Lagrangian solver for vector fractional diffusion in bounded anisotropic aquifers: Development and application

Abstract

Abstract Fractional-derivative models (FDMs) are promising tools for characterizing non-Fickian transport in natural geological media. Hydrologic applications of FDMs, however, have been limited in the last two decades, due to the lack of feasible models and solvers to quantify multi-dimensional anomalous diffusion for pollutants in bounded aquifers. This study develops and applies FDM tools to capture vector fractional dispersion for both conservative and reactive pollutants in fractional Brownian motion (fBm) random fields with bounded domains. A d-dimensional anisotropic fBm field for hydraulic conductivity (K) is first generated numerically. A particle-tracking based, fully Lagrangian solver is then developed to approximate particle dynamics in the fBm K fields under various boundary conditions, where the governing equation is the vector FDM subordination to regional flow. Numerical experiments show that the Lagrangian solver can combine nonlocal anomalous transport and local aquifer properties to quantify pollutant transport in bounded aquifers. Application analyses further reveal that the K correlation can significantly enhance the spreading of conservative pollutant particles, and increase the reaction rate by enhancing the mobility and mixing of reactant particles undergoing bimolecular reactions. Extension of the Lagrangian solver is also discussed, including modeling transient flow, generalizing boundary conditions, and capturing complex chemical reactions. This study therefore provides the hydrologic community an efficient Lagrangian solver to model reactive anomalous transport in bounded anisotropic aquifers with any dimension, size, and boundary conditions.