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• W2059301796 abstract "Abstract Homogenization is a powerful upscaling technique, which has been successfully applied to a variety of problems of interest, such as reactive contaminant transport and two phase flow in layered and fractured media. It has several advantages over other upscaling techniques, such as REV averaging. It does not use intuitive closure equations and it explicitly shows the dependence of the upscaled equations on the characteristic dimensionless numbers of interest. It is based on a well defined procedure, which precludes ad hoc assumptions. A disadvantage is that the underlying assumptions of this procedure have not received sufficient attention in the existing literature. This paper examines the existing homogenization models for two phase flow in fractured media with the purpose to clarify the underlying physical assumptions. We give the derivation for a specific case for which we discuss the validity of the assumptions. Finally, we discuss an example to show the applicability of the ensuing model equations. Introduction Naturally fractured petroleum reservoirs (NFR's) represent over 20% of the world's oil and gas reserves [19], but are among the most complicated class of reservoirs to produce efficiently. NFR's comprise an interconnected fracture system that provides the main flow paths and the reservoir rock or matrix that acts as the main source of hydrocarbons. There are various types of fractured media with different types of flow behavior. Characterization of fractured reservoirs presents unique challenges in comparison with conventional reservoirs [17], [23], [24], i.e. without regions of interconnected highly permeable paths. Characteristics of fractured reservoirs that are important for the flow modeling comprise:continuity of fractured networks [18],anisotropy of fractured systems,existence of capillary pressure continuity between matrix blocks, i.e. reservoirs where the matrix blocks do (dual permeability) or do not (dual porosity) contribute significantly to the overall permeability,the value of the permeability ratio of fractures and matrix blocks, andgeometry of the fracture systems, i.e. consisting of regions with different fracture geometries or systems consisting of hierarchy of fracture systems at different scales (multi-scale fractures) [26]. Flow modeling in fractured reservoirs was greatly advanced by Barenblatt [6] who introduced the concept of dual porosity. In addition, he introduced the transfer function and shape factor. From the geometrical point of view, Barenblatt assumes that the fracture system is regular to some extent. Warren and Root [25] used the double porosity model and applied it to a well test analysis. They also introduced the sugar cube model, which has been the basis of many of the fractured reservoir simulators since that time. The double porosity model of Warren and Root for examining pressure drawdown and buildup phenomena in naturally fractured reservoirs was extended by Kazemi [13], [14] to interpret interference test results. A new approach was introduced by Douglas and Arbogast [8], [9], [10], where they applied a new upscaling technique (homogenization) to derive the model equations for flow in fractured reservoirs. This method leads to the same overall mass balance as used in the references mentioned above. Moreover, it gives a basis for deriving transfer functions between a matrix and fracture. This is in particular relevant for transfer functions describing countercurrent imbibition of water, which forces oil out of the matrix into the fracture. Also, more intuitive approaches can be found in the literature. Dutra and Aziz [11] presented a model that takes into account the transient nature of the imbibition process and the effect of variation in fracture saturation. Sarma and Aziz [21] proposed a general numerical technique to calculate the shape factor for any arbitrary shape of the matrix block, i.e. non-orthogonal fractures." @default.
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• W2059301796 date "2007-06-11" @default.
• W2059301796 modified "2023-10-16" @default.
• W2059301796 title "Upscaling in fractured reservoirs using homogenization" @default.
• W2059301796 doi "https://doi.org/10.2118/107383-ms" @default.
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