  Geologic carbon sequestration (GCS) is a safety-critical technology that aims
to reduce the amount of carbon dioxide in the atmosphere, which also places
high demands on reliability. Multiphase flow in porous media is essential to
understand CO$_2$ migration and pressure fields in the subsurface associated
with GCS. However, numerical simulation for such problems in 4D is
computationally challenging and expensive, due to the multiphysics and
multiscale nature of the highly nonlinear governing partial differential
equations (PDEs). It prevents us from considering multiple subsurface scenarios
and conducting real-time optimization. Here, we develop a Fourier-enhanced
multiple-input neural operator (Fourier-MIONet) to learn the solution operator
of the problem of multiphase flow in porous media. Fourier-MIONet utilizes the
recently developed framework of the multiple-input deep neural operators
(MIONet) and incorporates the Fourier neural operator (FNO) in the network
architecture. Once Fourier-MIONet is trained, it can predict the evolution of
saturation and pressure of the multiphase flow under various reservoir
conditions, such as permeability and porosity heterogeneity, anisotropy,
injection configurations, and multiphase flow properties. Compared to the
enhanced FNO (U-FNO), the proposed Fourier-MIONet has 90% fewer unknown
parameters, and it can be trained in significantly less time (about 3.5 times
faster) with much lower CPU memory ($<$ 15%) and GPU memory ($<$ 35%)
requirements, to achieve similar prediction accuracy. In addition to the lower
computational cost, Fourier-MIONet can be trained with only 6 snapshots of time
to predict the PDE solutions for 30 years. The excellent generalizability of
Fourier-MIONet is enabled by its adherence to the physical principle that the
solution to a PDE is continuous over time.
