Simulation of a Hydrometallurgical Leaching Reactor modeled as a DAE system

An existing dynamic model of the main reactor in the Silgrain process for the production of Si from FeSi has been extended here in order to resemble more closely the behavior of the real reactor. The previous model was based on the application of macroscopic mass conservation law, the population balance equation and the assumptions of complete mixing and isothermic conditions. The major modifications are the inclusion of the condition governing the entrainment of particles in the outflow, and the formulation of the energy balance. The extended model consists of 1 integrodifferential equation, 4 implicit ordinary differential equations, 7 algebraic equations and 3 integral equations. After discretization in the particle size space, a system of differential and algebraic equations (DAE) is obtained. DAEs are not ODEs and they require analysis and characterization and may require reformulation. After such analysis, it was concluded that the system is implicit index-one for the usual range of operation and that a method based on the Backward Differentiation formulas (BDF) can be used for its solution. The model was implemented in Matlab and the ode15s code was used for solving the system of equations. The simulation results are satisfactory and seem to match qualitatively with the known operation of the reactor. The model is suitable for further use in designing a model-based control scheme

Avaliação de um sistema simplificado de tratamento de esgotos visando a utilização em áreas rurais Evaluation of a simple system of wastewater treatment aiming at use in rural areas

O Brasil enfrenta sérios problemas relacionados a uma grande população que vive na área rural, lançando os esgotos diretamente nos corpos hídricos. Este comportamento contribui a olhos vistos com a degradação do meio ambiente, além de trazer impasses à saúde pública; nesses casos, o emprego de sistemas de tratamento simplificados seria muito vantajoso, pois poderia depurar os esgotos dessas comunidades rurais a um custo baixo e ser operado e construído pela própria mão-de-obra local, embora pouco qualificada. Um dos sistemas estudados na UNICAMP e que se enquadra nessas características é, sem dúvida, a associação dos filtros anaeróbios com filtros de areia. Os resultados desta pesquisa demonstraram que o efluente gerado apresentava valores de matéria orgânica inferiores ao limite máximo estipulado pela legislação pertinente (CONAMA, 2005). Quanto aos compostos nitrogenados, demonstrou-se que os leitos de areia tinham grande capacidade de nitrificá-los e, no tocante ao fósforo, ressalta-se que nas maiores profundidades de leito de areia (0,75 e 1,00 m), a remoção superava 98%.<br>Brazil faces problems related to the large population which lives in the rural areas and discharges the wastewater directly into water bodies. This occurrence contributes not only to environmental damage but also to public health problems. In this case, the use of simple treatments would be beneficial, since the local wastewater could be treated with low cost and be built and operated by local labor even though it is not specialized. A system investigated in UNICAMP and which has these characteristics is, undoubtedly, the association of anaerobic filters with sand filters. The results from the research showed that the effluent had an organic matter concentration lower than the maximum permitted by Brazilian law (Brasil, 2005). Regarding the nitrogen compounds, the sand filters showed a great capacity of nitrification and, in reference to phosphorus, in the deepest depths (0.75 and 1.00 m), the removal was more than 98