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Contaminant transport in fractured media exhibits complex dynamics, including multiple peaks in breakthrough curves (BTCs) and non-Fickian diffusion, thereby posing significant challenges to the application of traditional transport models. Here we undertook a detailed study of a natural-gradient tracer test conducted in a regional-scale fractured carbonate aquifer situated in southwestern Germany, where the observed BTCs contained both dual peaks and positive skewness. These BTCs were used to optimize parameters and interpret their physical meanings for several transport models, including the dual-continuum model (DCM) and the fractional derivative equation (FDE) model. Tracer concentration distributions were simulated in both single- and dual-continuum media employing the DCM and FDE models. Our results demonstrated that while the DCM model could reasonably replicate the bimodal BTC, the FDE (which accounts for solute retention) outperformed in capturing the heavy-tailed BTC. This was attributed to the limitations of grid-based numerical models that assume Fickian diffusion and fail to map small-scale medium heterogeneity exhaustively. In contrast, a parsimonious model like the FDE, with upscaled parameters, was found to be more effective in capturing regional-scale non-Fickian transport. To further characterize the multiple BTC peaks the standard FDE missed, we proposed a fractional derivative dual-continuum model (fDCM). This model was found to be adept at capturing both the multi-peak and late-time heavy tail in the BTC. Our study thus opens an alternate pathway for modeling solute transport in regional-scale fractured to partially karstified aquifers. • Numerical models were developed and compared for simulation of complex transport dynamics in fractured media. • A fractional derivative dual-continuum model (fDCM) effectively captured non-Fickian transport observed in the field. • A kilometer-scale tracer test in a fractured aquifer provided a good testbed for validating regional transport modeling. [ABSTRACT FROM AUTHOR]