A Method of Distributing Error to Predict Mass Balances For Instantaneous Sampling of Copper Flotation Circuits

Several series of time-instantaneous samples were taken on a cell-by-cell basis in the flotation circuits of the Pinto Valley, AZ copper concentrator. These samples were used to calculate mass flow rates throughout the circuit using standard, deterministic metallurgical formulae and also a variety of more statistically oriented techniques. Because of the magnitude of the errors associated with the individual cell samples, the standard metallurgical formulae are not sufficient. Consequently, it is necessary to utilize some type of statistical technique capable of distributing the individual cell sample errors in such a way so as to provide a physically useful mass balance for the entire circuit. This paper explores the use of linear and least squares programming as one technique to providing credible mass balance calculations. For linear programming this was done by distributing the error using two different criteria involving specific linear programming formulations: least absolute sum minimization (which assumes an underlying double exponential distribution error structure) and minimax (which minimizes the maximum absolute deviation and assumes an underlying rectangular distribution error structure). These results were then compared to the more standard formulation of minimization of the sum of least squares which assumes an underlying normal distribution error structure. The least absolute sum approach was particularly attractive due to its simplicity of use and the ease in which repetitive calculations can be done with no user intervention.