Publication Details

Category Text Publication
Reference Category Journals
DOI 10.1016/j.advwatres.2006.10.011
Title (Primary) Upscaling hydraulic conductivity based on the topology of the sub-scale structure
Author Samouëlian, A.; Vogel, H.-J.; Ippisch, O.
Journal Advances in Water Resources
Year 2007
Department BOPHY
Volume 30
Issue 5
Page From 1179
Page To 1189
Language englisch
Keywords porous media; effective hydraulic properties; hydraulic conductivity; unsaturated flow; upscaling; topology; connectivity; heterogeneous structure
Abstract The hydraulic conductivity of heterogeneous porous media depends on the distribution function and the geometry of local conductivities at the smaller scale. There are various approaches to estimate the effective conductivity Keff at the larger scale based on information about the small scale heterogeneity. A critical geometric property in this 'upscaling' procedure is the spatial connectivity of the small-scale conductivities. We present an approach based on the Euler-number to quantify the topological properties of heterogeneous conductivity fields, and we derive two key parameters which are used to estimate Keff. The required coefficients for the upscaling formula are obtained by regression based on numerical simulations of various heterogeneous fields. They are found to be generally valid for various different isotropic structures. The effective unsaturated conductivity function Keff (wm) could be predicted satisfactorily. We compare our approach with an alternative based on percolation theory and critical path analysis which yield the same type of topological parameters. An advantage of using the Euler-number in comparison to percolation theory is the fact that it can be obtained from local measurements without the need to analyze the entire structure. We found that for the heterogeneous field used in this study both methods are equivalent.
Persistent UFZ Identifier
Samouëlian, A., Vogel, H.-J., Ippisch, O. (2007):
Upscaling hydraulic conductivity based on the topology of the sub-scale structure
Adv. Water Resour. 30 (5), 1179 - 1189