Goethe Center for Scientific Computing (G-CSC)

Goethe University Frankfurt

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A. Grillo, D. Logashenko, S. Stichel, and G. Wittum (2010)

Simulation of density-driven flow in fractured porous media

Adv. Water Resour., 33(12):1494–1507.

In this work, we propose a model of the density-driven flow in a fractured porous medium with the representation of the fracture network as set of low-dimensional man- ifolds. We consider a hydrogeological system consisting of a fluid-phase filtrating in a porous medium. The porous medium (for example, rock) is regarded as undeformable and at rest. The fluid-phase, a mixture of water and brine, saturates the pore space and undergoes diffusion and transport. The fracture network is regarded as a porous medium whose physical properties are essentially different from those of the bulk. Within this setting, we model the density-driven flow both in the fractures and in the surrounding medium under the hypotheses that: i) the thickness of the fractures is much smaller than the smallest length scale in the bulk, and ii) the fractures and the surrounding medium interact through ideal interfaces. The PDEs in the low-dimensional representation of the fractures are found by averaging the full-dimensional PDEs along the fracture width. For the validation of the model, we perform numerical experiments using the finite-volume discretization for the proposed model and the full-dimensional resolution of the fractures and observe good agreement of the results.