Lagrangian reconciliation of expeditious analyzes on microflotation of hematite and dolomite by carboxylates

Abstract

Microflotation campaign of a synthetic binary mixture of hematite and dolomite was carried out in order to evaluate the potential of saponified cottonseed oil as a collector. Hematite content was determined by expeditious methods, namely image analysis, pycnometry, and carbonate thermolysis by calcination. An algebraic reconciliation algorithm of redundant data (via Lagrange multipliers) was developed to treat the raw data from the different analytical techniques, aiming to increase the accuracy of the results, with the additional piece of information arising from product weighing, by introducing a dummy variable. At the stage of the study reported here, the physicochemical conditions for the selective flotation of hematite were not optimized; however, the results showed potential (both under acid and alkaline conditions) for the selective anionic flotation of the hematite/dolomite system. Prospective tests evaluating the analytical techniques employed showed pycnometry and calcination tended to be more reliable methods. Although the imaging method has shown promise, it still lacks some improvement in procedure for greater accuracy. The minimization of closure errors in mass balancing by using the mentioned optimization algorithm under constraints showed to be very relevant for the adequate evaluation of the separation process, using very small samples, as in the case of microflotation.