استفاده از تجزیه و تحلیل حساسیت جهانی برای بهبود فرآیندها: برنامه های کاربردی برای فرآوری مواد معدنی

This paper analyzes the application of global sensitivity analysis (GSA) to the improvement of processes using various case studies. First, a brief description of the methods applied is given, and several case studies are examined to show how GSA can be applied to the study to improve the processes. The case studies include the identification of processes; comparisons of the Sobol, E-FAST and Morris GSA methods; a comparison of GSA with local sensitivity analysis; an examination of the effect of uncertainty levels and the type of distribution function on the input factors; and the application of GSA to the improvement of a copper flotation circuit. We conclude that GSA can be a useful tool in the analysis, comparison, design and characterization of separation circuits. In addition, we conclude that using the stage's recoveries of each species as input factors is a suitable choice for the GSA of a flotation plant.

Mineral processing comprises many unit operations, such as gravitational, magnetic and flotation stages, which are aimed at extracting valuable material from ores. Usually, the processes’ operating conditions are defined to control the balance between a high recovery rate of the desired metal and a high grade value of the metal in the product outflow (Méndez, Gálvez, & Cisternas, 2009a). These processes usually include multiple stages that are interconnected (forming circuits) to maximize the recovery rate and concentrate grade. The design and analysis of these circuits, including the design and analysis of each stage, continues to be a challenging task (Ghobadi, Yahyaei, & Banisi, 2011). A designer initially solves a synthesis problem (for any process) by trial-and-error. There are many arrangements of a concentration circuit that correspond to an acceptable trial-and-error solution; however, many of these arrangements can be incorrect, ineffective or uneconomical, which is realized when feedback on an existing process becomes available. Concentration circuits commonly evolve over time solving a number of existing problems while creating new ones (Schena & Casali, 1994). Several methods for the design of these circuits have been presented in the literature; these methods attempt to develop a systematic procedure to replace the trial-and-error method, which is time-consuming and requires much experimentation. Among the methods developed are those that use heuristics to develop a feasible design or that improve an existing design (Connolly & Prince, 2000). However, these procedures use rules that are not always satisfied or that contradict each other and therefore do not guarantee an optimal design. Other methods use optimization or mathematical programming procedures (Cisternas et al., 2006, Ghobadi et al., 2011 and Méndez et al., 2009b) using a superstructure to create a set of alternatives from which an optimum design can be selected. However, the use of these methods requires training in optimization techniques because the problems are usually formulated as MINLP models for which there are no commercial codes available that ensure optimality. For the aforementioned reasons, none of the developed methodologies are widely used in industry. The concentration stage is difficult to model, and ore characteristics vary among mining operations. Currently, there is no theoretical model that can predict the floatability of different species of a mineral and thus experimentation is necessary to develop models that can be used to design these systems. However, these experimentally based models have a limited range of application depending on the experimental conditions and the number of experiments used. The compositions and mineralogical species vary among mining operations, which in turn affects the floatability behavior and undermines the model validity as well as the operational parameters that are limited based on design ranges. Thus, there are at least two sources of uncertainty: the model and the ore characteristics. Sensitivity analysis (SA) can be employed to address uncertainties in the model and application scenarios, thereby facilitating the evaluation of process structures and operational behaviors. Lucay, Mellado, Cisternas, and Gálvez (2012) applied a local SA to analyze and design separation circuits. The authors studied the effect of each stage on the general circuit by identifying the relation between the recovery rate of each stage and the global recovery rate of the circuit. Mellado, Gálvez, Cisternas, and Ordoñez (2012) applied local SA to heap leaching to validate the analytical model as well. However, local SA only considers the neighborhood of the input variation, and the effect of each input parameter is measured by keeping all the other input parameters at their nominal values. Global sensitivity analysis (GSA) can overcome these limitations and has other advantages (Saltelli, Tarantola, & Campolongo, 2000). Fesanghary, Damangir, and Soleimani (2009) studied the use of GSA and a harmony search algorithm for the design optimization of shell and tube heat exchangers (STHXs) from the economic viewpoint. GSA was used to reduce the size of the optimization problem; non-influential geometrical parameters that have the least effect on total cost of STHXs are identified and are ignored in the optimization calculation. Later, Schwier, Hartge, Werther, and Gruhn (2010) used GSA in the flow sheet simulation of solid processes, which allowed for the examination and quantification of the influences of given parameters on specific target criteria. GSA was used to decrease the effort required for the parameter estimation in a given process simulation by focusing the effort on the most influential parameters. This work attempts to show how a GSA can be used in the analysis, design and retrofit of concentration circuits and the equipment that compose it. This work is expected to complement current design techniques, such as trial-and-error methods, heuristics or optimization. Various methodologies of GSA are analyzed and the effect of the nature of the uncertainty of the input factors is studied.

Based on these case studies, we conclude that GSA is a tool that can help analyze, design and improve processes. The Morris, Sobol and E-FAST methods give similar results, which is why the Morris method is recommended because of its computationally inexpensive nature. The type of distribution function and the ranges of the values of the input factors have an effect on the results. If the range in which an input factor can be changed is known, those values should be used. If not, ranges proportional to the mean values should be used. The GSA methods help to identify the process behavior and/or help to identify the most important process stages that affect a given process variable (model output). With this information, it is possible to redesign or change the operational condition to improve processes’ performance. We conclude that using the stage's recoveries of each species as input factors is a suitable choice for a GSA of a flotation plant. Once key stages have been identified to improve the process, experimental tests, modeling and analyses can be used to improve the plant.