Ensemble-based stochastic permeability and flow simulation of a sparsely sampled hard-rock aquifer supported by high performance computing

Calibrating the heterogeneous permeability distribution of hard-rock aquifers based on sparse data is challenging but crucial for obtaining meaningful groundwater flow models. This study demonstrates the applicability of stochastic sampling of the prior permeability distribution and Metropolis sampling of the posterior permeability distribution using typical production data and measurements available in the context of groundwater abstraction. The case study is the Hastenrather Graben groundwater abstraction site near Aachen, Germany. A three-dimensional numerical flow model for the Carboniferous hard-rock aquifer is presented. Monte Carlo simulations are performed, for generating 1,000 realizations of the heterogeneous hard-rock permeability field, applying Sequential Gaussian Simulation based on nine log-permeability values for the geostatistical simulation. Forward simulation of flow during a production test for each realization results in the prior ensemble of model states verified by observation data in four wells. The computationally expensive ensemble simulations were performed in parallel with the simulation code SHEMAT-Suite on the high-performance computer JURECA. Applying a Metropolis sampler based on the misfit between drawdown simulations and observations results in a posterior ensemble comprising 251 realizations. The posterior mean log-permeability is -11.67 with an uncertainty of 0.83. The corresponding average posterior uncertainty of the drawdown simulation is 1.1 m. Even though some sources of uncertainty (e.g. scenario uncertainty) remain unquantified, this study is an important step towards an entire uncertainty quantification for a sparsely sampled hard-rock aquifer. Further, it provides a real-case application of stochastic hydrogeological approaches demonstrating how to accomplish uncertainty quantification of subsurface flow models in practice.