Semi-analytical solutions for nonequilibrium transport and transformation of PFAS and other solutes in heterogeneous vadose zones with structured porous media

We present screening-type semi-analytical models for quantifying the fate and transport of PFAS, including perfluoroalkyl acids (PFAAs) and their precursors (i.e., polyfluoroalkyl substances that can transform to PFAAs), in a heterogeneous vadose zone. The models employ one-dimensional multi-continuum representations with varying complexities (dual-porosity, dual-permeability, or triple-porosity). They account for PFAS-specific transport processes, including multi-site rate-limited adsorption at solid–water and air–water interfaces, and first-order biochemical transformation. Assuming steady-state infiltration, we derive semi-analytical solutions for all models under arbitrary initial and boundary conditions. We validate these new solutions using literature experimental breakthrough curves of PFAS and other solutes for various soils and wetting conditions. Furthermore, we demonstrate the models’ capability by analyzing the long-term leaching and mass discharge of two example PFAS (PFOS and a precursor PFOSB) in a heterogeneous vadose zone beneath a model PFAS-contaminated site. The results demonstrate that the precursor undergoes significant transformation and adds additional PFOS mass discharge to groundwater. Additionally, the simulations suggest that, due to strong retention in the vadose zone (i.e., large residence time), the PFAS in the high- and low-conductivity transport pathways can be considered as in equilibrium. Taking advantage of this result, we illustrate that the multi-continuum models may be simplified to an effective single-porosity model for simulating the transport of longer-chain PFAS in a heterogeneous vadose zone. Overall, the semi-analytical models provide practical tools for assessing long-term fate and transport of PFAS in the vadose zone and mass discharge to groundwater in the presence of precursor transformations.