[pt] O petróleo é constituído por uma cadeia de hidrocarbonetos, os quais se precipitam na forma de partículas sólidas de parafina, quando a sua temperatura cai abaixo de um patamar conhecido como TIAC (Temperatura Inicial de Aparecimento de Cristais). Essas partículas podem se depositar nas paredes internas dos dutos obstruindo o escoamento, podendo gerar prejuízos da ordem de milhões de dólares. Por esse motivo, a habilidade de previsão e controle da deposição de parafina em eventos futuros é de fundamental importância tanto para projetistas como operadores de tubulações. Visando lidar com esse problema, grande esforço vem sendo feito pela comunidade científica com o intuito de aperfeiçoar as metodologias para previsão do depósito de parafina. Frequentemente, a modelagem da difusão das espécies é realizada utilizando a Lei de Fick, válida para misturas binárias, apesar dos hidrocarbonetos presentes no petróleo formarem uma mistura multicomponente. O presente trabalho propõe avaliar o fluxo difusivo de massa das espécies utilizando o modelo Stefan-Maxwell, compatível com sistemas multicomponentes. Para determinar a evolução axial e temporal da espessura do depósito de parafina, o escoamento foi modelado como uma mistura líquido/sólido e equações de conservação de energia, massa, quantidade de movimento linear e continuidade das espécies são resolvidas, acopladas com o modelo termodinâmico de múltiplas soluções sólidas, para determinação da precipitação da parafina. As equações de conservação foram resolvidas utilizando o software de código livre OpenFOAM (marca registrada). Uma comparação das previsões obtidas com a modelagem de Fick e de Stefan-Maxwell com dados experimentais, mostrou que no início do processo de deposição, o impacto do modelo difusivo é desprezível. Porém, observou-se que a medida que o tempo passa, o modelo de Stefan Maxwell prevê um maior incremento da concentração das espécies mais pesadas no interior do depósito de parafina quando comparado com a previsão da modelagem de Fick. / [en] Petroleum is formed by a chain of hydrocarbons, which precipitates in the form of solid particles of paraffin, when its temperature drops below a threshold known as Wax Appearance Temperature (WAT). These particles can be deposited on the inner walls of the pipelines, obstructing the flow, which can generate losses in the order of several millions of dollars. For this reason, the ability to predict and control wax deposition in future events is of fundamental importance for both designers and operators of pipelines. In an attempt to deal with this problem, a great effort has been made by the scientific community aiming to improve wax deposition prediction methodologies. Often, the modeling of species diffusion is performed using Fick s law, valid for binary mixtures, although the hydrocarbons present in the oil form a multicomponent solution. The present work proposes to evaluate the species mass diffusive flux employing the Stefan-Maxwell model, compatible with multicomponent systems. To determine the axial and temporal evolution of the wax deposition thickness, the flow was modelled as a liquid/solid mixture and the conservation equations of energy, mass, linear momentum and species continuity were solved coupled with the thermodynamic model of multiple solid solutions, to determine the paraffin precipitation. The conservation equations were solved using the open-source software OpenFOAM (trademark). A comparison of the predictions obtained with the Fick and Stefan-Maxwell models with experimental data showed that at the beginning of the deposition process, the impact of diffusive model is negligible. However, it was observed that as time passes, the Stefan-Maxwell model predicts a greater increase in the concentration of heaviest species inside the wax deposit when compared to the prediction of Fick s law

Solid oxide fuel cells (SOFCs) are solid-state ceramic cells, typically operating between 1073 K and 1273 K. Because of high operating temperature, SOFCs are mostly applicable in stationary power generation. Among various configurations in which SOFCs exist, the planar configuration of solid oxide fuel cell (SOFC) has the potential to offer high power density due to shorter current path. Moreover, the planar configuration of SOFC is simple to stack and closely resemble the stacking arrangement of polymer electrolyte membrane (PEM) fuel cells. However, due to high operating temperature, there are problems associated with the development and commercialization of planar SOFCs, such as requirement of high temperature gas seals, internal stresses in cell components, and high material and manufacturing costs. Mathematical modeling is an essential tool for the advancement of SOFC technology. Mathematical models can help in gaining insights on the processes occurring inside the fuel cell, and can also aid in the design and optimization of fuel cells by examining the effect of various operating and design conditions on performance. A multi-component and multi-dimensional mathematical model of SOFCs has been developed in this thesis research. One of the novelties of the present model is its treatment of electrodes. An electrode in the present model is treated as two distinct layers referred to as the backing layer and the reaction zone layer. Reaction zone layers are thin layers in the vicinity of the electrolyte layer where electrochemical reactions occur to produce oxide ions, electrons and water vapor. The other important feature of the present model is its flexibility in fuel choice, which implies not only pure hydrogen but also any reformate composition can be used as a fuel. The modified Stefan-Maxwell equations incorporating Knudsen diffusion are used to model multi-component diffusion in the porous backing and reaction zone layers. The coupled governing equations of species, charge and energy along with the constitutive equations in different layers of the cell are solved for numerical solution using the finite volume method and developed code written in the computer language of C++. In addition, the developed numerical model is validated with various experimental data sets published in the open literature. Moreover, it is verified that the electrode in an SOFC can be treated as two distinct layers referred to as the backing layer and the reaction zone layer. The numerical model not only predicts SOFC performance at different operating and design conditions but also provides insight on the phenomena occurring within the fuel cell. In an anode-supported SOFC, the ohmic overpotential is the single largest contributor to the cell potential loss. Also, the cathode and electrolyte overpotentials are not negligible even though their thicknesses are negligible relative to the anode thickness. Moreover, methane reforming and water-gas shift reactions aid in significantly reducing the anode concentration overpotential in the thick anode of an anode-supported SOFC. A worthwhile comparison of performance between anode-supported and self-supported SOFCs reveals that anode-supported design of SOFCs is the potential design for operating at reduced temperatures. A parametric study has also been carried out to investigate the effect of various key operating and design parameters on the performance of an anode-supported SOFC. Reducing the operating temperature below 1073 K results in a significant drop in the performance of an anode-supported SOFC; hence ionic conductivity of the ion-conducting particles in the reaction zone layers and electrolyte needs to be enhanced to operate anode-supported SOFCs below 1073 K. Further, increasing the anode reaction zone layer beyond certain thickness has no significant effect on the performance of an anode-supported SOFC. Moreover, there is a spatial limitation to the transport of oxide ions in the reaction zone layer, thereby reflecting the influence of reaction zone thickness on cell performance.

Solid oxide fuel cells (SOFCs) are solid-state ceramic cells, typically operating between 1073 K and 1273 K. Because of high operating temperature, SOFCs are mostly applicable in stationary power generation. Among various configurations in which SOFCs exist, the planar configuration of solid oxide fuel cell (SOFC) has the potential to offer high power density due to shorter current path. Moreover, the planar configuration of SOFC is simple to stack and closely resemble the stacking arrangement of polymer electrolyte membrane (PEM) fuel cells. However, due to high operating temperature, there are problems associated with the development and commercialization of planar SOFCs, such as requirement of high temperature gas seals, internal stresses in cell components, and high material and manufacturing costs. Mathematical modeling is an essential tool for the advancement of SOFC technology. Mathematical models can help in gaining insights on the processes occurring inside the fuel cell, and can also aid in the design and optimization of fuel cells by examining the effect of various operating and design conditions on performance. A multi-component and multi-dimensional mathematical model of SOFCs has been developed in this thesis research. One of the novelties of the present model is its treatment of electrodes. An electrode in the present model is treated as two distinct layers referred to as the backing layer and the reaction zone layer. Reaction zone layers are thin layers in the vicinity of the electrolyte layer where electrochemical reactions occur to produce oxide ions, electrons and water vapor. The other important feature of the present model is its flexibility in fuel choice, which implies not only pure hydrogen but also any reformate composition can be used as a fuel. The modified Stefan-Maxwell equations incorporating Knudsen diffusion are used to model multi-component diffusion in the porous backing and reaction zone layers. The coupled governing equations of species, charge and energy along with the constitutive equations in different layers of the cell are solved for numerical solution using the finite volume method and developed code written in the computer language of C++. In addition, the developed numerical model is validated with various experimental data sets published in the open literature. Moreover, it is verified that the electrode in an SOFC can be treated as two distinct layers referred to as the backing layer and the reaction zone layer. The numerical model not only predicts SOFC performance at different operating and design conditions but also provides insight on the phenomena occurring within the fuel cell. In an anode-supported SOFC, the ohmic overpotential is the single largest contributor to the cell potential loss. Also, the cathode and electrolyte overpotentials are not negligible even though their thicknesses are negligible relative to the anode thickness. Moreover, methane reforming and water-gas shift reactions aid in significantly reducing the anode concentration overpotential in the thick anode of an anode-supported SOFC. A worthwhile comparison of performance between anode-supported and self-supported SOFCs reveals that anode-supported design of SOFCs is the potential design for operating at reduced temperatures. A parametric study has also been carried out to investigate the effect of various key operating and design parameters on the performance of an anode-supported SOFC. Reducing the operating temperature below 1073 K results in a significant drop in the performance of an anode-supported SOFC; hence ionic conductivity of the ion-conducting particles in the reaction zone layers and electrolyte needs to be enhanced to operate anode-supported SOFCs below 1073 K. Further, increasing the anode reaction zone layer beyond certain thickness has no significant effect on the performance of an anode-supported SOFC. Moreover, there is a spatial limitation to the transport of oxide ions in the reaction zone layer, thereby reflecting the influence of reaction zone thickness on cell performance.