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- Title
Inertial effects in dispersion in porous media.
- Authors
Wood, Brian D.
- Abstract
In this work we develop the macroscale transport equation for dispersion of a nonreactive chemical species, with a particular focus on the influence of inertial contributions at moderate Reynolds numbers. Our starting point is the continuum level description of transport written at the subpore scale. Volume averaging is used to upscale these equations to develop the macroscale solute balance that applies at the Darcy scale. We develop a fully transient version of the ancillary closure problem that predicts the total dispersion tensor, and we solve the closure using finite Fourier transforms. The result of this effort is a nonlocal macroscale transport equation, where the nonlocal dispersion depends upon the microscale geometry of the pore space and the physical characteristics of the fluid. Both the longitudinal and transverse components of the total dispersion tensor are computed for a simple three-dimensional unit cell. The computational results indicate that a simple three-dimensional periodic unit cell is able to capture the correct behavior for the longitudinal dispersion in the range 101 < Pe p < 2.5 × 105, although the magnitude of the longitudinal dispersion coefficient is underpredicted by up to a factor of about 4. For the transverse dispersion coefficient, the simple unit cell provides much less satisfactory results when compared with experimental data. The inertial effects for the longitudinal dispersion coefficient were relatively small, but for the transverse dispersion coefficient, inertial effects were predicted to increase the transverse dispersion coefficient up to 40 times that which would be predicted for Stokes flow.
- Publication
Water Resources Research, 2007, Vol 43, Issue 12, pn/a
- ISSN
0043-1397
- Publication type
Article
- DOI
10.1029/2006WR005790