Unlike the traditional two-stage methods, a conditional and inverse-conditional simulation approach may directly generate independent, identically distributed realizations to honor both static data and state data in one step. The Markov chain Monte Carlo (McMC) method was proved a powerful tool to perform such type of stochastic simulation. One of the main advantages of the McMC over the traditional sensitivity-based optimization methods to inverse problems is its power, flexibility and well-posedness in incorporating observation data from different sources. In this work, an improved version of the McMC method is presented to perform the stochastic simulation of reservoirs and aquifers in the framework of multi-Gaussian geostatistics. First, a blocking scheme is proposed to overcome the limitations of the classic single-component Metropolis-Hastings-type McMC. One of the main characteristics of the blocking McMC (BMcMC) scheme is that, depending on the inconsistence between the prior model and the reality, it can preserve the prior spatial structure and statistics as users specified. At the same time, it improves the mixing of the Markov chain and hence enhances the computational efficiency of the McMC. Furthermore, the exploration ability and the mixing speed of McMC are efficiently improved by coupling the multiscale proposals, i.e., the coupled multiscale McMC method. In order to make the BMcMC method capable of dealing with the high-dimensional cases, a multi-scale scheme is introduced to accelerate the computation of the likelihood which greatly improves the computational efficiency of the McMC due to the fact that most of the computational efforts are spent on the forward simulations. To this end, a flexible-grid full-tensor finite-difference simulator, which is widely compatible with the outputs from various upscaling subroutines, is developed to solve the flow equations and a constant-displacement random-walk particle-tracking method, which enhances the com / Fu, J. (2008). A markov chain monte carlo method for inverse stochastic modeling and uncertainty assessment [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/1969

[pt] A incorporação de dados de produção a modelos de reservatórios é uma etapa fundamental para se estimar adequadamente a recuperação de uma jazida de petróleo e, na última década, o método ensemble smoother with multiple data assimilation (ES-MDA) tem se destacado dentre as estratégias disponíveis para realizar tal tarefa. Entretanto, este é um método que apresenta melhores resultados quando os parâmetros a serem ajustados no modelo são caracterizados por uma distribuição de probabilidades próxima à gaussiana, apresentando um desempenho reduzido ao lidar com o ajuste de parâmetros categóricos, como por exemplo as fácies geológicas. Uma proposta para lidar com esse problema é recorrer a redes de aprendizado profundo, em particular redes para tradução imagem-imagem (I2I), valendo-se da analogia existente entre a representação matricial de imagem e a estrutura em malha das propriedades de um modelo de reservatórios. Assim, é possível adaptar a arquitetura de redes I2I disponíveis e treiná-las para, a partir de uma matriz de parâmetros contínuos que serão ajustados pelo método ES-MDA (como porosidade e permeabilidade), gerar a representação matricial do parâmetro categórico correspondente (fácies), de forma similar à tarefa de segmentação semântica no contexto de imagens. Portanto, o parâmetro categórico seria atualizado de maneira indireta pelo método ES-MDA, sendo a sua reconstrução realizada pela rede I2I. / [en] Reservoir model data assimilation is a key step to properly estimate the final recovery of an oil field and, in the last decade, the ensemble smoother with multiple data assimilation method (ES-MDA) has stood out among all available strategies to perform this task. However, this method achieves better results when model parameters are described by an approximately Gaussian distribution and hence presents reduced performance when dealing with categorical parameters, such as geological facies. An alternative to deal with this issue is to adopt a deep learning based approach, particularly using image-to-image translation (I2I) networks and taking into account the analogy between the matrix representation of images and the reservoir model grid properties. Thus, it is possible to adapt I2I network architectures, training them to generate the categorical parameter (facies) from its correlated continuous properties modified by the ES-MDA method (such as porosity and permeability), similar to semantic segmentation tasks in an image translation context. Therefore, the categorical parameter would be indirectly updated by the ES-MDA method, with its reconstruction carried out by the I2I network.

Dans ce travail, nous proposons de suivre une approche multi-échelles pour simuler des propriétés spatiales des réservoirs, permettant d'intégrer des données directes (observation de puits) ou indirectes (sismique et données de production) de résolutions différentes. Deux paramétrisations sont utilisées pour résoudre ce problème: les ondelettes et les pyramides gaussiennes. A l'aide de ces paramétrisations, nous démontrons les avantages de l'approche multi-échelles sur deux types de problèmes d'estimations des incertitudes basés sur la minimisation d'une distance. Le premier problème traite de la simulation de propriétés à partir d'un algorithme de géostatistique multipoints. Il est montré que l'approche multi-échelles basée sur les pyramides gaussiennes améliore la qualité des réalisations générées, respecte davantage les données et réduit les temps de calculs par rapport à l'approche standard. Le second problème traite de la préservation des modèles a priori lors de l'assimilation des données d'historique de production. Pour re-paramétriser le problème, nous développons une transformée en ondelette 3D applicable à des grilles stratigraphiques complexes de réservoir, possédant des cellules mortes ou de volume négligeable. Afin d'estimer les incertitudes liées à l'aspect mal posé du problème inverse, une méthode d'optimisation basée ensemble est intégrée dans l'approche multi-échelles de calage historique. A l'aide de plusieurs exemples d'applications, nous montrons que l'inversion multi-échelles permet de mieux préserver les modèles a priori et est moins assujettie au bruit que les approches standards, tout en respectant aussi bien les données de conditionnement. / In this work, we propose to follow a multi-scale approach for spatial reservoir properties characterization using direct (well observations) and indirect (seismic and production history) data at different resolutions. Two decompositions are used to parameterize the problem: the wavelets and the Gaussian pyramids. Using these parameterizations, we show the advantages of the multi-scale approach with two uncertainty quantification problems based on minimization. The first one concerns the simulation of property fields from a multiple points geostatistics algorithm. It is shown that the multi-scale approach based on Gaussian pyramids improves the quality of the output realizations, the match of the conditioning data and the computational time compared to the standard approach. The second problem concerns the preservation of the prior models during the assimilation of the production history. In order to re-parameterize the problem, we develop a new 3D grid adaptive wavelet transform, which can be used on complex reservoir grids containing dead or zero volume cells. An ensemble-based optimization method is integrated in the multi-scale history matching approach, so that an estimation of the uncertainty is obtained at the end of the optimization. This method is applied on several application examples where we observe that the final realizations better preserve the spatial distribution of the prior models and are less noisy than the realizations updated using a standard approach, while matching the production data equally well.