Data-Space Inversion With a Recurrent Autoencoder for Naturally Fractured Systems - Jiang, Su; Hui, Mun-Hong; Durlofsky, Louis J. (Frontiers in Applied Mathematics and Statistics, 2021)
Data-space inversion (DSI) is a data assimilation procedure that directly generates posterior flow predictions, for time series of interest, without calibrating model parameters. No forward flow simulation is performed in the data assimilation process. DSI instead uses the prior data generated by performing O(1000) simulations on prior geomodel realizations. Data parameterization is useful in the DSI framework as it enables representation of the correlated time-series data quantities in terms of low-dimensional latent-space variables. In this work, a recently developed parameterization based on a recurrent autoencoder (RAE) is applied with DSI for a real naturally fractured reservoir. The parameterization, involving the use of a recurrent neural network and an autoencoder, is able to capture important correlations in the time-series data. An ensemble smoother with multiple data assimilation (ESMDA) is applied to provide posterior DSI data samples. To train the RAE model, 1350 prior model realizations are simulated. This modeling is much more complex than that considered in previous DSI studies as it includes multiple 3D discrete fracture realizations, three-phase flow, tracer injection and production, and complicated field-management logic leading to frequent well shut-in and reopening. Results for the reconstruction of the prior simulation data, using both the RAE-based parameterization and a simpler approach based on principal component analysis (PCA) with histogram transformation, are presented. The RAE-based procedure is shown to provide a high degree of accuracy, and to outperform the PCA method, for the reconstruction of the fractured reservoir prior data. Detailed posterior DSI results are presented for a particular `true' model, and summary results are provided for four additional `true' models. These results again demonstrate the advantages of DSI with RAE-based parameterization for this challenging fractured reservoir case.