Categorical parameter distributions consisting of geologic facies with distinct properties, for example, high-permeability channels embedded in a low-permeability matrix, are common at contaminated sites. At these sites, low-permeability facies store solute mass, acting as secondary sources to higher-permeability facies, sustaining concentrations for decades while increasing risk and cleanup costs. Parameter estimation is difficult in such systems because the discontinuities in the parameter space hinder the inverse problem. This paper presents a novel approach based on Traveling Pilot Points (TRIPS) and an iterative ensemble smoother (IES) to solve the categorical inverse problem. Groundwater flow and solute transport in a hypothetical aquifer with a categorical parameter distribution are simulated using MODFLOW 6. Heads and concentrations are recorded at multiple monitoring locations. IES is used to generate posterior ensembles assuming a TRIPS prior and an approximate multi-Gaussian prior. The ensembles are used to predict solute concentrations and mass into the future. The evaluation also includes an assessment of how the number of measurements and the choice of the geological prior determine the characteristics of the posterior ensemble and the resulting predictions. The results indicate that IES was able to efficiently sample the posterior distribution and showed that even with an approximate geological prior, a high degree of parameterization and history matching could lead to parameter ensembles that can be useful for making certain types of predictions (heads, concentrations). However, the approximate geological prior was insufficient for predicting mass. The analysis demonstrates how decision-makers can quantify uncertainty and make informed decisions with an ensemble-based approach.
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