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Various models featuring horizontal wells with multiple induced fractures have been proposed to characterize flow behavior over time in tight gas and shale gas systems. Currently, there is little consensus regarding the effects of non-ideal fracture geometries and coupled primary-secondary fracture interactions on reservoir performance in these unconventional gas reservoirs. This thesis provides a grid construction tool to generate high-resolution unstructured meshes using Voronoi grids, which provides the flexibility required to accurately represent complex geologic domains and fractures in three dimensions. Using these Voronoi grids, the interaction between propped hydraulic fractures and secondary "stress-release" fractures were evaluated. Additionally, various primary fracture configurations were examined, where the fractures may be non-planar or non-orthogonal. For this study, a numerical model was developed to assess the potential performance of tight gas and shale gas reservoirs. These simulations utilized up to a half-million grid-blocks and consider a period of up to 3,000 years in some cases. The aim is to provide very high-definition reference numerical solutions that will exhibit virtually all flow regimes we can expect in these unconventional gas reservoirs. The simulation results are analyzed to identify production signatures and flow regimes using diagnostic plots, and these interpretations are confirmed using pressure maps where useful. The coupled primary-secondary fracture systems with the largest fracture surface areas are shown to give the highest production in the traditional "linear flow" regime (which occurs for very high conductivity vertical fracture cases). The non-ideal hydraulic fracture geometries are shown to yield progressively lower production as the angularity of these fractures increases. Hence, to design optimum fracture completions, we should endeavor to keep the fractures as orthogonal to the horizontal well as possible. This work expands the current understanding of flow behavior in fractured tight-gas and shale-gas systems and may be used to optimize fracture and completion design, to validate analytical models and to facilitate more accurate reserves estimation.

CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior / Este trabalho apresenta estudos sobre sistemas de comunicaÃÃo cujos sinais utilizados para a transmissÃo das informaÃÃes sÃo nÃo-ortogonais, superpostos em frequÃncia, e com espaÃamento entre portadoras menor do que a taxa de sÃmbolo. As pesquisas estÃo direcionadas na obtenÃÃo de estruturas de transmissor e receptor Ãtimos e sub-Ãtimos, na modelagem e anÃlise matemÃtica dos sistemas incluindo o canal, em propostas de estratÃgias para detecÃÃo de sÃmbolo, e na avaliaÃÃo de desempenho. SÃo propostas sete estratÃgias de recepÃÃo de N sinais m-QAM nÃo-ortogonais atravÃs do canal AWGN. Dentre as estratÃgias de detecÃÃo duas sÃo Ãtimas e as outras cinco sÃo subÃtimas. As duas estruturas de receptores Ãtimos apresentados neste trabalho sÃo: o receptor de mÃxima verossimilhanÃa (ML) clÃssico e o receptor de mÃxima verossimilhanÃa com base na decomposiÃÃo de Gram-Schmidt. Os receptores sub-Ãtimos desenvolvidos neste trabalho sÃo de dois tipos: receptores com equalizaÃÃo linear e receptores com equalizaÃÃo nÃo-linear. O primeiro tipo de receptor à desenvolvido com base nos critÃrios de erro quadrÃtico mÃdio mÃnimo (MMSE) e o de forÃagem a zero (ZF). à apresentado o desenvolvimento analÃtico do projeto de cada uma das arquiteturas de receptores lineares, assim como à determinado o erro dos estimadores. Os receptores com equalizaÃÃo nÃo-linear sÃo baseados no cancelamento de interferÃncia sucessiva (SIC). Neste trabalho, à proposta uma modificaÃÃo no algoritmo do SIC original, resultando em uma nova arquitetura de equalizaÃÃo. O desempenho dos receptores propostos à avaliado em diferentes condiÃÃes de nÃmero de portadoras e de grau de superposiÃÃo espectral atravÃs de simulaÃÃo computacional. Por fim, sÃo apresentados as conlusÃes e as perspectivas futuras de pesquisa. / This work presents studies on communication systems, whose signals used for transmission of information are non-orthogonal, overlapping in frequency and carrier spacing less than the rate of symbols. The research is aimed to obtain structures of transmitter, optimal and sub-optimal receivers using modeling and mathematical analysis of systems including the channel. Furthermore, propose strategies for symbol detection and performance evaluation. Seven strategies of reception to N signals m-QAM non-orthogonal through the AWGN channel. Among the strategies of detection two are optimal and the others five are suboptimal. The two optimal receivers structures presented in this paper are: the classical receiver maximum likelihood (ML) receiver and maximum likelihood based on the Gram-Schmidt decomposition. The suboptimal receivers in this work are of two types: receivers with linear and nonlinear equalization. The first type of receiver is developed based on the criteria of minimum mean square error (MMSE) and the zero forcing (ZF). It is presented the development of analytical design of each linear receiver architectures, as well as determined the error of the estimators. The receivers with nonlinear equalization are based on successive interference cancellation (SIC). In this paper, we propose a modification to the original algorithm of SIC, resulting in a new architecture of equalization. The performance of the proposed receivers is evaluated under different number of carriers and the degree of spectral overlap using computer simulation. Finally, we present the conclusions of this work and future prospects of the research.

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