Optimal control problems arising in the zinc sulphate electrolyte purification process

Before zinc electrolysis, zinc powder is added to the zinc sulphate electrolyte solution to facilitate the removal of harmful metallic ions. This purification process can be modeled by a time delay differential equation. Since some of the parameters in this model are unknown, zinc powder is normally added excessively. We use an optimization technique to estimate the unknown parameters from experimental data. Then, we formulate an optimal control problem to minimize the amount of zinc powder added. We solve this optimal control problem numerically by using the control parametrization method. The results indicate that the amount of zinc powder added can be decreased, on average, by approximately 7%

A class of optimal state-delay control problems

We consider a general nonlinear time-delay system with state-delays as control variables. The problem of determining optimal values for the state-delays to minimize overall system cost is a non-standard optimal control problem – called an optimal state-delay control problem – that cannot be solved using existing optimal control techniques. We show that this optimal control problem can be formulated as a nonlinear programming problem in which the cost function is an implicit function of the decision variables. We then develop an efficient numerical method for determining the cost function’s gradient. This method, which involves integrating an auxiliary impulsive system backwards in time, can be combined with any standard gradient-based optimization method to solve the optimal state-delay control problem effectively. We conclude the paper by discussing applications of our approach to parameter identification and delayed feedback control

Influence of lead impurity and manganese addition on main operating parameters of zinc electrowinning

L'influence des ions Pb2+ sur le dépôt de zinc a été étudiée dans l'électrolyte acide de sulfate de zinc avec et sans Mn2+. La polarisation galvanostatique, la polarisation potentiodynamique, la voltammétrie cyclique (VC), les mesures de bruit électrochimique (MBE) et la spectroscopie d'impédance électrochimique (SIE) en conjonction avec la microscopie électronique à balayage (MEB) et la diffraction des rayons-X (XRD) ont été considérés. L'effet de différents paramètres de fonctionnement tels que la concentration de Zn2+, la concentration d’acide sulfurique, la densité de courant, l'agitation de l’électrolyte et la température a été étudié en présence de Mn2+ et Pb2+. Les résultats galvanostatiques utilisant un électrolyte standard de zinc contenant 12 g/L de Mn2+ (ES) ont montré que les ions de plomb ajoutés à l’ES conduisaient à une augmentation du potentiel cathodique et de l'efficacité de courant (EC) du dépôt de zinc. L'augmentation de la concentration de Mn2+ dans l'électrolyte a entraîné une diminution du potentiel cathodique et d’EC du dépôt de zinc à cause de l'effet de dépolarisation du MnO4- formé. En outre, l'augmentation de la densité de courant de 45 à 60 mA/cm2 et de l'agitation de 60 à 412 tr/min ont donné lieu à une augmentation du potentiel et à une diminution d’EC. L'augmentation de la température de 35 à 45°C a conduit à une diminution du potentiel cathodique. Pour l'électrolyse de longue durée (72 h), la teneur de Pb dans le dépôt de zinc en utilisant l'anode Pb-0,7%Ag était de 1,90-1,98 ppm, presque équivalente à celle employant l'anode de Pt avec l’addition de 0,15-0,2 mg/L de Pb2 +. L'électrolyse à 40°C et 52,5 mA/cm2 en présence de plomb jusqu'à 0,1-0,2 mg/L dans un électrolyte contenant 12 g/L Mn2+ pourrait être considérée comme des meilleurs paramètres opérationnels pour le procédé d'extraction électrolytique. Les études SIE ont montré que le dépôt de zinc sur le zinc est plus facile que celui du zinc sur l'aluminium. L’analyse des MBE a révélé que l'augmentation des concentrations de Pb2+ (0,05-0,8 mg/L) dans l'électrolyte de zinc sans Mn2+ s'accompagne d'une diminution de l'inclinaison et d'une augmentation des valeurs du kurtosis qui puissent être corrélées à la morphologie du dépôt de zinc.The influence of Pb2+ ions on zinc deposition was investigated in acidic zinc sulfate electrolyte with and without Mn2+ ions. Galvanostatic polarization, potentiodynamic polarization, cyclic voltammetry (CV), electrochemical noise measurements (ENM) and electrochemical impedance spectroscopy (EIS) in conjunction with scanning electron microscopy (SEM) and X-ray diffraction (XRD) have been considered. Effects of different operating parameters such as Zn2+ ions concentration, sulfuric acid concentration, current density, electrolyte agitation and temperature were investigated in presence of Mn2+ and Pb2+ ions. The galvanostatic results using standard zinc electrolyte containing 12 g/L Mn2+ (SE) showed that lead ions added to the SE led to an increase in the cathodic potential and current efficiency (CE) of zinc deposit. Increasing Mn2+ concentration in the electrolyte resulted in decrease of cathodic potential and CE of zinc deposit due to the depolarization effect of formed MnO4-. In addition, increases of current density from 45 to 60 mA/cm2 and agitation from 60 to 412 rpm resulted in an increase of overpotential and decrease of CE. Increase of temperature from 35 to 45°C led to a decrease of cathodic potential. For long time electrolysis (72 h), the Pb content in zinc deposit using Pb-0.7%Ag anode was 1.90-1.98 ppm, almost equivalent to that employing Pt anode with addition of 0.15-0.2 mg/L of Pb2+. Electrolysis at 40°C and 52.5 mA/cm2 in presence of lead up to 0.1-0.2 mg/L in an electrolyte containing 12 g/L of Mn2+ could be considered as best conducted operating parameters for electrowinning process. EIS studies showed that zinc deposition on zinc is easier than that of zinc on aluminum. ENM revealed that increase of Pb2+ concentration (0.05-0.8 mg/L) in zinc electrolyte without Mn2+ is accompanied with a decrease of skew and increase of kurtosis values that could be correlated to the morphology of zinc deposit

Chemical Investigation of Leaching and Electrochemical Behaviour of Sensor-based Pre-concentrated Copper Ores with Alkaline Lixiviant

OKAbstract While the production of copper metal from primary ores is still increasing, the gradual depletion of high-grade ores implies that the recovery of the metal from low-grade ores is presenting a challenge. A major problem associated with processing of low-grade copper ores can be their high calcite content and concentration of other metals such as Fe, Mn, Co, As, Pb, and Ni. These other metals make the processing of such ores expensive due to the high cost of the leaching chemicals. Therefore, in this study a novel, integrated copper processing method is developed to enhance the economic extraction of copper from such ores. This research investigated the chemical leaching behaviour of porphyry copper ore samples from Chile, South America. Ores were pre-concentrated and classified with near infrared sensing into product, middling and waste fractions. Mineralogical analysis of the ore was conducted using QEMSCAN®, XRD and NIR. The elemental investigation of the ore was carried out using PXRF, ICP-MS and SEM. Analyses revealed that the major copper-bearing mineral is chrysocolla and that the ore is composed mainly of silicate, oxide and carbonate gangue. Calcite in the ore is considered problematic due to acid consumption. In terms of abundance of gangue in the classified ore the order is waste > middling and product. A systematic comparison of the complexometric behaviour of the ore was investigated with Na2EDTA reagent while the leaching behaviour of the classified ore was investigated in NH4Cl and H2C2O4 lixiviants. The influence of process variables such as lixiviant concentrations, particle sizes, solid-to-liquid ratio, temperature, time and stirring speed on the behaviour of the classified ore were investigated. The rate of Cu dissolution and formation of Cu-EDTA complex in Na2EDTA was higher in the product than the middling while that of the waste was found to be insignificant at 0.01 M, even when the concentration of the complexing agent was increased from 0.01 M to 0.05 M. The rate of Cu-EDTA complex formation was found to increase with decreasing particle sizes and solid-to-liquid ratio across the ore categories. Ammonium chloride leaching of the product and middling revealed contrasting behaviour. The rate of Cu extraction was found to increase significantly from 21.5 % to 75.0 % and 27.3 % to 89.0 % when the temperature was increased from 40 ˚C to 90 ˚C, respectively. On increasing the concentration of NH4Cl from 0.5 M to 5 M, the extraction of Cu was found to increase from 20.0 % to 65.0 % and 26.5% to 83.3 %, respectively. It was found that the leaching yield of Cu increased substantially when the particle size was decreased from –125+90 μm to –90+63 μm and –63+45 μm and with decreasing solid-to-liquid ratio (middling and product), respectively. A steady decrease in Cu extraction was obtained when the stirring speed was increased from 300 rpm to 800 rpm. Similarly, the effectiveness of the leaching process was investigated over an extended time period from 2 h to 4 h with an NH4Cl concentration range of 0.55 M to 1.65 M, a temperature of 70 ˚C to 90 ˚C, and at a constant stirring speed of 300 rpm, particle size fraction of -64+45 μm and a solid to liquid volume of 6 g/ 250 mL. It was found that Cu extraction was enhanced by about 90 % during the experiment. The estimated activation energy of the leaching process was characterized using the shrinking core model under the experimental conditions. It was found to range between 45 and 71 KJ/mol in the first and second batch experiments, which is indicative of a chemically controlled leach process. XRD and ICP-MS characterization of mineralogical and chemical composition of residues suggested that the NH4Cl lixiviant leaching is selective for Cu. Examination of leachate with ICP-MS for co-extraction of Mn, Co, Ni and Zn indicated insignificant solubilisation of the metals during leaching. Comparison of Cu extraction in NH4Cl and H2C2O4 under the same experimental conditions revealed that NH4Cl is a better extractant than H2C2O4. Furthermore, the electrodeposition of Cu metal was studied with ore leachate containing Cu(NH3)42+ complexes and with Cu(NH3)4SO4 synthetic electrolyte. Cyclic voltammetric measurements were conducted across a range of cathodic potentials from 0.8 V to – 1.0 V for selected scan rates of 20, 30, 50, 100 and 200 mV/s. Chemical reduction and electrodeposition of Cu from the complexes was found to proceed via two reversible electrochemical processes, each involving the transfer of a single electron. Cu(NH3)42+ complexes are first reduced to Cu(NH3)2+, which is in turn reduced to metallic Cu. The result is compared with the behaviour of synthetic Cu(NH3)4SO4 electrolyte. It was observed that the reduction of Cu(NH3)4SO4 to metallic Cu proceeds as two sequential, single electron transfer processes. The Cu/Cu(NH3)42+ redox reaction was observed to be fast compared to Cu/Cu2+ redox reaction in the Cu(NH3)4SO4 solution. Investigation of the electrochemical kinetics shows that the cathodic peak current varied linearly with the square root of the scan rate, which is indicative of the Cu(NH3)2+ and Cu(NH3)4SO4 reduction to Cu proceeding through a diffusion-controlled process. Assessment of the effect of calcite for leaching of copper from classified ore fractions indicated the potential of NH4Cl lixiviant for the leaching application. Three processing routes to handle the ore fractions on the basis of variation in calcite, gangue and copper content are proposed.Nigerian Tertiary Education Trust Fund (TETFund

Performance of lead anodes used for zinc electrowinning and their effects on energy consumption and cathode impurities

Dans cette thèse, les performances de différentes anodes Pb-Ag utilisées pour l'extraction électrolytique du zinc ± electrowinning ¿ ont été étudiées dans un electrolyte acide de sulfate de zinc avec ou sans la présence d'ions Mn²+ à 38°C, à l'aide de méthodes conventionnelles et plus récentes telles le bruit électrochimique et la spectroscopic d'impédance électrochimique. En outre, l'influence de la gélatine, de l'acide malonique et d'autres additifs sur l'efficacité du courant, la surtension anodique et la morphologie du dépôt de zinc a été examinée pendant l'extraction électrolytique du zinc dans des solutions acides de sulfate de zinc contenant des ions de manganèse avec ou sans impuretés sous une densité de courant de 50 mA/cm² à 38°C. On a montré, par voltammétrie cyclique, que l'utilisation d'une anode en alliage Pb-0,7%Ag pour l'extraction électrolytique du zinc dans un electrolyte acide de sulfate de zinc permettrait de diminuer le pic d'oxydation Pb ?? PbS0₄ par 40% et d'augmenter la hauteur du pic d'oxydation de PbS0₄ -> β-Pb0₂ de 40%. (Chapitre 4) Le comportement de trois anodes en alliage Pb-Ag (avec 0,5%Ag, 0,6%Ag et 0,7%Ag) a été évalué par des mesures galvanostatiques, potentiodynamiques et du bruit électrochimique pendant l'extraction électrolytique du zinc. On a observé que l'anode Pb-0,5%Ag avait la plus haute surtension anodique, suivie par celles contenant 0,6%Ag et 0,7%Ag. En comparaison, l'anode de Pb-0,5%Ag présentait plus de produits de corrosion pendant la polarisation (ou l'électrolyse), avec un plateau important d'une valeur moyenne de 1,61 V/SHE pendant la plus longue période (45 minutes), alors que l'anode en alliage Pb-0,7%Ag a montré la formation de cellules galvaniques plus actives en début de chute de potentiel (11-16 h de chute de potentiel) pouvant correspondre à une corrosion localisée plus importante dû à la présence en plus grande quantité des phases contenant Ag et ce, après 24 h d'électrolyse. Durant la décroissance du potentiel électrochimique, un contenu plus élevé en Ag dans l'anode favorise donc une meilleure résistance à la corrosion. Toutefois, à la toute fin de la chute du potentiel, on a observé qu'une teneur plus élevée en argent dans l'anode augmentait légèrement la vitesse de corrosion. (Chapitre 5) À l'aide de la technique du bruit électrochimique, on a pu montrer que la valeur absolue des pentes reliées à la puissance de la densité spectrale ± PDS ¿ des trois anodes Pb-Ag pouvait correspondre à différentes réactions de corrosion et/ou types de corrosion. En effet, l'anode de plomb contenant 0,5%Ag montre une corrosion uniforme en début d'analyse (première heure) et une corrosion localisée à la fin d'une chute de potentiel de 16 h, alors qu'avec une anode contenant 0,7%Ag, on observe une corrosion localisée importante au début, suivie d'une corrosion uniforme, pour revenir finalement à une corrosion localisée. En comparant les paramètres du bruit électrochimique avec les résultats obtenus par les méthodes conventionnelles, on constate que cette nouvelle approche constitue une technique très valable pour étudier l'influence de l'argent comme élément d'alliage sur la vitesse de corrosion des anodes en plomb. (Chapitre 6) Une anode de l'alliage Pb contenant 0,56%Ag a été étudiée par spectroscopic d'impédance électrochimique ± SIE ¿ dans un electrolyte acide de sulfate de zinc conventionnel contenant MnSO₄ pour évaluer son activité électrochimique pendant et après l'électrolyse. La polarisation galvanostatique sous 50 mA/cm² et à 38°C a été effectuée pendant 5 h. Une chute de potentiel de 6 h a été observée. Durant la première heure de la chute de potentiel, le procédé de diffusion ionique contrôle la réaction électrochimique, alors que durant la période suivante de la chute du potentiel (2 à 6 h), la capacité électrochimique de la couche double et celle du film en surface diminuent en fonction du temps d'immersion. Par contre, la résistance de la couche externe ainsi que la charge de transfert augmentent en fonction du temps. (Chapitre 7) Une anode de l'alliage Pb-0,25%Ag-0,1l%Ca et trois anodes commerciales en plomb contenant 0,56%Ag, 0,6%Ag et 0,69%Ag ont aussi été étudiées dans un electrolyte acide de sulfate de zinc avec ou sans additions de MnS0₄ utilisant les méthodes électrochimiques conventionnelles et la spectroscopic d'impédance électrochimique ± SIE ¿ afin d'évaluer leur activité et comportement à la corrosion durant la chute de potentiel après une electrolyse de 5 h. Un examen des surfaces polies des échantillons ont montré que l'anode renfermant un contenu le plus élevé en Ag possédait le plus bas courant de corrosion parmi les quatre types d'anode examinés, suivie par les anodes contenant 0,6%Ag, 0,25%Ag-0, l%Ca et 0,56%Ag. (Chapitre 8) On a constaté que l'addition d'acide malonique pouvait augmenter l'efficacité de courant d'electrolyse et diminuer les potentiels anodique et cathodique ainsi que le potentiel de la cellule électrolytique dans un electrolyte standard. De plus, dans le cas d'un electrolyte industriel contenant de l'antimoine comme impureté, l'ajout de l'acide malonique ± MA ¿ a conduit à une augmentation du pourcentage d'efficacité de courant non négligeable. Le chlorure de Triethylbenzylammonium ± TEBAC1 ¿ est le meilleur additif pour favoriser une efficacité de courant en présence d'impuretés Ni²⁺ (concentration de ~5 mg/L). On a aussi observé que le TEBAC1 contrecarrait mieux l'effet délétère du Sb³⁺ que les autres additifs tels que le polyethylene glycol, le sulfate laurique de sodium, l'acide de perfluoroheptanoique et l'acide malonique, mais pas aussi efficace que la colle et le chlorure ensemble. L'ajout de 2 mg/L de ± TEBAC1 ¿ à la solution d'acide sulfurique en présence d'ions nickel a augmenté le potentiel cathodique de la réaction d'évolution de l'hydrogène sur le dépôt de zinc de façon plus importante qu'avec une solution contenant 100 mg/L d'acide malonique. (Chapitre 9) L'analyse du bruit électrochimique dans le domaine des temps (paramètres de skewness et de kurtosis) était appropriée pour indiquer l'effet combiné de différentes concentrations de gélatine et d'antimoine sur le procédé d'extraction électrolytique du zinc. Les valeurs des pentes de skewness et de kurtosis tout autour de la moyenne ± 0 ¿ signifient que la distribution des données est symétrique autour de la valeur moyenne et que la forme des courbes est semblable à celle d'une distribution normale. Cela semble correspondre à la meilleure combinaison de l'effet synergique de l'impureté et de l'additif pour une efficacité de courant plus élevée, des surtensions anodique et cathodique faibles et de meilleurs dépôts denses et uniformes. (Chapitre 10

The development of an alternative process for the recovery of lead from sulphide ores

M.Tech. (Minerals Engineering)This report deals with the feasibility study of a novel concept whereby a lead sulphide concentrate and a solid reductant are reacted with a manganese ore at a temperature of approximately lOOO=C. The manganese oxides are reduced to their lower oxides, which, having a higher affinity for sulphur than lead. scavenge the sulphur from the lead sulphide. A manganese sulphide mane is formed. and liquid lead metal is tapped off. The manganese sulphide mane is then leached with sulphuric acid. After a purification step to remove the base metals from solution, the electrolyte proceeds to an electrolytic manganese metal or manganese dioxide facility where the manganese is recovered. The benefits of this process are fourfold: firstly, lead ores may be beneficiated locally; secondly, the separate and often lengthy processes for the recovery of lead and manganese are combined into a simplified process, thereby reducing the capital expense: thirdly, the Leadman process can be applied to any scale of operation: and fourthly, no 502 is produced. Details of the investigation included the following: a literature survey. a laboratory scale study where the operating conditions were narrowed down, a smelting campaign on a rotary kiln, a mineralogical study, a brief leaching study, a leach liquor purification step and a techno-economic assessment. This study has shown the technical and economical feasibility of the Leadman process. The lead and manganese recoveries were both approximately 93%, with good accountability of all the other elements of interest. Depending on the operating conditions, between 80 and 100 per cent of silver, originally in the galena, was recovered with the lead bullion. The purity of the lead metal produced was good with a lead content of approximately 97 per cent, and low levels of contaminants. It was also shown that the manganese matte produced is suitable for use as feed to an existing manganese electrowinning operation. The techno-economic assessment showed a return of R 3 118/t of Pb, compared with R 939/t and R 240/t for the conventional manganese and lead blast processes, respectively

The mechanism of cathodic depolarization exhibited by sulphate-reducing bacteria during metallic corrosion processes

Includes bibliographical references.The mechanism of the corrosive action of sulphate reducing bacteria of the genus Desulfovibrio towards ferrous metals has been investigated. This corrosive action is anomalous when considered in the light of established knowledge of corrosion processes, since it occurs in the absence of oxygen, at more or less neutral pH values and at ordinary ambient temperatures. The hypothesis of von Wolzogen Kuhr and van der Vlugt, published in 1934, proposing that enzymic catalysis of sulphate reduction by cathodic charge constituted a "cathodic depolarizing" process, which appears t o be widely accepted as the most likely mechanism for this corrosive effect, is evaluated critically here in the light of established electrochemical and biochemical knowledge. The theoret ical arguments presented in this thesis show that this process, if it does occur, is unlikely to affect corrosion rates. The experimental results presented here indicate that all cathodic depolarizing activity demonstrated in pure cultures of these organisms is attributable to the cathodic activity of dissolved hydrogen sulphide produced by the organisms. The conclusions of other workers, quoted in support of proposed enzymic catalysis of charge transfer from cathodes to redox dyes in laboratory systems, are considered, in view of experimental work performed during this investigation, to be a misinterpretation of experimental results

An assessment of the potential for waste minimisation in small and medium size enterprises in South Africa

Against a background of a chemical engineering degree and a few years of industrial experience, I undertook this M.Sc. degree with the conviction that chemical engineering skills have a unique role to play in addressing environmental problems of pollution generated by industrial activity. Moreover, given that, of industrial activity, it is chemical processing industries (CPI) and mining industries which are the major contributors to generation of waste, hazardous waste in particular, it is appropriate that the chemical engineering profession, which populates such industry activities, should assume such responsibility. In response to increasingly vociferous demands for more stringent environmental control over industrial activity, and regulatory compliance with stricter constraints on emissions of pollutants, there is a tendency to rely on readily available end-of-pipe solutions to resolve environmental management problems. This strategy is embodied in current practices in South Africa at effluent treatment- and landfill disposal facilities. Yet this is a costly solution in the long term, with implications for increasing operating costs, investment costs for development of new facilities, as well as closure and potential liability costs for old facilities. Furthermore, this strategy fails to address problems of resource depletion and the potential for resource recovery from materials considered to be "waste". Waste minimisation offers an alternative waste management strategy which seeks to reduce the generation of waste before end-of-pipe management is required, and to recover resources for reuse, thereby reducing resource consumption. The Department of Environment Affairs in the South African government has recommended that there should be research in the application of waste minimisation. While clearly there is a need for fundamental research into particular technological problems (such research is being undertaken at some institutions), the approach I adopted was to investigate potential for effecting meaningful waste minimisation solutions using procedures and techniques which constitute popular waste minimisation assessment methodologies. I focused specifically on small and medium scale industry operators which traditionally do not employ chemical engineering skills and which need a practical tool to improve in-house environmental management capability