Diffusion-Controlled Solute and Isotope Transport in the Milk River Aquifer System, Alberta, Canada: Implications for Dating Old Groundwater

Krypton-81 (⁸¹Kr) and chlorine-36 (³⁶Cl) are among the few isotopic tracers capable of constraining groundwater residence times on 10⁵–10⁶ year timescales. In sedimentary aquifer systems bounded by low-permeability units, however, diffusive solute exchange can strongly modify tracer distributions and bias apparent ages derived from concentration ratios. In the transboundary Milk River Aquifer (MRA), progressive chloride enrichment caused by diffusion across shale aquitards complicates the interpretation of ³⁶Cl/Cl as a chronometer. Here, we combine new measurements of 81Kr, 36Cl, stable chlorine isotopes (³⁷Cl/³⁵Cl), and 14C with advection–diffusion transport modeling to quantify the importance of matrix diffusion on tracer systematics and inferred groundwater ages. The simulations reproduce the observed decrease in ³⁶Cl/Cl and concomitant increase in δ³⁷Cl along regional flow paths, demonstrating that diffusive influx of Cl-rich aquitard water dominates the evolution of the chlorine isotope system. In contrast, modeled and observed ⁸¹Kr activities show substantially lower sensitivity to diffusive exchange over the timescales considered. A comparison of simulated and measured tracer relationships indicates that, in the MRA, apparent ages derived from ³⁶Cl primarily reflect chloride addition rather than radioactive decay, whereas ⁸¹Kr provides a more robust and conservative chronometer for fossil groundwater. These results highlight the value of integrating stable and radioactive chlorine isotopes with noble gas dating and explicit transport modeling to disentangle decay from transport effects. The approach developed here provides a quantitative framework for interpreting multitracer data sets in regional aquifers affected by long-term diffusive exchange and has broader implications for assessing fossil groundwater resources in similar hydrogeological settings.