Upscaling and effective parameters in porous media transport

Heterogeneous porous media cannot be described in every detail. Therefore the need for defining effective parameters on a larger scale arises. Upscaling is achieved if the transport process can be expressed by the same equation as on a microscopic level only with new parameters. For a flow field, which is on the average uniform, effective parameters have been derived some time ago. Basically, the subscale heterogeneity shows up in an enlarged dispersion coefficient, also called macrodispersion coefficient. Here a radial flow field is investigated into. A new formula for the dispersion coefficient is derived. The analysis is then taken to two phase flow which occurs for example when injecting air into a water filled fracture. In this case a dispersion term originates where there was no such term in the microscopic equations. The necessity of differentiating between ensemble dispersion and effective dispersion is shown.

Main publications

Neuweiler, I., S. Attinger, W. Kinzelbach, 2001. Macrodispersion in a radially divergent flow field with finite Peclet numbers 1: Perturbation theory approach. WRR, Vol. 37 (3), p. 481-493,

Attinger, S., I. Neuweiler, W. Kinzelbach, 2001. Macrodispersion in a radially divergent flow field with finite Peclet numbers 2: Homogenization theory approach. WRR, Vol. 37 (3), p. 495-505.

Neuweiler, I., S. Attinger, W. Kinzelbach, P. King, 2003. Large scale mixing for immiscible displacement in heterogeneous porous media, TIPM, 51: 287-314.

Contacts

W. Kinzelbach

Agency/Funding

ETH/88 kCHF

Partners

Imperial college, University of Southern California

Status

Finished in 2003

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