Multiscale Methods
Several reasons motivate us to develop a multiscale framework for a naturally fractured rock. Among them is intrinsic multiscale nature of the natural geologic formation; mainly, heterogeneous anisotropic properties with different multiscale spatial features. The wide range of length and times scales requires high-resolution discretization, which is, given fine geologic data, is computationally inefficient. Standard upscaling techniques can lead to inaccurate results, especially for the fractured formations, where it is hard to calculate an accurate effective, or homogenized, stiffness tensor. This is critical in presence of fractures; for near-wellbore stability; CO2 sequestration problems; in shale gas or hydrate formations.
Importantly, in contrast with fluid flow in a heterogeneous permeability field, where inaccurate resolving of fine-scale features (channels, faults/barriers, layers) can result in incorrect flow and saturation paths, and, ultimately, in an incorrect breakthrough time and production rate, a microscale mechanical heterogeneity affects macroscopic deformation, and the way fractures are being created. For example, small-scale damage processes can lead to large faults reactivation and instabilities (large-scale response).