Atualmente, restrições ambientais impostas à industria de refino de petróleo estão fazendo com que se procure otimizar os seus processos. Uma das maneiras de se alcançar este objetivo é através da melhoria dos métodos analíticos de caracterização e dos métodos de representação, cuja finalidade é permitir maior precisão na simulação. O método mais comum de representação através de pseudocomponentes, apresenta algumas desvantagens, as quais não permitem precisão adequada em determinadas situações. Uma nova metodologia apresentada neste trabalho, que permite superar essas desvantagens foi aplicada em um exemplo de flash de petróleo. Esta metodologia envolve varias etapas: a implementação dos algoritmos necessários à representação das composições da mistura por funções de distribuição contínua e sua aproximação por funções wavelets, e a simplificação do modelo flash com a discretização \"Wavelet-Galerkin\" e sua resolução através de um enfoque multi-malha adaptativo. Neste contexo, na primeira etapa da tese foram apresentados diferentes aspectos relacionados ao processo complexo de caracterização de petróleos, que consideram sua importância tanto econômica quanto tecnológica. Mostraram-se também, o uso de ferramentas matemáticas e suas vantagens para resolver os problemas complexos em diversas áreas científicas. Na segunda etapa foi desenvolvida a metodologia proposta. Para tanto, os algoritmos foram construídos na linguagem de programação de Matlab. Em seguida, duas simulações do modelo flash permitiram avaliar sua precisão e sua eficiência. A primeira foi realizada sem a implementação de seleção de malhas adaptativamente, enquanto que a segunda foi realizada utilizando dita implementação, a qual permitiu construir quatro casos e analisar os resultados dos mesmos. Finalmente, com o objetivo de avaliar seu potencial de utilização em um ambiente de simulação, estes resultados foram comparados com uma terceira simulação, utilizando o simulador HYSYS, o qual se baseia na representação de pseudocomponentes. / Current environmental constraints to the refining industry make process optimization a necessary task. It can be achieved by improving the analysis methods applied to oil characterization and the representation methods, in order to improve simulation accuracy. The most common method of representation based on pseudocomponents presents some disadvantages, which do not enable a detailed accuracy in some situations. In this work a new methodology is proposed to surpass these disadvantages, and applied to oil flash as an example. The proposed methodology involves the representation of the mixture compositions by continuous distribution functions, which are approximated by wavelet functions, and the simplification of the flash model by the \"Wavelet-Galerkin\" discretization which are solved by multigrid adaptive approach. In this contex, in the first part of this work different aspects related to the complex process of petroleum characterization are discussed, considering their economical and technological importance. Besides, the utility of mathematical tools, and their advantages to solve complex problems in different scientific fields, are presented. In the second part, the proposed methodology is developed. All algorithms are built with MatLab programming languages. Two simulations of the model of flash process enabled to evaluate the precision and the efficiency of the methodology. The first simulation was developed without the implementation of an adaptability selection grid. The second was carried out with this implementation, which enabled to build four cases and analyze their results. Finally, with the objective of evaluating its potential of utilization in a simulation environment, the results were compared with a third simulation, using the simulator HYSYS, which itself is based on the representation of pseudo-components.

This document serves as a reference for the beta version of our evaluation library ITL. First, it describes a library which gives an easy way for programmers to evaluate the 3D image and the normal vector corresponding to a parameter value which belongs to the unit square. The API functions which are described in this document let programmers make those evaluations without the need to understand the underlying CAD complica- tions. As a consequence, programmers can concentrate on their own scien- tific interests. Our second objective is to describe the input which is a set of parametric four-sided surfaces that have the structure required by some integral equation solvers.

Atualmente, restrições ambientais impostas à industria de refino de petróleo estão fazendo com que se procure otimizar os seus processos. Uma das maneiras de se alcançar este objetivo é através da melhoria dos métodos analíticos de caracterização e dos métodos de representação, cuja finalidade é permitir maior precisão na simulação. O método mais comum de representação através de pseudocomponentes, apresenta algumas desvantagens, as quais não permitem precisão adequada em determinadas situações. Uma nova metodologia apresentada neste trabalho, que permite superar essas desvantagens foi aplicada em um exemplo de flash de petróleo. Esta metodologia envolve varias etapas: a implementação dos algoritmos necessários à representação das composições da mistura por funções de distribuição contínua e sua aproximação por funções wavelets, e a simplificação do modelo flash com a discretização \"Wavelet-Galerkin\" e sua resolução através de um enfoque multi-malha adaptativo. Neste contexo, na primeira etapa da tese foram apresentados diferentes aspectos relacionados ao processo complexo de caracterização de petróleos, que consideram sua importância tanto econômica quanto tecnológica. Mostraram-se também, o uso de ferramentas matemáticas e suas vantagens para resolver os problemas complexos em diversas áreas científicas. Na segunda etapa foi desenvolvida a metodologia proposta. Para tanto, os algoritmos foram construídos na linguagem de programação de Matlab. Em seguida, duas simulações do modelo flash permitiram avaliar sua precisão e sua eficiência. A primeira foi realizada sem a implementação de seleção de malhas adaptativamente, enquanto que a segunda foi realizada utilizando dita implementação, a qual permitiu construir quatro casos e analisar os resultados dos mesmos. Finalmente, com o objetivo de avaliar seu potencial de utilização em um ambiente de simulação, estes resultados foram comparados com uma terceira simulação, utilizando o simulador HYSYS, o qual se baseia na representação de pseudocomponentes. / Current environmental constraints to the refining industry make process optimization a necessary task. It can be achieved by improving the analysis methods applied to oil characterization and the representation methods, in order to improve simulation accuracy. The most common method of representation based on pseudocomponents presents some disadvantages, which do not enable a detailed accuracy in some situations. In this work a new methodology is proposed to surpass these disadvantages, and applied to oil flash as an example. The proposed methodology involves the representation of the mixture compositions by continuous distribution functions, which are approximated by wavelet functions, and the simplification of the flash model by the \"Wavelet-Galerkin\" discretization which are solved by multigrid adaptive approach. In this contex, in the first part of this work different aspects related to the complex process of petroleum characterization are discussed, considering their economical and technological importance. Besides, the utility of mathematical tools, and their advantages to solve complex problems in different scientific fields, are presented. In the second part, the proposed methodology is developed. All algorithms are built with MatLab programming languages. Two simulations of the model of flash process enabled to evaluate the precision and the efficiency of the methodology. The first simulation was developed without the implementation of an adaptability selection grid. The second was carried out with this implementation, which enabled to build four cases and analyze their results. Finally, with the objective of evaluating its potential of utilization in a simulation environment, the results were compared with a third simulation, using the simulator HYSYS, which itself is based on the representation of pseudo-components.

This document serves as a reference for the beta version of our evaluation library ITL. First, it describes a library which gives an easy way for programmers to evaluate the 3D image and the normal vector corresponding to a parameter value which belongs to the unit square. The API functions which are described in this document let programmers make those evaluations without the need to understand the underlying CAD complica- tions. As a consequence, programmers can concentrate on their own scien- tific interests. Our second objective is to describe the input which is a set of parametric four-sided surfaces that have the structure required by some integral equation solvers.

Among the presently known numerical solvers of integral equations, two main categories of approaches can be traced: mesh-free approaches, mesh-based approaches. We will propose some techniques to process geometric data so that they can be efficiently used in subsequent numerical treatments of integral equations. In order to prepare geometric information so that the above two approaches can be automatically applied, we need the following items: (1) Splitting a given surface into several four-sided patches, (2) Generating a diffeomorphism from the unit square to a foursided patch, (3) Generating a mesh M on a given surface, (4) Patching of a given triangulation. In order to have a splitting, we need to approximate the surfaces first by polygonal regions. We use afterwards quadrangulation techniques by removing quadrilaterals repeatedly. We will generate the diffeomorphisms by means of transfinite interpolations of Coons and Gordon types. The generation of a mesh M from a piecewise Riemannian surface will use some generalized Delaunay techniques in which the mesh size will be determined with the help of the Laplace-Beltrami operator. We will describe our experiences with the IGES format because of two reasons. First, most of our implementations have been done with it. Next, some of the proposed methodologies assume that the curve and surface representations are similar to those of IGES. Patching a mesh consists in approximating or interpolating it by a set of practical surfaces such as B-spline patches. That approach proves useful when we want to utilize a mesh-free integral equation solver but the input geometry is represented as a mesh.

Among the presently known numerical solvers of integral equations, two main categories of approaches can be traced: mesh-free approaches, mesh-based approaches. We will propose some techniques to process geometric data so that they can be efficiently used in subsequent numerical treatments of integral equations. In order to prepare geometric information so that the above two approaches can be automatically applied, we need the following items: (1) Splitting a given surface into several four-sided patches, (2) Generating a diffeomorphism from the unit square to a foursided patch, (3) Generating a mesh M on a given surface, (4) Patching of a given triangulation. In order to have a splitting, we need to approximate the surfaces first by polygonal regions. We use afterwards quadrangulation techniques by removing quadrilaterals repeatedly. We will generate the diffeomorphisms by means of transfinite interpolations of Coons and Gordon types. The generation of a mesh M from a piecewise Riemannian surface will use some generalized Delaunay techniques in which the mesh size will be determined with the help of the Laplace-Beltrami operator. We will describe our experiences with the IGES format because of two reasons. First, most of our implementations have been done with it. Next, some of the proposed methodologies assume that the curve and surface representations are similar to those of IGES. Patching a mesh consists in approximating or interpolating it by a set of practical surfaces such as B-spline patches. That approach proves useful when we want to utilize a mesh-free integral equation solver but the input geometry is represented as a mesh.