Asymptotic transport parameters in a heterogeneous porous medium: Comparison of two ensemble-averaging procedures

Autor: Insa Neuweiler, Wolfgang Kinzelbach, Harald Kinzelbach, D. Metzger
Rok vydání: 1999
Předmět:
Zdroj: Stochastic Environmental Research and Risk Assessment (SERRA). 13:396-415
ISSN: 1436-3259
1436-3240
DOI: 10.1007/s004770050046
Popis: We analyze the movement of a solute cloud in a saturated aquifer, resulting from a point-like instantaneous solute injection. Physical heterogeneities of the medium due to spatial variations of the hydraulic conductivity, as well as the chemical heterogeneities due to variations in the linear adsorption coefficient and the degradation rate, are modeled as spatial stochastic processes with exponential autocorrelation functions. Furthermore, cross-correlations between the chemical properties and the conductivity are taken into account. For large transport times, the movement of the solute cloud is characterized by its center-of-mass velocity, by the macroscopic dispersion constant, and the macroscopic degradation rate. These quantities are evaluated using perturbation theory and two different averaging procedures. The first procedure derives the large-scale properties from the central moments of the concentration distribution in a given aquifer realization, and averages over the ensemble afterwards. The second method which is mathematically less demanding obtains large scale transport coefficients from the central moments of the ensemble-averaged concentration distribution. Under the assumption that both prescriptions lead to the same macro-scale quantities, the second approach is usually preferred in literature. The present paper is an extension of the work of Metzger et al. (1996). We show that the two averaging procedures lead to different results in one-dimensional systems, whereas the difference vanishes for higher dimensions. Taking into account the influence of small scale dispersion, we give explicit results for the macroscopic parameters characterizing the solute plume. We analyze the various contributions to these parameters and show how the physical origin of these contributions can be traced back uniquely to fluctuations in the retardation factor, in the flow field, and in the degradation rate, and to the cross-correlations between these inhomogeneities, respectively.
Databáze: OpenAIRE
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