Homogenization for porous media


In a porous medium, one has to deal with processes encountered at different, well-separated scales, involving complex media with hierarchically-organized structures and highly oscillatory characteristics. This imposes severe limitations on simulations that are necessary to quantify the model behaviour at a larger, laboratory, or even field scale, at least when starting from the scale of the pore. A natural way to deal with this issue is to derive effective models describing the averaged behaviour of the system at the scale of interest, but incorporating the micro-scale processes. Given by Professor Sorin Pop (Hasselt University/University of Bergen), these lectures are introducing the homogenization methods, based on standard models for flow and reactive transport in porous media.

The key issues in these lectures are:
• Deriving upscaled models by means of homogenization methods
• Applications to porous media processes like flow and reactive transport


Lecture I: Introduction to homogenization

• Asymptotic expansions and the underlying idea of homogenization
• The diffusion problem: highly oscillatory coefficients, perforated media

Lecture II: Flow and reactive transport in a porous medium (from the pore scale to the Darcy scale)

• The derivation of the Darcy law
• Homogenization for reactive flow in porous media

Lecture III: Situations of practical interest

• Scaling in reactive porous media flow models
• Applications

Lecture notes

Lecture notes

Slides for lecture I
Slides for lecture II
Slides for lecture IIIa
Slides for lecture IIIb