Applicable Analysis, 2003, Vol. 82, No. 2, pp. 103–116 Singular Double Porosity Model ALAIN BOURGEAT a, * , GREGORY A. CHECHKIN b,y and ANDREY L. PIATNITSKI c,z a Universite¤ Lyon1,MCS ö Ba“ t.ISTIL,15Bld Latarjet, 69622,VilleurbanneCedex France; b Department of Differential Equations, Faculty of Mechanics and Mathematics, MoscowStateUniversity,Moscow119899,Russia; c Narvik University College, Postboks385,8505Narvik,NorwayandP.N.LebedevPhysicalInstituteofRAS, Leninskipr.,53,Moscow117924,Russia We consider the linear parabolic equation describing the transport of a contaminant in a porous media crossed by a net of infinitely thin fractures. The permeability is very high in the fractures but very low in the porous blocks. We derive the homogenized model corresponding to a net of infinitely thin fractures, by means of the singular measures technique. We assume that these singular measures are supported by hyperplanesofcodimensionone.Weproveinasecondstepthatthishomogenizedmodelcouldbeobtained indistinctlyeitherbylettingthefracturethickness,inthestandarddoubleporositymodel,tendtozero,orby homogenizing a model with infinitely thin fractures. Keywords: Scaling-up; Fractured porous media; Modeling; Homogenization; Double porosity; Singular constructions AMS Subject Classifications: 35K20; 35Q35; 35R60 1. INTRODUCTION The so called double porosity model has received a lot of attention both from mathe- maticians and from engineers, like, for instance, in [4,12]. The model was introduced first for describing the global behavior of fractured porous media by Barenblatt etal. [3] and it is since used in a wide range of engineering specialities related to geohydrol- ogy, petroleum reservoir engineering, civil engineering or soil science. In such a model, the ‘‘fractured porous medium’’ is made of two kinds of porous media with different permeability. There is first a set of isolated porous blocks of low permeability (sometimes called matrix), surrounded by a network of high perme- ability connected porous medium (usually called fractures network). The double porosity model, like in [2], is assuming that the width of the fractures containing highly permeable porous media (fracture width, in short) is of the same order as the blocks sizes. *Corresponding author. E-mail: bourgeat@mcs.univ-lyon1.fr y E-mail: chechkin@mech.math.msu.su z E-mail: andrey@sci.lebedev.ru ISSN 0003-6811 print; ISSN 1563-504X online ß 2003 Taylor & Francis Ltd DOI: 10.1080/0003681031000063739