Online Metallurgical Mass Balance and Reconciliation

Abstract: In mineral processing, one of the most important and versatile separation methods is flotation. Flotation utilizes the different surface properties of the valuable minerals in the ore to separate them from the less valuable gangue material in the ore. Crushed and ground ore is mixed with water and fed into flotation tanks. In the flotation tanks, the particles of valuable mineral are made hydrophobic. That way, they can be floated by attaching to air bubbles and gather on top of the flotation tank as froth. This froth, containing higher concentrations of valuable mineral, is recovered and then processed further. The flotation circuit is controlled and maintained using measurements on the mass flows and grades of different materials. Due to economical, practical, and technological limitations, these measurements are performed at a chosen number of points in the circuit and at discrete points in time. Poor measurement data can have devastating consequences if the operators are left with limited information and errors in the circuit remain undetected. The accuracy of the acquired measurements is improved by performing mass balance and reconciliation. Traditionally, mass balance uses the sum of the total mass flows and the average grades over long times to avoid including the internal mass of the circuit in the calculations. It is desirable to perform mass balance directly to allow for faster intervention if any failures occur in the circuit during the on-line process. This report describes an on-line dynamic approach towards mass balancing and reconciliation of the mass flows and grades in a flotation circuit. Here, physical models of the flotation circuit are used to construct mass balance constraints using interpolation and test functions and the mass balance problem is posed as an optimization problem. The optimization problem is to adjust the assay such that the residual, the difference between the measured and the adjusted assay, is minimized while maintaining mass balance. An implementation in MATLAB and tests on synthetic data show that the dynamic formulation of mass balance does adjust 'erroneous' measurements such that mass balance is fulfilled. Given this result, there are still important aspects of the implementation that have to be addressed. The model uses the unknown and cell specific parameters flotation rate and recovery. Thus, these must be found or properly modeled. This report proposes a possible model for flotation rate as well as a strategy to find the recovery. The requirements of accuracy and speed of the implementation are also discussed. Possible next steps of this project is to further confirm a time effective implementation using synthetic data. Consequently, the implementation can be adapted for natural data in order to verify correctness of models.