  Numerical simulation of multiphase flow in porous media is essential for many
geoscience applications. Machine learning models trained with numerical
simulation data can provide a faster alternative to traditional simulators.
Here we present U-FNO, a novel neural network architecture for solving
multiphase flow problems with superior accuracy, speed, and data efficiency.
U-FNO is designed based on the newly proposed Fourier neural operator (FNO),
which has shown excellent performance in single-phase flows. We extend the
FNO-based architecture to a highly complex CO2-water multiphase problem with
wide ranges of permeability and porosity heterogeneity, anisotropy, reservoir
conditions, injection configurations, flow rates, and multiphase flow
properties. The U-FNO architecture is more accurate in gas saturation and
pressure buildup predictions than the original FNO and a state-of-the-art
convolutional neural network (CNN) benchmark. Meanwhile, it has superior data
utilization efficiency, requiring only a third of the training data to achieve
the equivalent accuracy as CNN. U-FNO provides superior performance in highly
heterogeneous geological formations and critically important applications such
as gas saturation and pressure buildup "fronts" determination. The trained
model can serve as a general-purpose alternative to routine numerical
simulations of 2D-radial CO2 injection problems with significant speed-ups than
traditional simulators.
