Effects of single-fracture aperture statistics on entrapment, dissolution and source depletion behavior of dense non-aqueous phase liquids

Understanding of the entrapment and dissolution behavior of dense non-aqueous phase liquids (DNAPLs) in single fractures is important for modeling contaminant flux generation from fractured sites. Here a systematic numerical study is presented to investigate the effect of fracture aperture statistics on DNAPL migration, entrapment and dissolution within individual, variable-aperture fractures. Both fractures with open and closed bottom boundaries were considered. For the simulation a continuum-based two-phase model was used with a capillary pressure function which calculates the entry pressure based on the local aperture. Prior to application the model was compared against the invasion percolation approach and found more suitable for the present study, in particular as it allows a more versatile presentation of boundary conditions. The results showed that increasing aperture standard deviation and/or decreasing correlation length lead to larger amounts of entrapped DNAPL (due to the fact that larger standard deviation produces more distinct contrast between small and large aperture regions and the fact that longer correlation length provides more possible channels through the fracture) as well as larger maximum and average sizes of DNAPL blobs, and subsequently lead to longer times for complete dissolution. To understand the relationship between the solute flux and the remaining mass, a simplified source depletion function which links the outflow concentration to the DNAPL saturation was found adequate to describe the dissolution process for the case where the bottom boundary is open for DNAPL migration and thus the DNAPL does not accumulate to form a pool. The parameters in this function were not very sensitive to variations in correlation length but were sensitive to aperture standard deviation. The same average entrapped DNAPL saturation produced considerably smaller solute concentrations in cases with larger aperture variability due to the larger average size of DNAPL blobs (i.e., smaller contact area for DNAPL dissolution). Boundary conditions had a significant impact on DNAPL entrapment and dissolution. A closed boundary at the bottom led to DNAPL pooling (i.e., large continuous blobs) which causes significant tailing in the dissolution breakthrough curve due to water bypassing.