The development of a mathematical model for the bioextraction of the critical raw material magnesium from mine waste using acidithiobacillus caldus

Raeburn, Yael

The development of a mathematical model for the bioextraction of the critical raw material magnesium from mine waste using acidithiobacillus caldus

Thesis / Dissertation

2025

Publisher

University of Cape Town

Department

Department of Chemical Engineering

Faculty

Faculty of Engineering and the Built Environment

Abstract

This investigation aimed to develop a model to describe the bioleaching of magnesium mine wastes, ultimately maximising magnesium extraction while minimising reliance on synthetic acid. In the absence of experimental data on the dissolution profiles of the waste, kinetic models were developed to describe the leaching of individual minerals: periclase, calcite, and goethite. These leaching kinetics, combined with the extracted microbial growth kinetics for Acidithiobacillus (At.) caldus, formed the basis of the bioleaching model. Both batch and continuous flow reactor systems were investigated for their suitability and performance in magnesium recovery. The system was optimised using a pH control system and a two-stage flowsheet design. Chemical leaching kinetics were determined by fitting the models to experimental data from the liter-ature. The extracted reaction orders were 0.3, 3 and 1 for periclase, goethite and calcite, respectively. This indicated that iron dissolution was most sensitive to pH, while magnesium dissolution was the least. The relative magnitude of the activation energies suggested that calcium would dissolve most readily, followed by magnesium, and then iron under the same reaction conditions (EaCa = 32 kJ/mol, EaM g = 67.8 kJ/mol, average EaF e = 90.2 kJ/mol). Investigation into two goethite samples of differing crystal morphologies demonstrated negligible impact on dissolution rate, with only a 0.01 kJ/mol variation per 1 dm2/g difference in surface area. To investigate the production rate of the biogenic acid lixiviant, At. caldus, a chemoautotrophic microor-ganism that oxidises elemental sulfur, was used to facilitate the production of sulfuric acid. Both the Monod and Michaelis-Menten equations were investigated to describe the growth kinetics, assuming 55% availability of initial elemental sulfur due to limited surface area availability for microbial attachment. The Monod expression yielded a maximum specific growth rate (μmax) of 0.275 h−1 and a saturation coefficient (Ks) of 1.5 mol/L, resulting in a maximum sulfate production rate (rp,max) of 0.0009 mol/Lh. However, the model incorporating the Michaelis-Menten equation provided more accurate pH predic-tions throughout the experimental duration, making it more reliable for predicting the acid production rate. Consequently, a Michaelis constant (Km) of 2.25 mol/L, maximum utilisation rate (Vmax) of 0.008 mol/Lh, and maximum sulfate production rate (rp,max) of 0.0004 mol/Lh were incorporated in the subsequent investigations. The extracted chemical leaching and microbial kinetics were combined to describe the bioleaching system in which the acid produced by the oxidation of elemental sulfur by At. caldus leached magnesium, calcium, and iron from the magnesium mine waste. Development of the batch system showed that calcium dissolved rapidly, consuming most of the initial acid. Magnesium followed, reacting with the remaining acid and the biogenic acid as it was produced, indicating that the rate of biooxidation was the rate-limiting step. Negligible iron dissolution was observed. Systematic optimisation of the initial pH and solids loading resulted in optimised conditions of pHi = 1 and 0.75% solids loading (m/v). These conditions achieved 98.5% extraction of magnesium, complete extraction of calcium, and a processing throughput of 0.005 gM g−waste/h over a 60 day period. Two configurations were developed for the continuous flow system: one without acid addition and the other introducing acid in the reactor feed. The former resulted in similar dissolution profiles to the batch system, with complete extraction of calcium at pHi ≤ 2. However, magnesium extraction remained ∼35.6% across pHi 1-3 due to the limited rate of acid production. The optimised system achieved 100% calcium extraction with 82.3% of the magnesium going into solution at an equivalent throughput to the batch system (0.005 gM g−waste/h). Operating at 0.5% solids loading (m/v), pHi = 2 and τ = 41.7 days. The inclusion of acid in the reactor feed (pHin = pHi) significantly increased the extraction of magnesium from 35.6% to 80% at pHi = 1. The optimised case (pHi = pHin = 1, 1 0.5% solids loading, τ = 14.6 days) achieved complete extraction of both magnesium and calcium at a throughput of 0.014 gM g−waste/h. However, the addition of acid did not align with the project's aim of decreasing the demand for synthetic acid. With this in mind, the CSTR system was further optimised by investigating the high-impacting param-eters: pH and mean residence time. Implementation of a two-stage system allowed for the independent optimisation of the microbial oxidation stock (Vs), and mineral (V1) reactors. Using the previously de-termined mineral reactor conditions (0.5% solids loading, τ1 = 14.6 days, pHi = 1), complete extraction of magnesium was achieved at a stock reactor mean residence time (τs) ≥ 10.4 days, establishing an optimal threshold at Vs : 1.4V1. This set-up achieved the same performance as the CSTR with acid in the feed while eliminating the need for synthetic acid. pH control was achieved using a PI controller for the rate of acid addition, for which ITAE tuning parameters were optimised for both disturbance (Kc = 40.7 mol−1.L, τI = 12 h) and set-point changes (Kc = 20 mol−1.L, τI = 326 h). The control system improved the system response times from 14 days to 11.5 and 9 days in the case of a set-point change and disturbance, respectively, while maintaining stable operation. The predictive model developed provided a fundamental understanding of the bioleaching mechanisms. However, the extraction of the CRM, magnesium, was limited by the rate of biooxidation in the CSTR system (with no additional acid) and the batch system. The single-stage CSTR with acid in the reactor feed achieved complete extraction of magnesium, processing 0.014 gM g−waste/h. Implementing a two-stage process achieved the same degree of extraction as the single-stage system while eliminating the need for synthetic acid. pH control decreased the system's natural response time to both set-point changes and disturbances. While this model combined individual chemical leaching and microbial growth kinetics, it is recommended that this model be validated against experimental data for the dissolution of complex waste. This would allow for the validation of selective extraction at different pH levels and confirm whether the effects of surface area are negligible for waste samples.

Keywords

Waste

Acidithiobacillus caldus

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