Feasibility Study of Solving Oil-Water Two-Phase Flow Equations Using Fourier Neural Operator

In petroleum reservoir engineering, deep learning shows promising potential for solving partial differential equations (PDEs) in reservoir numerical simulations. However, traditional neural network-based methods for PDE solutions are often limited, typically requiring retraining for different equations. This study introduces the Fourier Neural Operator (FNO) approach, incorporating the fast Fourier transform mechanism to facilitate operator learning. We conduct a feasibility analysis of using FNO for solving two-dimensional oil-water two-phase flow PDEs. Through extensive literature review, we summarize the current state and limitations of deep learning in oil-water two-phase flow modeling, highlighting the application and advancements of neural operators for PDE solutions. This study demonstrates the potential of FNO to solve high-dimensional oil-water two-phase flow equations, offering valuable insights into intelligent predictions for complex subsurface reservoirs and presenting new methods and perspectives for further development in reservoir numerical modeling.