Shortcut simulation
Problem/objective
The shortcut simulation delimits the optimum operating range of a rectification column for
almost ideally behaving mixtures. The results are to be regarded as reference values only. A
detailed column simulation and the simulation of non-ideal mixtures are performed with a
rigorous column simulation, e.g. SCDS.
The advantages of the shortcut column are the delimitation of the reflux ratio and the direct
calculation of the feed tray. It offers a quick overview of the total solution.
This tutorial focuses on a simple two-substance mixture of benzene and o-xylene. This
substance is to be separated through rectification to achieve a minimum benzene purity of 99%
at the top. A benzene concentration of 1% shall not be exceeded on the bottom. The simulation
is performed via the shortcut column to determine the optimum reflux ratio and the feed tray.
Figure 1: Flow sheet shortcut column
Implementation of the shortcut simulation in CHEMCAD
The simulation is performed with CHEMCAD Steady State. Prior to the simulation, the
components and the thermodynamic models must be set.
At "Select Components", the components benzene (CAS no. 71-43-2) and o-xylene (CAS no. 9547-6) are selected. The subsequent "Thermodynamics Wizard" suggests a suitable model after
specification of the pressure and the temperature. For the given example, CHEMCAD suggests
the k-value model UNIFAC. For the enthalpy model, LATE (latent heat) is suggested.
This selection is a preselection made by the program, and should always be verified by the user
or synchronized with a decision diagram ([3], figure 8/9).
First, the T-x diagram and the phase diagram are generated at [Plot]  [TPXY] to examine the
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behaviour of the mixture. The T-x diagram shows the boiling points, from which the light
component and the heavy component are easy to read. The equilibrium diagram shows that
the benzene/o-xylene mixture does not form an azeotropic mixture and that it features an
almost ideal behaviour. The shortcut simulation can be used for the mixture.
Figure 2: T-x diagram and equilibrium diagram
The UnitOp (unit operation) for the shortcut column is entered in the flow sheet and allocated a
feed stream and two product streams. The feed stream is set with the data stated in table 1
(see figure 3).
Table 1: Relevant data for the example simulation
Units
SI
Components
Thermodynamics
Feed streams
Unit operations
Benzene (feed)
o-xylene (feed)
K: UNIFAC, H: LATE
Benzene: 50 kg/h
o-xylene: 50 kg/h
T = 20°C
p = 1.013 bar
1Shortcut
column
1 Feed
2 Products
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The shortcut column is initialized in the next step. In the settings window (figure 3), you can
select three different design options at "Select Mode".
Figure 3: Settings window of the shortcut column
The first selection option, "Rating: Fenske-Underwood-Gilliland", cannot be used for the design.
It is used if the column data are already available and to get a quick overview of the separation
behaviour.
The other two options, "2 Design; FUG with Fenske feed tray location" and "3 Design; FUG with
Kirkbride feed tray location", are required for the design of the shortcut column. The difference
between these methods is summarized in table 2.
Table 2: Comparison of the design options in the shortcut column
Calculation basis for
-minimum number of stages
-minimum reflux ratio
-theoretical number of stages
Calculation basis for
-theoretical feed tray
Difference
2 Design; FUG with Fenske feed
tray location
according to
Fenske- Underwood- Gilliland
3 Design; FUG with Kirkbride
feed tray location
according to
Fenske- Underwood- Gilliland
according to
Fenske
Calculation of the theoretical
feed tray via minimum and
theoretical number of stages
according to
Kirkbride
Calculation of the theoretical
feed tray via the ratio of the
stages in the amplification and
output part
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For this tutorial, we will select design 2, "FUG with Fenske feed tray location". The details are
required to initialize the shortcut column: Light keysplit, heavy keysplit and the ratio
.
The keysplits state the ratio between the outgoing light component and the heavy component
in the top to that supplied to the feed. This is not equivalent to the desired purity at the top.
The simplification of the shortcut method is that the mixture to be examined is reduced to a
binary system. The two components to be separated are referred to as light and heavykey.
The mass streams at the head ( ̇ ) and bottom ( ̇ ) for the desired purity (
can be
determined via a balance. w corresponds to the mass fraction.
̇
̇
̇
̇
̇
̇
̇
̇
̇
̇
̇
̇
Figure 4: Column sketch
Now it is possible to calculate the light and the
heavy keysplit.
̇
̇
̇
̇
The problem demands a minimum benzene concentration of 99% at the head
(
. o-xylene shall not exceed a maximum concentration of 1% at the head
(
. For the data stated in table 1, this results in a light keysplit of LKS = 0.99 and a
heavy keysplit of HKS =0.01.
The last entry required for calculation of the shortcut column in CHEMCAD is the statement of
the ratio between the theoretical and the minimum reflux ratio
.
The objective of the simulation is to determine the optimum reflux ratio. Accordingly, only an
initial value is stated to begin with, which is then optimised by means of a sensitivity study. The
rule of thumb1 usually states a ratio between (1 – 3). If the ratio is 1, the reflux ratio
corresponds to the minimum reflux ratio, which would result in an infinite number of stages.
For this reason, we assume an initial vale of 1.1.
____________________________
1
Löwe, Eberhard : Destillation Rektifikation, TFH Berlin, 1989
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All settings are now complete and the simulation can be started. It is to be expected that the
column converges.
The apparatus energy curve (figure 5) is generated via a sensitivity study [6]
in the next step. For this purpose, the ratio
is varied from 1.01 to 3 and the theoretical
number of stages calculated for this is entered.
Figure5: Apparatus energy curve
The apparatus energy curve shows that the number of stages reduces with increasing
ratio
. However, when selecting the optimum ratio, please note that an increase in ratio
also increases the evaporator output and thus the operating costs.
is applied as optimum ratio and the simulation restarted.
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Assessment of the simulation results
The calculated column properties are displayed in the settings window of the shortcut column
(see figure 6). The theoretical number of stages calculated with the entered data is 13. The feed
tray is on the 7th stage. The results of the reflux ratio, minimum number of stages, evaporator
and condenser output are also listed.
Figure6: Results of the shortcut simulation
The properties of the process streams (see figure 8) are displayed at [Format][Add Stream
Box].
Figure7: Properties of the streams
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The mole fractions of the components at the top, bottom and in the feed are displayed in the
"Stream Box". We can see that the requirements stated in the problem at hand were achieved.
Benzene was obtained in nearly pure form. o-xylene is only discharged in a very low
concentration at the top.
The simulation results are reference values not suited for a real column design. A detailed
simulation must be performed with a rigorous column. However, the calculated column
properties delimit the operating range so that work and time can be saved with the simulation
of the rigorous column.
Fundamental principles
In the following, we will enhance the basic theoretic knowledge behind the shortcut function
and provide more detailed information.
The shortcut method allows an easy and fast estimation of the column properties for
separating ideal mixtures, because the system discussed herein is substantially simplified.
The simplification of the shortcut method is that the mixture to be examined is reduced to a
binary system. The two components to be separated are referred to as light and heavykey and
examined in the idealised calculation. Further components influence the relative volatility but
will not be considered further for this calculation.
Another simplification is that the relative volatility and the separation factors are assumed to
be constant within the examined temperature range. The relative volatility is defined as:
(1)
If one applies Dalton's laws for the steam phase fraction
(2)
with the partial pressure pi, and for the liquid phase fraction Raoul's law
(3)
With the activity coefficient and the steam pressure , one arrives at
(4)
For the calculation of the relative volatility, CHEMCAD merely requires the activity coefficients
and the steam pressure of the light component and the heavy component.
The calculation saved in the shortcut model takes place according to the calculation methods
by Fenske, Underwood and Gilliland, which will be explained in the following.
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The Fenske equation (5) is used to calculate the minimum number of plates at total reflux with
known substance/mass fraction in the distillate and the bottom. Here, the relative volatility is
assumed to be constant. However, as the relative volatility depends on the composition of the
mixture as well as on the pressure and the temperature, an average relative volatility is used
for the calculation.
(
)
(5)
̅
with the average relative volatility
̅
√
(6)
is the mole fraction of the light components at the top and the mole fraction of the heavy
fraction on the bottom.
In the next step, the minimum reflux ratio with an infinite number of plates is calculated with
the Underwood equation (7). This is an approximation calculation which depends on the phase
equilibrium and the feed properties.
̅
[
̅
]
(7)
is the mole fraction of the light component in the feed. As a rule of thumb, the minimum reflux
ratio is multiplied with a factor.
(8)
The Gilliland equation is an empirical approach for determining the theoretical number of
plates. This empirical approach is displayed in a diagram and can be described with the
Molokanov equation.
This diagram can be found in the literature ([5], p. 199).
The feed tray can be determined in two ways. The first possibility is that according
to Fenske. First, the number of plates at maximum reflux is determined via Fenske (9). This
number of plates corresponds to the number of plates required to achieve the desired top
concentrations of the light component and the heavy components in relation to the feed
concentration.
(
)
̅
(9)
The minimum number of plates and the number of plates according to Fenske can now be used
to calculate the theoretical feed tray .
(10)
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Alternatively, the feed tray can be determined using the Kirkbride equation. This is based on
empirical data. A ratio between the theoretical number of plates in the amplification part and
the theoretical number of plates in the output part is determined. This is subsequently used to
calculate the feed tray.
[(
) (
)
̇
̇
]
(11)
with
(12)
Table 3 provides an overview of the Fenske-Underwood-Gilliand method and a summary of the
most important calculation parameters.
Table 3: Overview of the previously applied equations
Specified values
Values to be determined
Underwood
- Top and
bottom concentrations
- relative volatility
- Feed and
top concentrations
- relative volatility
Gilliland
- minimum number of plates
- minimum
reflux ratio
- minimum number of plates
- Feed tray at maximum
Reflux
- minimum
reflux ratio at
infinite number of stages
- Actual
reflux ratio
- theoretical number of plates
with
calculated
reflux ratio
- theoretical feed tray
- theoretical feed tray
Fenske
Kirkbride
- Mole stream of top and
bottom
- Feed, top and
bottom concentrations
The above simulation was generated in CHEMCAD 6.4.0.
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Are you interested in further tutorials, seminars or other solutions with CHEMCAD?
Then please visit our website.
www.chemstations.eu
Or please contact us.
Mail: support@chemstations.eu
Phone:
+49 (0)30 20 200 600
Authors:
Lisa Weise
Daniel Seidl
Sources:
[1] Kister, Henry Z.: Distillation design. McGraw-Hill, 1992
[2] Gmehling, Jürgen: Kolbe, Bärbel: Kleiber, Micheal: Rarey, Jürgen: Chemical Thermodynamics
for Process Simulation. Wiley-VCH Verlag, 2012
[3] Edwards, John: Process Modeling Selection of Thermodynamic Methods
[4] Schmidt, Wolfgang: Ideales Phasengleichgewicht und Shortcut Kolonne, July 2011
[5] Sattler, Klaus: Thermische Trennverfahren: Grundlagen, Auslegung, Apparate. Wiley-VCH
Verlag, p. 199-202
[6] CHEMCAD help
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List of formulas
Formula
Meaning
̇
Mass stream
Mole fraction
Mass fraction
Reflux ratio
Relative volatility
k factor
Mole fraction in the liquid phase
Pressure
Saturation pressure
Number of stages
̇
Mole stream
Indexes
Meaning
F
Feed
D
Distillate
B
Bottom
L
Light component
H
Heavy component
min
minimum:
1,2
Component 1 & 2
i
i-te component
List of indexes
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