Implementation of a finite-volume method for the determination of effective parameters in fissured porous media

Many studies have proposed one-equation models to represent transport proce sses in heterogeneous porous media. This approach is based on the assumptio n that dependent variables such as pressure, temperature, or concentration can be expressed in terms of a single large-scale averaged quantity in regi ons having very different chemical and/or mechanical properties. However, o ne can also develop large-scale averaged equations that apply to the distin ct regions that make up a heterogeneous porous medium. This approach leads to legion-averaged equations that contain traditional convective and disper sive terms, in addition to exchange terms that account for the transfer bet ween the different media. In our approach, the fissures represent one regio n, and the porous media blocks represent the second region. The analysis le ads to upscaled equations having a domain of validity that is clearly ident ified in terms of time and length-scale constraints. Closure problems are d eveloped that lead to the prediction of the effective coefficients that app ear in the region averaged equations, and the main purpose of this article is to provide solutions to those closure problems. The method of solution m akes use of an unstructured grid and a joint element method in order to tak e care of the special characteristics of the fissured network. This new num erical method uses the theory developed by Quintard and Whitaker and is app lied on considerably more complex geometries than previously published resu lts. It has been tested for several special cases such as stratified system s and "sugarbox" media, and we have compared our calculations with other co mputational methods. (C) 2000 John Wiley & Sons, Inc.