**3. Methodology**

The combustion tests were performed to detect spectral characteristics of interest associated with copper oxides. The emission spectrum of a flame represented by I (λ, *T*) = Ic (λ, *T*)+Id (λ, *T*)+Imol (λ, *T*) + *n*, where λ is a wavelength sample, *T* is the flame temperature, Ic is the baseline, Imol and Id are components associated with molecular and elementals emissions (discontinuous), respectively [21], and *n* is a noise component related to the electronics and detectors themselves. The spectral range and the number of sampled wavelengths were defined by the spectrometer. Research methods and considerations are represented below.

#### *Experimental Setup and Sample Characteristic*

Briefly, the combustion experiments were performed in a bench-scale setup consisting of a drop-tube reactor under laminar flow conditions and heated by a controlled electrical furnace at 1273 K (Figure 1). The spectral data acquisition was composed of cooled optical fiber (Avantes®) and a VIS–NIR spectrometer (Ocean Optics USB4000®) which is sensitive in the spectral range between 344 and 1034 nm and can deliver 3648 wavelengths samples in such a range.

**Figure 1.** (**a**) Experimental setup [15] and (**b**) schematic diagram.

The measurement and interpretation of the emitted radiation from the cloud of particles in the reactor is a difficult task, especially for copper concentrates, since it involves many chemical and physical processes and interactions between the particles and the particles with their surroundings. In Figure 2, a sample of the incandescent cloud generated

during combustion is depicted. This figure also summarizes the spectral data acquisition and the implemented methodologies to process and analyze the spectral information.

**Figure 2.** Data acquisition and analysis pipeline. (**a**) Spectral data acquisition and preprocessing. (**b**) Principal component analysis (PCA) features extraction. (**c**) Multivariate curve resolution method alternate least squares (MCR-ALS) application for separation of pure spectral signals. Note that the depicted combustion image is only for visualization purposes, and the optical fiber is located at the central centered position.

In this research, spectral data processing with multivariate data analysis methods were implemented to extract important characteristics related to the formation of copper oxides. PCA was used for an exploratory analysis on the data matrix containing all the spectral information, whilst MCR-ALS was used to deconvolve the original emission spectrum based on its pure spectral components. The airPLS (adaptive iteratively reweighted penalized least squares) algorithm baseline correction [16,22] was used to unmix the continuous and discontinuous spectral components to ensure that the analysis was on the chemical behavior of the combustion and not on its energy. The data analysis was carried out in MATLAB™ (MathWorks, Inc., Natick, MA, USA) with the PLS Toolbox 8.9 (Eigenvector Research, Inc., Manson, WA, USA) and MCR-ALS GUI 2.0.

The chalcopyrite sample was purchased from Ward's Science® (Rochester, NY, USA), while the concentrate was donated by a Chilean mining company. The predominant mineralogical composition of the concentrates is detailed in Table 1.

**Table 1.** Copper concentrate mineralogical composition.


In this research, eight sets of tests were carried out. Six of them consisted of the combustion of chalcopyrite at different particle sizes, corresponding to 105 to 149, 74 to 105, 53 to 74, 44 to 53, 37 to 44, and <37 μm. From now on, these samples will be referred to as CpyA, CpyB, CpyC, CpyD, CpyE, and CpyF respective to the previous order. The

concentrates used had a granulometric distribution with a p80 of ~36 μm for sample Conc. A and ~47 μm for sample Conc. B. A Sympatec Helos-Succel™ particle size analyzer based on a diffraction laser was used for the particle size analysis. All the laboratory experiments were carried out under similar conditions. In addition, we worked with oxygen supply three times over the stoichiometric quantity to ensure the total oxidation of the chalcopyrite and the sulfurized species in the concentrates to form copper oxides. The calcines obtained in each test were analyzed using scanning electronic technology. For more details about the methodology and special considerations, see Toro et al. [16].
