Non-Fickian transport in porous media with bimodal structural heterogeneity

Abstract

Tracer tailing in breakthrough curves in porous media with two distinct porosities is analyzed in terms of the dynamic responses of experimental fixed bed columns filled either with solid or porous beads. The flow is fast in the column interstitial space between beads (for both solid and porous beads) but slow within the porous beads that act as controlled ‘traps’ constituting an immobile zone. The transport is quantified using a Continuous Time Random Walk (CTRW) framework, which accounts for domains with controlled structural and flow heterogeneity associated with two distinct spatial and time spectra. We first demonstrate that breakthrough curves for a column containing solid glass beads exhibit non-Fickian transport, quantifiable both in fitting and validation mode by a CTRW based on a power law transition time distribution. We then examine breakthrough curves in the porous bead case, obtaining fits with a two-scale CTRW model that accounts explicitly for the two time spectra. Because the porous beads are uniform, tracer trapping within them is described by a simple first-order approximation trap model, with relatively weak capture and relatively faster release rates. The extent of tailing apparent in the porous bead breakthrough curves, due to the traps, can be quantitatively distinguished from the contribution to tailing due to mobile zone non-Fickian transport. A parameter study of the two-scale CTRW adds further insight into the dynamics of the process, showing the interaction between the advective non-Fickian transport and the mass exchange to immobile regions.