 |
| Titel |
Variance of Dispersion Coefficients in Heterogeneous Porous Media |
| VerfasserIn |
Marco Dentz, Felipe P. J. de Barros |
| Konferenz |
EGU General Assembly 2013
|
| Medientyp |
Artikel
|
| Sprache |
Englisch
|
| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 15 (2013) |
| Datensatznummer |
250079390
|
|
|
|
|
|
| Zusammenfassung |
| We study the dispersion of a passive solute in heterogeneous porous media using a stochastic
modeling approach. Heterogeneity on one hand leads to an increase of solute spreading,
which is described by the well-known macrodispersion phenomenon. On the other hand, it
induces uncertainty about the dispersion behavior, which is quantified by ensemble averages
over suitably defined dispersion coefficients in single medium realizations. We focus here on
the sample to sample fluctuations of dispersion coefficients about their ensemble mean
values for solutes evolving from point-like and extended source distributions in
d = 2 and d = 3 spatial dimensions. The definition of dispersion coefficients in
single medium realizations for finite source sizes is not unique, unlike for point-like
sources. Thus, we first discuss a series of dispersion measures, which describe the
extension of the solute plume, as well as dispersion measures that quantify the solute
dispersion relative to the injection point. The sample to sample fluctuations of these
observables are quantified in terms of the variance with respect to their ensemble
averages. We find that the ensemble averages of these dispersion measures may
be identical, their fluctuation behavior, however, may be very different. This is
quantified using perturbation expansions in the fluctuations of the random flow
field. We derive explicit expressions for the time evolution of the variance of the
dispersion coefficients. The characteristic time scale for the variance evolution is given
by the typical dispersion time over the characteristic heterogeneity scale and the
dimensions of the source. We find that the dispersion variances asymptotically
decrease to zero in d = 3 dimensions, which means, the dispersion coefficients are
self-averaging observables, at least for moderate heterogeneity. In d = 2 dimensions, the
variance converges towards a finite asymptotic value that is independent of the source
distribution. Dispersion is not self-averaging, which may be traced back to the lesser
sampling efficiency in d = 2. This work sheds some new light on the concepts
of dispersion in single medium realizations and their quantification in terms of
ensemble averages in a stochastic modeling framework. These findings may be relevant
for the interpretation of dispersion data from field and laboratory experiments. |
|
|
|
|
|
|