Multilevel Multiscale Method for Embedded Discrete Fracture Modeling Approach (F-MLMS)

Abstract

Accurate numerical simulations of multiphase flow in fractured porous media require high resolution grids to explicitly capture the effect of fractures on the flow field without using excessively up-scaled quantities (e.g., modified rock permeabilities). For field-scale applications, as the consequence of large-scale domains and many explicit fractures, the size of the (non)linear systems becomes out of the scope of the classical numerical methods. Thus, various advanced numerical methods have been introduced to reduce this computational challenge. The Embedded Discrete Fracture Model (EDFM) which employs sets of independent grids for the rock matrix and the fractures (represented as lower dimensional domains). By employing two separate grids, coupled by a transfer function, EDFM allows to avoid adapting the matrix grid to accommodate the presence of fractures. Therefore, computational complexities with respect to the fracture geometries are significantly reduced. Even after employing EDFM, the size of the systems for real-field applications is still too large to be solved accurately with classical solvers. This challenge motivates the development of Multiscale Finite Volume (MSFV) method, which is the focus of this work, as well. The MSFV method efficiently solves the pressure (flow) equations by solving it at a coarser resolution, while honoring the fine-scale heterogeneous data. Recently, an efficient MSFV method for EDFM approach (F-AMS) was developed and tested for many cases of practical interests. Even though the F-AMS was found efficient for many scenarios, its applicability is limited to only the use of 2 levels of grids (fine and coarse). For real-field applications, where there exist several millions (or billions) degrees of freedom, the construction of only 1 level of coarse grid resolution may not be sufficient. Of high interest to the community is the development of a multiscale method which allows for arbitrary number of accurate coarse resolutions. In this work, for the first time in the multiscale community, a novel multilevel multiscale finite volume method for fractured porous media (F-MLMS) is developed. F-MLMS is successfully applied to a set of synthetic 2D test cases and its performance is carefully studied. Employing a multilevel strategy becomes crucial for field-scale applications, where a single level of coarsening is not enough to reduce significantly the size of the linear systems to be solved. The use of two independent grids allows to employ different coarsening strategies for the two media. Consequently, F-MLMS represents an important step forward for the application of multiscale methods to naturally and induced fractured reservoirs, with complex fracture networks.Civil Engineering and GeosciencesGeoscience & EngineeringPetroleum Engineering and Geo-science