Analysis of kinetic models for chalcopyrite flotation: effect of operating parameters

Influence of operating parameters on nanobubble-assisted flotation of graphite

04/02670 Reduced ductility of in-service 9Cr1Mo piping revealed during welding procedure qualification: Gray, G. M. and Croker, A. B. L. International Journal of PressureVessels and Piping, 2004, 81, (6), 543–555

The efficiency of froth flotation, a cornerstone of modern mineral processing, depends strongly on the chemistry of frothing agents that regulate froth formation, stability, and dynamics. This study investigates the effect of frother type and dosage on froth height, stability, bubble morphology, and flotation kinetics through laboratory-scale and industrially relevant experiments. A set of frothers, including conventional methyl isobutyl carbinol (MIBC) and advanced reagents such as T-92, Penoflot-1304, TPM, DF-1012, and three composite formulations, were systematically evaluated. Surface tension measurements, critical coalescence concentration (CCC) analysis, and pendant-drop techniques were applied to characterize physicochemical properties, while chalcopyrite flotation tests provided kinetic data and recovery profiles. Results revealed clear structure–property–performance relationships. MIBC promoted rapid froth generation but limited stability, whereas complex reagents such as DF-1012 and TPM produced highly stable froths with persistent fine bubbles. Kinetic modeling showed that composite frothers, particularly Composition-3, markedly enhanced chalcopyrite recovery, achieving flotation rate constants up to 0.24 min⁻¹ compared with 0.10 min⁻¹ for MIBC. In addition, economic and environmental assessments indicated that novel frothers can lower reagent consumption while improving selectivity and sustainability. Overall, this study establishes a direct link between frother chemistry and froth layer dynamics, providing practical guidelines for reagent selection in sulfide ore flotation. The findings not only improve metallurgical performance but also highlight pathways toward more sustainable and environmentally responsible mineral processing.

In recent years, most of the studies have been adapted to determine the optimum conditions for the flotation of very fine minerals. In this context, besides parameters such as particle size, morphology, and pH, the effects of frother type and its concentration present a very significant role in optimizing the flotation conditions. Therefore, the effects of froth stability during flotation can be considered one of the most important issues. Considering that knowledge in mind, in this study, the foamability and froth decay rate of six frothers (PPG200, PPG400, PPG600, BTEG, BTPG, and BDPG) having different molecular weights but similar polyglycol structures were investigated. In addition, methyl isobutyl carbinol (MIBC) which is a well-known frother type in the industry was also used as a reference. Additionally, a series of tests were also performed in the presence of collectors (Dodecylamine hydrochloride, DAH, and sodium oleate, NaOL) + frother mixtures to mimic the flotation conditions. The results of these tests indicated that the bubble size became finer at even low concentrations of PPG600 and PPG400 frothers. Following that, a significant decrease in bubble size was also found for the collector + frother mixtures system regardless of the concentration of the frothers.

A linear relationship has been found under certain conditions between the 1st order flotation rate constant, k, and Sb, the bubble surface area flux produced in a flotation cell. Sb is the total surface area of bubbles moving up through a unit cell cross-sectional area per unit time and gives a measure of the hydrodynamic and gas dispersion properties in the cell. This relationship has been found to be independent of the size of the cell and, in mechanical cells, independent of the type of impeller used ie. method of Sb production, which allows scale-up possibilities. These findings are, however, only related to metalliferous flotation in conventional mechanical cells and to date no work has been carried out to study this effect in coal or non-conventional cells. The aims of this thesis were to firstly determine whether the k-Sb relationship, which has found to be an effective scale-up tool for base metal flotation, is evident in coal flotation and secondly, to determine whether it exists for non-conventional flotation technologies, commonly used in coal flotation. Testwork was performed at two industrial sites and consisted of: . • Site measurements of bubble size, superficial air velocity and air hold-up to determine the value of Sb in operating plant scale cells. This characterised the particular cell under investigation and identified the existing hydrodynamic conditions. The measurements were combined with conventional sampling of feed and products followed by analysis and mass balancing to reveal the prevailing rate constant k. . • Simultaneous operation of the JKMRC 60 litre conventional flotation cell or pilot scale Jameson cell (depending on plant cell being used) in parallel with the site cell under investigation. It was possible to make major changes to the operating conditions of the test cell (as opposed to the site cell) in order to determine the k-Sb relationship for the coal under investigation. . • Measurement of froth recovery in site cells. The effect of froth residence time and other parameters on froth recovery was determined in the 60-litre conventional cell or pilot Jameson cell. • Keeping the cell hydrodynamic conditions (as specified by the Sb value) fixed, and independently evaluating the effect of other parameters such as reagent regime and froth depth, using the 60-litre cell. Results for conventional flotation (and, it is assumed, all coal flotation) showed that particle size and feed composition effects are significant and can override the effect a change in Sb has on cell performance. Decoupling these effects indicated a distinct relationship between Sb and flotation rate. Also, the range of Sb values under which linearity is maintained was found to be limited. Further work to investigate these effects in more detail was unsuccessful, therefore additional testwork is recommended to enable firm conclusions to be made. Feed changes made analysis of the effect of the froth phase inconclusive for the conventional cell, however, the froth phase was found to be a significant factor in the performance of the plant scale Microcel. It was found that conditions inside the downcomer of the Jameson cell appear to be most significant in terms of the k-Sb relationship, indicating that, in line with popular opinion, collection occurs solely within the downcomer of the Jameson cell. Conditions in the pilot scale Jameson cell rig exhibited perfect mixing behaviour with mixing conditions in the plant cell inconclusive but most likely perfect mixing or axial dispersion with large amounts of dispersion. Improvements in gas dispersion measurement techniques in the plant cells, in particular bubble size, need to be developed for specific application to coal flotation to allow further investigation into the findings of this work.

We monitored the occupancy of a functionally important non-coordinated water molecule in the distal heme pocket of sperm whale myoglobin over the pH range 4.3-9.4. Water occupancy was assessed by using time-resolved spectroscopy to detect the perturbation of the heme visible band absorption spectrum caused by water entry after CO photodissociation ( Goldbeck, R. A., Bhaskaran, S., Ortega, C., Mendoza, J. L., Olson, J. S., Soman, J., Kliger, D. S., and Esquerra, R. M. (2006) Proc. Natl. Acad. Sci. U. S. A. 103, 1254-1259 ). We found that the water occupancy observed during the time interval between ligand photolysis and diffusive recombination decreased by nearly 20% as the pH was lowered below 6. This decrease accounted for most of the concomitant increase in the observed CO bimolecular recombination rate constant, as the lower water occupancy presented a smaller kinetic barrier to CO entry into the pocket at lower pH. These results were consistent with a model in which the distal histidine, which stabilizes the water molecule within the distal pocket by accepting a hydrogen bond, tends to swing out of the pocket upon protonation and destabilize the water occupancy at low pH. Extrapolation of this model to lower pH suggests that the additional increase in ligand association rate constant observed previously in stopped-flow studies at pH 3 may also be due in part to reduced distal water occupancy concomitant with further His64 protonation and coupled protein conformational change.

Differential flotation of pyrite and arsenopyrite: Effect of hydrogen peroxide and collector type

The present study investigated the effects of rhamnolipid (RL) biosurfactant on the flotation performance of a coal sample. The significance of the effect of RL on the system responses, including ash content, coal recovery, yield and separation efficiency, and process kinetics and selectivity, was statistically assessed using One-Way Analysis of Variance (ANOVA) methodology. The ANOVA results revealed that adding RL to the system significantly challenged the studied metallurgical aspects. Briefly, RL biosurfactant depressed coal flotation through physical interaction with the surface of coal particles through chemical bonding between the carboxyl group in the RL structure with those on the surface of coal particles. The potential mechanisms involved were schematically proposed. The correlation between the condition of RL addition and process responses was modeled using the Artificial Neural Network (ANN) approach. Rested in the mean squared error (MSE), root mean squared error (RMSE), and percentage error as the measures of model accuracy, the Levenberg-Marquardt algorithm (LMA) with [7–16-1] structure was found to be the most reliable algorithm to predict the process response. As evidenced, the correlation coefficient values of test data were 98.09%, 96.93%, 98.37%, 98.46%, 99.50%, and 97.37% for ash content, coal recovery, yield, separation efficiency, the rate constant, and selectivity index, respectively. These values confirmed that the process could be simulated using the ANN method with an appropriate structure.

A biosurfactant-producing bacterial species (Pseudomonas aeruginosa) was grown in a mineral solution with gas oil as the source of carbon and energy. The biosurfactant was recovered from the solution by collecting the foam on the surface and drying. It had critical micelle concentration of 100 ppm. Froth characterization showed that the biosurfactant was superior to methyl isobutyl carbinol (MIBC) in terms of froth height and stability. The biosurfactant was examined in coal flotation as a frother. The combustible matter recovery of 72–79% with 10–15.5% ash content supporting 55–57.5% separation efficiency seemed promising enough to introduce the biosurfactant from Pseudomonas aeruginosa as a new frother.

3 - Frothers

Cytotoxicity associated with pathophysiological Ca(2+) overload (e.g. in stroke) appears mediated by an event termed the mitochondrial permeability transition (mPT). We built and solved a kinetic model of the mPT in populations of isolated rat liver mitochondria that quantitatively describes Ca(2+)-induced mPT as a two-step sequence of pre-swelling induction followed by Ca(2+)-driven, positive feedback, autocatalytic propagation. The model was formulated as two differential equations, each directly related to experimental parameters (Ca(2+) flux/mitochondrial swelling). These parameters were simultaneously assessed using a spectroscopic approach to monitor multiple mitochondrial properties. The derived kinetic model correctly identifies a correlation between initial Ca(2+) concentration and delay interval prior to mPT induction. Within the model's framework, Ru-360 (a ruthenium complex) and Mg(2+) were shown to compete with the Ca(2+)-stimulated initiation phase of mPT induction, consistent with known inhibition at the phenomenological level of the Ca(2+) uniporter. The model further reveals that Mg(2+), but not Ru-360, inhibits Ca(2+)-induced effects on a downstream stage of mPT induction at a site distinct from the uniporter. The analytical approach was then applied to promethazine, an FDA-approved drug previously shown to inhibit both mPT and ischemia-reperfusion injury. Kinetic analysis revealed that promethazine delayed mPT induction in a manner qualitatively distinct from that of lower concentrations of Mg(2+). In summary, we have developed a kinetic model to aid in the quantitative characterization of mPT induction. This model is consistent with/informative about the biochemistry of several mPT inhibitors, and its success suggests that this kinetic approach can aid in the classification of agents or targets that modulate mPT induction.

It is essential to know the process efficiency in the industrial magnetic separation process under different operating conditions because it is required to control the process parameters to optimize the process efficiency. To our knowledge, there is no information about using artificial intelligence for modeling the magnetic separation process. Hence, finding a robust and more accurate estimation method for predicting the separation efficiency and selectivity index is still necessary. In this regard, a feed-forward neural network was developed to predict the separation efficiency and selectivity index. This model was trained to present a predictive model based on the percentage of iron, iron oxide and sulfur in mill feed and cobber feed, 80% passing size in mill feed and cobber feed and plant capacity. Therefore, this work aims to develop an intelligent technique based on an artificial neural network and a hybrid neural-genetic algorithm for modeling the concentration process. Results indicated that the values of mean square error and coefficient of determination for the testing phase were obtained 0.635 and 0.86 for selectivity index and of 4.646 and 0.84 for separation efficiency, respectively. In order to improve the performance of neural network, genetic algorithm was used to optimize the weights and biases of neural network. The results of modeling with GA-ANN technique indicated that the mean square error and coefficient of determination for the testing phase were achieved by 0.276 and 0.95 for selectivity index and of 1.782 and 0.92 for separation efficiency, respectively. The other statistical criteria for the GA-ANN model were better than those of the ANN model.

Upgrading titanium bearing Na-feldspar by flotation using sulphonates, succinamate and soaps of vegetable oils

The present study evaluates the performance of ion flotation process for removal of uranyl tricarbonate complex, UO2(CO3)3 4−, which is the dominant species in many aqueous media particularly seawater, from aqueous solutions using cetyltrimethylammonium bromide, CTAB, as a cationic surfactant. Flotation of UO2(CO3)3 4− as a function in the solution pH is investigated in absence and in presence of carbonate. Removal percentage >99% is achieved in the pH range 8.5–11.5 in presence of 5×10−3 M carbonate. The influence of concentrations of ethanol (0.1–2% v/v) and CTAB (5×10−5–1.4×10−3 M) show that UO2(CO3)3 4− is efficiently removed at concentrations of 0.5–1.5% v/v and 4×10−4–1×10−3 M, respectively. Based on the obtained kinetic data, the flotation mechanism and the flotation rate are investigated using two different flotation models. Floatability of UO2(CO3)3 4− in presence of different cations (Ba2+, Ca2+, Mg2+ and Sr2+) and anions (NO3 −, Br−, Cl−, SO4 2− and HPO4 2−) is studied. Except for Mg2+ and NO3 −, the flotation efficiency of UO2(CO3)3 4− is significantly decreased at concentrations higher than 1×10−3 and 5×10−3 M of the studied cations and anions, respectively. Ion flotation process is efficiently applied for removal of uranium(VI), R%>98.5%, from seawater. Accordingly, ion flotation can be considered as a promising technique and thus its feasibility for removal and/or recovery of uranium(VI) from many aqueous environment.

Sulfide lead resources are being depleted and the exploitation of carbonate lead deposits is now the main focus of lead mining. Cerussite, PbCO3, is majorly discarded to tailing damps because it is difficult to be processed by flotation in lead concentration units. This paper not only investigates the optimization of cerussite flotation, but it also proposes a model for predicting the recovery. Froth flotation was used for cerussite recovery from a previously existing tailing damp in the ChahGaz mine in Kerman Province, Iran. The response surface method was used for experimental design and optimization of Pb flotation in which a statistical experimental model was suggested to model flotation kinetics based on the effective parameters. The results showed that particle size, pH, solid content, Na2S dosage, collector dosage and collector type to be the most effective parameters. These parameters were applied for investigating flotation kinetics. A three-fraction (with seven-parameter) flotation model, with fast, medium and slow kinetics rate constants was obtained via 64 designed tests. The proposed model showed a good agreement with experimental data (R2 more than 0.8). Also optimum conditions of cerussite flotation were set at pH= 9, d80= 53 µm, solid content= 26%, Na2S= 4000 g/t and collector dosage = 1500g/t of PAX.