs energy 
function, which is defined as the observed Gibbs energy of a 
mixture in excess of what it would be if the solution behaved 
ideally, at the same temperature and pressure.
For a multi-component mixture consisting of ni moles of 
component i, the total excess Gibbs free energy is represented 
by the following expression:
where: γi is the activity coefficient for component i
The individual activity coefficients for any system can be 
obtained from a derived expression for excess Gibbs energy 
function coupled with the Gibbs-Duhem equation. The early 
models (Margules, van Laar) provide an empirical 
representation of the excess function that limits their 
application. The newer models such as Wilson, NRTL and 
UNIQUAC use the local composition concept and provide an 
improvement in their general application and reliability. All of 
these models involve the concept of binary interaction 
parameters and require that they be fitted to experimental data.
Since the Margules and van Laar models are less complex than 
the Wilson, NRTL and UNIQUAC models, they require less CPU 
time for solving flash calculations. However, these are older and 
more empirically based models and generally give poorer results 
for strongly non-ideal mixtures such as alcohol-hydrocarbon 
systems, particularly for dilute regions.
(3.269)GE RT ni γiln( )∑=3-99
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ThThe following table briefly summarizes recommended models for 
different applications. 
Vapour phase non-ideality can be taken into account for each 
activity model by selecting the Redlich-Kwong, Peng-Robinson 
or SRK equations of state as the vapour phase model. When one 
of the equations of state is used for the vapour phase, the 
standard form of the Poynting correction factor is always used 
for liquid phase correction.
The binary parameters required for the activity models have 
been regressed based on the VLE data collected from DECHEMA, 
Chemistry Data Series. There are over 16,000 fitted binary pairs 
in the library. The structures of all library components applicable 
for the UNIFAC VLE estimation have been stored. The Poynting 
correction for the liquid phase is ignored if ideal solution 
behaviour is assumed.    
Application Margules van Laar Wilson NRTL UNIQUAC
Binary Systems A A A A A
multi-component 
Systems
LA LA A A A
Azeotropic Systems A A A A A
Liquid-Liquid Equilibria A A N/A A A
Dilute Systems ? ? A A A
Self-Associating Systems ? ? A A A
Polymers N/A N/A N/A N/A A
Extrapolation ? ? G G G
A = Applicable; N/A = Not Applicable;? = Questionable; G = Good; LA = Limited 
Application
All the binary parameters stored in the properties library 
have been regressed using an ideal gas model for the vapour 
phase.3-100
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ThIf you are using the built-in binary parameters, the ideal gas 
model should be used. All activity models, with the exception of 
the Wilson equation, automatically calculate three phases given 
the correct set of energy parameters. The vapour pressures 
used in the calculation of the standard state fugacity are based 
on the pure component library coefficients using the modified 
form of the Antoine equation.   
3.2.1 Ideal Solution Model
The ideal solution model is the simplest activity model that 
ignores all non-idealities in a liquid solution. Although this model 
is very simple, it is incapable of representing complex systems 
such as those with azeotropes.
Property Methods
A quick reference of calculation methods is shown in the table 
below for the Ideal Solution model.
The calculation methods from the table are described in the 
following sections.
The internally stored binary parameters have NOT been 
regressed against three-phase equilibrium data.
Calculation 
Method
Applicable 
Phase
Property Class Name
Activity coefficient Liquid COTHIdealSolLnActivityCoeff 
Class
Fugacity coefficient Liquid COTHIdealSolLnFugacityCoeff 
Class
Fugacity Liquid COTHIdealSolLnFugacity Class
Activity coefficient 
differential wrt 
temperature
Liquid COTHIdealSolLnActivityCoeffDT 
Class
Enthalpy Liquid COTHIdealSolEnthalpy Class
Gibbs energy Liquid COTHIdealSolGibbsEnergy Class3-101
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ThIdeal Solution Ln Activity Coefficient
This method calculates the activity coefficient of components, i, 
using the Ideal Solution model. The extended, multi-component 
form of the Ideal Solution is shown in the following relation:
where:  γi = activity coefficient of component i
Property Class Name and Applicable Phases
Ideal Solution Ln Fugacity 
Coefficient
This method calculates the fugacity coefficient of components 
using the Ideal Solution activity model. The fugacity coefficient 
of component i, φi, is calculated from the following relation.
where: γi = 1
P = pressure
fi = standard state fugacity
(3.270)
Property Class Name Applicable Phase
COTHIdealSolLnActivityCoeff Class Liquid
(3.271)
γiln 0=
φln i ln 
fi
std
P
-------
⎝ ⎠
⎜ ⎟
⎛ ⎞
=
3-102
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ThProperty Class Name and Applicable Phases
Ideal Solution Ln Fugacity
This method calculates the fugacity of components using the 
Ideal Solution activity model. The fugacity of component i, fi, is 
calculated from the following relation.
where: γi = 1
fi 
std = standard state fugacity
xi = mole fraction of component i
Property Class Name and Applicable Phases 
Property Class Name Applicable Phase
COTHIdealSolLnFugacityCoeff Class Liquid
For the standard fugacity, fi 
std, refer to Section 5.4 - 
Standard State Fugacity.
(3.272)
Property Class Name Applicable Phase
COTHIdealSolLnFugacity Class Liquid
For the standard fugacity, fi 
std, refer to Section 5.4 - 
Standard State Fugacity.
ln fi ln xifi
std( )=3-103
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ThIdeal Solution Activity Coefficient 
Differential wrt Temperature
This method calculates the activity coefficient differential wrt to 
temperature using the Ideal Solution model from the following 
relation.
Property Class Name and Applicable Phases
Ideal Solution Gibbs Energy
This method calculates the Gibbs free energy using the Ideal 
Solution activity model from the following relation.
where: xi = mole fraction of component i
Gi = Gibbs energy of component i 
(3.273)
Property Class Name Applicable Phase
COTHIdealSolLnActivityCoeffDT Class Liquid
(3.274)
∂ γiln
∂T
------------ 0=
G xiGi RT xi xiln
i
n
∑+
i
n
∑=3-104
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ThProperty Class Name and Applicable Phases
Ideal Solution Enthalpy
This method calculates the enthalpy using the Ideal Solution 
activity model from the following relation.
where: xi = mole fraction of component i
Hi = enthalpy of component i
Property Class Name and Applicable Phases
Property Class Name Applicable Phase
COTHIdealSolGibbsEnergy Class Liquid
(3.275)
Property Class Name Applicable Phase
COTHIdealSolEnthalpy Class Liquid
H xiHi
i
n
∑=3-105
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Th3.2.2 Regular Solution Model
The Regular Solution model as defined by 40Hildebrand (1970) is 
one in which the excess entropy is eliminated when a solution is 
mixed at constant temperature and volume. The model is 
recommended for non-polar components in which the molecules 
do not differ greatly in size. By the attraction of intermolecular 
forces, the excess Gibbs energy may be determined. Scatchard 
and Hildebrand assumed that the activity coefficients are a 
function of pure component properties only relating mixture 
interactions to those in pure fluids. The solubility parameter is a 
required and important pure component property which is 
related to the energy required to vaporize a liquid component to 
an ideal gas state. This method should not be used for highly 
non-ideal mixtures, especially if they contain polar components.
Property Methods
A quick reference of calculation methods is shown in the table 
below for the Regular Solution activity model.
The calculation methods from the table are described in the 
following sections.
Calculation Method
Applicable 
Phase
Property Class Name
Fugacity coefficient Liquid COTHRegSolLnFugacityCoeff Class
Activity coefficient Liquid COTHRegSolLnActivityCoeff Class
Fugacity Liquid COTHRegSolLnFugacity Class
Activity coefficient 
differential wrt 
temperature
Liquid COTHRegSolLnActivityCoeffDT 
Class
Standard Fugacity Liquid COTHIdealStdFug Class
Excess Gibbs Energy Liquid COTHRegSolExcessGibbsEnergy 
Class3-106
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ThRegular Solution Ln Activity 
Coefficient
This method calculates the activity coefficient of components, i, 
using the Regular Solution model as shown in the expression 
below. 
where:  γi = activity coefficient of component i
Vi = liquid molar volume of component i
δi = solubility parameter of component i
Property Class Name and Applicable Phases
(3.276)
(3.277)
Property Class Name Applicable Phase
COTHRegSolLnActivityCoeff Class Liquid
γi
Vi
RT
------ δi ϕjδi
j
∑–
2
=ln
ϕj
xjVj
xkVk
k
∑
-----------------=3-107
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ThRegular Solution Ln Fugacity 
Coefficient
This method calculates the fugacity coefficient of components 
using the Regular Solution activity model. The fugacity 
coefficient of component i, φi, is calculated from the following 
relation.
where: γi = activity coefficient of component i
P = pressure
fi 
std= standard state fugacity
Property Class Name and Applicable Phases
Regular Solution Ln Fugacity
This method calculates the fugacity of components using the 
Regular Solution activity model. The fugacity of component i, fi, 
is calculated from the following relation.
(3.278)
Property Class Name Applicable Phase
COTHRegSolLnFugacityCoeff Class Liquid
The term, ln γi, in the above equation is exclusively 
calculated using the Regular Solution Ln Activity Coefficient. 
For the standard fugacity, fi 
std, refer to Section 5.4 - 
Standard State Fugacity.
(3.279)
φln i ln γi
fi
std
P
-------
⎝ ⎠
⎜ ⎟
⎛ ⎞
=
ln fi ln γixifi
std( )=3-108
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Thwhere: γi = activity coefficient of component i
fi 
std = standard state fugacity
xi = mole fraction of component i
Property Class Name and Applicable Phases
Regular Solution Activity Coefficient 
Differential wrt Temperature
This method calculates the activity coefficient differential wrt to 
temperature using the Regular Solution model from the 
following relation.
Property Class Name and Applicable Phases
Property Class Name Applicable Phase
COTHRegSolLnFugacity Class Liquid
The term, lnγi, in the above equation is exclusively calculated 
using the Regular Solution Ln Activity Coefficient. For the 
standard fugacity, fi 
std, refer to Section 5.4 - Standard State 
Fugacity.
(3.280)
Property Class Name Applicable Phase
COTHVanLaarLnActivityCoeffDT Class Liquid
d γiln
dT
------------3-109
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ThRegular Solution Excess Gibbs 
Energy
This method calculates the excess Gibbs energy using the 
Regular Solution activity model from the following relation.
where: γi = activity coefficient of component i
xi = mole fraction of component i
T = temperature
R = universal gas constant
Property Class Name and Applicable Phases
(3.281)
Property Class Name Applicable Phase
COTHRegSolLnActivityCoeffDT Class Liquid
The term, ln γi, in the above equation is exclusively 
calculated using the Regular Solution Ln Activity Coefficient.
GE RT xi γiln
i
n
∑=3-110
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Th3.2.3 van Laar Model
In the Van Laar (2Prausnitz et al., 1986) activity model, it is 
assumed that, if two pure liquids are mixed at constant pressure 
and temperature, no volume expansion or contraction would 
happen (VE = 0) and that the entropy of mixing would be zero. 
Thus the following relation: 
simplifies to: 
To calculate the Gibbs free energy of mixing, the simple Van 
Laar thermodynamic cycle is shown below:
(3.282)
(3.283)
 Figure 3.2
G E U E PV E TS E–+=
GE HE UE==
Pr
e
ss
ur
e
Pure
Liquid
Liquid
Mixture
Vapourize each liquid
dropping system P to
a very low value
(Ideal Gas)
Compress
Vapour
Mixture
Ideal Gas
Mix Ideal Cases3-111
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ThSince U is a point function, the value of UE is:
The expression for ΔUI is:
The following is true:
Therefore:
In the van Laar model, it is assumed that the volumetric 
properties of the pure fluids could be represented by the van der 
Waals equation. This leads to:
(3.284)
(3.285)
(3.286)
(3.287)
(3.288)
U E UI UII UIII+ +=
UΔ I V∂
∂U
⎝ ⎠
⎛ ⎞
T
T T∂
∂P
⎝ ⎠
⎛ ⎞
V
P–= =
The expression 
can be derived from 
fundamental 
thermodynamic 
relationships.
V∂
∂U
⎝ ⎠
⎛ ⎞
T
T T∂
∂P
⎝ ⎠
⎛ ⎞
V
P–=
T∂
∂P
⎝ ⎠
⎛ ⎞
V T∂
∂V
⎝ ⎠
⎛ ⎞–
P V∂
∂P
⎝ ⎠
⎛ ⎞
T
P–=
T∂
∂P
⎝ ⎠
⎛ ⎞
V T∂
∂V
⎝ ⎠
⎛ ⎞–
P P∂
∂V
⎝ ⎠
⎛ ⎞
T
⁄=
V∂
∂U
⎝ ⎠
⎛ ⎞
T
P T T∂
∂V
⎝ ⎠
⎛ ⎞
P
P∂
∂V
⎝ ⎠
⎛ ⎞
T
--------------+
⎝ ⎠
⎜ ⎟
⎜ ⎟
⎜ ⎟
⎛ ⎞
–=
V∂
∂U
⎝ ⎠
⎛ ⎞
T
a
V 2
-----=3-112
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ThAssuming that there are x1 moles of component 1 and x2 of 
component 2 and x1 + x2 = 1 mole of mixture:
thus:
and:
Using the van der Waals equation:
and for a real fluid well below its critical point,  should be a 
large negative number (since liquids exhibit low compressibility) 
and consequently:
Therefore,
(3.289)
(3.290)
(3.291)
(3.292)
(3.293)
(3.294)
x1 Uid U–( )1
a1x1
V 2
---------- Vd
V1
L
∞
∫
a1x1
V1
L
----------= =
x2 Uid U–( )2
a1x1
V 2
---------- Vd
V2
L
∞
∫
a2x2
V1
L
----------= =
UIΔ x1 Uid U–( )1 x2 Uid U–( )2+=
UIΔ
a1x1
V2
L
----------
a2x2
V1
L
----------+=
V∂
∂P
⎝ ⎠
⎛ ⎞
T
RT
V b–( )2
-------------------– 2a
V 3
-----+=
V∂
∂P
⎝ ⎠
⎛ ⎞
T
V b 0≅– or V b≅
UIΔ
a1x1
b1
----------
a2x2
b2
----------+=3-113
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ThIt follows that:
And since two ideal gases are being mixed,
Again, it is assumed that the van der Waals equation applies.
Using the simple mixing rules for the van der Waals equation:
Finally, after some manipulation:
and:
(3.295)
(3.296)
(3.297)
(3.298)
(3.299)
(3.300)
UIIΔ 0=
UIIIΔ
amix
bmix
----------–=
amix xixj aiaj∑∑ x1
2a1 x2
2a2 2x1x2 a1a2+ += =
bmix xi
i 1=
nc
∑ bi x1b1 x2b2+= =
GE x1x2b1b2
x1b1 x2b2+
----------------------------
a1
b1
---------
a2
b2
---------–
⎝ ⎠
⎜ ⎟
⎛ ⎞
2
=
γ1ln A
1 A
B
---x1
x2
----+
2
--------------------------=
γ2ln B
1 B
A
---x2
x1
----+
2
--------------------------=3-114
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Thwhere:
Two important features that are evident from the activity 
coefficient equations are that the log of the activity coefficient is 
proportional to the inverse of the absolute temperature, and 
that the activity coefficient of a component in a mixture is 
always greater than one. The quantitative agreement of the van 
Laar equation is not good, mainly due to the use of the van der 
Waals equation to represent the behaviour of the condensed 
phase, and the poor mixing rules for the mixture. 
If one uses the van Laar equation to correlate experimental data 
(regarding the A and B parameters as purely empirical), good 
results are obtained even for highly non-ideal systems. One 
well-known exception is when one uses the van Laar equation to 
correlate data for self-associating mixtures like alcohol-
hydrocarbon.
Application of the van Laar Equation
The van Laar equation was the first Gibbs excess energy 
representation with physical significance. The van Laar equation 
is a modified form of that described in "Phase Equilibrium in 
Process Design" by Null. This equation fits many systems quite 
well, particularly for LLE component distributions. It can be used 
for systems that exhibit positive or negative deviations from 
Raoult's Law, however, it cannot predict maximas or minimas in 
the activity coefficient. Therefore, it generally performs poorly 
for systems with halogenated hydrocarbons and alcohols. Due to 
the empirical nature of the equation, caution should be 
exercised in analyzing multi-component systems. It also has a 
tendency to predict two liquid phases when they do not exist.
(3.301)
A
b1
RT
------
a1
b1
---------
a2
b2
---------–
⎝ ⎠
⎜ ⎟
⎛ ⎞
=
B
b2
RT
------
a1
b1
---------
a2
b2
---------–
⎝ ⎠
⎜ ⎟
⎛ ⎞
=
Ethanol: Tc=513.9 K
Pc=6147 kPa
a=1252.5 l2/
gmol2
b=0.087 l2/
gmol2
Water: Tc=647.3 K
Pc=22120 kPa
a=552.2 l2/
gmol2
b=0.030 l2/
gmol2
System: T = 25 C
Aij = 4.9763-115
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ThThe van Laar equation has some advantages over the other 
activity models in that it requires less CPU time and can 
represent limited miscibility as well as three-phase equilibrium.
Property Methods
A quick reference of calculation methods is shown in the table 
below for the van Laar model.
The calculation methods from the table are described in the 
following sections.
Calculation Method
Applicable 
Phase
Property Class Name
Activity coefficient Liquid COTHVanLaarLnActivityCoeff Class
Fugacity coefficient Liquid COTHVanLaarLnFugacityCoeff 
Class
Fugacity Liquid COTHVanLaarLnFugacity Class
Activity coefficient 
differential wrt 
temperature
Liquid COTHVanLaarLnActivityCoeffDT 
Class
Excess Gibbs Liquid COTHVanLaarExcessGibbsEnergy 
Class
Excess enthalpy Liquid COTHVanLaarExcessEnthalpy Class
Enthalpy Liquid COTHVanLaarEnthalpy Class
Gibbs energy Liquid COTHVanLaarGibbsEnergy Class
The Van Laar equation also 
performs poorly for dilute 
systems and cannot 
represent many common 
systems, such as alcohol-
hydrocarbon mixtures, 
with acceptable accuracy.3-116
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Thvan Laar Ln Activity Coefficient
This method calculates the activity coefficient of components, i, 
using the van Laar activity model. The extended, multi-
component form of the van Laar equation is shown in the 
following relation:
where:  γi = activity coefficient of component i
xi = mole fraction of component i
where: T = temperature (K)
n = total number of components
aij = non-temperature-dependent energy parameter between 
components i and j
bij = temperature-dependent energy parameter between 
components i and j [1/K]
aji = non-temperature-dependent energy parameter between 
components j and i
bji = temperature-dependent energy parameter between 
components j and i [1/K]
(3.302)
(3.303)
(3.304)
Ei = -4.0 if AiBi < 0.0, otherwise 0.0
(3.305)
γiln Ai 1.0 zi–[ ]2 1.0 Eizi+( )=
Ai xj
aij bijT+( )
1.0 xi–( )
--------------------------
j 1=
n
∑=
Bi xj
aji bjiT+( )
1.0 xi–( )
--------------------------
j 1=
n
∑=
zi
Aixi
Aixi Bi 1.0 xi–( )+[ ]
------------------------------------------------=
The four adjustable 
parameters for the Van 
Laar equation are the aij, 
aji, bij, and bji terms. The 
equation will use stored 
parameter values stored 
or any user-supplied value 
for further fitting the 
equation to a given set of 
data.3-117
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ThProperty Class Name and Applicable Phases
van Laar Ln Fugacity Coefficient
This method calculates the fugacity coefficient of components 
using the van Laar activity model. The fugacity coefficient of 
component i, φi, is calculated from the following relation.
where: γi = activity coefficient of component i
P = pressure
fi = standard state fugacity
Property Class Name and Applicable Phases
Property Class Name Applicable Phase
COTHVanLaarLnActivityCoeff Class Liquid
(3.306)
Property Class Name Applicable Phase
COTHVanLaarLnFugacityCoeff Class Liquid
The term, ln γi, in the above equation is exclusively 
calculated using the van Laar Ln Activity Coefficient. For the 
standard fugacity, fi 
std, refer to Section 5.4 - Standard State 
Fugacity.
φln i ln γi
fi
std
P
-------
⎝ ⎠
⎜ ⎟
⎛ ⎞
=
3-118
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Thvan Laar Ln Fugacity
This method calculates the fugacity of components using the 
van Laar activity model. The fugacity of component i, fi, is 
calculated from the following relation.
where: γi = activity coefficient of component i
fi 
std = standard state fugacity
xi = mole fraction of component i
Property Class Name and Applicable Phases
(3.307)
Property Class Name Applicable Phase
COTHVanLaarLnFugacity Class Liquid
The term, lnγi, in the above equation is exclusively calculated 
using the van Laar Ln Activity Coefficient. For the standard 
fugacity, fi 
std, refer to Section 5.4 - Standard State Fugacity.
ln fi ln γixifi
std( )=3-119
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Thvan Laar Activity Coefficient 
Differential wrt Temperature
This method calculates the activity coefficient differential wrt to 
temperature using the van Laar model from the following 
relation.
where:
Property Class Name and Applicable Phases
(3.308)
Property Class Name Applicable Phase
COTHVanLaarLnActivityCoeffDT Class Liquid
d γiln
dT
------------ 1 zi–( )2 1 Eizi+( )
dAi
dT
------- 2Ai 1 zi–( ) 1 Ezi+( )
dzi
dT
------– A 1 zi–( )2Ei
dzi
dT
------+=
dAi
dT
-------
xjbij
1 xi–
------------
j 1=
n
∑=
dBi
dT
-------
xjbji
1 xi–
------------
j 1=
n
∑=
dZi
dT
-------
xi 1 xi–( )
dAi
dT
------- Bi
dBi
dT
------- Ai–⎝ ⎠
⎛ ⎞
Aixi Bi 1 xi–( )+[ ]2
--------------------------------------------------------------=3-120
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Thvan Laar Excess Gibbs Energy
This method calculates the excess Gibbs energy using the van 
Laar activity model from the following relation.
where: γi = activity coefficient of component i
xi = mole fraction of component i
Property Class Name and Applicable Phases
van Laar Gibbs Energy
This method calculates the Gibbs free energy using the van Laar 
activity model from the following relation.
where: GE = excess Gibbs energy
xi = mole fraction of component i
Gi = Gibbs energy of component i 
(3.309)
Property Class Name Applicable Phase
COTHVanLaarExcessGibbsEnergy 
Class
Liquid
The term, ln γi, in the above equation is exclusively 
calculated using the van Laar Ln Activity Coefficient.
(3.310)
GE RT xi γiln
i
n
∑=
G xiGi RT xi xi GE+ln
i
n
∑+
i
n
∑=3-121
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ThProperty Class Name and Applicable Phases
van Laar Excess Enthalpy
This method calculates the excess enthalpy using the van Laar 
activity model from the following relation.
where: γi = activity coefficient of component i
xi = mole fraction of component i
Property Class Name and Applicable Phases
Property Class Name Applicable Phase
COTHVanLaarGibbsEnergy Class Liquid
The term, GE, in the above equation is exclusively calculated 
using the van Laar Excess Gibbs Energy.
(3.311)
Property Class Name Applicable Phase
COTHVanLaarExcessEnthalpy Class Liquid
The term, , in the above equation is exclusively 
calculated using the van Laar Activity Coefficient Differential 
wrt Temperature.
HE RT2 xi
d γiln
dT
------------
i
n
∑–=
d γiln
dT
------------3-122
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Thvan Laar Enthalpy
This method calculates the enthalpy using the van Laar activity 
model from the following relation.
where: ΗΕ= excess enthalpy
xi = mole fraction of component i
Hi = enthalpy of component i
Property Class Name and Applicable Phases
3.2.4 Margules Model
The Margules equation was the first Gibbs excess energy 
representation developed. The equation does not have any 
theoretical basis, but is useful for quick estimates and data 
interpolation. The software has an extended multi-component 
Margules equation with up to four adjustable parameters per 
binary.
The four adjustable parameters for the Margules equation are 
the aij and aji (temperature independent) and the bij and bji 
terms (temperature dependent). The equation will use stored 
parameter values or any user-supplied value for further fitting 
the equation to a given set of data.
(3.312)
Property Class Name Applicable Phase
COTHVanLaarEnthalpy Class Liquid
The term, HE, in the above equation is exclusively calculated 
using the van Laar Ln Activity Coefficient.
H xiHi HE+
i
n
∑=
This equation should not 
be used for extrapolation 
beyond the range over 
which the energy 
parameters have been 
fitted.3-123
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ThProperty Methods
A quick reference of calculation methods is shown in the table 
below for the Margules property model.
The calculation methods from the table are described in the 
following sections.
Margules Ln Activity Coefficient
This method calculates the activity coefficient for components, i, 
using the Margules activity model from the following relation: 
where: γi = activity Coefficient of component i
xi = mole fraction of component i
Calculation Method
Applicable 
Phase
Property Class Name
Activity Coefficient Liquid COTHMargulesLnActivityCoeff 
Class
Fugacity coefficient 
calculation 
Liquid COTHMargulesLnFugacityCoeff 
Class
Fugacity calculation Liquid COTHMargulesLnFugacity Class
Activity coefficient 
differential wrt 
temperature
Liquid COTHMargulesLnActivityCoeffDT 
Class
Excess Gibbs Liquid COTHMargulesExcessGibbsEnergy 
Class
Excess enthalpy Liquid COTHMargulesExcessEnthalpy 
Class
Enthalpy Liquid COTHMargulesEnthalpy Class
Gibbs energy Liquid COTHMargulesGibbsEnergy Class
(3.313)
(3.314)
γiln 1.0 xi–[ ]2 Ai 2xi Bi Ai–( )+[ ]=
Ai xj
aij bijT+( )
1.0 xi–( )
--------------------------
j 1=
n
∑=3-124
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Thwhere: T = temperature (K)
n = total number of components
aij = non-temperature-dependent energy parameter between 
components i and j
bij = temperature-dependent energy parameter between 
components i and j [1/K]
aji = non-temperature-dependent energy parameter between 
components j and i
bji = temperature-dependent energy parameter between 
components j and i [1/K]
Property Class Name and Applicable Phases
Margules Ln Fugacity Coefficient
This method calculates the fugacity coefficient of components 
using the Margules activity model. The fugacity coefficient of 
component i,  φi, is calculated from the following relation.
where: γi = activity coefficient of component i
fi = standard state fugacity
(3.315)
Property Class Name Applicable Phase
COTHMargulesLnActivityCoeff 
Class
Liquid
(3.316)
Bi xj
aji bjiT+( )
1.0 xi–( )
--------------------------
j 1=
n
∑=
φln i ln γi
fi
std
P
-------
⎝ ⎠
⎜ ⎟
⎛ ⎞
=
3-125
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ThProperty Class Name and Applicable Phases 
Margules Fugacity
This method calculates the fugacity logarithm of components 
using Margules activity model. The fugacity of component i, fi, is 
calculated from the following relation.
where: γi = activity coefficient of component i
fi 
std = Standard state fugacity
xi = mole fraction of component i
Property Class Name and Applicable Phases
Property Class Name Applicable Phase
COTHMargulesLnFugacityCoeff 
Class
Liquid
The term, lnγi, in the above equation is exclusively calculated 
using the Margules Ln Activity Coefficient. For the standard 
fugacity, fi 
std, refer to Section 5.4 - Standard State Fugacity.
(3.317)
Property Class Name Applicable Phase
COTHMargulesLnFugacity Class Liquid
The term, lnγi, in the above equation is exclusively calculated 
using the Margules Ln Activity Coefficient. For the standard 
fugacity, fi 
std, refer to Section 5.4 - Standard State Fugacity.
ln fi ln γixifi
std( )=3-126
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ThMargules Activity Coefficient 
Differential wrt Temperature
This method calculates the activity coefficient wrt to 
temperature from the following relation.
Property Class Name and Applicable Phases
Margules Excess Gibbs Energy
This method calculates the excess Gibbs energy using the 
Margules activity model from the following relation.
where: γi = activity coefficient of component i
xi = mole fraction of component i
(3.318)
Property Class Name Applicable Phase
COTHMargulesLnActivityCoeffDT 
Class
Liquid
(3.319)
∂ γiln
∂T
------------
GE RT xi γiln
i
n
∑=3-127
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ThProperty Class Name and Applicable Phases
Margules Gibbs Energy
This method calculates the Gibbs free energy using the Margules 
activity model from the following relation.
where: GE = excess Gibbs energy
xi = mole fraction of component i
Gi = Gibbs energy of component i 
Property Class Name and Applicable Phases
Property Class Name Applicable Phase
COTHMargulesExcessGibbsEnergy 
Class
Liquid
The term, ln γi, in the above equation is exclusively 
calculated using the Margules Ln Activity Coefficient.
(3.320)
Property Class Name Applicable Phase
COTHMargulesGibbsEnergy Class Liquid
The term, GE, in the above equation is exclusively calculated 
using the Margules Excess Gibbs Energy.
G xiGi RT xi xi GE+ln
i
n
∑+
i
n
∑=3-128
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ThMargules Excess Enthalpy
This method calculates the excess enthalpy using the Margules 
activity model from the following relation.
where: γi = activity coefficient of component i
xi = mole fraction of component i
Property Class Name and Applicable Phases
Margules Enthalpy
This method calculates the enthalpy using the Margules activity 
model from the following relation.
where: ΗΕ= excess enthalpy
xi = mole fraction of component i
Hi = enthalpy of component i
(3.321)
Property Class Name Applicable Phase
COTHMargulesExcessEnthalpy Class Liquid
The term, , in the above equation is exclusively 
calculated using the Margules Activity Coefficient Differential 
wrt Temperature.
(3.322)
HE RT2 xi
d γiln
dT
------------
i
n
∑–=
d γiln
dT
------------
H xiHi HE+
i
n
∑=3-129
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ThProperty Class Name and Applicable Phases
3.2.5  Wilson Model
The 20Wilson (1964) equation is based on the Flory-Huggins 
theory, assuming that intermolecular interactions are negligible. 
First, imagine that the liquid mixture can be magnified to a point 
where molecules of type 1 and type 2 in a binary mixture can be 
visualized. Consider molecules of type 1, and determine the 
ratio of the probability of finding a molecule of type 2 over the 
probability of finding a molecule of type 1 in the surrounding of 
this particular molecule of type 1.
Wilson proposed that:
The parameters a21 and a11 are related to the potential energies 
of the 1-1 and 1-2 pairs of molecules. Similarly, to see what is 
happening in the region of a specific molecule of type 2, you 
have:
Property Class Name Applicable Phase
COTHMargulesEnthalpy Class Liquid
The term, HE, in the above equation is exclusively calculated 
using the Margules Excess Enthalpy.
(3.323)
(3.324)
x21
x11
------
x2
a21
RT
-------–⎝ ⎠
⎛ ⎞exp
x1
a11
RT
-------–⎝ ⎠
⎛ ⎞exp
-------------------------------=
x12
x22
------
x1
a12
RT
-------–⎝ ⎠
⎛ ⎞exp
x2
a22
RT
-------–⎝ ⎠
⎛ ⎞exp
-------------------------------=3-130
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ThWilson defined the local volume fractions based on the two 
equations above, using the pure component molar volumes as 
weights:
When the above relations for φ are substituted into the Flory-
Huggins equation:
where:  
and:
The Wilson equation, although fundamentally empirical, 
provides a fair description of how real liquid systems behave. 
Also, it is a powerful framework for regression and extension of 
experimental data. Of primary importance, the Wilson equation 
can be extended to multi-component mixtures without the use 
of simplifications (as in the case of van Laar and Margules) or 
ternary or higher parameters. In other words, if one has the λij - 
λii parameters for all binaries in a multi-component mixture, the 
Wilson equation can be used to model the multi-component 
behaviour. 
(3.325)
(3.326)
(3.327)
(3.328)
φ1
V1x11
V1x11 V2x21+
----------------------------------= φ2
V2x22
V1x12 V2x22+
----------------------------------=
φi is the volume fraction of 
component i.
GE
RT
------ xi
φi
xi
----⎝ ⎠
⎛ ⎞ln∑= GE
RT
------ x1 x1 Λ12x2+( ) x2 x2 Λ21x1+( )ln–ln–=
Λ12
V2
V1
-----
λ12
RT
-------–⎝ ⎠
⎛ ⎞exp=
Λ21
V1
V2
-----
λ21
RT
-------–⎝ ⎠
⎛ ⎞exp=
γ1ln x1 Λ12x2+( ) x2
Λ12
x1 Λ12x2+
-------------------------
Λ21
x2 Λ21x1+
-------------------------–+ln–=
γ2ln x2 Λ21x1+( ) x1
Λ12
x1 Λ12x2+
-------------------------
Λ21
x2 Λ21x1+
-------------------------–+ln–=3-131
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ThThis is very important, since multi-component data are rather 
scarce and tedious to collect and correlate. In the same way that 
the CS correlation opened the doors for VLE modeling of fairly 
complex hydrocarbon systems, the Wilson equation enabled the 
systematic modeling of fairly complex non-ideal systems. 
However, one still has to measure the VLE behaviour to obtain 
the binary parameters. Only in very specific situations can the 
parameters be generalized (30Orye and Prausnitz, 1965). 
Perhaps more importantly, the Wilson equation can not predict 
phase splitting, thus it cannot be used for LLE calculations. An 
empirical additional parameter proposed by Wilson to account 
for phase splitting did not find wide acceptance, since it cannot 
be easily extended for multi-component mixtures. An interesting 
modification of the Wilson equation to account for phase 
splitting is the one by Tsuboka and Katayama, as described in 
the 21Walas (1985).
To extend the applicability of the Wilson equation
It is modeled as a simple linear function of temperature:
(3.329)
(3.330)
aij Λi j Λj i–=
aij bij cijT+=3-132
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ThApplication of Wilson Equation
The Wilson equation was the first activity coefficient equation 
that used the local composition model to derive the excess 
Gibbs energy expression. It offers a thermodynamically 
consistent approach to predicting multi-component behaviour 
from regressed binary equilibrium data. Experience also shows 
that the Wilson equation can be extrapolated with reasonable 
confidence to other operating regions with the same set of 
regressed energy parameters. 
Although the Wilson equation is more complex and requires 
more CPU time than either the van Laar or Margules equations, 
it can represent almost all non-ideal liquid solutions 
satisfactorily, except electrolytes and solutions exhibiting limited 
miscibility (LLE or VLLE). It provides an excellent prediction of 
ternary equilibrium using parameters regressed from binary 
data only. The Wilson equation will give similar results as the 
Margules and van Laar equations for weak non-ideal systems, 
but consistently outperforms them for increasingly non-ideal 
systems. 
The Wilson equation used in this program requires two to four 
adjustable parameters per binary. The four adjustable 
parameters for the Wilson equation are the aij and aji 
(temperature independent) terms, and the bij and bji terms 
(temperature dependent). Depending upon the available 
information, the temperature dependent parameters may be set 
to zero. Although the Wilson equation contains terms for 
temperature dependency, caution should be exercised when 
extrapolating. 
Setting all four parameters to zero does not reduce the 
binary to an ideal solution, but maintains a small effect due 
to molecular size differences represented by the ratio of 
molar volumes.3-133
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ThProperty Methods
A quick reference of calculation methods is shown in the table 
below for the Wilson property model.
The calculation methods from the table are described in the 
following sections.
Wilson Ln Activity Coefficient
This method calculates the activity coefficient for components, i, 
using the Wilson activity model from the following relation.
Calculation 
Method
Applicable 
Phase
Property Class Name
Activity Coefficient Liquid COTHWilsonLnActivityCoeff Class
Fugacity coefficient 
calculation 
Liquid COTHWilsonLnFugacityCoeff Class
Fugacity calculation Liquid COTHWilsonLnFugacity Class
Activity coefficient 
differential wrt 
temperature
Liquid COTHWilsonLnActivityCoeffDT 
Class
Excess Gibbs Liquid COTHWilsonExcessGibbsEnergy 
Class
Excess enthalpy Liquid COTHWilsonExcessEnthalpy Class
Enthalpy Liquid COTHWilsonEnthalpy Class
Gibbs energy Liquid COTHWilsonGibbsEnergy Class
(3.331)γiln 1.0 xj Λij
j 1=
n
∑ln–
xk Λki
xk Λkj
j 1=
n
∑
----------------------
k 1=
n
∑–=3-134
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Thwhere:  γi = Activity coefficient of component i
xi = Mole fraction of component i 
T = Temperature (K)
n = Total number of components
aij = Non-temperature dependent energy parameter between 
components i and j (cal/gmol)
bij = Temperature dependent energy parameter between 
components i and j (cal/gmol-K)
Vi = Molar volume of pure liquid component i in m3/kgmol 
(litres/gmol)
Property Class Name and Applicable Phases
Property Class Name Applicable Phase
COTHWilsonLnActivityCoeff Class Liquid
This method uses the Henry’s convention for non-
condensable components. 
Λij
Vj
Vi
----
aij bijT+( )
RT
--------------------------–exp=3-135
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ThWilson Fugacity Coefficient
This method calculates the fugacity coefficient of components 
using the Wilson activity model. The fugacity coefficient of 
component i,  φi, is calculated from the following relation.
where: γi = activity coefficient of component i
P = Pressure
fi = Standard state fugacity
Property Class Name and Applicable Phases
(3.332)
Property Class Name Applicable Phase
COTHWilsonLnFugacityCoeff Class Liquid
The term, ln γi, in the above equation is exclusively 
calculated using the Wilson Ln Activity Coefficient. For the 
standard fugacity, fi 
std, refer to Section 5.4 - Standard State 
Fugacity.
φln i ln γi
fi
std
P
-------
⎝ ⎠
⎜ ⎟
⎛ ⎞
=
3-136
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ThWilson Fugacity
This method calculates the fugacity of components using the 
Wilson activity model. The fugacity of component i, fi, is 
calculated from the following relation.
where: γi = activity coefficient of component i
fi 
std = Standard state fugacity
xi = mole fraction of component i
Property Class Name and Applicable Phases
Wilson Activity Coefficient 
Differential wrt Temperature
This method calculates the activity coefficient wrt to 
temperature from the following relation.
(3.333)
Property Class Name Applicable Phase
COTHWilsonLnFugacity Class Liquid
The term, ln γi, in the above equation is exclusively 
calculated using the Wilson Ln Activity Coefficient. For the 
standard fugacity, fi 
std, refer to Section 5.4 - Standard State 
Fugacity.
(3.334)
ln fi ln γixifi
std( )=
d γiln
dT
------------
xjdΛij
dT
--------------
j 1=
n
∑
xjΛij
j 1=
n
∑
------------------------–
xk
dΛki
dT
---------- xjΛkj
j 1=
n
∑
⎝ ⎠
⎜ ⎟
⎜ ⎟
⎛ ⎞
xkΛij xj
dΛkj
dT
----------
j 1=
n
∑
⎝ ⎠
⎜ ⎟
⎜ ⎟
⎛ ⎞
–
xjΛkj
j 1=
n
∑
⎝ ⎠
⎜ ⎟
⎜ ⎟
⎛ ⎞ 2
-----------------------------------------------------------------------------------------------
k 1=
n
∑–=3-137
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ThProperty Class Name and Applicable Phases
Wilson Excess Gibbs Energy
This method calculates the excess Gibbs energy using the 
Wilson activity model from the following relation.
where: γi = activity coefficient of component i
xi = mole fraction of component i
T = temperature
R = universal gas constant
Property Class Name and Applicable Phases
Property Class Name Applicable Phase
COTHWilsonLnActivityCoeffDT 
Class
Liquid
(3.335)
Property Class Name Applicable Phase
COTHWilsonExcessGibbsEnergy Class Liquid
The term, ln γi, in the above equation is exclusively 
calculated using the Wilson Ln Activity Coefficient.
GE RT xi γiln
i
n
∑=3-138
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ThWilson Gibbs Energy
This method calculates the Gibbs free energy using the Wilson 
activity model from the following relation.
where: GE = excess Gibbs energy
xi = mole fraction of component i
Gi = Gibbs energy of component i 
Property Class Name and Applicable Phases
(3.336)
Property Class Name Applicable Phase
COTHWilsonGibbsEnergy Class Liquid
The term, GE, in the above equation is exclusively calculated 
using the Wilson Excess Gibbs Energy.
G xiGi RT xi xi GE+ln
i
n
∑+
i
n
∑=3-139
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ThWilson Excess Enthalpy
This method calculates the excess enthalpy using the Wilson 
activity model from the following relation.
where: γi = activity coefficient of component i
xi = mole fraction of component i
Property Class Name and Applicable Phases
Wilson Enthalpy
This method calculates the enthalpy using the Wilson activity 
model from the following relation.
where: ΗΕ= excess enthalpy
xi = mole fraction of component i
Hi = enthalpy of component i
(3.337)
Property Class Name Applicable Phase
COTHWilsonExcessEnthalpy Class Liquid
The term, , in the above equation is exclusively 
calculated using the Wilson Activity Coefficient Differential 
wrt Temperature.
(3.338)
HE RT2 xi
d γiln
dT
------------
i
n
∑–=
d γiln
dT
------------
H xiHi HE+
i
n
∑=3-140
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ThProperty Class Name and Applicable Phases
3.2.6 NRTL Model
The Wilson equation is very successful in the representation of 
VLE behaviour of completely miscible systems, but is not 
theoretically capable of predicting VLE and LLE. 22Renon and 
Prausnitz (1968) developed the Non-Random Two-Liquid 
Equation (NRTL). In developing the NRTL, they used the quasi-
chemical theory of Guggenheim and the two-liquid theory from 
Scott. To take into account the "structure" of the liquid 
generated by the electrostatic force fields of individual 
molecules, the local composition expression suggested by 
Wilson is modified:
where: α12 = is a parameter which characterizes the non-randomness 
of the mixture.
x = is mole fraction of component
g = is free energies for mixture
Property Class Name Applicable Phase
COTHWilsonEnthalpy Class Liquid
The term, HE, in the above equation is exclusively calculated 
using the Wilson Excess Enthalpy.
(3.339)
(3.340)
x21
x11
------
x2
x1
----
α12g21–
RT
-------------------⎝ ⎠
⎛ ⎞exp
α12g11–
RT
-------------------⎝ ⎠
⎛ ⎞exp
----------------------------------=
x21
x22
------
x1
x2
----
α12g12–
RT
-------------------⎝ ⎠
⎛ ⎞exp
α12g22–
RT
-------------------⎝ ⎠
⎛ ⎞exp
----------------------------------=3-141
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ThThe local model fractions are restricted by material balance to
 x12 + x22 = 1 and x21 + x11 = 1. If the ratios  and  are 
multiplied:
When the material balance equations are substituted:
Scotts Two Liquid Theory
The quasi-chemical theory of Guggenheim with the non-random 
assumption can be written as:
where: Z = is the coordination number
ω = is the energy of interaction between pairs
(3.341)
(3.342)
 Figure 3.3
(3.343)
x21
x11
------
x12
x22
------
x21
x11
------
x12
x22
------× α12
2g12 g11– g22–( )
RT
-------------------------------------------–⎝ ⎠
⎛ ⎞exp=
1 x21–( ) 1 x12–( ) α12
2g12 g11– g22–( )
RT
-------------------------------------------–⎝ ⎠
⎛ ⎞exp x21x12=
Pr
e
ss
ur
e
Pure
Liquid
Liquid
Mixture
Vapourize each liquid
dropping system P to
a very low value
(Ideal Gas)
Compress
Vapour
Mixture
Ideal Gas
Mix Ideal Cases
1 x21–( ) 1 x12–( ) 1
Z
--
2ω12 ω11– ω22–( )
RT
----------------------------------------------–⎝ ⎠
⎛ ⎞exp x21x12=3-142
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Thx = is mole fraction of components
This gives a physical interpretation of the αij parameter. Since 
the coordination number represents the number of neighbour 
molecules a given molecule may have, the usual value is 
somewhere between 6 and 12, giving an α value in the order of 
positive 0.1 to 0.3. The significance of α is somewhat ambiguous 
when its value is greater than 0.3, where a hypothetical fluid 
mixture in which a molecule with very few neighbours should 
exist. The following equations for the local compositions exist:
and
Renon and Prausnitz used the above equations in the two-liquid 
theory of Scott. Scott assumed that a liquid mixture can be 
idealized as a set of cells, in which there are cells with molecules 
of type 1 and type 2 in the centre. "For cells with molecules of 
type 1 in the centre, the residual Gibbs free energy (the Gibbs 
free energy when compared with that of an ideal gas at the 
same temperature, pressure and composition) is the sum of all 
the residual Gibbs free energies for two body interactions 
experienced by centre molecule of type 1" (22Renon and 
Prausnitz, 1968). Thus:
(3.344)
(3.345)
(3.346)
x21
x2 α12
g21 g11–( )
RT
-------------------------–exp
x1 x+ 2 α12
g21 g11–( )
RT
-------------------------–exp
----------------------------------------------------------------------=
x12
x1 α12
g12 g22–( )
RT
-------------------------–exp
x1 x+ 2 α12
g12 g22–( )
RT
-------------------------–exp
----------------------------------------------------------------------=
g 1( ) x11g11 x21g21+=
gpure
1( ) g11=3-143
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ThA molecule of type 2 in the centre can be:
The Gibbs excess energy is the sum of the changes where 
molecules of type 1 from a cell of pure component 1 are 
transferred into the centre of a cell of liquid 2; the same 
reasoning applies for molecule 2. 
Consequently:
substituting and finally:
where: gE is the excess Gibbs free energy
g is Gibbs free energy for interaction between components
and the activity coefficients are:
(3.347)
(3.348)
(3.349)
(3.350)
(3.351)
g 2( ) x22g22 x12g12+=
gpure
2( ) g22=
gE x1 g 1( ) gpure
1( )–( ) x2 g 2( ) gpure
2( )–( )+=
gE x1x21 g21 g11–( ) x2x12 g12 g22–( )+=
γ1ln x2
2 τ21
2α12τ21–( )exp
x1 x2 α12τ21–( )exp+[ ]2
---------------------------------------------------------- τ12
2α12τ12–( )exp
x2 x1 α12τ12–( )exp+[ ]2
----------------------------------------------------------+
⎝ ⎠
⎜ ⎟
⎛ ⎞
=
γ2ln x1
2 τ12
2α12τ12–( )exp
x2 x1 α12τ12–( )exp+[ ]2
---------------------------------------------------------- τ21
2α12τ21–( )exp
x1 x2 α12τ21–( )exp+[ ]2
----------------------------------------------------------+
⎝ ⎠
⎜ ⎟
⎛ ⎞
=
3-144
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Thwhere:
The NRTL equation offers little advantage over Wilson for 
systems that are completely miscible. On the other hand, the 
NRTL equation can be used for systems that will phase split. 
When the gij - gji parameters are temperature dependent, the 
NRTL equation is very flexible and can be used to model a wide 
variety of chemical systems. Although the αij term has a 
physical meaning and 22Renon and Prausnitz (1968) suggested a 
series of rules to fix its value depending on the mixture type, it 
is better treated as an empirical parameter to be determined 
through regression of experimental data. That is, if there is 
enough data to justify the use of 3 parameters. 
The NRTL equation is an extension of the original Wilson 
equation. It uses statistical mechanics and the liquid cell theory 
to represent the liquid structure. These concepts, combined with 
Wilson's local composition model, produce an equation capable 
of representing VLE, LLE and VLLE phase behaviour. Like the 
Wilson equation, the NRTL is thermodynamically consistent and 
can be applied to ternary and higher order systems using 
parameters regressed from binary equilibrium data. It has an 
accuracy comparable to the Wilson equation for VLE systems.
The NRTL combines the advantages of the Wilson and van Laar 
equations, and, like the van Laar equation, it is not extremely 
CPU intensive and can represent LLE quite well. It is important 
to note that because of the mathematical structure of the NRTL 
equation, it can produce erroneous multiple miscibility gaps. 
Unlike the van Laar equation, NRTL can be used for dilute 
systems and hydrocarbon-alcohol mixtures, although it may not 
be as good for alcohol-hydrocarbon systems as the Wilson 
equation.
(3.352)
τ12
g12 g22–
RT
---------------------=
τ21
g21 g11–
RT
---------------------=
g12 α12τ12–( )exp=
g21 α12τ21–( )exp=3-145
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ThProperty Methods
A quick reference of calculation methods is shown in the table 
below for the NRTL property model.
The calculation methods from the table are described in the 
following sections.
Calculation Method
Applicable 
Phase
Property Class Name
Activity Coefficient Liquid COTHNRTLLnActivityCoeff Class
Fugacity coefficient 
calculation 
Liquid COTHNRTLLnFugacityCoeff 
Class
Fugacity calculation Liquid COTHNRTLLnFugacity Class
Activity coefficient 
differential wrt temperature
Liquid COTHNRTLLnActivityCoeffDT 
Class
NRTL temperature 
dependent binary 
interaction parameters
Liquid COTHNRTLTempDep Class
Excess Gibbs Liquid COTHNRTLExcessGibbsEnergy 
Class
Excess enthalpy Liquid COTHNRTLExcessEnthalpy Class
Enthalpy Liquid COTHNRTLEnthalpy Class
Gibbs energy Liquid COTHNRTLGibbsEnergy Class3-146
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ThNRTL Ln Activity Coefficient
This method calculates the activity coefficient for components, i, 
using the NRTL activity model from the following relation:
where:  γi = Activity coefficient of component i
xi = Mole fraction of component i
n = Total number of components
τij = Temperature-dependent energy parameter between 
components i and j (cal/gmol-K)
Property Class Name and Applicable Phases
(3.353)
Property Class Name Applicable Phase
COTHNRTLLnActivityCoeff Class Liquid
This method uses Henry’s convention for non-condensable 
components.
The values Gij and τij are calculated from the temperature 
dependent binary interaction parameters.
γiln
τjixjGji
j 1=
n
∑
xkGki
k 1=
n
∑
---------------------------
xjGij
xkGkj
------------ τi j
τmixmGmi
m 1=
n
∑
xkGkj
k 1=
n
∑
-----------------------------------–
⎝ ⎠
⎜ ⎟
⎜ ⎟
⎜ ⎟
⎜ ⎟
⎜ ⎟
⎜ ⎟
⎛ ⎞
j 1=
n
∑+=3-147
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ThNRTL Fugacity Coefficient
This method calculates the fugacity coefficient of components 
using the NRTL activity model. The fugacity coefficient of 
component i,  φi, is calculated from the following relation.
where: γi = activity coefficient of component i
P = Pressure
fi = Standard state fugacity
Property Class Name and Applicable Phases     
 
NRTL Fugacity
This method calculates the fugacity of components using the 
NRTL activity model. The fugacity of component, fi, is calculated 
from the following relation.
where: γi = activity coefficient of component i
fi 
std = Standard state fugacity
xi = mole fraction of component i
(3.354)
Property Class Name Applicable Phase
COTHNRTLLnFugacityCoeff Class Liquid
The term, lnγi, in the above equation is exclusively calculated 
using the NRTL Ln Activity Coefficient. For the standard 
fugacity, fi 
std, refer to Section 5.4 - Standard State Fugacity.
(3.355)
φln i ln γi
fi
std
P
-------
⎝ ⎠
⎜ ⎟
⎛ ⎞
=
ln fi ln γixifi
std( )=3-148
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ThProperty Class Name and Applicable Phases
NRTL Activity Coefficient Differential 
wrt Temperature
This method analytically calculates the differential activity 
coefficient with respect to temperature from the following 
relation.
Property Class Name and Applicable Phases
Property Class Name Applicable Phase
COTHNRTLLnFugacity Class Liquid
The term, lnγi, in the above equation is exclusively calculated 
using the NRTL Ln Activity Coefficient. For the standard 
fugacity, fi 
std, refer to Section 5.4 - Standard State Fugacity.
(3.356)
Property Class Name Applicable Phase
COTHNRTLLnActivityCoeffDT Class Liquid
d γiln
dT
------------3-149
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ThTemperature Dependent Binary 
Interaction Parameters
This method calculates the temperature dependent binary 
interaction parameters for the NRTL model from the following 
relation.   
where:  
where: aij, bij, cij, dij, eij, = Temperature-dependent energy 
parameter between components i and j (cal/gmol-K)
αij = NRTL non-randomness parameters for binary interaction 
(note that aij = aji for all binaries)
Property Class Name and Applicable Phases
(3.357)
(3.358)
Property Class Name Applicable Phase
COTHNRTLTempDep Class Liquid
τij aij
bij
T
----- cij Tln dijT
eij
T2
-----+ + + +
⎝ ⎠
⎜ ⎟
⎛ ⎞
=
Gij EXP ατij–( )=
α α0 α1T+=
aij 0   bi j 0   cij 0   dij 0   eij 0
τij 0=
=;=;=;=;=3-150
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ThNRTL Excess Gibbs Energy
This method calculates the excess Gibbs energy using the NRTL 
activity model from the following relation.
where: γi = activity coefficient of component i
xi = mole fraction of component i
Property Class Name and Applicable Phases 
NRTL Gibbs Energy
This method calculates the Gibbs free energy NRTL activity 
model from the following relation.
where: GE = excess Gibbs energy
xi = mole fraction of component i
Gi = Gibbs energy of component i 
(3.359)
Property Class Name Applicable Phase
COTHNRTLExcessGibbsEnergy Class Liquid
The term, ln γi, in the above equation is exclusively 
calculated using the NRTL Ln Activity Coefficient.
(3.360)
GE RT xi γiln
i
n
∑=
G xiGi RT xi xi GE+ln
i
n
∑+
i
n
∑=3-151
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ThProperty Class Name and Applicable Phases
NRTL Excess Enthalpy
This method calculates the excess enthalpy using the NRTL 
activity model from the following relation.
where: γi = activity coefficient of component i
xi = mole fraction of component i
Property Class Name and Applicable Phases
Property Class Name Applicable Phase
COTHNRTLGibbsEnergy Class Liquid
The term, GE, in the above equation is exclusively calculated 
using the NRTL Gibbs Energy.
(3.361)
Property Class Name Applicable Phase
COTHNRTLExcessEnthalpy Class Liquid
The term, , in the above equation is exclusively 
calculated using the NRTL Activity Coefficient Differential 
wrt Temperature.
HE RT2 xi
d γiln
dT
------------
i
n
∑–=
d γiln
dT
------------3-152
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ThNRTL Enthalpy
This method calculates the enthalpy using the NRTL activity 
model from the following relation.
where: ΗΕ= excess enthalpy
xi = mole fraction of component i
Hi = enthalpy of component i
Property Class Name and Applicable Phases
(3.362)
Property Class Name Applicable Phase
COTHNRTLEnthalpy Class Liquid
The term, HE, in the above equation is exclusively calculated 
using the NRTL Excess Enthalpy.
H xiHi HE+
i
n
∑=3-153
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Th3.2.7 HypNRTL Model
The methods in the HypNRTL model are same as the Section 
3.2.6 - NRTL Model explained in the previous section. The 
difference between the models is that the HypNRTL does not 
offer a flexible temperature dependence for τij. The HypNRTL is 
represented by the following relation:
xi = Mole fraction of component i
T = Temperature (K)
n = Total number of components
aij = Non-temperature-dependent energy parameter between 
components i and j (cal/gmol)*
bij = Temperature-dependent energy parameter between 
components i and j (cal/gmol-K)*
αij = NRTL non-randomness parameters for binary interaction 
(note that aij = aji for all binaries)
(3.363)
(3.364)
Gij τi jαij–[ ]exp=
τi j
aij bijT+
RT
---------------------=3-154
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ThProperty Methods
A quick reference of calculation methods is shown in the table 
below for the HYPNRTL property model.
3.2.8 The General NRTL Model
The General NRTL model is a variation of the NRTL model. More 
binary interaction parameters are used in defining the 
component activity coefficients. You may apply either model to 
systems:
• with a wide boiling point range between components.
• where you require simultaneous solution of VLE and LLE, and there 
exists a wide boiling point range or concentration range between 
components.
Calculation 
Method
Applicable 
Phase
Property Class Name
Activity Coefficient Liquid COTHHYPNRTLLnActivityCoeff 
Class
Fugacity coefficient 
calculation 
Liquid COTHHYPNRTLLnFugacityCoeff 
Class
Fugacity calculation Liquid COTHHYPNRTLLnFugacity Class
Activity coefficient 
differential wrt 
temperature
Liquid COTHHYPNRTLLnActivityCoeffDT 
Class
Excess Gibbs Liquid COTHHYPNRTLExcessGibbsEnerg
y Class
Excess enthalpy Liquid COTHHYPNRTLExcessEnthalpy 
Class
Enthalpy Liquid COTHHYPNRTLEnthalpy Class
Gibbs energy Liquid COTHHYPNRTLGibbsEnergy Class3-155
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ThWith the General NRTL model, you can specify the format for the 
equations of  τij and aij to be any of the following:
Depending on the form of the equations that you choose, you 
can specify values for the different component energy 
parameters. The General NRTL model provides radio buttons on 
the Binary Coeffs tab which access the matrices for the Aij, Bij, 
Cij, Fij, Gij, Alp1ij and Alp2ij energy parameters.
τij and αij Options
The equations options can 
be viewed in the Display 
Form drop down list on the 
Binary Coeffs tab of the 
Fluid Package property 
view.
τij Aij
Bij
T
------
Cij
T2
------ FijT Gij T( )ln+ + + +=
αij Alp1ij Alp2i jT+=
τij
Aij
Bij
T
------+
RT
-------------------=
αij Alp1i j=
τij Aij
Bij
T
------ FijT Gij T( )ln+ + +=
αij Alp1ij Alp2i jT+=
τij Aij Bijt
Cij
T
------+ +=
αij Alp1ij Alp2i jT+=
where: T is in K and t is °C
τij Aij
Bij
T
------+=
αij Alp1i j=3-156
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Th3.2.9 HYSYS - General NRTL
Method Description Equation
HYSIMStdLiquidVolum
e
Standard Liquid 
Volume
HYSIMLiqDensity Density Hankinson, R.W. and Thompson, G.H., A.I.Ch.E. 
Journal 25, No.4, P. 653, (1979).
HYSIMLiqVolume Volume Hankinson, R.W. and Thompson, G.H., A.I.Ch.E. 
Journal 25, No.4, P. 653, (1979).
GenLiquid1Fug 
Coefficient
Fugacity Coefficient
NRTLActCoeff Activity Coefficient
ActivityLiquid1Fugacit
y
Fugacity
CavettEnthalpy Enthalpy
CavettEntropy Entropy
CavettGibbs Gibbs Free Energy
CavettHelmholtz Helmholtz Energy
CavettInternal Internal Energy
CavettCp Cp
CavettCv Cv
V
MWi
ρi
-------------- xi
i 1=
nc
∑=
φi γi
fi
std
P
---------
⎝ ⎠
⎜ ⎟
⎜ ⎟
⎛ ⎞
=
γiln
τjixjGji
j 1=
n
∑
xkGki
k 1=
n
∑
--------------------------------
xjGij
xkGkj
-------------- τi j
τmixmGmi
m 1=
n
∑
xkGkj
k 1=
n
∑
-------------------------------------------–
⎝ ⎠
⎜ ⎟
⎜ ⎟
⎜ ⎟
⎜ ⎟
⎜ ⎟
⎜ ⎟
⎜ ⎟
⎜ ⎟
⎜ ⎟
⎛ ⎞
j 1=
n
∑+=
fi γixifi
std=
Hl xwaterHwater
steam67 xi H i° ΔHi
Cavett+⎝ ⎠
⎛ ⎞
i
∑+=
Sl xwaterSwater
steam67 xi S° ΔSi
Cavett+⎝ ⎠
⎛ ⎞
i
∑+=
G G° A A°–( ) RT Z 1–( )+ +=
A A° H H°–( ) T S S°–( ) RT Z 1–( )–+ +=
U U° A A°–( ) T S S°–( )+ +=
Cpl xwaterCpwater
steam67 xi Cp i° ΔCpi
Cavett+⎝ ⎠
⎛ ⎞
i
∑+=
Cv Cp R–=3-157
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Th3.2.10 UNIQUAC Model
23Abrams and Prausnitz (1975) derived an equation with a semi-
theoretical basis like NRTL, but using only two adjustable 
parameters per binary pair. Their approach is heavily dependent 
on some statistical mechanics concepts which are outside the 
scope of this guide. Only a few highlights from their work will be 
presented here.
"Guggenheim proposed that a liquid mixture can be seen as a 
set of tri-dimensional lattice sites, the volume in the immediate 
vicinity of a site is called a cell. Each molecule in the liquid is 
divided in segments such that each segment occupies one cell" 
(23Abrams and Prausnitz, 1975). Using the configurational 
partition function, it can be shown that:
where: A = Helmholtz function
n = number of moles
NRTLGe Excess Gibbs free 
energy
MRTLHe Excess enthalpy
HYSIMLiquidViscosity
*
Viscosity Light Hydrocarbons (NBP<155 F) - Modified Ely & 
Hanley (1983)
Heavy Hydrocarbons (NVP>155 F) - Twu (1984)
Non-Ideal Chemicals - Modified Letsou-Stiel (see Reid, 
Prausnitz and Poling, 1987).
HYSIMVapourThermal
K*
Thermal Conductivity Misic and Thodos; Chung et al. methods (see Reid, 
Prausnitz and Poling, 1987).
HYSIMSurfaceTension Surface Tension
Method Description Equation
GE RT xi γiln
i 1=
nc
∑=
HE GE T T∂
∂GE
⎝ ⎠
⎜ ⎟
⎛ ⎞
–=
σ Pc
2
3
--
Tc
1
3
--
Q 1 TR–( )
ab=
(3.365)gE aE≅ AΔ
n1 n2+
---------------- RT x1 x1 x2 x2ln+ln( )–=3-158
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Thx = mole fraction
In the original work of Guggenheim, he assumed that the liquid 
was composed of molecules with relatively the same size; thus 
the number of neighbours of type 2 to a molecule of type 1 was 
a reasonable measure of the local composition.
Since Prausnitz and Abrams proposed to handle molecules of 
different sizes and shapes, they developed a different 
measurement of the local composition, i.e., a local area fraction. 
Using this idea, coupled with some arguments based on 
statistical thermodynamics, they reached the following 
expression for the Gibbs free energy:
and:
where:     
q = parameter proportional to the area
(3.366)
(3.367)
(3.368)
(3.369)
(3.370)
GE Gcombinational
E Gresdiual
E+=
Combinational refers to 
the non-ideality caused by 
differences in size and 
shape (entropic effects).
Gcombinational
E x1
φ1
x1
-----⎝ ⎠
⎛ ⎞ x2
φ2
x2
-----⎝ ⎠
⎛ ⎞ Z
2
-- q1x1
θ1
φ1
-----⎝ ⎠
⎛ ⎞ q2x2
θ2
φ2
-----⎝ ⎠
⎛ ⎞ln+ln⎝ ⎠
⎛ ⎞+ln+ln=
Gresdiual
E q1x1 θ1 θ2τ21+( )ln– q2x2 θ2 θ1τ12+( )ln–=
τ21
u21 u11–
RT
---------------------–⎝ ⎠
⎛ ⎞exp=
τ12
u12 u22–
RT
---------------------–⎝ ⎠
⎛ ⎞exp=
Residual refers to non-
idealities due to energetic 
interactions between 
molecules (temperature or 
energy dependent).
θ1
q1x1
q1x1 q2x2+
----------------------------=
φ1
r1x1
r1x1 r2x2+
--------------------------=
θ2
q2x2
q1x1 q2x2+
----------------------------=
φ2
r2x2
r1x1 r2x2+
--------------------------=3-159
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Thr = parameter proportional to the volume of the individual 
molecules.
And finally, the expressions for the activity coefficients are:
and lnγ2 can be found by interchanging the subscripts. 
As with the Wilson and NRTL equations, the UNIQUAC equation 
is readily expanded for a multi-component system without the 
need for ternary or higher data. Like NRTL, it is capable of 
predicting two liquid phases, but unlike NRTL, it needs only two 
parameters per binary pair. 
One interesting theoretical result from the UNIQUAC equation is 
that it is an equation for which the entropy contributions to the 
Gibbs free energy are separated from the temperature (energy) 
contributions. The idea of looking at the entropy portion based 
on segments of molecules suggests that one can divide a 
molecule into atomic groups and compute the activity coefficient 
as a function of the group. This idea was explored in full by 
24Fredenslund et al (1975, 251977) and is implemented in the 
UNIFAC method.
The UNIQUAC equation has been successfully used to predict 
VLE and LLE behaviour of highly non-ideal systems.
Application of UNIQUAC 
The UNIQUAC (UNIversal QUASI-Chemical) equation uses 
statistical mechanics and the quasi-chemical theory of 
Guggenhiem to represent the liquid structure. The equation is 
capable of representing LLE, VLE and VLLE with accuracy 
comparable to the NRTL equation, but without the need for a 
non-randomness factor. The UNIQUAC equation is significantly 
more detailed and sophisticated than any of the other activity 
(3.371)
γ1ln
φ1
x1
-----⎝ ⎠
⎛ ⎞ Z
2
-- q1
θ1
φ1
-----⎝ ⎠
⎛ ⎞ φ2 l1
r1
r2
----l2–⎝ ⎠
⎛ ⎞ q1 θ1 θ2τ21+( ) θ2q1
τ21
θ1 θ2τ21+
------------------------
τ12
θ2 θ1τ21+
-------------------------–⎝ ⎠
⎛ ⎞+ln–+ln+ln=
l1
Z
2
-- r1 q1–( ) r1 1–( )–=3-160
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Thmodels. Its main advantage is that a good representation of 
both VLE and LLE can be obtained for a large range of non-
electrolyte mixtures using only two adjustable parameters per 
binary. The fitted parameters usually exhibit a smaller 
temperature dependence which makes them more valid for 
extrapolation purposes.
The UNIQUAC equation uses the concept of local composition as 
proposed by Wilson. Since the primary concentration variable is 
a surface fraction as opposed to a mole fraction, it is applicable 
to systems containing molecules of very different sizes and 
shapes, such as polymers. The UNIQUAC equation can be 
applied to a wide range of mixtures containing water, alcohols, 
nitriles, amines, esters, ketones, aldehydes, halogenated 
hydrocarbons and hydrocarbons.
This software uses the following four-parameter extended form 
of the UNIQUAC equation. The four adjustable parameters for 
the UNIQUAC equation are the aij and aji terms (temperature 
independent), and the bij and bji terms (temperature 
dependent). 
The equation uses stored parameter values or any user-supplied 
value for further fitting the equation to a given set of data.3-161
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ThProperty Methods
A quick reference of calculation methods is shown in the table 
below for the UNIQUAC property model.
The calculation methods from the table are described in the 
following sections.
UNIQUAC Ln Activity Coefficient
This method calculates the activity coefficient for components, i, 
using the UNIQUAC activity model from the following relation.
where: γi = Activity coefficient of component i
xi = Mole fraction of component i
T = Temperature (K)
Calculation Method
Applicable 
Phase
Property Class Name
Activity Coefficient Liquid COTHUNIQUACLnActivityCoeff 
Class
Fugacity coefficient 
calculation 
Liquid COTHUNIQUACLnFugacityCoeff 
Class
Fugacity calculation Liquid COTHUNIQUACLnFugacity Class
Activity coefficient 
differential wrt 
temperature
Liquid COTHUNIQUACLnActivityCoeffDT 
Class
Excess Gibbs Liquid COTHUNIQUACExcessGibbsEnergy 
Class
Excess enthalpy Liquid COTHUNIQUACExcessEnthalpy 
Class
Enthalpy Liquid COTHUNIQUACEnthalpy Class
Gibbs energy Liquid COTHUNIQUACGibbsEnergy Class
(3.372)γiln
Φi
xi
-----⎝ ⎠
⎛ ⎞ 0.5Zqi
θi
Φi
-----⎝ ⎠
⎛ ⎞ Li
Φi
xi
-----⎝ ⎠
⎛ ⎞ Ljxj qi 1.0 θjτj i
j 1=
n
∑ln–
⎝ ⎠
⎜ ⎟
⎜ ⎟
⎛ ⎞
qi
θjτji
θkτkj
k 1=
n
∑
----------------------
⎝ ⎠
⎜ ⎟
⎜ ⎟
⎜ ⎟
⎜ ⎟
⎜ ⎟
⎜ ⎟
⎛ ⎞
j 1=
n
∑–+
j 1=
n
∑–+ln+ln=3-162
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Thn = Total number of components
Z = 10.0 (coordination number)
aij = Non-temperature-dependent energy parameter between 
components i and j (cal/gmol)
bij = Temperature-dependent energy parameter between 
components i and j (cal/gmol-K)
qi = van der Waals area parameter - Awi /(2.5x109)
Aw = van der Waals area
ri = van der Waals volume parameter - Vwi /(15.17)
Vw = van der Waals volume
Property Class Name and Applicable Phases
(3.373)
(3.374)
(3.375)
Property Class Name Applicable Phase
COTHUNIQUACLnActivityCoeff 
Class
Liquid
Lj 0.5Z rj qj–( ) rj– 1+=
θi
qixi
qjxj∑
---------------=
τi j
aij bijT+
RT
---------------------–exp=3-163
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ThUNIQUAC Fugacity Coefficient
This method calculates the fugacity coefficient of components 
using the UNIQUAC activity model. The fugacity coefficient of 
component i,  φi, is calculated from the following relation.
where: γi = activity coefficient of component i
fi = Standard state fugacity
Property Class Name and Applicable Phases
(3.376)
Property Class Name Applicable Phase
COTHUNIQUACLnFugacityCoeff 
Class
Liquid
The term, lnγi, in the above equation is exclusively calculated 
using the UNIQUAC Ln Activity Coefficient. For the standard 
fugacity, fi 
std, refer to Section 5.4 - Standard State Fugacity.
φln i ln γi
fi
std
P
-------
⎝ ⎠
⎜ ⎟
⎛ ⎞
=
3-164
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ThUNIQUAC Fugacity
This method calculates the fugacity of components using the 
UNIQUAC activity model. The fugacity of component i, fi, is 
calculated from the following relation.
where: γi = activity coefficient of component i
fi 
std = Standard state fugacity
xi = mole fraction of component i
Property Class Name and Applicable Phases
(3.377)
Property Class Name Applicable Phase
COTHUNIQUACLnFugacity 
Class
Liquid
The term, lnγi, in the above equation is exclusively calculated 
using the UNIQUAC Ln Activity Coefficient. For the standard 
fugacity, fi 
std, refer to Section 5.4 - Standard State Fugacity.
ln fi ln γixifi
std( )=3-165
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ThUNIQUAC Activity Coefficient 
Differential wrt Temperature
This method analytically calculates the differential activity 
coefficient wrt to temperature from the following relation.
Property Class Name and Applicable Phases
(3.378)
Property Class Name Applicable Phase
COTHUNIQUACLnActivityCoeffDT 
Class
Liquid
d γiln
dT
------------3-166
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ThUNIQUAC Excess Gibbs Energy
This method calculates the excess Gibbs energy using the 
UNIQUAC activity model from the following relation.
where: γi = activity coefficient of component i
xi = mole fraction of component i
Property Class Name and Applicable Phases
(3.379)
Property Class Name Applicable Phase
COTHUNIQUACExcessGibbsEnergy 
Class
Liquid
The term, ln γi, in the above equation is exclusively 
calculated using the UNIQUAC Ln Activity Coefficient.
GE RT xi γiln
i
n
∑=3-167
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ThUNIQUAC Gibbs Energy
This method calculates the Gibbs free energy using the 
UNIQUAC activity model from the following relation.
where: GE = excess Gibbs energy
xi = mole fraction of component i
Gi = Gibbs energy of component i 
Property Class Name and Applicable Phases
UNIQUAC Excess Enthalpy
This method calculates the excess enthalpy using the UNIQUAC 
activity model from the following relation.
where: γi = activity coefficient of component i
xi = mole fraction of component i
(3.380)
Property Class Name Applicable Phase
COTHUNIQUACGibbsEnergy Class Liquid
The term, GE, in the above equation is exclusively calculated 
using the UNIQUAC Excess Gibbs Energy.
(3.381)
G xiGi RT xi xi GE+ln
i
n
∑+
i
n
∑=
HE RT2 xi
d γiln
dT
------------
i
n
∑–=3-168
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ThProperty Class Name and Applicable Phases
UNIQUAC Enthalpy
This method calculates the enthalpy using the UNIQUAC activity 
model from the following relation.
where: ΗΕ= excess enthalpy
xi = mole fraction of component i
Hi = enthalpy of component i
Property Class Name and Applicable Phases 
Property Class Name Applicable Phase
COTHUNIQUACExcessEnthalpy Class Liquid
The term, , in the above equation is exclusively 
calculated using the UNIQUAC Activity Coefficient 
Differential wrt Temperature.
(3.382)
Property Class Name Applicable Phase
COTHUNIQUACEnthalpy Class Liquid
The term, HE, in the above equation is exclusively calculated 
using the UNIQUAC Excess Enthalpy.
d γiln
dT
------------
H xiHi HE+
i
n
∑=3-169
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Th3.2.11 UNIFAC Model
For more complex mixtures, 26Wilson and Deal (1962), and 
27Derr and Deal (1969), proposed a group contribution method 
in which the mixture was treated as a solution of atomic groups 
instead of a solution of molecules. The concept of atomic group 
activity, although not new in chemical engineering (28Le Bas, 
1915), was shown to be applicable to the prediction of mixture 
behaviour, thus increasing its utility many times. The Wilson, 
Deal and Derr approach was based on the athermal Flory-
Huggins equation and it found acceptance, especially in Japan 
where it modified to a computer method called ASOG (Analytical 
Solution of Groups) by 29Kojima and Toguichi (1979).
In 1975, 24Fredenslund et al presented the UNIFAC (1975) 
method (UNIQUAC Functional Group Activity Coefficients), in 
which he used the UNIQUAC equation as the basis for the atomic 
group method. In 1977, the UNIFAC group was published in a 
book (1977), which included a thorough description of the 
method by which the atomic group contributions were 
calculated, plus the computer code which performed the activity 
coefficient calculations (including fugacity coefficients using the 
virial equation, vapour phase association and a distillation 
column program). The method found wide acceptance in the 
engineering community and revisions are continuously being 
published to update and extend the original group interaction 
parameter matrix for VLE calculations.
 Figure 3.4
ethanol
ethanol
H2O
H2O
OH
OH
CH2
CH2
CH3CH3
H2O
H2O
Classical
View
Solution of
Groups
Point
of View3-170
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ThAlso, there are specially-developed UNIFAC interaction 
parameter matrices for LLE calculations (31Magnussen et al, 
1981), vapour pressure estimation (32Jensen et al, 1981), gas 
solubility estimation (33Dahl et al, 1991) and polymer properties 
(34Elbro, 1991).
The UNIFAC method has several interesting features:
• Coefficients are based on a data reduction using the 
Dortmund Data Bank (DDB) as a source for VLE data 
points.
• Parameters are approximately independent of 
temperature.
• Area and volume group parameters are readily available.
• Group interaction parameters are available for many 
group combinations.
• The group interaction parameter matrix is being 
continuously updated.
• Gives reasonable predictions between 0 and 150°C, and 
pressures up to a few atmospheres.
• Extensive comparisons against experimental data are 
available, often permitting a rough estimate of errors in 
the predictions.
The original UNIFAC method also has several shortcomings that 
stem from the assumptions used to make it a useful engineering 
tool. Perhaps the most important one is that the group activity 
concept is not correct, since the group area and volume should 
be a function of the position in the molecule, as well as the other 
groups present in the molecule. Also, 35Sandler suggested that 
the original choice of groups might not be optimal (1991a, 
361991b) and sometimes wrong results are predicted.
Also, the original UNIFAC VLE produces wrong LLE predictions 
(which is not surprising). This was remedied by 31Magnussen 
(1981) with the publication of interaction parameter tables for 
LLE calculations. This area has received considerably less 
attention than the VLE, and hopefully new revisions for the LLE 
interaction parameter matrix will appear.3-171
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ThOne more interesting point is that the amk interaction parameter 
term is not, in reality, temperature independent. Thus, serious 
errors can be expected when predicting excess enthalpies. 
There is work being done to extend the applicability and 
reliability of the UNIFAC method, especially in Denmark (1984) 
and Germany (1987). 
The main idea is to modify the amk term to include a temperature 
dependency, in a form such as:
These refinements will probably continue for several years and 
UNIFAC will be continuously updated.
For more complex mixtures, 26Wilson and Deal (1962), and 
27Derr and Deal (1969), proposed a group contribution method 
in which the mixture was treated as a solution of atomic groups 
instead of a solution of molecules. The concept of atomic group 
activity, although not new in chemical engineering (28Le Bas, 
1915), was shown to be applicable to the prediction of mixture 
behaviour, thus increasing its utility many times. 
(3.383)amk amk
0( ) amk
1( )
T
-------- amk
2( ) Tln+ +=3-172
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ThThe Wilson, Deal and Derr approach was based on the athermal 
Flory-Huggins equation and it found acceptance, especially in 
Japan where it modified to a computer method called ASOG 
(Analytical Solution of Groups) by 29Kojima and Toguichi (1979).
 Figure 3.5
ethanol
ethanol
H2O
H2O
OH
OH
CH2
CH2
CH3CH3
H2O
H2O
Classical
View
Solution of
Groups
Point
of View3-173
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ThProperty Methods
A quick reference of calculation methods is shown in the table 
below for the UNIFAC property model.
The calculation methods from the table are described in the 
following sections.
Calculation 
Method
Applicable 
Phase
Property Class Name
Activity Coefficient 
(VLE)
Liquid COTHUNIFAC1_VLELnActivityCoef
f Class
Fugacity coefficient 
calculation (VLE)
Liquid COTHUNIFAC1_VLELnFugacityCoe
ff Class
Fugacity calculation 
(VLE)
Liquid COTHUNIFAC1_VLELnFugacity 
Class
Activity coefficient 
differential wrt 
temperature (VLE)
Liquid COTHUNIFAC1_VLELnActivityCoef
fDT Class
Enthalpy (VLE) Liquid COTHUNIFAC1_VLEEnthalpy Class
Gibbs energy (VLE) Liquid COTHUNIFAC1_VLEGibbsEnergy 
Class
Activity Coefficient 
(LLE)
Liquid COTHUNIFAC1_LLELnActivityCoeff 
Class
Fugacity coefficient 
calculation (LLE)
Liquid COTHUNIFAC1_LLELnFugacityCoe
ff Class
Fugacity calculation 
(LLE)
Liquid COTHUNIFAC1_LLELnFugacity 
Class
Activity coefficient 
differential wrt 
temperature (LLE)
Liquid COTHUNIFAC1_LLELnActivityCoeff
DT Class
Enthalpy (LLE) Liquid COTHUNIFAC1_LLEEnthalpy Class
Gibbs energy (LLE) Liquid COTHUNIFAC1_LLEGibbsEnergy 
Class3-174
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ThUNIFAC Ln Activity Coefficient
This method calculates the activity coefficient for components, i, 
using the UNIFAC activity model from the following relation.
In γi
c is calculated in the same way as for the UNIQUAC 
equation, but the residual part is calculated as follows:
where: k = functional group in the mixture
νk
i = number of atomic groups of type k in molecule i
Γk = residual activity coefficient of the functional group k in 
the actual mixture
Γk
(i) = residual activity coefficient of the functional group k in 
a mixture that contains only molecules i (this is 
necessary to ensure the prediction of γi = 1 for a pure 
liquid)
The summation is extended over all the groups present in the 
mixture. Γk is calculated in a similar manner as  γi
R in the 
UNIQUAC equation:
(3.384)
(3.385)
(3.386)
This relation is from the 
UNIQUAC method γiln γi
cln γi
eln+=
γi
eln vk
i( ) Γk Γk
i( )ln–( )ln
k
∑=
Notice that normalization 
is required to avoid the 
spurious prediction of an 
activity coefficient 
different than one for a 
pure component liquid.
Γkln Qk 1 θmτmk
m
∑⎝ ⎠
⎜ ⎟
⎛ ⎞ θmτmk
θnτnm
n
∑
---------------------
⎝ ⎠
⎜ ⎟
⎜ ⎟
⎜ ⎟
⎜ ⎟
⎛ ⎞
m
∑–ln–=3-175
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Thwhere: θm = area function of group m defined as:
where: xm = mole fraction of component m in the mixture:
where: τmk = group interaction parameter similar to the one defined 
in UNIQUAC:
In which amk = 0 when m = k. Also, the area and volume for the 
molecules are computed by:
where: Rk = van der Waals volume of group k
Qk = van der Waals area of group k
(3.387)
(3.388)
(3.389)
(3.390)
θm
xmQk
θnτnm
n
∑
---------------------=
xm
xmQm
j
∑
θnτnm
n
∑
---------------------=
τmk
vm
j( )xj
vm
j( )xj
n
∑
j
∑
--------------------------=
ri vk
i( )Rk
k
∑= qi vk
i( )Qk
k
∑=3-176
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ThProperty Class Name and Applicable Phases
UNIFAC Fugacity Coefficient
This method calculates the fugacity coefficient of components 
using the UNIFAC activity model. The fugacity coefficient of 
component i,  φi, is calculated from the following relation.
where: γi = activity coefficient of component i
P = Pressure
fi = Standard state fugacity
Property Class Name Applicable Phase
COTHUNIFAC1_VLELnActivityCoeff 
Class
Liquid
COTHUNIFAC1_LLELnActivityCoeff 
Class
Liquid
The UNIFAC VLE model uses the interaction parameters 
which have been calculated from the experimental VLE data, 
whereas, the UNIFAC LLE uses the interaction parameters 
calculated from LLE experimental data. 
(3.391)φln i ln γi
fi
std
P
-------
⎝ ⎠
⎜ ⎟
⎛ ⎞
=
3-177
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ThProperty Class Name and Applicable Phases 
UNIFAC Fugacity
This method calculates the fugacity of components using the 
UNIFAC activity model. The fugacity of component i, fi, is 
calculated from the following relation.
where: γi = activity coefficient of component i
fi 
std = Standard state fugacity
xi = mole fraction of component i
Property Class Name Applicable Phase
COTHUNIFAC1_VLELnFugacityCoeff 
Class
Liquid
COTHUNIFAC1_LLELnFugacityCoeff 
Class
Liquid
The term, lnγi, in the above equation is exclusively calculated 
using the UNIFAC Ln Activity Coefficient. For the standard 
fugacity, fi 
std, refer to Section 5.4 - Standard State Fugacity.
The UNIFAC VLE model uses the interaction parameters 
which have been calculated from the experimental VLE data, 
whereas, the UNIFAC LLE uses the interaction parameters 
calculated from LLE experimental data. 
(3.392)ln fi ln γixifi
std( )=3-178
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ThProperty Class Name and Applicable Phases
UNIFAC Activity Coefficient Differential wrt 
Temperature
This method calculates the activity coefficient wrt to 
temperature from the following relation.
Property Class Name and Applicable Phases
Property Class Name Applicable Phase
COTHUNIFAC1_VLELnFugacity Class Liquid
COTHUNIFAC1_LLELnFugacity Class Liquid
The term, lnγi, in the above equation is exclusively calculated 
using the UNIFAC Ln Activity Coefficient. For the standard 
fugacity, fi 
std, refer to Section 5.4 - Standard State Fugacity.
The UNIFAC VLE model uses the interaction parameters 
which have been calculated from the experimental VLE data, 
whereas, the UNIFAC LLE uses the interaction parameters 
calculated from LLE experimental data.
(3.393)
Property Class Name Applicable Phase
COTHUNIFAC1_VLELnActivityCoeffDT 
Class
Liquid
COTHUNIFA1_LLECLnActivityCoeffDT 
Class
Liquid
The UNIFAC VLE model uses the interaction parameters 
which have been calculated from the experimental VLE data, 
whereas, the UNIFAC LLE uses the interaction parameters 
calculated from LLE experimental data.
d γiln
dT
------------3-179
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ThUNIFAC Gibbs Energy
This method calculates the Gibbs free energy using the UNIFAC 
activity model from the following relation.
where: GE = excess Gibbs energy
xi = mole fraction of component i
Gi = Gibbs energy of component i 
Property Class Name and Applicable Phases
(3.394)
Property Class Name Applicable Phase
COTHUNIFAC1_VLEGibbsEnergy Class Liquid
COTHUNIFAC1_LLEGibbsEnergy Class Liquid
The term, GE, in the above equation is exclusively calculated 
by the UNIQUAC Excess Gibbs Energy.
The UNIFAC VLE model uses the interaction parameters 
which have been calculated from the experimental VLE data, 
whereas, the UNIFAC LLE uses the interaction parameters 
calculated from LLE experimental data.
G xiGi RT xi xi GE+ln
i
n
∑+
i
n
∑=3-180
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ThUNIFAC Enthalpy
This method calculates the enthalpy using the UNIFAC activity 
model from the following relation.
where: ΗΕ= excess enthalpy
xi = mole fraction of component i
Hi = enthalpy of component i
Property Class Name and Applicable Phases
(3.395)
Property Class Name Applicable Phase
COTHUNIFAC1_VLEEnthalpy Class Liquid
COTHUNIFAC1_LLEEnthalpy Class Liquid
The term, HE, in the above equation is exclusively calculated 
by the UNIQUAC Excess Enthalpy.
The UNIFAC VLE model uses the interaction parameters 
which have been calculated from the experimental VLE data, 
whereas, the UNIFAC LLE uses the interaction parameters 
calculated from LLE experimental data.
H xiHi HE+
i
n
∑=3-181
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Th3.2.12 Chien-Null Model
The Chien-Null (CN) model provides a consistent framework for 
applying existing activity models on a binary by binary basis. In 
this manner, the Chien-Null model allows you to select the best 
activity model for each pair in the case.
The Chien-Null model allows three sets of coefficients for each 
component pair, accessible via the A, B and C coefficient 
matrices. Refer to the following sections for an explanation of 
the terms for each of the models.
Chien-Null Form
The Chien-Null generalized multi-component equation can be 
expressed as:
Each of the parameters in this equation are defined specifically 
for each of the applicable activity methods. 
Description of Terms
The Regular Solution equation uses the following:
(3.396)
(3.397)
2 Γi
Lln
Aj i,  xj
j
∑⎝ ⎠
⎜ ⎟
⎛ ⎞
Rj i,  xj
j
∑⎝ ⎠
⎜ ⎟
⎛ ⎞
Sj i,  xj
j
∑⎝ ⎠
⎜ ⎟
⎛ ⎞
Vj i,  xj
j
∑⎝ ⎠
⎜ ⎟
⎛ ⎞
------------------------------------------------------- xk
Aj k,   xj
j
∑⎝ ⎠
⎜ ⎟
⎛ ⎞
Rj k,   xj
j
∑⎝ ⎠
⎜ ⎟
⎛ ⎞
Sj k,  xj
j
∑⎝ ⎠
⎜ ⎟
⎛ ⎞
Vj i,  xj
j
∑⎝ ⎠
⎜ ⎟
⎛ ⎞
------------------------------------------------------------  ⋅
k
∑+=
Ai k,  
Aj k,  xj
j
∑
----------------------
Ri k,  
Rj k,  xj
j
∑
----------------------
Si k,  
Sj k,  xj
j
∑
---------------------–
Vi k,  
Vj k,  xj
j
∑
----------------------–+
Ai j,
vi
L δi δj–( )2
RT
---------------------------= Ri j,
Ai j,
Aj i,
--------= Vi j, Ri j,= Si j, Ri j,=3-182
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Thδi is the solubility parameter in (cal/cm3)½ and vi
L is the 
saturated liquid volume in cm3/mol calculated from:
The van Laar, Margules and Scatchard Hamer use the 
following:
For the van Laar, Margules and Scatchard Hamer equations:
where:  T must be in K
This equation is of a different form than the original van Laar 
and Margules equations in HYSYS, which used an a + bT 
relationship. However, since HYSYS only contains aij values, the 
difference should not cause problems.
The NRTL form for the Chien-Null uses:
The expression for the τ term under the Chien-Null incorporates 
(3.398)
Model Ai,j Ri,j Si,j Vi,j
van Laar
Margules
Scatchard Hamer
(3.399)
vi
L vω i, 5.7 3Tr i,+( )=
γi j,
∞ln Ai j,
Aj i,
-------- Ri j, Ri j,
2 γi j,
∞ln
1
γi j,
∞ln
γj i,
∞ln
----------------
⎝ ⎠
⎜ ⎟
⎛ ⎞
+
-------------------------------
Ai j,
Aj i,
-------- 1 1
2 γi j,
∞ln
1
γi j,
∞ln
γj i,
∞ln
----------------
⎝ ⎠
⎜ ⎟
⎛ ⎞
+
-------------------------------
Ai j,
Aj i,
--------
vi
∞
vj
∞
-----
vi
∞
vj
∞
-----
γi j,
∞ln ai j,
bi j,
T
------- cijT+ +=
(3.400)Ai j, 2τi j, Vi j,= Ri j, 1= Vi j, ci j,– τi j,( )exp= Si j, 1= τi j, ai j,
bi j,
T K( )
-----------+=3-183
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Ththe R term of NRTL into the values for aij and bij. As such, the 
values initialized for NRTL under Chien-Null will not be the same 
as for the regular NRTL. When you select NRTL for a binary pair, 
aij will be empty (essentially equivalent to the regular NRTL bij 
term), bij will be initialized and cij will be the α term for the 
original NRTL, and will be assumed to be symmetric. 
The General Chien-Null equation is:
In all cases:
With the exception of the Regular Solution option, all models 
can use six constants, ai,j, aj,i, bi,j, bj,i, ci,j and cj,i for each 
component pair. For all models, if the constants are unknown 
they can be estimated from the UNIFAC VLE or LLE methods, 
the Insoluble option, or using Henry's Law coefficients for 
appropriate components. For the general Chien-Null model, the 
cij values are assumed to be 1.
(3.401)
(3.402)
Ai j, ai j,
bi j,
T K( )
-----------+= Ri j,
Ai j,
Aj i,
--------= Vi j, Ci j,= Si j, Ci j,=
Ai i, 0= Ri i, Si i, Vi i, 1= = =3-184
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ThProperty Methods
A quick reference of calculation methods is shown in the table 
below for the Chien-Null (CN) property model.
The calculation methods from the table are described in the 
following sections.
Chien-Null Ln Activity Coefficient
Refer to Equation (3.379) to Equation (3.385) for methods 
on calculating the activity coefficient for components, i, using 
the CN activity model.
Property Class Name and Applicable Phases
Calculation Method
Applicable 
Phase
Property Class Name
Activity Coefficient Liquid COTHCNLnActivityCoeff Class
Fugacity coefficient 
calculation 
Liquid COTHCNLnFugacityCoeff Class
Fugacity calculation Liquid COTHCNLnFugacity Class
Activity coefficient 
differential wrt 
temperature
Liquid COTHCNLnActivityCoeffDT 
Class
NRTL temperature 
dependent properties
Liquid COTHNRTLTempDep Class
Excess Gibbs Liquid COTHCNExcessGibbsEnergy 
Class
Excess enthalpy Liquid COTHCNExcessEnthalpy Class
Enthalpy Liquid COTHCNEnthalpy Class
Gibbs energy Liquid COTHCNGibbsEnergy Class
Property Class Name Applicable Phase
COTHCNLnActivityCoeff Class Liquid3-185
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ThChien-Null Fugacity Coefficient
This method calculates the fugacity coefficient of components 
using the CN activity model. The fugacity coefficient of 
component i,  φi, is calculated from the following relation.
where: γi = activity coefficient of component i
fi = Standard state fugacity
Property Class Name and Applicable Phases
Chien-Null Fugacity
This method calculates the fugacity of components using the 
UNIFAC activity model. The fugacity of component i, fi, is 
calculated from the following relation.
where: γi = activity coefficient of component i
fi 
std = Standard state fugacity
xi = mole fraction of component i
(3.403)
Property Class Name Applicable Phase
COTHCNLnFugacityCoeff Class Liquid
The term, lnγi, in the above equation is exclusively calculated 
using the Chien-Null Ln Activity Coefficient. For the standard 
fugacity, fi 
std, refer to Section 5.4 - Standard State Fugacity.
(3.404)
φln i ln γi
fi
std
P
-------
⎝ ⎠
⎜ ⎟
⎛ ⎞
=
ln fi ln γixifi
std( )=3-186
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ThProperty Class Name and Applicable Phases
Chien-Null Activity Coefficient 
Differential wrt Temperature
This method analytically calculates the activity coefficient 
differential wrt to temperature from the following relation.
Property Class Name and Applicable Phases
Property Class Name Applicable Phase
COTHCNLnFugacity Class Liquid
The term, lnγi, in the above equation is exclusively calculated 
using the Chien-Null Ln Activity Coefficient. For the standard 
fugacity, fi 
std, refer to Section 5.4 - Standard State Fugacity.
(3.405)
Property Class Name Applicable Phase
COTHCNLnActivityCoeffDT Class Liquid
∂ γiln
∂T
------------3-187
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ThChien-Null Excess Gibbs Energy
This method calculates the excess Gibbs energy using the CN 
activity model from the following relation.
where: γi = activity coefficient of component i
xi = mole fraction of component i
Property Class Name and Applicable Phases
Chien-Null Gibbs Energy
This method calculates the Gibbs free energy using the CN 
activity model from the following relation.
where: GE = excess Gibbs energy
xi = mole fraction of component i
Gi = Gibbs energy of component i 
(3.406)
Property Class Name Applicable Phase
COTHCNExcessGibbsEnergy Class Liquid
The term, ln γi, in the above equation is exclusively 
calculated using the Chien-Null Ln Activity Coefficient.
(3.407)
GE RT xi γiln
i
n
∑=
G xiGi RT xi xi GE+ln
i
n
∑+
i
n
∑=3-188
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ThProperty Class Name and Applicable Phases
Chien-Null Excess Enthalpy
This method calculates the excess enthalpy using the CN activity 
model from the following relation.
where: γi = activity coefficient of component i
xi = mole fraction of component i
Property Class Name and Applicable Phases
Property Class Name Applicable Phase
COTHCNGibbsEnergy Class Liquid
The term, GE, in the above equation is exclusively calculated 
using the Chien-Null Excess Gibbs Energy.
(3.408)
Property Class Name Applicable Phase
COTHCNExcessEnthalpy Class Liquid
The term, , in the above equation is exclusively 
calculated using the Chien-Null Activity Coefficient 
Differential wrt Temperature.
HE RT2 xi
d γiln
dT
------------
i
n
∑–=
d γiln
dT
------------3-189
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ThChien-Null Enthalpy
This method calculates the enthalpy using the CN activity model 
from the following relation.
where: ΗΕ= excess enthalpy
xi = mole fraction of component i
Hi = enthalpy of component i
Property Class Name and Applicable Phases
(3.409)
Property Class Name Applicable Phase
COTHCNEnthalpy Class Liquid
The term, HE, in the above equation is exclusively calculated 
using the Chien-Null Excess Enthalpy.
H xiHi HE+
i
n
∑=3-190
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Th3.3 Chao-Seader Model
The 47Chao-Seader (CS, 1961) method is an older and semi-
empirical method. This method has also been adopted by and is 
recommended for use in the API Technical Data Book.
Property Class Name and Applicable Phases
The following table gives an approximate range of applicability 
for this method, and under what conditions it is applicable. 
Model Description
Chao-Seader Use this method for heavy hydrocarbons, where the 
pressure is less than 10342 kPa (1500 psia), and 
temperatures range between -17.78 and 260°C (0-
500°F).
Property Class Name Applicable Phase
COTHChaoSeaderLnFugacityCoeff 
Class
Liquid
COTHChaoSeaderLnFugacity Class Liquid
Method Temp. (°C) Temp.  (°C)
Press.  
(psia)
Press. 
(kPa)
CS 0 to 500 18 to 260 < 1,500 < 10,000
Conditions of Applicability
For all hydrocarbons (except 
CH4):
0.5 < Tri < 1.3 and Prmixture < 0.8
If CH4 or H2 is present: • molal average Tr < 0.93 
• CH4 mole fraction < 0.3
• mole fraction dissolved gases < 0.2
When predicting K values for:
Paraffinic or Olefinic Mixtures
Aromatic Mixtures
liquid phase aromatic mole fraction < 
0.5
liquid phase aromatic mole fraction > 
0.53-191
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Th3.4 Grayson-Streed Model
The Grayson-Streed (GS) method is an older, semi-empirical 
method. The GS correlation is an extension of the Chao-Seader 
method with special emphasis on hydrogen. This method has 
also been adopted by and is recommended for use in the API 
Technical Data Book.
Property Class Name and Applicable Phases
The following table gives an approximate range of applicability 
for this method, and under what conditions it is applicable. 
Grayson-Streed 
Model
Description
Grayson-Streed Recommended for simulating heavy hydrocarbon 
systems with a high hydrogen content.
Property Class Name Applicable Phase
COTHGraysonStreedLnFugacityCoeff 
Class
Liquid
COTHGraysonStreedLnFugacity Class Liquid
Method Temp. (°C) Temp.  (°C)
Press.  
(psia)
Press. 
(kPa)
GS 0 to 800 18 to 425 < 3,000 < 20,000
Conditions of Applicability
For all hydrocarbons (except 
CH4):
0.5 < Tri < 1.3 and Prmixture < 0.8
If CH4 or H2 is present: • molal average Tr < 0.93 
• CH4 mole fraction < 0.3
• mole fraction dissolved gases < 0.2
When predicting K values for:
Paraffinic or Olefinic Mixtures
Aromatic Mixtures
liquid phase aromatic mole fraction < 
0.5
liquid phase aromatic mole fraction > 
0.53-192
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ThThe GS correlation is recommended for simulating heavy 
hydrocarbon systems with a high H2 content, such as 
hydrotreating units. The GS correlation can also be used for 
simulating topping units and heavy ends vacuum applications. 
The vapour phase fugacity coefficients are calculated with the 
Redlich Kwong equation of state. The pure liquid fugacity 
coefficients are calculated via the principle of corresponding 
states. Modified acentric factors are included in the library for 
most components. Special functions have been incorporated for 
the calculation of liquid phase fugacities for N2, CO2 and H2S. 
These functions are restricted to hydrocarbon mixtures with less 
than five percent of each of the above components. As with the 
Vapour Pressure models, H2O is treated using a combination of 
the steam tables and the kerosene solubility charts from the API 
data book. This method of handling H2O is not very accurate for 
gas systems. Although three phase calculations are performed 
for all systems, it is important to note that the aqueous phase is 
always treated as pure H2O with these correlations. 3-193
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Th3-194
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Physical Property Calculation Methods 4-1
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Th4   Physical Property 
Calculation Methods4-1
4.1  Cavett Method................................................................................ 2
4.2  Rackett Method.............................................................................. 8
4.3  COSTALD Method ......................................................................... 11
4.4  Viscosity ...................................................................................... 14
4.5  Thermal Conductivity ................................................................... 18
4.6  Surface Tension ........................................................................... 21
4.7  Insoluble Solids ........................................................................... 22
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4-2 Cavett Method
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Th4.1 Cavett Method
Aspen HYSYS Thermodynamics COM Interface uses the three-
parameter corresponding states method to represent the 
enthalpy of a liquid when working with the activity models. 
Water is the only exception which uses the 1967 formulation for 
steam (37McClintock and Silvestri, 1967). For the Cavett method, 
a generalized slope for the liquid enthalpy is correlated using Pc, 
Tc and the Cavett parameter (an empirical constant fitted to 
match the heat of vapourization at the normal boiling point). 
The Cavett parameter may be approximated by the critical 
compressibility factor of a component if no heat of vapourization 
data is available.
Property Methods
A quick reference of calculation methods is shown in the table 
below for the Cavett method.
The calculation methods from the table are described in the 
following sections.
Calculation Method
Phase 
Applicable
Property Class Name
Enthalpy Liquid COTHCavettEnthalpy Class
Entropy Liquid COTHCavettEntropy Class
Isobaric heat capacity Liquid COTHNCavettCp Class
Helmholtz energy Liquid COTHCavettHelmholtz Class
Gibbs energy Liquid COTHCavettGibbs Class
Internal energy Liquid COTHCavettInternalEnergy 
Class4-2
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Physical Property Calculation Methods 4-3
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ThCavett Enthalpy
This method calculates the liquid enthalpy using the Cavett 
model from the following relation.
where: the calculation of the change in Cavett enthalpy is shown 
below
where: i = non-aqueous components
xi = mole fraction of component i
For subcritical, non-hydrocarbon components, the change in 
enthalpy is:
(4.1)
(4.2)
(4.3)
(4.4)
(4.5)
(4.6)
(4.7)
(4.8)
(4.9)
Hl xwaterHwater
steam67 xi H i° ΔHi
Cavett+( )
i
∑+=
ΔHnon aqueous–
cavett min ΔHi
cavett( )xi
i 1 i 1≠;=
nc
∑=
ΔHi
1 Tc i, a1 a2 1 Tr i,–( )e1+( )=
a1 b1 b2χi b3χi
2 b4χi
3+ + +=
a2 b5 b6χi b7χi
2 b8χi
3+ + +=
a9 b9 b10χi b11χi
2 b12χi
3+ + +=
e1 1 a3 Tr i, 0.1–( )–=
ΔHi
2 Tc i, max c1 c2Tr i,
2 c3Tr i,
3 c4Tr i,
4 c5Tr i,
2 0,+ + + +( )( )=
ΔHi
cavett ΔHi
1=4-3
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ThFor subcritical, hydrocarbon components, the change in 
enthalpy is:
For supercritical components, the change in enthalpy is:
Property Class Name and Phases Applicable
Cavett Entropy
This method calculates the liquid entropy using the Cavett 
model from the following relation:
For subcritical, non-hydrocarbon components, the change in 
entropy is:
For subcritical, hydrocarbon components, the change in entropy 
(4.10)
(4.11)
Property Class Name Phase Applicable
COTHCavettEnthalpy Class Liquid
(4.12)
(4.13)
ΔHi
cavett min ΔHi
1 ΔHi
2,( )=
ΔHi
cavett ΔHi
2=
Sl xwaterSwater
steam67 xi S i° ΔSi
Cavett+( )
i
∑+=
ΔSi
cavett ΔHi
1
T
-----------=4-4
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This:
For supercritical components, the change in entropy is:
where: i = non-aqueous components
xi = mole fraction of component i
T = Temperature (K)
Property Class Name and Phases Applicable
Cavett Cp (Isobaric)
This method calculates the liquid isobaric heat capacity using 
the Cavett model from the following relation.
where: i = non-aqueous components
For subcritical hydrocarbons with ΔHi
1>ΔHi
2, the change in heat 
capacity is:  
(4.14)
(4.15)
Property Class Name Phase Applicable
COTHCavettEntropy Class Liquid
(4.16)
(4.17)
ΔSi
cavett min ΔHi
1 ΔHi
2,( )
T
------------------------------------------=
ΔSi
cavett ΔHi
2
T
-----------=
Cpl xwaterCpwater
steam67 xi Cp i° ΔCpi
Cavett+( )
i
∑+=
ΔCpi
cavett Tr i, 2 c2 c5Pr i,+( ) Tr i, 3c3 Tr i, 4c4( )+( )+( )=4-5
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ThFor other subcritical components, the change in heat capacity is:
For supercritical components with ΔHi
2 equal to zero, the change 
in heat capacity is:
For supercritical components with ΔHi
2 different than zero, the 
change in heat capacity is: 
where:
Property Class Name and Phases Applicable
(4.18)
(4.19)
(4.20)
b1 = -67.022001 b7 = -23612.5670 c1 = 10.273695
b2 = 644.81654 b8 = 34152.870 c2 = -1.5594238
b3 = -1613.1584 b9 = 8.9994977 c3 = 0.019399
b4 = 844.13728 b10 = -78.472151 c4 = -0.03060833
b5 = -270.43935 b11 = 212.61128 c5 = -0.168872
b6 = 4944.9795 b12 = -143.59393
Property Class Name Phase Applicable
COTHCavettCp Class Liquid
The term, ΔHi
1, in the above equation is exclusively 
calculated using the Cavett Enthalpy.
ΔCpi
cavett a1
ΔHi
1
Tc i,
-----------–
⎝ ⎠
⎜ ⎟
⎛ ⎞
a3 1 Tr i,–( )
e1
1 Tr i,–
-----------------+⎝ ⎠
⎛ ⎞log⎝ ⎠
⎛ ⎞=
ΔCpi
cavett 0=
ΔCpi
cavett Tr i, 2 c2 c5Pr i,+( ) Tr i, 3c3 Tr i, 4c4( )+( )+( )=4-6
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Physical Property Calculation Methods 4-7
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ThCavett Helmholtz Energy
This method calculates the liquid Helmholtz energy using the 
Cavett model from the following relation.
Property Class Name and Phases Applicable
Cavett Gibbs Energy
This method calculates the liquid Gibbs free energy using the 
Cavett model from the following relation.
where: H = Cavett enthalpy
S = Cavett entropy
(4.21)
Property Class Name Phase Applicable
COTHCavettHelmholtz Class Liquid
The term, G, in the above equation is exclusively calculated 
using the Cavett Gibbs Energy.
(4.22)
A G PV–=
G H TS–=4-7
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4-8 Rackett Method
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ThProperty Class Name and Phases Applicable
Cavett Internal Energy
This method calculates the liquid internal energy using the 
Cavett model from the following relation.
Property Class Name and Phases Applicable
4.2 Rackett Method
Liquid densities and molar volumes can be calculated by 
generalized cubic equations of state, although they are often 
inaccurate and often provide incorrect estimations. Aspen 
HYSYS Thermodynamics COM Interface allows for alternate 
methods of calculating the saturated liquid volumes including 
the Rackett Liquid Density correlations. This method was 
developed by Rackett (1970) and later modified by Spencer and 
Danner.
Property Class Name Phase Applicable
COTHCavettGibbs Class Liquid
The terms, H and S, in the above equation are exclusively 
calculated using the Cavett Enthalpy and Cavett Entropy, 
respectively.
(4.23)
Property Class Name Phase Applicable
COTHCavettInternal Class Liquid
The term, H, in the above equation is exclusively calculated 
using the Cavett Enthalpy.
U H PV–=
Property Packages with 
this option currently 
available:
NRTL-Ideal-Zra
Peng-Robinson-Rackett 
Liq Density4-8
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Physical Property Calculation Methods 4-9
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ThThe Rackett Equation has been found to produce slightly more 
accurate estimations for chemical groups such as acetylenes, 
cycloparaffins, aromatics, flurocarbons, cryogenic liquids, and 
sulfides.
Property Methods
A quick reference of liquid density and volume calculations are 
shown in the table below for the Rackett method.
The calculation methods from the table are described in the 
following sections.
Rackett Liquid Volume
This method calculates the liquid volume using the Rackett 
method from the following relation. 
where: Vs = saturated liquid volume
R = ideal gas constant
Tc & Pc = critical constants for each compound
ZRA = Rackett compressibility factor 
Tr = reduced temperature, T/Tc
Calculation 
Method
Phase 
Applicable
Property Class Name
Liquid Volume Liquid COTHRackettVolume 
Class
Liquid Density Liquid COTHRackettDensity 
Class
(4.24)Vs
RTc
Pc
-------- ZRA
1 1 Tr–( )
2
7
--
+
=
4-9
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4-10 Rackett Method
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ThProperty Class Name and Phases Applicable
Rackett Liquid Density
This method calculates the liquid density using the Rackett 
method from the following relation. 
where: Vs = saturated liquid volume
R = ideal gas constant
Tc & Pc = critical constants for each compound
ZRA = Rackett compressibility factor 
Tr = reduced temperature, T/Tc
Property Class Name and Phases Applicable
Property Class Name Phase Applicable
COTHRackettVolume Class Liquid
The Rackett Compressibility factor (ZRA) is a unique constant 
for each compound and is usually determined from 
experimental data, however if no data is available, Zc can be 
used as an estimate of ZRA.
(4.25)
Property Class Name Phase Applicable
COTHRackettDensity Class Liquid
ρs 1
RTc
Pc
---------⎝ ⎠
⎛ ⎞⁄⎝ ⎠
⎛ ⎞ ZRA
1 1 Tr–( )
2
7
--
+
=
4-10
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Physical Property Calculation Methods 4-11
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Th4.3 COSTALD Method
Saturated liquid volumes are obtained using a corresponding 
states equation developed by 38R.W. Hankinson and G.H. 
Thompson which explicitly relates the liquid volume of a pure 
component to its reduced temperature and a second parameter 
termed the characteristic volume. This method has been 
adopted as an API standard.
The pure compound parameters needed in the corresponding 
states liquid density (COSTALD) calculations are taken from the 
original tables published by Hankinson and Thompson, and the 
API data book for components contained in the HYSYS library. 
The parameters for hypothetical components are based on the 
API gravity and the generalized Lu equation. 
Although the COSTALD method was developed for saturated 
liquid densities, it can be applied to sub-cooled liquid densities 
(i.e., at pressures greater than the vapour pressure), using the 
Chueh and Prausnitz correction factor for compressed fluids. It 
is used to predict the density for all systems whose pseudo-
reduced temperature is below 1.0. Above this temperature, the 
equation of state compressibility factor is used to calculate the 
liquid density. 
38R.W. Hankinson and G.H. Thompson (1979) published a new 
method of correlating saturated densities of liquids and their 
mixtures. This method was superior to its predecessors in that it 
overcame the mathematical discontinuities presented in 
methods by Yen and Woods (1966) and was not limited to pure 
compounds. COSTALD was later successfully applied to 
compressed liquids and liquid mixtures.4-11
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4-12 COSTALD Method
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ThProperty Methods
A quick reference of liquid density and volume calculations are 
shown in the table below for the Rackett method.
The calculation methods from the table are described in the 
following sections.
COSTALD Liquid Volume
This method calculates the liquid volume using the COSTALD 
method for pure compounds:
Calculation 
Method
Phase 
Applicable
Property Class Name
Liquid Volume Liquid COTHCOSTALDVolume Class
Liquid Density Liquid COTHCOSTALDDensity Class
(4.26)
Vs V∗⁄ Vr
o( ) 1 ωSRKVr
δ( )–[ ]=
Vr
o( ) 1 Ak 1 Tr–( )k 3⁄
k 1=
4
∑+= 0.25 Tr 0.95< <
Vr
δ( ) BkTr
k
k 0=
3
∑ Tr 1.00001–( )⁄= 0.25 Tr 1.0< <4-12
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Physical Property Calculation Methods 4-13
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Thand for mixtures:
where: Ak and Bk are constants
V* = the characteristic volume
ωSRK = SRK acentric factor
Tc = critical temperature for each compound
Tr = reduced temperature, T/Tc
Property Class Name and Phases Applicable
(4.27)
Property Class Name Phase Applicable
COTHCOSTALDVolume Class Liquid
Tcm xixjVij∗Tcij
j
∑
i
∑⎝ ⎠
⎜ ⎟
⎛ ⎞
Vm∗⁄=
Vm∗ 1 4⁄ xiVi∗
i
∑ 3 xiVi∗
2
3
--
i
∑
⎝ ⎠
⎜ ⎟
⎜ ⎟
⎛ ⎞
xiVi∗
1
3
--
i
∑
⎝ ⎠
⎜ ⎟
⎜ ⎟
⎛ ⎞
+=
Vij∗Tcij
Vi∗Tci
Vj∗Tcj
( )
1
2
--
=
ωSRKm
xiωSRKi
i
∑=4-13
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4-14 Viscosity
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ThCOSTALD Liquid Density
This method calculates the liquid density using the COSTALD 
method from the following relation. 
where: Vs = saturated liquid volume
Property Class Name and Phases Applicable
4.4 Viscosity
This method will automatically select the model best suited for 
predicting the phase viscosities of the system under study. The 
model selected will be from one of the three available in this 
method: a modification of the NBS method (39Ely and Hanley), 
Twu's model, or a modification of the Letsou-Stiel correlation. 
This method will select the appropriate model using the 
following criteria:
(4.28)
Property Class Name Phase Applicable
COTHCOSTALDDensity Class Liquid
The saturated liquid volume, Vs, is calculated from Equations 
(4.26) and (4.27).
Chemical System Vapour Phase Liquid Phase
Lt Hydrocarbons (NBP < 
155°F)
Mod Ely & Hanley Mod Ely & Hanley
Hvy Hydrocarbons (NBP > 
155°F)
Mod Ely & Hanley Twu
Non-Ideal Chemicals Mod Ely & Hanley Mod Letsou-Stiel
ρ 1
Vs
-----=4-14
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Physical Property Calculation Methods 4-15
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ThAll of the models are based on corresponding states principles 
and have been modified for more reliable application. Internal 
validation showed that these models yielded the most reliable 
results for the chemical systems shown. Viscosity predictions for 
light hydrocarbon liquid phases and vapour phases were found 
to be handled more reliably by an in-house modification of the 
original Ely and Hanley model, heavier hydrocarbon liquids were 
more effectively handled by Twu's model, and chemical systems 
were more accurately handled by an in-house modification of 
the original Letsou-Stiel model. 
A complete description of the original corresponding states 
(NBS) model used for viscosity predictions is presented by Ely 
and Hanley in their NBS publication. The original model has 
been modified to eliminate the iterative procedure for 
calculating the system shape factors. The generalized Leech-
Leland shape factor models have been replaced by component 
specific models. This method constructs a PVT map for each 
component using the COSTALD for the liquid region. The shape 
factors are adjusted such that the PVT map can be reproduced 
using the reference fluid.
The shape factors for all the library components have already 
been regressed and are included in the Pure Component Library. 
Hypocomponent shape factors are regressed using estimated 
viscosities. These viscosity estimations are functions of the 
hypocomponent Base Properties and Critical Properties.
Hypocomponents generated in the Oil Characterization 
Environment have the additional ability of having their shape 
factors regressed to match kinematic or dynamic viscosity 
assays. 
The general model employs CH4 as a reference fluid and is 
applicable to the entire range of non-polar fluid mixtures in the 
hydrocarbon industry. Accuracy for highly aromatic or 
naphthenic crudes will be increased by supplying viscosity 
curves when available, since the pure component property 
generators were developed for average crude oils. The model 
also handles H2O and acid gases as well as quantum gases. 4-15
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4-16 Viscosity
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ThAlthough the modified NBS model handles these systems very 
well, the Twu method was found to do a better job of predicting 
the viscosities of heavier hydrocarbon liquids. The Twu model is 
also based on corresponding states principles, but has 
implemented a viscosity correlation for n-alkanes as its 
reference fluid instead of CH4. A complete description of this 
model is given in the paper entitled "42Internally Consistent 
Correlation for Predicting Liquid Viscosities of Petroleum 
Fractions". 
For chemical systems, the modified NBS model of Ely and 
Hanley is used for predicting vapour phase viscosities, whereas 
a modified form of the Letsou-Stiel model is used for predicting 
the liquid viscosities. This method is also based on 
corresponding states principles and was found to perform 
satisfactorily for the components tested.
The shape factors contained within this methods Pure 
Component Library have been fit to match experimental 
viscosity data over a broad operating range. 
Property Class Name and Phases Applicable
Property Class Name Phase Applicable
COTHViscosity Class Liquid and vapour4-16
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Physical Property Calculation Methods 4-17
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ThLiquid Phase Mixing Rules for 
Viscosity
The estimates of the apparent liquid phase viscosity of 
immiscible Hydrocarbon Liquid - Aqueous mixtures are 
calculated using the following "mixing rules":
• If the volume fraction of the hydrocarbon phase is 
greater than or equal to 0.5, the following equation is 
used51:
where:  μeff = apparent viscosity
μoil = viscosity of Hydrocarbon phase
νoil = volume fraction Hydrocarbon phase
• If the volume fraction of the hydrocarbon phase is less 
than 0.33, the following equation is used52:
where:  μeff = apparent viscosity
μoil = viscosity of Hydrocarbon phase
μH2O= viscosity of Aqueous phase
νoil = volume fraction Hydrocarbon phase
• If the volume of the hydrocarbon phase is between 0.33 
and 0.5, the effective viscosity for combined liquid phase 
is calculated using a weighted average between 
Equation (4.29) and Equation (4.30).
The remaining properties of the pseudo phase are calculated as 
(4.29)
(4.30)
μeff μoile
3.6 1 νoil–( )
=
μeff 1 2.5νoil
μoil 0.4μH2O+
μoil μH2O+
-----------------------------------
⎝ ⎠
⎜ ⎟
⎛ ⎞
+ μH2O=4-17
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4-18 Thermal Conductivity
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Thfollows:
4.5 Thermal Conductivity
As in viscosity predictions, a number of different models and 
component specific correlations are implemented for prediction 
of liquid and vapour phase thermal conductivities. The text by 
Reid, Prausnitz and Poling6 was used as a general guideline in 
determining which model was best suited for each class of 
components. For hydrocarbon systems, the corresponding 
states method proposed by Ely and Hanley39 is generally used. 
The method requires molecular weight, acentric factor and ideal 
heat capacity for each component. These parameters are 
tabulated for all library components and may either be input or 
calculated for hypothetical components. It is recommended that 
all of these parameters be supplied for non-hydrocarbon 
hypotheticals to ensure reliable thermal conductivity coefficients 
and enthalpy departures. 
The modifications to the method are identical to those for the 
viscosity calculations. Shape factors calculated in the viscosity 
routines are used directly in the thermal conductivity equations. 
The accuracy of the method will depend on the consistency of 
the original PVT map.
The Sato-Reidel method is used for liquid phase thermal 
conductivity predictions of glycols and acids, the Latini et al 
method is used for esters, alcohols and light hydrocarbons in the 
range of C3-C7, and the Missenard and Reidel method is used for 
the remaining components.
For vapour phase thermal conductivity predictions, the Misic and 
(4.31)
MWeff xiMWi∑=
ρeff
1
xi
ρi
----⎝ ⎠
⎛ ⎞∑
-----------------=
Cpeff
xiCpi∑=
(molecular weight)
(mixture density)
(mixture specific heat)4-18
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Physical Property Calculation Methods 4-19
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ThThodos, and Chung et al methods are used. The effect of higher 
pressure on thermal conductivities is taken into account by the 
Chung et al method.
Property Class Name and Phases Applicable
Property Class Name Phase Applicable
COTHThermCond Class Liquid and vapour4-19
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4-20 Thermal Conductivity
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ThAs with viscosity, the thermal conductivity for two liquid phases 
is approximated by using empirical mixing rules for generating a 
single pseudo liquid phase property. The thermal conductivity 
for an immiscible binary of liquid phases is calculated by the 
following equation53:
where: λLmix = mixture liquid thermal conductivity at temperature T 
(K)
κij = liquid thermal conductivity of pure component i or j at 
temperature T
λL1 = liquid thermal conductivity of liquid phase 1
λL2 = liquid thermal conductivity of liquid phase 2
φ1 = 
φ2 = 
xi = mole fraction of component i
Vi = molar volume of component i
(4.32)λLmix
φ1
2λL1
2φ1φ2λ12 φ2
2λL2
+ +=
λLmix φiφjkij
j
∑
i
∑=
kij
2
1 ki⁄( ) 1 kj⁄( )+
-------------------------------------=
x1V1
xiVi
i 1=
2
∑
-------------------
x2V2
xiVi
i 1=
2
∑
-------------------4-20
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Physical Property Calculation Methods 4-21
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Th4.6 Surface Tension
Surface tensions for hydrocarbon systems are calculated using a 
modified form of the Brock and Bird equation. 
Property Class Name and Phases Applicable
The equation expresses the surface tension, σ, as a function of 
the reduced and critical properties of the component. The basic 
form of the equation was used to regress parameters for each 
family of components.
where: σ = surface tension (dynes/cm2)
Q = 0.1207[1.0 + TBR ln Pc /(1.0 - TBR)] - 0.281
TBR = reduced boiling point temperature (Tb/Tc)
a = parameter fitted for each chemical class
b = c0 + c1 ω + c2 ω2 + c3 ω3 (parameter fitted for each 
chemical class, expanded as a polynomial in 
acentricity)
For aqueous systems, HYSYS employs a polynomial to predict 
the surface tension. It is important to note that HYSYS predicts 
only liquid-vapour surface tensions. 
Property Class Name Phase Applicable
COTHSurfaceTension Class Liquid and vapour
(4.33)σ Pc
2 3⁄ Tc
1 3⁄ Q 1 TR–( )a b×=4-21
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4-22 Insoluble Solids
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Th4.7 Insoluble Solids
An insoluble solid is identified from its pure compound "family" 
classification.
Property Methods
A quick reference of calculation methods for insoluble solids is 
shown in the table below.
The calculation methods from the table are described in the 
following sections.
Calculation 
Method
Phase 
Applicable
Property Class Name
MolarDensity xptInsolubleSoli
d
COTHSolidDensity Class
MolarVolume xptInsolubleSoli
d
COTHSolidVolume Class
Enthalpy xptInsolubleSoli
d
COTHSolidEnthalpy Class
Entropy xptInsolubleSoli
d
COTHSolidEntropy Class
Cp xptInsolubleSoli
d
COTHSolidCp Class4-22
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Physical Property Calculation Methods 4-23
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ThInsoluble Solid Molar Density
Property Class Name and Phases Applicable
Insoluble Solid MolarVolume
Property Class Name and Phases Applicable
Property Class Name Phase Applicable
COTHSolidDensity Class xptInsolubleSolid
Property Class Name Phase Applicable
COTHSolidVolume Class xptInsolubleSolid4-23
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4-24 Insoluble Solids
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ThInsoluble Solid Enthalpy
Property Class Name and Phases Applicable
Insoluble Solid Entropy
Property Class Name and Phases Applicable
Insoluble Solid Cp
Property Class Name and Phases Applicable
Property Class Name Phase Applicable
COTHSolidEnthalpy Class xptInsolubleSolid
Property Class Name Phase Applicable
COTHSolidEnthalpy Class xptInsolubleSolid
Property Class Name Phase Applicable
COTHSolidCp Class xptInsolubleSolid4-24
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References & Standard States 5-1
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Th5  References & 
Standard States5-1
5.1  Enthalpy Reference States ............................................................. 2
5.1.1  Ideal Gas Enthalpy Offset .......................................................... 2
5.1.2  Enthalpy Offset ........................................................................ 3
5.2  Entropy Reference States............................................................... 4
5.2.1  Ideal Gas Entropy Offset ........................................................... 4
5.2.2  Entropy Offset ......................................................................... 5
5.3  Ideal Gas Cp................................................................................... 5
5.4  Standard State Fugacity................................................................. 6
5.4.1  Standard State without Poynting Correction ................................. 8
5.4.2  Standard State with Poynting Correction...................................... 9
5.4.3  Ideal Standard State with Fugacity Coefficient............................ 10
5.4.4  Ideal Standard State with Fugacity Coeff & Poynting ................... 11
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5-2 Enthalpy Reference States
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Th5.1 Enthalpy Reference 
States
All enthalpy calculations are determined with respect to a 
reference enthalpy which are defined in the following methods.
Property Methods
The enthalpy reference state calculation methods are shown in 
the table below.
5.1.1 Ideal Gas Enthalpy 
Offset
The Ideal Gas enthalpy calculates and returns an array of:
for all components.
Calculation Method Phase Applicable
Property Class 
Name
Ideal Gas Enthalpy 
Offset
Vapour & Liquid COTHOffsetIGH 
Class
Enthalpy Offset Vapour & Liquid COTHOffsetH Class
(5.1)Hi
ig offset Hi+5-2
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References & Standard States 
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ThProperty Class Name and Phases Applicable
5.1.2 Enthalpy Offset
The enthalpy offset calculates and returns an array of:
for all components.
where: Hig(25°C) = ideal gas enthalpy at 25°C.
Hfig(25°C) = ideal gas enthalpy with heat of formation of the 
component at 25°C.
Property Class Name and Phases Applicable
Property Class Name Phase Applicable
COTHOffsetIGH Class Vapour & Liquid
The term, offset Hi, is calculated by Section 5.1.2 - Enthalpy 
Offset.
(5.2)
Property Class Name Phase Applicable
COTHOffsetH Class Vapour & Liquid
Offset Hi Hi
ig 25°C( )– Hi
fig 25°C( )+=5-3
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5-4 Entropy Reference States
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Th5.2 Entropy Reference 
States
All entropy calculations are determined with respect to a 
reference enthalpy which are defined in the following methods.
Property Methods
The entropy reference state calculation methods are shown in 
the table below.
5.2.1 Ideal Gas Entropy Offset
The Ideal Gas entropy calculates and returns an array of:
for all components.
Calculation Method Phase Applicable
Property Class 
Name
Ideal Gas Entropy 
Offset
Vapour & Liquid COTHOffsetIGS 
Class
Entropy Offset Vapour & Liquid COTHOffsetS Class
(5.3)Si
ig offset Si+5-4
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References & Standard States 
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ThProperty Class Name and Phases Applicable
5.2.2 Entropy Offset
The entropy offset calculates and returns an array of:
for all components.
Property Class Name and Phases Applicable
5.3 Ideal Gas Cp
The ideal gas Cp calculates and returns an array containing the 
ideal gas Cp of all components.
Property Class Name Phase Applicable
COTHOffsetIGS Class Vapour & Liquid
The term, offset Si, is calculated by Section 5.2.2 - Entropy 
Offset.
(5.4)
Property Class Name Phase Applicable
COTHOffsetS Class Vapour & Liquid
Offset S 0=5-5
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5-6 Standard State Fugacity
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Th5.4 Standard State 
Fugacity
The fugacity of component, i, in the mixture is related to its 
activity coefficient composition through the following equation. 
where: γi = activity coefficient of component i
fi 
std = standard state fugacity of component i
xi = mole fraction of component i
The standard state fugacity, fi
std, is defined at the temperature 
and pressure of the mixture. As, γi, approaches one in the limit 
, the standard state fugacity may be related to the vapour 
pressure of component i.
where: Pi
sat = vapour pressure of component i at the temperature of 
the system
φi
sat = fugacity coefficient of pure component i at temperature 
T and pressure Pi
sat
P = pressure of the system
Vi = liquid molar volume of component i at T and P
R = gas constant
T = temperature of system
The Poynting factor accounts for the effect of pressure on liquid 
fugacity and is represented by the exponential term in the 
above equation. The correction factor generally is neglected if 
the pressure does not exceed a few atmospheres. The liquid 
(5.5)
(5.6)
 fi  γixifi
std=
xi 1→
fi
std P= i
satφi
sat Vi
RT
------ Pd
Pi
sat
P
∫exp5-6
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Thvolume has little effect on pressure and the above equation 
simplifies to:
The vapour phase fugacity can be calculated by any method 
when liquid activity coeffiecients are used.
Property Methods
The standard state fugacity calculation methods are shown in 
the following table.
(5.7)
Calculation 
Method
Phase 
Applicable
Property Class Name
LnStdFugacity Liquid COTHIdealStdFug Class
LnStdFugacity Liquid COTHPoyntingStdFug 
Class
LnStdFugacity Liquid COTHPhiStdFug Class
LnStdFugacity Liquid COTHPoyntingPhiStdFug 
Class
fi
std P= i
satφi
sat P Pi
sat–( )Vi RT( )⁄ ][exp5-7
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5-8 Standard State Fugacity
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Th5.4.1 Standard State without 
Poynting Correction
This method calculates the standard state fugacity for all 
components. The effects of the poynting correction and φi
sat in 
Equation (5.5) are neglected.
For condensible components, the standard state fugacity is 
calculated as:
Property Class Name and Phases Applicable     
Notes
For non-condensible components in the presence of any 
condensible components, Henry’s law is used as shown below.
In a system of all non-condensible components and no 
condensible components, the standard state fugacity is 
calculated as:
(5.8)
Property Class Name Phase Applicable
COTHIdealStdFug Class Liquid
(5.9)
(5.10)
fi
std P= i
sat
fi
std H= i j,
fi
std P= i
sat5-8
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Th5.4.2 Standard State with 
Poynting Correction
This method calculates the standard state fugacity for all 
components. The effect of the poynting correction is included 
and accounts for the effect of pressure on the liquid fugacity. 
The effect of the fugacity coefficient, φi
sat, in Equation (5.5) is 
neglected.
For condensible components, the standard state fugacity is 
calculated as:
Property Class Name and Phases Applicable
Notes
For non-condensible components in the presence of any 
condensible components, Henry’s law is used as shown below.
In a system of all non-condensible components and no 
condensible components, the standard state fugacity is 
calculated as:
(5.11)
Property Class Name Phase Applicable
COTHPoyntingStdFug Class Liquid
(5.12)
(5.13)
fi
std P= i
sat P Pi
sat–( )Vi RT( )⁄ ][exp
fi
std H= i j,
fi
std P= i
sat P Pi
sat–( )Vi RT( )⁄ ][exp5-9
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5-10 Standard State Fugacity
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Th5.4.3 Ideal Standard State 
with Fugacity Coefficient
This method calculates the standard state fugacity for all 
components. The effect of the fugacity coefficient, φi
sat, is 
included although the poynting factor in Equation (5.5) is 
neglected.
For condensible components, the standard state fugacity is 
calculated as:
Property Class Name and Phases Applicable
Notes
For non-condensible components in the presence of any 
condensible components, Henry’s law is used as shown below. 
In a system of all non-condensible components and no 
condensible components, the standard state fugacity is 
calculated as:
The fugacity coefficient, φi
sat, is calculated from the specified 
vapour model.
(5.14)
Property Class Name Phase Applicable
COTHPhiStdFug Class Liquid
(5.15)
(5.16)
fi
std P= i
satφi
sat
fi
std H= i j, P Pi
sat–( )Vi RT( )⁄ ][exp
fi
std P= i
sat P Pi
sat–( )Vi RT( )⁄ ][exp5-10
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References & Standard States 
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Th5.4.4 Ideal Standard State 
with Fugacity Coeff & 
Poynting
This method calculates the standard state fugacity for all 
components. The effects of the fugacity coefficient, φi
sat, and the 
poynting correction in Equation (5.5) are included.
For condensible components, the standard state fugacity is:
Property Class Name and Phases Applicable
Notes
For non-condensible components in the presence of any 
condensible components, Henry’s law is used as shown below. 
In a system of all non-condensible components and no 
condensible components, the standard state fugacity is 
calculated as:
The fugacity coefficient, φi
sat, is calculated from the specified 
vapour model.
(5.17)
Property Class Name Phase Applicable
COTHPoyntingPhiStdFug Class Liquid
(5.18)
(5.19)
fi
std P= i
satφi
sat P Pi
sat–( )Vi RT( )⁄ ][exp
fi
std H= i j, P Pi
sat–( )Vi RT( )⁄ ][exp
fi
std P= i
sat P Pi
sat–( )Vi RT( )⁄ ][exp5-11
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5-12 Standard State Fugacity
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Th5-12
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Flash Calculations 6-1
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Th6  Flash Calculations6-1
6.1  Introduction................................................................................... 2
6.2  T-P Flash Calculation...................................................................... 3
6.3  Vapour Fraction Flash .................................................................... 4
6.3.1  Dew Points .............................................................................. 4
6.3.2  Bubble Points/Vapour Pressure................................................... 5
6.3.3  Quality Points .......................................................................... 5
6.4  Flash Control Settings.................................................................... 7
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6-2 Introduction
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Th6.1 Introduction
Rigorous three phase calculations are performed for all 
equations of state and activity models with the exception of the 
Wilson equation, which only performs two phase vapour-liquid 
calculations. 
Aspen HYSYS Thermodynamics COM Interface uses internal 
intelligence to determine when it can perform a flash calculation 
on a stream, and then what type of flash calculation needs to be 
performed on the stream. This is based completely on the 
degrees of freedom concept. When the composition of a stream 
and two property variables are known, (vapour fraction, 
temperature, pressure, enthalpy or entropy, one of which must 
be either temperature or pressure), the thermodynamic state of 
the stream is defined.  
Aspen HYSYS Thermodynamics COM Interface automatically 
performs the appropriate flash calculation when sufficient 
information is known. Depending on the known stream 
information, one of the following flashes are performed: T-P, 
T-VF, T-H, T-S, P-VF, P-H, or P-S.
Specified variables can 
only be re-specified by you 
or via the Recycle Adjust, 
or SpreadSheet 
operations. They will not 
change through any heat 
or material balance 
calculations6-2
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Flash Calculations 6-3
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Th6.2 T-P Flash Calculation
The independent variables for this type of flash calculation are 
the temperature and pressure of the system, while the 
dependent variables are the vapour fraction, enthalpy and 
entropy.
Using the specified models, rigorous calculations are performed 
to determine the coexistence of immiscible liquid phases and the 
resulting component distributions by minimization of the Gibbs 
free energy term. For Vapour Pressure models or the Semi-
empirical methods, the component distribution is based on the 
Kerosene solubility data (Figure 9 A1.4 of the API Data Book). 
If the mixture is single-phase at the specified conditions, the 
property package calculates the isothermal compressibility (dv/
dp) to determine if the fluid behaves as a liquid or vapour. Fluids 
in the dense-phase region are assigned the properties of the 
phase that best represents their current state.         
Material solids appear in the liquid phase of two-phase 
mixtures, and in the heavy (aqueous/slurry) phase of three-
phase system.
Use caution in specifying 
solids with systems that 
are otherwise all vapour. 
Small amounts of non-
solids may appear in the 
“liquid” phase.6-3
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6-4 Vapour Fraction Flash
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Th6.3 Vapour Fraction Flash
Vapour fraction and either temperature or pressure are the 
independent variables for this type of calculation. This class of 
calculation embodies all fixed quality points including bubble 
points (vapour pressure) and dew points. To perform bubble 
point calculation on a stream of known composition, simply 
specify the Vapour Fraction of the stream as 0.0 and define the 
temperature or pressure at which the calculation is desired. For 
a dew point calculation, simply specify the Vapour Fraction of 
the stream as 1.0 and define the temperature or pressure at 
which the dew point calculation is desired. Like the other types 
of flash calculations, no initial estimates are required.
6.3.1 Dew Points 
Given a vapour fraction specification of 1.0 and either 
temperature or pressure, the property package will calculate the 
other dependent variable (P or T). If temperature is the second 
independent variable, the dew point pressure is calculated. 
Likewise, if pressure is the independent variable, then the dew 
point temperature will be calculated. Retrograde dew points may 
be calculated by specifying a vapour fraction of -1.0. It is 
important to note that a dew point that is retrograde with 
respect to temperature can be normal with respect to pressure 
and vice versa.
The vapour fraction is always shown in terms of the total 
number of moles. For instance, the vapour fraction (VF) 
represents the fraction of vapour in the stream, while the 
fraction, (1.0 - VF), represents all other phases in the stream 
(i.e. a single liquid, 2 liquids, a liquid and a solid).
All of the solids will appear 
in the liquid phase.6-4
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Flash Calculations 6-5
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Th6.3.2 Bubble Points/Vapour 
Pressure
A vapour fraction specification of 0.0 defines a bubble point 
calculation. Given this specification and either temperature or 
pressure, the flash will calculate the unknown T or P variable. As 
with the dew point calculation, if the temperature is known, the 
bubble point pressure is calculated and conversely, given the 
pressure, the bubble point temperature is calculated. For 
example, by fixing the temperature at 100°F, the resulting 
bubble point pressure is the true vapour pressure at 100°F. 
6.3.3 Quality Points
Bubble and dew points are special cases of quality point 
calculations. Temperatures or pressures can be calculated for 
any vapour quality between 0.0 and 1.0 by specifying the 
desired vapour fraction and the corresponding independent 
variable. If HYSYS displays an error when calculating vapour 
fraction, then this means that the specified vapour fraction 
doesn't exist under the given conditions, i.e., the specified 
pressure is above the cricondenbar, or the given temperature is 
to the right of the cricondentherm on a standard P-T envelope.
Enthalpy Flash
Given the enthalpy and either the temperature or pressure of a 
stream, the property package will calculate the unknown 
dependent variables. Although the enthalpy of a stream cannot 
be specified directly, it will often occur as the second property 
variable as a result of energy balances around unit operations 
such as valves, heat exchangers and mixers. 
If an error message appears, this may mean that an internally 
set temperature or pressure bound has been encountered. Since 
these bounds are set at quite large values, there is generally 
some erroneous input that is directly or indirectly causing the 
problem, such as an impossible heat exchange.
Vapour pressure and 
bubble point pressure are 
synonymous.6-5
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6-6 Vapour Fraction Flash
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ThEntropy Flash
Given the entropy and either the temperature or pressure of a 
stream, the flash will calculate the unknown dependent 
variables.
Solids
Aspen HYSYS Thermodynamics COM Interface flash does not 
check for solid phase formation of pure components within the 
flash calculations.
Solids do not participate in vapour-liquid equilibrium (VLE) 
calculations. Their vapour pressure is taken as zero. However, 
since solids do have an enthalpy contribution, they will have an 
effect on heat balance calculations. Thus, while the results of a 
temperature flash will be the same whether or not such 
components are present, an Enthalpy flash will be affected by 
the presence of solids.6-6
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Flash Calculations 6-7
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Th6.4 Flash Control Settings
Flash control settings are used to control tolerances, iteration 
numbers, and some other flash options. You can set flash 
options through applications that support Aspen HYSYS 
Thermodynamics COM Interface. These include HYSYS, HYCON, 
and HTFS amongst others.
Flash control values are stored in the flash control object and 
can be set through interface functions. The Flash XML file is 
described by the Aspen HYSYS Thermodynamics COM Interface 
property manager. It identifies the flash control settings and 
sets it into the flash control object where flash can now get the 
controls.
In flash control, there are two kinds of controls:
Refer to the Flash Control Settings in the Flash XML File section 
in the Programmer’s guide of the Aspen HYSYS 
Thermodynamics COM Interface development kit for more 
information.
Control Description
Fixed Control Fixed controls are hard coded controls that have 
fixed names and default values. If the user does 
not set the controls, the default values are used.
Additional Control Additional controls are called SecantSetting 
controls. SecantSettings such as Temperature and 
Pressure are set by default, as others can be 
defined by Aspen HYSYS Thermodynamics COM 
Interface flash and/or the user. If the user defines 
a control (the name given by the user), in the user 
created flash object users can use the same name 
to get the values of that control set in the flash 
XML file.6-7
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Th6-8
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Property Packages 7-1
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Th7  Property Packages7-1
7.1  Introduction................................................................................... 2
7.2  Vapour Phase Models ..................................................................... 2
7.3  Liquid Phase Models..................................................................... 13
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7-2 Introduction
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Th7.1 Introduction
A summary of the property packages used within the Aspen 
HYSYS Thermodynamics COM Interface framework are grouped 
into the following sections:
• Section 7.2 - Vapour Phase Models
• Section 7.3 - Liquid Phase Models
Each section consists of tables which include the file name, 
description, property names, and class names within Aspen 
HYSYS Thermodynamics COM Interface.
7.2 Vapour Phase Models
Property package information for vapour phase models is shown 
in the following sections.
Ideal Gas
PV=nRT can be used to model the vapour phase but is only 
suggested for ideal systems under moderate conditions.
XML File Name Name Description
Ideal_vapour Ideal Gas Ideal Gas Equation of State
Property Name Class Name Description
Enthalpy COTHIGEnthalpy Ideal gas enthalpy.
Entropy COTHIGEntropy Ideal gas entropy.
Cp COTHIGCp Ideal gas heat capacity.
LnFugacityCoeff COTHIGLnFugacityCoe
ff
Ideal gas fugacity coefficient.
LnFugacity COTHIGLnFugacity   Ideal gas fugacity.
MolarVolume COTHIGVolume Ideal gas molar volume.
Viscosity COTHViscosity Viscosity.
ThermalConductiv
ity
COTHThermCond   Thermal conductivity.
ZFactor COTHIGZFactor Ideal gas compressibility 
factor.
IGCp COTHIdealGasCp Ideal gas heat capacity.
OffsetIGH COTHOffsetIGH Ideal gas offset enthalpy.7-2
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Property Packages 
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ThPeng-Robinson
This model is ideal for VLE calculations as well as calculating 
liquid densities for hydrocarbon systems. However, in situations 
where highly non-ideal systems are encountered, the use of 
Activity Models is recommended.
OffsetH COTHOffsetH Offset enthalpy with heat of 
formation.
OffsetIGS COTHOffsetIGS Ideal gas offset entropy.
OffsetS COTHOffsetS Offset entropy.
XML File Name Name Description
pr_vapour Peng-Robinson Peng-Robinson Equation of 
State using Mixing Rule 1 for all 
properties.
Property Name Class Name Description
Enthalpy COTHPREnthalpy Peng-Robinson enthalpy.
Entropy COTHPREntropy Peng-Robinson entropy.
Cp COTHPRCp Peng-Robinson heat capacity.
LnFugacityCoeff COTHPRLnFugacityCoe
ff
Peng-Robinson fugacity 
coefficient.
LnFugacity COTHPRLnFugacity    Peng-Robinson fugacity.
MolarVolume COTHPRVolume   Peng-Robinson molar volume.
Viscosity COTHViscosity Viscosity.
ThermalConductiv
ity
COTHThermCond   Thermal conductivity.
ZFactor COTHPRZFactor   Peng-Robinson 
compressibility factor.
amix COTHPRab_1 Peng-Robinson amix.
IGCp COTHIdealGasCp Ideal gas heat capacity.
OffsetIGH COTHOffsetIGH Ideal gas offset enthalpy 
OffsetH COTHOffsetH Offset enthalpy with heat of 
formation.
OffsetIGS COTHOffsetIGS Ideal gas offset entropy.
OffsetS COTHOffsetS Offset entropy.
Property Name Class Name Description7-3
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7-4 Vapour Phase Models
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ThHysysPR
The HysysPR EOS is similar to the PR EOS with several 
enhancements to the original PR equation. It extends its range 
of applicability and better represents the VLE of complex 
systems.
XML File Name Name Description
hysyspr_vapour HysysPR HysysPR Equation of State 
using Mixing Rule 1 for all 
properties.
Property Name Class Name Description
Enthalpy COTHPR_HYSYS_Enthalp
y
Peng-Robinson enthalpy.
Entropy COTHPR_HYSYS_Entrop
y
Peng-Robinson entropy.
Cp COTHPR_HYSYS_Cp Peng-Robinson heat 
capacity.
LnFugacityCoeff COTHPR_HYSYS_LnFuga
cityCoeff 
Peng-Robinson fugacity 
coefficient.
LnFugacity COTHPR_HYSYS_LnFuga
city
Peng-Robinson fugacity.
MolarVolume COTHPR_HYSYS_Volume Peng-Robinson molar 
volume.
Viscosity COTHViscosity Viscosity.
ThermalConductiv
ity
COTHThermCond Thermal conductivity.
ZFactor COTHPRZFactor   Peng-Robinson 
compressibility factor.
amix COTHPRab_1 Peng-Robinson amix.
IGCp COTHIdealGasCp Ideal gas heat capacity.
OffsetIGH COTHOffsetIGH Ideal gas offset enthalpy 
OffsetH COTHOffsetH Offset enthalpy with heat of 
formation.
OffsetIGS COTHOffsetIGS Ideal gas offset entropy.
OffsetS COTHOffsetS Offset entropy.7-4
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ThPeng-Robinson-Stryjek-Vera
This is a two-fold modification of the PR equation of state that 
extends the application of the original PR method for moderately 
non-ideal systems. It provides a better pure component vapour 
pressure prediction as well as a more flexible mixing rule than 
Peng robinson.
XML File Name Name Description
prsv_vapour PRSV Peng-Robinson Stryjek-Vera 
using Mixing Rule 1 for all 
properties.
Property Name Class Name Description
Enthalpy COTHPRSVEnthalpy    PRSV enthalpy.
Entropy COTHPRSVEntropy    PRSV entropy.
Cp COTHPRSVCp    PRSV heat capacity.
LnFugacityCoeff COTHPRSVLnFugacityCoe
ff
PRSV fugacity coefficient.
LnFugacity COTHPRSVLnFugacity PRSV fugacity.
MolarVolume COTHPRSVVolume PRSV molar volume.
Viscosity COTHViscosity Viscosity.
ThermalConductiv
ity
COTHThermCond   Thermal conductivity.
ZFactor COTHPRSVZFactor   PRSV compressibility factor.
amix COTHPRSVab_1 PRSV amix.
IGCp COTHIdealGasCp Ideal gas heat capacity.
OffsetIGH COTHOffsetIGH Ideal gas Offset enthalpy.
OffsetH COTHOffsetH Offset enthalpy with heat of 
formation.
OffsetIGS COTHOffsetIGS Ideal gas offset entropy.
OffsetS COTHOffsetS Offset entropy.7-5
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7-6 Vapour Phase Models
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ThSoave-Redlich-Kwong
In many cases it provides comparable results to PR, but its 
range of application is significantly more limited. This method is 
not as reliable for non-ideal systems.
XML File Name Name Description
srk_vapour SRK Soave-Redlich-Kwong Equation of 
State using Mixing Rule 1 for all 
properties.
Property Name Class Name Description
Enthalpy COTHSRKEnthalpy     SRK enthalpy.
Entropy COTHSRKEntropy    SRK entropy.
Cp COTHSRKCp    SRK heat capacity.
LnFugacityCoeff COTHSRKLnFugacityCoe
ff 
SRK fugacity coefficient.
LnFugacity COTHSRKLnFugacity SRK fugacity.
MolarVolume COTHSRKVolume SRK molar volume.
Viscosity COTHViscosity Viscosity.
ThermalConductiv
ity
COTHThermCond   Thermal conductivity.
ZFactor COTHSRKZFactor   SRK compressibility factor.
amix COTHSRKab_1 SRK amix.
IGCp COTHIdealGasCp Ideal gas heat capacity.
OffsetIGH COTHOffsetIGH Ideal gas Offset enthalpy.
OffsetH COTHOffsetH Offset enthalpy with heat of 
formation.
OffsetIGS COTHOffsetIGS Ideal gas offset entropy.
OffsetS COTHOffsetS Offset entropy.7-6
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ThRedlich-Kwong
The Redlich-Kwong equation generally provides results similar to 
Peng-Robinson. Several enhancements have been made to the 
PR as described above which make it the preferred equation of 
state.
XML File Name Name Description
rk_vapour Redlich-Kwong Redlich-Kwong Equation of 
State using Mixing Rule 1 for all 
properties.
Property Name Class Name Description
Enthalpy COTHRKEnthalpy     RK enthalpy.
Entropy COTHRKEntropy    RK entropy.
Cp COTHRKCp    RK heat capacity.
LnFugacityCoeff COTHRKLnFugacityCoe
ff 
RK fugacity coefficient.
LnFugacity COTHRKLnFugacity RK fugacity.
MolarVolume COTHRKVolume RK molar volume.
Viscosity COTHViscosity Viscosity.
ThermalConductiv
ity
COTHThermCond   Thermal conductivity.
ZFactor COTHRKZFactor   SRK compressibility factor.
amix COTHRKab_1 SRK amix.
IGCp COTHIdealGasCp Ideal gas heat capacity.
OffsetIGH COTHOffsetIGH Ideal gas Offset enthalpy.
OffsetH COTHOffsetH Offset enthalpy with heat of 
formation.
OffsetIGS COTHOffsetIGS Ideal gas offset entropy.
OffsetS COTHOffsetS Offset entropy.7-7
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7-8 Vapour Phase Models
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ThZudkevitch-Joffee
This is a modification of the Redlich-Kwong equation of state, 
which reproduces the pure component vapour pressures as 
predicted by the Antoine vapour pressure equation. This model 
has been enhanced for better prediction of vapour-liquid 
equilibrium for hydrocarbon systems, and systems containing 
Hydrogen.
XML File Name Name Description
zj_vapour Zudkevitch-Joffee Zudkevitch-Joffee Equation of 
State
Property Name Class Name Description
Enthalpy COTHLeeKeslerEnthalp
y
Lee-Kesler enthalpy.
Entropy COTHLeeKeslerEntropy Lee-Kesler entropy.
Cp COTHLeeKeslerCp     Lee-Kesler heat capacity.
LnFugacityCoeff COTHZJLnFugacityCoe
ff   
ZJ fugacity coefficient.
LnFugacity COTHZJLnFugacity ZJ fugacity.
MolarVolume COTHZJVolume ZJ molar volume.
Viscosity COTHViscosity Viscosity.
ThermalConductiv
ity
COTHThermCond   Thermal conductivity.
ZFactor COTHZJZFactor   ZJ compressibility factor.
amix COTHZJab_1 ZJ amix.
IGCp COTHIdealGasCp Ideal gas heat capacity.
OffsetIGH COTHOffsetIGH Ideal gas Offset enthalpy.
OffsetH COTHOffsetH Offset enthalpy with heat of 
formation.
OffsetIGS COTHOffsetIGS Ideal gas offset entropy.
OffsetS COTHOffsetS Offset entropy.7-8
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ThKabadi-Danner
This model is a modification of the original SRK equation of 
state, enhanced to improve the vapour-liquid-liquid equilibrium 
calculations for water-hydrocarbon systems, particularly in 
dilute regions.
XML File Name Name Description
kd_vapour Kabadi-Danner Kabadi-Danner Equation of 
State using Mixing Rule 1 for all 
properties.
Property Name Class Name Description
Enthalpy COTHKDEnthalpy KD enthalpy.
Entropy COTHKDEntropy KD entropy.
Cp COTHKDCp KD heat capacity.
LnFugacityCoeff COTHKDLnFugacityCo
eff   
KD fugacity coefficient.
LnFugacity COTHKDLnFugacity KD fugacity.
MolarVolume COTHKDVolume KD molar volume.
Viscosity COTHViscosity Viscosity.
ThermalConductiv
ity
COTHThermCond   Thermal conductivity.
ZFactor COTHKDZFactor   KD compressibility factor.
amix COTHKDab_1 KD amix.
IGCp COTHIdealGasCp Ideal gas heat capacity.
OffsetIGH COTHOffsetIGH Ideal gas Offset enthalpy.
OffsetH COTHOffsetH Offset enthalpy with heat of 
formation.
OffsetIGS COTHOffsetIGS Ideal gas offset entropy.
OffsetS COTHOffsetS Offset entropy.7-9
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7-10 Vapour Phase Models
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ThVirial
This model enables you to better model vapour phase fugacities 
of systems displaying strong vapour phase interactions. 
Typically this occurs in systems containing carboxylic acids, or 
compounds that have the tendency to form stable hydrogen 
bonds in the vapour phase. In these cases, the fugacity 
coefficient shows large deviations from ideality, even at low or 
moderate pressures.
XML File Name Name Description
virial_vapour Virial The Virial Equation of State
Property Name Class Name Description
Enthalpy COTHVirial_Enthalpy Virial enthalpy.
Entropy COTHVirial_Entropy Virial entropy.
Cp COTHVirial_Cp Virial heat capacity.
LnFugacityCoeff COTHVirial_LnFugacityCo
eff
Virial fugacity coefficient.
LnFugacity COTHVirial_LnFugacity Virial fugacity.
MolarVolume COTHVirial_Volume Virial molar volume.
Viscosity COTHViscosity Viscosity.
ThermalConductiv
ity
COTHThermCond   Thermal conductivity.
ZFactor COTHVirial_ZFactor   Virial compressibility factor.
IGCp COTHIdealGasCp Ideal gas heat capacity.
OffsetIGH COTHOffsetIGH Ideal gas Offset enthalpy.
OffsetH COTHOffsetH Offset enthalpy with heat 
of formation.
OffsetIGS COTHOffsetIGS Ideal gas offset entropy.
OffsetS COTHOffsetS Offset entropy.7-10
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ThLee-Kesler-Plöcker
This model is the most accurate general method for non-polar 
substances and mixtures.
XML File Name Name Description
lkp_vapour Lee-Kesler-Plöcker Lee-Kesler-Plöcker EOS using 
Mixing Rule 1 for all properties.
Property Name Class Name Description
Enthalpy COTHLeeKeslerEnthalpy Lee-Kesler enthalpy.
Entropy COTHLeeKeslerEnthalpy Lee-Kesler entropy.
Cp COTHLeeKeslerCp Lee-Kesler heat capacity.
LnFugacityCoeff COTHLKPLnFugacityCoe
ff    
LKP fugacity coefficient.
LnFugacity COTHLKPLnFugacity   LKP fugacity.
MolarVolume COTHLKPMolarVolume   LKP molar volume.
Viscosity COTHViscosity Viscosity.
ThermalConductiv
ity
COTHThermCond   Thermal conductivity.
SurfaceTension COTHSurfaceTension HYSYS surface tension.
ZFactor COTHLKPZFactor    LKP compressibility factor.
IGCp COTHIdealGasCp Ideal gas heat capacity.
OffsetIGH COTHOffsetIGH Ideal gas Offset enthalpy.
OffsetH COTHOffsetH Offset enthalpy with heat of 
formation.
OffsetIGS COTHOffsetIGS Ideal gas offset entropy.
OffsetS COTHOffsetS Offset entropy.7-11
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7-12 Vapour Phase Models
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ThBraun K10
This model is strictly applicable to heavy hydrocarbon systems 
at low pressures. The model employs the Braun convergence 
pressure method, where, given the normal boiling point of a 
component, the K-value is calculated at system temperature and 
10 psia (68.95 kPa).
XML File Name Name Description
braunk10_vapour Braun K10 Braun K10 Vapour Pressure 
Property Model.
Property Name Class Name Description
Enthalpy COTHLeeKeslerEnthalpy Lee-Kesler enthalpy.
Entropy COTHLeeKeslerEntropy Lee-Kesler entropy.
Cp COTHLeeKeslerCp Lee-Kesler heat 
capacity.
LnFugacityCoeff COTHIGLnFugacityCoeff Ideal gas fugacity 
coefficient.
LnFugacity COTHIGLnFugacity Ideal gas fugacity.
MolarVolume COTHIGVolume Ideal gas molar volume.
MolarDensity COTHIGDensity Ideal gas molar density.
Viscosity COTHViscosity   Viscosity.
ThermalConductiv
ity
COTHThermCond    Thermal conductivity.
SurfaceTension COTHSurfaceTension HYSYS surface tension.
IGCp COTHIdealGasCp Ideal gas heat capacity.
OffsetIGH COTHOffsetIGH Ideal gas Offset 
enthalpy.
OffsetH COTHOffsetH Offset enthalpy with 
heat of formation.
OffsetIGS COTHOffsetIGS Ideal gas offset entropy.
OffsetS COTHOffsetS Offset entropy.7-12
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Th7.3 Liquid Phase Models
The property package information for the liquid phase models is 
shown in the following sections.
Ideal Solution
Assumes the volume change due to mixing is zero. This model is 
more commonly used for solutions comprised of molecules not 
too different in size and of the same chemical nature.
XML File Name Name Description
idealsol_liquid Ideal Solution Ideal Solution Model
Property Name Class Name Description
Enthalpy COTHCavettEnthalpy    Cavett enthalpy.    
Entropy COTHCavettEntropy   Cavett entropy.
Cp COTHCavettCp   Cavett heat capacity.   
LnFugacityCoeff COTHIdealSolLnFugacityCoe
ff
Ideal Solution fugacity 
coefficient. 
LnFugacity COTHIdealSolLnFugacity   Ideal solution fugacity.
LnActivity Coeff COTHIdealSolLnActivityCoeff Ideal solution activity 
coefficient.
LnStdFugacity COTHIdealStdFug Ideal standard fugacity 
with or without poynting 
correction.
LnActivityCoeffDT COTHIdealSolLnActivityCoeff
DT
Ideal solution activity 
coefficient wrt 
temperature.
MolarDensity COTHCOSTALDDensity COSTALD molar density.
MolarVolume COTHCOSTALDVolume   COSTALD molar volume. 
Viscosity COTHViscosity   Viscosity.   
ThermalConductiv
ity
COTHThermCond    Thermal conductivity.   
SurfaceTension COTHSurfaceTension Surface Tension. 
Helmholtz COTHCavettHelmholtz Cavett Helmholtz 
energy.
InternalEnergy COTHCavettInternalEnergy Cavett Internal energy. 
GibbsEnergy COTHIdealSolGibbsEnergy Cavett Gibbs energy.7-13
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ThIGCp COTHIdealGasCp Ideal gas heat capacity. 
OffsetIGH COTHOffsetIGH Ideal gas Offset 
enthalpy.
OffsetH COTHOffsetH Offset enthalpy with 
heat of formation.
OffsetIGS COTHOffsetIGS Ideal gas offset entropy.
OffsetS COTHOffsetS Offset entropy.
MolarDensity COTHSolidDensity Solid molar density.
MolarVolume COTHMolarVolume Solid molar volume.
Enthalpy COTHSolidEnthalpy Solid enthalpy.
Entropy COTHSolidEntropy Solid entropy.
Cp COTHSolidCp Solid heat capacity.
Property Name Class Name Description7-14
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ThRegular Solution
This model eliminates the excess entropy when a solution is 
mixed at constant temperature and volume. The model is 
recommended for non-polar components where the molecules 
do not differ greatly in size. By the attraction of intermolecular 
forces, the excess Gibbs energy may be determined.
XML File Name Name Description
regsol_liquid Regular Solution Regular Solution Model.
Property Name Class Name Description
Enthalpy COTHCavettEnthalpy     Cavett enthalpy.    
Entropy COTHCavettEntropy   Cavett entropy.
Cp COTHCavettCp   Cavett heat capacity.   
LnFugacityCoeff COTHRegSolLnFugacityCoef
f     
Regular Solution 
fugacity coefficient. 
LnFugacity COTHRegSolLnFugacity   Regular solution 
fugacity.
LnActivity Coeff COTHRegSolLnActivityCoeff Regular solution activity 
coefficient.
LnStdFugacity COTHIdealStdFug Ideal standard fugacity 
with or without poynting 
correction.
LnActivityCoeffDT COTHRegSolLnActivityCoeff
DT 
Regular solution activity 
coefficient wrt 
temperature.
MolarDensity COTHCOSTALDDensity COSTALD molar density.
MolarVolume COTHCOSTALDVolume   COSTALD molar volume. 
Viscosity COTHViscosity   Viscosity.   
ThermalConductiv
ity
COTHThermCond    Thermal conductivity.   
SurfaceTension COTHSurfaceTension Surface Tension. 
Helmholtz COTHCavettHelmholtz Cavett Helmholtz 
energy.
InternalEnergy COTHCavettInternalEnergy Cavett Internal energy. 
GibbsEnergy COTHCavettGibbs    Cavett Gibbs energy.
IGCp COTHIdealGasCp Ideal gas heat capacity. 
OffsetIGH COTHOffsetIGH Ideal gas Offset 
enthalpy.
OffsetH COTHOffsetH Offset enthalpy with 
heat of formation.7-15
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ThOffsetIGS COTHOffsetIGS Ideal gas offset entropy.
OffsetS COTHOffsetS Offset entropy.
MolarDensity COTHSolidDensity Solid molar density.
MolarVolume COTHMolarVolume Solid molar volume.
Enthalpy COTHSolidEnthalpy Solid enthalpy.
Entropy COTHSolidEntropy Solid entropy.
Cp COTHSolidCp Solid heat capacity.
Property Name Class Name Description7-16
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Thvan Laar
This equation fits many systems quite well, particularly for LLE 
component distributions. It can be used for systems that exhibit 
positive or negative deviations from Raoult’s Law; however, it 
cannot predict maxima or minima in the activity coefficient. 
Therefore it generally performs poorly for systems with 
halogenated hydrocarbons and alcohols.
XML File Name Name Description
vanlaar_liquid van Laar Two-parameter temperature 
dependent van Laar Model
Property Name Class Name Description
Enthalpy COTHCavettEnthalpy     Cavett enthalpy.    
Entropy COTHCavettEntropy   Cavett entropy.
Cp COTHCavettCp   Cavett heat capacity.   
LnFugacityCoeff COTHVanLaarLnFugacityCoef
f      
Van Laar fugacity 
coefficient. 
LnFugacity COTHVanLaarLnFugacity   Van Laar fugacity.
LnActivity Coeff COTHVanLaarLnActivityCoeff Van Laar activity 
coefficient.
LnStdFugacity COTHVanLaarStdFug Ideal standard fugacity 
with or without 
poynting correction.
LnActivityCoeffDT COTHVanLaarLnActivityCoeff
DT 
Van Laar activity 
coefficient wrt 
temperature.
MolarDensity COTHCOSTALDDensity COSTALD molar density.
MolarVolume COTHCOSTALDVolume   COSTALD molar 
volume. 
Viscosity COTHViscosity   Viscosity.   
ThermalConductiv
ity
COTHThermCond    Thermal conductivity.   
SurfaceTension COTHSurfaceTension Surface Tension. 
Helmholtz COTHCavettHelmholtz Cavett Helmholtz 
energy.
InternalEnergy COTHCavettInternalEnergy Cavett Internal energy. 
GibbsEnergy COTHCavettGibbs    Cavett Gibbs energy.
IGCp COTHIdealGasCp Ideal gas heat capacity. 
OffsetIGH COTHOffsetIGH Ideal gas Offset 
enthalpy.7-17
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ThOffsetH COTHOffsetH Offset enthalpy with 
heat of formation.
OffsetIGS COTHOffsetIGS Ideal gas offset entropy.
OffsetS COTHOffsetS Offset entropy.
MolarDensity COTHSolidDensity Solid molar density.
MolarVolume COTHMolarVolume Solid molar volume.
Enthalpy COTHSolidEnthalpy Solid enthalpy.
Entropy COTHSolidEntropy Solid entropy.
Cp COTHSolidCp Solid heat capacity.
Property Name Class Name Description7-18
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ThMargules
This was the first Gibbs excess energy representation 
developed. The equation does not have any theoretical basis, 
but is useful for quick estimates and data interpolation.
XML File Name Name Description
margules_liquid Margules Two-parameter temperature 
dependent Margules Model
Property Name Class Name Description
Enthalpy COTHCavettEnthalpy     Cavett enthalpy.    
Entropy COTHCavettEntropy   Cavett entropy.
Cp COTHCavettCp   Cavett heat capacity.   
LnFugacityCoeff COTHMargulesLnFugacityCoe
ff      
Margules fugacity 
coefficient. 
LnFugacity COTHMargulesLnFugacity   Margules fugacity.
LnActivity Coeff COTHMargulesLnActivityCoeff Margules activity 
coefficient.
LnStdFugacity COTHMargulesStdFug Ideal standard fugacity 
with or without 
poynting correction.
LnActivityCoeffDT COTHMargulesLnActivityCoeff
DT 
Margules activity 
coefficient wrt 
temperature.
MolarDensity COTHCOSTALDDensity COSTALD molar 
density.
MolarVolume COTHCOSTALDVolume   COSTALD molar 
volume. 
Viscosity COTHViscosity   Viscosity.   
ThermalConductiv
ity
COTHThermCond    Thermal conductivity.   
SurfaceTension COTHSurfaceTension Surface Tension. 
Helmholtz COTHCavettHelmholtz Cavett Helmholtz 
energy.
InternalEnergy COTHCavettInternalEnergy Cavett Internal energy. 
GibbsEnergy COTHCavettGibbs    Cavett Gibbs energy.
IGCp COTHIdealGasCp Ideal gas heat 
capacity. 
OffsetIGH COTHOffsetIGH Ideal gas Offset 
enthalpy.
OffsetH COTHOffsetH Offset enthalpy with 
heat of formation.7-19
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ThOffsetIGS COTHOffsetIGS Ideal gas offset 
entropy.
OffsetS COTHOffsetS Offset entropy.
MolarDensity COTHSolidDensity Solid molar density.
MolarVolume COTHMolarVolume Solid molar volume.
Enthalpy COTHSolidEnthalpy Solid enthalpy.
Entropy COTHSolidEntropy Solid entropy.
Cp COTHSolidCp Solid heat capacity.
Property Name Class Name Description7-20
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ThWilson
First activity coefficient equation to use the local composition 
model to derive the Gibbs Excess energy expression. It offers a 
thermodynamically consistent approach to predicting multi-
component behaviour from regressed binary equilibrium data. 
However the Wilson model cannot be used for systems with two 
liquid phases.
XML File Name Name Description
wilson_liquid Wilson Two-parameter temperature 
dependent Wilson Model
Property Name Class Name Description
Enthalpy COTHCavettEnthalpy     Cavett enthalpy.    
Entropy COTHCavettEntropy   Cavett entropy.
Cp COTHCavettCp   Cavett heat capacity.   
LnFugacityCoeff COTHWilsonLnFugacityCoef
f      
Wilson fugacity 
coefficient. 
LnFugacity COTHWilsonLnFugacity   Wilson fugacity.
LnActivity Coeff COTHWilsonLnActivityCoeff Wilson activity 
coefficient.
LnStdFugacity COTHWilsonStdFug Ideal standard fugacity 
with or without poynting 
correction.
LnActivityCoeffDT COTHWilsonLnActivityCoeff
DT 
Wilson activity coefficient 
wrt temperature.
MolarDensity COTHCOSTALDDensity COSTALD molar density.
MolarVolume COTHCOSTALDVolume   COSTALD molar volume. 
Viscosity COTHViscosity   Viscosity.   
ThermalConductiv
ity
COTHThermCond    Thermal conductivity.   
SurfaceTension COTHSurfaceTension Surface Tension. 
Helmholtz COTHCavettHelmholtz Cavett Helmholtz energy.
InternalEnergy COTHCavettInternalEnergy Cavett Internal energy. 
GibbsEnergy COTHCavettGibbs    Cavett Gibbs energy.
IGCp COTHIdealGasCp Ideal gas heat capacity. 
OffsetIGH COTHOffsetIGH Ideal gas Offset enthalpy.
OffsetH COTHOffsetH Offset enthalpy with heat 
of formation.
OffsetIGS COTHOffsetIGS Ideal gas offset entropy.7-21
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ThOffsetS COTHOffsetS Offset entropy.
MolarDensity COTHSolidDensity Solid molar density.
MolarVolume COTHMolarVolume Solid molar volume.
Enthalpy COTHSolidEnthalpy Solid enthalpy.
Entropy COTHSolidEntropy Solid entropy.
Cp COTHSolidCp Solid heat capacity.
Property Name Class Name Description7-22
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ThGeneral NRTL
This variation of the NRTL model uses five parameters and is 
more flexible than the NRTL model. Apply this model to systems 
with a wide boiling point range between components, where you 
require simultaneous solution of VLE and LLE, and where there 
exists a wide boiling point or concentration range between 
components.
XML File Name Name Description
nrtl_liquid General NRTL The General NRTL Model with 
five-coefficient temperature 
dependent parameters.
Property Name Class Name Description
Enthalpy COTHCavettEnthalpy     Cavett enthalpy.    
Entropy COTHCavettEntropy   Cavett entropy.
Cp COTHCavettCp   Cavett heat capacity.   
ActTempDep COTHNRTLTempDep HYSYS NRTL temperature 
dependent properties.
LnFugacityCoeff COTHNRTLLnFugacityCoeff NRTL fugacity coefficient.
LnFugacity COTHNRTLLnFugacity   NRTL fugacity.
LnActivity Coeff COTHNRTLLnActivityCoeff NRTL activity coefficient.
LnStdFugacity COTHNRTLStdFug Ideal standard fugacity 
with or without poynting 
correction.
LnActivityCoeffDT COTHNRTLLnActivityCoeff
DT 
NRTL activity coefficient 
wrt temperature.
MolarDensity COTHCOSTALDDensity COSTALD molar density.
MolarVolume COTHCOSTALDVolume   COSTALD molar volume. 
Viscosity COTHViscosity   Viscosity.   
ThermalConductiv
ity
COTHThermCond    Thermal conductivity.   
SurfaceTension COTHSurfaceTension Surface Tension. 
Helmholtz COTHCavettHelmholtz Cavett Helmholtz energy.
InternalEnergy COTHCavettInternalEnerg
y 
Cavett Internal energy. 
GibbsEnergy COTHCavettGibbs    Cavett Gibbs energy.
IGCp COTHIdealGasCp Ideal gas heat capacity. 
OffsetIGH COTHOffsetIGH Ideal gas Offset enthalpy.7-23
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ThOffsetH COTHOffsetH Offset enthalpy with heat 
of formation.
OffsetIGS COTHOffsetIGS Ideal gas offset entropy.
OffsetS COTHOffsetS Offset entropy.
MolarDensity COTHSolidDensity Solid molar density.
MolarVolume COTHMolarVolume Solid molar volume.
Enthalpy COTHSolidEnthalpy Solid enthalpy.
Entropy COTHSolidEntropy Solid entropy.
Cp COTHSolidCp Solid heat capacity.
Property Name Class Name Description7-24
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ThUNIQUAC
This model uses statistical mechanics and the quasi-chemical 
theory of Guggenheim to represent the liquid structure. The 
equation is capable of representing LLE, VLE, and VLLE with 
accuracy comparable to the NRTL equation, but without the 
need for a non-randomness factor.
XML File Name Name Description
uniquac_liquid UNIQUAC UNIQUAC Model with two-
coefficient temperature 
dependent parameters.
Property Name Class Name Description
Enthalpy COTHCavettEnthalpy     Cavett enthalpy.    
Entropy COTHCavettEntropy   Cavett entropy.
Cp COTHCavettCp   Cavett heat capacity.   
LnFugacityCoeff COTHUNIQUACLnFugacityCoef
f         
UNIQUAC fugacity 
coefficient.
LnFugacity COTHUNIQUACLnFugacity   UNIQUAC fugacity.
LnActivity Coeff COTHUNIQUACLnActivityCoeff UNIQUAC activity 
coefficient.
LnStdFugacity COTHIdeallStdFug Ideal standard 
fugacity with or 
without poynting 
correction.
LnActivityCoeffDT COTHUNIQUACLnActivityCoeff
DT 
UNIQUAC activity 
coefficient wrt 
temperature.
MolarDensity COTHCOSTALDDensity COSTALD molar 
density.
MolarVolume COTHCOSTALDVolume   COSTALD molar 
volume. 
Viscosity COTHViscosity   Viscosity.   
ThermalConductiv
ity
COTHThermCond    Thermal conductivity.   
SurfaceTension COTHSurfaceTension Surface Tension. 
Helmholtz COTHCavettHelmholtz Cavett Helmholtz 
energy.
InternalEnergy COTHCavettInternalEnergy Cavett Internal 
energy. 
GibbsEnergy COTHCavettGibbs    Cavett Gibbs energy.7-25
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ThIGCp COTHIdealGasCp Ideal gas heat 
capacity. 
OffsetIGH COTHOffsetIGH Ideal gas Offset 
enthalpy.
OffsetH COTHOffsetH Offset enthalpy with 
heat of formation.
OffsetIGS COTHOffsetIGS Ideal gas offset 
entropy.
OffsetS COTHOffsetS Offset entropy.
MolarDensity COTHSolidDensity Solid molar density.
MolarVolume COTHMolarVolume Solid molar volume.
Enthalpy COTHSolidEnthalpy Solid enthalpy.
Entropy COTHSolidEntropy Solid entropy.
Cp COTHSolidCp Solid heat capacity.
Property Name Class Name Description7-26
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ThChien-Null
This model provides consistent framework for applying existing 
Activity Models on a binary by binary basis. It allows you to 
select the best Activity Model for each pair in your case.
XML File Name Name Description
cn_liquid Chien-Null Three-parameter temperature 
dependent Chien-Null Model.
Property Name Class Name Description
Enthalpy COTHCavettEnthalpy       Cavett enthalpy.    
Entropy COTHCavettEntropy     Cavett entropy.
Cp COTHCavettCp     Cavett heat capacity.   
LnFugacityCoeff COTHCNLnFugacityCoeff CN fugacity coefficient.
LnFugacity COTHCNLnFugacity   CN fugacity.
LnActivity Coeff COTHCNLnActivityCoeff CN activity coefficient.
LnActivityCoeffDT COTHCNLnActivityCoeff
DT 
CN activity coefficient wrt 
temperature.
LnStdFugacity COTHIdealStdFug Ideal standard fugacity with 
or without poynting 
correction.
ActTempDep COTHCNTempDep HYSYS CN temperature 
dependent properties.
MolarDensity COTHCOSTALDDensity COSTALD molar density.
MolarVolume COTHCOSTALDVolume   COSTALD molar volume. 
Viscosity COTHViscosity   Viscosity.   
ThermalConductivi
ty
COTHThermCond    Thermal conductivity.   
SurfaceTension COTHSurfaceTension Surface Tension. 
Helmholtz COTHCavettHelmholtz Cavett Helmholtz energy.
InternalEnergy COTHCavettInternalEner
gy 
Cavett Internal energy. 
GibbsEnergy COTHCavettGibbs Cavett Gibbs energy.
IGCp COTHIdealGasCp Ideal gas heat capacity. 
OffsetIGH COTHOffsetIGH Ideal gas Offset enthalpy.
OffsetH COTHOffsetH Offset enthalpy with heat of 
formation.
OffsetIGS COTHOffsetIGS Ideal gas offset entropy.
OffsetS COTHOffsetS Offset entropy.
MolarDensity COTHSolidDensity Solid molar density.7-27
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ThMolarVolume COTHMolarVolume Solid molar volume.
Enthalpy COTHSolidEnthalpy Solid enthalpy.
Entropy COTHSolidEntropy Solid entropy.
Cp COTHSolidCp Solid heat capacity.
Property Name Class Name Description7-28
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ThAntoine
This model is applicable for low pressure systems that behave 
ideally.
XML File Name Name Description
antoine_liquid Antoine UNIQUAC activity model with 
two-coefficient temperature 
dependent parameters.
Property Name Class Name Description
Enthalpy COTHLeeKeslerEnthalpy      Lee-Kesler enthalpy.
Entropy COTHLeeKeslerEntropy    Lee-Kesler entropy.
Cp COTHLeeKeslerCp    Lee-Kesler heat capacity.
LnFugacityCoeff COTHAntoineLnFugacityCo
eff          
Antoine fugacity 
coefficient.
LnFugacity COTHAntoineLnFugacity   Antoine fugacity.
LnActivity Coeff COTHAntoineLnActivityCoe
ff 
Antoine activity 
coefficient.
MolarDensity COTHCOSTALDDensity COSTALD molar density.
MolarVolume COTHCOSTALDVolume   COSTALD molar volume.
Viscosity COTHViscosity   HYSYS Viscosity.
ThermalConductiv
ity
COTHThermCond    HYSYS Thermal 
conductivity.
SurfaceTension COTHSurfaceTension Surface Tension.
IGCp COTHIdealGasCp Ideal gas heat capacity. 
OffsetIGH COTHOffsetIGH Ideal gas Offset enthalpy.
OffsetH COTHOffsetH Offset enthalpy with heat 
of formation.
OffsetIGS COTHOffsetIGS Ideal gas offset entropy.
OffsetS COTHOffsetS Offset entropy.
MolarDensity COTHSolidDensity Solid molar density.
MolarVolume COTHMolarVolume Solid molar volume.
Enthalpy COTHSolidEnthalpy Solid enthalpy.
Entropy COTHSolidEntropy Solid entropy.
Cp COTHSolidCp Solid heat capacity.7-29
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ThBraun K10
This model is strictly applicable to heavy hydrocarbon systems 
at low pressures. The model employs the Braun convergence 
pressure method, where, given the normal boiling point of a 
component, the K-value is calculated at system temperature and 
10 psia (68.95 kPa).
XML File Name Name Description
braunk10_liquid Braun K10 Braun K10 Vapour Pressure 
Property Model.
Property Name Class Name Description
Enthalpy COTHLeeKeslerEnthalpy      Lee-Kesler enthalpy.
Entropy COTHLeeKeslerEntropy    Lee-Kesler entropy.
Cp COTHLeeKeslerCp    Lee-Kesler heat 
capacity.
LnFugacityCoeff COTHBraunK10LnFugacityCo
eff 
Braun K10 fugacity 
coefficient.
LnFugacity COTHBraunK10LnFugacity   Braun K10 fugacity.
LnActivity Coeff COTHBraunK10LnActivityCoe
ff 
Braun K10 molar 
volume.
MolarDensity COTHCOSTALDDensity Costald molar density.
MolarVolume COTHCOSTALDVolume   Costald molar volume.
Viscosity COTHViscosity   HYSYS viscosity.
ThermalConductiv
ity
COTHThermCond    HYSYS thermal 
conductivity.
SurfaceTension COTHSurfaceTension HYSYS surface tension.
IGCp COTHIdealGasCp Ideal gas heat capacity.
OffsetIGH COTHOffsetIGH Ideal gas Offset 
enthalpy.
OffsetH COTHOffsetH Offset enthalpy with 
heat of formation.
OffsetIGS COTHOffsetIGS Ideal gas offset entropy.
OffsetS COTHOffsetS Offset entropy.
MolarDensity COTHSolidDensity Solid molar density.
MolarVolume COTHMolarVolume Solid molar volume.
Enthalpy COTHSolidEnthalpy Solid enthalpy.
Entropy COTHSolidEntropy Solid entropy.
Cp COTHSolidCp Solid heat capacity.7-30
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ThEsso Tabular
This model is strictly applicable to hydrocarbon systems at low 
pressures. The model employs a modification of the Maxwell-
Bonnel vapour pressure model.
XML File Name Name Description
essotabular_liqui
d
Esso Tabular Esso Tabular vapour Pressure 
Property Model.
Property Name Class Name Description
Enthalpy COTHLeeKeslerEnthalpy Lee-Kesler enthalpy.
Entropy COTHLeeKeslerEntropy Lee-Kesler entropy.
Cp COTHLeeKeslerCp Lee-Kesler heat capacity.
LnFugacityCoeff COTHEssoLnFugacityCoe
ff
Esso fugacity coefficient.
LnFugacity COTHEssoLnFugacity Esso fugacity.
LnActivity Coeff COTHEssoLnActivityCoef
f 
Esso activity coefficient.
MolarDensity COTHCOSTALDDensity Costald molar density.
MolarVolume COTHCOSTALDVolume Costald molar volume.
Viscosity COTHViscosity HYSYS viscosity.
ThermalConductiv
ity
COTHThermCond    HYSYS thermal 
conductivity.
SurfaceTension COTHSurfaceTension HYSYS surface tension.
IGCp COTHIdealGasCp Ideal gas heat capacity.
OffsetIGH COTHOffsetIGH Ideal gas Offset enthalpy.
OffsetH COTHOffsetH Offset enthalpy with heat of 
formation.
OffsetIGS COTHOffsetIGS Ideal gas offset entropy.
OffsetS COTHOffsetS Offset entropy.
MolarDensity COTHSolidDensity Solid molar density.
MolarVolume COTHMolarVolume Solid molar volume.
Enthalpy COTHSolidEnthalpy Solid enthalpy.
Entropy COTHSolidEntropy Solid entropy.
Cp COTHSolidCp Solid heat capacity.7-31
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ThChao-Seader
This method for heavy hydrocarbons, where the pressure is less 
than 10342 kPa (1500 psia), and temperatures range between -
17.78 and 260°C (0-500°F).
XML File Name Name Description
cs_liquid Chao-Seader Chao-Seader Model is a semi-
empirical property method
Property Name Class Name Description
Enthalpy COTHLeeKeslerEnthalpy Lee-Kesler enthalpy.
Entropy COTHLeeKeslerEntropy Lee-Kesler entropy.
Cp COTHLeeKeslerCp Lee-Kesler heat 
capacity.
LnFugacityCoeff COTHChaoSeaderLnFugacityCo
eff
Chao-Seader fugacity 
coefficient.
LnFugacity COTHChaoSeaderLnFugacity Chao-Seader 
fugacity.
MolarVolume COTHRKVolume   Redlich-Kwong molar 
volume.
ZFactor COTHRKZFactor Redlich-Kwong 
compressibility factor.
amix COTHRKab_1 Redlich-Kwong EOS 
amix.
Viscosity COTHViscosity   HYSYS viscosity.
ThermalConductiv
ity
COTHThermCond    HYSYS thermal 
conductivity.
SurfaceTension COTHSurfaceTension HYSYS surface 
tension.
IGCp COTHIdealGasCp Ideal gas heat 
capacity.
OffsetIGH COTHOffsetIGH Ideal gas Offset 
enthalpy.
OffsetH COTHOffsetH Offset enthalpy with 
heat of formation.
OffsetIGS COTHOffsetIGS Ideal gas offset 
entropy.
OffsetS COTHOffsetS Offset entropy.
MolarDensity COTHSolidDensity Solid molar density.
MolarVolume COTHMolarVolume Solid molar volume.
Enthalpy COTHSolidEnthalpy Solid enthalpy.7-32
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ThEntropy COTHSolidEntropy Solid entropy.
Cp COTHSolidCp Solid heat capacity.
Property Name Class Name Description7-33
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ThGrayson-Streed
This model is recommended for simulating heavy hydrocarbon 
systems with a high hydrogen content.
XML File Name Name Description
gs_liquid Grayson-Streed Grayson-Streed Model is a 
semi-empirical property 
method.
Property Name Class Name Description
Enthalpy COTHLeeKeslerEnthalpy Lee-Kesler enthalpy.
Entropy COTHLeeKeslerEntropy Lee-Kesler entropy.
Cp COTHLeeKeslerCp Lee-Kesler heat 
capacity.
LnFugacityCoeff COTHGraysonStreedLnFugaci
tyCoeff 
Grayson-Streed 
fugacity coefficient.
LnFugacity COTHGraysonStreedLnFugaci
ty 
Grayson-Streed 
fugacity.
MolarVolume COTHRKVolume Redlich-Kwong molar 
volume.
ZFactor COTHRKZFactor Redlich-Kwong 
compressibility factor.
amix COTHRKab_1 Redlich-Kwong EOS 
amix.
Viscosity COTHViscosity   HYSYS viscosity.
ThermalConductiv
ity
COTHThermCond    HYSYS thermal 
conductivity.
IGCp COTHIdealGasCp Ideal gas heat 
capacity.
OffsetIGH COTHOffsetIGH Ideal gas Offset 
enthalpy.
OffsetH COTHOffsetH Offset enthalpy with 
heat of formation.
OffsetIGS COTHOffsetIGS Ideal gas offset 
entropy.
OffsetS COTHOffsetS Offset entropy.
MolarDensity COTHSolidDensity Solid molar density.
MolarVolume COTHMolarVolume Solid molar volume.
Enthalpy COTHSolidEnthalpy Solid enthalpy.
Entropy COTHSolidEntropy Solid entropy.
Cp COTHSolidCp Solid heat capacity.7-34
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Property Packages 
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ThHysysPR
The HysysPR EOS is similar to the PR EOS with several 
enhancements to the original PR equation. It extends the range 
of applicability and better represents the VLE of complex 
systems.
XML File Name Name Description
hysyspr_liquid HysysPR Peng-Robinson EOS using Mixing 
Rule 1 for all properties.
Property Name Class Name Description
Enthalpy COTHPR_HYSYS_Enthalpy   Peng-Robinson 
enthalpy.
Entropy COTHPR_HYSYS_Entropy   Peng-Robinson 
entropy.
Cp COTHPR_HYSYS_Cp   Peng-Robinson heat 
capacity.
LnFugacityCoeff COTHPR_HYSYS_LnFugacityCo
eff 
Peng-Robinson 
fugacity coefficient.
LnFugacity COTHPR_HYSYS_LnFugacity Peng-Robinson 
fugacity.
MolarVolume COTHPR_HYSYS_Volume Peng-Robinson molar 
volume.
Viscosity COTHViscosity HYSYS viscosity.
ThermalConductiv
ity
COTHThermCond   HYSYS thermal 
conductivity.
ZFactor COTHPRZFactor   Peng-Robinson 
compressibility 
factor.
amix COTHPRab_1 Peng-Robinson amix.
IGCp COTHIdealGasCp Ideal gas heat 
capacity.
OffsetIGH COTHOffsetIGH Ideal gas Offset 
enthalpy.
OffsetH COTHOffsetH Offset enthalpy with 
heat of formation.
OffsetIGS COTHOffsetIGS Ideal gas offset 
entropy.
OffsetS COTHOffsetS Offset entropy.
MolarDensity COTHSolidDensity Solid molar density.
MolarVolume COTHMolarVolume Solid molar volume.
Enthalpy COTHSolidEnthalpy Solid enthalpy.7-35
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7-36 Liquid Phase Models
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ThEntropy COTHSolidEntropy Solid entropy.
Cp COTHSolidCp Solid heat capacity.
Property Name Class Name Description7-36
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Property Packages 
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ThKabadi-Danner
This model is a modification of the original SRK equation of 
state, enhanced to improve the vapour-liquid-liquid equilibrium 
calculations for water-hydrocarbon systems, particularly in 
dilute regions.
XML File Name Name Description
kd_liquid Kabadi-Danner Kabadi-Danner EOS using Mixing 
Rule 1 for all properties.
Property Name Class Name Description
Enthalpy COTHKDEnthalpy Kabadi-Danner enthalpy.
Entropy COTHKDEntropy Kabadi-Danner entropy.
Cp COTHKDCp Kabadi-Danner heat 
capacity.
LnFugacityCoeff COTHKDLnFugacityCoe
ff   
Kabadi-Danner fugacity 
coefficient.
LnFugacity COTHKDLnFugacity Kabadi-Danner fugacity.
MolarVolume COTHKDVolume Kabadi-Danner molar 
volume.
Viscosity COTHViscosity HYSYS viscosity.
ThermalConductiv
ity
COTHThermCond   HYSYS thermal conductivity.
SurfaceTension COTHSurfaceTension HYSYS surface tension.
ZFactor COTHKDZFactor   Kabadi-Danner 
compressibility factor.
amix COTHKDab_1 Kabadi-Danner amix.
IGCp COTHIdealGasCp Ideal gas heat capacity.
OffsetIGH COTHOffsetIGH Ideal gas Offset enthalpy.
OffsetH COTHOffsetH Offset enthalpy with heat of 
formation.
OffsetIGS COTHOffsetIGS Ideal gas offset entropy.
OffsetS COTHOffsetS Offset entropy.
MolarDensity COTHSolidDensity Solid molar density.
MolarVolume COTHMolarVolume Solid molar volume.
Enthalpy COTHSolidEnthalpy Solid enthalpy.
Entropy COTHSolidEntropy Solid entropy.
Cp COTHSolidCp Solid heat capacity.7-37
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7-38 Liquid Phase Models
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ThPeng-Robinson
This model is ideal for VLE calculations as well as calculating 
liquid densities for hydrocarbon systems. However, in situations 
where highly non-ideal systems are encountered, the use of 
Activity Models is recommended.
XML File Name Name Description
pr_liquid Peng-Robinson Peng-Robinson EOS using Mixing 
Rule 1 for all properties.
Property Name Class Name Description
Enthalpy COTHPREnthalpy Peng-Robinson enthalpy.
Entropy COTHPREntropy Peng-Robinson entropy.
Cp COTHPRCp Peng-Robinson heat capacity.
LnFugacityCoeff COTHPRLnFugacityCoe
ff   
Peng-Robinson fugacity 
coefficient.
LnFugacity COTHPRLnFugacity    Peng-Robinson fugacity.
MolarVolume COTHPRVolume   Peng-Robinson molar 
volume.
Viscosity COTHViscosity HYSYS viscosity.
ThermalConductivi
ty
COTHThermCond   HYSYS thermal conductivity.
SurfaceTension COTHSurfaceTension HYSYS surface tension.
ZFactor COTHPRZFactor   Peng-Robinson 
compressibility factor.
amix COTHPRab_1 Peng-Robinson amix.
IGCp COTHIdealGasCp Ideal gas heat capacity.
OffsetIGH COTHOffsetIGH Ideal gas Offset enthalpy.
OffsetH COTHOffsetH Offset enthalpy with heat of 
formation.
OffsetIGS COTHOffsetIGS Ideal gas offset entropy.
OffsetS COTHOffsetS Offset entropy.
MolarDensity COTHSolidDensity Solid molar density.
MolarVolume COTHMolarVolume Solid molar volume.
Enthalpy COTHSolidEnthalpy Solid enthalpy.
Entropy COTHSolidEntropy Solid entropy.
Cp COTHSolidCp Solid heat capacity.7-38
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ThPeng-Robinson-Stryjek-Vera
This is a two-fold modification of the PR equation of state that 
extends the application of the original PR method for moderately 
non-ideal systems. It provides a better pure component vapour 
pressure prediction as well as a more flexible Mixing Rule than 
Peng robinson.
XML File Name Name Description
prsv_liquid PRSV Peng-Robinson-Stryjek-Vera 
EOS using Mixing Rule 1 for all 
properties.
Property Name Class Name Description
Enthalpy COTHPRSVEnthalpy    PRSV enthalpy.
Entropy COTHPRSVEntropy    PRSV entropy.
Cp COTHPRSVCp    PRSV heat capacity.
LnFugacityCoeff COTHPRSVLnFugacityCoe
ff 
PRSV fugacity coefficient.
LnFugacity COTHPRSVLnFugacity PRSV fugacity.
MolarVolume COTHPRSVVolume PRSV molar volume.
Viscosity COTHViscosity HYSYS viscosity.
ThermalConductiv
ity
COTHThermCond   HYSYS thermal 
conductivity.
SurfaceTension COTHSurfaceTension HYSYS surface tension.
ZFactor COTHPRSVZFactor   PRSV compressibility 
factor.
amix COTHPRSVab_1 PRSV amix.
IGCp COTHIdealGasCp Ideal gas heat capacity.
OffsetIGH COTHOffsetIGH Ideal gas Offset enthalpy.
OffsetH COTHOffsetH Offset enthalpy with heat 
of formation.
OffsetIGS COTHOffsetIGS Ideal gas offset entropy.
OffsetS COTHOffsetS Offset entropy.
MolarDensity COTHSolidDensity Solid molar density.
MolarVolume COTHMolarVolume Solid molar volume.
Enthalpy COTHSolidEnthalpy Solid enthalpy.
Entropy COTHSolidEntropy Solid entropy.
Cp COTHSolidCp Solid heat capacity.7-39
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7-40 Liquid Phase Models
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ThSoave-Redlich-Kwong
In many cases it provides comparable results to PR, but its 
range of application is significantly more limited. This method is 
not as reliable for non-ideal systems.
XML File Name Name Description
srk_liquid SRK Soave-Redlich-Kwong EOS using 
Mixing Rule 1 for all properties.
Property Name Class Name Description
Enthalpy COTHSRKEnthalpy     SRK enthalpy.
Entropy COTHSRKEntropy    SRK entropy.
Cp COTHSRKCp    SRK heat capacity.
LnFugacityCoeff COTHSRKLnFugacityCoe
ff 
SRK fugacity coefficient.
LnFugacity COTHSRKLnFugacity SRK fugacity.
MolarVolume COTHSRKVolume SRK molar volume.
Viscosity COTHViscosity HYSYS viscosity.
ThermalConductiv
ity
COTHThermCond   HYSYS thermal conductivity.
SurfaceTension COTHSurfaceTension HYSYS surface tension.
ZFactor COTHSRKZFactor   SRK compressibility factor.
amix COTHSRKab_1 SRK amix.
IGCp COTHIdealGasCp Ideal gas heat capacity.
OffsetIGH COTHOffsetIGH Ideal gas Offset enthalpy.
OffsetH COTHOffsetH Offset enthalpy with heat of 
formation.
OffsetIGS COTHOffsetIGS Ideal gas offset entropy.
OffsetS COTHOffsetS Offset entropy.
MolarDensity COTHSolidDensity Solid molar density.
MolarVolume COTHMolarVolume Solid molar volume.
Enthalpy COTHSolidEnthalpy Solid enthalpy.
Entropy COTHSolidEntropy Solid entropy.
Cp COTHSolidCp Solid heat capacity.7-40
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Property Packages 
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ThVirial
This model enables you to better model vapour phase fugacities 
of systems displaying strong vapour phase interactions. 
Typically this occurs in systems containing carboxylic acids, or 
compounds that have the tendency to form stable hydrogen 
bonds in the vapour phase. In these cases, the fugacity 
coefficient shows large deviations from ideality, even at low or 
moderate pressures.
XML File Name Name Description
virial_liquid Virial Virial Equation of State.
Property Name Class Name Description
LnFugacityCoeff COTHPR_LnFugacityCoeff Peng-Robinson fugacity 
coefficient.
LnFugacity COTHPR_LnFugacity Peng-Robinson fugacity.
LnStdFugacity COTHIdealStdFug Ideal standard fugacity.
MolarVolume COTHSolidVolume Molar solid volume.
Viscosity COTHViscosity HYSYS viscosity.
ThermalConductiv
ity
COTHThermCond HYSYS thermal 
conductivity.
SurfaceTension COTHSurfaceTension HYSYS surface tension.
ZFactor COTHPR_ZFactor Peng-Robinson 
compressibility factor.
Enthalpy COTHPR_Enthalpy Peng-Robinson enthalpy.
Enthalpy COTHSolidEnthalpy Insoluble solid enthalpy.
Entropy COTHPR_Entropy Peng-Robinson entropy.
Entropy COTHSolidEntropy Insoluble solid entropy.
Cp COTHPR_Cp Peng-Robinson heat 
capacity.
Cp COTHSolidCp Insoluble solid heat 
capacity.
amix COTHPRab_1 Peng-Robinson amix.
IGCp COTHIdealGasCp Ideal gas heat capacity.
OffsetIGH COTHOffsetIGH Ideal gas Offset enthalpy.
OffsetH COTHOffsetH Offset enthalpy with heat 
of formation.
OffsetIGS COTHOffsetIGS Ideal gas offset entropy.
OffsetS COTHOffsetS Offset entropy.7-41
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7-42 Liquid Phase Models
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ThZudkevitch-Joffee
This is a modification of the Redlich-Kwong equation of state, 
which reproduces the pure component vapour pressures as 
predicted by the Antoine vapour pressure equation. This model 
has been enhanced for better prediction of vapour-liquid 
equilibrium for hydrocarbon systems, and systems containing 
Hydrogen.
XML File Name Name Description
zj_liquid Zudkevitch-Joffee Zudkevitch-Joffee Equation of 
State.
Property Name Class Name Description
Enthalpy COTHLeeKeslerEnthal
py
Lee-Kesler enthalpy.
Entropy COTHLeeKeslerEntrop
y 
Lee-Kesler entropy.
Cp COTHLeeKeslerCp     Lee-Kesler heat capacity.
LnFugacityCoeff COTHZJLnFugacityCoe
ff   
Zudkevitch-Joffee fugacity 
coefficient.
LnFugacity COTHZJLnFugacity Zudkevitch-Joffee fugacity.
MolarVolume COTHZJVolume Zudkevitch-Joffee molar 
volume.
Viscosity COTHViscosity HYSYS viscosity.
ThermalConductiv
ity
COTHThermCond   HYSYS thermal conductivity.
SurfaceTension COTHSurfaceTension HYSYS surface tension.
ZFactor COTHZJZFactor   Zudkevitch-Joffee 
compressibility factor.
amix COTHZJab_1 Zudkevitch-Joffee amix.
IGCp COTHIdealGasCp Ideal gas heat capacity.
OffsetIGH COTHOffsetIGH Ideal gas Offset enthalpy.
OffsetH COTHOffsetH Offset enthalpy with heat of 
formation.
OffsetIGS COTHOffsetIGS Ideal gas offset entropy.
OffsetS COTHOffsetS Offset entropy.
MolarDensity COTHSolidDensity Solid molar density.
MolarVolume COTHMolarVolume Solid molar volume.
Enthalpy COTHSolidEnthalpy Solid enthalpy.7-42
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Property Packages 
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ThEntropy COTHSolidEntropy Solid entropy.
Cp COTHSolidCp Solid heat capacity.
Property Name Class Name Description7-43
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7-44 Liquid Phase Models
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ThLee-Kesler-Plöcker
This model is the most accurate general method for non-polar 
substances and mixtures.
XML File Name Name Description
lkp_liquid Lee-Kesler-Plöcker Lee-Kesler-Plöcker EOS using 
Mixing Rule 1 for all properties.
Property Name Class Name Description
Enthalpy COTHLeeKeslerEnthalpy   Lee-Kesler enthalpy.
Entropy COTHLeeKeslerEnthalpy   Lee-Kesler entropy.
Cp COTHLeeKeslerCp Lee-Kesler heat capacity.
LnFugacityCoeff COTHLKPLnFugacityCoef
f    
LKP fugacity coefficient.
LnFugacity COTHLKPLnFugacity   LKP fugacity.
MolarVolume COTHLKPMolarVolume   LKP molar volume.
Viscosity COTHViscosity HYSYS viscosity.
ThermalConductiv
ity
COTHThermCond   HYSYS thermal conductivity.
SurfaceTension COTHSurfaceTension HYSYS surface tension.
ZFactor COTHLKPZFactor    LKP compressibility factor.
IGCp COTHIdealGasCp Ideal gas heat capacity.
OffsetIGH COTHOffsetIGH Ideal gas Offset enthalpy.
OffsetH COTHOffsetH Offset enthalpy with heat of 
formation.
OffsetIGS COTHOffsetIGS Ideal gas offset entropy.
OffsetS COTHOffsetS Offset entropy.
MolarDensity COTHSolidDensity Solid molar density.
MolarVolume COTHMolarVolume Solid molar volume.
Enthalpy COTHSolidEnthalpy Solid enthalpy.
Entropy COTHSolidEntropy Solid entropy.
Cp COTHSolidCp Solid heat capacity.7-44
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Utilities 8-1
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Th8  Utilities8-1
8.1  Introduction................................................................................... 2
8.2  Envelope Utility.............................................................................. 2
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8-2 Introduction
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Th8.1 Introduction
The utility commands are a set of tools, which interact with a 
process by providing additional information or analysis of 
streams or operations. In HYSYS, utilities become a permanent 
part of the Flowsheet and are calculated automatically when 
appropriate.
8.2 Envelope Utility
Currently there are two utilities in HYSYS that are directly 
related to Aspen HYSYS Thermodynamics COM Interface:
• HYSYS Two-Phase Envelope Utility
• Aspen HYSYS Thermodynamics COM Interface Three-Phase 
Envelope Utility
They can be accessed through the Envelope utility in HYSYS. 
Refer to the Envelope Utility section in Chapter 14 in the 
Operations Guide for more information.8-2
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References 
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Th9  References
 1 Prausnitz, J.M.; Lichtenthaler, R.N., and de Azeuedo, E.G. “Molecular 
Thermodynamics of Fluid Phase Equilibria”, 2nd Ed. Prentice Hall, 
Inc. (1986).
 2 Prausnitz, J.M.; Anderson, T.; Grens, E.; Eckert, C.; Hsieh, R.; and 
O'Connell, J.P. “Computer Calculations for Multi-Component 
Vapour-Liquid and Liquid-Liquid Equilibria” Prentice-Hall Inc. 
(1980).
 3 Modell, M. and Reid, R.D., “Thermodynamics and its Applications”, 
2nd Ed., Prentice-Hall, Inc. (1983).
 4 Michelsen, M.L., “The Isothermal Flash Problem. Part I. Stability, Part 
II. Phase Split Calculation, Fluid Phase Equilibria”, 9 1-19; 21-40. 
(1982).
 5 Gautam, R. and Seider, J.D., “Computation of Phase and Chemical 
Equilibrium. I. Local and Constrained Minima in Gibbs Free Energy; 
II. Phase Splitting, III. Electrolytic Solutions.”, AIChE J. 24, 991-
1015. (1979).
 6 Reid, J.C.; Prausnitz, J.M. and Poling, B.E. “The Properties of Gases 
and Liquid” McGraw-Hill Inc. (1987).
 7 Henley, E.J.; Seader, J.D., “Equilibrium-Stage Separation Operations 
in Chemical Engineering”, John Wiley and Sons. (1981).
 8 Feynman, R.P., Leighton, R.B., and Sands, M., “The Feyman Lectures 
on Physics” Addison-Wesley Publishing Company. (1966).
 9 Peng, D.Y. and Robinson, D.B. “A New Two Constant Equation of 
State” Ind. Eng. Chem. Fundamen. 15, 59-64. (1976).
 10Stryjek, R. and Vera, J.H. “PRSV: An Improved Peng-Robinson 
Equation of State for Pure components and Mixtures” The Canadian 
Journal of Chemical Eng. 64. (1986).
 11 Soave, G. “Equilibrium Constants from a Modified Redlich-Kwong 
Equation of State”. Chem. Eng. Sci. 27, 1197-1203. (1972).
 12Graboski, M.S. and Daubert, T.E., “A Modified Soave Equation of State 
for Phase Equilibrium Calculations. 3. Systems Containing 
Hydrogen” Ind. Eng. Chem. Fundamen. 15, 59-64. (1976).
 13Zudkevitch, D. and Joffee, J., Correlation and Prediction of Vapor-
Liquid Equilibria with the Redlich Kwong Equation of State, AIChE 9-1
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9-2 
ww
ThJ.; 16, 112-119. (1970).
 14Mathias, P.M., “Versatile Phase Equilibrium Equation of State”, Ind. 
Eng. Chem. Process Des. Dev. 22, 385-391. (1983).
 15Mathias, P.M. and Copeman, T.W. “Extension of the Peng Robinson of 
state to Complex Mixtures: Evaluations of the Various Forms of the 
Local Composition Concept”. (1983).
 16Kabadi, V.N.; Danner, R.P., “A Modified Soave Redlich Kwong Equation 
of State for Water-Hydrocarbon Phase Equilibria”, Ind. Eng. Chem. 
process Des. Dev., 24, 537-541. (1985).
 17Twu, C.H. and Bluck, D., “An Extension of Modified Soave-Redlich-
Kwong Equation of State to Water-Petroleum Fraction Systems”, 
Paper presented at the AIChE Meeting. (1988).
 18Tsonopoulos, C. AIChE Journal 20, 263. (1974).
 19Hayden, J.G. and O'Connell, J.P. “A Generalized Method for Predicting 
Second Virial Coefficients” Ind. Eng. Chem. Process Des. Dev. 14, 
209-216. (1975).
 20Wilson, G.M. “Vapour-Liquid Equilibrium XI: A New Expression for the 
Excess Free Energy of Mixing” J. Am. Chem Soc. 86, 127-130. 
(1964).
 21Walas, S.M. “Phase Equilibria in Chemical Engineering” Butterworth 
Publishers. (1985).
 22Renon, H. and Prausnitz, J.M. “Local Compositions in Thermodynamic 
Excess Functions for Liquid Mixtures” AIChE Journal 14, 135-144. 
(1968).
 23Abrams, D.S. and Prausnitz, J.M., “Statistical Thermodynamics of 
Liquid Mixtures: A New Expression for the Excess Gibbs Energy of 
Partly of Completely Miscible Systems” AIChE Journal 21, 116-128. 
(1975).
 24Fredenslund, A. Jones, R.L. and Prausnitz, J.M. “Group Contribution 
Estimations of Activity Coefficients in non-ideal Liquid Mixtures” 
AIChE Journal 21, 1086-1098. (1975).
 25Fredenslund, A.; Gmehling, J. and Rasmussen, P. “Vapour-Liquid 
Equilibria using UNIFAC” Elsevier. (1977).
 26Wilson, G.M. and Deal, C.H. “Activity Coefficients and Molecular 
Structure” Ind. Eng. Chem. Fundamen. 1, 20-33. (1962).
 27Derr, E.L. and Deal, C.H., Instn. Chem. Eng. Symp. Ser. No. 32, Inst. 
Chem. Engr. London 3, 40-51. (1969).
 28Le Bas, G. “The Molecular Volumes of Liquid Chemical Compounds” 
Longmans, Green and Co., Inc. New York. (1915).9-2
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References 
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Th 29Kojima, K. and Tochigi, K. “Prediction of Vapour-Liquid Equilibria 
using ASOG” Elsevier. (1979).
 30Orye, R.V. and Prausnitz, J.M. “Multi-Component Equilibria with the 
Wilson Equation” Ind. Eng. Chem. 57, 18-26. (1965).
 31Magnussen, T.; Rasmussen, P. and Fredenslund, A. “UNIFAC 
Parameter Table for Prediction of Liquid-Liquid Equilibria” Ind. Eng. 
Chem. Process Des. Dev. 20, 331-339. (1981).
 32Jensen, T.; Fredenslund, A. and Rasmussen, “Pure Component 
Vapour-Pressures using UNIFAC Group Contribution” Ind. Eng. 
Chem. Fundamen. 20, 239-246. (1981).
 33Dahl, Soren, Fredenslund, A. and Rasmussen, P., “The MHV2 Model: A 
UNIFAC Based Equation of State Model for Prediction of Gas 
Solubility and Vapour-Liquid Equilibria at Low and High Pressures” 
Ind. Eng. Chem. Res. 30, 1936-1945. (1991).
 34“Group Contribution Method for the Prediction of Liquid Densities as a 
Function of Temperature for Solvents, Oligomers and Polymers”, 
Elbro, H.S., Fredenslund, A. and Rasmussen, P., Ind. Eng. Chem. 
Res. 30, 2576-2586. (1991).
 35W.H., H.S. and S.I. Sandler, “Use of ab Initio Quantum Mechanics 
Calculations in Group Contribution Methods. 1. Theory and the 
Basis for Group Identifications” Ind. Eng. Chem. Res. 30, 881-889. 
(1991).
 36W.H., H.S., and S.I. Sandler, “Use of ab Initio Quantum Mechanics 
Calculations in Group Contribution Methods. 2. Test of New Groups 
in UNIFAC” Ind. Eng. Chem. Res. 30, 889-897. (1991).
 37McClintock, R.B.; Silvestri, G.J., “Formulations and Iterative 
Procedures for the Calculation of Properties of Steam”, The 
American Society of Mechanical Engineers, New York. (1967).
 38Hankinson, R.W. and Thompson, G.H., AIChE J., 25, 653. (1979).
 39Ely, J.F. and Hanley, H.J.M., “A Computer Program for the Prediction 
of Viscosity and Thermal Conductivity in Hydrocarbon Mixtures”, 
NBS Technical Note 1039. (1983).
 40Hildebrand, J.H., Prausnitz, J.M. and Scott, R.L “Regular and Related 
Solutions”, Van Nostrand Reinhold Co., New York. (1970).
 41Soave, G., Direct Calculation of Pure-Component Vapour Pressure 
through Cubic Equations of State, Fluid Phase Equilibria, 31, 203-
207. (1986).
 42Twu, C.H., I.E.C. Proc. Des. & Dev. 24, 1287. (1985).
 43Twu, C.H., “An Internally Consistent Correlation for Predicting the 9-3
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9-4 
ww
ThCritical Properties and Molecular Weight of Petroleum and Coal-tar 
Liquids”, Fluid Phase Equilibria, 16, 137-150. (1984).
 44Wilson, G.M. “Vapour-Liquid Equilibria, Correlation by Means of a 
Modified Redlich Kwong Equation of State”.
 45Wilson, G.M. “Calculation of Enthalpy Data from a Modified Redlich 
Kwong Equation of State”.
 46Soave, G. “Improvement of the van der Waals Equation of State” 
Chem. Eng. Sci 39, 2, 357-369. (1984).
 47Chao, K.C and Seader, J.D. “A General Correlation of Vapour-Liquid 
Equilibria in Hydrocarbon Mixtures” AIChE Journal 7, 598-605. 
(1961).
 48Larsen, B.L.; Fredenslund, A. and Rasmussen, P. “Predictions of VLE, 
LLE, and HE with Superfac” CHISA. (1984).
 49Pierotti, G.J.; Deal, C.H. and Derr, E.L. Ind. Eng. Chem. 51, 95. 
(1959).
 50Lee, B.I. and Kesler, M.G. AIChE Journal 21, 510. (1975).
 51Woelflin, W., “Viscosity of Crude-Oil Emulsions”, presented at the 
spring meeting, Pacific Coast District, Division of Production, Los 
Angeles, California, March 10, 1942.
 52Gambill, W.R., Chem. Eng., March 9, 1959.
 53Perry, R.H. and Green, D.W. Perry’s Chemical Engineers’ Handbook 
(Seventh Edition) McGraw-Hill. (1997).
 54Reid, C.R., Prausnitz, J.M. and Sherwood, T.K., “The Properties of 
Gases and Liquids”, McGraw-Hill Book Company. (1977).9-4
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Index
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The doA
Activity Coefficient Models
vapour phase options 2-31
Activity Coefficients 2-9
See individual activity models
Activity Models 3-98
 See individual Activity models
Asymmetric Phase Representation 2-26
B
Bubble Point 6-5
BWR Equation 3-96
C
carboxylic acid 2-24
Cavett Method 4-2
Chao Seader 3-191
semi-empirical method 3-191
Chao-Seader Model 3-191
Chemical Potential
ideal gas 2-7
real gas 2-8
Chien-Null Model 3-182
property classes 3-185
property methods 3-185
COSTALD Method 4-11
Cp 2-38
D
Departure Functions
Enthalpy 2-38
Dew Point 6-4
Dimerization 2-21
E
Enthalpy Flash 6-5
Enthalpy Reference States 5-2
Entropy Flash 6-6
Entropy Reference States 5-4
Equations of State
See also individual equations of state
Equilibrium Calculations 2-24
Equilibrium calculations 2-24
F
Flash
T-P Flash 6-3
vapour fraction 6-3–6-4
Flash Calculations
temperature-pressure (TP) 6-2
Flash calculations 2-24
Fugacity 2-8
ideal gas 2-18
simplifications 2-18
G
General NRTL Model 3-155
Gibbs Free Energy 2-34
Gibbs-Duhem Equation 2-16
Grayson Streed 3-192
semi-empirical method 3-192
Grayson-Streed Model 3-192
H
Henry’s Law 2-12, 2-31
estimation of constants 2-15
HypNRTL Model 3-154
HysysPR Equation of State 3-17
mixing rules 3-24
property classes 3-18
property methods 3-18
I
Ideal Gas Cp 5-5
Ideal Gas Equation of State 3-3
property classes 3-4
property methods 3-4
Ideal Gas Law 2-31
Ideal Solution Activity Model 3-101
property classes 3-101
property methods 3-101
Insoluble Solids 4-22
Interaction Parameters 2-27
Internal Energy 2-3
K
Kabadi-Danner Equation of State 3-65
mixing rules 3-74
property classes 3-68
property methods 3-68
K-values 2-24
L
Lee-Kesler Equation of State 3-92
mixing rules 3-96
property classes 3-93I-1
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The doproperty methods 3-93
Lee-Kesler-Plocker Equation 3-96
Liquid Phase Models 7-13
M
Margules Model 3-123
property classes 3-124
property methods 3-124
N
Non-Condensable Components 2-14
NRTL Model 3-141
property classes 3-146, 3-155
property methods 3-146, 3-155
P
Peng Robinson Equation of State
mixing rules 3-14
property classes 3-8
property methods 3-8
Peng-Robinson Equation 2-31
Peng-Robinson Equation of State 3-7
Peng-Robinson Stryjek-Vera Equation of State 
3-2335
mixing rules 3-33
property classes 3-27
property methods 3-27
Phase Stability 2-33
Property Packages 7-1
recommended 2-30
selecting 2-28
Q
Quality Pressure 6-5
R
Rackett Method 4-8
Redlich-Kwong Equation of State 3-46
mixing rules 3-53
property classes 3-48
property methods 3-48
Regular Solution Activity Model 3-106
property classes 3-106
property methods 3-106
S
Scott's Two Liquid Theory 3-142
Soave-Redlich-Kwong Equation 2-31
Soave-Redlich-Kwong Equation of State 3-36
mixing rules 3-43
property classes 3-37
property methods 3-37
Solids 6-6
Standard State Fugacity 5-6
Surface Tension 4-21
Symmetric Phase Representation 2-26
T
Thermal Conductivity 4-18
T-P Flash Calculation 6-3
U
UNIFAC Model 3-170
property classes 3-174
property methods 3-174
UNIQUAC Equation 3-158
application 3-160
UNIQUAC Model 3-158
property classes 3-162
property methods 3-162
V
Van Laar Equation
application 3-115
Van Laar Model 3-111
property classes 3-116
property methods 3-116
Vapour Phase Models 7-2
Vapour Pressure 6-5
Virial Equation 3-86
calculating second virial coefficient 3-78
vapour phase chemical association 3-84
Virial Equation of State 3-77
mixing rules 3-83
property classes 3-87
property methods 3-87
Viscosity 4-14
liquid phase mixing rules 4-17
W
Wilson Equation
application 3-133
Wilson Model 3-130
property classes 3-134
property methods 3-134I-2
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I-3
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The doZ
Zudkevitch-Joffee Equation of State 3-56
mixing rules 3-62
property classes 3-57
property methods 3-57I-3
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The doI-4
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