Upscaled Unstructured Computational Grids for Efficient Simulation of Flow in Fractured Porous Media

Abstract

Discrete fracture modeling (DFM) is currently the most promising approach for modeling of naturally fractured reservoirs and simulation of multiphase fluid flow therein. In contrast with the classical double-porosity/double permeability models, in the DFM approach all the interactions and fluid flow in and between the fractures and within the matrix are modeled in a unified manner, using the same computational grid. There is no need for computing the shape factors, which are crucial to the accuracy of the double-porosity models. We have exploited this concept in order to develop a new method for the generation of unstructured computational grids. In the new approach the geological model (GM) of the reservoir is first generated, using square or cubic grid blocks. The GM is then upscaled using a method based on the multiresolution wavelet transformations that we recently developed. The upscaled grid contains a distribution of the square or cubic blocks of various sizes. A map of the blocks' centers is then used with an optimized Delauney triangulation method and the advancingfront technique, in order to generate the final unstructured triangulated grid suitable for use in any general reservoir simulator with any number of fluid phases. The new method also includes an algorithm for generating fractures that, contrary to the previous methods, does not require modifying their paths due to the complexities that may arise in spatial distribution of the grid blocks. It also includes an effective partitioning of the simulation domain that results in large savings in the computation times. The speed-up in the computations with the new upscaled unstructured grid is about three orders of magnitude over that for the initial GM. Simulation of waterflooding indicates that the agreement between the results obtained with the GM and the upscaled unstructured grid is excellent. The method is equally 123 196 M. Sahimi et al. applicable to the simulations of multiphase flow in unfractured, but highly heterogeneous, reservoirs.

Interior boundary-aligned unstructured grid generation and cell-centered versus vertex-centered CVD-MPFA performance

“…[69], in addition reservoirs can have a complex spatial distribution of wells in place. In order to minimize discretization error, it is common practice to generate meshes which are aligned with such features, thereby leading to feature based triangulations.…”

“…In addition to robust numerical methods for solving the flow equations, grid generation methods are required which can honor geometric complexity and permit local grid cell density control. Grid generation for large-scale porous media poses the challenge of complex geometries and random distribution of spatial heterogeneities in the domain, e.g., [42,69].…”

Unstructured Grid Generation in Porous Domains for Flow Simulations with Discrete-Fracture Network Model

“…Many researchers have studied or employed unstructured grids in geological simulations (Gable et al 1996;Kim and Deo 2000;Karimi-fard and Firoozabadi 2001;Monteagudo and Firoozabadi 2004;Karimi-fard et al 2004;Caumon et al 2005;Prévost et al 2005;Reichenberger et al 2006;Hoteit and B Alireza Daneh Dezfuli a.danehdezfuli@scu.ac.ir Firoozabadi 2008; Blessent et al 2009;Haegland et al 2009;Blöcher et al 2010;Sahimi et al 2010;Mustapha 2011;Tatomir et al 2011). Most of these researchers have utilized Delaunay triangulation or advancing front methods (Delaunay 1934;Bowyer 1981;Watson 1981;Weatherill 1985;Baker 1987;Löhner and Parikh 1988;Frey et al 1998;Pirzadeh 1999;Ito et al 2004).…”

Physics-based preconditioners for flow in fractured porous media

“…An alternative approach, which is less reliant on heuristic assumptions, is to tackle the fine‐scale problem directly with a linear solver, for instance based on algebraic multigrid (AMG) [ Stüben , ]. Even though AMG‐based solvers are routinely employed in reservoir simulations, it is yet not feasible to resolve individual fractures in realistic reservoir scale simulations [ Sahimi et al ., ]. Instead the upscaled models reviewed in the previous paragraph are commonly applied in spite of their known limitations.…”