Mixed integer nonlinear optimization framework applied to a platinum group metals flotation circuit

Abstract

This study described an alternative approach for flotation circuit optimization using a mathematical programming technique. Mathematical formulation resulted in mixed integer nonlinear programming problem. Experimental method was used to determine operating conditions of flotation circuit such as flotation circuit stream grades. These conditions were used as the basis for solving optimization problem formulated. The results of the optimization problem were obtaining by setting up the problem in MATLAB optimization toolbox. Performance of flotation circuit in terms of recovery with respect to operating conditions such as residence, number of cells and rate constant has been presented. Stage recoveries were presented as well as overall recovery of the entire flotation circuit. Optimization strategy used superstructure to compare and analyse different alternatives flotation circuits configurations on the basis of stage recoveries. Five circuit alternatives were evaluated are best performing were identified. The statistical analysis was carried out using Statistical Package for Social Sciences (SPSS) software for analysing data derived from mathematical formulation developed for three stages of flotation circuit. Statistically, alternatives A and B can be considered as the most efficient alternatives for the Rougher recovery since they have the same highest means relative to others. Alternative B has the highest mean of 0.995 followed by Alternative A with a mean of 0.991, the least being alternatives D, C and E, respectively. These results imply that Alternative B could be the most efficient alternatives for overall circuit recovery against all other alternatives. One of the key findings were that recovery rate at the rougher stage is higher than the one at the cleaner stage. This results also showed flotation circuits with recycle streams yield comparatively good performance in terms of recovery at rougher stage as compared to circuit without recycle stream.