Modeling NAPL dissolution fingering with upscaled mass transfer rate coefficients

The dissolution of nonaqueous phase liquids (NAPLs) at residual saturation in porous media has sometimes resulted in the development of preferential dissolution pathways or NAPL dissolution fingers. While NAPL dissolution fingering may be modeled using numerical simulators with fine discretization, this approach is computational intensive. We derived an expression for an upscaled mass transfer rate coefficient that accounts for the growth of dissolution fingers within porous media contaminated uniformly with residual NAPL. This expression was closely related to the lengthening of the dissolution front. Data from physical experiments and numerical simulations in two dimensions were used to examine the growth of the dissolution front and the corresponding upscaled mass transfer rate coefficient. Using this upscaled mass transfer rate coefficient, the time when dissolution fingering results in a reduction in the overall mass transfer rate and thus controls the rate of NAPL dissolution was determined. This crossover time is a convenient parameter for assessing the influence of dissolution fingering on NAPL removal. For the physical experiments and numerical simulations analyzed in this study, the crossover time to dissolution fingering control always occurred before the dissolution front had moved 14 cm within NAPL-contaminated porous media, which is small compared to the scale of typical systems of concern. To verify the utility of this approach, data from a three-dimensional physical experiment were predicted reasonably well using an upscaled mass transfer rate coefficient that was determined independently from this experiment.