DEVELOPMENT OF A MATHEMATICAL MODEL OF THE SULFONATION PROCESS OF ALKYLBENZENES

Аннотация

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 =АBSA -225,9 -209,8 38,0 3 2 АB + АBSA = sulfone + H O 0 -227,6 35,0 2 3 sulfone + H O = АB + АBSA 0 227,6 100,0 2 4 АBSA + SO = angABSA -47,7 -162,9 40,0 3 5 АB + SO = PSA -94,2 -181,2 110,0 3 6 АB + PSA = АBSA -37,1 -140,7 100,0 7 angABSA + H O = 2АBSA+ SO -191,5 -153,2 115,0 2 3 28 ACADEMIC RESEARCH IN MODERN SCIENCE International scientific-online conference 8 ABnepr + SO = Connection -34,0 -171,2 41,3 3 without S. 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, Ci = C , where i is the corresponding hydrocarbon. 0i 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. 𝐶 ∙𝑝∙𝜐∙𝐿 𝑃 = 𝑝 𝑒 𝜆 29 ACADEMIC RESEARCH IN MODERN SCIENCE International scientific-online conference 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/m3 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 = 𝑘 ∙ 𝑎 ∙ 𝐶 𝑗 𝑖 𝑑𝜏 𝑁 𝑑𝑇 𝑝𝐶 = ±∑(−∆𝐻 )𝑊 𝑝 𝑗 𝑗 𝑑𝜏 { 𝑗=1 N. s.: t=t0 C=C0; Т=Т0 da where Ci - concentration of the i-th component, mol/l; kj - rate constant of the j-th reaction, l/ (mol s); t - residence time of