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A study was made on the effect of Ca, Sr, and Ba chloride complexes with dibenzo-18-crown-6 ether as catalysts on the process criteria of the efficiency of industrial cumene oxidation using kinetic modeling. It is the first stage in the process chain of polymer composite production. The kinetic scheme of the process is made of classical reactions of the radical chain mechanism (reactions of initiation, chain propagation, and chain termination), molecular reactions, reactions of formation of intermediate adducts “component of the reaction mixture—catalyst” and their decomposition, as well as reactions that take into account the specifics of the catalyst used: (1) formation of planar catalyst complexes with various substances; (2) formation of acetophenone along the catalytic path; (3) hydration of the intermediate adduct “α-methylstyrene—catalyst” to the required alcohol. It is shown that the kinetic model fully reproduces the experimental time dependencies of the cumene hydroperoxide concentration in the cumene oxidation and cumene hydroperoxide decomposition. Using the kinetic model, computational experiments were carried out, as a result of which the following conclusions were made: (1) among the considered catalysts, the complex of Sr chloride with dibenzo-18-crown-6 ether should be recognized as the best, provided that it is used at temperatures of 393–413 K and an initial concentration < 2 mmol/L; (2) to ensure selectivity comparable to the selectivity of a non-catalytic process, it is necessary to conduct the catalytic process at a lowest possible initial concentration of any of the considered catalysts. Full article