Physically-Aware Deep Learning for Accurate Simulation and Prediction of Two-Phase Fluid Flow in Porous Media

Core Concepts

A novel physics-informed deep learning framework that combines neural networks with discretized governing equations to accurately simulate and predict two-phase fluid flow in porous media, addressing challenges with discontinuities and sharp gradients.

Abstract

The paper presents a novel approach called Knowledge-based Encoder-Decoder (KED) that combines the power of neural networks with the dynamics imposed by the discretized differential equations governing two-phase Darcy flow in porous media. Key highlights: The KED framework incorporates the discretized forms of the governing equations into the physics-informed neural network (PINN) architecture to account for discontinuities and sharp gradients in the data. By discretizing the governing equations, the neural network learns to capture the underlying relationships between inputs (permeability fields) and outputs (pressure and saturation maps) more accurately compared to traditional interpolation techniques. The computational cost associated with numerical simulations is substantially reduced by leveraging the power of neural networks. The model is evaluated on a large-scale dataset for two-phase flow prediction, demonstrating high accuracy compared to non-physically aware models. The proposed approach addresses the challenges faced by mainstream PINNs in handling discontinuous input data, leading to improved prediction accuracy in porous media applications.

Stats

The permeability field K(x, y, z) has two distinct facies - sand (K=2000md) and mud (K=20md), with corresponding porosities of 0.25 and 0.1. The simulation is performed on a 40m x 40m x 20m grid with block dimensions of dx = 20, dy = 20, dz = 2, over 21 timesteps of 50 days each. The fluid parameters are: C = 9.10^-5, ρwater = 1838 Kg/m^3, ρoil = 787 Kg/m^3, μwater = 0.31 cp, μoil = 1.14 cp.

Quotes

"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." "The computational cost associated with numerical simulations is substantially reduced by leveraging the power of neural networks."

Key Insights Distilled From

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

by Zakaria Elab... at arxiv.org 04-05-2024

https://arxiv.org/pdf/2404.03240.pdf

Deeper Inquiries

How can the proposed KED framework be extended to handle more complex multi-phase flow scenarios in porous media, such as the inclusion of capillary pressure and gravity effects?

The KED framework can be extended to handle more complex multi-phase flow scenarios by incorporating additional physics-informed constraints related to capillary pressure and gravity effects. To include capillary pressure effects, the model can integrate the Brooks-Corey and Van Genuchten soil-water retention models to capture the non-linear relationship between saturation and capillary pressure. This addition would enhance the model's ability to simulate the behavior of fluids in porous media under varying capillary pressures. Moreover, to incorporate gravity effects, the framework can be modified to include terms in the governing equations that account for gravitational forces acting on the fluids. By including gravitational potential terms in the mass conservation equations, the model can accurately predict the flow behavior of fluids in porous media under the influence of gravity. This extension would enable the KED framework to simulate multi-phase flow scenarios more realistically, considering the impact of both capillary pressure and gravity effects on fluid dynamics in porous media.

What are the potential limitations of the discretization approach used in the KED framework, and how can they be addressed to further improve the model's performance?

One potential limitation of the discretization approach in the KED framework is the sensitivity to grid resolution and time step sizes. Inaccuracies may arise if the discretization is not fine enough to capture small-scale variations in the flow field accurately. To address this limitation, adaptive mesh refinement techniques can be implemented to dynamically adjust the grid resolution based on the complexity of the flow field. By refining the grid in regions with high gradients or discontinuities, the model can improve its accuracy without significantly increasing computational costs. Another limitation is the potential introduction of numerical diffusion and dispersion artifacts during the discretization process, which can lead to smearing of sharp gradients in the flow field. To mitigate these effects, higher-order discretization schemes such as spectral methods or finite element methods can be employed to reduce numerical errors and improve the model's accuracy. Additionally, incorporating stabilization techniques like artificial viscosity or artificial diffusion can help suppress spurious oscillations and enhance the robustness of the discretization approach.

Given the success of the KED framework in porous media applications, how could the integration of physical knowledge into deep learning architectures be leveraged to solve other challenging problems in scientific computing and engineering?

The integration of physical knowledge into deep learning architectures, as demonstrated by the KED framework in porous media applications, can be leveraged to address various challenging problems in scientific computing and engineering across different domains. One potential application is in climate modeling, where physics-informed neural networks can be used to simulate complex atmospheric dynamics and predict climate patterns with improved accuracy. By incorporating physical constraints related to fluid dynamics, thermodynamics, and radiative transfer, these models can provide more reliable long-term climate projections. In the field of material science, physics-informed deep learning architectures can be utilized to predict material properties, optimize material designs, and accelerate materials discovery processes. By encoding fundamental physical principles into the neural network structures, these models can simulate material behaviors under different conditions and guide the development of novel materials with tailored properties. Furthermore, in structural engineering, physics-informed neural networks can be applied to predict structural responses, optimize designs, and assess structural integrity under varying loads and environmental conditions. By integrating knowledge of structural mechanics, material properties, and boundary conditions, these models can offer valuable insights into the performance of complex structures and aid in the design of safer and more efficient engineering systems.