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Os modelos de covariância são ferramentas geoestatísticas essenciais para mapear a continuidade espacial. A abordagem atual busca um modelo de continuidade espacial lícito com mínima ou até mesmo sem nenhuma interferência do usuário. Alinhado a essa visão moderna, é proposto obter uma tabela de covariância que visa substituir na prática o modelo tradicional explicitamente definido de covariância. Essa tabela de covariância é obtida por meio de três etapas: interpolar o conjunto de dados para preencher um grid regular, aplicar a convolução através do algoritmo da transformada rápida de Fourier e, por fim, transformar de volta para o domínio espacial. O modelo base para extrair covariância representa o ponto chave comparando com os métodos anteriores que propuseram o uso da tabela de covariância. Os resultados são satisfatórios, tanto na validação estatística do método, quanto na rapidez de obtenção de uma análise de continuidade espacial. Um estudo de caso tridimensional ilustra a aplicação prática através de krigagem e simulação geoestatística em comparação com a modelagem espacial tradicional. / Covariance models are essential geostatistical tools to map spatial continuity. The current approach pursues a licit spatial continuity model with minimum or even no user interference. Aligned with this modern view we propose to obtain a covariance table that aims at replacing in practice traditional covariance explicit defined model. This covariance table is obtained through a three steps work flow: interpolating the dataset to fill up a regular grid, auto convolute via Fast Fourier Transform algorithm and back transform to spacial domain. The base model to extract covariance represents the turning point comparing with previous methods that proposed covariance table usage. The results are satisfactory, both in the statistical validation of the method and in the speed of obtaining a spatial continuity analysis. A three dimensional case study illustrates the practical application for kriging and geostatistical simulation in comparison with traditional spatial modeling.

This thesis aims to find out the effective diffusivity (Deff) of a porous material – γ-alumina, using an unsteady state method with two inert gases at ambient condition with no reactions. For porous materials, Deff is important because it determines the amount of reactants that transfers to the surface of pores. When Deff is known, the apparent tortuosity factor of γ-alumina is calculated using the parallel pore model. The apparent tortuosity factor is important because: (a) it can be used to back-calculate Deff at reacting conditions; (b) once Deff with reactions is known, the Thiele modulus can be calculated and hence the global reaction rate can be found; (c) apparent tortuosity factor is also important for modelling purposes (e.g. modelling a packed-bed column or a catalytic combustion reactor packed with porous γ-alumina in various shapes and monoliths). Experimental measurements were performed to determine the effective diffusivity of a binary pair of non-reacting gases (He in N2, and N2 in He) in spherical γ-alumina pellets (1 mm diameter), and in γ-alumina washcoated monoliths (washcoat thickness 20 to 60 µm, on 400 cpsi (cells per square inch) cordierite support). The method used is based on the chromatographic technique, where a gas flows through a tube, which is packed with the sample to be tested. A pulse of tracer gas is injected (e.g. using sample loops: 0.1, 0.2, 0.5 ml) and by using an on-line mass spectrometer the response in the outlet of the packed bed is monitored over time. For the spherical pellets, the tube i.d. = 13.8 mm and the packed bed depths were 200 and 400 mm. For monoliths the tube i.d. = 7 mm and the packed lengths were 500 and 1000 mm. When the chromatographic technique was applied to the monoliths, it was observed that experimental errors can be significant, and it is very difficult to interpret the data. However, the technique worked well with the spherical pellets, and the effective diffusivity of He in N2 was 0.75 – 1.38 × 10-7 m2 s-1, and for N2 in He was 1.81 – 3.10 × 10-7 m2 s-1. Using the parallel pore model to back-calculate the apparent tortuosity factor, then a value between 5 to 9.5 was found for the pellets.