Two-phase optimization methodology for the design of mineral flotation plants, including multispecies and bank or cell models

Froth flotation processes are carried out in flotation cells that are grouped into banks, and these banks are interconnected, forming a flotation circuit. A literature review shows the existence of papers related to flotation circuit design based on mathematical programming. However, due to the complexity of solving the mathematical model in most of the work, it is considered that a small number of species is present in the feed to the circuit, which differs from practice. In addition, simple bank models are generally used. This paper presents a methodology for designing mineral concentration circuits that overcomes the problems mentioned. It allows the use of more suitable cell or bank models and the inclusion of several species. The methodology is based on two phases. The first phase identifies the set of optimal structures using discrete values of stage recoveries, solving several mixed integer linear programming (MILP) problems. In the second phase, the optimal design for each of the structures obtained in the previous phase is determined using a suitable model for the recovery at each cell or bank, which results in a mixed integer nonlinear programming (MINLP) model. The design of a copper concentration plant with eight species and the design of a zinc concentration plant with three species and five size fractions by species are used to validate the proposed methodology. The structure of the cells in the rougher and cleaner banks deliver structures that are novel.