OPTIMUM SEQUENCE OF NONSHARP DISTILLATION COLUMNS FOR
TERNARY SEPARATION
Javad Ivakpour, Norollah Kasiri*
Computer Aided Process Engineering Lab, Chemical Engineering Department,
Iran University of Science & Technology
*Email: [email protected]
Abstract: The optimization of distillation column sequences for nonsharp separation of
ternary mixture is studied. The four possible basic sequences are compared based on the
cost functions. Each sequence contains one or two distillation columns and an adequate
number of splitters and mixers for considering possible bypass streams. The column
specifications and bypass stream flow rates are optimized by genetic algorithm based on
rigorous simulation results. In the proposed method each component can be distributed in
each column and no constraint is applied for component recovery fraction.
Implementation of the proposed method for three examples shows that nonsharp
separators with distributed components and complex column arrangements can frequently
reduce the separation costs up to 77% compared to the optimum sequence with sharp
separators.
Keywords: Distillation, Sequencing, Optimization, Nonsharp Separation, Bypass
1. INTRODUCTION
For separation of multi-component mixtures, different sequences of distillation columns can be used with different
separation costs. This fact provides a saving possibility in separation cost by selecting the optimum sequence
(Doherty and Malone, 2001). The amount of possible saving is a function of many factors the most important ones
being the required separation specifications, components physical properties and the structure types of sequences.
Separation of a mixture using the simple sharp-split columns is the most frequently used situation in distillation
column sequencing problems. Direct and indirect sequences are two well known examples of this type. In this kind
of sequences, number of possible states is a function of the number of products (King, 1980). There are 3, 5 and 14
possible states for separation of 2, 3 and 4 products, respectively. The differences between the costs of these
sequences are significant and can be up to 70% for a five product separation (Doherty and Malone, 2001).
Implementation of complex columns with more than one feed and/or side-stream(s) products can result in new
sequences and consequently further cost reduction possibility. Prefractionator structure is a commonly used
sequence of this category. Sequences in which each column has its own condenser and reboiler are known as basic
states (Agrawal, 2003). More complex configurations such as thermally coupled, heat integrated (Caballero and
Grossmann, 2006) and dividing wall columns (Schultz et al., 2002) can be generated from the basic state sequences
(Agrawal, 2003).
When the products purity are not required to be very high, there is a possibility of bypassing some parts of streams
and as a result the separation costs can be decreased significantly (Heckl et al., 2007; Kovacs et al.; 2000, Floudas,
1987; Wehe and Westerberg, 1987). Also, it is possible to turn to non-sharp separation with lower cost. Hence, there
is a trade-off between the amount to be bypassed and the degree of non-sharp separation. Bampoulos et al (1988)
show that employing non-sharp separation on an example problem of four components can result in annual cost
savings of 42% compared to the best sequence with sharp separation. This result was obtained from sequences
consisting of sharp distillation columns and bypass streams only. Also, Aggarwal and Floudas (1990) show that
using non-sharp separations can result in savings of 10-70% as compared to sharp separation based on simple nonsharp distillation columns and mixing and bypassing possibilities.
In nonsharp separation problems, it is also possible to perform the required separation using less than N-1 columns
(Kim and Wankat, 2004). Although the less number of columns is used in these sequences, but the separation cost
may be higher than the sequences with more columns because of the impurity in the side-streams locations.
In the previous works, the approximated methods have been used for design and optimization purposes. The most
commonly use approximated methods are Fenske-Underwood-Gilliland methods (Kister, 1992) for design of simple
distillation columns. Malone extended the approximated method to complex columns (1987) and the proposed
method has been used in a number of works. The approximated methods are based on two main assumptions:
constant relative volatility and constant molar overflow. Therefore, their accuracy is a function of the assumptions
validity. Furthermore, as a rule of thumb the optimum reflux is considered to be 1.1 to 1.2 times of the minimum
required value from the Underwood equation. All the assumptions used in the approximated method can result in
low accuracy and possible wrong selection of optimum sequences.
In the current work, the separation of a ternary feed mixture through four possible basic state sequences of Figure 1
is studied. The possibility of bypass streams, nonsharp separation, complex columns and separation with one column
are considered in the sequences. Design of each column is performed based on the entire sequence purpose.
Therefore, it is not required to specify the columns separation duty because it is optimized in the optimization step.
The optimization is done by Genetic Algorithm (Goldberg, 1989) based on the rigorous simulation results to
optimize the separation cost while the required separation is obtained.
2. SEQUENCE DESIGN & OPTIMIZATION
1.1. Sequence Structures
There are two methods for selection of optimum distillation column sequence; optimization of superstructure and
optimize each possible structure individually. In the first method the superstructure is proposed so that all possible
sequence structures can be derived from it by setting one or more stream(s) flow rate to zero. In the second method
an algorithm is proposed to generate all possible structures systematically and the optimum one can be determined
by optimization of the sequence structure. Therefore, the optimum cost of each structure must be evaluated initially
before the best structure is determined comparing the optimum values. However, in the former method the number
of local optima are higher while in the second approach the two step optimization required results in a larger
execution time.
In this work, because there are only four possible sequence structures all of them are optimized separately. The four
possible states are shown in Figure 1. As can be seen in this figure, the structure of Figure (1.a) can be considered as
a superstructure for all sequences because all other sequences are a special case of it. Figure 1.a represents a
prefractionator structure. Direct and indirect sequences have been shown in Figure 1.b and 1.c respectively. Figure
1.d illustrates a sequence with single column only that can be used in nonsharp separations.
1.2. Design & Optimization
The investigated problem can be stated as follow:
Given the feed specifications and the desired products flow rates and compositions, find the optimum structure to
perform the required separation with the minimum Total Annual Cost (TAC) using the following assumptions:
a. Consider nonsharp separation in each column.
b. Implement one or two column(s) in each structure to separate feed stream into three final products.
c. Consider desired products as the mixtures of other products.
d. Consider the bypass streams.
Therefore, the objective function to be minimized is TAC. Genetic Algorithm is used for optimization of column
specifications and stream flow rates. Deviation from the desired products specifications is considered as the penalty
function relative to the deviation value added to objective function. The penalty function of equation 1 is used in the
current work as follow:
P
A
in which F is the main feed flow rate,
( x ji ) 2
(F
j
Pj )
i
1
Pj is deviation from the required flow rate of desired product j,
x ji is
deviation from the required composition of component i in the desired product j and A is a constant value that
determine the importance of constraints. Very high value of A causes any deviation to be considered as an
impossible condition. Conversely, very low value of A cause disregarding of constraints. In this work it is found
that the mean value of TACs in the first iteration of Genetic Algorithm is a good estimate for A .
Figure 1: four possible basic state structures for ternary separation
The TAC and deviation values must be determined from the simulation results. Distillation column simulation is
performed based on the inside-out algorithm (Seader and Henley, 1998). Damping factor procedure proposed by
Ivakpour and Kasiri is implemented to increase the speed and convergence properties (2008). Each column is
simulated having determined column pressure, number of trays, feeds tray location, side-stream(s) tray locations,
reflux ratio and the products flow rate ratios from GA optimization algorithm. Furthermore, the splitters products
flow rate ratios are determined by GA. The products flow rate ratios are determined independently and normalized
later. Therefore, the summation of them over each column or splitter remains unity and the ratios can change
unboundedly.
The variables values are determined randomly at the first iteration of GA for each individual. Then the equipments
are simulated and columns are designed based on the simulation results and the costs are evaluated. Evaluations are
performed based on the TAC values from Guthrie’s cost correlations (Douglas, 1988). Penalty values will be added
to the objective function if there is any deviation. Having all individuals evaluated, the optimum ones can be
selected for generating new and better individuals by the combination and changing of the selected individuals’
variables. The procedure is iterated until the optimum objective value in the latest iteration loop improves relative to
the specified number of previous iteration loops (in this work relative to the 100 iteration loops before the current
one).
3. RESULTS
A previously published nonsharp example has been examined with the proposed method with three different
conditions. The main feed and desired products specifications have been shown in Table 1. This example previously
was studied in sequences with sharp separators and bypass streams possibility for separation of hypothetical ternary
component set (Wehe and Westerberg, 1987). In this work, the effects of component properties and nonsharp
separators on the optimum structure have been studied for the separation given at Table 1. Therefore, this separation
is run with two different sets of components; set 1 consists of n-Pentane, n-Hexane and n-Heptane and set 2 consists
of i-Butane, n-Butane and n-Pentane. The component relative volatilities are obviously higher in set 1.
Table 1: Main feed stream and desired products component flow rates (kmol/hr)
(These specifications are same for all studied examples)
Component
Feed
Desired Product 1
Desired Product 2
A
100
70
30
B
100
50
50
C
100
70
30
Total
300
190
110
Example 1 is considered as the separation with nonsharp separators for component set 1. The optimization results
have been shown in Table 2. As can be seen in this table the prefractionator structure is the optimum structure for
this separation. Also, single column sequence separates the feed mixture with lower cost than direct and indirect
sequences. Therefore, in this nonsharp example the structures with complex columns have lower cost than structures
with only simple column. In this example, prefractionator sequence can cause in 36% saving comparing to the direct
sequence.
Table 2: Optimized TACs for studied examples
TAC (105 $/yr)
Component Set
Nonsharp Separators
Sequence Structure:
Prefractionator
Direct
Indirect
Single Column
Time* (hr)
*All of the optimizations were
Example 1
1
Yes
Example 2
1
No
Example 3
2
Yes
0.983
1.555
1.835
1.458
3.1
5.712
4.287
5.410
--2.8
2.520
2.173
3.401
2.679
3.4
performed in Microsoft Visual C++.Net platform with parallel
processing possibility on an 8*2.33 GHz CPU (Intel Xeon) with 3 GB of RAM.
Furthermore, the streams flow rates and compositions are shown in Figure 2 for the optimum sequence
(prefractionator structure). Closer look at this table reveals that in the optimum condition nonsharp separation is
performed in both columns. Also, it can be seen that a part of main feed stream is injected to the second column
directly. A part of each middle product is bypassed to the desired product too. Hence, combination of nonsharp
separation and bypass streams can be seen in the optimum condition.
Table 3: Stream flow rates at optimum condition of sequence structure 1.a
From
To
Feed
S1
S1 S1P1 Feed S1P2 S2
S2
S2 Feed S1P1 S1P2 S2F1 S2F3 S1P2 S2F2 S2F3
S1 S1P1 S1P2 S2
S2
S2 S2F1 S2F2 S2F3 D1
D1
D1
D1
D1
D2
D2
D2
Flow
246.1
12.8
233.4
11.1
51.8 149.1
38.7
76.4
96.9
2.1
1.6
57.2
38.7
90.4
27.0
76.4
6.5
190.0 110.0
X1
X2
X3
0.33
0.33
0.33
0.82
0.17
0.01
0.31
0.34
0.35
0.82
0.17
0.01
0.33
0.33
0.33
0.95
0.05
0.00
0.29
0.49
0.22
0.14
0.32
0.54
0.33
0.33
0.33
0.82
0.17
0.01
0.31
0.34
0.35
0.95
0.05
0.00
0.14
0.32
0.54
0.31
0.34
0.35
0.29
0.49
0.22
0.14
0.32
0.54
0.36
0.27
0.37
0.31
0.34
0.35
D1
-
D2
-
0.28
0.44
0.27
Repetition of the optimization procedure for the same structure frequently results in optimum values which are
slightly different (less than 5%). Despite the slight difference between the final optimum values of different
repetition, the optimum stream flow rates and columns operating conditions may differ significantly. This fact
reveals that there are many local optima with close objective function values in the search space. However, the
difference between two successive optimum values of the same sequence structure is much smaller than the
difference between optimum values of two different structures and therefore the sorted ordering of sequences remain
constant. It must be noted that this small difference is negligible compared to the accuracy of simulation results and
cost function correlations.
It can be interesting to perform the separation with sharp separators and bypass streams. Sharp separator is
considered as a separator with the key component recovery larger than 99%. Example 2 of Table 2 shows the
optimization results at this condition. As can be seen in this table the TACs increase significantly for all sequences
comparing to the same sequences with nonsharp separators. Comparison of Example 1 with Example 2 from Table 2
shows that nonsharp separation can decrease the separation cost up to 77% compared to the best sequence with
sharp separators for this ternary separation case study. Furthermore, the sorted ordering of sequences can change.
Hence, using sharp separators for nonsharp separation can result in wrong selection of optimum sequence and
significant higher separation cost.
Optimization results of Table 1 with the component set 2 are shown in Example 3 of Table 2. Results show that the
optimum structure is the direct sequence in this example. But differences between direct structure with
prefractionator and single column structure are negligible. This new order is proved by the well known heuristic rule
that the more difficult separation must be left to the end. Therefore, the optimum sequence structure can be changed
with the component properties.
4. CONCLUSION
Optimization of nonsharp distillation column sequencing has been examined in this article. Four possible basic state
structures with bypass streams and nonsharp separator possibility have been optimized with three examples. The
optimization has been performed based on the rigorous simulation results. The effects of using nonsharp separators
and component physical properties on the optimum structure and TACs have been studied separately. Results show
that using nonsharp separators can result in significant saving in costs. Also it was shown that the different
component set can change the optimum structure.
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