Abstract: Three alternative conceptual methods are presented for numerical modeling of solute transport in fractured reservoirs. All are based on the double porosity concept to simulate solute exchange between fractures and porous rock due to diffusion processes in the rock matrix. The Galerkin Finite Element Method is used to approximate the advection/dispersion process in the fracture domain combined with different techniques to represent the concentration profile in the porous rock blocks. The proposed methods are compared in terms of accuracy and computational efficiency:
Resume: Trois methodes sont presentees pour la simulation numerique du transport en solution dans les reservoirs fractures. Toutes trois utilisent le concept de double porosite pour simuler le transfert entre les fractures et la roche poreuse du au processus de diffusion dans la matrice poreuse. La methode des elements finis de type Galerkin est utilisee pour approximer le processus d"advection/dispersion dans le reseau de fractures. Cette methode est associce avec differentes techniques pour representer le profil de concentration dans les blocks de roche poreuse. Les comparaisons sont effectuees en termes de precision,et d"efficacite.
Zusammenfassung: Drei alternative Verfahren zur"numerischen Modellierung von Stofftransportvorgangen in Kluftgrundwasserleitern werden vorgestellt. Alle,drei beruhen auf dem Zweiporositatenansatz, um den auf Diffusions-vorgangen in der Felsmatrix beruhenden Stoffaustausch zwischen Gesteinsklueften und porösem Fels zu simulieren. Die Approximation der Xonvektions-Dispersionsgleichung das Xluftsystem erfolqt mit der Galerkin Finite Elemente Methode, wahrend die Xonzentrationswerte des Felsmediums ueber unterschiedliche Lösungsansatze ermittelt werden. Die vorgestellten Verfahren werden hinsichtlich Genauigkeit und Effizienz miteinander verglichen.
1 INTRODUCTION Due to the low permeability of the rock matrix most of the fluid mobility in a fractured reservoir occurs in a small volume of high-permeable interconnected fractures. However, most of the fluid is located in the porous rock. Considering solute transport in such a system, advection and dispersion are relevant in the fracture network while molecular diffusion is dominant in the rock matrix. Although this diffusive process is very slow the concentration field can significantly be influenced by the solute exchange between fractures and rock. A contaminant plume spreading in the fracture network loses part of the pollutant to the porous blocks. There the solute is stored temporarily and slowly rendered to the fracture system when the contaminant front has passed.
Despite of major advances in the past, numerical modeling of this behaviour is still a difficult problem. Discrete approaches are not applicable in field scale studies because of the enormous amount of input data and accompanying computer work to describe fractures and porous blocks. Porous media approximations have been shown to be1nadequate in many cases since the "retarding" influence of matrix diffusion is not taken into account. To overcome this drawback, Barenblatt et.al. (1960) proposed the socalled "double porosity" concept which allows continuum simulations in a fractured aquifer incorporating the effect of ma- trix diffusion. The aquifer is idealized as two overlapping homogeneous media, one representing the fracture system with high conductivity, the second representing the rock matrix with high storage capacity.