A Mathematical Model of the Synthesis of Pentaerythritol


Based on the results of a kinetic study of the condensation of acetaldehyde and formaldehyde in the presence of sodium hydroxide and taking into account well-known data, we compiled a reaction scheme of the process, in which pentaerythritol, dipentaerythritol, tripentaerythritol, bispentaerythritolformal, pentaerythritol methyl ether, and sodium 2,2-bis(hydroxymethyl)propanoate are formed. According to the reaction scheme, we developed a mathematical model of the process, which includes reaction rate equations and formulas for calculating the activity coefficients of ions and the degrees of ionization and equilibrium concentrations of intermediate substances. The effective kinetic parameters and activation energies of reactions were found. The adequacy of the mathematical model was statistically evaluated under the following conditions: an acetaldehyde–formaldehyde–sodium hydroxide molar ratio of 1 : 4–9 : 1.2, an initial acetaldehyde concentration of 0.4–0.9 mol/L, and a temperature of 13–47°C.

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Correspondence to D. I. Belkin.

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Translated by V. Makhlyarchuk

Symbols and abbreviations: A, acetaldehyde; AA, 3-hydroxybutanal; A1, 3-hydroxypropanal; A2, 2-hydroxymethyl-3-hydroxypropanal; A3, 2,2-bis(hydroxymethyl)-3-hydroxypropanal; AD, 2,4-dimethyl-6-hydroxy-1,3-dioxacyclohexane; AD1, 2-(2-hydroxypropyl)-4-methyl-6-hydroxy-1,3-dioxacyclohexane; A1X, 2-propenal; A2X, 2-hydroxymethyl-2-propenal; D2, 2-hydroxymethyl-4-oxa-6,6-bis(hydroxymethyl)-7-hydroxyheptanal; B2, 2-hydroxymethyl-4,6-dioxa-8,8-bis(hydroxymethyl)-9-hydroxynonanal; M2, 2-hydroxymethyl-4-oxapentanal; T2, 2-hydroxymethyl-4,8-dioxa-6,6,10,10-tetrakis(hydroxymethyl)-11-hydroxyundecanal; AE, A1E, A2E, D2E, B2E, M2E, and T2E, corresponding enolate ions; D1E, the enolate ion of 4-oxa-6,6-bis(hydroxymethyl)-7-hydroxyheptanal; B1E, the enolate ion of 4,6-dioxa-8,8-bis(hydroxymethyl)-9-hydroxynonanal; M1E, the enolate ion of 4-oxapentanal; T1E, the enolate ion of 4,8-dioxa-6,6,10,10-tetrakis(hydroxymethyl)-11-hydroxyundecanal; D3, 2,2,6,6-tetrakis(hydroxymethyl)-4-oxa-7-hydroxyheptanal; B3, 2,2,8,8-tetrakis(hydroxymethyl)-4,6-dioxa-9-hydroxynonanal; M3, 2,2-bis(hydroxymethyl)-4-oxapentanal; T3, 2,2,6,6,10,10-hexakis(hydroxymethyl)-4,8-dioxa-11-hydroxyundecanal; P, pentaerythritol; PN, sodium 2,2-bis(hydroxymethyl)propanoate; FN, sodium formate; BP, bispentaerythritolformal; F, formaldehyde; B, sodium hydroxide; M, methanol; DP, dipentaerythritol; TP, tripentaerythritol; MP, pentaerythritol methyl ether; PF, pentaerythritol formaldehyde hemiacetal; FM, methanol formaldehyde hemiacetal; TF, formaldehyde trimer; AL, aldehydes; M, formaldehyde to acetaldehyde molar ratio; KA, equilibrium constant of aldol condensation; k, rate constant; Z, ratio between the rate constants of fast reactions; S, complex associated with the steady-state concentration of enolate ions; pKa(i), ionization constant; α, degree of ionization; γ, ionic activity coefficient; z, ion charge; f, number of degrees of freedom; S2, dispersion; N, number of experiments; n, number of factors; FT, Fisher test value; e, experimental; c, calculated; O, reverse reaction; (0), initial concentration; s, total concentration; (A), AL consumption in reactions not accompanied by the consumption of B.

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Belkin, D.I., Demchenko, O.A. A Mathematical Model of the Synthesis of Pentaerythritol. Kinet Catal 61, 374–383 (2020). https://doi.org/10.1134/S0023158420030052

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  • pentaerythritol
  • synthesis
  • mathematical model
  • kinetic parameters