 |
| Titel |
Temporal behavior of a solute cloud in a fractal heterogeneous porous medium at different scales |
| VerfasserIn |
Katharina Ross, Sabine Attinger |
| Konferenz |
EGU General Assembly 2010
|
| Medientyp |
Artikel
|
| Sprache |
Englisch
|
| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 12 (2010) |
| Datensatznummer |
250041271
|
|
|
|
|
|
| Zusammenfassung |
| ABSTRACT
Water pollution is still a very real problem and the need for efficient models for flow and
solute transport in heterogeneous porous or fractured media is evident. In our study we focus
on solute transport in heterogeneous fractured media.
In heterogeneous fractured media the shape of the pores and fractures in the subsurface
might be modeled as a fractal network or a heterogeneous structure with infinite correlation
length. To derive explicit results for larger scale or effective transport parameters in such
structures is the aim of this work.
To describe flow and transport we investigate the temporal behavior of transport
coefficients of solute movement through a spatially heterogeneous medium. It is necessary to
distinguish between two fundamentally different quantities characterizing the solute
dispersion: The effective dispersion coefficient Deff(t) represents the physical (observable)
dispersion in one given realization of the medium. It is conceptually different from the
mathematically simpler ensemble dispersion coefficient Dens(t) which characterizes the
(abstract) dispersion with respect to the set of all possible realizations of the medium. In the
framework of a stochastic approach DENTZ ET AL. (2000 I[2] & II[3]) derive explicit
expressions for the temporal behavior of the center-of-mass velocity and the dispersion of the
concentration distribution, using a second order perturbation expansion. In their model the
authors assume a finite correlation length of the heterogeneities and use a GAUSSIAN
correlation function.
In a first step, we model the fractured medium as a heterogeneous porous medium with
infinite correlation length and neglect single fractures. ZHAN & WHEATCRAFT (1996[4])
analyze the macrodispersivity tensor in fractal porous media using a non-integer exponent
which consists of the HURST coefficient and the fractal dimension D. To avoid this
non-integer exponent for numerical reasons we extend the study of DENTZ ET AL. (2000 I[2]
& II[3]) and derive explicit expressions for the center-of-mass velocity and the longitudinal
dispersion coefficient for isotropic and anisotropic media as well as for point-like (where the
extent of the source distribution is small compared to the correlation lengths of the
heterogeneities) and spatially extended injections. Our results clearly show that the
difference between Deff and Dens persists for all times. In other words, ensemble
mixing and effective mixing coefficients do not approach the same asymptotic limit.
The center-of-mass fluctuations between different flow paths for a plume traveling
through the medium never become irrelevant and ergodicity breaks down in such
media.
Our ongoing work concerns the investigation of the transversal dispersion coefficient and
the extension of the upscaling method coarse graining[1] to heterogeneous fractal porous
media with embedded single fractures.
References
[1]ATTINGER, S. (2003): Generalized coarse graining procedures for flow in porous media, Computational Geosciences, 7 (4),
pp. 253-273.
[2]DENTZ, M. / KINZELBACH, H. / ATTINGER, S. and W. KINZELBACH (2000): Temporal behavior of a solute cloud in a
heterogeneous porous medium: 1. Point-like injection, Water Resources Research, 36 (12), pp. 3591-3604.
[3]DENTZ, M. / KINZELBACH, H. / ATTINGER, S. and W. KINZELBACH (2000): Temporal behavior of a solute cloud in a
heterogeneous porous medium: 2. Spatially extended injection, Water Resources Research, 36 (12), pp. 3605-3614.
[4]ZHAN, H. and S. W. WHEATCRAFT (1996): Macrodispersivity tensor for nonreactive solute transport in isotropic and
anisotropic fractal porous media: Analytical solutions, Water Resources Research, 32 (12), pp. 3461-3474.
|
|
|
|
|
|
|