A Physics‐Enhanced Neural Network for Estimating Longitudinal Dispersion Coefficient and Average Solute Transport Velocity in Porous Media

• Published in: Geophysical research letters 2024-09, Vol.51 (17), p.n/a
• Main Authors: Meng, Yinquan, Jiang, Jianguo, Wu, Jichun, Wang, Dong
• Format: Article
• Language: English
• Subjects: Advective flow; Artificial neural networks; Deep learning; Diffusion; Diffusion coefficient; Diffusion rate; Dispersion; Flow rates; Groundwater; hydrodynamic dispersion; Longitudinal dispersion; Media; Modelling; Neural networks; Numerical simulations; Parameter estimation; parameter prediction; Parameters; Peclet number; Performance prediction; Physics; Porous media; Solute transport; Solutes; Transport phenomena; Velocity; Water resources
• ISSN: 0094-8276; 1944-8007
• DOI: 10.1029/2024GL110683

Dispersion coefficients and the average solute transport velocity are pivotal for groundwater solute transport modeling. Accurately and efficiently determining these parameters is challenging due to difficulties in directly correlating them with pore‐space structure. To address this issue, we introduced the Physics‐enhanced Convolutional Neural Network‐Transformer (PhysenCT‐Net), an innovative model designed to concurrently estimate the longitudinal dispersion coefficient and average solute transport velocity in three‐dimensional porous media. PhysenCT‐Net exhibited excellent predictive performance on unseen testing datasets and significantly reduced computational demands. Comprehensive evaluations confirmed its robust generalization across various flow conditions and pore structures. Notably, the longitudinal dispersion coefficient predictions closely align with established empirical relationships involving Péclet number, affirming the model's physical interpretability and potential to aid in simulating transport phenomena in porous media. Plain Language Summary The migration of solutes in geological media is a complex process that involves both dispersion and advective motions. Therefore, the dispersion coefficient and advective flow rate are crucial parameters for modeling and predicting solute migration, with the former being determined by the complex flow field and solute diffusion coefficient within the medium. These two parameters are typically obtained through the experiment results of solute concentration distribution or through complex numerical simulations, which take a lot of time and resources. In this letter, we introduce a deep learning model that can provide a more efficient way to determine the two parameters describing substance movements. The model uses three‐dimensional images and properties of the media, the diffusion coefficient of solute and the mean flow speed of water as the inputs. We tested the model under a variety of conditions, and the dispersion coefficients predicted by the trained model agreed well with physical laws. The model can not only improve how we estimate these parameters, but also help us understand the physical laws that govern how substances move through groundwater. This could lead to better ways of modeling and managing these important water resources. Key Points Accurately predicting key parameters of the advection‐dispersion equation for solute transport in porous media Developing direct mapping relationship