A Variational Auto-Encoder for Reservoir Monitoring

Carbon dioxide Capture and Storage (CCS) is an important strategy in mitigating anthropogenic CO$_2$ emissions. In order for CCS to be successful, large quantities of CO$_2$ must be stored and the storage site conformance must be monitored. Here we present a deep learning method to reconstruct pressure fields and classify the flux out of the storage formation based on the pressure data from Above Zone Monitoring Interval (AZMI) wells. The deep learning method is a version of a semi conditional variational auto-encoder tailored to solve two tasks: reconstruction of an incremental pressure field and leakage rate classification. The method, predictions and associated uncertainty estimates are illustrated on the synthetic data from a high-fidelity heterogeneous 2D numerical reservoir model, which was used to simulate subsurface CO$_2$ movement and pressure changes in the AZMI due to a CO$_2$ leakage.

Semi Conditional Variational Auto-Encoder for Flow Reconstruction and Uncertainty Quantification from Limited Observations

We present a new data-driven model to reconstruct nonlinear flow from spatially sparse observations. The model is a version of a conditional variational auto-encoder (CVAE), which allows for probabilistic reconstruction and thus uncertainty quantification of the prediction. We show that in our model, conditioning on the measurements from the complete flow data leads to a CVAE where only the decoder depends on the measurements. For this reason we call the model as Semi-Conditional Variational Autoencoder (SCVAE). The method, reconstructions and associated uncertainty estimates are illustrated on the velocity data from simulations of 2D flow around a cylinder and bottom currents from the Bergen Ocean Model. The reconstruction errors are compared to those of the Gappy Proper Orthogonal Decomposition (GPOD) method.