Development and optimization of a deep-learning reduced-order model for multiphase flow

Significant research has been done over the years on developing many sophisticated and powerful fluid flow simulators using numerical discretization. Such simulators can be computationally costly, especially when many simulations are required for complicated flow problems.
The high computation requirements have motivated the development of Reduced-Order Models (ROM). The idea is to solve the same problems with similar accuracy to the full physics simulators and significantly reduce computational cost. This interest, and the availability of extensive observational and simulation data in oil and gas, attracted many researchers to explore the idea of learning physics from data and integrating data-driven models with constitutive relationships and mass conservation laws. In this work, we develop a physics-based deep-learning ROM for multiphase flow. It is based on an existing Embed-to-Control (E2C) framework, developed by Watter et al (2015), which is an autoencoder that learns to generate images from latent space. Our deep-learning ROM consists of an encoder, a linear transition model that approximates the dynamics of the system in low dimension space, and a decoder to project the system back to high dimensions. We introduce a physics-based loss function on top of the data mismatch to enforce local mass conservation. The model was applied to a two-dimensional oil-water flow problem. The deep-learning ROM was approximately 1000 times faster than the full-physics model. This timing does not include the time to generate the training dataset. Global properties and well responses predictions were compared with data from the simulation model, and the results were accurate. Next, we introduce a novel approach to select an optimal set of snapshots for training the deep-learning ROM. Snapshot selection is based on the jump in the number of local refinements between two consecutive snapshots provided by a Space-Time geometric multigrid solver. Results from the deep-learning ROM show that we can achieve faster convergence to the solution using only 65% of the snapshots generated at fixed intervals. Computational time savings accrued while generating the snapshots and while using the optimized snapshots in the deep-learning model. Results generated using fixed time interval snapshots, and adaptively selected snapshots show similar accuracy. Finally, we introduce modifications to the deep-learning ROM framework to enhance the sequential predictions. We modify the encoder in the original framework to consider a sequence of snapshots for predictions. We use a Long-Short Term Memory (LSTM) Recurrent Neural Network (RNN) in the encoder to mitigate the original architecture's error accumulation. The result shows that the error accumulation no longer exists and that the overall prediction is more accurate. The new model is not as fast as the original framework; however, it is relatively easy to train, and a 5-year prediction scenario takes only seconds to complete.