  This paper proposes a deep neural network approach for predicting multiphase
flow in heterogeneous domains with high computational efficiency. The deep
neural network model is able to handle permeability heterogeneity in high
dimensional systems, and can learn the interplay of viscous, gravity, and
capillary forces from small data sets. Using the example of carbon dioxide
(CO2) storage, we demonstrate that the model can generate highly accurate
predictions of a CO2 saturation distribution given a permeability field,
injection duration, injection rate, and injection location. The trained neural
network model has an excellent ability to interpolate and to a limited extent,
the ability to extrapolate beyond the training data ranges. To improve the
prediction accuracy when the neural network model needs to extrapolate, we
propose a transfer learning (fine-tuning) procedure that can quickly teach the
neural network model new information without going through massive data
collection and retraining. Based on this trained neural network model, a
web-based tool is provided that allows users to perform CO2-water multiphase
flow calculations online. With the tools provided in this paper, the deep
neural network approach can provide a computationally efficient substitute for
repetitive forward multiphase flow simulations, which can be adopted to the
context of history matching and uncertainty quantification.
