Upscaled modeling of well singularity for simulating flow in heterogeneous formations |
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Authors: | Yuguang Chen Xiao-Hui Wu |
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Institution: | (1) Department of Petroleum Engineering (now Energy Resources Engineering), Stanford University, Stanford, CA 94305, USA;(2) Present address: Chevron Energy Technology Company, P.O. Box 6019, San Ramon, CA 94583, USA;(3) ExxonMobil Upstream Research Company, P.O. Box 2189, Houston, TX 77252, USA |
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Abstract: | Subsurface flows are affected by geological variability over a range of length scales. The modeling of well singularity in
heterogeneous formations is important for simulating flow in aquifers and petroleum reservoirs. In this paper, two approaches
in calculating the upscaled well index to capture the effects of fine scale heterogeneity in near-well regions are presented
and applied. We first develop a flow-based near-well upscaling procedure for geometrically flexible grids. This approach entails
solving local well-driven flows and requires the treatment of geometric effects due to the nonalignment between fine and coarse
scale grids. An approximate coarse scale well model based on a well singularity analysis is also proposed. This model, referred
to as near-well arithmetic averaging, uses only the fine scale permeabilities at well locations to compute the coarse scale
well index; it does not require solving any flow problems. These two methods are systematically tested on three-dimensional
models with a variety of permeability distributions. It is shown that both approaches provide considerable improvement over
a simple (arithmetic) averaging approach to compute the coarse scale well index. The flow-based approach shows close agreement
to the fine scale reference model, and the near-well arithmetic averaging also offers accuracy for an appropriate range of
parameters. The interaction between global flow and near-well upscaling is also investigated through the use of global fine
scale solutions in near-well scale-up calculations. |
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Keywords: | Upscaling Permeability Heterogeneity Well model Well index Singularity Reservoir simulation Subsurface flow |
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