Second order accurate finite volume method for multidimensional modeling of PFAS transport in unsaturated porous media

Per- and polyfluoroalkyl substances (PFASs) have become emerging contaminants of critical concern. Comprehensive understanding of the transport and fate of PFAS in the vadose-zone, a type of water-unsaturated porous media, is key to determination of the risks of the PFAS contamination in the subsurface and to the development of the effective remediation strategies. Accurate modeling of the PFAS transport in the unsaturated porous media is still a challenge due to the variable surface tension induced by the adsorption of PFAS to the air-water interfaces. In an effort to address this challenge, we propose a multidimensional modeling framework for the transient PFAS transport in the unsaturated porous media based on the second order accuracy finite volume method. In the modeling, the adsorption of PFAS to the solid surfaces and to the air-water interfaces is described by the two-domain sorption kinetics model, i.e., both the instantaneous and the rate limited PFAS adsorptions are taken into account. The diffusive and convective terms in the governing equations for the PFAS transport and the water flow are discretized by the central difference and the quadratic upstream interpolation for convective kinetics schemes, respectively. Both of these two schemes have the second order accuracy. We investigate the effects of the convergent criteria, iterative scheme, and variation of the surface tension on the average and the local PFAS concentration and water content in the computational domain. We find that the convergent criteria should be chosen carefully so as to get the accurate results. The differences between the different iterative schemes are affected by the boundary conditions. The variation in the surface tension due to the variation of the PFAS concentration cannot be neglected. These studies not only guide the numerical schemes used in the modeling but also provide the insights into the PFAS transport in the unsaturated porous media. The multidimensional modeling framework presented in this work can be further extended to explore in detail the PFAS transport in the vadose-zone.