Computation of the Longitudinal Dispersion Coefficient in an Adsorbing Porous Medium Using Homogenization

A. Rijnks[1], M. Darwish[2], and H. Bruining[3]
[1]StatoilHydro ASA, Bergen, Norway
[2]Shell Exploration & Production International Centre, Rijswijk,
The Netherlands
[3]Section of Geoengineering, Faculty of Civil Engineering and Geosciences, TU Delft, Delft, The Netherlands
Published in 2009

The method to derive upscaled expressions for the dispersion coefficients for reactive flow in a porous medium uses a periodic unit cell (PUC), which consists for instance of a spherical grain in a cube, but nothing prohibits defining more complex PUC's. Homogenization leads to a coupled system of equations where the flow is described by Stokes equation and the concentration fluctuation is described by a convection diffusion source term equation. We show that the commercial finite element software COMSOL can be readily used to compute longitudinal and transversal dispersion coefficients in 2-D and 3-D; this makes homogenization accessible to the engineering practice. The results are for the first time compared with experimental data of the dispersion coefficient versus Péclet number; there is good agreement.

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