MATHEMATICAL MODELING OF THE VEGETABLE OIL DEODORIZATION PROCESS USING FLOATING NOZZLES

ABSTRACT

This article presents mathematical and computer models of the deodorization process of cottonseed oil using floating packing elements. By employing MATLAB Simulink, the dynamics of light volatile components in both the liquid and vapor phases were investigated over time. The developed models allow for the simulation of key technological parameters, such as temperature, concentration, and partial pressure, offering insight into mass and heat transfer phenomena within a multistage deodorization column. The analysis showed that the concentration of volatile components in the liquid phase rapidly decreases at the beginning of the process, gradually reaching a stationary state. Conversely, their concentration in the vapor phase initially increases sharply before stabilizing. The results demonstrate the effectiveness of using floating wooden packing elements to intensify the mass transfer and reduce deodorization time. This approach supports optimization and control of deodorization processes and can serve as a basis for further theoretical and practical advancements in edible oil refining.

АННОТАЦИЯ

В данной статье представлены математические и компьютерные модели процесса дезодорации хлопкового масла с использованием плавающих насадочных элементов. С использованием MATLAB Simulink исследована динамика изменения концентрации лёгких летучих компонентов как в жидкой, так и в паровой фазах во времени. Разработанные модели позволяют моделировать ключевые технологические параметры, такие как температура, концентрация и парциальное давление, что позволяет получить представление о явлениях массо- и теплопереноса в многоступенчатой дезодорирующей колонне. Анализ показал, что концентрация летучих компонентов в жидкой фазе быстро снижается в начале процесса, постепенно достигая стационарного состояния. В паровой фазе же их концентрация, наоборот, сначала резко возрастает, а затем стабилизируется. Результаты демонстрируют эффективность использования плавающих деревянных насадочных элементов для интенсификации массопереноса и сокращения времени дезодорации. Данный подход способствует оптимизации и управлению процессами дезодорации и может служить основой для дальнейшего теоретического и практического развития в области рафинации пищевых масел.

Keywords: deodorization process, mathematical model, computer model, floating nozzle, concentration.

Ключевые слова: процесс дезодорация, математическая модель, компьютерная модель, плавающее насадки,концентрация.

Introduction

The article presents mathematical and computer models of the cottonseed oil deodorization process. Using the computer model, the change in concentration and temperature of light volatile components in the liquid and vapor phases over time is studied. A significant increase in the demand for edible oils such as soybean, palm, sunflower, rapeseed, and cottonseed oils is observed worldwide. According to the recommendation of the Food Institute of the Russian Academy of Medical Sciences, annual per capita consumption of vegetable oils should be 13 kilograms. However, in recent years, this figure has remained at 9–10 kilograms. Moreover, due to unfavorable climatic and agrochemical conditions, the oils extracted from plant raw materials may contain residues of chlorinated pesticides and toxins, highlighting the need for deodorization of fats and oils. Therefore, solving technical and technological problems related to the production of vegetable oils that comply with international standards is of particular importance for oil and fat processing enterprises.

One of the most powerful and universal software packages used to solve typical mathematical problems arising in various fields of human activity is MATLAB, developed by MathWorks. The spectrum of mathematical analysis methods implemented in MATLAB is quite wide, including numerical integration, interpolation and function approximation, linear algebra, nonlinear equations and systems of ordinary differential equations, equations of mathematical physics, optimization problems, logic, and others. MATLAB also has well-developed tools for interpreting two- and three-dimensional array data and includes a programming language that allows for easy creation of custom programs. Users of MATLAB can improve their knowledge in computer modeling, programming, and result visualization while working in the software [1, 2].

The purpose  of this study is to develop a mathematical and computer model of the deodorization process of cottonseed oil using floating packing elements. The research aims to analyze the changes in concentration and temperature of light volatile components in both the liquid and vapor phases over time. By modeling the process in MATLAB Simulink, the study seeks to optimize technological parameters and better understand mass and heat transfer mechanisms, thereby improving the efficiency and design of deodorization equipment.

Modern food technology, characterized by high temperatures and pressures in multiphase systems operating at high speeds, is inherently nonlinear. It involves numerous changing parameters that determine the course of the processes, with complex internal relationships and interactions among these variables.

In addition, external random disturbances that are often ignored in calculations of chemical and food production processes and equipment can also affect the process. As a result, the amount of data to be processed becomes significantly large, and to eliminate the influence of weak factors, it becomes necessary to reduce or correct the data volume and limit the number of available choices. This is achieved through modeling the process and understanding the phenomena using simplified "equivalents" that reflect the key directions of process development [3,4].

Through mathematical modeling, any mass transfer process can be described as a large system made up of several subsystems such as equilibrium, mass transfer, hydrodynamics, heat transfer, and mass and energy balance. In the deodorization process, due to the evaporation of light volatile components from the liquid, their amount in the liquid phase decreases and increases in the vapor phase. The remaining liquid, which does not evaporate, mainly consists of heavy, less volatile components—i.e., oil. To reduce the boiling point of the oil during the process, considering that the mixture components are insoluble in water, high-temperature steam is introduced openly into the mixture as an additional component [5].

Materials and methods

The countercurrent flow of liquid and vapor phases in the column creates numerous quasi-apparatus zones. Each quasi-apparatus consists of floating nozzles, a liquid phase, and a vapor phase. The intensive interaction of wooden nozzles with the open steam supplied from the lower part of the device significantly reduces these

The computer model of the deodorization process was developed in the MATLAB Simulink package using the following formulas [5].

                                              (1)

where: М₁, М₂, М₃ and М₄ -molecular masses of light volatile components and cottonseed oil, kg/kmol, х₁, х₂ and х₃ -mass fractions (concentrations) of light volatile components in the oil, %

The change in the concentration of volatile components in the gas phase in the third stage of the deodorization unit is calculated using the following formula:

                                                          (2)

 For the quasi-apparatus of the oil phase in the third stage of the deodorization object, the change in the concentration of volatile components is calculated using the following formula:

                                                                     (3)

The degree of use of direct steam in the deodorization process is characterized by the saturation coefficient of the secondary vapor.

,                                                               (4)

where: – actual partial pressure of fatty acid vapors on the oil surface, kPa,  – partial pressure of fatty acid vapors in equilibrium with the solution, kPa
In the deodorization process using direct steam, the vapor phase can be considered an ideal gas.

The concentration of each component’s molecules is proportional to their partial pressure.

This condition can be expressed as follows

                                              (5)

where: N_fa, Р_fa, G_fa and М_fa – respectively, the number of molecules, partial pressure, flow rate, and molecular weight of the light volatile component vapor, N_wv, Р_wv, G_{wv and} М_wv – respectively, the number of molecules, partial pressure, flow rate, and molecular weight of the water vapor.

The general form of the mathematical model describing the change in concentration and temperature of light volatile components in both the liquid and vapor phases during the cottonseed oil deodorization process is given in the system of equations (6).

                             (6)

To perform calculations using the computer model developed based on the mathematical model, constant values of the technological parameters were accepted within the following limits.

Results and discussions

The analysis of the simulation results shows that when the initial values of the process parameters in the floating nozzle apparatus are set uniformly, the progress of the process was observed over time. At this stage, the concentration of light volatile components in the liquid phase changes rapidly at first. Over time, as the process approaches a steady-state condition, the rate of change in concentration gradually slows down.

Figure 1 illustrates the time-dependent change in the concentration of light volatile components transitioning to the vapor phase. As seen from the figure, the concentration of light volatile components in the vapor phase initially increases rapidly and intensively. As the process approaches a steady state, the rate of change in concentration slows down.

The effect of partial pressure of fatty acids (palmitin) on the oil temperature at the fourth stage of the deodorization unit was calculated using the following formula:

In the quasi-apparatus level of the cottonseed oil deodorization system, the variation of palmitin vapor partial pressure depending on temperature was analyzed. A graphical interpretation of the research results is presented in Figure 2.

The dependence of the equilibrium concentration of the oil phase processes in the quasi-apparatus of the third stage of the deodorization unit on temperature is shown in Figure 2. It indicates that when the temperature rises to 180°C, the equilibrium concentration increases significantly compared to the initial state.

From these graphs, it is evident that the main technological parameters of the deodorization process - temperature and the total pressure inside the apparatus - across their entire variation ranges (t_v=140÷240 ⁰C, Р_a=0,13÷1,3  kPa) - result in increasing values of both the working and equilibrium concentrations in the vapor phase as the temperature rises.

The change in equilibrium concentration of the oil phase processes in the quasi-apparatus at the third stage of the deodorization unit is shown in Figure 3. This situation can be explained as follows: since the boiling point of the light volatile components is lower than that of the oil, when the oil enters a high-temperature zone, within 1-1.5 seconds almost all of the volatile components evaporate and transfer to the vapor phase. After approximately 4 seconds, the process reaches a steady state, and the concentration in the vapor phase approaches around 0.9%.

Figure 3. Change in equilibrium concentration of the oil phase processes in the quasi-apparatus during deodorization

Analysis of the modeling results shows that, when identical initial values of process parameters are set in the floating packing device and the process is observed over time, the concentration of the light volatile component in the liquid phase initially changes rapidly. As time progresses and the process approaches a steady state, the change in the concentration of volatile components in the oil slows down.

Furthermore, in carrying out the deodorization process, variable parameters were considered, including: initial concentration of volatile components in the oil X_n=0,003, initial concentration of volatile components in the gas Y_n=0,00001, initial temperature of volatile components in the oil phase t_n=220 ^oC, initial temperature in the gas phase t_n=220+10 ^oC, initial temperature in the oil phase t_n=220^oC, and the mass transfer coefficient between the oil and gas phases K=0,5.

The variation of volatile component concentrations in the oil and gas phases during the deodorization process is analyzed. The green curve (1) in the graph represents the enrichment of the vapor phase with volatile components, while the red curve (2) shows the reduction of volatile components in the oil due to their transfer into the vapor phase.

Conclusion

It is difficult to imagine modern knowledge of food industry processes and equipment without mathematical and computer modeling. The essence of this methodology lies in replacing the original object - in this case, the cottonseed oil deodorization process - with its mathematical model, and then studying it by implementing computational algorithms on a computer. This allows for the investigation of the process by varying its technological parameters as needed.

This approach to analysis, construction, and design combines both practical and theoretical advantages. Working with a model rather than the real object allows for faster and cost-free examination of its properties, even under hypothetical (mainly theoretical) conditions. Conducting experiments on the deodorization process using a computer model makes it possible to deeply and thoroughly study problems that cannot be solved by theoretical methods alone.

References:

1. Patent No. 192869 RF, IPC C11B 3/16 (2006.01). Deodorizer for fats and oils / Nikonov O.I., Belina N.N., Gukasyan A.V. – Application No. 2019119478; Filed: 14.05.2019; Published: 20.06.2019.
2. Khamdamov A., Asqarova O., Mansurov O., Sultonov S. Simulation of a multistage distillation process in a rotary disc device // Annals of Romanian Society for Cell Biology, 2021. – Vol. 25, Issue 4, pp. 5939–5948.
3. Khamdamov A., Saribaeva D. Modeling the deodorization process of cottonseed oil fatty acids // Universum: Technical Sciences: Scientific Journal. Moscow: “MCNO”, 2020. – No. 11(80), Part 2, pp. 100–105.
4. T.Kh. Sultonov, A.M. Khamdamov, A.A. Khudoyberdiev. Improving the deodorization process of vegetable oil in a liquid–vapor–floating packing system. “SUNRISE-PRO”, 2023, 115 p.
5. Khamdamov A.M., Sultonov S.Kh., Bozorov S.A. Key findings on the deodorization of vegetable oils using wooden packing. Journal of Pharmaceutical Negative Results, 2022. – pp. 3844–3851.
6. Yusufbekov N.R., Nurmukhammedov H.S., Zokirov S.G. Fundamentals of Chemical Technology: Main Processes and Equipment. – Tashkent: Sharq, 2023.