Algorithm for Calculating the Optimization of the Parameters for the Electroextraction of Metal Based on the Example of Zinc

A numerical algorithm combining the fourth-order Runge–Kutta scheme with the Hooke–Jeeves direct-search optimiser is proposed to solve an inverse kinetic problem that arises during zinc powder electrodeposition from alkaline electrolytes. The model describes two competing cathodic chains – zinc reduction and parasitic hydrogen evolution – through a coupled Cauchy system with positivity constraints. Unknown rate constants are estimated by minimising the squared deviation between calculated and experimental zinc yields, which reduces the amount of laboratory testing required. An applied result of the calculations also provides the ability to predict the yield of the deposited metal powder. Verification against published data at current densities of 125–500 A/m² shows relative errors below 5 % after 60 min of electrolysis and confirms that nucleation effects dominate only at the earliest stages. The approach therefore offers an efficient tool for parametrising and optimising electroextraction processes for zinc and other metals. At the same time, the velocity constants that are found can be used for calculations based on larger-dimensional models when calculating the spatial characteristics of an electrical system.