Value-Based Objective Functions Applied to Circuit Analysis

"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.IntroductionOver the past 30 years, numerous scientific and industrial studies have proposed various mineral processing circuit design methodologies that attempt to optimize the allocation of separation resources within the processing plant. Over this period, the methodologies have undergone various transitions, including the increased inclusion of process models and computationally intensive algorithms, as well as a general shift from a purely technical solution (Lauder and McKee, 1986) to partially economic solutions (Abu-Ali and Sabour, 2003; Cisternas et al., 2014). Today, circuit design is largely driven by flowsheet simulation; however, no consistent design methodology is used across the industry.One intriguing approach for circuit evaluation is linear circuit analysis (Meloy, 1983a). This method evaluates the separation potential of the circuit solely considering the unit configuration and stream interconnections. No preliminary data other than the basic circuit configuration is required to use the approach."