Integration of Deep Learning‐Based Inversion and Upscaled Mass‐Transfer Model for DNAPL Mass‐Discharge Estimation and Uncertainty Assessment

The challenges posed by high-resolution characterization of dense nonaqueous phase liquid (DNAPL) source zone architecture (SZA) have motivated the development of simpler upscaled models that rely on domain-averaged metrics to capture the average mass discharge downstream of source zones (SZ). However, SZA is highly irregular, making estimation of these domain-averaged metrics from sparse borehole data extremely difficult. Poor estimation of SZ metrics means that upscaled models cannot reproduce the multistage effluent concentrations. Bayesian inversion methods can be used to obtain accurate estimates of SZ metrics and their uncertainties from sparse data, and from there, upscaled models can better reproduce multistage effluent concentrations. This work presents a framework for integrating a deep-learning-based 3D SZA inversion method named Convolutional Variational AutoEncoder—Ensemble Smoother with Multiple Data Assimilation (CVAE-ESMDA) with a process-based (PB) upscaled mass-transfer model. This framework can utilize sparse SZ data to estimate directly mass discharge without multiphase modeling. First, CVAE-ESMDA estimates the SZA by conditioning on sparse data, which is then used as input in the upscaled model for mass-discharge estimation. We evaluated our framework on two real and 30 synthetic bench-scale experiments, with significantly different SZAs and multistage effluent concentrations. The results demonstrate that the CVAE-based inversion method captures the temporal variations in SZ metrics better than standard ordinary kriging. With the improved SZ metrics, the PB model more accurately reproduces the salient patterns of the multistage mass-discharge profiles and associated uncertainty. This approach can be used to provide valuable input for risk-based decision making in remediation applications.