Chemical Engineering December 2019 - 54

Classification
Ideal gas equation
Generalized correlations
(such as LeeKesler-Plocker)
Virial
equations
Cubic EOS (such as
Peng Robinson (PR),
SRK, RK and others)
Low
pressure
Yes
Yes
Yes
Yes
High
pressure
No
Yes
No
<1,000
bar for
PR, and
<350 bar
for SRK
More complex EOS
(such as BenedictWebb-Rubin;
BWR))
Yes
Yes
TABLE 1. EQUATION OF STATE (EOS) APPLICABILITY GUIDE
Comments
Liquid
phase
No
No
No
Yes
Polar
molecules
No
Yes
No
No (unless
specifically
modified)
Strictly applicable to ideal gas systems
The compressibility factor and accentric factor attempt to account for non-ideality. These
correlations are of a graphical form and are easy to use. The basic premise is that all gaseous
components with similar accentricity behave similarly at the same reduced temperature
(Tr) and reduced pressure (Pr)
Though these equations have reasonable accuracy for non-polar gas mixtures at low to
medium pressures, they have limited applicability, as they have not been developed to the
extent of the more popular cubic EOS
Cubic EOS (cubic with respect to specific volume) are the most popular EOS used in the
oil-and-gas and petrochemical industries. They are relatively simple to apply and are able
to predict the behavior of saturated liquid-phase components, in addition to vapor-phase
behavior. They are all susceptible to errors in prediction at or very near the critical point,
but are considered to be more accurate than activity coefficient methods in that region.
However, by themselves they cannot predict within the two-phase (V-L) region of a pure
component
Yes
specific (molar) volume of a component
(or mixture of components) in a
single phase can be termed an EOS.
The ideal gas law represents the
simplest EOS.
PV = nRT
Where:
P = The pressure of the gas
V = The volume of the gas
n = The number of moles
T = The absolute temperature
R = The ideal gas constant
This equation makes no allowance
for intermolecular forces, and assumes
individual molecules do not
occupy any volume relative to the
total volume. Due to these simplifying
assumptions, this EOS is only
applicable to simple, spherical molecules
in the gas or vapor-phase that
Method
Ideal solution
Regular solution
Binary
parameters
None
None
Two-suffix Margules One
Two-constant Margules
Three-suffix
Margules
Van
Laar
Wilson
NRTL
UNI-QUAC
52
Two
Two
Two
Two
Three -Five
Two
Different-sized
molecules
No
Yes
No
No
No
Yes
Yes
Yes
Yes
Yes
Such EOS contain many adjustable parameters, which can extend their applicability,
though often only for a limited range of components. Their applicability to describing
liquid-phase behavior is equation-specific
are present at relatively low pressure
and high temperature.
In order to extend the applicability
of the ideal gas equation to real
gas
systems and include liquidphase
pressure-vapor-temperature
(PVT) behavior, a number of parameters
and modifications are
introduced below:
* The compressibility factor
* Acentric factor
* Van der Waal a and b correction
factor
* The binary interaction parameter
Proprietary modifications to various
EOS can help to extend their
applicability to moderately non-ideal
mixtures of components commonly
encountered in oil-and-gas and petrochemical
processes. For example,
mixtures of glycol, alcohol, water
and hydrocarbons can be described
by some modified EOS. These EOS
Non-ideal/
Polar binary
mixtures
No
Phase
splitting
No
Yes
No
No
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
No
Yes
Yes
contain binary interaction parameters,
which have been determined
from experimental data and actual
plant operating data. Descriptions
of the applicability of various EOS
to various chemical systems can be
found in online or in published operating
manuals such as those found
in Refs. 1 and 2 that accompany
most commercial computer simulation
packages. The general applicability
of EOS methods is summarized
in Table 1.
However, EOS typically have a
number of limitations, which restrict
their application to relatively
simple and primarily non-polar components,
such as hydrocarbons
and light gases. The main
limitations include the following:
* Complexities introduced by the
mathematical methods that are
used to determine the fugacity coTABLE
2. LIQUID ACTIVITY COEFFICIENT METHOD APPLICABILITY GUIDE
Comments
Only applicable to similarly sized molecules and components consisting of similar
molecular species
Allows pure component data to be used to predict activity coefficients. Non-adjustable
parameters attempt to account for differences in polarity and molecular
size. Applicable to typical non-polar molecules such as hydrocarbons
Simplistic. Assumes all molecules are of a similar size and only considers interactions
between two molecules (hence two-suffix) throughout a mixture
Assumes similarly sized molecules, but assumes that intermolecular interactions
between pairs of molecules (of different molecular species) are not equal
By extending the number of molecules involved in interactions to three, the
range of applicability is extended. Most widely used of the Margules methods
Does not assume similar sized molecular components, and has been extended
to non-ideal mixtures. Wide usage and simple to apply
The main drawback is its inability to predict LLE (for instance, liquid-liquid immiscibility)
Widely
applicable. Good for VLE, LLE and VLLE
Parameters not as dependent on temperature as NRTL parameters. Its form
makes it more applicable to solutions containing small or large molecules (such
as polymers)
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