@Article{CiCP-6-162,
author = {Peter Popov, Yalchin Efendiev and Guan Qin},
title = {Multiscale Modeling and Simulations of Flows in Naturally Fractured Karst Reservoirs},
journal = {Communications in Computational Physics},
year = {2009},
volume = {6},
number = {1},
pages = {162--184},
abstract = {<p style="text-align: justify;">Modeling and numerical simulations of fractured, vuggy, porus media is a
challenging problem which occurs frequently in reservoir engineering. The problem
is especially relevant in flow simulations of karst reservoirs where vugs and caves are
embedded in a porous rock and are connected via fracture networks at multiple scales.
In this paper we propose a unified approach to this problem by using the Stokes-Brinkman
equations at the fine scale. These equations are capable of representing
porous media such as rock as well as free flow regions (fractures, vugs, caves) in a single
system of equations. We then consider upscaling these equations to a coarser scale.
The cell problems, needed to compute coarse-scale permeability of Representative Element
of Volume (REV) are discussed. A mixed finite element method is then used to
solve the Stokes-Brinkman equation at the fine scale for a number of flow problems,
representative for different types of vuggy reservoirs. Upscaling is also performed by
numerical solutions of Stokes-Brinkman cell problems in selected REVs. Both isolated
vugs in porous matrix as well as vugs connected by fracture networks are analyzed by
comparing fine-scale and coarse-scale flow fields. Several different types of fracture
networks, representative of short- and long-range fractures are studied numerically.
It is also shown that the Stokes-Brinkman equations can naturally be used to model
additional physical effects pertaining to vugular media such as partial fracture with
fill-in by some material and/or fluids with suspended solid particles.</p>},
issn = {1991-7120},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/cicp/7676.html}
}