Quantifications of the spreading of acid mine drainage (AMD) in groundwater are needed for risk assessments of mining sites. However, due to subsurface heterogeneity, available field data may prove insufficient for deterministic process descriptions, even at well-characterized sites. Here, the probabilistic LaSAR-PHREEQC model is used to consider multicomponent reactions and transport in heterogeneous (flow and geochemistry) groundwater surrounding a mine waste site, with specific focus on the spreading of Zn. Model results, using field data from a mill tailings impoundment in northern Sweden (including major component geochemistry), indicate that precipitation of smithsonite (ZnCO3) may drastically delay the downstream arrival of Zn, but may also cause a peak concentration once the retained Zn is released. The amount of smithsonite formed is, however, minute and its spatial variation large, such that detection of smithsonite in soil samples may be difficult. Results further show that even a low degree of flow heterogeneity can effectively smooth otherwise distinctive temporal concentration changes attributed to the considered chemical reactions, and thereby mask the attenuation processes. By contrast, the existence of preferential flow paths can cause temporally separated concentration peaks in response to a single chemical reaction chain, even in a geochemically homogeneous domain, making the interpretation of the concentration curves non-trivial. The stochastic modelling results for Zn considering flow and/or mineralogical heterogeneity indicate a less efficient Zn attenuation than predicted by standard, deterministic reactive-transport models. In addition, in all considered probabilistic Zn and SO42- scenarios, the spatial variability in downstream pollutant concentration was high, implying that a relatively large number of point samples are needed to determine field-scale mean concentrations.