Multiscale modeling and simulations of flows in naturally fractured Karst reservoirs

Peter Popov*, Yalchin Efendiev, Guan Qin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

110 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)162-184
Number of pages23
JournalCommunications in Computational Physics
Issue number1
StatePublished - Jul 2009
Externally publishedYes


  • Brinkman equation
  • Homogenization
  • Porous media
  • Stokes equation

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)


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