Effect of Epistemic Uncertainty in the Selection of Concentration Circuit Structures

The optimal design of flotation circuits is a complex task as the mathematical model is nonconvex and includes binary variables, making it difficult to obtain the global optimum solution. Furthermore, there are epistemic uncertainties in the evaluation of the performance of flotation and grinding units. This epistemic uncertainty is generated because semi-empirical models are used with parameters that are a function of the circuit design. Therefore, it is not possible to adjust these models based on experimental data as the experimental conditions are not known at the design stage. This paper analyzed the effect of the uncertainties in flotation units, grinding units, and both units simultaneously. As a result, this paper demonstrated that, for a specific mineral, few structures exist that are optimal for a wide range of values in flotation stage recoveries and liberation fractions in the grinding units. A remarkable aspect of this work is that it introduces grinding, one of the operations that most influences energy consumption in mining and has not been studied in depth in the design of flotation circuits. To demonstrate that there are few optimal structures for a specific mineral when there is high uncertainty in the process units, an a priori approach or first principles was used. Two methods of proof were used: proof by construction and proof by exhaustion. Proof by construction is the construction of a concrete example with a property to demonstrate that something having that property exists. In this work, two examples were considered in the proof by construction. In proof by exhaustion, the conclusion was established by dividing it into a finite number of cases and proving each one separately. Here, 30,000 cases were included for each example. This knowledge can be useful in circuit design including grinding, e.g., after selecting the circuit (or the most promising circuits), and the equipment design parameters and operating conditions can be defined based on simulation and laboratory tests.