Upscaling dispersivity for conservative solute transport in naturally fractured media

Physical heterogeneities are prevalent features of fracture systems and significantly impact transport processes in aquifers across different spatiotemporal scales. Upscaling solute transport parameter is an effective way of quantifying parameter variability in heterogeneous aquifers including fractured media. This paper develops conceptual models for upscaling conservative transport parameters in fracture media. The focus is on upscaling dispersivity. Lagrangian-based transport model (LBTM) for dispersivity upscaling are derived for the solute transport in two-dimensional fractures surrounded by an impermeable matrix. The LBTM is validated against the random walk particle tracking (RWPT) model, which enables highly efficient and accurate predictions of conservative solute transport. The results show that the derived scale-dependent analytical expressions are in excellent agreement with RWPT model results. In addition, LBTM results are also compared to experimental results from the observed breakthrough curve of a conservative solute transport through a single natural fracture within a granite core. Comparing results from the LBTM and transport experiment shows that LBTM based estimated dispersivity is 10.55% higher than the measured value. Errors introduced by the experiments, the conceptual assumptions in deriving models, and the heterogeneities of fracture apertures not fully sampled by measuring instruments are main factor for such discrepancy. The sensitivity analysis indicates that the longitudinal and transverse dispersivities are positively related to the integral scale and the variance of the log-fracture aperture. The longitudinal dispersivity is strongly contolled by the variance of the log-fracture aperture. The LBTM may be useful for directly predicting solute transports, requiring only the acquisition of fractured geostatistical data. This work provides a better understanding of transport processes in fractured media which ultimately control water quality across scales.