Experimental study of solute transport under non-Darcian flow in a single fracture

SummaryWe have experimentally studied solute transport in a single fracture (SF) under non-Darcian flow condition which was found to closely follow the Forchheimer equation at Reynolds numbers around 12.2–86.0 when fracture apertures were between 4 mm and 9 mm. The measured breakthrough curves (BTCs) under the non-Darcian flow condition had some features that are difficult to explain using the Fickian type advection–dispersion equation (ADE). All the measured BTCs showed long tails, which might be caused by mass transfer between the boundary layer near the fracture wall and the mobile domain near the plane of symmetry, as supported by the boundary layer dispersion theories of Koch and Brady, 1985 and Koch and Brady, 1987. A mobile–immobile (MIM) model was used to simulate the measured BTCs. To show that the MIM model was doing a better job than the ADE model in describing the observed BTCs, we conducted statistical analysis on the goodness of fitting with these two models. The results showed that the correlation coefficients for the MIM model were greater than those for the ADE model and were close to unity, indicating a nearly perfect fit with the MIM. The mass transfer rate between the mobile domain and the boundary layer increased when the mobile water fraction became larger. The best fit dispersivity values using the MIM model varied between 1.05 mm and 9.29 mm whereas their counterparts using the ADE model varied between 245 mm and 462 mm for the experimental condition of this study. Several issues such as the possible bimodal concentration distribution and the scale-dependent transport in a SF were discussed and would be investigated in the future.

Research highlights
► Laboratory studies of solute transport in a single fracture under non-Darcian flow are conducted.
► Non-Fickian transport behavior has been observed from the measured breakthrough curves (BTCs).
► Boundary layer dispersion can be used to understand the transport process.
► The mobile–immobile model can be approximately used to deal with the boundary layer dispersion.