Graph Convolutional Networks for Predicting Multi-phase Flow and Transport Dynamics in Porous Media

Core Concepts

Graph Convolutional Networks can effectively approximate the spatial-temporal solutions of multi-phase flow and transport processes in porous media, providing computationally efficient alternatives to high-fidelity numerical simulators.

Abstract

The content presents a novel approach to construct surrogate models for predicting the dynamics of multi-phase fluid flow and transport in porous media using Graph Convolutional Networks (GCNs). The key highlights are: The coupled multi-phase flow system exhibits an intricate mixture of elliptic and hyperbolic characteristics. The authors design specialized GCN architectures suited to the specific characteristics of the PDE system to better capture the dynamics of fluid pressure and saturation. The GCN-based surrogate models are trained on high-fidelity simulation data, and can provide much faster predictions compared to the original numerical simulators. The results show that the trained surrogates accurately predict the evolutions of pressure and saturation states, and the predicted rollouts remain stable for multiple timesteps. The GCN models demonstrate strong generalization capabilities to irregular domain geometries and unstructured meshes that are not present in the training dataset. This is a significant advantage over the commonly used convolutional neural networks (CNNs), which are restricted to specific discretizations of the physical domain. The authors evaluate the prediction performance of the GCN surrogates on 2D heterogeneous test cases, and compare different GCN architectures incorporating specialized operators like EdgeConv. The results indicate that the combined GCN architectures can accurately capture the hyperbolic transport dynamics. Overall, the work showcases the effectiveness of GCNs in constructing data-driven surrogate models for complex multi-phase flow and transport processes in porous media, which can have important applications in various energy and environmental domains.

Stats

The simulation domain has sizes of 182 m × 3 m × 182 m. The initial reservoir pressure is 2000 psi. The initial water saturation is 0.01. The water density is 1000 kg/m³. The non-wetting phase (e.g., oil) reference density is 800 kg/m³. The water viscosity is 1.0 cP. The non-wetting phase viscosity is 2.0 cP. The rock compressibility is 1e-8 1/bar. The non-wetting phase compressibility is 1e-4 1/bar. The production well BHP is 1800 psi. The injection well BHP is 2200 psi. The total simulation time is 100 days with 20 timesteps.

Quotes

"Graph Convolutional Networks can effectively approximate the spatial-temporal solutions of multi-phase flow and transport processes in porous media, providing computationally efficient alternatives to high-fidelity numerical simulators." "The GCN-based surrogate models demonstrate strong generalization capabilities to irregular domain geometries and unstructured meshes that are not present in the training dataset."

Key Insights Distilled From

Graph Convolutional Networks for Simulating Multi-phase Flow and Transport in Porous Media

by Jiamin Jiang... at arxiv.org 04-16-2024

https://arxiv.org/pdf/2307.04449.pdf

Deeper Inquiries

How can the proposed GCN-based surrogate modeling framework be extended to handle more complex multi-phase flow scenarios, such as compressible, compositional, or reactive transport processes

The proposed GCN-based surrogate modeling framework can be extended to handle more complex multi-phase flow scenarios by incorporating additional features and considerations specific to compressible, compositional, or reactive transport processes. For compressible flow scenarios, the model can be adapted to include equations of state to account for changes in fluid density with pressure variations. This would require incorporating additional variables related to fluid compressibility and the equation of state into the node features. The GCN architecture can be modified to handle these additional variables and their interactions within the porous media. In the case of compositional flow, where multiple fluid components are present, the model can be expanded to include components such as gas, oil, and water. Each component would have its own set of equations governing phase behavior, such as phase equilibrium and component transport. The GCN can be enhanced to capture the interactions between different components and their impact on the overall flow behavior. For reactive transport processes, where chemical reactions occur between the fluids and the porous media, the model can be extended to include reaction kinetics and species transport equations. The GCN architecture can be modified to incorporate variables related to species concentrations, reaction rates, and mineral dissolution/precipitation. This would enable the model to predict the evolution of reactive transport processes within the porous media accurately. By integrating these additional features and considerations into the GCN framework, the surrogate modeling approach can be tailored to address the complexities of compressible, compositional, and reactive transport processes in multi-phase flow scenarios.

What are the potential limitations of the current GCN architectures, and how can they be further improved to better capture the intricate coupling between the elliptic and hyperbolic characteristics of the PDE system

The current GCN architectures may have limitations in capturing the intricate coupling between the elliptic and hyperbolic characteristics of the PDE system due to several factors. One potential limitation is the complexity of the underlying physics, which may require more sophisticated modeling techniques to accurately represent the flow dynamics in porous media. To improve the GCN architectures for better capturing the coupling between elliptic and hyperbolic characteristics, several enhancements can be considered: Incorporating Hybrid Architectures: Combining different types of graph convolutional layers, such as GraphConv, GATConv, and EdgeConv, in a hybrid architecture can leverage the strengths of each type of layer to handle both elliptic and hyperbolic characteristics effectively. Adaptive Learning Mechanisms: Implementing adaptive learning mechanisms within the GCN models can help the network dynamically adjust its parameters based on the characteristics of the PDE system. This can enhance the model's ability to capture the complex interactions between different flow processes. Incorporating Physical Constraints: Integrating physical constraints and domain knowledge into the GCN architecture can guide the learning process and ensure that the model generates physically meaningful solutions. This can help in better capturing the intricate coupling between elliptic and hyperbolic characteristics. By addressing these limitations and implementing these improvements, the GCN architectures can be further enhanced to better capture the complexities of multi-phase flow and transport processes in porous media.

Given the promising results on 2D cases, how can the GCN surrogate models be scaled up to handle realistic 3D reservoir models with complex geological features and heterogeneity

Scaling up the GCN surrogate models to handle realistic 3D reservoir models with complex geological features and heterogeneity involves several key considerations and strategies: Increased Model Complexity: As the dimensionality increases from 2D to 3D, the model complexity also needs to scale accordingly. This includes expanding the input features to capture the additional spatial dimensions and incorporating more sophisticated graph convolutional layers to handle the increased complexity of the 3D data. Data Preprocessing and Augmentation: Preprocessing the 3D reservoir data to represent it in a graph format suitable for GCNs is crucial. This may involve segmenting the reservoir into smaller subdomains, defining the connectivity between nodes in 3D space, and augmenting the dataset to include a diverse range of geological features. Parallel Processing and Optimization: Given the computational demands of 3D simulations, optimizing the GCN models for parallel processing and efficient memory utilization is essential. Techniques such as batch processing, distributed computing, and model parallelism can be employed to handle the increased computational load. Validation and Calibration: Validating the 3D GCN models against high-fidelity numerical simulators and calibrating the model parameters to match real-world data are critical steps in ensuring the accuracy and reliability of the predictions. This may involve sensitivity analysis, uncertainty quantification, and model validation against field data. By carefully addressing these considerations and strategies, the GCN surrogate models can be successfully scaled up to handle realistic 3D reservoir models with complex geological features and heterogeneity, providing accurate predictions of multi-phase flow and transport processes in porous media.