| Abstract: | Many studies have proposed one‐equation models to represent transport processes in heterogeneous porous media. This approach is based on the assumption that dependent variables such as pressure, temperature, or concentration can be expressed in terms of a single large‐scale averaged quantity in regions having very different chemical and/or mechanical properties. However, one can also develop large‐scale averaged equations that apply to the distinct regions that make up a heterogeneous porous medium. This approach leads to region‐averaged equations that contain traditional convective and dispersive terms, in addition to exchange terms that account for the transfer between the different media. In our approach, the fissures represent one region, and the porous media blocks represent the second region. The analysis leads to upscaled equations having a domain of validity that is clearly identified in terms of time and length‐scale constraints. Closure problems are developed that lead to the prediction of the effective coefficients that appear in the region averaged equations, and the main purpose of this article is to provide solutions to those closure problems. The method of solution makes use of an unstructured grid and a joint element method in order to take care of the special characteristics of the fissured network. This new numerical method uses the theory developed by Quintard and Whitaker and is applied on considerably more complex geometries than previously published results. It has been tested for several special cases such as stratified systems and “sugarbox” media, and we have compared our calculations with other computational methods. © 2000 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 16: 237–263, 2000 |
