A Dual Heterogeneous Domain Model for Upscaling Anomalous Transport With Multi-Peaks in Heterogeneous Aquifers

Natural aquifers are often characterized by multiscale heterogeneity and complex flow networks, challenging the reliable simulation and prediction of contaminant transport. Classic stochastic transport models usually assume independent, identically distributed probability density functions when upscaling solute dynamics, but this assumption is not valid for media with multiscale heterogeneity. To address this issue, a dual heterogeneous domain model (DHDM) was proposed to quantify solute transport in heterogeneous aquifers where solute breakthrough curves (BTCs) exhibit multiple peaks and transient tailing behaviors. To efficiently solve the resultant DHDM, a Lagrangian solver was developed by combining the renewal-reward process (to capture solute dynamics in each domain) and the state transition probability (to capture solute particle transfer between the two heterogeneous domains). The DHDM and its Lagrangian solver were then applied to simulate solute transport in three different aquifer settings (alluvial, fractured, and karst). Analyses showed that in the alluvial aquifer, early arrivals and bi-peaks of the observed solute BTC might be caused by interconnected preferential flow paths consisting of high conductivity sediments, while the front edge or long tails of local peaks might be a result of small-scale heterogeneity. Fracture networks and karst conduits also resulted in anomalous transport with multiple peaks, and mass transfer between the preferential flow channels and matrix led to solute retention. All these complex, coexisting anomalous transport characteristics can be simultaneously and accurately captured by the unifying DHDM approach, significantly expanding the capability of nonlocal transport models.