Foi desenvolvido um programa computacional escrito na linguagem de programação C++ denominado CALFRAC para quantificar o processo de cristalização fracionada em sistemas ígneos, utilizando para isso as concentrações dos elementos maiores, menores e traços. O algoritmo moderniza, torna mais eficiente e aprimora os programas publicados na literatura e possui a grande vantagem de poder calcular, automaticamente, todas as possíveis combinações de evolução das amostras envolvidas na diferenciação, além de associar aos cálculos os elementos-traço, os quais servem para confirmar os resultados sugeridos pelos ajustes dos elementos maiores e menores. O CALFRAC calcula a fração total subtraída do magma inicial e as frações referentes a cada mineral fracionado através do cálculo do balanço de massa, utilizando as concentrações de elementos maiores e menores, empregando os métodos de estimativa de máxima verossimilhança e dos multiplicadores de Lagrange para a resolução por mínimos quadrados, enquanto para os elementos-traço o programa utiliza a Equação de Rayleigh. Em ambos os casos a média dos erros percentuais relativos é usada como indicação das melhores evoluções. O programa CALFRAC foi aplicado na investigação da possibilidade de diferenciação por cristalização fracionada em amostras de soleiras de diabásio da Bacia do Paraná, que ocorrem nos municípios de Salto do Itararé, Ponta Grossa, Prudentópolis, Rebouças, Irati, Reserva e Jaguariaíva (PR), as quais foram coletadas para essa finalidade. Nas 33 amostras coletadas foram realizadas determinações de elementos maiores, menores e traços, incluindo terras raras, empregando-se os métodos de Fluorescência de Raios X e Ativação Neutrônica. Os resultados fornecidos pelo programa foram insatisfatórios, não sendo possível estabelecer um percurso de diferenciação das rochas mais primitivas para as mais diferenciadas das intrusões, devido ao fato de que provavelmente muitas das amostras analisadas representam a mistura de magmas com porções contendo acumulação de fases minerais causada pelo próprio processo de cristalização fracionada in situ. / CALFRAC is a computer program written in C++ programming language developed to quantify fractional crystallization processes in igneous systems. Major, minor and trace element concentrations are used as input for calculations. The new algorithm enhances and makes the program more efficient than those published in the literature. Besides it is capable to automatically calculating all possible rock sample combinations involving differentiation by fractional crystallization process, using in addition trace element concentrations to corroborate the results obtained by the fitting of major and minor element abundances. CALFRAC calculates the total fraction subtracted from the original magma and the percentage of each fractionated mineral by solving least-squares mass balance equations based on major and minor element concentrations. The methods of maximum likelihood estimate and Lagrange multipliers are used to solve the equations, whereas for the quantification of trace elements the program uses the Rayleigh Equation. In both cases the mean relative percentage errors is used as an indication of the best results. The program CALFRAC was applied to investigate the possibility of differentiation by fractional crystallization of diabase samples from Paraná Basin sills, which outcrop nearby Salto do Itararé, Ponta Grossa, Prudentópolis, Rebouças, Irati, Reserva and Jaguariaíva towns (PR). The 33 collected samples were analyzed for major, minor and trace elements, including rare earths, employing X-Ray Fluorescence and Neutron Activation methods. The program output was not satisfactory, since it was not possible to establish a differentiation sequence from the more primitive to the more differentiated rocks of the intrusions. This is probably due to the fact that many rock samples are the result of mixing of magmatic melts with mineral accumulation zones, which were formed by the in situ fractional crystallization process.

The purpose of the work described in this thesis was to explore the use of fractional crystallization as a technology that can be used to separate medium-curie waste from the Hanford Site tank farms into a high-curie waste stream, which can be sent to a Waste Treatment and Immobilization Plant (WTP), and a low-curie waste stream, which can be sent to Bulk Vitrification. The successful semi-batch crystallization of sodium salts from two single shell tank simulant solutions (SST Early Feed, SST Late Feed) demonstrated that the recovered crystalline product met the purity requirement for exclusion of cesium, sodium recovery in the crystalline product and the requirement on the sulfate-to-sodium molar ratio in the stream to be diverted to the WTP. The experimental apparatus, procedures and results obtained in this thesis on scaled-down experiments of SST Early and Late Feed simulated solutions were adapted and reproduced under hot-cell with actual wastes by our partners at Hanford. To prepare the application of the pretreatment process to pilot scale process, several varation to the feed solutions were investigated including the presence of carboxylates and amines organics compounds and solids particles. Results of the study showed that 4 organics species presented complications to the process (NTA, HEDTA, EDTA and sodium citrate) while the other species (Formate, acetate, glycolate and IDA) and solids particles did not in the conditions of the stored wastes. In this thesis, the kinetics of the crystalline species formed at the condition of the early feed certification run (66 °C and 25 g/h evaporation) were determined along with the effect of the operating temperature and evaporation rate on these kinetics. On one hand, the study of evaporation rate values ranging from 25g/h to 75g/h showed that an increase in evaporation rate increased the specific nucleation while decreasing the specific growth rate. On the other hand, experiments on operating temperature ranging from 35 °C to 75 °C displayed that the nucleation rate of all species increased with temperature at the exception of sodium carbonate monohydrate and burkeite crystals, and that the growth rate of all species increased with temperature at the exception of sodium nitrate. Furthermore, sulfate based crystals such as trisodium fluoride sulfate were only roduced at 45 °C and 75 °C. A simple steady state MSMPR population balance model was developed expressing the total population density function as the sum of the specific population density functions. The specific semi-batch crystallization kinetics were implemented in this model.

The purpose of the work described in this thesis was to explore the use of fractional crystallization as a technology that can be used to separate medium-curie waste from the Hanford Site tank farms into a high-curie waste stream, which can be sent to a Waste Treatment and Immobilization Plant (WTP), and a low-curie waste stream, which can be sent to Bulk Vitrification. The successful semi-batch crystallization of sodium salts from two single shell tank simulant solutions (SST Early Feed, SST Late Feed) demonstrated that the recovered crystalline product met the purity requirement for exclusion of cesium, sodium recovery in the crystalline product and the requirement on the sulfate-to-sodium molar ratio in the stream to be diverted to the WTP. In this thesis, experimental apparatus, procedures and results are given on scaled-down experiments of SST Early Feed for hot-cell adaptation along with operating parameters and crystallization mechanism studies on early feed multi-solute crystallization. Moreover, guidance is given regarding future steps towards adapting the technology to multi-salt crystallization kinetic parameter estimates and modeling. Crystallization, Evaporative Fractional Crystallization, Nuclear Waste Pretreatment, Cesium Removal, Hanford, SST Early and Late feed, Multi-solute, Multi-salts, Simulant Testing

Foi desenvolvido um programa computacional escrito na linguagem de programação C++ denominado CALFRAC para quantificar o processo de cristalização fracionada em sistemas ígneos, utilizando para isso as concentrações dos elementos maiores, menores e traços. O algoritmo moderniza, torna mais eficiente e aprimora os programas publicados na literatura e possui a grande vantagem de poder calcular, automaticamente, todas as possíveis combinações de evolução das amostras envolvidas na diferenciação, além de associar aos cálculos os elementos-traço, os quais servem para confirmar os resultados sugeridos pelos ajustes dos elementos maiores e menores. O CALFRAC calcula a fração total subtraída do magma inicial e as frações referentes a cada mineral fracionado através do cálculo do balanço de massa, utilizando as concentrações de elementos maiores e menores, empregando os métodos de estimativa de máxima verossimilhança e dos multiplicadores de Lagrange para a resolução por mínimos quadrados, enquanto para os elementos-traço o programa utiliza a Equação de Rayleigh. Em ambos os casos a média dos erros percentuais relativos é usada como indicação das melhores evoluções. O programa CALFRAC foi aplicado na investigação da possibilidade de diferenciação por cristalização fracionada em amostras de soleiras de diabásio da Bacia do Paraná, que ocorrem nos municípios de Salto do Itararé, Ponta Grossa, Prudentópolis, Rebouças, Irati, Reserva e Jaguariaíva (PR), as quais foram coletadas para essa finalidade. Nas 33 amostras coletadas foram realizadas determinações de elementos maiores, menores e traços, incluindo terras raras, empregando-se os métodos de Fluorescência de Raios X e Ativação Neutrônica. Os resultados fornecidos pelo programa foram insatisfatórios, não sendo possível estabelecer um percurso de diferenciação das rochas mais primitivas para as mais diferenciadas das intrusões, devido ao fato de que provavelmente muitas das amostras analisadas representam a mistura de magmas com porções contendo acumulação de fases minerais causada pelo próprio processo de cristalização fracionada in situ. / CALFRAC is a computer program written in C++ programming language developed to quantify fractional crystallization processes in igneous systems. Major, minor and trace element concentrations are used as input for calculations. The new algorithm enhances and makes the program more efficient than those published in the literature. Besides it is capable to automatically calculating all possible rock sample combinations involving differentiation by fractional crystallization process, using in addition trace element concentrations to corroborate the results obtained by the fitting of major and minor element abundances. CALFRAC calculates the total fraction subtracted from the original magma and the percentage of each fractionated mineral by solving least-squares mass balance equations based on major and minor element concentrations. The methods of maximum likelihood estimate and Lagrange multipliers are used to solve the equations, whereas for the quantification of trace elements the program uses the Rayleigh Equation. In both cases the mean relative percentage errors is used as an indication of the best results. The program CALFRAC was applied to investigate the possibility of differentiation by fractional crystallization of diabase samples from Paraná Basin sills, which outcrop nearby Salto do Itararé, Ponta Grossa, Prudentópolis, Rebouças, Irati, Reserva and Jaguariaíva towns (PR). The 33 collected samples were analyzed for major, minor and trace elements, including rare earths, employing X-Ray Fluorescence and Neutron Activation methods. The program output was not satisfactory, since it was not possible to establish a differentiation sequence from the more primitive to the more differentiated rocks of the intrusions. This is probably due to the fact that many rock samples are the result of mixing of magmatic melts with mineral accumulation zones, which were formed by the in situ fractional crystallization process.