A generic, semi-empirical approach to the stochastic modelling of bath-type pyrometallurgical reactors

Eksteen, Jacobus Johannes ; Reuter, M. A. ; Bradshaw, S. M. (2004-03)

Thesis (PhD)--University of Stellenbosch, 2004.

388 leaves printed on single pages, preliminary pages i- xv and numbered pages 1-371. Includes bibliography, list of tables and figures.

Digitized at 330 dpi black and white and 330 dpi color PDF format (OCR), using KODAK i 1220 PLUS scanner.

Thesis

ENGLISH ABSTRACT: Bath type furnaces have become an established technology for the intensive smelting, converting and refining of primary and secondary raw materials. Since these furnaces normally have large inventories, long time constants and complex metallurgies, a dynamic model-based prediction strategy is the only feasible approach to operator decision support and process control. This dissertation presents a semi-empirical approach to the stochastic modelling of bath-type pyrometallurgical reactors, which leads to a generic model type called the Equilib-ARMAX model. The modelling approach is applied to three case studies: • A nickel-copper matte converting operation using a submerged lance injection reactor • A chromite smelting operation to produce high carbon ferrochrome using a direct current (DC) plasma smelting furnace • An ilmenite smelting operation to produce high titania slag and pig iron, using a direct current (DC) plasma smelting furnace. In each case, the industrial operations were analysed with regard to the practical and technological constraints which influence the type and quality of the process data. The fundamental process phenomena associated with each operation have been analysed to ascertain which fundamental variables should be included within the overall semi-empirical approach, without sacrificing model transparency, simplicity, accuracy and calculation time. It was considered that an overly complex model would be inappropriate given that data from industrial smelting operations show significant random variance. The thermochemistry and phase equilibria associated with each operation are discussed in detail, as they become the fundamental backbone of the semi-empirical models. The equilibria have been modelled with software that uses non-ideal solutions models and Gibbs free energy minimisation to predict the phase and chemical equilibria that could be expected for a given feed recipe and operating temperature. As the thermodynamic modelling software is not stable within an industrial environment, an artificial intelligent mapping technique has been developed to map process inputs to equilibrium outputs. A multi-layer perceptron neural network has been used as the convenient mapping method to represent equilibrium. The neural networks were trained using tens of thousands of feed recipes, where the feed component ratios were varied based on a 3N factorial design. The amounts and chemistries of all equilibrium phases could be calculated with high accuracies (R2 > 0.95) in all cases. Further stochastic analysis and modelling require additional information about the property distributions associated with each measurement. The homogeneities of the furnace products (slag, alloy and flue dust) critically influence the level of confidence that one can associate with plant measurements. The homogeneities were characterised for the DC plasma arc furnaces and they were benchmarked against a submerged arc furnace. It was found that the homogeneity varied per element, with silicon and sulphur tending to show highest variations in the alloy melts. The observation that the variation in these two elements are both high can partially be attributed to the fact that SiS evaporates from the bath surface, especially in regions close to the arc attachment zone. A significant negative correlation was found between the relative standard deviation per tap (using silicon) and the degree of superheat / subcooling of the alloy, indicating that the homogeneity can be strongly influenced by the changes in rheology due to subcooling below the liquidus (which leads to the precipitation of solid phases and increases the observed melt viscosity). Mixedness or homogeneity and data uncertainty are therefore inseparably linked. The relative standard deviations associated with the homogeneity characterisation, as well as known sampling and assaying variances were used to develop reconciled material balances based on measured plant data. Material balance closure was therefore obtained within the inherent uncertainties of the plant data. Biases in the plant data were identified simultaneously with data reconciliation. Moreover, it was shown using Fast Fourier Power Spectra and statespace analysis that the data reconciliation was a good low-pass filter, as it extracted the major process trends components in the noisy data and it also improved the overall dynamic behaviour characteristics of the data. Finally systems identification techniques were used to develop dynamic transfer function models that were linear in the parameters to be estimated. These systems models were based on the reconciled plant data and equilibrium predictions. The final systems models are therefore equilibrium-autoregressive-moving-average models with exogenous variables (Equilib-ARMAX). The model parameters can be estimated recursively using a simple least squares method. The final models could dynamically predict the metallurgy of the subsequent tap 4-6 hours in advance, based on a given suite of set-points, within the inherent accuracy of the data. These models may be used to suggest the optimal operating conditions through an operator guidance system, or more simply, the models are simple enough to be used in a spreadsheet on a manager's desk.

AFRIKAANSE OPSOMMING: Bad-tipe oonde is reeds 'n gevestigde tegnologie wat algemeen gebruik word vir die intensiewe smelting, omsetting en raffinering van primere en sekondere roumateriale. Aangesien hierdie oonde normaalweg groot inventarisse, lang tydkonstantes en komplekse metallurgiee het, is dinamiese, modelgebaseerde voorspelling die enigste uitvoerbare benadering tot operateur besluitnemingsteunstelsels en prosesbeheer. Hierdie proefskrif stel 'n nuwe generiese, semi-empiriese benadering voor om die bad-tipe oonde stogasties te modelleer en lei tot die sogenaamde Equilib-ARMAX model. Die modelleringsbenadering word geevalueer deur drie gevallestudies: • 'n Nikkel-koper swawelsteen omsettingsproses in 'n dompel-Ians inspuit reaktor • 'n Chromiet smeltingsproses om hoe-koolstof ferrochroom te produseer in 'n gelykstroom (GS) plasmaboogoond • 'n Ilmeniet smeltingsproses om hoe titania slak en ruyster te produseer in 'n gelykstroom (GS) plasmaboogoond. In elke geval is die industriele prosesse ontleed met betrekking tot die praktiese en tegnologiese beperkings wat die tipe en die gehalte van die prosesdata beinvloed. Die fundamentele prosesgedrag van elke proses is ontleed om te bepaal welke fundamentele veranderlikes ingesluit moet word in die semi-empiriese benadering, sonder om model deursigtigheid, eenvoud, akkuraatheid en berekeningstyd in te boet. Die ontwikkeling van oor-komplekse modelle is beskou as ongepas, gegewe dat die data van industriele smeltingsprosesse beduidende onsekerhede toon. Die termochemiese en fase-ewewigte geassosieer met elke proses word breedvoerig bespreek, aangesien dit die fundamente1e grondslag van die semi-empiriese modelle verskaf. Die ewewigte is gemodelleer met rekenaar simulasie-programmatuur wat nie-ideale oplossingsmodelle en Gibbs vrye-energie minimering gebruik om die fase en chemiese ewewigte, wat verwag kan word vir 'n gegewe toevoerresep en bedryfstemperatuur, te voorspel. Aangesien termodinamiese modelleringsprogrammatuur normaalweg nie stabiele gedrag toon in 'n intydse industriele omgewing nie, word kunsmatig intelligente projeksietegnieke gebruik om prosesinsette te projekteer na die ekwavilente ewewigsvoorspellings. 'n Multilaag perseptron neurale netwerk is gebruik as 'n eenvoudige metode om hierdie ewewigsprojeksies voor te stel. Die neurale netwerke is afgerig deur van tienduisende toevoer resepte gebruik te maak. Die verhoudings van die komponente in die voer is gewissel gebaseer op 'n 3N faktoriaalontwerp. Die hoeveelhede en samestelling van al die ewewigsfases kon in alle gevalle bereken word met hoe akkuraatheid (R2 > 0.95). Verdere stogastiese analise en modellering is slegs moontlik met kennis oor die eienskapsverspreidings geassosieer met elke komponent. Die homogeniteite van die oondprodukte (slak, legering en vlieg-as) bepaal, tot 'n groot mate, die betroubaarheidsvlak van die aanlegmetings. Homogeniteite is gekarakteriseer vir die GS-plasmaboogoonde en is vergelyk met die homogeniteite wat in dompelboogoonde gevind word. Die homogeniteite het gevarieer per komponent. Silikon en swawel neig om die grootste ruimtelike variasies te toon in die legerings wat bestudeer is. 'n Beduidende negatiewe korrelasie is gevind tussen die relatiewe standaardafwyking per tap (gebaseer op silikon) en die graad van superverhitting / onderverkoeling van die legering. Dit dui aan dat die homogeniteit sterk beinvloed word deur veranderinge in die smelt reologie. Vermenging, reologie, homogeniteit en data onsekerheid (integriteit) is daarom ten nouste gekoppel. Die relatiewe standaardafwykings geassosieer met die homogeniteitsbepaling, asook die monsternemings- en ontledingsvariansies, is gebruik om die aanlegdata te rekonsilieer onderhewig aan die behoud van die komponent en totale stroom massabalanse. Die massabalanse is dus gesluit deur aanpassings aan die metings te maak binne die inherente onsekerhede in die data. Sistematiese foute in die data is gelyktydig met die rekonsiliasie geidentifiseer. Verder is deur diskrete Fourier energiespektra en toestand-ruimte analises getoon dat massabalans-rekonsiliasie dien as 'n goeie seinfilter om hoe-frekwensie geraas te verminder en tergelykertyd die dinamiese gedragseienskappe van die data te verbeter. Stelsel-identifikasietegnieke is gebruik om dinamiese oordragsfunksiemodelle te ontwikkel wat linieer is met betrekking tot die modelparameters. Hierdie stelselmodelle is gebaseer op gerekonsilieerde data, eksogene prosesdata en ewewigsberekeninge, en word vervolgens ewewigs-autoregressiewe-lopende-gemiddelde modelle met eksogene veranderlikes (Equilib ARMAX) genoem. Die modelparameters kan deur gewone kleinste-kwadrate metodes beraam word. Die finale modelle kan die metallurgie van toekomstige tappe 4-6 uur voortydig voorspel, gebaseer op beskikbare stelpunte en binne die inherente presisie van die data. Hierdie modelle kan gebruik word om optimale bedryfskondisies vir prosesbeheer te identifiseer, en is eenvoudig genoeg om in sigbladformaat op 'n aanlegbetuurder se rekenaar gebruik te kan word.

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