Exposition of Applications of Uncertainty Quantification to Modeling Pyrometallurgical Processes Using a Model of Copper Fire Refining as an Example

Additonal authors: Krane, M.J.M.. Book title: Proceedings of the 58th Conference of Metallurgists Hosting Copper 2019. Chapter: . Chapter title:

Proceedings, Vol. Proceedings of the 58th Conference of Metallurgists Hosting Copper 2019, 2019

Mather, P.E.

Uncertainty quantification is a means of articulating the reliability of model estimations. Models of copper pyrometallurgical processes have been published for decades but discussion of their reliability has typically been terse and qualitative, mitigating understanding of their exact applicability to industrial situations. This presentation shows basic uncertainty propagation and Bayesian model calibration, two powerful uncertainty quantification tools, applied to a reduced order model of copper fire/anode refining. The implications of the uncertainty quantification analyses on the applicability of the model results to industrial practice are then discussed. Finally, other possible applications of uncertainty quantification to copper extractive metallurgy are explored. INTRODUCTION Modern copper production operations, including mining operations through wire drawing factories, are ubiquitously heavily instrumented. Most mine-sites and smelters have large repositories of historical data. That said, much of this data is not exploited to its maximum effect. This proceeding provides examples of using uncertainty quantification (UQ) to maximize the informational yield of the data collected from a fire-refining operation. Anode/Fire Refining is the final pyrometallurgical step in the production of copper anodes; it is an essential and universally employed processing step at smelters (Schlesinger, King, Sole, & Davenport, 2011). Much like the smelting and converting furnaces further up the process stream, anode furnaces are difficult to instrument due to their high temperature and the corrosive and/or caking quality of their offgas. This makes continuous and accurate measurement of the streams leaving the unit operation, e.g. liquid copper, slag, and offgas very difficult. As an example, offgas flowmeters, while providing continuous draft values, could miss the actual draft value by tens of percent due to caking or corrosion. UQ methods account for the uncertainty in process measurements and parameter values; they use a process model with measurements of performance indices to provide better and better estimations of process performance. This proceeding will first introduce a surrogate model for copper fire refining, made from a 1D, transient, reacting flow model of the process presented elsewhere in these proceedings (Mather & Krane, 2019). Discussion of the data used to make the surrogate model, as well as the creation of the surrogate model, will be included. Then, a Monte Carlo simulation will be performed, showing the expected soot production rate based on the surrogate model and assumptions about the uncertainty in the model’s parameters. Finally, the surrogate model parameters will be calibrated in a Bayesian way; this will tell what the actual uncertainty in the parameters are, given a set of observed industrial data and prior assumptions of the observations’ and parameters’ uncertainty.
Keywords: Copper 2019, COM2019