CC BY
2
CHEMISTRY SCIENCES
KINETICS AND CATALYSIS
DOI - 10.32743/UniChem.2024.125.11.18377
MATHEMATICAL MODELING OF THE RESULTS OF PHTHAL ANHYDRIDE
SYNTHESIS CATALYSTS
Kamola Ziyadullaeva
Candidate of Technical Sciences, Associate Professor, University of Geological Sciences, Republic of Uzbekistan, Tashkent city. E-mail: [email protected]
Dilrabo Turayeva
PhD student,
Tashkent Institute of Chemical Technology, Republic of Uzbekistan, Tashkent city Е-mail: [email protected]
МАТЕМАТИЧЕСКОЕ МОДЕЛИРОВАНИЕ РЕЗУЛЬТАТОВ КАТАЛИЗАТОРОВ СИНТЕЗА
ФТАЛЕВОГО АНГИДРИДА
Зиядуллаева Камола Хаитбоевна
канд. техн. наук, доцент, Университет геологических наук, Республика Узбекистан, г. Ташкент
Тураева Дилрабо Фахриддиновна
аспирант,
Ташкентский химико-технологический институт, Республика Узбекистан, г. Ташкент
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
Библиографическое описание: Ziyadullaeva K.Kh., Turayeva D.F. MATHEMATICAL MODELING OF THE RESULTS OF PHTHAL ANHYDRIDE SYNTHESIS CATALYSTS // Universum: химия и биология : электрон. научн. журн. 2024. 11(125). URL: https://7universum.com/ru/nature/archive/item/183 77
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
x1 *2 x3 Xn-1 xn
y yi y2 ya yn-1 yn
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 f(x,a1,a2,...,ak) 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, f(x,a1,a2,...,ak) in the unit size must be less than that of this function Yi = /o,a2,..., ak) [2-4].
5(alva2.....afe) = £f=1[y¿ - Y¿]2 =2f=iLVi ~ f(x,alfa2.....%)]
mm
(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. Y = f(x, a±, a2,..., fllfc) the dependence coefficient in the function was chosen and this dependence was extracted by Ct[ in the first function [5-6].
( ay.C'2.....n) (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 Y = f (x, CIj, 0.2, ■■■, Gt^) we get
the following system (c) from k linear equations with k unknowns.
df
X X
< ¿-"1=
2 № 21
x=i'[y¿
Li2Ly¿ -
f(x, Ct^CL 2, fix,
fix, ai, a 2,
=0
m£=O (c)
df
in the system of equations fij is multi-numbers at the
k — 1 — level and takes from Y — Xf=i 1
A_i in the system of equations is a large number at the k-1 level and takes the form Y=7, (i=1)Ak [a_i xA(i-1) ] and is represented by the following system (d)
ain + «2 + % If=i*2 + - + ak If=ixf 1 = !f=iy¿ % + «2 If=i*2 + «3 + - + ak If=ixf = If=iX¿y¿ (d)
<-ai Z?=1 xf + «2 I?=1 xf+1 + «31?=1 xf+2 + - + afc 21=1 x(2fc-2 = 21=1 xfy¿
Then (d) system is written in matrix form.
Ca = g, (f)
C matrix and g vector elements were calculated by this formula.
Cij = 2fc=i xi+j-2 ,i = 1.....k + 1J = 1.....k + 1,
9i = K=iyfc4 1,i = !,-,k + 1.
(g) (h)
From the given system (d) Y = a1 + a2x + a3x2 + —+ ak+1xk 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)
Catalyst Temperature, oC Reaction rate, mol/l.s Product yield, %
V2O5+TIO2 300-340 21.2 85.0
350-400 22.5 90.0
410-450 21.0 84.0
VBK-33 300-340 21.4 84.4
350-400 22.4 89.5
410-450 20.6 82.5
VBK-44 300-340 21.5 86.2
350-400 22.6 90.4
410-450 20.5 80.2
VBK-55 300-340 22.1 88.4
350-400 23.0 92.1
410-450 21.1 84.3
VBK-66 300-340 21.7 86.9
350-400 23.5 94.2
410-450 21.4 85.6
To determine the kinetic parameters of the catalysts, an analytical function and a mathematical model were
An analytical function
created and explained based on the following table 3 model.
Table 3.
a mathematical model
k 320 350 400 450
Ui 21.1 21.8 22.37 20.6
Here is the temperature, U¡ is the product yield.
a2la3,aA) — a± + a2ti + a3ti2 + o4 tf
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.
f[l] := 320; t[2] := 360; *[3] := 400; t[4] := 450;
(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.
A ■= Matrix{[[sum{{t[i]f,i= 1 ..4),,sw/w((i[i])5,i = 1 .A),sum{{t[i])*,i = 1 ..4), (3)
,swm((i[i])3, i = 1 ..4)], [jMiw((i[/])5,1 = 1 ..4),sum{(t[i])4,i= 1 ..4),sum{(t[i])3, i = 1 .A),sum{{t[i])2, i= 1 ..4)], [sum{{t[i])4, i= 1 ,A),sum{{t[i])3, i = 1 .A),sum{{t[i\)2, i = 1 .A),sum{{t[i])\i= 1 ..4)], = 1 .A),sum{{t[i])2,i = 1 ..4),
sum{ (f[i])\ i = 1 -4), 4]])
Matrix A has the following value.
A=
15650289785000000 38094873300000 93888170000 234549000
38094873300000 93888170000 234549000 594500
93888170000 234549000 594500 1530
234549000 594500 1530 4
The inverse of Matrix A was calculated.
16819 215543 9240781 143633
175219200000000 1946880000000 219024000000 27040000
215543 2763771 118554107 16593769
1946880000000 21632000000 2433600000 2704000
9240781 118554107 20353482301 158359879
219024000000 2433600000 1095120000 67600
143633 16593769 158359879 49930145
27040000 2704000 67600 169
A-1
Matrices B and C were created for the duration of the reaction and had the following values (6,7,8,9).
(4)
(5)
B ■= Matrix{[[sum{y[i]-{t[i])3, i= 1 ..4)], [sww(;y[iHi[i])2,i = 1 ..4)], [sum{y[i]-t[i],i (6) = 1-4)], [«m№],/ = 1..4)]]);
B •■--
2.00938317010 5.10088100 107 131433.0 343.9
10
(7)
-0.000013595 0.014339 -4.9524 646.4
C := Matrix([[a],[b],[cl[d]]); (8)
For this process, initially from equation (8) (9), the system is brought to the following state and brought to the following value.
a ■= -0.000013595; b ■= 0.014339; c == -4.9524; d ■= 646.4; yl ■= a- 3203 + b- 3202 + c-3201 + d; yl ■.= 84.464640 y2 ■■= a-3603 + b-3602 + c-3601 + d\ y2 ■= 87.582080 y3 ~ a-4003 + b-4002 + c-4001 + d; y3 ■■= 89.600000 y4 ■= a-4503 + b-4502 + c-4501 + d y4 ■■= 82.623125
(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.
89-
86-
84-
83'
320
340
360
380
400
420
440
(a)
(b)
Figure 2: Effect of temperature on the production ofphthalic anhydride using the VBK-33 catalyst;
- in the experime (a) plot{a-t3 + b-t2 + c-t1 +d,t = 320 ..450,= 82 ..90) when (b) modeled plot{ [ [320, 84.4], [360, 87.5], [400, 89.5], [450, 82.5]])
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
Vj := 21.1 V2 := = 21.8
v3 := 22.37 V4 : := 20.6
M1 := 84.4 u2 ■ := 87.5
«3 := 89.5 U4 := 82.5
ti 320 320 400 450
tii 21.1 21.8 22.37 20.6
iq 84.4 87.5 89.5 82.5
In here t;- is temprature, 1is average rate of reaction, Uj -is phthalic anhydride product
(12)
i[l] := 320; i[2] := 360; i[3] := 400; t[4] := 450;
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.
K ■= Matrix{[[sum{{t[i])Z,i = 1 .A),sum{(t[i])1',i= 1 ..4), sum{ ((i[i'])2-v[i]), i = 1 ..4), jMm((i[*]-(v[i])2), * = 1 ..4)],[jM/»((i[i])3, i= 1 ,A),sum{(t[i])*, i= 1 ..4), ™«(((i[i])3-v[f]),i = 1 -4),stti«(((i[/])2-(v[f])2),f = 1 ..4)], [«o»(((i[i])2-v[i]),i = 1 ..4),«im(((i[i])3-v[»]),i = 1 .A),sum{{(t[i])2-(v[i])2),i= 1 ..4),««»((Mi])1 •(v[«])3),i = 1..4)], [W(№])1-(v[»1)2),i-=1.4),5«m(((i[»])2-(v[/])2),« = 1..4), ™«(((«[i])1 ■ (v[i])3), f = 1 ..4),™( (v[f])4, i = 1 ..4) ]]);
(13)
K-matrix value is:
K ■■=
594500 234549000
234549000 1.27366200010'
704682.3600
93888170000 5.01736060010* 2.73180212010°
1.273662000107 5.017360600109 2.73180212010s 1.514728906107
704682.3600 2.73180212010s 1.514728906107
854563.4851
(14)
L :=
/
m n f
(15)
U •=
131433.0 5.10088100 107 2.822189800106 158956.2366
(16)
0.233362245144235 -0.0000857085207428554 -0.00804148870520294 0.163511087404913
(17)
I ■= 0.233362245144235 m n := -0.00804148870520294
The following values are obtained by solving the resulting system (18) u =-0.857085207428554, t2-0.80414887052029, (t, v, )+163511087404913 and
-0.0000857085207428554 /:= 0.163511087404913
(18)
v2+.233362245144235 were obtained and the parameters of the dependence functions of temperature and product yield were determined.
ul u2 u3 u4
= l-320 + w-3202 + n-320-21.1 +/-21.12; ul
= 1-360 + m-3602 + w-360-21.8 +/-21.82; u2 = 1400 + m4002 + «400-22.37 +/-22.372; u3
= 1-450 + m-4502 + n-450-20.6 +/-20.62; u4
= 84.40000539 = 87.49998977 = 89.50000526 = 82.49999960
According to the obtained results, an iconogram of the results was created using the Maple 18 program
based on the product yield and the average reaction rate for the process (Fig. 4).
720 400
--■-441!
(a) (b)
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,
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
ноябрь, 2024 г.
the following results were obtained, and based on these results, a diagram and an iconogram were created.
yl ■■= 86.251296 y2 := 87.540032 y3 -.= 90.428000 y4 ■= 80.212250
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.
yl := a-3203 + b-3202 + c-3201 + d; y2 — a-3 603 + b-3602 + c-3601 + d\ y3 := a-4003 + b-4002 + c-4001 + d, y4 ■= a-4503 + b-4502 + c-4501 + d
References:
1. Ziyadullaeva Kamola Khaitboevna, Nurmanov Suvonkul Erkhanovich, Kurbanova Aipara Dzhodosovna, Akhmedova N.A., Technological foundations of preparation and study of properties of catalysts for obtaining phthalic anhydride based on naphthalene., Universum: Technical science scientific journal. Moscow 2020. - No. 12 (81). -PP. 39 - 42.
2. N.V. Usheva, O.E. Moyzes, O.E. Mityanina, E.A. Kuzmenko. Mathematical modeling of chemical-technological processes: a tutorial. Tomsk: Publishing House of Tomsk Polytechnic University, 2014. - PP. 135.
3. Nasim Movaghamezhad Peyman Najafi Moghadam. Hexamethylene diamine/carboxymethyl cellulose grafted on magnetic nanoparticles for controlled drug delivery// Springer-Verlag Berlin Heidelberg 2017, Polym. Bull. (2017) No.74. - PP. 4645 - 4658.
4. Adam V. Wisnewski., Morgen Mhike., Justin M. Hettick., Jian Liu., Paul D. Siegel. Hexamethylene diisocyanate (HDI) vapor reactivity with glutathioneand subsequent transfer to human albumin// Elsevier, Toxicology in Vitro No.27 (2013) - PP. 662 - 671.
5. Jing Lu., Wenlian Wang., Tianxiang Yang., Shuai Li., Xiaoyang Zhao., Weizhen Fan., Chaojun Fan., Xiaoxi Zuo., Junmin Nan. Hexamethylene diisocyanate (HDI)-functionalized electrolytematching LiNio^Coo^Mno^O2/ graphite batteries with enhanced performances// Elsevier, Electrochimica Acta No.352 (2020). - PP.136 - 456.
6. D. Manjula Dhevi., A. Anand Prabu., Kap Jin Kim. Hyperbranched polyester as a crosslinker in polyurethane formation: real-time monitoring using in situ FTIR// Springer, Polym. Bull. (2016) No.73. - PP. 2867 - 2888.
