Using a conjugate gradient method, optimal flux and concentrate addition rates with standard and oxygen enriched air are determined for maximum heat recovery from exothermic copper converter reactions and for good temperature control.
Summary--Exothermic copper conversion reactions release heat energy which can be used to melt fluxing materials required in the reverberatory furnace. Oxygen enrichment of the air supplied to the converter results in shorter processing times and increased ability to smelt flux but with increased air supply costs.
A conjugate gradient method in function space is employed to determine the optimal rate of flux addition to a calibrated mathematical model of the converter for various levels of enriched oxygen. The smelting of flotation concentrates in the converter and the effect of converter parameter variations in the optimal solutions are also considered. The mathematical model is derived from material and heat balance relationships and is calibrated using data from an operating converter.
The paper also shows how the method of conjugate gradients in function space can be applied to a bounded control problem, in particular, one in which intervals of singular optimal control arise. The conjugate gradient method is found to converge substantially faster to a higher value of the performance index than a conventional steepest ascent procedure.