Modeling NAPL dissolution from pendular rings in idealized porous media

The dissolution rate of nonaqueous phase liquid (NAPL) often governs the remediation time frame at subsurface hazardous waste sites. Most formulations for estimating this rate are empirical and assume that the NAPL is the nonwetting fluid. However, field evidence suggests that some waste sites might be organic wet. Thus, formulations that assume the NAPL is nonwetting may be inappropriate for estimating the rates of NAPL dissolution. An exact solution to the Young‐Laplace equation, assuming NAPL resides as pendular rings around the contact points of porous media idealized as spherical particles in a hexagonal close packing arrangement, is presented in this work to provide a theoretical prediction for NAPL‐water interfacial area. This analytic expression for interfacial area is then coupled with an exact solution to the advection‐diffusion equation in a capillary tube assuming Hagen‐Poiseuille flow to provide a theoretical means of calculating the mass transfer rate coefficient for dissolution at the NAPL‐water interface in an organic‐wet system. A comparison of the predictions from this theoretical model with predictions from empirically derived formulations from the literature for water‐wet systems showed a consistent range of values for the mass transfer rate coefficient, despite the significant differences in model foundations (water wetting versus NAPL wetting, theoretical versus empirical). This finding implies that, under these system conditions, the important parameter is interfacial area, with a lesser role played by NAPL configuration.Key Points:Exact solution to the Young‐Laplace equation for pendular ringsTheoretical determination of the mass transfer rate coefficient under hydrophobic conditionsPredicts similar NAPL dissolution rates for oil‐wet and water‐wet conditionsPeer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/145506/1/wrcr21729.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/145506/2/wrcr21729_am.pd