DOI: 10.3303/CET2188034

Paper Received: 18 May 2021; Revised: 4 August 2021; Accepted: 8 October 2021
Please cite this article as: Álvarez V.M., Popescu A.E.P., Ruiz J.B., Curcó D., 2021, Genetic Algorithm for Pressure-Swing Distillation
Optimisation: Ethanol and Ethyl Acetate Mixture, Chemical Engineering Transactions, 88, 205-210 DOI:10.3303/CET2188034

CHEMICAL ENGINEERING TRANSACTIONS

VOL. 88, 2021

A publication of

The Italian Association
of Chemical Engineering
Online at www.cetjournal.it

Guest Editors: Petar S. Varbanov, Yee Van Fan, Jiří J. Klemeš

ISBN 978-88-95608-86-0; ISSN 2283-9216

Genetic Algorithm for Pressure-Swing Distillation
Optimisation: Ethanol and Ethyl Acetate Mixture

Víctor Manso Álvarez*, Alexandra Elena Plesu Popescu, Jordi Bonet Ruiz, David
Curcó

University of Barcelona, Faculty of Chemistry, Department of Chemical Engineering and Analytical Chemistry, c/ Martí i
Franquès 1, 6th floor, 08028 Barcelona, Spain
vmansoal22@alumnes.ub.edu

In the acetic acid esterification, ethanol (EtOH) in excess is used to produce ethyl acetate (EtAc), which is
commonly used as an organic solvent in biochemical and food industries. On the other hand, EtOH is useful
considering the growing production of bioethanol for the fuel market. The resulting mixture of EtAc with
unreacted EtOH forms an azeotrope which is difficult to separate by conventional distillation. Literature data
shows that the azeotropic binary mixture EtOH – EtAc is separated mostly through extractive distillation.
Unfortunately, this procedure has some drawbacks, such as high energy cost and environmental concerns (quite
related to the extracting agent recovery). However, taking advantage of the azeotrope sensitivity on pressure,
the extracting agent use can be avoided. This paper presents an optimal design for the separation of the above-
mentioned mixture, using pressure-swing distillation (PSD) as separation process. In order to achieve a fully
optimised system in terms of energy and capital, the method followed consists in simulating the process with
Aspen Plus® and making use of genetic algorithms (GAs) to optimise the process variables, including, among
others, the pressure of the high-pressure column. This process variable is of great importance, and from our
point of view, this factor has not been properly studied nor discussed in literature so far. The starting population
consists of points that group a set of values for all the design variables. These sets are a mixture of random and
calculated values, obtained by application of heuristics, so that the initial population contains some potentially
good initial individuals. The optimisation code is written in Visual Basic language and the link between Aspen
Plus® and Visual Basic is also programmed so that a continuous connection can assure information flow from
the optimisation program to Aspen Plus® and vice-versa.

1. Introduction

Distillation is defined as the process of separating the components of a liquid mixture by its partial evaporation,
in such a way that a second phase is obtained from the vapor whose composition is different from the liquid in
equilibrium. The equilibrium in both phases is usually assumed, hence, the knowledge of the equilibrium
relations is essential to model distillation systems (García and Barreiro, 1986). More important, the equilibrium
relationships determine the feasibility of the distillation. Distillation includes conventional distillation for the
separation of zeotropic systems and enhanced distillations to separate azeotropic systems. Enhanced
distillation methods include pressure-swing distillation, heterogeneous azeotropic distillation, extractive
distillation, catalytic distillation among others (Wang et al., 2018).
An azeotrope is a mixture that exhibits the same concentration in the vapor and the liquid phase. This prevents
the separation of the pure compounds thorough conventional distillation. To use PSD to separate azeotropic
mixtures the azeotropic composition must be sensitive enough to pressure (Xi et al., 2018). Pressure-
insensitive binary azeotropes can be separated by distillation itself, but it usually requires the introduction of
entrainers. The way in which these entrainers operate is diverse; some of them generate immiscible liquid
phases that allow to break the azeotrope (heterogeneous azeotropic distillation) (Li et al., 2021). Others
generate a new azeotrope that allows the breaking of the original one (homogeneous azeotropic distillation),
and others, “extract” some component from the original mixture, which is separated afterwards from the entrainer
(extractive distillation) (Yuan et al., 2015). All these methods require an extra component, the entrainer, that is

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continuously recycled in a system of two columns. These sequences can be thermally integrated (Knapp and
Doherty, 1992) but operating with an entrainer is likely to involve an increase in operating cost compared to a
separation system that would not require such entrainer.
Pressure-swing distillation prevents the problem of introducing a third component and has gained lots of
attention from researchers in recent years, by comparison with the aforesaid methods (Zhu et al., 2016).
According to a literature research developed by Risco et. al. (2019), column operating pressures are chosen
rather arbitrarily: for a first assessment of a PSD, is usually considered that the azeotropic composition must
vary at least 5 percent, over not more than ten atmospheres between the two pressures (Perry and Green,
1998). Luyben (2021) studied the importance of pressure selection since relative volatilities depends largely on
the pressure.
The aim of the present study is to optimise the separation process of EtOH and EtAc system by means of the
PSD. To do this, the TAC (Total Annualized Cost) function based on Luyben (2012) cost correlations is selected
as the objective function to be minimized. The simulation is carried out with Aspen Plus ® and making use of
GAs to optimise the process variables, including, among others, the pressure of the high-pressure column
(HPC). Yang et al. (2017) optimised the PSD process for the ternary mixture of EtAc-EtOH-Water, not including
as design variables any of the pressures. Wang et al. (2018) applied PSD to three case systems, being one of
them EtOH-EtAc, most of the variables were optimised but pressures were fixed. Liang et al. (2021) compared
extractive distillation and PSD to separate a mixture of water, pyridine and acetonitrile, for the PSD study,
pressures were also predefined. The starting points for the GA are a mixture of random and calculated values,
which are obtained by application of heuristics.

2. Genetic algorithms

Genetic algorithms (GAs) are an optimisation algorithm that imitates the Natural Selection. It is based on the
concept that individuals best adapted to their environments are more likely to survive and reproduce.
GAs have been widely studied by mathematicians, programmers, and engineers due to its versatility and proper
performance when solving nonlinear optimisation problems. GAs are executed iteratively on a set of coded
solutions (chromosomes), called population, with three basic operators: selection, crossover, and mutation (Tao
et al., 2020). To find out the optimum of a problem, GA starts from an initial population, which can be randomly
generated, or, on the other hand, it can be a mixture of random and calculated values (as in the case). In each
generation the objective function determines the suitability of each solution, and depending on these values,
some of them are selected to be “parent” for the mutation and/or the crossover process. The procedure is then
more likely to select the best solutions for the next generations, while eliminating the worst (Pal and Wang,
2017).

Figure 1: Structure of the GA

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The framework of the GA used in this work is made up of three parts:
 Inputs (Figure 1a), where four basic parameters of the GA are defined, i.e., crossover rate, mutation

rate, number of elite individuals (those which go through the next generation) and the population size.
As well as other parameters such as the number of desired decimals (the more precision the longer
the chromosome) and boundary conditions. These values are shown in Table 1.

 Initialization (Figure 1b), where first calculations are made, i.e., the length of the chromosome and
the generation of random initial population. In this part, the fitness evaluation of the initial points is
also done.

 Generation (Figure 1c), this is the iterative step, the offspring is obtained by mutation and crossover
operations, these new points are evaluated, and the new generation is settled. For the stop condition,
it is stated that the objective function must vary at least by 1 % between successive generations to
keep iterating. If the generation is lower than the “minimum generation” value, although the stop
condition is met, the program keeps running. This is done to ensure that there is a minimum number
of evaluations, and it does not stop in the first steps.

Table 1: Parameters for the GA

Parameter Value
Crossover rate 0.80
Mutation rate 0.15
Number of elite individuals 1
Population size 20
Number of decimals (only applicable in continuous variables) 2

3. Materials and methods

The design specifications defined for the problem have been arbitrarily chosen, with the only condition that the
feed contains a high concentration of EtAc (resembling a possible case in an EtAc production plant). Table 2
summarizes this data.

Table 2: Design specifications

Feed
Product 1
(bottoms
column 1)

Product 2
(bottoms
column 2)

Temperature (K) 293 - -
Molar flow rate (kmol/h) 100 90 -
Molar fraction EtOH (XEtOH) 0.100 <0.010 >0.990
Molar fraction EtAc (XEtAc) 0.900 >0.990 <0.010

In addition, it has been assumed that the low-pressure column (LPC) operates at atmospheric pressure, as
working at vacuum pressure leads to complications in the design, as well as an increase in the weight and cost
of the column.
On the other hand, eight design variables have been chosen to be optimised (Table 3), the remainder being
dependent variables, which are calculated trough the simulation software (e.g., the diameter of the columns) or
by means of calculations integrated in the optimisation program (e.g., recirculation molar flow rate).

Table 3: Design variables

Name Type Name Type
Number of stages in column 1 Discrete Stage of feed in column 2 Discrete
Number of stages in column 2 Discrete Pressure of column 1 Continuous
Stage of fresh feed in column 1 Discrete Reflux ratio in column 1 Continuous
Stage of feed recirculating
from column 2 in column 1

Discrete Reflux ratio in column 2 Continuous

With regard to GA, 10 out of 20 initial points have been obtained manually by means of heuristic optimisations
in the simulation software, fixing the pressures and calculating the rest of variables, considering that the optimum
reflux ratio is 1.3 times the minimum. This is done to provide the algorithm some initial points where the optimum
is likely to be, in order to improve its convergence.

207

The simulations were performed using Aspen Plus ® V11 using rigorous models (RadFrac). In the base case
scenario, shown in Figure 2, the fresh feed enters the HPC, obtaining 99 % mol EtAc in bottoms, and a mixture
on its azeotropic point at the pressure of the HPC in heads. On the second column, 99 % mol EtOH is obtained
in bottoms, and a mixture on its azeotropic point at ambient pressure is obtained in heads, which will be
pressurized and recirculated to the HPC.

Figure 2: Flowsheet for the PSD process

Concerning thermodynamics, it has been reported that Aspen provides experimental data for the mixture of the
study at high pressures, for this reason the UNIQUAC - Redlich Kwong model is selected.

4. Results

4.1 Initial pre-set population

Table 4 presents the values of the design variables for the 10 starting calculated points and their TAC. These
points have been obtained (as said in the previous paragraph) applying heuristic rules and will be used along
with 10 randomly obtained points as initial data for the GA, giving a total of 20 points initial population.

Table 4: Calculated starting points for the GA

1 2 3 4 5 6 7 8 9 10
Number of stages in
column 1

38 26 24 23 23 23 24 24 24 24

Number of stages in
column 2

25 26 26 26 26 25 25 25 25 25

Stage of fresh feed in
column 1

31 17 15 14 14 14 14 14 14 14

Stage of feed recirculating
from column 2 in column 1

21 7 6 5 5 5 5 5 5 5

Stage of feed in column 2 16 17 17 17 17 16 16 16 16 16
Pressure of column 1 (bar) 4 6 8 9 10 12 14 16 18 20
Reflux ratio in column 1 3.07 2.38 2.31 2.28 2.31 2.33 2.27 2.35 2.45 2.58
Reflux ratio in column 2 1.91 1.87 1.89 1.90 1.91 1.99 1.90 1.91 1.93 1.94
TAC (k$/y) 860.2 717.4 689.6 681.3 716.9 711.2 692.3 691.9 694.2 699.1

4.2 Results

By using the parameters and specifications listed in Table 1 and Table 2 respectively, a series of generations is
carried out. Figure 3 plots the TAC of the best (elite) individual for each generation. After 15 generations no
noticeable improvement is obtained. The design variables corresponding to the optimum are shown in Table 5.
Noteworthy is that this optimum lies in the maximum pressure that has been achieved during the optimisation
procedure, which is 20 bar.

208

The results were as follows: for the HPC, stage number is 16, reflux ratio is 2.32 and feeding stages are 5 and
14; for the LPC, stage number is 25, reflux ratio is 2.19 and feeding stage is 18. The optimum is found at 20 bar
on the high-pressure column, in contrast with most of the studies, which is usually established at 10 atm.

Figure 3: Evolution of the objective function in each generation

Table 5: Values of design variables for the optimum point

Generation 15
Number of stages in column 1 16
Number of stages in column 2 25
Stage of fresh feed in column 1 14
Stage of feed recirculating from
column 2 in column 1

Stage of feed in column 2 18
Pressure of column 1 (bar) 20
Reflux ratio in column 1 2.32
Reflux ratio in column 2 2.19
TAC (k$/y) 574.2

The simulation results of the major streams are shown in Table 6. Fresh feed (stream 1) is defined as in Table
2 and enters the first column (HPC) at its boiling point, obtaining a distillate (stream 2) corresponding to the
azeotropic composition at 20 bars, and a residue (stream 3) whereby EtAc is collected. Distillate stream is fed
to the second column (LPC), where EtOH is collected in bottoms (stream 5) and a mixture on its azeotropic
composition at 1 bar in top of the column (stream 4), which is pressurized and recirculated to the first column
(stream 6).

Table 6: Simulation results of the pressure-swing distillation for EtOH – EtAc

Item / Stream 1 2 3 4 5 6
Temperature (ºC) 200.4 183.7 206.9 71.4 77.6 74.2
Pressure (bar) 20 20 20 1 1 20
Molar flow rate (kmol/h) 100 29.9 90.8 20.8 9.2 20.8
Molar fractions

EtOH 0.10 0.62 0.01 0.45 0.99 0.45
EtAc 0.90 0.38 0.99 0.55 0.01 0.55

500

520

540

560

580

600

620

640

660

680

700

0 2 4 6 8 10 12 14 16

T
A

C
(

k
$

/y
)

Generation

209

5. Conclusions

Genetic algorithms appear to be a powerful tool to optimise complex distillation processes. Linking Visual Basic
and Aspen Plus ® provides a way to separately carry out the optimisation procedure and the simulation process,
improving the task of finding the optimal solution. Giving some initial good estimations to the initial population
increases the convergence pace, for this reason an initial set of simulations based on well stablished heuristics
is recommended. In reference to the specific studied case, it has been seen that the best solution lies on the
one that implies a maximum pressure in the HPC column, which is 20 bar. The HPC has 16 stages and a reflux
ratio of 2.32. The LPC has 25 stages and a reflux ratio of 2.19. Final TAC value for 100 kmol/h of crude feed is
574.2 k€/year.

Nomenclature

EtAc – Ethyl acetate
EtOH – Ethanol
GA – Genetic algorithm
HPC – High-pressure column
LPC – Low-pressure column
PSD – Pressure-Swing distillation
TAC – Total annualized cost

Acknowledgements

Author Alexandra Elena Plesu Popescu is a Serra Húnter fellow.

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