Optimizing the Process of Soybean Oil Epoxidation by the
means of Artificial Intelligence
Oleksandr Bauzha 1, Taras Chaikivskyi 2, Valentyna Maliarenko 1, Bohdan Sus 1, Sergiy
Zagorodnyuk 1
1
    Taras Shevchenko National University of Kyiv, Kyiv 01033, Ukraine
2
    Lviv Polytechnic National University, Bandera Str, 12, Lviv, 79013, Ukraine

                  Abstract
                  The study of the process of soybean oil epoxidation was conducted in solution of hydrogen
                  peroxide H2O2 and acetic anhydride (CH3CO)2O in the presence of the KU-2×8 catalyst. As a
                  result of the study, experimental data were obtained, which were used for training an artificial
                  neural network. With the help of a trained neural network, it was possible not only to control
                  the epoxidation process at the synthesis stage, but also select the most favorable parameters
                  and conditions of the experiment, and improve the technology for obtaining chemical
                  products.
                  A new mechanism for calculating the results of epoxidation of mixtures of unsaturated
                  compounds has been developed. It was demonstrated that by the means of this mechanism it
                  is possible to control the epoxidation process at the stage of synthesis of compounds and in
                  this way to improve the technology of obtaining final products of this reaction.

                  Keywords 1
                  Neural network, Epoxidation, Optimization, Soybean oil, Peroxide

1. Introduction
    The process of deep machine learning used to solve a system of practical problems. This approach
is characterized by a high level of information technology, which is determined by the development of
modern computer technology [1].
    An artificial neural network (ANN) has been used to solve practical problems in various fields,
particularly in medicine. The human speech synthesizer was created based on electroencephalograms
of patients, on which their utterances were recorded. The materials were analyzed by the multilayer
differential neural network method. With the help of a human speech synthesizer, it is possible to
predict and express words and fixed expressions that the patient used, but cannot remember during the
operation of the synthesizer [2]. An artificial neural network was used to analyze X-ray images, which
were used to determine the service life and degree of use of artificial implants and prostheses installed
in the patient's body. [3].
    In chemistry, an artificial neural network was used to predict the result of a chemical reaction
under different conditions and concentrations of catalysts [4,5].
    In robotics, ANN is used to calculate the trajectories of automated mechanisms and manipulators,
rational consumption of energy carriers and resources. [6].
    In the natural sciences, which include mathematics, physics, and mathematical physics, the use of
ANN allowed solving classical fundamental equations [7]. They describe real multidimensional
systems for which numerical solutions were previously unavailable [8].


MoMLeT+DS 2022: 4th International Workshop on Modern Machine Learning Technologies and Data Science, November, 25-26, 2022,
Leiden-Lviv, The Netherlands-Ukraine
EMAIL: asb@univ.kiev.ua (O. Bauzha); taras.v.chaikivskyi@lpnu.ua (T. Chaikivskyi); vmalyarenko12@gmail.com (V. Maliarenko);
bnsuse@gmail.com (B. Sus); szagorodniuk@gmail.com (S. Zagorodnyuk)
ORCID: 0000-0002-4920-0631 (O. Bauzha); 0000-0002-1166-8749 (T. Chaikivskyi); 0000-0003-4585-3114 (V. Maliarenko); 0000-0002-
2566-5530 (B. Sus); 0000-0003-3415-7746 (S. Zagorodnyuk)
             ©️ 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)
   In physics, with the help of neural networks, a mathematical description of the energy transfer
phenomenon in the form of electromagnetic radiation became possible. It includes several
simultaneous processes: absorption, secondary radiation and scattering [9], as well as the processing
of information received from sensors as a result of the identification of substances [10] to solve
physical problems of propagation of electromagnetic waves and ultrasound, Neural networks are also
used [11]. Neural networks are widely implemented in atmospheric science, remote sensing, and
optics[12].
   Research is being conducted on the synthesis of solid polymer materials based on soybean oil with
mechanical properties that can be used as construction materials.
   Green chemistry is entrenched the principle of sustainable development, based on the use of
renewable and environmentally friendly raw materials. It ensures biodegradation and reduction of
product toxicity during the production of polymers. [13]. Polymers for the production of printing inks
were created as a result of the polymerization of soybean oil. Epoxidized oils are used to improve the
properties of rubbers, which are a component for obtaining light-sensitive films, packaging materials
for baby food and the production of medical materials. [14]. Soybean oil is a raw material used in
research of the synthesis of solid polymer materials. They have mechanical properties that allow them
for structural materials.
   Epoxides are cyclic ethers, metabolites that are often formed by cytochromes as a result of the
action on aromatic or double bonds. The site on the molecule that undergoes epoxidation is its site of
epoxidation (SOE).
   Thanks to artificial neural networks, it is possible to improve the identification of the SOE of the
molecule and to choose the best parameters for controlling the epoxidation process at the stage of
product synthesis. ANN is a technical software implementation of the biological neural structure of
the human brain. The main part of ANN is a system of connections that allow one neuron to form a
signal propagation route to other neurons and receive signals in the reverse direction.
   The volume of use of epoxidized oils is increasing, which is connected with the intensive
production of polyvinyl chloride (PVC) and polymers based on it. Since epoxidized oils are one of the
best stabilizers-plasticizers of such polymers. They have advantages over stabilizers of other types.
The introduction of an epoxidized stabilizer into the polymer dramatically increases its thermal
stability, prevents the decomposition of the polymer under the action of ionizing radiation as well.
Their main functions are: hardeners in compositions with various oligomers and stabilizers in PVC
compositions. In the paint industry, epoxidized oils are part of paint products based on epoxy,
ethercellulosic oligomers, PVC, as well as plasticizers for organodisperse coatings. [15, 16].
   Organic peracids are introduced for liquid-phase epoxidation of unsaturated organic substances.
[17,18].

2. Experiment
    Based on research [19] was proposed to introduce the H2O2/formic acid/catalyst epoxidizing
system. Organic peracid, is formed during the interaction of H2O2 with an organic acid in the presence
of a catalyst, is an epoxidizing agent (Fig. 1). In this system, there was no stage of production and
release of peracid, while the organic acid remained circulating.
    Replacement of the formic acid with a more affordable option were considered. Among the acids,
they chose the cheaper one - acetic [20].
    It is suggested to use organic acid anhydride instead of organic acid in our research. As a result,
the amount of water in the reaction mixture was reduced, and the reaction of peracetic acid was
accelerated.
    The purpose of the work is to improve the technology of obtaining epoxidized oils. The selection
of optimal conditions for the economical production of epoxidized oils, the quality of which meets the
standards (Table 1), modification of the production technology of this product.
Figure 1: Scheme of epoxidation by H2O2/organic acid/catalyst system

Table 1
Quality indicators of epoxidized oils
                                                                     Norm for brands (technical
                  Physical-chemical indicator                              conditions*)
                                                                  ST          SU             C
   Epoxy number, % (oxyran oxygen content), not less than         6.5         6.4           6.0
           Iodine number, g I2/100 g, no more than                1.5         2.0           8.0
   *As stabilizers and plasticizers for PVC-based polymers

   Practical value Using a model of the process obtained with the help of a neural network allows
control of epoxidized oil during the synthesis stage.
   A study of the dependence of the reaction speed of the epoxidation process on:
   •    Initial concentration of acetic anhydride (AA)
   •    Initial concentration of hydrogen peroxide
   •    Initial concentration of ion exchange resin KU-2x8
   •    Temperature of the process
   to establish the optimal concentration of reactants of the epoxidizing mixture, duration of the
process, and temperature.

   It was experimentally established that at different concentrations of acetic anhydride, hydrogen
peroxide, the amount of catalyst, and the duration of the process, the dependence of the epoxide
number of epoxidized soybean oil has a complex essence. Increasing the temperature and
concentration of the catalyst contributes to the growth of the reaction rate. However, a temperature
more than 348K and a catalyst concentration above 15% may decrease the achieved epoxy number.
   It is necessary to optimize the conditions for carrying out the process. It is relevant to create a
mathematical model and calculate optimal conditions using special methods.
   To create the model, the following factors and their limitations were adopted:
   •     X1 – concentration of acetic anhydride, wt.% 2<x1<9
   •     X2 – concentration of hydrogen peroxide 46%, wt.% 25<x2<40
   •     X3 - Amount of catalyst, wt.%, x3<15
   •     X4 – temperature, K, 333<x4<353
   •     X5 – duration of the process, min, x5<360

3. Methods
   A sample set was created for neural network training from the array of experimental data obtained.
The inputs of the neural network are the conditions of the experiment, and the outputs are the final
results, in the form of the acquired properties of substances.
   Input parameters:
   1. Concentration of AA (normalized)
   2. Concentration of H2O2 (normalized)
   3. Catalyst KU-2×8 (Kat) (normalized)
   4. Normalized temperature
   5. Normalized reaction time
   6. Initial value of Epoxy number (normalized)
   7. Initial value of Iodine number (normalized)
   For calculations it was accepted that the initial values of the Epoxy and Iodine numbers influence
the course of the experiment. The total reaction time for the experimental data sample was within 400
minutes, and the temperature range is 423 - 443 K.
   Output parameters:
   1. Final value of Epoxy number (normalized)
   2. Final value of Iodine number (normalized)
   The training of the neural network was carried out on the input experimental data. It were obtained
during the epoxidation of soybean oil. For this, 7 input parameters were taken. Their values were
normalized to 1. The output layer of the neural network consisted of 2 neurons. As a result, a five-
layer network with three hidden layers of 20 neurons each was created (Fig. 2).




Figure 2: A neural network for data processing obtained during the epoxidation of soybean oil

   Neural network training occurs thanks to the mechanism of training with a teacher. The minimum
of the error function was determined using the error backpropagation algorithm and the stochastic
gradient descent model. The training took place during 1000 epochs.

4. Results and Discussion
   As can be seen from Fig. 3, which was obtained after neural network training, an increase in
catalyst concentration in the mixture does not lead to a significant change in the growth of the Epoxy
number in the first 60 minutes of the reaction. However, during the continuation of the reaction at a
higher concentration of the catalyst, the growth of the epoxy number, although it slows down, quickly
reached its maximum value. After 1 hour of reaction, at low catalyst concentrations in the mixture,
the growth of the Epoxy number stops and is restored around the 4th hour of reaction, at the given
concentrations of the substances included in the mixture (see caption under figure 3). Despite the fact
that the amount of data and their range of arguments is insignificant, the neural network managed to
increase the range of argument values and build a detailed graph, according to which intermediate
values were found. It made possible by the neural network's ability to learn. It will be possible to
specify this dependence thanks to the replenishment of the database with new experimental data on
which the neural network is trained.




Figure 3: Dependence of the epoxy number on the concentration of the catalyst and the time of the
chemical reaction of soybean oil. The calculations were carried out during the interaction of a
solution of soybean oil in toluene with the epoxidizing system H2O2/acetic anhydride/catalyst
Concentration of AA = 5.72 concentration H2O2=33.1 wt.%, reaction temperature T=343 K




Figure 4: Comparison of dependences of the epoxy number on catalyst concentration and time of
soybean oil epoxidation reaction. Experimental data - red lines, and studied (predicted) neural
network - blue lines. The calculations were carried out during the interaction of a solution of
soybean oil in toluene with the epoxidizing system H2O2/acetic anhydride/catalyst. Concentration of
AA = 5.72 wt.%, H2O2=33.1 wt.%, reaction temperature T=343 K. a - catalyst concentrations in the
mixture 2.5 wt.%, b – 5.0 wt.%, c – 7.5 wt.%
   The experimental data were compared with the data obtained after training the neural network
(Fig. 4). As can be seen, after training, the neural network reproduces the input data with high
accuracy and can make experimental predictions beyond the experimental data.
   Since the neural network was trained on the intermediate results of the experiment, a bulge
appeared at low time limits (Fig. 4a). This convexity is a consequence of the fact that the totality of all
input data was considered.




Figure 5: Dependence of Iodine number on catalyst concentration and time of soybean oil
epoxidation reaction. The calculations were carried out during the interaction of a solution of
soybean oil in toluene with the epoxidizing system H2O2/acetic anhydride /catalyst Concentration of
AA = 5.72 wt.%, H2O2 =33.1 wt.%, reaction temperature T=343 K




Figure 6: Comparison of dependences of Iodine number on catalyst concentration and time of
soybean oil epoxidation reaction. Experimental data - red lines, and studied (predicted) neural
network - blue lines. The calculations were carried out during the interaction of a solution of
soybean oil in toluene with the epoxidizing system H2O2/acetic anhydride /catalyst Concentration of
AA = 5.72 wt.%, H2O2 =33.1 wt.%, reaction temperature T=343 K. a - catalyst concentrations in the
mixture 2.5 wt.%, b – 5.0 wt.%, c – 7.5 wt.%
Figure 7: Dependence of the epoxy number on the concentration of AA and the concentration of the
catalyst during the epoxidation reaction of soybean oil. The calculations were carried out during the
interaction of a solution of soybean oil in toluene with the epoxidizing system H2O2/acetic
anhydride/catalyst. The concentration of H2O2 =33.1 wt.%, the reaction temperature is Т=343 K. The
reaction time is 60 minutes

    As can be seen from Fig. 5, which was obtained after neural network training, an increase in the
catalyst concentration does not lead to a significant change in the dependence of the decrease in the
ionic number. However, at low concentrations of the catalyst, the decrease in the ionic number is a
slightly slower.
    As with the Fig. 3 dependence, the data obtained during the experiment are limited by the number
and range of argument values. However, as a result of training, the neural network details the
dependence of the Iodine number on the selected arguments.
    Figure 6, as well as Figure 4, shows a comparison of experimental data with data obtained after
neural network training. As a result of the training, the neural network accurately reproduces the
experimental data and predicts the result of the experiment based on this data.
    Due to the fact that the neural network during training process uses the output functions from
seven variables, it becomes possible to see the projections of the calculated functions on the selected
axes of the required parameters. The dependence of the epoxy number after a one-hour interval of the
epoxidation reaction of soybean oil on the concentration of AA and the catalyst is shown in Figure 7.
The duration of the reaction and the concentration of H2O2 are constants.
    A simultaneous increase in the concentration of AA and the catalyst contributes to the growth of
the reaction rate (Fig. 7).
    The optimal concentrations of AA and catalyst were calculated to achieve the maximum Epoxy
number and minimum Iodine number during the interaction of a solution of soybean oil in toluene
with the epoxidizing system H2O2/acetic anhydride/catalyst (Fig. 7, 8).
    Conditions:
    •    Х2= 33.1 wt.% (H2O2)
    •    X4= 343 K. (reaction temperature)
    •    X5= 60 minutes (Reaction time).
    Optimum values of Epoxy number occur at:
    •    Х1= 8 wt.% (AA concentration)
    •    Х3= 2 wt.% (Catalyst concentration)
    Optimum values of Iodine number occur at:
    •    Х1= 9 wt.% (AA concentration)
    •    X3= 3 wt.% (Catalyst concentration)
Figure 8: Dependence of Iodine number on AA concentration and catalyst concentration during the
epoxidation reaction of soybean oil. The calculations were carried out during the interaction of a
solution of soybean oil in toluene with the epoxidizing system H2O2/acetic anhydride/catalyst. The
concentration of H2O2 is 33.1 wt.%, and the reaction temperature is Т=343 K. The reaction time is 60
minutes

    If we fix the reaction time, temperature and concentration of AA in the mixture, we will get the
following dependences presented in Fig. 9, 10.




Figure 9: Dependence of the epoxy number on the concentration of H2O2 and the concentration of
the catalyst during the epoxidation reaction of soybean oil. The calculations were carried out during
the interaction of a solution of soybean oil in toluene with the epoxidizing system H2O2/acetic
anhydride/catalyst. The concentration of AA is 5.72 wt.%, the reaction temperature is Т=343 K. The
reaction time was 60 minutes.

   Simultaneous increase in concentration H2O2 and the concentration of the catalyst contributes the
increase of the Epoxy number (Fig. 9). The figure also shows a local minimum, which indicates the
most suboptimal values of the H2O2 concentration and concentrations at which the reaction will
proceed very slowly.
Figure 10: Dependence of the iodine number on the H2O2 concentration and the catalyst
concentration during the epoxidation reaction of soybean oil. The calculations were carried out
during the interaction of a solution of soybean oil in toluene with the epoxidizing system H2O2/acetic
anhydride/catalyst. The concentration of AA is 5.72 wt.%, and the reaction temperature is Т=343 K.
The reaction time is 60 minutes

   In Figure 10, we have similar dependencies as in Figure 9 for the Iodine number.
   As can be seen from the figure, at the maximum concentration (in the selected range) of H2O2 and
the almost maximum concentration of the catalyst, the Iodine number becomes the minimum value.
By analogy with Fig. 8, we calculate the optimal concentrations of ) H2O2 and the catalyst to achieve
the minimum Iodine number during the interaction of a solution of soybean oil in toluene with the
epoxidizing system H2O2/acetic anhydride/catalyst, we obtain:
   Conditions:
   •    X1= 5.72 wt.% (AA concentration)
   •    X4= 343 K. (reaction temperature)
   •    X5= 60 minutes (Reaction time).
   Optimum values of Iodine number occur at:
   •    X2= 40.0 wt.% (H2O2)
   •    X3= 7 wt.% (Catalyst concentration)

5. Conclusions
    The process of optimal parameters and conditions selection for the epoxidation process of soybean
oil has been presented. As an example of the application of the search method, the dependence of the
reaction parameters on the concentration of hydrogen peroxide, acetic anhydride, and the catalyst is
demonstrated. The implementation of a neural network showed that even with a small experimental
dataset, it is possible to predict the quantitative result of epoxidation, especially, epoxy and iodine
numbers. Therefore, the proposed approach makes it possible to more accurately and quantitatively
predict the result of the epoxidation reaction of soybean oil.
    The optimal conditions for the oil epoxidation process were established using an initial set of
specific determined values for the concentration of acetic anhydride, hydrogen peroxide, KU-2x8
catalyst, reaction duration and temperature conditions.
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.

7. References
[1] E. Weinan and Yu. Bing, The Deep Ritz Method: A Deep Learning-Based Numerical Algorithm
     for Solving Variational Problems, Commun. Math. Stat. 6.1 (2018) 1–12. doi: 10.1007/s40304-
     018-0127-z.
[2] D. Llorente, M. Ballesteros, D. Cruz-Ortiz, I. Salgado, and I. Chairez, Brain Computer Interface
     for Speech Synthesis Based on Multilayer Differential Neural Networks, Cybernetics and
     Systems 53.1 (2022) 126–140. doi: 10.1080/01969722.2021.2008685.
[3] A. Karacı, Detection and classification of shoulder implants from X-ray images: YOLO and
     pretrained convolution neural network based approach, Journal of the Faculty of Engineering and
     Architecture of Gazi University 37 (2022) 283–294. doi: 10.17341/gazimmfd.888202.
[4] T. Chaikivskyi, BB Sus, OS Bauzha, SP Zagorodnyuk, and V. Reutskyy, “Development of
     Neural Network for Cyclohexane Oxidation Data Processing.” in 2021 IEEE 3rd Ukraine
     Conference on Electrical and Computer Engineering (UKRCON), Lviv, Ukraine, Aug. 2021, pp.
     10–14. doi: 10.1109/UKRCON53503.2021.9575213.
[5] H. Li, Z. Zhang, and Z. Liu, Application of Artificial Neural Networks for Catalysis: A Review,
     Catalysts 7.10 (2017) 306. doi: 10.3390/catal7100306.
[6] H. Jiang, H. Zhang, Y. Liu, and J. Han, Neural-network-based control scheme for a class of
     nonlinear systems with actuator faults via data-driven reinforcement learning method,
     Neurocomputing 239 (2017) 1–8. doi: 10.1016/j.neucom.2017.01.047.
[7] K. O. Lye, S. Mishra, and D. Ray, Deep learning observables in computational fluid dynamics,
     Journal of Computational Physics 410 (2020) 109339. doi: 10.1016/j.jcp.2020.109339.
[8] J. Han, A. Jentzen, and Weinan E., “Solving high-dimensional partial differential equations using
     deep learning.” Proc. Natl. Acad. Sci. U.S.A., vol. 115, no. 34, pp. 8505–8510, Aug. 2018, doi:
     10.1073/pnas.1718942115.
[9] S. Mishra and R. Molinaro, Physics informed neural networks for simulating radiative transfer,
     Journal of Quantitative Spectroscopy and Radiative Transfer 270 (2021) 107705. doi:
     10.1016/j.jqsrt.2021.107705.
[10] T. Chaikivskyi, B. Sus, O. Bauzha, and S. Zagorodnyuk, Multicomponent analyzer of volatile
     compounds characterization based on artificial neural networks, CEUR Workshop Proceedings
     2608 (2020) 819–831. [Online]. Available: https://ceur-ws.org/Vol-2608/paper61.pdf
[11] T. Kusumoto and K. Mori, Prediction of ultrashort pulse laser ablation processing using machine
     learning, Laser Applications in Microelectronic and Optoelectronic Manufacturing (LAMOM)
     XXVI, Online Only, United States, Mar. 2021, p. 1. doi: 10.1117/12.2577447.
[12] K. Shukla, P. C. Di Leoni, J. Blackshire, D. Sparkman, and G. E. Karniadakis, Physics-Informed
     Neural Network for Ultrasound Nondestructive Quantification of Surface Breaking Cracks, J
     Nondestruct Eval 39.3 (2020) 61. doi: 10.1007/s10921-020-00705-1.
[13] T. B. Hughes, G. P. Miller, and S. J. Swamidass, Modeling Epoxidation of Drug-like Molecules
     with a Deep Machine Learning Network, ACS Cent. Sci. 1.4 (2015) 168–180. doi:
     10.1021/acscentsci.5b00131.
[14] L. Montero de Espinosa and M. A. R. Meier, Plant oils: The perfect renewable resource for
     polymer science?!, European Polymer Journal 47.5 (2011) 837–852. doi:
     10.1016/j.eurpolymj.2010.11.020.
[15] M. Stemmelen, F. Pessel, V. Lapinte, S. Caillol, J.-P. Habas, and J.-J. Robin, A fully biobased
     epoxy resin from vegetable oils: From the synthesis of the precursors by thiol-ene reaction to the
     study of the final material: A Fully Biobased Epoxy Resin, J. Polym. Sci. A Polym. Chem. 49.11
     (2011), 2434–2444. doi: 10.1002/pola.24674.
[16] T. Tsujimoto, H. Uyama, S. Kobayashi, H. Oikawa, and M. Yamahiro, Green Nanocomposites
     from Renewable Plant Oils and Polyhedral Oligomeric Silsesquioxanes, Metals 5.3 (2015) 1136–
     1147. doi: 10.3390/met5031136.
[17] O. I. Slavgorodskaya, V. G. Bondaletov, A. A. Lyapkov, J. P. Ustimenko, and D. Vervacke,
     Kinetics of Petroleum Resin Epoxidation by Peracetic Acid, Procedia Chemistry 10 (2014) 555–
     559. doi: 10.1016/j.proche.2014.10.094.
[18] T. Voronchak, I. Nykulyshyn, Z. Pikh, A. Rypka, and Z. Gnativ, Cooligomerization of dominant
     monomers of C9 fraction of liquid pyrolysis products: comparison of heterogeneous catalytic
     approach with common methods, Open Chemistry, 12.2 (2014) 266–280. doi: 10.2478/s11532-
     013-0369-2.
[19] Patent UA83020 Process for the preparation of epoxidized vegetable oil // Hrynchuk YM,
     Starchevskyi VL, Nykypanchuk MV 27.08.2013 (https://uapatents.com/4-83020-sposib-
     oderzhannya-epoksidovano-roslinno-oli.html
[20] I. Nykulyshyn, Z. Pikh, L. Shevchuk, and S. Melnyk, Examining the epoxidation process of
     soybean oil by peracetic acid, EEJET 87 (2017) 21–28. doi: 10.15587/1729-4061.2017.99787.