Predicting Transient Anomalous Transport in Two-Dimensional Discrete Fracture Networks With Dead-End Fractures

Abstract

Pollutant transport in discrete fracture networks (DFNs) exhibits complex dynamics that challenge reliable model predictions, even with detailed fracture data. To address this issue, this study derives an upscaled integral-differential equation to predict transient anomalous diffusion in two-dimensional (2D) DFNs. The model includes both transmissive and dead-end fractures (DEFs), where stagnant water zones in DEFs cause non-uniform flow and transient sub-diffusive transport, as shown by both literature and DFN flow and transport simulations using COMSOL. The upscaled model's main parameters are quantitatively linked to fracture properties, especially the probability density function of DEF lengths. Numerical experiments show the model's accuracy in predicting the full-term evolution of conservative tracers in 2D DFNs with power-law distributed fracture lengths and two orientation sets. Field applications indicate that while model parameters for transient sub-diffusion can be predicted from observed DFN distributions, predicting parameters controlling solute displacement in transmissive fractures requires additional field work, such as tracer tests. Parameter sensitivity analysis further correlates late-time solute transport dynamics with fracture properties, such as fracture density and average length. Potential extensions of the upscaled model are also discussed. This study, therefore, proves that transient anomalous transport in 2D DFNs with DEFs can be at least partially predicted, offering an initial step toward improving model predictions for pollutant transport in real-world fractured aquifer systems.