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The Low Level Waste Repository (LLWR) is the UK’s central facility for the disposal of low-level radioactive waste. The facility is required periodically to submit a safety case to the UK Environment Agency, demonstrating the continued safety of its operations for both people and the environment. Key to this is the development of a 3D hydrogeological model of the site, together with a suitable treatment of uncertainty. A baseline model, built in ConnectFlow®, conceptualises the site as a collection of distinct lithofacies units and uses observed groundwater head data to constrain the bulk permeabilities of these units. However, to quantify the effects of potential heterogeneity on flow variability, it is necessary to develop a geostatistical model for the formation process. Near-surface deposits in the region are the result of a complex Quaternary history marked by multiple glacial cycles, and recent work has interpreted the primary constituents of the regional aquifer as outwash deposits which formed following the last glacial maximum. Such deposits form as high-energy meltwaters flow from a retreating ice margin, and modern-day analogues show braided channel structures exhibiting increased channel density and decreased flow velocity with increasing distance from the glacial front. This results in a complex stratigraphy of interbedded sands and gravels. The standard Gaussian method for treating heterogeneity, whereby permeabilities are correlated as a function of distance, provides an important model, however it is unlikely to produce fluvial features such as channels which may provide preferential pathways for flow. To simulate a fluvial geology, we use the open-source AlluvSim package with stochastic parameters selected to represent a layering of braided channels and map the outputs into ConnectFlow. We generate thousands of probabilistic simulations across multiple geostatistical models and use observed groundwater head data to condition the resulting estimates for flow variability. The talk will overview these aspects in more detail, and will outline some challenges involved in heterogeneous modelling and uncertainty quantification in this setting.