Bayesian uncertainty estimation of adsorption closure models in the computational simulation of contaminant transport

Identifying sources and understanding the evolution of the spread of contaminants in aquifers is critical and often results in a high-dimensional inverse problem. Computer contaminant transport models are developed by combining physical principles and phenomenological closure equations. However, such models suffer from considerable conceptual uncertainties, mainly due to using phenomenological closures to describe the contaminant adsorption in the media. In the present work, we investigated the impact of employing phenomenological state equations in the contaminant transport model to characterize the adsorption of contaminants in a porous media. Also, we adopted an embedded Bayesian error approach to understand the limits of using adsorption isotherms to describe the contaminant adsorption. We phrase it as a probabilistic error model and test the efficacy of a deep learning surrogate to replace the partial differential equations-based subsurface flow and contaminant transport model. The results show that the adsorption term plays a key role, yielding a higher level of uncertainty in the contaminant transport modeling, and the use of such a closure must be taken with care since the parameters are chosen to meet certain geochemical conditions.