Well2Flow: Reconstruction of reservoir states from sparse wells using score-based generative models

TL;DR

Reconstructs heterogeneous reservoir states by inferring the joint distribution of permeability $K$ and saturation $S$ from sparse well observations. The authors develop a score-based diffusion framework that guides sampling with well-log data and enforces physics via PDE constraints, learning the joint distribution of $(K,S)$ from high-fidelity simulations. Key contributions include observation-guided posterior sampling, physics-informed regularization during denoising, and demonstrated generalization across varying geological scenarios, enabling both forward prediction and inverse reconstruction with limited data. The approach offers a data-efficient, physically consistent surrogate for reservoir management in data-scarce settings, with potential extensions to integrate seismic data and additional measurements.

Abstract

This study investigates the use of score-based generative models for reservoir simulation, with a focus on reconstructing spatially varying permeability and saturation fields in saline aquifers, inferred from sparse observations at two well locations. By modeling the joint distribution of permeability and saturation derived from high-fidelity reservoir simulations, the proposed neural network is trained to learn the complex spatiotemporal dynamics governing multiphase fluid flow in porous media. During inference, the framework effectively reconstructs both permeability and saturation fields by conditioning on sparse vertical profiles extracted from well log data. This approach introduces a novel methodology for incorporating physical constraints and well log guidance into generative models, significantly enhancing the accuracy and physical plausibility of the reconstructed subsurface states. Furthermore, the framework demonstrates strong generalization capabilities across varying geological scenarios, highlighting its potential for practical deployment in data-scarce reservoir management tasks.

Figures (5)

• Figure 1: Work flow
• Figure 2: Uncertainty analysis based on two well points.
• Figure 3: Permeability inversion with saturation and well guidance
• Figure 4: Saturation prediction with permeability and well guidance
• Figure 5: Ablation study: The first and third rows show the ground truth and generated permeability ($K$) and saturation ($S$) with different noise levels at well locations. The second and fourth rows display the corresponding root mean squared errors (rMSE).