Abstract: |
Distance-based method has been successfully applied to various kinds of geological modeling problems such as history matching, uncertainty qualification and pattern-based geostatistical simulation as an effective means of model parameterization or pattern classification. Individual reservoir models or geological patterns are parameterized as points in a space defined by a distance function which measures similarity between a pair of models or geological patterns. The reservoir models or geological patterns are positioned in this similarity space in such a way that similar ones are clustered and dissimilar ones are separated. Because of such nature of the space, statistical clustering method or search technique can be efficiently implemented. This paper proposes a new application of the distance-based method to the area of multi-phase flow upscaling. The proposed upscaling technique relies on dynamic pseudo function method utilizing local boundary condition. The major limitation of existing methods is that different simulation gridblock obtains different pseudo function, resulting in the requirement of generation and usage of too many pseudo relative permeability curves that exceed the capability of conventional flow simulation practices. Several attempts to group pseudo functions have been made since 1990s. However, they have not yet attained enough efficiency and robustness for commercial applications. In the method proposed in this paper, we quickly generate a subgrid-scale pattern of displacement front for each simulation gridblock based on fine-scale geological description. Fast static method that uses shortest-path algorithm enables such a rapid generation of displacement front profile without running flow or streamline simulation. Then, by using distance-based approach, simulation gridblocks are clustered in accordance with the similarity of the shape of displacement front. All simulation gridblocks belonging to the same cluster can share the same dynamic pseudo function because of the strong correlation between displacement front profile and pseudo relative permeability curves.
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