SYSTEMATIC ANALYSIS AND MATHEMATICAL MODELING OF ULTRASONIC EXTRACTION PROCESS

ABSTRACT

Systematic analysis of extraction allows a complete study of the object as a system, to determine the input and output parameters of the process and their interaction, and as a result to find the right solution. Initially, the object of research was to classify medicinal plants as a single system (single hierarchical level). Taking the following assumptions, we construct a mathematical model of mass transfer in the inner and middle quasi layers of a particle, as well as in quasi layers in direct contact with the solvent. It is known that in the quasi layers of the leaves of the mint plant, the substance passes through molecular diffusion to the surface in contact with the solvent.

АННОТАЦИЯ

Системный анализ добычи позволяет всесторонне изучить объект как систему, определить входные и выходные параметры процесса и их взаимодействие и в результате найти правильное решение. Изначально объектом исследования была классификация лекарственных растений как единой системы (единого иерархического уровня). Принимая следующие допущения, построим математическую модель массопереноса во внутреннем и среднем квазислоях частицы, а также в квазислоях, непосредственно контактирующих с растворителем. Известно, что в квазислоях листьев растения мяты вещество переходит путем молекулярной диффузии на поверхность, контактирующую с растворителем.

Keywords: modeling, systematic analysis, ultrasonic, extraction, hierarchical scheme

Ключевые слова: моделирование, систематический анализ, ультразвук, извлечение, иерархическая схема

The proposed method of systematic thinking of the object of obtaining medicinal plants, which we offer, allows you to easily analyze the system of isolation of medicinal plants in the installation of existing methods [1]. According to the proposed method, first of all, the indicators - the object of separation of medicinal plants - the extraction system and the input and output parameters of the process that takes place at the object of separation of medicinal plants are determined. The system under consideration in the device (element) for the production of medicinal plants is then divided into components, the parameters for each selected element and the process in the element are indicated. And similarly, the division of an element (a plant extraction system in an extraction plant) into subsequent systems is not limited. Optimal extraction of medicinal plants in the device was performed depending on the level of need for decision-making and research capabilities [2].

The process of obtaining medicinal plants can be divided into 3 stages [1,2,3]:

1) "internal diffusion", which includes all the phenomena of transfer of substances within the raw material particles (penetration of the solvent into the pores of particles of plant materials; melting of the component);

2) direct distribution of the substance within the boundary layer;

3) The passage of the extracted substance through the shell of the moving extractant and its distribution throughout the entire extractor mass (convective diffusion).

For mathematical modeling of the process, we determined the input and output parameters of the plant extraction process. Fig. 1 shows a level 1 diagram of the hierarchy of medicinal plants.

Figure 1. Level 1 hierarchical scheme of plant separation.

The main input parameters at this level are: M - mass of raw material; а_т - valuable components of raw materials; м_erit - the mass of the solvent; а_erit - the concentration of the solvent; Т_erit - solution temperature. Output parameters are as follows: т_м - the mass of the remaining medicinal plants; а_м - valuable components of medicinal plant residues; а(τ) - change in concentration (valuable components) in the apparatus over time; м_erit2 - solvent output consumption.

The block diagram of the laboratory experimental equipment and the computer model of the process of obtaining a valuable component from the leaf of the mint plant are as follows:

Figure 2. Structural diagram of laboratory and experimental equipment and computer model of the process of obtaining a valuable component from the leaves of the mint plant

The structure of the holes in many ways affects the extraction mechanism and the speed of its flow. The particle size of a mint leaf is much larger than the diameter of the pores, so they can be obtained as isotropic porous bodies. Let us assume another: the extracts obtained are a group of components with different diffusion and physicochemical properties.

In a one-dimensional system with a concentration gradient x dc/dx, the rate of change in the concentration of a substance at a given point depends on the diffusion and is determined by Fick's [3] second law. The result of Fick's second law is a second-order diffusion equation:

,                                                            (1)

where t is the time and x is the thickness coordinate of the mint leaf.

Or the time distribution of the concentration of extractives in the particle size of a mint leaf is written by the equation:

,                                          (2)

Such an equation has been solved by scientists to linearly describe the initial conditions. In the actual process, the initial conditions, in particular the distribution of the concentration of the crushed mint leaf in the body, are related to taking into account the concentration of the valuable component in the external environment, which changes over time. The order of derivation of computational equations, there are also large errors in the application of the third type of boundary conditions.

Therefore, the development and application of computational solutions based on multi-stage computer modeling techniques will be more optimal. it begins with modeling the distribution of concentration within a body of material.

Modeling of the extraction process in quasi-layers of a material particle. Taking the above assumptions, we construct a mathematical model of the mass transfer in the inner and middle quasi layers of the particle, as well as in the quasi layers in direct contact with the solvent. It is known that in the quasi layers of the leaves of the mint plant, the substance passes through the molecular diffusion to the surface in contact with the solvent.

Equation of material equilibrium in the middle quasi layer of a particle:

                                              (3)

Here G_qk3 is the arrival of a valuable component in the quasi-layer of the leaf particle of the mint plant (m3 / s); G_sarf3 is the consumption of the valuable component through the quasi-layer of the mint particle, (m³ / s).

It is known that the amount of M_mas3 valuable component passing through the middle quasi-layer to the outer layer is equal to the product of the amount of M_qk3 solution passing through this layer to the concentration of the valuable component in this layer a_mas3:

                                          (4)

In this case:

                                  (5)

The following is an analysis of a mathematical expression describing a change in the concentration of a valuable component in a solution:

                                        (6)

The results of experiments conducted on a computer model of the process of extraction of extractive substances from mint analyzed the changes in the concentration in the solvent and quasi-layers (Fig. 3). It is known that over time, the concentration of the valuable component from each layer decreases.

Figure 3. Change of the concentration of the valuable component in the solid phase quasi-layers with diffusion coefficient D=0,7∙10^-11 m²/s (decrease in the concentration of the valuable component)

As can be seen from Fig. 3, intensive extraction of extractives from the raw material continued for 3000 s from open holes and capillaries. Subsequently, the process proceeded more slowly and approached equilibrium after 8100 s. The nature of the change in diffusion coefficient over time in the study does not contradict modern ideas about the mechanism of obtaining a porous structure from plant raw materials.

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