Numerical simulation of different-scale fracture effects on saturation distributions in waterflooding via the finite volume method

Capturing the heterogeneity and multiple scales in fractured media is important for understanding the underlying mechanisms controlling the flow behavior, as both natural and hydraulic fractures can dominate the flow patterns in media of this type. Fracture characteristics, such as heterogeneity, multiple scales, and extreme size-to-aperture ratios, challenge standard macroscale mathematical and numerical modeling methods of the flow based on the concept of volume averaging. This paper presents a finite volume method approach for solving a two-phase flow model of discrete fractures that accounts for the heterogeneity and multiscale fracture distribution in fractured reservoirs. Fracture model combinations, obtained by restricting different models to different parts of a domain or by using models with explicit representations of fractures as a basis for upscaled continuum models, are also presented. Furthermore, the model error correction method due to fracture dimensionality reduction and an inappropriate upwind scheme is also analyzed.