Conservative transport upscaling based on information of connectivity

Connected structures in highly heterogeneous hydraulic conductivity fields lead to channels and preferential pathways for the main fluid flux and fastest solute particles. Their spatial complement is zones of slow advection, where solutes are delayed, causing tailing of solute breakthrough curves. These delays depend on the inclusion's size and the hydraulic conductivity contrast between inclusion and channel. The interplay between channels and small-scale low conductivity inclusions leads to anomalous transport at larger scales. We test whether a simple separation of transport processes between channels and inclusions could be used to parameterize an effective transport model accounting for anomalous transport. Effective transport is represented by a multirate mass transfer model (MRMT): fast channel transport is controlled by parameters of the mobile zone, while slow advective delays are controlled by parameters of the mobile-immobile exchange. We delineate the connected channels and analyze their connectivity followed by characterizing the low conductivity inclusions. We parameterize a MRMT model using connectivity and the statistics of the low permeable inclusions. Finally, we compare the parameterized MRMT with detailed numerical simulations in heterogeneous hydraulic conductivity fields with a clear separation between connected channel network and inclusions. In intermediately connected hydraulic conductivity fields only the cut-off time of the tails is represented while early and intermediate time behavior is not reproduced. We suggest that an effective model for the latter case should account for additional processes like variability in advective velocity.