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Knowledge-Based Convolutional Neural Network for the Simulation and Prediction of Two-Phase Darcy Flows

Zakaria Elabid, Daniel Busby, Abdenour Hadid

TL;DR

This work tackles the difficulty of applying physics-informed neural networks to discontinuous two-phase Darcy flow in porous media by embedding discretized governing equations directly into the learning process. It introduces Knowledge-Based Encoder-Decoder (KED), comprising two U-Net encoders–decoders that predict pressure and saturation from permeability and time, trained with both supervised losses and a physics loss derived from a finite-difference discretization. The method leverages semi-supervised learning with virtual permeability to enforce the discretized dynamics, achieving higher accuracy and physically coherent predictions than non-physics baselines on a large sand/mud dataset, including pressure, saturation, and production outputs via the Peaceman metric. The results demonstrate improved predictive fidelity and practical relevance for reservoir simulation, with potential extensions to GAN-based architectures and reproducible code release forthcoming.

Abstract

Physics-informed neural networks (PINNs) have gained significant prominence as a powerful tool in the field of scientific computing and simulations. Their ability to seamlessly integrate physical principles into deep learning architectures has revolutionized the approaches to solving complex problems in physics and engineering. However, a persistent challenge faced by mainstream PINNs lies in their handling of discontinuous input data, leading to inaccuracies in predictions. This study addresses these challenges by incorporating the discretized forms of the governing equations into the PINN framework. We propose to combine the power of neural networks with the dynamics imposed by the discretized differential equations. By discretizing the governing equations, the PINN learns to account for the discontinuities and accurately capture the underlying relationships between inputs and outputs, improving the accuracy compared to traditional interpolation techniques. Moreover, by leveraging the power of neural networks, the computational cost associated with numerical simulations is substantially reduced. We evaluate our model on a large-scale dataset for the prediction of pressure and saturation fields demonstrating high accuracies compared to non-physically aware models.

Knowledge-Based Convolutional Neural Network for the Simulation and Prediction of Two-Phase Darcy Flows

TL;DR

This work tackles the difficulty of applying physics-informed neural networks to discontinuous two-phase Darcy flow in porous media by embedding discretized governing equations directly into the learning process. It introduces Knowledge-Based Encoder-Decoder (KED), comprising two U-Net encoders–decoders that predict pressure and saturation from permeability and time, trained with both supervised losses and a physics loss derived from a finite-difference discretization. The method leverages semi-supervised learning with virtual permeability to enforce the discretized dynamics, achieving higher accuracy and physically coherent predictions than non-physics baselines on a large sand/mud dataset, including pressure, saturation, and production outputs via the Peaceman metric. The results demonstrate improved predictive fidelity and practical relevance for reservoir simulation, with potential extensions to GAN-based architectures and reproducible code release forthcoming.

Abstract

Physics-informed neural networks (PINNs) have gained significant prominence as a powerful tool in the field of scientific computing and simulations. Their ability to seamlessly integrate physical principles into deep learning architectures has revolutionized the approaches to solving complex problems in physics and engineering. However, a persistent challenge faced by mainstream PINNs lies in their handling of discontinuous input data, leading to inaccuracies in predictions. This study addresses these challenges by incorporating the discretized forms of the governing equations into the PINN framework. We propose to combine the power of neural networks with the dynamics imposed by the discretized differential equations. By discretizing the governing equations, the PINN learns to account for the discontinuities and accurately capture the underlying relationships between inputs and outputs, improving the accuracy compared to traditional interpolation techniques. Moreover, by leveraging the power of neural networks, the computational cost associated with numerical simulations is substantially reduced. We evaluate our model on a large-scale dataset for the prediction of pressure and saturation fields demonstrating high accuracies compared to non-physically aware models.
Paper Structure (12 sections, 8 equations, 4 figures, 1 algorithm)

This paper contains 12 sections, 8 equations, 4 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Darcy's Law and Mass Conservation Equations
  4. Proposed Method
  5. Supervised Learning
  6. Knowledge-Based Learning
  7. Experimental Analysis
  8. Performance measures
  9. Implementation of the proposed framework
  10. Visualization of 2D pressure and saturation fields
  11. Production values
  12. Conclusion

Figures (4)

  • Figure 1: Permeability map with sand and mud facies
  • Figure 2: Comparison between reference (left), KED (middle) and non-physics prediction baseline (right) of 2D Pressure maps (top) and saturation maps (bottom)
  • Figure 3: Comparison of oil production in production wells between reference (orange), baseline (blue) and our approach (green)
  • Figure 4: Crossplot of the real oil production and the predicted oil production levels using our approach on 500 test samples