Calculation of the eective 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 ̄ux. These ``e€ective 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 ®rst involves a ®nite 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 ®rst approach (simple unit cells containing a small number of pores). The two approaches are presented and the in ̄uence of NAPL volume fraction and the orientation of the average velocity ®eld are studied in terms of the P eclet number for simple unit cells and more complex ones containing a thousand pores. Ó 2001 Elsevier Science Ltd. All rights reserved.