966 resultados para Lorenz, Equações de


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Três estudos foram conduzidos no Núcleo de Pesquisas Avançadas em Matologia (NUPAM) pertencente à UNESP/FCA - campus de Botucatu-SP, com o objetivo de avaliar a estabilidade dos corantes Azul Brilhante FDC-1 e Amarelo Tartrasina FDC-5 quanto a diferentes períodos de exposição à luz solar e contato com folhas de Eichhornia crassipes. No primeiro estudo, soluções de 0,3125, 0,625, 1,25, 2,5, 5, 10 e 20 ppm dos corantes Azul Brilhante FDC-1 e Amarelo Tartrasina FDC-5 foram acondicionadas em tubos de quartzo hermeticamente fechados e submetidos a 0, 0,5, 1, 2, 4, 6 e 10 horas de exposição à luz solar e ao escuro. Ao final de cada período, amostras de 10 mL foram retiradas dos tubos e analisadas. No segundo estudo, os tratamentos foram dispostos no esquema fatorial 2x7: duas condições luminosas (escuro e pleno sol) e sete períodos de exposição (0, 0,5, 1, 2, 4, 6 e 10 horas), com seis repetições. Com o auxílio de micropipeta, oito gotas de 5 µL das soluções Azul Brilhante e Amarelo Tartrasina a 4.000 ppm foram depositadas em placas de Petri de vidro. Após o término dos períodos de exposição, as placas foram lavadas com 50 mL de água destilada, com o objetivo de extrair o corante depositado sobre elas. No terceiro estudo, adotaram-se os mesmos tratamentos do segundo experimento, com quatro repetições, porém as soluções foram depositadas sobre as folhas de plantas de Eichhornia crassipes. Foram adotados também os mesmos procedimentos de extração dos corantes após o término dos períodos de exposição. As soluções finais obtidas nos três estudos foram submetidas à leitura óptica de absorbância em espectrofotômetro UV-visível nos comprimentos de onda de 630 e 427 nm, para os corantes Azul Brilhante FDC-1 e Amarelo Tartrasina FDC-5, respectivamente. As várias concentrações das soluções de ambos os corantes não sofreram degradação pela luz solar quando submetidas aos vários períodos de incidência luminosa nos tubos de quartzo (ambiente fechado), visto que as curvas de recuperação apresentaram equações semelhantes àquelas concentrações que foram mantidas no escuro. A mesma estabilidade também foi observada quando os corantes foram submetidos à luz solar em ambiente aberto, ou seja, nas placas de Petri. O corante Amarelo Tartrasina também se apresentou muito estável quando depositado sobre as folhas de E. crassipes, independentemente da exposição ou não à luz solar. Para o corante Azul Brilhante, ocorreram significativas perdas de 7,8 e 18,6% quando esteve depositado na superfície da folha de aguapé pelo período de 10 horas sob condições de escuro e plena luz solar, respectivamente.

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This work aims at the implementation and adaptation of a computational model for the study of the Fischer-Tropsch reaction in a slurry bed reactor from synthesis gas (CO+H2) for the selective production of hydrocarbons (CnHm), with emphasis on evaluation of the influence of operating conditions on the distribution of products formed during the reaction.The present model takes into account effects of rigorous phase equilibrium in a reactive flash drum, a detailed kinetic model able of predicting the formation of each chemical species of the reaction system, as well as control loops of the process variables for pressure and level of slurry phase. As a result, a system of Differential Algebraic Equations was solved using the computational code DASSL (Petzold, 1982). The consistent initialization for the problem was based on phase equilibrium formed by the existing components in the reactor. In addition, the index of the system was reduced to 1 by the introduction of control laws that govern the output of the reactor products. The results were compared qualitatively with experimental data collected in the Fischer-Tropsch Synthesis plant installed at Laboratório de Processamento de Gás - CTGÁS-ER-Natal/RN

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The objective of this work was the development and improvement of the mathematical models based on mass and heat balances, representing the drying transient process fruit pulp in spouted bed dryer with intermittent feeding. Mass and energy balance for drying, represented by a system of differential equations, were developed in Fortran language and adapted to the condition of intermittent feeding and mass accumulation. Were used the DASSL routine (Differential Algebraic System Solver) for solving the differential equation system and used a heuristic optimization algorithm in parameter estimation, the Particle Swarm algorithm. From the experimental data food drying, the differential models were used to determine the quantity of water and the drying air temperature at the exit of a spouted bed and accumulated mass of powder in the dryer. The models were validated using the experimental data of drying whose operating conditions, air temperature, flow rate and time intermittency, varied within the limits studied. In reviewing the results predicted, it was found that these models represent the experimental data of the kinetics of production and accumulation of powder and humidity and air temperature at the outlet of the dryer

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The present work has the main goal to study the modeling and simulation of a biphasic separator with induced phase inversion, the MDIF, with the utilization of the finite differences method for the resolution of the partial differencial equations which describe the transport of contaminant s mass fraction inside the equipment s settling chamber. With this aim, was developed the deterministic differential model AMADDA, wich was admensionalizated and then semidiscretizated with the method of lines. The integration of the resultant system of ordinary differential equations was realized by means of a modified algorithm of the Adam-Bashfort- Moulton method, and the sthocastic optimization routine of Basin-Hopping was used in the model s parameter estimation procedure . With the aim to establish a comparative referential for the results obtained with the model AMADDA, were used experimental data presented in previous works of the MDIF s research group. The experimental data and those obtained with the model was assessed regarding its normality by means of the Shapiro-Wilk s test, and validated against the experimental results with the Student s t test and the Kruskal-Wallis s test, depending on the result. The results showed satisfactory performance of the model AMADDA in the evaluation of the MDIF s separation efficiency, being possible to determinate that at 1% significance level the calculated results are equivalent to those determinated experimentally in the reference works

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O óleo produzido nos novos campos de petróleo está cada vez mais parafínico e viscoso, com isso, à medida que o óleo é escoado, parafinas são depositadas sobre as paredes internas do tubo, e ao longo do tempo, tendem a reduzir drasticamente a área transversal ao escoamento. Visando estudar o processo de solubilização da parafina em dutos, esse trabalho objetiva desenvolver modelos matemáticos que represente o processo, com base nos fenômenos envolvidos no mesmo tais como transferência de massa, transferência de energia e equilíbrio sólido-líquido, implementando-os em um ambiente de desenvolvimento VBA (Visual Basic) for Excel ®. O presente trabalho foi realizado em quatro etapas: i) modelagem dos fenômenos de transferência de calor e massa, ii) modelagem da rotina dos coeficientes de atividade através do modelo UNIFAC e modelagem do sistema de equilíbrio sólido-líquido; iii) modelagem matemática do processo de solubilização e cálculo da espessura da parafina ao longo do tempo; iv) implementação dos modelos em um ambiente de desenvolvimento VBA for Excel® e criação de um simulador com uma interface gráfica, para simular o processo de solubilização da parafina depositada em dutos e sua otimização. O simulador conseguiu produzir soluções bastante adequadas, mantendo continuidade das equações diferenciáveis do balanço de energia e de massa, com uma interpretação física viável, sem a presença de dissipação de oscilações nos perfis de temperatura e massa. Além disso, esse simulador visa permitir a simulação nas diversas condições de escoamento, bem como compreender a importância das variáveis (vazão, temperatura de entrada, temperatura externa, cadeia carbônica do solvente). Através dos resultados foram possíveis verificar os perfis de temperatura, fração molar e o de solubilização

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In the present work are established initially the fundamental relationships of thermodynamics that govern the equilibrium between phases, the models used for the description of the behavior non ideal of the liquid and vapor phases in conditions of low pressures. This work seeks the determination of vapor-liquid equilibrium (VLE) data for a series of multicomponents mixtures of saturated aliphatic hydrocarbons, prepared synthetically starting from substances with analytical degree and the development of a new dynamic cell with circulation of the vapor phase. The apparatus and experimental procedures developed are described and applied for the determination of VLE data. VLE isobarics data were obtained through a Fischer s ebulliometer of circulation of both phases, for the systems pentane + dodecane, heptane + dodecane and decane + dodecane. Using the two new dynamic cells especially projected, of easy operation and low cost, with circulation of the vapor phase, data for the systems heptane + decane + dodecane, acetone + water, tween 20 + dodecane, phenol + water and distillation curves of a gasoline without addictive were measured. Compositions of the equilibrium phases were found by densimetry, chromatography, and total organic carbon analyzer. Calibration curves of density versus composition were prepared from synthetic mixtures and the behavior excess volumes were evaluated. The VLE data obtained experimentally for the hydrocarbon and aqueous systems were submitted to the test of thermodynamic consistency, as well as the obtained from the literature data for another binary systems, mainly in the bank DDB (Dortmund Data Bank), where the Gibbs-Duhem equation is used obtaining a satisfactory data base. The results of the thermodynamic consistency tests for the binary and ternary systems were evaluated in terms of deviations for applications such as model development. Later, those groups of data (tested and approved) were used in the KijPoly program for the determination of the binary kij parameters of the cubic equations of state original Peng-Robinson and with the expanded alpha function. These obtained parameters can be applied for simulation of the reservoirs petroleum conditions and of the several distillation processes found in the petrochemistry industry, through simulators. The two designed dynamic cells used equipments of national technology for the determination of VLE data were well succeed, demonstrating efficiency and low cost. Multicomponents systems, mixtures of components of different molecular weights and also diluted solutions may be studied in these developed VLE cells