The geological complexity of fractured reservoirs necessitates the use of simplified models for flow simulation. This is often addressed in practice by using flow modeling procedures based on the dual-porosity/dual-permeability concept. However, there is often not a systematic and quantitative link between the underlying discrete fracture model (DFM) and the parameters appearing in the flow model.
In this work, a systematic upscaling methodology is presented to construct a generalized dual-porosity/dual-permeability model from detailed discrete fracture characterizations. The technique, referred to as a multiple subregion (MSR) method, introduces local subregions (or subgrids) to resolve dynamics within the matrix and provides appropriate coarse-scale parameters describing fracture/fracture, matrix/fracture, and matrix/matrix flow. The geometry of the local subregions, as well as the required parameters for the coarse-scale model, are determined efficiently from local single-phase flow solutions using the underlying DFM. Three variants of the method are developed and tested. The first procedure provides a generalized dual-porosity model and is appropriate for systems with weak or nonexistent gravitational effects. The second procedure introduces connections between matrix regions in vertically adjacent blocks to capture phase segregation due to gravity. The third approach is a full dual-porosity/dual-permeability representation and includes connections between matrix regions in vertically and horizontally adjacent blocks.
The methods are applied to simulate single-phase, two-phase, three-phase, and compositional flows in 2D and 3D fractured reservoir models. Viscous, gravitational, and capillary pressure effects are considered. The MSR models are shown to provide results in close agreement with the underlying DFMs at computational speedups of order 100 for oil/water simulations and 1,000 for compositional simulations.
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