MATHEMATICAL MODELING OF THE RESULTS OF PHTHAL ANHYDRIDE SYNTHESIS CATALYSTS

ABSTRACT

This article describes the use of the MARPLE 2018 program in mathematical modeling of chemical processes and result processing. When the process is carried out in the temperature range of 350-400 0C, the activity results of the catalysts affecting the production of phthalic anhydride and the results of the dependence on various factors show that the experiments conducted based on the conclusions of the mathematical modeling are 90-94% accurate.

АННОТАЦИЯ

В данной статье описывается использование программы MARPLE 2018 при математическом моделировании химических процессов и обработке результатов. При проведении процесса в диапазоне температур 350-400 0С результаты активности катализаторов, влияющих на получение фталевого ангидрида, и результаты зависимости от различных факторов показывают, что эксперименты, проведенные на основе выводов математического моделирования, имеют точность 90-94%.

Keywords: phthalic anhydride, catalyst, mathematical modeling, matrix, maple-soft 2018 program

Ключевые слова: фталевый ангидрид, катализатор, математическое моделирование, матрица, программа maple-soft 2018

Phthalic anhydride and its various derivatives are widely used in various fields of chemical and oil and gas industry. Preparation of catalysts of various composition based on local raw materials for the production of phthalic anhydride, thereby increasing product yield, reducing the price of catalysts and the main product is one of the modern requirements of today [1]. Mathematical effect modeling of phthalic anhydride production catalysts on chemical processes allows to determine technological parameters in the synthesis of compounds. Mathematical modeling of the experimental results obtained during the synthesis of phthalic anhydride with the catalyst help of different compositions was carried out using the method of least squares. The correlation status of the experimental results is presented in Table 1.

Table 1.

Correlation status of experimental results

In this case, it is necessary to create an analytical connection that explains the results of the experiment as clearly as possible. To create such parameters, we use the following method of least squares. In this process, the function  should be set in such a way that the squares of the result obtained, the displacements of this function, in the unit size must be less than that of this function [2-4].

     (a)

Figure 1. Analytical dependence of product yield on temperature

Process modeling was carried out in two stages:

1. The appearance of the selected dependency is defined.

2.  the dependence coefficient in the function was chosen and this dependence was extracted by   in the first function [5-6].

 (a) is zero in all derivatives of the function. The minimum function was performed by the following equation.

                                                                      (b)

If the parameters  are linear with dependence in the function  we get the following system (c)  from   linear equations with  unknowns.

                                (c)

in the system of equations  is multi-numbers at the   level and takes from   A_i in the system of equations is a large number at the k-1 level and takes the form Y=∑_(i=1)^k▒〖a_i x^(i-1) 〗  and is represented by the following system (d)

Then (d) system is written in matrix form.

                                                               (f)

 matrix and g vector elements were calculated by this formula.

               (g)

                                         (h)

From the given system (d)  dependence parameters are defined [111, 135-138 b].

In the process of obtaining phthalic anhydride, catalysts were created using vanadium pentaoxide, potassium sulfate, acetic acid and local bentonite, the results of the effect of the obtained catalysts on the synthesis of phthalic anhydride were mathematically modeled. In order to determine the kinetic parameters of the catalysts, the reaction rate was calculated based on the following table (Table 2).

Table 2.

Effect of temperature and duration of reaction on product yield

(Duration of reaction, 4 hours)

To determine the kinetic parameters of the catalysts, an analytical function and a mathematical model were created and explained based on the following table 3 model.

Table 3.

An analytical function and a mathematical model

Here  is the temperature,  is the product yield.

Kinetic parameters of catalysts during the reaction, temperature, product yield, reaction duration, and reaction rate values ​​were entered step by step into the Maple-soft 2018 program, and matrices with correct and inverse values ​​were developed for the entered values. Initially, the selected temperature for the process was entered into the program.

                   (1)

At different temperatures, the product was formed in the following yields.

y[1] := 84.4; y[2] := 87.5; y[3] := 89.5; y[4] := 82.5                                      (2)

Matrix A was developed based on reaction temperature and product yield.

    (3)

Matrix A has the following value.

A=            (4)

The inverse of Matrix A was calculated.

A^-1               (5)

Matrices B and C were created for the duration of the reaction and had the following values ​​(6,7,8,9).

 (6)

                                                              (7)

                                                (8)

                                                            (9)

For this process, initially from equation (8) (9), the system is brought to the following state and brought to the following value.

     (10)

                       (11)

Based on the above system matrices, the function and diagram of the temperature effect on the product yield of the initial VBK-33 catalyst used in the synthesis of phthalic anhydride was created using the Maple18 program.

 Figure 2: Effect of temperature on the production of phthalic anhydride using the VBK-33 catalyst;

- in the experime (a)

when (b) modeled

The mathematical model of the average speed of the VBK-33 catalyst in the process of obtaining phthalic anhydride was given on the basis of the following table: 

Table 3.

The mathematical model of the average speed

In here  - is temprature, - is average rate of reaction, -is  phthalic anhydride product

                                (12)

K, L, U matrices were developed and their values ​​were calculated in order to determine the analytical relationship between the influence of catalysts on product yield, temperature dependence and the average speed of the reaction and to obtain its iconogram.

       (13)

K-matrix value is:

       (14)

                                                                    (15)

                                                       (16)

                                               (17)

                     (18)

The following values ​​are obtained by solving the resulting system (18) u =-0.857085207428554,  t2-0.80414887052029,   (t, v, )+163511087404913 and v²+.233362245144235 were obtained and the parameters of the dependence functions of temperature and product yield were determined.

According to the obtained results, an iconogram of the results was created using the Maple18 program based on the product yield and the average reaction rate for the process (Fig. 4).

Figure 3: Effect of temperature on phthalic anhydride yield of VBK-33 catalyst;

a) according to the results of the experiment f*v²+m*t²+n*t*v+l*t, t = 320. 450, v = 20. 23

b) –modeled [[320, 21.1, 84.4], [360, 21.8, 87.5], [400, 22.37, 89.5], [450, 20.6, 82.5]]

In the Maple-Soft program, the parameters and dependencies of the effect of the VBK-44 catalyst on the product yield were also analyzed. According to it, the following results were obtained, and based on these results, a diagram and an iconogram were created.

Conclusion

Currently, computer technology programs are widely used for mathematical modeling of chemical processes and processing of results. MARLE-2018 program was used for mathematical processing of experimental processes. When the process is carried out in the temperature range of 350-400 0C, the results of the catalyst activity affecting the production of phthalic anhydride and the results of the dependence on various factors show that the experiments conducted based on the conclusions of the mathematical modeling are 90-94% accurate.

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