Publication Details

Category Text Publication
Reference Category Journals
DOI 10.1007/s00477-019-01739-2
Licence creative commons licence
Title (Primary) Ensemble and effective dispersion in three-dimensional isotropic fractal media
Author Ross, K.; Heße, F.; Musuuza, J.L.; Attinger, S.
Source Titel Stochastic Environmental Research and Risk Assessment
Year 2019
Department CHS
Volume 33
Issue 11-12
Page From 2089
Page To 2107
Language englisch
Keywords Solute transport; Fractal media; Anomalous dispersion; Non-Fickian transport; Fractional advection dispersion equations
Abstract We determine the time-dependent behavior of the dispersion coefficient for transport in formations with isotropic log-conductivity fields showing fractal behavior. We consider two different dispersion coefficients for point-like injection: (1) the ensemble dispersion coefficients, defined as half the rate of change of the second central moments of the ensemble-averaged concentration distribution and (2) the effective dispersion, which is half the rate of change of the expected second central moments. Our results show, that the two longitudinal macrodispersion coefficients steadily grow with time and remain different at all times in a fully fractal regime, indicating that no Fickian transport regime is ever reached. The resulting effective longitudinal transport model is consequently a fractional advection–dispersion equation. In the semi-fractal regime, a Gaussian transport regime is reached eventually. However, compared to the case of a classic non-fractal regime, the transient non-Gaussian regime lasts much longer. In the transverse direction, the two dispersion coefficients approach the same large-time limit also in fractal media highlighting the fundamental difference between longitudinal and transverse dispersion.
Persistent UFZ Identifier
Ross, K., Heße, F., Musuuza, J.L., Attinger, S. (2019):
Ensemble and effective dispersion in three-dimensional isotropic fractal media
Stoch. Environ. Res. Risk Assess. 33 (11-12), 2089 - 2107 10.1007/s00477-019-01739-2