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DEVELOPMENT OF A MATHEMATICAL MODEL OF THE
SULFONATION PROCESS OF ALKYLBENZENES
Turdikulov T.N.
Kodirov O.Sh.
Bakhramov H.K.
Kadirov H.I.
Tashkent Institute of Chemical Technology
https://doi.org/10.5281/zenodo.15363101
Abstract.
In this research work, as a result of considering the mechanism
and chemistry of the sulfonation process, as well as the thermodynamic analysis
of the ongoing reactions using quantum-chemical calculation methods, based on
the thermodynamic probability of the reactions occurring during the sulfonation
process, the main goals and side reactions were determined.
Keywords:
surfactants, sulfonation of alkylbenzenes, mathematical
modeling, Peclet diffusion criterion, thermodynamic parameters of reactions.
Surfactants (surfactants) are substances that reduce the surface tension of
the interface between liquid, solid, or gas phases, and these properties open up
broad prospects for their application. Most surfactants are used in the national
economy (as detergents, stain removers, and finishing agents). Surfactants are
used in more than 100 sectors of the national economy. One of the important
areas of application of surfactants is the synthetic detergent industry. Other
areas include drilling oil wells, increasing oil recovery from reservoirs, flotation
of metal ores, emulsion polymerization, production of additives for mineral oils,
synthesis of lubricating-cooling fluids used in metal processing, obtaining
synthetic fibers, and the production of building materials [1-3].
Table 1 presents the thermodynamic parameters of the existing reactions
occurring during the sulfonation of alkylbenzenes at a temperature of 303 K and
a pressure of 110 kPa.
Table 1
Calculated kinetic and thermodynamic parameters of reactions
№
Reaction
∆G, kJ/mol ∆H, kJ/mol Ea, kJ/mol
1 АB + SO
3
=АBSA
-225,9
-209,8
38,0
2 АB + АBSA = sulfone + H
2
O
0
-227,6
35,0
3 sulfone + H
2
O = АB + АBSA
0
227,6
100,0
4 АBSA + SO
3
= angABSA
-47,7
-162,9
40,0
5 АB + SO
3
= PSA
-94,2
-181,2
110,0
6 АB + PSA = АBSA
-37,1
-140,7
100,0
7 angABSA + H
2
O = 2АBSA+ SO
3
-191,5
-153,2
115,0
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8 ABnepr + SO
3
= Connection
without S.
-34,0
-171,2
41,3
Based on the values of the thermodynamic parameters given in Table 1,
reactions can occur under the conditions of the process.
As a result of considering the mechanism and chemistry of the AB
sulfonation process, as well as thermodynamic analysis of ongoing reactions
using quantum chemical calculation methods based on the thermodynamic
probability of the reactions occurring during the sulfonation process, the main
goal and side reactions were identified.
To reduce the size of mathematical calculations, a formalized scheme of
hydrocarbon transformation has been developed, which is compiled using the
method of assembly according to homologous principles and a structural-
chemical approach. In this case, the simplified model satisfies the law of mass
action, and the responses of the original and simplified systems to single
influences coincide.
Sulfons are crystalline substances with melting points above 100°C and
high chemical and thermal stability [4, 5]. In this case, sulfons can be dissolved
in a mixture of ABSK and sulfuric acid.
Based on the developed formalized transformation scheme, a kinetic model
of the AB sulfonation process was constructed.
According to the law of mass action, expressions for the rate of ongoing
reactions are written as follows:
W1 = k1CABCSO3.
W2 = k2CABSABSK
W3 = k3CsulfemCH2O
W4 = k4CABSK2 CSO3
W5 = k5CABCSO2.
W6 = k6CPSKCAB
W7 = k7CangABSKCH2O
W8 = k8CtotalABCSO3
Initial conditions:
l
= 0, C
i
= C
0i
, where i is the corresponding hydrocarbon.
In this case, the constants k0 - k6 are the combinations of the constants of all
intermediate stages of the reaction mechanism.
The criterion for determining the hydrodynamic regime in the reactor is the
Pecklet number, which is determined by the following formula.
𝑃
𝑒
=
𝐶
𝑝
∙𝑝∙𝜐∙𝐿
𝜆
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where
L
- characteristic linear size of the apparatus, m; v - flow velocity,
m/s; Cp - heat capacity at constant pressure, J/ (kg K); - liquid density, kg/m3; -
thermal conductivity coefficient of the liquid, J/ (m·s·K).
The preliminary data for calculating the Peclet criterion for the reactor for
sulfonation of alkylbenzenes with sulfur trioxide are presented in Table 2.
Table 2
Initial data for calculating the Peclet criterion
𝜆
, Vt/(m*K)
Cp , kJ/(kg K)
𝑝
, kg/m
3
Alkylbenzenes
151,2
1,884
853,6
Design features of the existing sulfonation reactor:
Н
=6 m,
D
=0.025 m.
The Peclet criterion values, calculated using the formula for the sulfonation
reactor of alkylbenzenes with sulfur dioxide, were 240.
An ideal substitution model was chosen to characterize the sulfonation
reactor of alkylbenzenes with sulfur dioxide. This model is modified taking into
account changes in the activity of the reaction medium:
{
𝑑𝐶
𝑖
𝑑𝜏
= 𝑘
𝑗
∙ 𝑎 ∙ 𝐶
𝑖
𝑝𝐶
𝑝
𝑑𝑇
𝑑𝜏
= ± ∑(−∆𝐻
𝑗
)𝑊
𝑗
𝑁
𝑗=1
N.
s.:
t
=
t
0
C
=
C
0;
Т
=
Т
0 da
where C
i
- concentration of the i-th component, mol/l; kj - rate constant of
the j-th reaction, l/ (mol s); t - residence time of reagents in the reaction zone,
sec; -
DHj
- heat of chemical reaction, J/mol;
Wj
- rate of chemical reaction, m3/
(mol·s);
Cp
- mass heat capacity of the reaction mixture, J/ (kg K);
p
- density of
the reaction mixture, kg/m3;
T
- temperature, K.
The concept of reaction medium activity to account for the instability of the
sulfonation process of alkylbenzenes with sulfuric anhydride, caused by the
accumulation of HC in the reactor tube walls and disruption of the
hydrodynamic regime of the organic fluid flow. Taking into account the non-
stationarity of the process allows for the predictive ability of the mathematical
model to calculate the conditions for achieving maximum productivity and the
optimal technological conditions for its achievement. The activity of the reaction
medium is determined as the ratio of the current free amount of acid not
activated by the viscous component to the initial amount in which the viscous
component is absent in the system.
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At the same time
𝑎 = 𝑒
−𝑎𝐶
𝑞.𝑘.
where a - activity of the reaction medium, rel. units, Sv.k - molar fraction of
the MPC in the reactor; a - a parameter influencing the change in the rate of the j-
th reaction due to the accumulation of MPC.
N.U.:
С
в.к.=0
α
=1;
G.u.:
С
в.к.=1
α
=0.
In accordance with the foregoing, the developed mathematical model of the
sulfonation reactor can be characterized as follows:
where С
i
- is the concentration of the i-th component; T - temperature, K; l -
coordinate along the reactor tube axis, m; Q - heat of the j-th reaction, J/mol;
aj - activity of the reaction medium in the j-th reaction process, relative units; G -
consumption (kg/1); Z - total volume of processed raw materials (m3); AB -
hydrocarbon substituent alkylbenzenes C
10
- C
13
; ABSA - hydrocarbon-
substituting alkylbenzenesulfonic acids C
10
- C
13
; PSA - pyrosulfonic acid; ABSA
anhydride - sulfonic acid anhydride; ABnepr - residual hydrocarbon substituent
alkylbenzenes C
10
- C
13
; Non-sulfonated compounds are sulfones and tetralins.
The algorithm for solving the system of linear non-stationary differential
equations of the material and thermal balances of the sulfonation process is as
follows: This idea is based on calculating the approximate solution of y1 at the
node x0+h in the form of a linear compound with constant coefficients [9, 10]:
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Here
The developed mathematical model was implemented using the Delphi
object-oriented programming language.
To assess the adequacy of the developed mathematical model, calculations
were carried out and compared with the experimental data of the operating
device for sulfonation of alkylbenzenes with sulfur dioxide.
As a result of calculations using a mathematical model, the dynamics of
changes in the concentration of ABSK and H
2
SO
4
during mutual washing periods
were obtained (Fig. 1).
Figure 1. Change in experimental and calculated concentrations of
alkylbenzenesulfonic acids and sulfuric acid in the 1st cycle of mutual washing
The standard deviation of the calculated values for this period is σABSA =
0.6 for ABSA and σH
2
SO
4
= 0.1 for sulfuric acid.
Model adequacy check using Fisher's criterion
where y
i
-is the average value of the output parameter based on the results
of parallel experiments; y is the calculated value of the output parameter
If F < F tab. (q, f1, f2), the linear regression equation adequately describes
the process.
Number of degrees of freedom:
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For the share of ABSA:
For the sulfuric acid ratio:
The values of the calculated criteria are less than those in the table, therefore the
regression equation sufficiently describes the process under study.
References:
1.
M. Pletnev. Green and natural surfactants - recent developments SOFW J.
Intl. Version. - 2006. - № 132 (6). - P. 2-12.
2.
T.V. Pilipenko, V.V. Astaf'yeva, N.YU. Stepanova. Izucheniye kachestven-
nykh kharakteristik rastitel'nykh masel razlichnymi metodami // Izvestiya
Sankt-Peterburgskogo gosudarstvennogo agrarnogo universiteta. -2015. - № 39.
- S. 90-96.
3.
K.R. Lange. Poverkhnostno-aktivnyye veshchestva: sintez, svoystva, analiz,
primeneniye. - SPb.: Professiya. 2005. - 240 s.
4.
Соколов В.Н. Газожидкостные реакторы: учебник / В.Н. Соколов, И.В.
Доманский. - Л., «Машиностроение» (Ленингр. отд-ние). - 1976. – 216 с.
5.
Закгейм, А.Ю. Введение в моделирование химико-технологических
процессов. / А.Ю. Закгейм – М.: Химия, – 1982. – 288 с.
