Modeling of water flow in double-porosity soils by the method of homogenization

May 6, 2004, 4:00 p.m. (CEST)

Time: 5/6/04, 4:00 p.m. – 5:30 p.m.
Lecturer: Adam Szymkiewicz, Laboratoire LTHE, Université Joseph Fourier, Grenoble, France / Gdansk University of Technology, Gdansk, Poland
Venue: Pfaffenwaldring 61, Raum U1.003 (MML), Universität Stuttgart
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Double-porosity soils are characterized by the presence of two regions withvery different hydraulic properties. One region is associated with highlypermeable intra-aggregate pores, macropores or fissures, the other regionconsists of weakly permeable aggregates or porous blocks. This particularstructure gives rise to non-equilibrium phenomena during flow and transportprocesses. These effects cannot be captured by standard single-porosity modelsand special approaches are required.
The presentation focuses on the development of macroscopic models of flow indouble-porosity soils by the method of asymptotic homogenization. This methodallows to derive the macroscopic models from the description of physicalprocesses at the local scale, without any a priori assumptions on the finalform of the model. The domain of validity of the model is precisely defined bythe analysis of dimensionless numbers governing the flow. The effectivemacroscopic conductivity of the medium is defined as the function of localconductivity and geometry of the medium. For the non-equilibrium flow oneobtains a single macroscopic equation with integral source term describing thewater transfer between two regions.
Several numerical examples are presented. The results obtained byhomogenization are compared to the phenomenological model of Gerke and vanGenuchten and to the fine scale reference solution, where the heterogeneousstructure of the medium is explicitly represented. The simulations show thatthe model obtained by homogenization gives results close to the referencesolution and correctly estimates the effective parameters.

References:

  1. Auriault, J.-L. (1991), Heterogeneous medium: Is an equivalent macroscopicdescription possible?, Int. J. Engng Sci., 29(7), 785-795.
  2. Gerke H. H., and M. Th. van Genuchten (1993) A dual-porosity model forsimulating the preferential movement of water and solutes in structured porousmedia, Water Resour. Res., 29(2), 305-319.
  3. Lewandowska, J., A. Szymkiewicz, K. Burzy?ski, and M. Vauclin (2004) Modelingof unsaturated water flow in double porosity soils by the homogenizationapproach, Advances in Water Resources, in press.
  4. Sanchez-Palencia, E. (1980) Non-homogeneous media and vibration theory, LectureNote in Physics, vol. 127, Springer-Verlag, Berlin.
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