A critical evaluation of the local-equilibrium assumption in modeling NAPL-pool dissolution

Abstract

An analytical modeling analysis was used to assess when local equilibrium (LE) and nonequilibrium (NE) modeling approaches may be appropriate for describing nonaqueous-phase liquid (NAPL) pool dissolution. NE mass-transfer between NAPL pools and groundwater is expected to affect the dissolution flux under conditions corresponding to values of Sh′St (the modified Sherwood number ( L x k l/ D z ) multiplied by the Stanton number ( k l/ v x ))<≈400. A small Sh′St can be brought about by one or more of: a large average pore water velocity ( v x ), a large transverse dispersivity ( α z ), a small pool length ( L x ), or a small mass-transfer coefficient ( k l). On the other hand, at Sh′St>≈400, the NE and LE solutions converge, and the LE assumption is appropriate. Based on typical groundwater conditions, many cases of interest are expected to fall in this range. The parameter with the greatest impact on Sh′St is k l. The NAPL pool mass-transfer coefficient correlation of Pfannkuch [Pfannkuch, H.-O., 1984. Determination of the contaminant source strength from mass exchange processes at the petroleum–ground-water interface in shallow aquifer systems. In: Proceedings of the NWWA/API Conference on Petroleum Hydrocarbons and Organic Chemicals in Ground Water—Prevention, Detection, and Restoration, Houston, TX. Natl. Water Well Assoc., Worthington, OH, Nov. 1984, pp. 111–129.] was evaluated using the toluene pool data from Seagren et al. [Seagren, E.A., Rittmann, B.E., Valocchi, A.J., 1998. An experimental investigation of NAPL-pool dissolution enhancement by flushing. J. Contam. Hydrol., accepted.]. Dissolution flux predictions made with k l calculated using the Pfannkuch correlation were similar to the LE model predictions, and deviated systematically from predictions made using the average overall k l=4.76 m/day estimated by Seagren et al. [Seagren, E.A., Rittmann, B.E., Valocchi, A.J., 1998. An experimental investigation of NAPL-pool dissolution enhancement by flushing. J. Contam. Hydrol., accepted.] and from the experimental data for v x >18 m/day. The Pfannkuch correlation k l was too large for v x >≈10 m/day, possibly because of the relatively low Peclet number data used by Pfannkuch [Pfannkuch, H.-O., 1984. Determination of the contaminant source strength from mass exchange processes at the petroleum–ground-water interface in shallow aquifer systems. In: Proceedings of the NWWA/API Conference on Petroleum Hydrocarbons and Organic Chemicals in Ground Water—Prevention, Detection, and Restoration, Houston, TX. Natl. Water Well Assoc., Worthington, OH, Nov. 1984, pp. 111–129.]. The results of the modeling analyses were evaluated by comparing pool dissolution fluxes from the literature to each other and to the corresponding LE and NE model predictions. The LE model described most of the pool dissolution flux data reasonably well, given the uncertainty in some of the model parameter estimates, suggesting that the LE model can be a useful tool for describing steady-state NAPL pool dissolution under some conditions. However, a conclusive test of the LE assumption was difficult due to the limited range of experimental conditions covered and the uncertainties in some of the model input parameters, including the mass-transfer coefficient correlation required for the NE model.