Mathematical modeling of thermophilic bioleaching of chalcopyrite

Previous studies have shown that the different preferences of thermophiles to oxidize S⁰ or Fe²⁺ is reflected by different [Fe³⁺]/[Fe²⁺] levels in solution. In those studies it was concluded that [Fe³⁺]/[Fe²⁺] governs the thermophilic bioleaching of chalcopyrite rather than temperature or pH. Therefore, the proposed model is mainly based on the finding that thermophilic bioleaching of chalcopyrite is governed by [Fe³⁺]/[Fe²⁺] that result from the activity of thermophiles. A direct interaction between chalcopyrite and thermophiles is neglected because it has been reported that this is not a general behavior for all thermophiles. The case of constant temperature, initial pH 1.5-2.5, and chalcopyrite concentrates is considered. The main assumption is that chalcopyrite can be anodically oxidized or cathodically reduced depending on [Fe³⁺]/[Fe²⁺] in solution. When chalcopyrite is oxidized at high [Fe³⁺]/[Fe²⁺] levels, Cu²⁺ is formed directly at low rates: CuFeS₂ + 4Fe³⁺ → Cu²⁺ + 5Fe²⁺ + S⁰. Whereas, when chalcopyrite is reduced at low [Fe³⁺]/[Fe²⁺] levels, an intermediate (Cu₂S) is formed at higher rates: CuFeS₂ + Fe²⁺ + Cu²⁺ + 2H⁺ → Cu₂S + 2Fe³⁺ + H₂S. Because the oxidation of Cu₂S is relatively fast: Cu₂S + 4Fe³⁺ → 2Cu²⁺ + S⁰ + 4Fe²⁺, its accumulation is assumed to be negligible. To take into account the possibility of chalcopyrite being oxidized or reduced depending on [Fe³⁺]/[Fe²⁺] in solution, the principle of mixed potentials is used. The model is validated by comparing the calculated and measured values of copper extraction, total iron in solution, and pH.