Frontiers in Applied Mathematics and Statistics (Jul 2021)
Data-Space Inversion With a Recurrent Autoencoder for Naturally Fractured Systems
Abstract
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. RAE training is accomplished using flow simulation results for 1,350 prior model realizations. An ensemble smoother with multiple data assimilation (ESMDA) is applied to provide posterior DSI data samples. The modeling in this work 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 new simulation data (not seen in training), 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 better accuracy for these data reconstructions. Detailed posterior DSI results are then presented for a particular “true” model (which is outside the prior ensemble), and summary results are provided for five additional “true” models that are consistent with the prior ensemble. These results again demonstrate the advantages of DSI with RAE-based parameterization for this challenging fractured reservoir case.
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