Complementary finite element methods applied to the numerical homogenization of 3D absolute permeability

✍ Scribed by Trykozko, Anna ;Zijl, Wouter

• Publisher: John Wiley and Sons
• Year: 2001
• Tongue: English
• Weight: 245 KB
• Volume: 18
• Category: Article
• ISSN: 1069-8299
• DOI: 10.1002/cnm.462

✦ Synopsis

Abstract

To be able to use a limited number of relatively large grid cells in numerical oil reservoir simulators and groundwater models, upscaling of the absolute permeability is frequently applied. The spatial fine‐scale permeability distribution, which is generally obtained from geological and geostatistical models, is incorporated in the relatively large grid cells of the numerical model. If the porous medium may be approximated as a periodic medium, upscaling can be performed by the homogenization method. Numerical homogenization gives rise to an approximation error. The complementarity between the conformal–nodal finite element method and the mixed–hybrid finite element method has been used to quantify this error. The two methods yield, respectively, upper and lower bounds for the eigenvalues of the coarse‐scale permeability tensor. Results of numerical experiments obtained using tetrahedral meshes are shown both in the far field and in the near well region. Copyright © 2001 John Wiley & Sons, Ltd.