VLE Data - Selection and Use

GBH Enterprises, Ltd.

Process Engineering Guide:
GBHE-PEG-MAS-601

VLE Data: Selection and Use

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Process Engineering Guide:

VLE Data: Selection and Use

CONTENTS

SECTION

0

INTRODUCTION/PURPOSE

3

1

SCOPE

3

2

FIELD OF APPLICATION

3

3

DEFINITIONS

3

4

DIAGRAMMATIC REPRESENTATION OF IDEAL
AND NON-IDEAL SYSTEMS

4

4.1
4.2

Ideal Mixtures
Non-Ideal Mixtures

4
4

5

REVIEW OF VLE MODELS

10

5.1
5.2
5.3
5.4

Ideal Behavior in Both Phases
Liquid Phase Non-Idealities
High Pressure Systems
Special Models

10
11
12
14

6

SETTING UP A VLE MODEL

19

6.1
6.2
6.3
6.4

Define Problem
Select Data
Select Correlation(s)
Produce Model

19
19
19
20


7

AVOIDING PITFALLS

20

7.1
7.2
7.3
7.4
7.5
7.6

Experimental Data is Better than Estimates
Check Validity of Fitted Model
Check Limitations of Estimation Methods
Know Your System
Appreciate Errors and Effects
If in Doubt – Ask

20
20
20
20
20
22

8

A CASE STUDY

22

8.1
8.2
8.3
8.4
8.5
8.6

The Problem
The System
Data Available
Selected Correlation
Simulation
Selection of Model

22
22
22
22
22
23

9

RECOMMENDED READING

27

10

VLE EXPERTS IN GBHE

27

APPENDICES

A

USE OF EXTENDED ANTOINE EQUATION

28

B

USE OF WILSON EQUATION

29

C

USEFUL METHODS OF ESTIMATING

31

D

EQUATIONS OF STATE FOR VLE CALCULATIONS

32


TABLES
1

SUMMARY OF VLE METHODS

18

2

LIST OF USEFUL REFERENCES

27

FIGURES
1

VAPOR-LIQUID EQUILIBRIUM - IDEAL SOLUTION
BEHAVIOR

5

VAPOR-LIQUID EQUILIBRIUM - A GENERALISED
Y-X DIAGRAM

6

VAPOR-LIQUID EQUILIBRIUM - MINIMUM BOILING
AZEOTROPE

7

VAPOR-LIQUID EQUILIBRIUM - MAXIMUM BOILING
AZEOTROPE

8

AZEOTROPE -TWO LIQUID PHASES

9

SENSITIVITY TO ERROR IN VLE DATA (BASED ON FENSKE
EQUATION)

21

7(a)

FITTING WILSON 'A' VALUES TO VLE DATA - CASE A

24

7(b)

FITTING WILSON 'A' VALUES TO VLE DATA - CASE B

25

7(c)

FITTING WILSON 'A' VALUES TO VLE DATA - CASE C

26

2

3

4

5

6

DOCUMENTS REFERRED TO IN THIS PROCESS
ENGINEERING GUIDE

34


0

INTRODUCTION/PURPOSE

The design or simulation of a distillation operation requires quantitative estimates
of the phase equilibrium properties of the mixture.
Unfortunately, reliable data covering the range of operating conditions
(temperature, pressure and composition) are only rarely available. In typical
cases, only fragmentary data (e.g. properties of pure components or of binary
mixtures) are at hand, and it is necessary to correlate the limited data to make
the best possible interpolations and extrapolations.

1

SCOPE

This Guide discusses the techniques for representing Vapor Liquid Equilibrium
(VLE) data for distillation calculations. It is presented in three sections:(a)

A REVIEW OF VLE MODELS in common use - their applicability and
limitations;

(b)

SETTING UP A VLE MODEL - a suggested method of approach when
modeling a system for the first time; and

(c)

AVOIDING PITFALLS - a few practical hints.

These are followed by:(d)

A CASE STUDY of a typical awkward problem;

(e)

BIBLIOGRAPHICAL REFERENCES which give recommended reading.

APPENDICES contain a summary of each of the models discussed in the guide.
This Guide is intended to give process engineers an appreciation of VLE in
practice. It does not list in detail all the equations that may be used to calculate
VLE data, or all the original references showing their derivation and application;
these may be found from the Recommended Reading list.


2

FIELD OF APPLICATION

This Guide applies to the process engineering community in GBH Enterprises
worldwide.

3

DEFINITIONS

For the purposes of this Guide, the following definition applies:
VLE

Abbreviation for Vapor Liquid Equilibrium

With the exception of terms used as proper nouns or titles, those terms with initial
capital letters which appear in this document and are not defined above are
defined in the Glossary of Engineering Terms.

4

DIAGRAMMATIC REPRESENTATION OF IDEAL AND NON-IDEAL
SYSTEMS.

This section introduces the concepts and implications of ideal and non-ideal
liquid phase behavior on vapor-liquid equilibrium. Azeotropic and two-liquid
phase systems are described. Vapor phase non-ideality is not discussed since it
introduces no major surprises such as azeotropes or additional phases.
For simplicity the discussion is restricted to binary systems - components A & B,
where A is taken to be the more volatile.
4.1

Ideal Mixtures

If a mixture of two liquids behaves ideally, then:

i.e. Raoult’s law is obeyed at all compositions in the liquid phase.

At constant temperature the plot of the partial pressure of each component in the
liquid mixture against its respective mole fraction in the liquid phase is a straight
line passing through the origin as shown in Figure 1(a) below. The total vapor
pressure, i.e. the sum of the two partial pressures is then also a straight
given in Figures 1(b), 1(c) and normal condition for a distillation 1(c), the y-x
diagram.

4.2 Non-Ideal Mixtures
To allow for deviations from ideality (i.e. from Raoult’s law) in the liquid phase,
the activity coefficients was introduced. Activity coefficients (ᵞ) are simply fudge
represent the non-ideality of the constituents of a mixture, thus

4.2.1 Non-ldeality in General
Deviations from ideality fall into two basic classes, conventionally called positive
and negative systems. In a positive system both activity coefficients are greater
than unity, while they are both less than unity in a negative system. The majority
of non-ideal systems (more than 90%) exhibit positive deviations from Raoult’s
law.
Figure 2 shows the effect of modest deviations on the shape of the y-x
equilibrium curve. Curve (a) shows an ideal system and is similar to Figure l(c).
Curve (b) shows a positive system and curve (c) shows a negative system. It is
evident from these curves that the greatest deviations from ideal behavior occur
at high dilution. In practice for the majority of systems (positive systems) it is
more difficult to obtain pure A, the more volatile component, than would be the
case if the system behaved ideally.
More extreme non-idealities (larger values of activity coefficients) result in more
extreme shapes of the curves (b) and (c), eventually leading to the formation of
azeotropes.


FIGURE 1 : VAPOR-LIQUID EQUILIBRIUM - IDEAL SOLUTION BEHAVIOR
(Binary mixture A - B, A being the more volatile component.)


FIGURE 2:

VAPOR-LIQUID EQUILIBRIUM - A GENERALIZED
Y-X DIAGRAM


4.2.2 Minimum Boiling Azeotrope
Figure 3 represents a solution forming a minimum boiling azeotrope, i.e.
exhibiting positive deviations from ideality.
These systems have a maximum total pressure greater than the vapor pressure
of either pure component (see Figure 3(a)). The activity coefficients of both
components are greater than unity (Figure 3(b)). The y-x diagram (Figure 3(c))
shows that at the azeotropic composition the vapor and liquid compositions are
the same. Figure 3(d), the boiling point diagram, shows a minimum temperature
at the composition of the azeotrope.
FIGURE 3:

AZEOTROPE (Binary mixture A - B, A being the more volatile
component)


4.2.3 Maximum Boiling Azeotrope
Figure 4 represents a solution forming a maximum boiling azeotrope, i.e.
exhibiting negative deviations from ideality. Negative deviations arise if the two
constituents of a mixture are strongly attracted and particularly if there is partial
compound formation between A and B.
In such systems the minimum total pressure is below the vapor pressure of either
pure component (see Figure 4(a)).
The activity coefficients of each component are less than unity (Figure 4(b)). The
y-x diagram (Figure 4(c)) shows vapor and liquid compositions to be the same at
the azeotropic composition. Figure 4(d), the boiling point diagram, shows a
maximum temperature at the composition of the azeotrope.


FIGURE 4: VAPOR-LIQUID EQUILIBRIUM - MAXIMUM BOILING
AZEOTROPE (Binary mixture A - B, A being the more volatile component).


4.2.4 Minimum Boiling Azeotrope - Two Liquid Phases
Figure 5 represents a mixture forming a minimum boiling azeotrope where
solubility in the liquid phase is limited.
Separation of the liquid into two liquid phases occurs over the concentration
range marked by a constant total pressure (see Figure 5(a)). In this region the
partial and total pressures remain constant as the relative amounts of the two
phases change. High activity coefficients are evident in the two phase region
(Figure 5(b)). The y-x diagram (Figure 5(c)) shows a horizontal line over the two
liquid phase region. Figure 5(d), the boiling point diagram for a heteroazeotrope
shows a minimum constant temperature and constant vapor composition over
this region.
FIGURE 5: VAPOR-LIQUID EQUILIBRIUM - MINIMUM BOILING AZEOTROPE
- TWO LIQUID PHASES (Binary mixture A - B, A being the more volatile
component)


5

REVIEW OF VLE MODELS

Consider a two-phase system in which a vapor mixture is in equilibrium with a
liquid mixture.
The quantities of interest are the temperature, pressure and compositions of both
phases. Given some of these variables, the problem is to calculate the others.
For every component i in the mixture, the conditions of thermodynamic
equilibrium are given by:-

The purpose of a VLE model is to relate these fugacities to temperature,
pressure and mixture compositions.


The most common methods of representation of VLE data fall into three
categories:(a)

Ideal behavior in both phases.

(b)

Liquid phase non-idealities.

(c)

High pressure systems.

These are described in 5.1 to 5.3, inclusive, together with a discussion of:(a)

The data required to establish each model,

(b)

Its complexity (i.e. computing time), and

(c)

Its applicability and limitations.

TABLE 1 gives a summary of the types of model and their main features.
Inevitably some systems display behavior which cannot readily be represented
by the 'common' models. Some of these special cases are discussed in 5.4.

5.1

Ideal Behavior in Both Phases

This, the simplest model, is Raoult's Law:-


5.1.1 Data Required
The only data required for this model is the vapor pressures of the pure
components. These are functions of temperature and are usually fitted by the
Extended Antoine equation (See Appendix A).

5.1.2 Complexity
The calculation is simple and very quick.

5.1.3 Applicability
This model does not make use of experimental VLE data. Owing to its simplicity
the method is often useful for preliminary feasibility studies. For serious design,
however, the model as a rule is reliable only when:(a)

The system is a mixture of non-polar components, preferably of the same
homologous series, and

(b)

The pressure is low (say below 5 bar), and

(c)

The relative volatility between the key components is reasonably high (say
above 3.0)

5.2

Liquid Phase Non-Idealities

The liquid shows significant deviations from ideality when the components belong
to different homologous series, or if any of them is polar. These deviations are
the result of interactions between different molecules, and are expressed in the
form of a correction factor for each component:-

where i is called the activity coefficient of component i.


Activity coefficients may be greater or less than 1.0. When greater, the mixture is
said to show positive deviations from Raoult's Law; when less, negative
Deviations. Systems showing negative deviations are comparatively rare.
Activity coefficients may be calculated in one of two ways:5.2.1 Local Composition Models
If experimental VLE data is available, it may be fitted statistically by the
parameters of a 'local composition' model, e.g. Wilson or UNIQUAC.
A summary of these and other similar models is given in Appendix B.
5.2.1.1

Data Required

Use of a local composition model requires the following data:(a)

Vapor pressure (e.g. Antoine constants) for each component.

(b)

The model coefficients which have been fitted to experimental VLE data.
Most practical models (e.g. Wilson) employ two such adjustable
parameters (Eij and E ji) for every pair i,j of components in the mixture.
Temperature dependent parameters (e.g. E = f (T)) may be used in place
of constant values, increasing the number of coefficients which must be
fitted to experimental VLE data.

(c)

Any other pure component constants in the model (e.g. molar volumes in
the E form of the Wilson equation).

5.2.1.2

Complexity

Activity coefficient equations are generally explicit expressions in composition
and temperature. Although cumbersome to use by hand, they are very quickly
evaluated by computer.
5.2.1.3

Applicability

Local composition models provide a powerful method of representing
experimental VLE data. They are normally used for moderately or strongly nonideal systems. In addition, they can be very useful for nearly ideal systems with
low relative volatility (say 1.2) where high accuracy is essential.

5.2.2 Activity Coefficient Estimation Methods
If experimental VLE data is not available, activity coefficients may be estimated
from the properties of the pure components. The two categories of method
available are:(a)

Those based on Regular Solution theory (solubility parameter), and

(b)

Those based on a molecular structure (group contributions).

A summary of these methods is given in Appendix C.

5.2.2.1

Data Required

These estimation methods require a variety of pure component constants and
group interaction parameters; these are detailed in Appendix C.

5.2.2.2

Complexity

Easily evaluated by computer.

5.2.2.3

Applicability

The solubility parameter methods are applicable only to non-polar systems, while
group contribution methods can also be applied to polar mixtures.
It is worth noting that some current distillation programs do not accept these
estimation methods as the source of VLE data. In such cases the chosen
estimation method should be used to generate a spectrum of VLE data points,
which in turn should be fitted to a local composition model.
Note:
Activity coefficients for VLE may sometimes also be estimated from other data for
the mixture, e.g. liquid-liquid equilibrium, heat of mixing, or infinite dilution activity
coefficients. These methods, however, require extreme caution and should be
attempted only by experts.


5.3

High Pressure Systems

At high pressures the vapor phase also shows deviations from ideal behavior.
These deviations again are expressed as a correction factor for each component:

Fugacity coefficients are calculated by an equation of state. Several equations of
state are in common use today, a summary is given in Appendix D.
When using such a rigorous model for the vapor phase, it is prudent to apply a
more sophisticated model to the liquid phase. This may be achieved in one of
two ways, as described below.

5.3.1 Vapor z/Liquid
We may retain the activity coefficient concept but use a rigorous expression for
liquid phase fugacity:


5.3.1.1

Data Required

This rigorous model requires the following data:(a)

Vapor pressure (e.g. Antoine constants) for each component.

(b)

Local composition model parameters for each pair.

(c)

Other constants used by the local composition model.

(d)

Constants required by the chosen equation of state (e.g. critical
properties, acentric factors, interaction coefficients).

5.3.1.2

Complexity

This is discussed in 5.3.2.

5.3.1.3

Applicability

This model is extremely powerful, as it can take account of experimental VLE
data fitted to a semi-empirical equation within a sound thermodynamic
framework. Naturally the preparation of data for this model can require
considerable effort, but this effort is well worth while with systems that are not
accurately represented by simpler models.
The main limitations are those of the individual models chosen to represent the
liquid and vapor phases (see Appendix B). Particular problems can arise with the
vapor phase when highly polar compounds are present at high pressures. In this
situation 'normal' equations of state may give poor predictions of vapor fugacities.


5.3.2 Vapor ø/Liquid ø

5.3.2.1

Data Required

The only data required is the constants employed by the chosen equation of
state (e.g. critical properties, acentric factors, interaction coefficients).

5.3.2.2

Complexity

The equations of state in use today range from the simple Virial to the
sophisticated BWR-Starling (BWR(S)). The complex equations, although usually
more accurate, often need iterative numerical solution and can lead to extremely
long computer run times. Two outstanding exceptions are the Redlich-Kwong
Soave (RKS) and the Peng-Robinson (PR) equations of state; these are cubic
equations which are easy to solve, yet are remarkably successful in the
prediction of hydrocarbon VLE.

5.3.2.3

Applicability

Use of an equation of state for both phases is essentially an estimation method.
It is very convenient, as very little input information is required, but the method
cannot ultimately match the accuracy achieved by a model based on
experimental data (e.g. 5.3.1).
Nevertheless, equations of state are widely used in the hydrocarbon industry.
Their accuracy can sometimes be improved by fitting binary interaction
parameters to experimental VLE data.


5.3.3 Local Composition Equations of State
In recent years methods have been developed for combining Local Composition
Models (see 5.2.1) with Cubic Equations of State (see 5.3.2) in order to improve
representations of polar systems at high pressures. Use of these methods is
similar to that of 'normal' cubic equations of state, but the equations are modified
in two ways:
(a)

They contain adjustable parameters which can be fitted to, and give an
accurate representation of, experimental pure component vapor
pressures.

(b)

For mixtures they have a mixing rule which contains a local composition
model such as the Wilson Equation.

These modifications force the equation of state to predict the same fugacities of
components in a liquid mixture as would be given by the local composition model
used as described in 5.2.1. The equations then give much improved predictions
of fugacities of polar components in a vapor mixture at high pressures.
Only very limited experience of use of these methods is available inside GBH
ENTERPRISES.

5.4 Special Models
This section describes some systems where the VLE cannot be represented
satisfactorily by the models presented above, and where some improvisation is
necessary.

5.4.1 Gas Absorption Systems
Absorption is an operation in which a gas mixture is contacted with a liquid for
the purpose of preferentially dissolving one or more components (solutes) of the
gas in the liquid (solvent). The VLE for an absorption process is not readily
modeled by conventional methods because:(a) The gas components are generally well above their critical temperatures,
so that saturation vapor pressure correlations are not valid; or


(b) The solvent and/or solute may be inorganic or polar, so that
equations of state are not reliable; or
(c) The absorption mechanism may be based on chemical reaction, so that
an inherently physical model is not applicable.
Instead the model should be based on experimental data to which empirical
equations have been fitted.
For physical absorption systems, the experimental data consists typically of gas
solubilities in the solvent at a range of temperatures and pressures. The
recommended approach is to convert this data to Henry's Law constants:-

At a given pressure, the variation of H i with temperature is similar to that of
vapor pressure. Thus Hi may be fitted as a function of temperature to the Antoine
equation (see Appendix A).
At high pressures it may be necessary to introduce a vapor phase correction
factor as in 5.3. Unlike vapor pressure, however, the Henry's law constant is a
binary property, i.e. it applies to a particular solute dissolved in a particular
solvent. At present there is no proven method of predicting the Henry's law
constant for a solute of a non-ideal solvent mixture from those for the
same solute in the individual pure solvents. Consequently gas absorption
systems using mixed solvents can present problems.
Chemical absorption systems, as a rule, require custom-built models, see 5.4.2.


5.4.2 Reacting Systems
Some distillation operations are carried out while the components undergo
chemical reaction on some or all stages. Such a reaction may be a deliberate
intention of the process, or may occur inadvertently at the prevailing conditions.
Commercial software is available to correct for the formation of dimers and
higher oligomers in the vapor phase. This occurs, for example, with carboxylic
acids and HF. When combined with the activity coefficient ( ) model for the liquid
phase, it is essential that the fitting program makes the same corrections to the
vapor phase.
Evidently such a system needs a custom-built model which correlates the VLE
simultaneously with the reaction equilibrium. This model may then be linked as a
modular subroutine to a general purpose distillation program. Some reacting
systems which have been simulated are:(a)

Ethylene Oxide/Water
Ethylene Oxide and Water react at higher temperatures to form small
quantities of glycols, which are to be taken into account in the VLE
calculation.

(b)

Acetic Acid/Water
Acetic Acid molecules tend to dimerize in the vapor phase; hence, the
partial pressure should be corrected for this effect.

(c)

Nitrogen Oxides/Water
This is a chemical absorption process whose complex mechanism has
been formulated successfully.

(d)

Urea Stripping
This process involves the stripping of ammonia, carbon dioxide and water
vapor in a column where ammonium carbonate decomposes into urea and
water.


5.4.3 Electrolytes
When distillation is carried out in a system of electrolytes, the VLE calculation
should take into account the ionic equilibrium in the liquid phase.
The most reliable correlations currently available are contained in the Aqueous
Electrolyte Equilibrium Package developed by OLI Systems Inc, which evaluates
liquid phase non-idealities as a function of the distribution of molecular and ionic
species. The model has been developed from theoretical and empirical ideas,
and used successfully in areas such as Chlorine and Chlor-Alkalis.

5.4.4 Systems with two liquid phases
Liquid immiscibility is the result of severe non-idealities in the liquid phase, i.e.
strong positive deviations from Raoult's Law. The problems associated with
simulating the phase equilibrium of such systems are mentioned in the
appropriate clauses of this guide. Here is an edited summary of our present
capabilities and limitations.

5.4.4.1

Correlation of Experimental Data

Experimental vapor-liquid-liquid equilibrium (VLLE) data may be fitted to a local
composition model. The Wilson equation, however, is algebraically incapable of
representing the conditions that lead to two liquid phases (but see 5.4.4.4). Thus
the UNIQUAC equation is recommended for most applications. The alternative
NRTL equation has been known to create practical difficulties and is not
recommended except on expert advice.
It is worth noting that at the present state of the art, although vapor-single liquid
equilibria and liquid-liquid equilibria can be correlated accurately, the equations
available often do not give a good fit to vapor-liquid-liquid equilibria
simultaneously.


5.4.4.2

Estimation Methods

When experimental VLLE data is not available, the activity coefficients in both
liquid phases may be estimated by a group contribution method (UNIFAC or
ASOG). The reliability of these methods in predicting liquid-liquid equilibria,
however, is unproven, and the methods should not be used for serious design
without some cross-check against mutual solubility data.

5.4.4.3

Hydrocarbon/Water Systems

Hydrocarbon mixtures containing water or steam are frequently encountered in
petrochemical plants and oil refineries. The hydrocarbon VLE may be computed
successfully by, say, the RKS equation of state, and it is desirable to represent
the water by some means within this framework. In recent years a simplified
model has proved very satisfactory. The aqueous phase is assumed to be pure
water, and the solubility of water in the hydrocarbon liquid phase is evaluated
using a derived RKS interaction parameter. This representation of VLE is
available in commercially available programs as the RKSL correlation, and may
be used in the COLUMN distillation algorithm.

5.4.4.4

Application

When simulating a distillation where two liquid phases may occur, it is evidently
essential to ensure that the algorithm itself can cope with the additional phase.
Although such algorithms exist (see - Computer Programs for Continuous
Distillation and Absorption Steady-State Material and Energy Balance), experience to date has shown that:(a)

For hydrocarbon/water systems, simulated by the method outlined in
5.4.4.3, satisfactory results are generally obtained; but

(b)

For other systems, the results are not always reliable. Note that incorrect
results will be obtained if the model (e.g. UNIQUAC) predicts the formation
of two liquid phases, but the user algorithm (in the applications program)
assumes the existence of only one liquid phase.


An alternative approach, which has been satisfactory with some systems, is to
treat them as single liquid phase systems by fitting the Wilson equation to VLE
data outside the immiscible region. When these fitted coefficients are used in a
vapor-single liquid phase algorithm it is assumed, in the immiscible region, that
the calculated liquid composition is a good approximation of the overall
composition of the two liquid phases which would actually exist. Multi-phase
options exist within the suite of programs associated with the physical property
data bank. Consistent use of the options is essential.
TABLE 1

SUMMARY OF VLE METHODS (CONDITION : f i V = f i L for all i,)


6

SETTING UP A VLE MODEL

Let it be said at the outset that modeling a VLE system for the first time is best
left to someone with experience, and Process Engineers are urged to seek the
advice of their local Physical Chemistry expert. The Process Engineer, however,
is responsible for defining the problem adequately and using the results sensibly.
Unfortunately, it is not possible to give a generalized check-list of steps to model
every mixture. The following is merely an appreciation of the issues to be
resolved.

6.1

Define Problem

The Process Engineer should define:(a)

The key components of the distillation.

(b)

Other significant components.

(c)

The composition, pressure and temperature range of operation.

(d)

How accurate the model needs to be.

6.2 Select Data
The expert will then select the data on which the model is to be based, by
considering:(a)

What experimental VLE data is available.

(b)

Whether these are at the right conditions, or can be reasonably
extrapolated.

(c)

Whether there is a pinch, an azeotrope, partial liquid miscibility, or other
possible problems.

(d)

Whether further experimental measurements are necessary.

(e)

Whether an estimation method will be adequate.


6.3 Select Correlation(s)
(a)

If a local composition model is to be fitted to experimental VLE data, then
the Wilson equation is preferred for most practical purposes. The
exceptional case is when the system shows partial liquid miscibility. In this
case, the UNIQUAC equation should be used, provided the distillation
algorithm itself can cope with two liquid phases.
In conjunction with the local composition model, a rigorous (equation of
state) vapor phase model should be used either if the pressure is high
(say above 10 bar), or if the relative volatility between the key components
is low (say less than 2.0).
For data fitting, it is possible to have a choice of objective functions to
minimize. Also, selected data points may be weighted preferentially. The
expert will fit the model in such a way that the errors in the most critical
parts of the separation are minimized. (See Case Study, Clause 8).

(b)

If experimental data is not available and an estimation method has to be
used, then it is recommended that:-

(1)

(2)

6.4

For non-polar mixtures use Redlich-Kwong-Soave (RKS), or
Peng-Robinson (PR).
For polar mixtures use UNIFAC.

Produce Model

The model produced by the expert will include a package of pure component
constants and fitted binary parameters. These should all be used together in the
application program.
The expert will also indicate the expected accuracy of the VLE model.


7

AVOIDING PITFALLS

Evidently the accuracy of the simulation depends on the quality of the
thermodynamic data on which it is based. Here are a few guidelines on making
the best use of a VLE model in distillation.

7.1

Experimental Data is Better than Estimates

Do not expect magic from thermodynamics. If you want reliable results, you need
reliable experimental data; either from the literature or from your laboratory.
Estimation methods may appear to provide the easy route, but they should never
be used for detailed design unless approved by a VLE specialist or when their
use for the system concerned is established practice and known to be reliable.

7.2

Check Validity of Fitted Model

When using a model fitted to experimental data, check the range of the original
data (temperature, pressure, composition) and the accuracy of the fit. If liquid
phase parameters have been fitted, find out what model was used for the vapor
phase, and be sure to use the same consistent model (including vapor pressure
constants, molar volumes, etc.) in the application program. Do not steal other
people's Wilson coefficients without establishing their applicability! Avoid
extrapolation.

7.3

Check Limitations of Estimation Methods

If you do use an estimation method, be sure to note its limitations in terms of
temperature, pressure and especially types of compound. Equations of state can
generally be applied only to non-polar mixtures; but again, beware of the
presence of ring compounds.

7.4

Know Your System

In these days of flashy computer terminals and elegantly interfaced data banks,
there is a real danger that you may never 'see' your thermodynamic data. Yet it is
essential for the process engineer to understand quantitatively the key
parameters of his/her distillation; e.g. the key components and their relative
volatility. Ask yourself, does this design look right?

How do the stages, reflux, energy, etc. compare with other similar separations?
Designs that look wrong usually are wrong.

7.5

Appreciate Errors and Effects

Develop an appreciation of the effect of VLE inaccuracy on your design. Figure 6
demonstrates this effect for simple Fenske-type systems. You will see that when
the relative volatility (a) is 5, a 20% error in a leads to only a 12% error in number
of stages;
FIGURE 6: SENSITIVITY TO ERROR IN VLE DATA (BASED ON FENSKE
EQUATION)


however, if α = 1.07 (e.g. propylene-propane), even a 2% error leads to a 30%
error in number of stages.
Although the assumptions of constant α and constant molar overflow do not
apply to most practical systems, the message is the same; the lower the relative
volatility, the more important it is to represent the VLE accurately. These
separations require larger numbers of trays, and smaller design margins can be
tolerated.
As a general rule, the following principles are strongly recommended:(a)

If α <2.0 Always use a model based on experimental data.

(b)

If α <1.2 Use a model based on experimental data which has also been
tested against plant performance or semi-technical simulation.

7.6

If in Doubt - Ask

Remember that phase equilibria in fluid mixtures is not a simple subject. If you
are inexperienced, seek advice.

8A

CASE STUDY

This section describes a typical awkward problem tackled by a Physical
Chemistry expert.

8.1

The Problem

The process was the distillation of Diethylamine (DEA) from Water at
atmospheric pressure, yielding a DEA product with a low concentration of water.
A model was required to represent the VLE data in a computer simulation of the
distillation.


8.2

The System

Pure DEA is considerably more volatile than water. In the binary mixture, the
volatility remains high at lower concentrations of DEA. However, at high
concentrations of DEA (>mole fraction 0.9) the system shows a severe 'pinch';
i.e. the relative volatility approaches 1.0. This means that it is easy to separate
most of the water out of the DEA, but very difficult to reduce the water
concentration to a low specification.

8.3

Data Available

The best data found in the literature was a set of isothermal measurements at
56.8°C, covering the composition range from 0.05 to 0.95 mole fraction DEA. The
data at xDEA = 0.95 looked suspect.
This data was supplemented by laboratory measurements at 1 atmosphere,
covering only the high concentration (>0.95) range of DEA. The temperature
range covered by this data was 55 to 56°C. This data suggests the formation of
an azeotrope at xDEA = approximately 0.998.
The combined data was thus essentially isothermal. This data was considered an
adequate basis for modeling, even though the atmospheric distillation would
cover temperatures between 55 and 100°C. The relative volatility at higher
temperatures (lower DEA concentration) was high, hence the number of trays
operating in that region was few, and extreme accuracy was less important.

8.4

Selected Correlation

It was decided to fit Wilson A-values to the VLE data. The vapor phase was
assumed ideal.


8.5

Simulation

In this example component 1 is DEA and 2 is water. The Wilson coefficients are
A12 and A21.
The first simulation attempted minimized the deviations between experimental
and calculated vapor mole fraction. The best fit was given by A12 = 0.0782, A21 =
0.853. The results are shown in Figure 7(a). The upper graph shows there is a
good fit to the y-x data over the entire composition range. The lower curve,
however, shows that the predicted relative volatilities at xDEA >0.9 are very
optimistic.
An improved fit was sought by minimizing errors in 1/(1 + 2 ln a) with the data
points weighted selectively. This gave A12 = 0.842, A21 = 0.231, and the results
are shown in Figure 7(b). This time the representation of the overall y - x data is
poorer, but the fit at high DEA concentrations is better. The predicted relative
volatilities at xDEA>0.9 are pessimistic.
A third attempt also minimized errors in 1/(1 + 2 ln a) with no weighting of data
points. The best fit was A12=1.4, A21 = 0.1017, and the results are shown in
Figure 7(c). This time there is an excellent fit to the relative volatilities in the pinch
region; in fact there is even a suggestion of an azeotrope at xDEA = 0.98. At lower
DEA concentrations the predicted volatilities, however, are significantly
optimistic.

8.6

Selection of Model

Clearly the three sets of Wilson coefficients described above will give very
different predictions of plant performance. The selection depends on the
operating concentration range.
The coefficients of Case (A) will give highly inaccurate results at the difficult end
of the separation, i.e. high DEA concentrations, and their use is futile.
If the aim is to produce DEA of say 0.95 to 0.98 mole fraction purity, then the
coefficients of Case (B) may be used - they are 'safe', i.e. predictions will be
pessimistic. These coefficients do not, however, predict the formation of an
azeotrope at high DEA concentration.


Finally, if the object is to produce DEA of >0.98 mole fraction purity, a large
number of trays will be required, and the coefficients of Case (C) might be
satisfactory, but ideally further experimental data (to confirm whether or not an
azeotrope is formed), followed by further fitting, would be wise.


FIGURE 7 (a):

FITTING WILSON 'A' VALUES TO VLE DATA - CASE A


FIGURE 7 (b):

FITTING WILSON 'A' VALUES TO VLE DATA - CASE B


FIGURE 7 (c) : FITTING WILSON 'A' VALUES TO VLE DATA - CASE C


9

RECOMMENDED READING

Table 2 lists useful background references.
TABLE 2

LIST OF USEFUL REFERENCES

Notes:
(1)
Ref 1 is probably the best concise discussion of theory and practice.
It Includes equations and data.
(2)

Ref 2 is a useful, engineering orientated book with a variety of numerical
examples.


APPENDIX A
A.1

USE OF EXTENDED ANTOINE EQUATION

VAPOR PRESSURE CORRELATION

Pure component vapor pressures in the form of an Extended Antoine equation:-

where

p*
=vapor pressure
T
=absolute temperature and
A, B, C, D, E are fitted constants.

In reality this is a combination of the three term Antoine equation (D = E = O) and
a four-term equation (C = O), i.e. all five constants are not used for any
component.
A.2

POINTS TO NOTE

A.2.1 Accuracy
Experimental vapor pressures can normally be fitted within errors less than 0.5%.
A.2.2 Extrapolation
Technically, vapor pressure should not be extrapolated above the critical
temperature. In practice, when a liquid contains one or more dissolved light ends
above their individual critical temperatures, a little judicious extrapolation is
acceptable.


APPENDIX B
B.1

USE OF WILSON EQUATION

LOCAL COMPOSITION MODELS

A local composition model expresses the activity coefficient of each component
in the liquid phase as a function of composition and temperature. These
expressions are derived from theoretical considerations, but employ adjustable
parameters which must be fitted to experimental data. Several such models have
been proposed, notably:Margules )
Van Laar )
Redlich-Kister )

These early models are now essentially obsolete.

Wilson

A simple equation, using two adjustable interaction
parameters for every pair of components.

NRTL

Also a simple equation, using three adjustable parameters
per binary.

UNIQUAC

A slightly more complex equation, using two parameters
per binary.

Of these the Wilson Model has proved to be the most useful, and is
recommended for most applications.

The Wilson equation is:-

and the A ij are the adjustable parameters.

An extended form of this equation, with:-

and the E ij are different adjustable parameters,
is often used in systems covering a temperature range.
Prediction by the Wilson equation, with E ij as adjustable parameters, of the effect
of temperature can be very poor for some systems; e.g. amines-water. The
temperature effects can often be correlated by making the parameters, E ij,
themselves functions of temperature. Several forms of temperature dependent
parameters are available within the suite of programs associated with the data
bank. A similar modification of the UNIQUAC equation is also available.

B.2

POINTS TO NOTE

B.2.1 Model
The model is made up by fitting two parameters Eij and Eji (or Aij and Aji) per
binary i>j. In a multi-component mixture a matrix of parameters may be set up by
fitting binary and/or multi-component VLE data, as available. There are no
ternary or higher order interaction constants.

B.2.2 Parameters
The fitted parameters should not be regarded as having any physical
significance. Indeed, more than one set of parameters may give an equally good
fit to the VLE data.


B.2.3 Accuracy
Reliable experimental data can usually be fitted to within 1 or 2% average error in
relative volatility. The quality of fit in important composition regions can often be
improved by minimizing a different objective function; consult your expert.
B.2.4 Extrapolation
In principle, VLE data should not be extrapolated for final design work, as fitted
coefficients are truly reliable only over the range of the original data.
Extrapolation to different mixture compositions can lead to large errors,
particularly in systems with low relative volatility.
Extrapolation to different temperatures (say up to 20°C away from the
experimental range) will often be satisfactory, provided:(a)

The relative volatility is greater than 1.2, and

(b)

There is no risk of an azeotrope occurring, and

(c)

There is no risk of two liquid phases forming.

The use of temperature-dependent parameters in the Wilson or UNIQUAC
equations is often recommended for extrapolation.
B.2.5 Application
Be sure to use the same pure component constants and the same vapor phase
model in the application program as those used when fitting the parameters.
B.2.6 Liquid Immiscibility
The Wilson equation is algebraically incapable of representing a system showing
liquid-liquid immiscibility. In some cases, where the VLE data on either side of
the immiscible region is accurately correlated, you may get away with the Wilson
equation if it gives a good approximation to the average liquid composition on a
distillation stage.
For rigorous simulation, the UNIQUAC equation is recommended; but do make
sure that the distillation algorithm itself can cope with two liquid phases.


APPENDIX C
C.1

USEFUL METHODS OF ESTIMATING

ACTIVITY COEFFICIENT ESTIMATION METHODS

When experimental VLE data are not available, liquid activity coefficients may be
estimated from pure component data. The most useful methods of estimation fall
into two categories, namely solubility parameter methods and group contribution
methods.

C.1.1 Solubility Parameter Methods
These methods are based on Regular Solution theory. The simplest model,
popular in the hydrocarbon industry, is the Scatchard-Hildebrand equation, which
expresses activity coefficient as a function of composition and temperature using
a 'solubility parameter' for each component. The only data required to calculate
this parameter are the molar liquid volume and the latent heat of vaporization of
the component. In fact solubility parameters are available in the literature
for many compounds.

C.1.2 Group Contribution Methods
These methods regard each molecule as an aggregate of functional groups, and
propose that each activity coefficient is the sum of contributions made by these
groups. The recommended method in this category is UNIFAC, which has proved
to give reasonable estimates even for strongly non-ideal mixtures.
The only data required by UNIFAC is the breakdown of the molecular structure of
each component into recognized functional groups. Thereafter, parameters for
each group and for interactions between groups are found from published tables.
Modified UNIFAC is an improved version of UNIFAC which gives better
estimations of the effect of temperature and the effect of molecular size and
shape on liquid activity coefficients.


C.2

POINTS TO NOTE

C.2.1 Method
Detailed descriptions of these methods will be found in the literature. As a rule,
implementation of these methods and appraisal of the results should be carried
out by your Physical Chemistry expert.
C.2.2 Accuracy
Solubility parameter methods should be used only for hydrocarbons. For
aliphatics, the predicted activity coefficients should be accurate to 10-15%; with
naphthenes and aromatics much larger errors can occur. UNIFAC, on the other
hand, can be used even for strongly non-ideal mixtures; the expected accuracy in
activity coefficient is also 10-15%.
C.2.3 Application
If the distillation program does not accept your chosen estimation method as the
source of VLE data, you should generate a spectrum of VLE data points and fit
these to say, the Wilson equation.


APPENDIX D
D.1

EQUATIONS OF STATE FOR VLE CALCULATIONS

EQUATION OF STATE MODELS

A system operating at moderate or high pressure is generally simulated with the
help of an equation of state.
An equation of state is a relation between the pressure, volume, and temperature
of a system, from which other thermodynamic properties may be derived. The
relation employs any number of 'constants' specific to the system; for a pure
component, the constants are functions of such properties as critical
temperature, critical pressure and acentric factor; for a mixture, customized
mixing rules dependent on composition are also necessary.
For VLE calculations we need the derived expression for fugacity coefficients (in
liquid and/or vapor) in terms of temperature, pressure and composition.
Several equations of state have been developed with VLE applications in mind.
The most popular have been:(a)

Redlich-Kwong (RK) : a simple equation with two constants

(b)

Redlich-Kwong-Soave (RKS) : a modification of RK

( c)

Peng-Robinson (PR): another simple two constant equation

(d)

Benedict-Webb-Rubin (BWR) - and various modifications : complex
equation with eight constants.

Of these the RKS and PR equations, despite their simplicity, have achieved
considerable success, and either is recommended for most applications.
The Hayden O'Connell* (Ref 3) virial correlation is a very useful method for
predicting the vapor fugacity coefficients, especially for mixtures of polar
compounds. It cannot, however, be used for the liquid phase and therefore has to
be combined with an activity coefficient ( ) model.


D.2

POINTS TO NOTE

D.2.1 Method
Detailed descriptions of the equations of state will be found in the literature.
D.2.2 Accuracy
In non-polar systems, a good equation of state should predict K-values to within
5-10% error. The accuracy may be improved by fitting selected binary interaction
constants to experimental VLE data - an option available with modern equations
of state. In polar systems, an equation of state can predict highly erroneous
results in the liquid phase and such use is not recommended; it can nevertheless
be used to simulate the vapor phase fugacity, in conjunction with an activity
coefficient model for the liquid.
D.2.3 Computing Time
Complex equations such as BWR are implicit in volume and need to be solved
iteratively and tediously before the fugacity coefficient can be evaluated. If you
have to use such an equation of state, be prepared for long computer run times.
Simpler equations like RKS and PR are essentially cubics and can be solved
quickly.
D.2.4 Hydrocarbon/Water Immiscibility
In recent years, systems where an aqueous liquid phase co-exists with a
hydrocarbon process phase have been modeled satisfactorily using the RKS or
PR equation. The aqueous phase is assumed to be pure water, and the solubility
of water in hydrocarbons is calculated using a derived interaction parameter. This
approximate representation is very useful in many applications.


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