Calculation of the effective properties describing active dispersion in porous media: from simple to complex unit cells

Dissolution of a trapped non-aqueous phase liquid (NAPL) in soils and aquifers is a matter of great interest for the remediation of contaminated geological structures. In this work, the Volume Averaging Method is used to upscale the “active dispersion” phenomenon, taking into account both dispersion and dissolution of the NAPL. The method provides a macroscopic equation involving a dispersion tensor, additional convective terms and a linear form for the interfacial mass flux. These “effective properties” are related to the pore-scale physics through closure problems. These closure problems are solved over periodic unit cells representative of the porous structure. Two alternative approaches are considered. The first involves a finite volume formulation of the closure problems and therefore a detailed discretisation of the pore structure. The second is based on a “network modeling” of the pore space and appears as a natural alternative for overcoming the limitations of the first approach (simple unit cells containing a small number of pores). The two approaches are presented and the influence of NAPL volume fraction and the orientation of the average velocity field are studied in terms of the Péclet number for simple unit cells and more complex ones containing a thousand pores.