Modeling of Epoxidation Process by the Means of Artificial
Neural Network
Taras Chaikivskyi1, Bohdan Sus2, Sergiy Zagorodnyuk2 and Oleksandr Bauzha,2
1
    Lviv Polytechnic National University, Bandera Str, 12, Lviv, 79013, Ukraine
2
    Taras Shevchenko National University of Kyiv, Kyiv 01033, Ukraine


                 Abstract
                 An artificial neural network based on experimental data from the process of epoxidation of
                 soybean oil with epoxidizing system: hydrogen peroxide / acetic anhydride / catalyst was
                 created. This allows you to select the optimal parameters, control the epoxidation process at
                 the stage of synthesis and improve the technology of epoxidized products. A method for
                 calculating the results of epoxidation of mixtures of unsaturated compounds has been
                 developed. It allows to control the epoxidation process at the stage of synthesis and to improve
                 the technology of obtaining epoxidized products. The obtained optimal conditions of the
                 epoxidation process are adequate for other vegetable oils.

                 Keywords 1
                 Artificial neural networks, Model, Soybean Oil, Catalyst, Epoxidation

1. Introduction
    The current state of computer technology and the level of information technology involves solving
a range of practical issues, including the procedure of deep machine learning [1]. Computational
problems are successfully solved by the means of artificial neural networks belonging to different areas.
In particular, by applying a multilayer differential neural network to the analysis of
electroencephalograms of a person expressing a phrase, it was possible to build a human speech
synthesizer [2] which can predict and define those words and fixed phrases, which a person has
previously expressed, but during the operation of the synthesis can be not remembered. In medicine,
artificial neural networks are used to analyze X-rays, which can determine the service life and degree
of wear of artificial implants and prostheses installed in the patient's body [3]. In chemistry, artificial
neural networks are implemented to predict the result of a chemical reaction under different sets of
experiment conditions and the concentration of different catalysts [4, 5]. Artificial neural networks in
robotics are used to calculate the trajectories of automated mechanisms and manipulators [6] as well as
for the rational consumption of energy and resources. In natural sciences, which include mathematics,
physics, oscillations, and waves, the mathematical physics of artificial neural networks find the solution
of classical fundamental equations [7], which describe real multidimensional systems for which such
numerical solutions were not available [8].
    In physics, artificial neural networks are used for mathematical description of the phenomenon of
energy conversion in the form of electromagnetic radiation, taking into account the processes of
absorption, secondary radiation, and scattering [9], processing information from sensors for substance
identification [10]. Artificial neural networks are especially widely used in physical problems of
electromagnetic wave propagation [11] and ultrasound [12] in bulk solid media, ie in optics,
astrophysics, atmospheric science and remote sensory technologies.

COLINS-2022: 6th International Conference on Computational Linguistics and Intelligent Systems, May 12–13, 2022, Gliwice, Poland
EMAIL: taras.v.chaikivskyi@lpnu.ua (T. Chaikivskyi); bnsuse@gmail.com (B. Sus); szagorodniuk@gmail.com (S. Zagorodnyuk);
asb@univ.kiev.ua (O. Bauzha)
ORCID: 0000-0002-1166-8749 (T. Chaikivskyi); 0000-0002-2566-5530 (B. Sus); 0000-0003-3415-7746 (S. Zagorodnyuk);
0000-0002-4920-0631 (O. Bauzha)
              ©️ 2022 Copyright for this paper by its authors.
              Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
              CEUR Workshop Proceedings (CEUR-WS.org)
    The main principle of green chemistry is the use of renewable, environmentally friendly raw
materials, which will further biodegrade and reduce the toxicity during the production of polymers. [13]
    Soybean oil polymerization is important to produce polymers for printing inks. Epoxidized oils are
widely used, especially to improve the performance of rubbers, as components for the production of
light-sensitive films, packaging materials for baby food, and in the production of medical materials
[14]. Studies on the synthesis of solid polymeric materials based on soybean oil with mechanical
properties. Such polymers can be used as structural materials. Epoxides are cyclic esters, metabolites
that are often formed by cytochromes that act on aromatic or double bonds. A specific site on a molecule
that experiences epoxidation is its site (SOE). Artificial intelligence technologies can significantly
improve the identification of SOE molecules and select the optimal pairs of parameters to control the
epoxidation process at the stage of product synthesis. Artificial neural networks, which are technical
software implementations of the biological neural structure of the human brain, allow such training.
Networks are also called connection systems because the principal part of artificial neural networks is
a structure of connections that allow one neuron to form a route of signal propagation to other neurons
and, conversely, to receive from them the same signals.
    The increase in the use of epoxidized oils is directly related to the growth of production of polyvinyl
chloride PVC and polymers based on it, as epoxidized oils are one of the best stabilizers-plasticizers of
such polymers. Epoxidized oils have several advantages over other types of stabilizers, so the
introduction of epoxidized stabilizers into the polymer significantly increases its thermal stability. It
also prevents the decomposition of the polymer under the action of ionizing radiation. Epoxidized oils
can perform the functions of hardener (in compositions with different oligomers) and stabilizer (in
compositions with PVC). The use of epoxidized oils in the paint industry is constantly increasing - they
are part of paint products based on epoxy, essential cellulose oligomers and PVC, as well as plasticizers
of organically dispersed coatings [15, 16].
    Organic peracids are used for liquid-phase epoxidation of unsaturated organic substances [17, 18].

2. Experimental
    Research [19] [suggested use of epoxidizing system hydrogen peroxide (H2O2)/ formic acid /
catalyst. In this system, the epoxidizing agent is also an organic peracid, which is formed in situ by the
interaction of hydrogen peroxide with organic acid in the presence of a catalyst (Figure 1). Organic acid
circulates in the system [20] replaced formic acid with acetic acid, which is more affordable and
cheaper.




Figure 1: Chemical scheme of liquid-phase epoxidation of vegetable oil by epoxidizing system:
hydrogen peroxide / organic acid / catalyst

  We have suggested using its anhydride instead of organic acid, which will reduce the amount of
water in the reaction mixture and accelerate the reaction of the formation of peracetic acid.
    Therefore, this work aims to improve the technology of epoxidized oils; specify optimal conditions
for economically feasible production of epoxidized oils, the quality of which meets the standards (Table
1); making changes in the technology of production of this product.

Table 1
Quality indicators of epoxidized oils
                                                                      Standard for brands (technical
                      Physico-chemical indicator                              conditions *)
                                                                         ST         SU         S
      Epoxy number,% (oxirane oxygen content), not less than            6.5        6.4        6.0
                Iodine number, g I2/100g, not more than                 1.5        2.0        8.0
   * As stabilizers and plasticizers for PVC-based polymers

   The practical value of the research is the use of a neural network process model that allows quality
control of epoxidized oil during the synthesis stage. epoxidation process on: initial concentration of
acetic anhydride, hydrogen peroxide, catalyst (ion exchange resin KU-2x8); process conditions for the
optimal concentration calculation of epoxy mixture reagents, process duration, and temperature.
   It has been experimentally established that the dependence of the epoxy number of epoxidized
soybean oil at different concentrations of acetic anhydride, hydrogen peroxide, the amount of catalyst,
and the duration of the process is complex. As the temperature and catalyst concentration increase, the
reaction rate increases, but at extremely high temperatures (> 348 K) and catalyst concentration (>15g
per 100 cm3) the achieved epoxy number may decrease due to secondary epoxy opening reactions.
   Therefore, to find the optimal conditions for the process, it is reasonable to develop a mathematical
model and calculate the optimal conditions for the process using special methods.
   To create a model, the following factors and limitations are accepted:
   • x1 - concentration of acetic anhydride, wt.% 2<x1<9
   • x2 - concentration of hydrogen peroxide 46%, wt.% 25<x2<40
   • x3 - concentration of catalyst, wt.%, x3<15
   • x4 - temperature, K, 333 <x4<353
   • x5 - process duration, min, x5<360

3. Methods
    A sample of data was created to study the neural network from experimental results. Neural network
inputs characterize the experimental conditions. Outputs characterize the results (concentrations of the
obtained substances).
    Input parameters:
    1. Acetic anhydride (AA) concentration (normalized)
    2. Hydrogen peroxide (H2O2) concentration (normalized)
    3. Catalyst (KU-2×8) concentration (normalized)
    4. Normalized temperature
    5. Normalized reaction time
    6. Initial value of Epoxy number (normalized)
    7. Initial value of Iodine number (normalized)
    It is assumed that the initial values of the Epoxy number and Iodine number affect the process of the
experiment. Reaction time (sampling of experimental data did not exceed 400 minutes with the
rationing. The temperature range of reactions was 423-443 K.
    Initial parameters:
    1. Final value of Epoxy number (normalized)
    2. Final value of Iodine number (normalized)
Figure 2: Type of neural network.

    Figure 2 shows a five-layer neural network, which was studied based on experimental data obtained
during the epoxidation of soybean oil used by the neural network are taken 7. The values of the input
parameters are normalized to 1. The output layer of the neural network has 2 neurons. This network has
three hidden layers of 20 neurons each.
    The neural network is trained based on the training mechanism. To determine the minimum of the
error function, it is necessary to perform an algorithm for the inverse propagation of errors using the
stochastic gradient descent model.
    In principle, the model is over fitted. It was possible to limit the number of hidden layers with fewer
neurons. The learning process of the network is fast and the training ends in about 800 epochs, because
a limited sample of experimental data was used..

4. Results and discussion
    As can be seen from Figure 3, which was obtained after training the neural network, increasing the
concentration of hydrogen peroxide in the mixture leads to a rapid increase in Epoxy number during
the first 100 minutes of reaction. At low concentrations of hydrogen peroxide in the mixture, in the first
60 minutes the Epoxy number increases rapidly to values of 3-4, and further growth is slow. The data
obtained during the experiment is limited by the number and range of argument values. However, as a
result of learning, the neural network increases the range of arguments and interpolates the resulting
values into a more detailed graph. New data will be added to the database on which the neural network
is trained, and will make it possible to clarify this relationship.




Figure 3: Dependence of Epoxy number on hydrogen peroxide and time of soybean oil epoxidation
reaction. The calculations were performed by the interaction of a solution of soybean oil in toluene
with the epoxidizing system: H2O2 / AA / catalyst. Concentration AA = 5.72 wt.%, catalyst concentration
5 wt.%, reaction temperature T = 343 K.
Figure 4: Comparison of the dependences Epoxy number on the concentration of hydrogen peroxide
and the time of the epoxidation reaction of soybean oil. Experimental data -red lines and predicted by
the neural network -blue lines. The calculations were performed by the interaction of a solution of
soybean oil in toluene with the epoxidizing system: H2O2/ AA / catalyst. Concentration AA = 5.72 wt.%,
Catalyst concentration 5 wt.%, reaction temperature T = 343 K. a - concentrations of H2O2 in a mixture
of 29 wt.%, b - 33.1 wt.%, c - 38.59 wt.%.

    Figure 4 shows a comparison of experimental data and data (large range) obtained after training the
neural network. As a result of training, the neural network processes the entered data quite accurately
to predict the result of the experiment beyond the experimental data.
    The convexity of the dependence, which can be seen from Figure 4 a, at low reaction times, is
because the network was studied on the intermediate results of the experiment. That is, the total input
data were considered.




Figure 5: Dependence of Iodine number on hydrogen peroxide and time of soybean oil epoxidation
reaction. The calculations were performed by the interaction of a solution of soybean oil in toluene
with the epoxidizing system H2O2/ AA / catalyst Concentration AA = 5.72 wt.%, Catalyst concentration
5 wt.%, reaction temperature T = 343 K.
    As can be seen from Figure 5, which was obtained after training in the neural network, the increase
of the concentration of hydrogen peroxide in the mixture leads to a sharp decrease in ionic number. At
low concentrations of hydrogen peroxide in the mixture, the Iodide number has a much slower
dependence of the decrease.
    As with the Figure 3, the data obtained during the experiment are limited by the number and range
of argument values. However, as a result of learning, the neural network increases the range of
arguments and interpolates the resulting values into a more detailed graph.




Figure 6: Comparison of the dependences of the iodine number on the concentration of hydrogen
peroxide and the time of the epoxidation reaction of soybean oil. Calculations were performed by the
interaction of a solution of soybean oil in toluene with epoxidizing system H2O2/AA/catalyst
Concentration AA = 5.72 wt.%, Catalyst concentration 5 wt.%, Reaction temperature T = 343 K. a -
concentrations H2O2 in the reaction mixture of 29 wt.%, b - 33.1 wt.%, c - 38.59 wt.%

   Figure 6 shows a comparison of experimental data and data (in a larger range) obtained after training
the neural network. As a result of training, the neural network accurately reproduces experimental data
and predicts the outcome of the experiment beyond this data.
   As shown in Figure 6, the convex dependence, a, at low reaction times, is provided by the neural
network. As can be seen from the figure, the first experimental point was taken after 120 minutes, and
the real dependence Iodine number on time is unknown. Based on the whole array of experimental data,
the neural network assumes that the iodine number must vary according to this dependence.
   As can be seen from Figure 7, which was obtained after neural network training, increasing the
concentration of acetic anhydride in the mixture leads to a rapid increase in the dependence of the Epoxy
number in the first 60 minutes of the reaction. At low concentrations of acetic anhydride mixture a
cascading increase in epoxy numbers is observed.
Figure 7: Dependence of Epoxy number on acetic anhydride concentration and time of soybean oil
epoxidation reaction. Calculations were performed by the interaction of a solution of soybean oil in
toluene with epoxidizing system H2O2/AA/catalyst. Concentration H2O2 = 38.59 wt.%, Catalyst
concentration 5 wt.%, Reaction temperature T = 343 K.




Figure 8: Comparison of the dependences Epoxy number on the concentration of acetic anhydride
and the time of the epoxidation reaction of soybean oil. The calculations were performed by the
interaction of a solution of soybean oil in toluene with the epoxidizing system H2O2/AA/catalyst.
Concentration H2O2 = 38.59 wt.%, Catalyst concentration 5 wt.%, Reaction temperature T = 343 K. a -
concentrations of AA in the mixture of 2.86 wt.%, b - 5.72 wt.%, c - 7.79 wt.%.

   As can be seen from Figure 8, the neural network repeats the experimental points well and expands
the range of points that predict the result of the reaction.
Figure 9: Dependence of Iodine number on acetic anhydride concentration and time of soybean oil
epoxidation reaction. Calculations were performed by the interaction of a solution of soybean oil in
toluene with the epoxidizing system H2O2/ AA / catalyst Concentration H2O2 = 38.59 wt.%, Catalyst
concentration 5 wt.%, Reaction temperature T = 343 K.

    As can be seen from Figure 9, which was obtained after training in the neural network, the increase
in the concentration of hydrogen peroxide in the mixture leads to a sharp decline in iodine value. At
low concentrations of hydrogen peroxide in the mixture, the ionic number does not change
monotonically, the dependence has a maximum.




Figure 10: Comparison of the dependences of the iodine number on the concentration of hydrogen
peroxide and the time of the epoxidation reaction of soybean oil. Calculations were performed by the
interaction of a solution of soybean oil in toluene with the epoxidizing system H2O2/AA/catalyst.
Concentration H2O2 = 38.59 wt.%, Catalyst concentration 5 wt.%, Reaction temperature T = 343 K. a -
concentrations of AA in the mixture of 2.86 wt.%, b - 5.72 wt.%, c - 7.79 wt.%.

   As can be seen from the data presented in Figure 10, the neural network repeats the experimental
points and expands the range of points that assume the consumption of unsaturated bonds (reduction of
iodine value).
Figure 11: Dependence of Epoxy number on acetic anhydride concentration and hydrogen peroxide
during soybean oil epoxidation reaction. Calculations were performed by reacting a solution of
soybean oil in toluene with epoxidizing system H2O2/ AA / catalyst. Catalyst concentration 5 wt.%
Mixture, reaction temperature T = 343 K. Reaction time 60 min.

   The neural network, after training, operates with initial functions from many variables (in our case
from 7), and gives the opportunity to see the projections of the calculated (learned) functions on the
selected axes of parameters that interest us. For example, in Figure 11 shows the dependence of the
Epoxy number after the epoxidation reaction of soybean oil on the concentration of acetic anhydride
and hydrogen peroxide. The reaction time and catalyst concentration are taken as constants.
   As can be seen from the figure, the simultaneous increase in the concentration of acetic anhydride
and the concentration of hydrogen peroxide leads to an increase in the reaction rate. However, the local
minimum of the Epoxy number is not at the point of minimum concentrations of acetic anhydride and
hydrogen peroxide.




Figure 12: Dependence of Iodine number on acetic anhydride concentration and hydrogen peroxide
during soybean oil epoxidation reaction. Calculations were performed by reacting a solution of
soybean oil in toluene with epoxidizing system H2O2/ AA / catalyst. Catalyst concentration 5 wt.%
Mixture, reaction temperature T = 343 K. Reaction time 60 minutes.

   In Figure 12 we have similar dependences as in Figure 11, for the Iodine number. As can be seen
from the figure, the maximum concentration (in the selected range) of the concentration of acetic
anhydride and hydrogen peroxide leads to the formation of the minimum value of the iodine value.
However, the slowest reaction does not occur at minimum concentrations of acetic anhydride and
hydrogen peroxide.

5. Conclusions
    In this paper, we presented a method for finding parameters of the epoxidation process of soybean
oil (in this case, the dependences on the concentration of acetic anhydride and hydrogen peroxide, the
amount of catalyst, and reaction time). The use of the neural network demonstrated the possibility of
quantitative prediction of the epoxidation result (Epoxy and Iodine numbers) with a small sample of
experimental data. The proposed approach makes it possible to obtain additional information about the
course of the epoxidation reaction of soybean oil.
    The optimal conditions for the process of epoxidation of oil by epoxidizing system acetic anhydride:
hydrogen peroxide: catalyst KU-2x8, duration, temperature.
    Although experimental studies were performed on soybean oil, the dependences obtained as a result
of the work were used for other vegetable oils (castor, rapeseed, flaxseed, sunflower). Experiments
conducted in these optimal conditions showed good results, especially for linseed (EN = 8.49%) and
sunflower oils (EN = 6.39%), which confirms the adequacy of the results of the neural network.

6. Acknowledgments
   This work has been supported by the Ministry of Education and Science of Ukraine: Grant of the
Ministry of Education and Science of Ukraine for perspective development of a scientific direction
"Mathematical sciences and natural sciences" at Taras Shevchenko National University of Kyiv.
   PhD Orest Pyrig for significant contribution to chemical research, OJSC "Gallak" (Borislav) for the
provided scientific laboratory, equipment and reagents.

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