**Gonzalo R. Quezada 1, Matías Jeldres 2,3, Norman Toro 4, Pedro Robles <sup>5</sup> and Ricardo I. Jeldres 3,\***


Received: 18 January 2020; Accepted: 24 February 2020; Published: 2 March 2020

**Abstract:** Experimental assays and mathematical models, through population balance models (PBM), were used to characterize the particle aggregation of mining tailings flocculated in seawater. Three systems were considered for preparation of the slurries: i) Seawater at natural pH (pH 7.4), ii) seawater at pH 11, and iii) treated seawater at pH 11. The treated seawater had a reduced magnesium content in order to avoid the formation of solid complexes, which damage the concentration operations. For this, the pH of seawater was raised with lime before being used in the process—generating solid precipitates of magnesium that were removed by vacuum filtration. The mean size of the aggregates were represented by the mean chord length obtained with the Focused beam reflectance measurement (FBRM) technique, and their descriptions, obtained by the PBM, showed an aggregation and a breakage kernel had evolved. The fractal dimension and permeability were included in the model in order to improve the representation of the irregular structure of the aggregates. Then, five parameters were optimized: Three for the aggregation kernel and two for the breakage kernel. The results show that raising the pH from 8 to 11 was severely detrimental to the flocculation performance. Nevertheless, for pH 11, the aggregates slightly exceeded 100 μm, causing undesirable behaviour during the thickening operations. Interestingly, magnesium removal provided a suitable environment to perform the tailings flocculation at alkaline pH, making aggregates with sizes that exceeded 300 μm. Only the fractal dimension changed between pH 8 and treated seawater at pH 11—as reflected in the permeability outcomes. The PBM fitted well with the experimental data, and the parameters showed that the aggregation kernel was dominant at all-polymer dosages. The descriptive capacity of the model might have been utilized as a support in practical decisions regarding the best-operating requirements in the flocculation of copper tailings and water clarification.

**Keywords:** copper tailings; enhanced flocculation; water recovering; magnesium removal; population balance model; seawater flocculation
