Sherwood correlation for dissolution of pooled NAPL in porous media

The rate of interphase mass transfer from non-aqueous phase liquids (NAPLs) entrapped in the subsurface into the surrounding mobile aqueous phase is commonly expressed in terms of Sherwood (Sh) correlations that are expressed as a function of flow and porous media properties. Because of the lack of precise methods for the estimation of the interfacial area separating the NAPL and aqueous phases, most studies have opted to use modified Sherwood expressions that lump the interfacial area into the interphase mass transfer coefficient. To date, there are only two studies in the literature that have developed non-lumped Sherwood correlations; however, these correlations have undergone limited validation. In this paper controlled dissolution experiments from pooled NAPL were conducted. The immobile NAPL mass is placed at the bottom of a flow cell filled with porous media with water flowing horizontally on top. Effluent aqueous phase concentrations were measured for a wide range of aqueous phase velocities and for two different porous media. To interpret the experimental results, a two-dimensional pore network model of the NAPL dissolution kinetics and aqueous phase transport was developed. The observed effluent concentrations were then used to compute best-fit mass transfer coefficients. Comparison of the effluent concentrations computed with the two-dimensional pore network model to those estimated with one-dimensional analytical solutions indicates that the analytical model which ignores the transport in the lateral direction can lead to under-estimation of the mass transfer coefficient. Based on system parameters and the estimated mass transfer coefficients, non-lumped Sherwood correlations were developed and compared to previously published data. The developed correlations, which are a significant improvement over currently available correlations that are associated with large uncertainties, can be incorporated into future modeling studies requiring non-lumped Sh expressions.