History Matching Geological Models Using an Embed-To-Control Observe Deep-Learning Reservoir Surrogate

Summary In this study, we propose the use of a deep learning reduced order surrogate model that can significantly lower computational costs while still maintaining high accuracy for data assimilation or history matching (HM) problems. The fundamental component is the Embed-to-control Observe (E2CO) deep-learning (DL) architecture. It serves as a reduced-order model mimicking the trajectory piecewise linearization coupled (TPWL) with proper orthogonal decomposition (POD) to simulate subsurface flow by using blocks of neural networks (NNs) trained with the snapshots generated from a high-fidelity model (or simulator). Although the E2CO architecture has been applied to both deterministic and robust production optimization problems, where it has shown to provide large computational speedups, its application to history problems has not been thoroughly investigated. The E2CO surrogate is made up of four blocks of neural networks: encoder, transition, transition output, and decoder, and it has already been utilized in a range of conventional black-oil and compositional models, producing successful outcomes by accurately forecasting the reservoir system states and well outputs. The proposed E2CO DL architecture for HM applications is referred to as E2CO-HM. We train the E2CO-HM surrogate model using a representation of data in latent space that is derived from realizations obtained through singular value decomposition (SVD) applied to petrophysical realizations of geological models. The E2CO-HM framework is then integrated with the ensemble smoother with multiple data assimilation (ES-MDA) algorithm designed for HM. Realizations from the 3D SPE10 model, featuring various channelized heterogeneous permeability distributions during waterflooding, are utilized to demonstrate the prediction and data assimilation capabilities of the E2CO-HM. Results indicate that a trained and cross-validated E2CO-HM surrogate can accurately predict state variables and well outputs in our case study. The trained E2CO-HM using SVD effectively captures geological information with acceptable reconstruction errors. When these structures are integrated into a unified deep learning-based history matching workflow, the resulting framework is particularly more computationally efficient.