Predicting CO 2 Plume Migration in Heterogeneous Formations Using Conditional Deep Convolutional Generative Adversarial Network
Numerical simulation of flow and transport in heterogeneous formations has long been studied, especially for uncertainty quantification and risk assessment. The high computational cost associated with running large-scale numerical simulations in a Monte Carlo sense has motivated the development of surrogate models, which aim to capture the important input-output relations of physics-based models but require only a fraction of the cost of full model runs. In this work, we formulate a conditional deep convolutional generative adversarial network (cDC-GAN) surrogate model to learn the dynamic functional mappings in multiphase models. The cDC-GAN belongs to a class of semisupervised learning methods that can be used to learn the data generation processes. Like the original GAN, a main strength of the cDC-GAN is that it includes a self-training scheme for improving the quality of generative modeling in a game theoretic framework, without requiring extensive statistical knowledge and assumptions on input data distributions. In particular, our cDC-GAN model is designed to learn cross-domain mappings between high-dimensional input (e.g., permeability) and output (e.g., phase saturations) pairs, with the ability to incorporate conditioning information (e.g., prediction time). As a use case, we demonstrate the performance of cDC-GAN for predicting the migration of carbon dioxide (CO 2 ) plume in heterogeneous carbon storage reservoirs, which has both numerical and practical significance because of the safe storage requirements now mandated in many countries. Results show that cDC-GAN achieves high accuracy in predicting the spatial and temporal evolution patterns of the injected CO 2 plume, as compared to the original results obtained using a compositional reservoir simulator. The performance of cDC-GAN models, trained using the same number of training samples, stays relatively robust when the level of spatial heterogeneity is increased. Our cDC-GAN is pattern based and is not limited by the underlying physics. Thus, it provides a general framework for developing surrogate models, and for conducting uncertainty analyses for a wide range of physics-based models used in both groundwater and subsurface energy exploration applications.