2025/04/12 by Rui Hu, Sanjeeb Poudel, Hu, Ruoyu +5
Earth and Planetary Sciences · Engineering · Environmental Science · #FOS: Mathematics #Groundwater flow and contamination studies #Numerical Analysis (math.NA) #Reservoir Engineering and Simulation Methods #Seismic Imaging and Inversion Techniques
paper · pdf · doi:10.48550/arxiv.2504.09245
openalex publication_date 2025/04/12 · openalex created_date 2025/10/14 · openalex updated_date 2026/07/28
Numerical modeling and simulation of two-phase flow in porous media is challenging due to the uncertainties in key parameters, such as permeability. To address these challenges, we propose a computational framework by utilizing the novel Ensemble Score Filter (EnSF) to enhance the accuracy of state estimation for two-phase flow systems in porous media. The forward simulation of the two-phase flow model is implemented using a mixed finite element method, which ensures accurate approximation of the pressure, the velocity, and the saturation. The EnSF leverages score-based diffusion models to approximate filtering distributions efficiently, avoiding the computational expense of neural network-based methods. By incorporating a closed-form score approximation and an analytical update mechanism, the EnSF overcomes degeneracy issues and handles high-dimensional nonlinear filtering with minimal computational overhead. Numerical experiments demonstrate the capabilities of EnSF in scenarios with uncertain permeability and incomplete observational data.