Uncertainty Quantification of CO2 Plume Migration in Highly Channelized Aquifers Using Probabilistic Convolutional Neural Networks

Characterization of the CO2 plume evolution in deep aquifers under geological uncertainties is crucial for designing geological carbon storage (GCS) projects. In this study, we are concerned with uncertainty quantification (UQ) of CO2 plume migration in uncertain permeability fields following non-Gaussian distributions. Specifically, we are concerned with the effect of intra-facies heterogeneity on plume migration in a multi-facies sedimentary setting. To alleviate the huge computational burden required for UQ, machine learning (ML) methods are broadly used to develop surrogate models. However, the quality of ML surrogate models is often not qualified. Here we present a probabilistic convolutional neural network (pCNN) method for fast surrogate modeling of the CO2 plume evolution. The dense and residual connections are adopted in the pCNN’s network architecture to enhance its performance in approximating the highly complex input–output mapping of the GCS model induced by non-Gaussian permeability heterogeneity. In addition, a Bayesian training strategy is utilized to train the pCNN surrogate model, enabling it to give predictions together with an estimate of the surrogate uncertainty. As a result, uncertainties associated with the pCNN surrogate can be quantified in addition to the model parameter uncertainty. The proposed method is demonstrated using a 3-D GCS model with an uncertain, non-Gaussian distributed, multi-facies permeability field. Results show that pCNN is able to provide a reliable and fast approximation of the highly complex GCS model. The pCNN-derived UQ estimates, obtained with negligible additional computational costs, show a good agreement with those derived from the computationally intensive GCS model. The generalization performance of pCNN is further investigated using “out-of-distribution” permeability samples. For such permeability fields, pCNN can still provide relatively accurate approximations, only showing slightly increased predictive errors and uncertainties relative to those having similar distributions to the training samples.