Is There a Representative Elementary Volume for Anomalous Dispersion?
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The concept of the representative elementary volume (REV) is often associated with the notion of hydrodynamic dispersion and Fickian transport. However, it has been frequently observed experimentally and in numerical pore-scale simulations that transport is non-Fickian and cannot be characterized by hydrodynamic dispersion. Does this mean that the concept of the REV is invalid? We investigate this question by a comparative analysis of the advective mechanisms of Fickian and non-Fickian dispersions and their representation in large-scale transport models. Specifically, we focus on the microscopic foundations for the modeling of pore-scale fluctuations of Lagrangian velocity in terms of Brownian dynamics (hydrodynamic dispersion) and in terms of continuous-time random walks, which account for non-Fickian transport through broad distributions of advection times. We find that both approaches require the existence of an REV that, however, is defined in terms of the representativeness of Eulerian flow properties. This is in contrast to classical definitions in terms of medium properties such as porosity, for example.
KeywordsRepresentative elementary volume Upscaling Anomalous dispersion Continuous-time random walks Velocity statistics
The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC Grant Agreement No. 617511 (MHetScale). This work was partially funded by the CNRS-PICS project CROSSCALE, Project Number 280090.
- Bear, J.: Dynamics of Fluids in Porous Media. Elsevier, New York (1972)Google Scholar
- Berkowitz, B., Cortis, A., Dentz, M., Scher, H.: Modeling non-Fickian transport in geological formations as a continuous time random walk. Rev. Geophys. 44(2), RG2003 (2006)Google Scholar
- Bigi, B.: Using Kullback–Leibler distance for text categorization. In: European Conference on Information Retrieval, pp. 305–319. Springer (2003)Google Scholar
- Gardiner, C.: Stochastic Methods. Springer, Berlin (2010)Google Scholar