Abstract
In the present work, the exergy analysis and economic study of 3 different samples of threecomponent
mixtures have been investigated (ESI>1, ESI≈1, and ESI<1). The feed mixture has been
tested under three different compositions (low, equal, and high contents of the intermediate
component). A quantitative comparison between simple and complex configurations, considering
thermally coupled, thermodynamically equivalent, and divided-wall column (DWC) has been carried
out. The results present that the best sequence could be found by TAC or exergy loss rate analysis.
Complex sequences have greater exergy losses in comparison to simple sequences. Despite
expectations, the Petlyuk sequence only performs well in a few cases and poorly on others. According
to the results, as the amount of intermediate component in the feed increases, both TAC and exergy
losses of each sequence increase. The results also demonstrated that the occurrence frequency as the
best sequence for DWC, thermodynamically equivalent, thermally coupled, and basic sequences are
36%, 28%, 25%, and 11% respectively. According to authors’ best knowledge, a quantitative exergy
and cost comparison (based on rigorous simulation and optimization) between these configurations
have never been carried out all together before.
Keywords: Distillation Sequence, Exergy Analysis, Divided-wall Column, Separation Matrix
1. Introduction
Distillation process is still the most promising separation technique used in oil, gas, chemical, and
petrochemical industries. But this process in most cases consumes a lot of energy, which is the
greatest part of operating costs in these industries. Thus improving the energy consumption of
distillation processes is still an interesting field of study.
Industrial mixtures commonly contain more than two components and these separation tasks could not
be implemented efficiently in a single column. Hence it is required to employ a number of columns
for the separation of multicomponent mixtures to the number of desired products. This leads to many
possible configurations (sequences) for separating a multicomponent mixture into relatively pure
products (sharp split) or several multicomponent product streams (non-sharp or sloppy split). On the
other hand, the distillation sequences for separating an n-component feed could be classified in
accordance with the number of distillation columns: having less than n-1 columns (intensified or
* Corresponding Author:
Email: capepub@cape.iust.ac.ir
A. H. Khalili-Garakani et al./ Three-component Distillation Columns Sequencing … 67
reduced), exactly n-1 columns (basic), or more than n-1 columns (Gridhar et al., 2010). The basic
sequences are divided into two categories: simple basic sequences, in which columns have one feed
and two products from condenser on top and reboiler at the bottom (direct, indirect); and basic
complex sequences, in which at least one column has more than one feed or has side products (prefractionator).
There are more categories which could be generated from basic configurations: thermally coupled
(TC), thermodynamically equivalent (TE), and divided-wall columns (DWC). Figure 1 presents the
different categories of three-component distillation sequences. A thermal coupling configuration
could be generated by the substitution of a condenser and/or a reboiler not associated with the final
product streams with a bidirectional vapor-liquid connection. Fully thermally coupled (FTC)
configurations are those in which all the vapor requirements of the sequence are supplied by a single
reboiler and the entire reflux by a single condenser. The FTC with an external pre-fractionator is a
Petlyuk configuration (Caballero et al., 2013). The thermodynamically equivalent configurations
could be generated from the thermally coupled sequences through moving one column section
associated to a condenser and/or a reboiler which provides the common reflux flow rate or the vapor
boil up between two consecutive columns. Divided-wall column sequences are other categories,
which could be considered to reduce investment costs (Caballero et al., 2013). These configurations
consist of two columns arranged in a single shell and divided by an internal wall.
Earlier approach to synthesis distillation schemes was to use experience-based heuristic rules (Seader
et al., 1977; Tedder et al., 1978; Westerberg, 1985). Heuristic-rule-based methods might lead to
feasible solutions but not necessarily the optimum configuration. A true optimal scheme could be
found precisely by a mathematical programming approach. The brief review and work performed by
Gridhar and Agrawal indicates that in order to achieve the optimum configuration, the first and most
important step is to predefine the search space as complete as possible (Gridhar et al., 2010). One of
the early methods, introducing a superstructure based on “states” and “tasks” was proposed initially
by Sargent and Gaminibandara (Sargent et al., 1976). This superstructure could be used in mixed
integer linear programming (MILP) (Doherty et al., 2001) or mixed integer nonlinear programming
(MINLP) (Caballero et al., 2004 and 2006) to find the optimum sequence. Simple and complex
distillation schemes could be considered with this superstructure.
Another systematic approach to synthesize distillation column sequences based on the column
products position, which could be distillate, bottoms, or side streams, was proposed by Agrawal
(2010). Recently Errico et al. presented a simple 4-step method for the systematic synthesis of the
search space considering the generation information saving from one configuration to another (Errico
et al., 2009 and 2014). Ivakpour and Kasiri introduced a method which generates simple and/or
complex distillation columns and bypass streams by introducing a separation matrix (Ivakpour et al.,
2008) to synthesize complete as well as reduced sequences. Later Khalili-Garakani et al. extended the
separation matrix method to cover thermally coupled, thermodynamically equivalent, and dividedwall
column sequences (Khalili-Garakani et al., 2015).
68 Iranian Journal of Oil & Gas Science and Technology, Vol. 5 (2016), No.2
Figure 1
Three-component distillation sequences considered in this study.
1.1. Exergy analysis of distillation sequences
Exergy analysis as a tool has been used to study the performance of distillation columns by many
researchers. Rivero et al. proved that exergy analysis could be used as a tool to provide a good insight
into the process inefficiencies and proving the viability of distillation process modification (Rivero et
al., 2004). Besides, this method has proved viable to be used in the synthesis of distillation sequences
A. H. Khalili-Garakani et al./ Three-component Distillation Columns Sequencing … 69
to avoid complexity, in laborious systems such as those formed by a large number of components,
trays, feeds, and side streams (Kencse et al., 2010).
Kencse and Mizsey compared simple and heat integrated forms of direct and indirect sequences and
fully thermally coupled schemes for three-component separation mixtures according to cost, exergy
loss, and greenhouse gas emissions (Kencse et al., 2010). They reported that an exergy analysis could
predict the best sequence as predicted by economic and gas emissions studies. There are other
researchers who used exergy analysis in distillation processes such as Suphanit et al. (2007), who
studied the performance of divided-wall column configurations using exergy analysis) or Pinto et al.
(2011), who presented a method for targeting side condensers and reboilers in distillation columns
based on exergy loss diagrams. Also, Cortez-Gonzalez et al. (2012) analyzed the reduced structures
that could be generated from simple basic four-component configurations by both economic and
exergy analysis. Sun et al. (2012a) used exergy analysis to compare the performance of two different
schemes for organo-silicon monomer distillation process. In another study, they present a five-column
heat integrated methanol distillation scheme using pinch and exergy analysis simultaneously (Sun et
al., 2012b).
In this work, the whole family of three-component distillation sequences, including simple, complex,
thermally coupled, thermodynamic equivalent, divided-wall column, and intensified sequences are
considered. All sequences (Figure 1) were simulated (based on rigorous simulation), optimized, and
compared according to both economic and exergy analysis indicators. As stated, most of the studies
were mostly reported for the exergy analysis of single distillation column and there are a few reports
of applying the exergy analysis to a large number of columns or distillation sequences (Kencse et al.,
2010). According to the authors’ best knowledge, these configurations have never been analyzed and
compared based on an economic study and exergy analysis all together before.
2. Methods
2.2. Separation matrix
The separation matrix used herein is extensively defied in our previous work (Ivakpour et al., 2008;
Khalili-Garakani et al., 2015). In Figure 2, the proposed separation matrix is demonstrated for threeand
four-component feed mixtures. φ is the sign used for the final products which could accept the
values {I, II, and S}; Ф is the symbol used for sub-mixtures, which could have the values {I, II, and
S}. In the separation matrix:
1- φ or Φ= {I} is used to demonstrate the column top product (from a condenser);
2- φ or Φ = {II} is applied to the column bottom product (from a reboiler);
3- And φ or Φ = {S} relates to the mixtures produced as a column side stream.
The mixture located in the first column is the original feed and is composed of all final products.
Furthermore, the arrays positioned on the same diagonal of the separation matrix have an analogous
heavy part. The structure of the distillation configuration could be obtained by the selection of the
mixture (φ or Φ) options in the separation matrix. For more clarification, the components in each
matrix array are indicated as subscript at the lower right of each array. Moreover, for the easier
programming of the algorithm, three more indices are added for each Φ in the matrix { Ф
,
, 
 ; the
first index, ψ, indicates the thermal coupling of the product in the relevant distillation columns. Hence
each of the sub-mixture streams that could be a candidate for thermal coupling has an additional ψ
70 Iranian Journal of Oil & Gas Science and Technology, Vol. 5 (2016), No.2
sign in the lower left of the sub-mixture array associated with it (Ф
). ψ could be “0” or “I”,
indicating the absence or presence of thermal coupling for its related reboiler or condenser
respectively. The second index, λ, added to the upper left part of the Φ array presents moving,
omitting sections, and divided wall between the columns in sequences. This superscript could also
accept values “I” or “0”. It must be noted that, in order to make a section movable in a distillation
column, the condenser or the reboiler associated with the sub-mixture must initially be omitted.
Therefore, in the separation matrix, the related array of the sub-mixture of moving sections should
have ψ equated to I. Hence in a systematic programming practice, in order to generate all possible
thermodynamically equivalent configurations, ψ should be checked to be “I” before changing λ for
each sub-mixture. As a result, the arrays which represent moving sections will have two “I” values for
both indices ψ and λ.
φ and Ф:{I, II, S}
I: Distillate Product
II: Bottom Product
S: Side Stream
Figure 2
Proposed separation matrix to present different sequences.
For intensified sequences, the deleted sections are illustrated by “X” in the separation matrix. λ
accepts “X” in the upper left of the array in these cases. In these sequences, the separation could not
take place completely and, for example in sequence Direct-I in Figure 3, a part of component C
appears in product B. The same is true for Indirect-I in Figure 3, in which a part of A is appearing in
product B. These components are called suspended components and are illustrated by the third index
in the upper right-hand side of the arrays.
A. H. Khalili-Garakani et al./ Three-component Distillation Columns Sequencing … 71
Figure 3
Separation matrices for each distillation sequences presented in Figure 1.
At last, for presenting the divided-wall columns, the value of ψ is changed to W. For more tedious
sequences with more divided-wall columns, the value of ψ accepts W1, W2… for more clarification.
Therefore, separation matrices in which both ψ and λ have value I ({ψ    
Ф
λ    
 }), which is the mark of a
side column in the sequence, the value of ψ is changed and the separation matrix for the divided-wall
column is generated. An example of these kinds of sequences could be seen in Figure 3.
72 Iranian Journal of Oil & Gas Science and Technology, Vol. 5 (2016), No.2
2.2. Exergy analysis of distillation columns
Exergy is based on the first and second laws of thermodynamics and is defined as the maximum work
which could be obtained from a stream or a source of energy until it reaches equilibrium with the
environment or any reference state. Each stream has an exergy value that is the result of the difference
between pressure, temperature, and chemical composition of the stream and those of the reference
state. The reference state as defined by Szargut et al. is T0=298.15 K and P0=101.325 kPa (Szargut, et
al. 1988). The exergy value of streams degenerates through the process. Thus, due to irreversibility
phenomena in distillation columns, exergy loss is unavoidable. The main irreversibility in distillation
columns is due to the mixing of the streams with different temperatures, pressures, and compositions
on the trays and loss of heat in the condensers and to the environment from the body of the columns.
The total exergy of a stream is classified into physical, chemical, and mixing parts, which are
calculated through the following equation (Hinderink et al., 1996):
Total exergy:


  .  .  Δ (1)
Physical exergy:
.   !, "# $  !%, "%#& $ !%' !, "# $ ' !%,"%#& (2)
Chemical exergy:
. (

. )., (

. Δ*+
, $(,%,
+.,

& (3)
Exergy of mixing:
Δ  Δ- $ !%Δ. (4)
where, the mixing rule is given by:
Δ/ (5)   0 / $(/#  1 /2 $(3/2#
 
Heat streams exergy:
4  5. 61 $ !%
! 8 (6)
The exergy loss in a distillation column could be easily calculated from the difference between exergy
values of the inlet and outlet heat and mass streams. The inlet streams are the feeds and heat duty of
reboilers, and the outlet streams are the products and the heats of the condensers.
9  Δ: $ Δ;
 (7)
A. H. Khalili-Garakani et al./ Three-component Distillation Columns Sequencing … 73
  5<. 61 $ !=
!<.8  5:>. 61 $ !=
!:>.8  ?> $ 

 $ 
@
(8)
However, here the exergy loss of the columns is calculated by adding up the exergy loss at each stage
of the column. The distribution of the exergy losses along the column (stage by stage) is more useful
in understanding the irreversibility in each part of the column and the improvement of the entire
system (Suphanit et al., 2007). The exergy losses of a stage in the distillation column could be
calculated by carrying out a simple exergy balance around each tray. By calculating the exergy losses
at each stage, the exergy loss diagram of the column could be achieved. Simulation methods are
employed for obtaining the required data for drawing an exergy loss diagram.
2.3. Proposed algorithm
The steps of the procedure are described below:
· The procedure starts by defining the problem information (n, To, Po, xf, Tf, Pf, and Utilities) and
parameter boundaries (xp, optimization parameters).
· In the next step, the possible configurations according to the number of components (n) are
generated and considered. The separation matrix method was utilized for this purpose as
described elsewhere (Khalili-Garakani et al., 2015).
· The first configuration is then selected and sent to the next step, in which the columns are
simulated by the short-cut method in order to find the initial data comprising of Nt, NF, Rmin, and
PCol. The pressure of the columns are optimized here to reach atmospheric pressure as close as
possible, but the boiling point of the liquid in the condenser could remain higher than 35 °C
(assume 25 °C for inlet cooling water temperature). Simulated annealing was applied as the
optimization method (Kirkpatrick et al., 1983; Mahmoodpour et al., 2015). For physical
property and equilibrium calculations, the Soave-Redlich-Kwang (SRK) equation-of-state was
selected.
· In the next step, the rigorous simulations and the outcome of the short-cut method were used as
the initial guess. The inside-out method, according to Seader et al., was used as the rigorous
simulation method (Seader et al., 2011). The reflux ratios of the columns are then optimized
with the objective of reaching the specified product purity with minimum usage of hot and cold
duty in the reboilers and condensers respectively. The simulated annealing was used again at
this stage as the optimization method.
· The results of the rigorous calculations (h, s, h0, s0, QH, and QC) were used for the exergy
analysis of distillation columns. The exergy loss for each tray was estimated and the total
exergy loss of the columns (Exdestruction) was evaluated by adding them up in this step. The
formulas and qualities of exergy analysis are presented in the former part.
· The results of the rigorous calculations (DCol., QH, and QC) were used for the economic study
(Total Annual Cost = annual capital cost + annual operation cost) of the distillation columns.
Guthrie’s cost calculation method is employed as modified in Douglas for the economic study
(capital cost) (Douglas, 1988). Utility prices for calculating operating costs are as demonstrated
in Table 1 (Seider et al., 2010).
74 Iranian Journal of Oil & Gas Science and Technology, Vol. 5 (2016), No.2
· This procedure was carried out for all the configurations and the results sorted according to
economic and exergy analysis separately.
Table1
Utility specification [28].
Utility Type Pressure (atm) Temperature (°C) Price ($/GJ)
Electricity - - 16.667
Cooling Water 1 25 0.254
Low Pressure Steam 4.4 144 3.102
Medium Pressure Steam 11.2 184 5.257
High Pressure Steam 31.6 254 8.174
The configurations studied were for mixtures containing three-components with three different
compositions (F1: [0.4, 0.2, 0.4], F2: [0.33, 0.34, 0.33], and F3: [0.15, 0.7, 0.15]) which are presented
in Table 2.
Table 2
Different samples considered in this study.
αAB=KA/KB αBC=KB/KC αAC=KA/KC
Vapor
Fraction
Pressure
(atm)
Mixture Components ESI*
1.86 4.5 0 2.38 1.28 3.05
n-Butane,
i-Pentane,
n-Pentane
M1
1.04 1.44 0 2.57 2.47 6.35
n-Pentane,
n-Hexane,
n-Heptane
M2
0.47 1.44 0 1.25 2.65 3.31
i-Pentane,
n-Pentane,
n-Hexane
M3
* ESI=αAB/αBC [4].
3. Results and discussion
Table 3 presents the ranking of the sequences presented in Figure 1 for different feed conditions.
Also, in Table 4, the economic study and exergy analysis of the first three sequences under each
condition are presented.
Table 3
The ranking of configurations for M1, M2, and M3 at different feed compositions.
M1
F1 F2 F3
1 Indirect-DWC Direct-TC Indirect-DWC
2 Indirect-TE Direct Indirect-TE
3 Symmetrical-DWC Indirect-TC Indirect-TC
4 Symmetrical-TC2 Indirect-DWC Direct
5 Symmetrical-TC3 Direct-DWC Direct-TC
6 Direct Indirect-TE Symmetrical-TE5
7 Symmetrical-TE4 Direct-TE Indirect
A. H. Khalili-Garakani et al./ Three-component Distillation Columns Sequencing … 75
8 Symmetrical-TE3 Indirect Direct-DWC
9 Symmetrical-TE2 Symmetrical-DWC Direct-TE
10 Symmetrical-TC1 Symmetrical-TC3 Symmetrical-TC1
11 Indirect Symmetrical-TC2 Symmetrical-TE2
12 Symmetrical-TE1 Symmetrical Symmetrical-TC2
13 Indirect-TC Symmetrical-TE4 Symmetrical-TE1
14 Symmetrical Symmetrical-TE3 Symmetrical-DWC
15 Direct-DWC Symmetrical-TC1 Symmetrical
16 Direct-TE Symmetrical-TE2 Symmetrical-TC3
17 Direct-TC Symmetrical-TE1 Symmetrical-TE4
18 Indirect-IC Symmetrical-TE5 Symmetrical-TE3
19 Symmetrical-TE5 Indirect-IC Indirect-IC
20 Direct-IC Direct-IC Direct-IC
M2
F1 F2 F3
1 Direct-TC Symmetrical-DWC Symmetrical-TE2
2 Direct-DWC Symmetrical-TC3 Symmetrical-TC1
3 Symmetrical-TC2 Direct-TC Symmetrical-TE1
4 Symmetrical-TE4 Symmetrical Indirect-DWC
5 Direct-TE Direct-DWC Symmetrical
6 Symmetrical-TE3 Direct-TE Indirect-TE
7 Symmetrical-DWC Indirect-DWC Indirect-TC
8 Indirect-DWC Indirect-TE Symmetrical-DWC
9 Indirect-TE Direct Symmetrical-TC3
10 Symmetrical-TC3 Symmetrical-TC2 Direct-DWC
11 Symmetrical Symmetrical-TE4 Direct-TE
12 Direct Symmetrical-TE3 Direct
13 Indirect-TC Indirect-TC Indirect
14 Indirect Indirect Direct-TC
15 Symmetrical-TE2 Symmetrical-TE2 Symmetrical-TC2
16 Symmetrical-TC1 Symmetrical-TC1 Symmetrical-TE4
17 Symmetrical-TE1 Symmetrical-TE1 Symmetrical-TE3
18 Indirect-IC Symmetrical-TE5 Symmetrical-TE5
19 Symmetrical-TE5 Indirect-IC Indirect-IC
20 Direct-IC Direct-IC Direct-IC
M3
F1 F2 F3
1 Direct-DWC Symmetrical-TE2 Indirect-DWC
2 Direct-TE Direct-DWC Symmetrical-TE2
3 Indirect-DWC Direct-TE Indirect-TE
4 Symmetrical-TE2 Indirect-DWC Indirect-TC
5 Indirect-TE Indirect-TE Direct-TC
6 Direct Symmetrical-TE1 Direct-TE
7 Symmetrical-TC1 Symmetrical-TC1 Direct-DWC
8 Symmetrical-TE1 Direct Symmetrical-TC1
9 Indirect-TC Direct-TC Direct
10 Direct-TC Indirect Symmetrical-TE1
76 Iranian Journal of Oil & Gas Science and Technology, Vol. 5 (2016), No.2
11 Indirect Indirect-TC Indirect
12 Symmetrical Symmetrical Symmetrical-TE4
13 Symmetrical-TC2 Symmetrical-DWC Symmetrical
14 Symmetrical-DWC Symmetrical-TC3 Symmetrical-TE3
15 Symmetrical-TE4 Symmetrical-TC2 Symmetrical-DWC
16 Symmetrical-TC3 Symmetrical-TE4 Symmetrical-TC3
17 Symmetrical-TE3 Symmetrical-TE3 Symmetrical-TC2
18 Direct-IC Direct-IC Symmetrical-TE5
19 Symmetrical-TE5 Indirect-IC Direct-IC
20 Indirect-IC Symmetrical-TE5 Indirect-IC
Table 4
The result of total annual cost ($/y) and exergy loss rate (GJ/hr) for the best three sequences under different feed
conditions.
Exergy loss rate
(GJ/hr)
Mixture Composition Sequences TAC ($/year)
1st Indirect-DWC 293,472.592 0.675
F1
M1
2nd Indirect-TE 296,297.113 0.676
3rd Symmetrical-DWC 303,743.586 0.679
1st Direct-TC 340,502.266 0.229
F2 2nd Direct 367,942.217 0.255
3rd Indirect-TC 3778,841.474 0.629
1st Indirect-DWC 508,593.831 1.531
F3 2nd Indirect-TE 512,115.351 1.535
3rd Indirect-TC 526,700.303 0.687
1st Direct-TC 138,095.912 0.696
F1
M2
2nd Direct-DWC 142,216.070 0.720
3rd Symmetrical-TC2 144,355.762 2.654
1st Symmetrical-DWC 170,791.224 0.599
F2 2nd Symmetrical-TC3 172,106.681 0.600
3rd Direct-TC 175,504.430 0.351
1st Symmetrical-TE2 196,042.597 1.177
F3 2nd Symmetrical-TC1 212,178.195 1.187
3rd Symmetrical-TE1 212,217.274 1.188
1st Direct-DWC 278,968.356 0.628
F1
M3
2nd Direct-TE 279,719.402 0.629
3rd Indirect-DWC 281,628.454 0.377
1st Symmetrical-TE2 326,486.558 0.956
F2 2nd Direct-DWC 329,243.256 0.785
3rd Direct-TE 329,686.667 0.786
1st Indirect-DWC 463,035.983 0.342
F3
2nd Symmetrical-TE2 469,954.929 0.718
A. H. Khalili-Garakani et al./ Three-component Distillation Columns Sequencing … 77
Exergy loss rate
(GJ/hr)
Mixture Composition Sequences TAC ($/year)
3rd Indirect-TE 472,286.012 0.344
When the feed content of component B is low, the composition of B in the liquid feed of the side
stripper is much lower than that of the vapor feed of the side rectifier. This is due to liquid feed of the
side stripper being diluted by a significant amount of component A, while in the vapor feed of the side
rectifier, this is done with the same amount of component C. As a result, for producing component B
with the same specification, vapor traffic in the side stripper is significantly more than side rectifier.
Therefore, more heat could be supplied at a mid-temperature of TB in side stripper configuration (in
comparison to the lower amount of rejected heat in the condenser at temperature TB in side rectifier).
This is the reason why Indirect-TE and Indirect-DWC perform better for M1 and composition F1.
Also, when the content of the middle component B is high in the feed, these two configurations have
superior performance compared to other sequences, with the only exception of M2 in which ESI≈1.
According to Malone et al. (1985), when component relative volatilities are close (αAB, αBC), as in M2
(F1 and F2), direct sequence is one of the best, as also demonstrated by the present results. As αB
approaches αA, the chance for direct family to be one of the preferred sequences increases. However,
this is not the case when component B content increases. When αAB is low, for the separation of A
from B, a large amount of vapor is needed; however, the condenser temperature for pure A (TA) is
nearer to the B bubble point (TB) than to pure component C reboiler temperature (TC). As a result, it is
better to supply the required heat for the separation of A from B at mid temperature level (TB). In
configurations like symmetrical-TC3 (Petlyuk sequence), supply of heat at TB is not possible and this
leads to the better performance of sequences such as indirect-TE in comparison to symmetrical-TC3.
This is true for divided-wall column sequences which are generated from these configurations.
Symmetrical (Brugma or pre-fractionator) sequence and the other sequences generated from it
(thermally coupled and equivalent thermodynamics) have their best performance in M2, in which
ESI≈1. The comparison of thermally coupled configurations (symmetrical-TC1, TC2, and TC3) with
side stripper, side rectifier, and other symmetrical configurations illustrate that side stripper and side
rectifier configurations have better performance for M1 (ESI>1) and M3 (ESI<1), and only in M2
(ESI≈1), the thermally coupled sequences present the reduction of energy consumptions. Similar
results are presented in the work by Agrawal and Fidkowski (1999), in which they calculate the
minimum total amount of vapor in sequences in minimum reflux condition. Thermally coupled
sequences for feed M2 and F3 composition illustrate 34% reduction of energy consumption in
comparison to simple sequences (direct and indirect).
The results of thermodynamically equivalent configurations presented by Agrawal and Fidkowski
(1998) (symmetrical-TE1-TE4) is nearly the same as thermally coupled configurations under all feed
conditions considered in this study. In these configurations, reboilers and condensers are located on
different columns; the column at a high pressure has a reboiler, and the column at a low pressure has a
condenser; in this way, the vapor stream could be flown from the column at a higher pressure to the
one at a lower pressure. The change to the structure of the sequence made it more operable and easy
to control. Comparing them to the symmetrical-TC3 illustrates that symmetrical-TC3 sequence
performs better for M1 with F1-F2 feed composition, and symmetrical-TE1 and symmetrical-TE2 are
better for F3 feed composition. For M2 and feed F1, symmetrical-TE3 and symmetrical-TE4 are
superior, while symmetrical-TC3 outperforms for feed F2, and symmetrical-TE1 and symmetrical78
Iranian Journal of Oil & Gas Science and Technology, Vol. 5 (2016), No.2
TE2 perform better for F3. In M3, symmetrical-TE1 and symmetrical-TE2 perform better at all three
different feed compositions.
Agrawal and Fidkowski (1998 and 1999) presented symmetrical-TE1-TE4 configurations and
analyzed them by the minimum total amount of vapor in sequences in a minimum reflux condition.
Then Jiménez et al. (2003) analyzed them by rigorous methods and compared their heat duty. In
comparison to their work, the research presented here uses more accurate total cost and exergy loss
analysis, which justifies some of the differences in ranking of the sequences. The column diameter
calculation procedure considered herein in TAC analysis is one of the main reasons behind the
differences between the two findings.
Furthermore, it should be noted that some of the configurations considered herein are not present in
the works of Caballero and Grossman (2001 and 2004), which employs a suggested superstructure
and optimizes the tray sections and energy performance of configurations.
Figure 4a presents the number of occurrences of the best three sequences for all the cases studied
here. Indirect-DWC sequence has the largest number of occurrences followed by Direct-DWC,
Direct-TC, Indirect-TE, and Direct-TE sequences respectively.
Also in Figure 4b, the distribution of the best sequence among different categories of configurations is
illustrated. As presented, DWC sequences have the biggest part and the basic sequences have the
lowest part among the best configurations.
Figure 5 illustrates the exergy loss diagram of symmetrical configurations (Brugma configurations)
for different feeds (M1-M3) and compositions (F1-F3). Brugma sequence was considered here
because from this sequence all the other configurations could be derived. As demonstrated, increasing
B content in the feed raises the peak in the exergy loss diagram. For M1 (ESI>1), the maximum loss
is in the upper feed of the second column. At the time (ESI≈1 (M2)), there were two peaks: one in the
upper feed of the second column and the other in the reboiler. At last for M3, the peaks are located on
the lower feed and the condenser of the second column.
a)
A. H. Khalili-Garakani et al./ Three-component Distillation Columns Sequencing … 79
b)
Figure 4
a) Number of occurrences of the best three configurations in different samples and b) distribution of the best
sequences among different configuration categories.
The location of peaks in the diagrams could be found by the relative volatility of the components. As
illustrated in Table 2 and Figure 5, the peaks are located in the place (section) where the feed with
higher relative volatility enters the second column. It is due to the superior separation ability of the
mixture with greater relative volatility in the pre-fractionator (first column). Thus in the next column,
the streams with much different compositions encounter each other, and as a result the exergy losses
due to mixing is increased. Since, αAB is higher in M1 (ESI>1), there is a peak in the upper feed of the
second column. However, the relative volatility becomes similar in M2 (ESI≈1) in the prefractionator,
where the separations (A/B and B/C) take place in the same order. Hence separation in
the next column would be easier, and, as a result, the exergy loss is decreased. This effect is more
significant when the content of the middle component (B) is lower in the feed. In these configurations,
the amount of loss in the upper (rectifier) and lower (stripper) sections of the second column are
nearly the same and the distribution of losses is more monotonous.
As stated before, when the amount of αAB is low (M3: ESI<1), a large amount of vapor is required for
the separation of A from B. As a result, the exergy loss in the condenser is increased and a peak could
be seen in the condenser.
Therefore, by these figures the designers could easily find the weak points in each column of the
sequence and employ the exergy loss diagram for improving the performance of the sequence.
Furthermore, the changes to the structure of the columns in these places similar to thermal coupling of
the streams between columns, generating thermodynamically equivalent structures by moving
sections in these areas, or using internal wall (DWC) could reduce the exergy loss of the system (as
presented in the results in the former section).
Basic
11%
Thermally Coupled
25%
Thermodynamically
Equivalent
28%
DWC
36%
Chart Title
80 Iranian Journal of Oil & Gas Science and Technology, Vol. 5 (2016), No.2
Figure 5
Exergy loss diagram of the symmetrical sequence (Brugma) for different feeds (M1-M3) and compositions (F1-
F3).
In addition, the knowledge of the weak points of the sequences and structural changes could lead to a
search space reduction algorithm. This algorithm helps designers to analyze a much smaller search
space containing only near optimal sequences, which could be sufficient to find an overall optimal ncomponent
configuration. The search space reduction algorithm is out of the scope of this paper and
would be presented in future works.
4. Conclusions
The analysis of the samples illustrates that the TAC of the sequences is totally dependent on the
amount of the intermediate component present in the feed. By increasing the amount of the
intermediate component, TAC is increased for each sequence. Also, despite expectations, the Petlyuk
sequence (symmetrical-TC3) only performs well in M2 (ESI≈1) and for F2 composition; it
demonstrates poor performance for other conditions (like different compositions of M3). In
comparison to economic study, exergy analysis is simpler in calculation and only requires some
A. H. Khalili-Garakani et al./ Three-component Distillation Columns Sequencing … 81
physical properties, which could easily be acquired; also, the exergy loss diagrams could give
designers an insight into the weak parts of the systems and help with improving the performance of
the processes. Knowing the weak points in each column of the sequence could be used for the
structural changes of the sequence, and could lead to the generation of new configurations. The results
presented that changes such as thermal coupling of the streams between columns, generating
thermodynamically equivalent structures by moving sections in these areas, or applying divided-wall
columns could reduce the exergy losses of the system (Khalili-Grakani, 2016).
At last, according to the ability and flexibility of the separation matrix in changing the structure of the
sequence, the method could be easily expanded to a larger number of components and other kinds of
sequences like multi-effects, pump around, compressor-aided separations, and internal heat integrated
distillation systems (HIDIC), which would be considered in future works. The detailed optimization
procedure is beyond the scope of this work and will be presented in future works.
Nomenclature
Symbols
Δ*+
, : Standard Gibbs energy of formation [kJ/mol]
Extotal : Total exergy content [kJ/kg]
Exphys. : Specific physical exergy [kJ/kg]
Exchem. : Specific chemical exergy [kJ/kg]
Ĕxchem : Standard chemical exergy [kJ/mol]
ExMix. : Specific exergy of mixing [kJ/kg]
h : Specific enthalpy [kJ/kg]
ho : Specific enthalpy at T0, p0 [kJ/kg]
I : Top product
II : Bottom product
III : Eliminated mixture in crossover complete sequences
L : Liquid fraction
n : Number of chemical species
Φ : All possible states for sub-mixtures
φ : All possible states for product type
po : Pressure of the reference state [101.325 kPa]
R : Gas constant [kJ/mol.K]
S : Side stream
s : Specific entropy [kJ/kg.K]
so : Specific entropy at T0, p0 [kJ/kg.K]
To : Temperature of the reference state [298.15 K]
V : Vapor fraction
x : Mole fraction of species
Superscripts
a, b : Presenting suspected components in each stream
82 Iranian Journal of Oil & Gas Science and Technology, Vol. 5 (2016), No.2
λ : Sign of moving section or omitting section in related distillation columns
Subscript
ψ : Sign of thermal coupling of the product in related distillation columns
r, k : Presenting components in each stream
References
Agrawal, R., Fidkowski Z. T., More Operable Arrangements of Fully Thermally Coupled Distillation
Columns, AIChE Journal, Vol. 44, No. 11, p. 2565-2568, 1998.
Agrawal, R., Fidkowski Z.T., New Thermally Coupled Schemes for Ternary Distillation, AIChE
Journal, Vol. 45, No. 3, p. 485-496, 1999.
Agrawal, R., Synthesis of Multicomponent Distillation Column Configurations, AIChE Journal, Vol.
49, p. 379-401, 2003.
Caballero, J. A., Grossmann I. E., Generalized Disjunctive Programming Model for the Optimal
Synthesis of Thermally Linked Distillation Columns, Industrial & Engineering Chemistry
Research, Vol. 40, No. 10 p. 2260-2274, 2001.
Caballero J. A., Grossmann I. E. Design of Distillation Sequences: from Conventional to Fully
Thermally Coupled Distillation Systems, Computer & Chemical Engineering, Vol. 28, p. 2307-
2329, 2004.
Caballero J. A., Grossmann I.E., Structural Considerations and Modeling in the Synthesis of Heatintegrated-
thermally Coupled Distillation Sequences., Industrial & Engineering Chemistry
Research, Vol. 45, p. 8454-8474, 2006.
Caballero J. A., Grossmann I. E., Synthesis of Complex Thermally Coupled Distillation Systems
Including Divided Wall Columns, AIChE Journal, Vol. 59, No. 4, p. 1139-1159, 2013.
Cortez-Gonzalez J., Segovia-Hernández J. G., Hernández D., Gutiérrez-Antonio C., Briones-Ramírez
A., Rong B.G. Optimal Design of Distillation Systems with Less than n-1 Columns for a Class
of Four-component Mixtures, Chemical Engineering Research and Design Vol. 9, p. 1425-1447,
2012.
Doherty M. F., Malone M. F., Conceptual Design of Distillation Systems, McGraw-Hill: Boston,
2001.
Douglas J. M. Conceptual Design of Chemical Processes, McGraw-Hill: United States, 1988.
Errico M., Rong B. G., Tola G., Turunen I., A Method for Systematic Synthesis of Multicomponent
Distillation Systems with Less than n-1 Columns, Chemical Engineering and Processing, Vol.
48, p. 907-920, 2009
Errico M., Rong B. G., Torres-Ortega C. E., Segovia-Hernandez J. G. The Importance of the
Sequential Synthesis Methodology in the Optimal Distillation Sequence Design, Computer and
Chemical Engineering, Vol. 6, p. 1-9, 2014.
Giridhar A., Agrawal R. Synthesis of Distillation Configurations: I., Characteristics of a Good Search
Space, Computer and Chemical Engineering, Vol. 34, p. 73-83, 2010.
Hinderink A., Kerkhof F., Lie A., De Swaan Arons J., Van der Koo H.J., Exergy Analysis with a
Flowsheeting Simulator I. Theory; Calculating Exergies of Material Streams, Chemical
Engineering Science, Vol. 51, No. 20, p. 4693-4700, 1996.
Ivakpour J., Kasiri N. Synthesis of Distillation Column Sequences for Non-sharp Separations,
Industrial & Engineering Chemistry Research, Vol. 48, p. 8635-8649, 2009.
A. H. Khalili-Garakani et al./ Three-component Distillation Columns Sequencing … 83
Jiménez, A., N. Ramírez, Castro, A., Hernández, S., Design and Energy Performance of Alternative
Schemes to the Petlyuk Distillation Systems, Chemical Engineering Research and Design, Vol.
81, p. 518-524, 2003.
Kencse H., Mizsey P. Methodology for the Design and Evaluation of Distillation Systems: Exergy
Analysis, Economic Features and GHG Emissions, AIChE Journal, Vol. 56, No. 7, p. 1776-
1786, 2010.
Khalili-Grakani A., Ivakpour J., Kasiri N., Matrix-based Method for Synthesis of Main Intensified
and Integrated Distillation Sequences, Korean Journal of Chemical Engineering, Vol. 33, No. 4,
p. 1134-1152, 2016b.
Khalili-Grakani A., Ivakpour J., Kasiri N., Evolutionary Synthesis of Optimum Light Ends Recovery
Unit with Exergy Analysis Application, Applied Energy, Vol. 168, p. 507-522, 2016a.
Kirkpatrick, S., Gellat, C.D., and Vechhi, M. P., Optimization by Simulated Annealing, Science, Vol.
220, p. 671-680, 1983.
Mahmoodpour S., Masihi M., Gholinejhad S. Comparison of Simulated Annealing, Genetic, and Tabu
Search Algorithms for Fracture Network Modeling. Iranian Journal of Oil & Gas Science and
Technology, Vol. 4, No. 2, p. 50-67, 2015.
Malone M. F., Glinos K., Marquez F. E., Douglas J. M. Simple, Analytical Criteria for the
Sequencing of Distillation Columns, AIChE Journal, Vol. 31, No. 4, p. 683-689, 1985.
Pinto F.S., Zemp R., Jobson M., Smith R., Thermodynamic Optimization of Distillation Columns,
Chem. Eng. Sci.,Vol. 66, p. 2920-2934, 2011.
Rivero R., Rendon C., Gallegos S., Exergy and Exergoeconomic Analysis of a Crude Oil Combined
Distillation Unit, Energy, Vol. 29, p. 1909-1927, 2004.
Sargent R.W.H., Gaminibandara K., Optimum Design of Plate Distillation Columns, In L.W. C.
Dixon (Ed.), Optimization in Action, New York, Academic Press, p. 267-314, 1976.
Seader J. D., Westerberg A. W., A Combined Heuristic and Evolutionary Strategy for Synthesis of
Simple Separation Sequences, AIChE Journal, Vol. 23, p. 951-954, 1977.
Seader J. D., Henley E. J., Keith Roper D. Separation Process Principles, Chemical and Biochemical
Operations, John Wiley and Sons Inc., New York, USA, 2011.
Seider W. D., Seader J. D., Lewin D. R., Widagdo S., Product and Process Design Principles,3rd
Edition, John Wiley and Sons Inc., Asia, 2010.
Sun J., Wang F., Ma T., Gao H., Liu Y., Cai F., Exergy Analysis of a Parallel Double-effect
Organosilicon Monomer Distillation Scheme, Energy, Vol. 47, p. 498-504, 2012a.
Sun J., Wang F., Ma T., Gao H., Wu P., Liu L., Energy and Exergy Analysis of a Five-column
Methanol Distillation Scheme, Energy, Vol. 45, p. 696-703, 2012b.
Suphanit B., Bischert A., Narataruksa P., Exergy Loss Analysis of Heat Transfer Across the Wall of
the Dividing-wall Distillation Column, Energy, Vol. 32, p. 2121-2134, 2007.
Szargut J., Morris D. R., Steward F. R., Exergy Analysis of Thermal, Chemical and Metallurgical
Processes, Springer, Berlin, Germany, 1988.
Tedder D. W., Rudd D. F., Parametric Studies in Industrial Distillation: Part 1, Design Comparisons,
AIChE Journal, Vol. 24, p. 303-315, 1978.
Westerberg A.W., The Synthesis of Distillation-based Separation Systems, Computer and Chemical
Engineering, Vol. 9, p. 421-429, 1985.