# Value-based objective functions applied to circuit analysis

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Minerals & Metallurgical Processing
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, 2015, Vol. 32, No. 1, pp. 45-58

Noble, A.; Luttrell, G.H.

ABSTRACT:

Linear circuit analysis (LCA) is a fundamental tool that may be used to evaluate, design and improve the performance of mineral separation. The traditional LCA methodology provides a comparative evaluation of circuit designs purely from the unit interconnections. The quantitative approach uses the analytical circuit solution to evaluate the slope of the circuit’s partition curve at the midpoint. Since the partition slope is often associated with a separation’s general selectivity, this numeric value is used to compare and rank alternative configurations. Unfortunately, the partition curve slope only reflects the separation potential of middling material. By itself, this value does not account for the relatively high unit dollar value of pure material or the gains and losses in mass yield associated with alternative circuit configurations. Realizing the value in the LCA methodology, but respecting the limitations of the partition slope valuation, the authors have derived two new performance indicators that quantitatively address pure particle misplacement (the Partition Moment of Inertia) and circuit mass yield (the Yield Score). Together, these parameters provide a better indication of separation economics in typical mineral and coal separation systems. Since the two parameters provide independent information on circuit selectivity and circuit yield, a Pareto efficiency, multi-objective function selection approach is proposed for preliminary circuit selection.