Two-medium description of dispersion in heterogeneous porous media: Calculation of macroscopic properties

In this paper, a numerical procedure is proposed to calculate effective properties associated with the generalized two-equation model developed by Ahmadi et al. [1998]. A transformation of the original closure problems was found that allowed the introduction of a finite volume formulation. Results are presented for a heterogeneous porous medium made up of nodules embedded in a continuous matrix. The properties of the effective parameters are discussed in terms of the influence of the Peclet number, the permeability ratio, and the local-scale dispersivity. In addition, the problem of the asymptotic behavior of the two-equation model is discussed in some details. Finally, a comparison is made with results available from the literature in simplified cases.