Mathematical Modeling of Cathodic Zinc Electroextraction Processes

Numerical optimization techniques are widely used for solving applied problems in economics, as well as problems related to the optimization of production processes. In this paper, the Hooke-Jeeves method of direct search and numerical optimization are used to solve the problem of inverse kinetics and described the electrochemical processes for obtaining zinc powder during its leaching. Calculations are complicated by the presence of competitive processes leading to the release of zinc and hydrogen. These processes are interralated through overvoltage at the electrode, which affects the rate of stepwise electrochemical reactions. The mathematical model of processes occurring at the electrode is governed by the Cauchy problem system. Contains relations of connections and nonnegativity constraints for the concentration of ions and molecules that participated in the reaction, as well as the rates of the electrochemical processes. The minimized functional is the sum of the squared deviations of the calculated weight of the precipitated zinc from the experimental weight at specific points in time. The initial conditions for the Cauchy problem are calculated based on the state of the system prior to the beginning of electrolysis. The calculations were verified by comparison with experimental data at time points that were not involved in the calculation of the minimized functional.