flow through porous media
The heterogeneity of the flow induces non-Gaussian velocity distributions, which can lead to a persistent non-Fickian dispersion regime. Various stochastic models have been proposed to represent this property. Different models may provide equally good fits to data; yet, their implications can be dramatic when transport controlled processes are considered, such as chemical reactions or biofilm growth.
The results of a numerical simulations (Smoothed Particles Hydrodynamics method) are show in the figure below. A sample particle trajectory is displayed as red dots (a). The time series of longitudinal Lagrangian velocities and accelerations along the trajectory are plotted as a function of travel time in (b) and (c). The temporal behavior of Lagrangian acceleration is intermittent, switching between low variability periods and strongly fluctuating periods. The first behavior corresponds to low velocity regions, where Lagrangian longitudinal velocities and accelerations are small and strongly correlated. The second behavior corresponds to high velocities in flow channels, where acceleration fluctuations are large.
A key challenge is to relate the upscaled flow models (e.g. macrodispersion theory) to the microscale flow properties. In this Letter(pdf), we demonstrate the existence of persistent intermittent properties of Lagrangian velocities in porous media, and we formulate a new dynamical picture of intermittency based on the spatial Markov property of Lagrangian velocities. The resulting upscaled transport model is a correlated continuous time random walks (CTRW), which is fully consistent with the microscale flow dynamics.
This correlated CTRW model correctly predicts both the scaling and the magnitude of the dispersion scale at all times. We also show that neglecting the correlation of successive transit times in the CTRW model (uncorrelated CTRW) leads to an under estimation of particle dispersion.
* Effective pore-scale dispersion upscaling with a correlated continuous time random walk approach (pdf), Water Resources Research
* Flow Intermittency, Dispersion, and Correlated Continuous Time Random Walks in Porous Media (pdf), Physical Review Letters