A simulação pluriGaussiana truncada é usada para simulação de dados categóricos, tais como fácies em um contexto geológico. Esse método é uma extensão da Gaussiana truncada, mas que permite a simulação de feições geológicas complexas. Nessa dissertação, a simulação pluriGaussiana truncada foi baseada nas curvas de proporção obtidas da interpolação multiquádrica. Esse método foi testado com uma amostra composta por 24 sondagens obtidas de um modelo geológico sintético. As realizações da simulação pluriGuassiana truncada foram pós-processadas para obter o modelo médio, bem como as incertezas associadas. Os resultados mostraram que as incertezas estão associadas com os contatos litológicos. / The truncated pluriGaussian simulation is used for categorical data simulation, such as facies in a geological context. This method is an extension of the Gaussian truncated, but it allows simulation of complex geological features. In this dissertation, the method of truncated pluriGaussian simulation was based on proportion curves computed form multiquadric interpolation. This method was tested with a sample composed of 24 drill holes drawn from a synthetic geologic model. Realizations of truncated pluriGaussian simulation are post-processed to get the average model and associated uncertainty as well. Result showed that uncertainties are always associated with geological contacts.

A simulação pluriGaussiana truncada é usada para simulação de dados categóricos, tais como fácies em um contexto geológico. Esse método é uma extensão da Gaussiana truncada, mas que permite a simulação de feições geológicas complexas. Nessa dissertação, a simulação pluriGaussiana truncada foi baseada nas curvas de proporção obtidas da interpolação multiquádrica. Esse método foi testado com uma amostra composta por 24 sondagens obtidas de um modelo geológico sintético. As realizações da simulação pluriGuassiana truncada foram pós-processadas para obter o modelo médio, bem como as incertezas associadas. Os resultados mostraram que as incertezas estão associadas com os contatos litológicos. / The truncated pluriGaussian simulation is used for categorical data simulation, such as facies in a geological context. This method is an extension of the Gaussian truncated, but it allows simulation of complex geological features. In this dissertation, the method of truncated pluriGaussian simulation was based on proportion curves computed form multiquadric interpolation. This method was tested with a sample composed of 24 drill holes drawn from a synthetic geologic model. Realizations of truncated pluriGaussian simulation are post-processed to get the average model and associated uncertainty as well. Result showed that uncertainties are always associated with geological contacts.

Doctor en Ingeniería de Minas / The conditional simulation of geological domains, coded through categorical regionalized variables, allows constructing outcomes (realizations) of the layout of these domains that reproduce their spatial continuity and dependence relationships. These realizations can be further processed to quantify geological uncertainty and to determine the probability that a given domain prevails at any unsampled location or jointly over several locations. This information is essential to geological control in order to take proper decisions when mining an ore deposit. Among the existing approaches for simulating geological domains, the plurigaussian model has become popular in the petroleum and mining industries. In this model, the domains are obtained by truncating one or more Gaussian random fields. Even so, the model is well-established only in the stationary case, when the spatial distribution of the domains is homogeneous in space, and suffers from theoretical and practical impediments in the non-stationary case. To overcome these limitations, this thesis proposes several improvements in plurigaussian modeling. The main one is the extension of the model to the truncation of intrinsic random fields of order k with Gaussian generalized increments, instead of stationary Gaussian random fields, which allows reproducing spatial trends and zonal patterns in the distribution of the geological domains, a feature commonly met in practice with lithological, mineralogical and alteration domains. To this end, methodological proposals are made in relation to the definition of geostatistical tools and algorithms for inferring the model parameters (truncation rule based on considerations of the domain chronology and contact relationships, truncation thresholds, and generalized covariance functions of the underlying intrinsic random fields of order k) and for the construction of realizations conditioned to existing data. Also, the proposals are put in practice through synthetic case studies and a real case study (Río Blanco ore deposit) to demonstrate their applicability. The benefits of the proposed non-stationary plurigaussian model are twofold: (i) it allows reproducing trends in the spatial distribution of the geological domains, and (ii) the local proportions of the domains are not needed in the simulation process, thus the model is not affected by possible misspecifications of these proportions. Despite the very limited number of conditioning data, the Río Blanco case study shows a remarkable agreement between the simulated rock type domains and the lithological model interpreted by geologists, and proves to be much more successful than the conventional stationary plurigaussian model. The proposal thus appears as an attractive alternative for stochastic geological domaining, based on a sound theoretical background and on the incorporation of qualitative geological knowledge, such as the chronology, contact relationships or spatial trends of the domains to be simulated, which is helpful for guiding the modeling process and validating it.

Ce travail porte sur la compréhension de l’impact de la microstructure sur les performances des Cellules à Oxyde Solide (SOC), avec une illustration sur l’électrode à oxygène en LSCF-CGO. Une approche couplant de la modélisation géométrique et électrochimique a été adoptée pour cet effet. Le modèle des champs aléatoires plurigaussiens et un autre basé sur des empilements de sphères ont été développés et adaptés pour les microstructures des SOCs. Ces modèles 3D de géométrie stochastique ont été ensuite validés sur différentes électrodes reconstruites par nano-holotomographie aux rayons X au synchrotron ou par tomographie avec un microscope électronique à balayage couplé à une sonde ionique focalisée. Ensuite, des corrélations semi-analytiques ont été proposées et validées sur une large base de microstructures synthétiques. Ces relations permettent de relier les paramètres ‘primaires’ de l’électrode (la composition, la porosité et les diamètres des phases) aux paramètres qui pilotent les réactions électrochimiques (la densité de points triples, les surfaces spécifiques interphases) et sont particulièrement pertinents pour les équipes de mise-en-forme des électrodes qui ont plus de contrôle sur ce premier ensemble de paramètres. Concernant la partie portant sur l’électrochimie, des tests sur une cellule symétrique en LSCF-CGO ont permis de valider un modèle déjà développé au sein du laboratoire, et qui permet de simuler la réponse électrochimique d’une électrode à oxygène à partir des données thermodynamiques et de microstructure. Finalement, le couplage des deux modèles validés a permis d’étudier l’impact de la composition des électrodes, leur porosité ou encore taille des grains sur leurs performances. Ces résultats pourront guider les équipes de mise-en-forme des électrodes vers des électrodes plus optimisées. / This work aims at better understanding the impact of Solid Oxide Cells (SOC) microstructure on their performance, with an illustration on an LSCF-CGO electrode. A coupled 3D stochastic geometrical and electrochemical modeling approach has been adopted. In this frame, a plurigaussian random field model and an in-house sphere packing algorithm have been adapted to simulate the microstructure of SOCs. The geometrical models have been validated on different electrodes reconstructed by synchrotron X-ray nano-holotomography or focused ion-beam tomography. Afterwards, semi-analytical microstructural correlations have been proposed and validated on a large dataset of representative synthetic microstructures. These relationships allow establishing the link between the electrode ‘basic’ parameters (composition, porosity and grain size), to the ‘key’ electrochemical parameters (Triple Phase Boundary length density and Specific surface areas), and are particularly useful for cell manufacturers who can easily control the first set of parameters. Concerning the electrochemical part, a reference symmetrical cell made of LSCF-CGO has been tested in a three-electrode setup. This enabled the validation of an oxygen electrode model that links the electrode morphological parameters to its polarization resistance, taking into account the thermodynamic data. Finally, the coupling of the validated models has enabled the investigation of the impact of electrode composition, porosity and grain size on the cell electrochemical performance, and thus providing useful insights to cell manufacturers.