Data-space inversion using a recurrent autoencoder for time-series parameterization

Abstract

Data-space inversion (DSI) and related procedures represent a family of methods applicable for data assimilation in subsurface flow settings. These methods differ from usual model-based techniques in that they provide only posterior predictions for quantities (time series) of interest, not posterior models with calibrated parameters. DSI methods require a large number (O(500–1000)) of flow simulations to first be performed on prior geological realizations. Given observed data, posterior predictions for time series of interest, such as well injection or production rates, can then be generated directly. DSI operates in a Bayesian setting and provides posterior samples of the data vector. In this work, we develop and evaluate a new approach for data parameterization in DSI. Parameterization is useful in DSI as it reduces the number of variables to determine in the inversion, and it maintains the physical character of the data variables. The new parameterization uses a recurrent autoencoder (RAE) for dimension reduction, and a long short-term memory (LSTM) recurrent neural network architecture to represent flow-rate time series. The RAE-based parameterization is combined with an ensemble smoother with multiple data assimilation (ESMDA) for posterior data sample generation. Results are presented for two- and three-phase flows in a 2D channelized system and a 3D multi-Gaussian model. The new DSI RAE procedure, along with several existing DSI treatments, is assessed through detailed comparison to reference rejection sampling (RS) results. The new DSI methodology is shown to consistently outperform existing approaches, in terms of statistical (P10–P90 interval and Mahalanobis distance) agreement with RS results. The method is also shown to accurately capture derived quantities which are computed from variables considered directly in DSI. This requires correlation and covariance between variables to be properly captured, and accuracy in these relationships is demonstrated. The RAE-based parameterization developed here is clearly useful in DSI, and it may also find application in other subsurface flow problems.