Integrating analytical solutions and U-Net model for predicting groundwater contaminant plumes in pump-and-treat systems

Abstract

Pump-and-treat (P&T) is a common technique for groundwater remediation involving the extraction and treatment of contaminated water above ground. Optimizing the design and operation of the P&T well network is essential for maximizing the system’s effectiveness and efficiency. However, this optimization often necessitates many model evaluations, leading to computationally demanding tasks. This study introduces a novel approach that integrates analytical solutions for groundwater dynamics with the U-Net deep learning framework to predict groundwater contaminant plume migration under dynamic pumping conditions. By incorporating the Thiem equation into the input preprocessing, the U-Net model transforms sparse well data into a continuous spatial field that captures the hydraulic impacts of pumping activities. This integration enables the model to leverage both deep learning capabilities and classical physics-based groundwater theories, enhancing prediction accuracy and computational efficiency. For example, in 2D synthetic cases, integrating analytical solutions reduced the RMSE from 2.76 µg/L to 0.7 µg/L. In a complex 3D heterogeneous model of the Hanford Site’s 200 West P&T facility, our trained surrogate model completed a 12-year simulation in just 600 ms on a single CPU core, achieving an accumulative RMSE of <1.6 µg/L—an improvement of over three orders of magnitude in simulation speed compared to a numerical model. These advancements support rapid evaluations of P&T optimization scenarios, enabling timely and effective decision-making for well placement and system management. Our findings highlight the potential of advanced machine learning models to significantly enhance the efficiency and sustainability of groundwater remediation efforts, offering a novel application of the U-Net architecture in environmental science.