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| Titel |
A procedure for the upscaling of longitudinal dispersivity in strongly heterogeneous formations |
| VerfasserIn |
A. Fiori, I. Jankovic |
| Konferenz |
EGU General Assembly 2009
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 11 (2009) |
| Datensatznummer |
250021507
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| Zusammenfassung |
| Quantification of solute transport in heterogeneous aquifers is usually carried out by the
spatial or temporal moments of the local concentration C. The heterogeneous medium is
characterized by a spatially variable logpermeability Y (x)=ln K(x), which is often modeled
as a space random function where Y is characterized by the mean < Y >=lnKG, variance
σY 2 and linear integral scale IY . As a consequence, local concentration and its moments are
also random. Transport is solved generally numerically by discretization of space by elements
of scale L, usually much smaller than IY . The latter requirement may lead to considerable
computational resources for three-dimensional problems, and for that reason larger values for
L are often adopted. The upscaling problem consists in analyzing the relation between
the small-scale and grid-scale logconductivities in order to obtain a reasonable
approximation for C or its moments in the numerical grid. We solve the upscaling problem
for the longitudinal macrodispersivity and the case of mean uniform flow and a
thin planar plume of size much larger than IY . The model we adopt is based on
the representation of the heterogeneous medium as a collection of independent
blocks of random conductivity. Flow and transport are solved in a semi-analytical
form by the embedding matrix approximation. Our results indicate that upscaling
causes smoothing of conductivity spatial variations at scales smaller than that of
discretization blocks. This results in a reduction of rate of spreading of solutes as
quantified by the longitudinal equivalent macrodispersivity. In order to correct for this
loss, a fictitious upscaling induced macrodispersivity is introduced. It is determined
quantitatively for mean uniform flow, simplified formation structure and approximate
solutions of flow and transport obtained in the past. It is found that the value of the
induced longitudinal macrodispersivity is enhanced by high degree of heterogeneity. |
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