# A deep-learning-based surrogate model for data assimilation in dynamic subsurface flow problems

## TL;DR

This paper introduces a deep learning surrogate model combining residual U-Net and convolutional LSTM architectures for fast, accurate prediction of dynamic subsurface flow, enabling efficient data assimilation and uncertainty reduction in geological models.

## Contribution

The paper develops a novel recurrent R-U-Net surrogate model that significantly accelerates and improves the accuracy of flow predictions and data assimilation in complex geological systems.

## Key findings

- High accuracy in pressure and saturation predictions for new geological realizations
- Substantial reduction in prediction uncertainty during data assimilation
- Speedup enabling practical posterior sampling in realistic problems

## Abstract

A deep-learning-based surrogate model is developed and applied for predicting dynamic subsurface flow in channelized geological models. The surrogate model is based on deep convolutional and recurrent neural network architectures, specifically a residual U-Net and a convolutional long short term memory recurrent network. Training samples entail global pressure and saturation maps, at a series of time steps, generated by simulating oil-water flow in many (1500 in our case) realizations of a 2D channelized system. After training, the `recurrent R-U-Net' surrogate model is shown to be capable of accurately predicting dynamic pressure and saturation maps and well rates (e.g., time-varying oil and water rates at production wells) for new geological realizations. Assessments demonstrating high surrogate-model accuracy are presented for an individual geological realization and for an ensemble of 500 test geomodels. The surrogate model is then used for the challenging problem of data assimilation (history matching) in a channelized system. For this study, posterior reservoir models are generated using the randomized maximum likelihood method, with the permeability field represented using the recently developed CNN-PCA parameterization. The flow responses required during the data assimilation procedure are provided by the recurrent R-U-Net. The overall approach is shown to lead to substantial reduction in prediction uncertainty. High-fidelity numerical simulation results for the posterior geomodels (generated by the surrogate-based data assimilation procedure) are shown to be in essential agreement with the recurrent R-U-Net predictions. The accuracy and dramatic speedup provided by the surrogate model suggest that it may eventually enable the application of more formal posterior sampling methods in realistic problems.