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Data-Driven Closure Parametrizations with Metrics: Dispersive Transport

Edward Coltman, Martin Schneider, Rainer Helmig

Abstract

This work presents a data-driven framework for multi-scale parametrization of velocity-dependent dispersive transport in porous media. Pore-scale flow and transport simulations are conducted on periodic pore geometries, and volume-averaging is used to isolate dispersive transport, producing parameters for the dispersive closure term at the Representative Elementary Volume (REV) scale. After validation on unit cells with symmetric and asymmetric geometries, a convolutional neural network (CNN) is trained to predict dispersivity directly from pore-geometry images. Descriptive metrics are also introduced to better understand the parameter space and are used to build a neural network that predicts dispersivity based solely on these metrics. While the models predict longitudinal dispersivity well, transversal dispersivity remains difficult to capture, likely requiring more advanced models to fully describe pore-scale transversal dynamics.

Data-Driven Closure Parametrizations with Metrics: Dispersive Transport

Abstract

This work presents a data-driven framework for multi-scale parametrization of velocity-dependent dispersive transport in porous media. Pore-scale flow and transport simulations are conducted on periodic pore geometries, and volume-averaging is used to isolate dispersive transport, producing parameters for the dispersive closure term at the Representative Elementary Volume (REV) scale. After validation on unit cells with symmetric and asymmetric geometries, a convolutional neural network (CNN) is trained to predict dispersivity directly from pore-geometry images. Descriptive metrics are also introduced to better understand the parameter space and are used to build a neural network that predicts dispersivity based solely on these metrics. While the models predict longitudinal dispersivity well, transversal dispersivity remains difficult to capture, likely requiring more advanced models to fully describe pore-scale transversal dynamics.
Paper Structure (38 sections, 15 equations, 20 figures, 2 tables)

This paper contains 38 sections, 15 equations, 20 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Pore-Scale Evaluations
  3. Flow and Transport Models
  4. Numerical Methods
  5. Pore Geometries and Preprocessing
  6. REV-Scale Model Parametrization
  7. Upscaling Dispersive Transport
  8. Dispersive Transport Model
  9. Optimal Parameters
  10. Volume Averaging
  11. Verification
  12. Symmetric Cases: Circles and Squares
  13. Asymmetric Cases: Ellipses and Triangles
  14. Multi-Scale Data-Driven Model
  15. Convolutional Neural Networks (CNNs)
  16. ...and 23 more sections

Figures (20)

  • Figure 1: Examples of the pseudo pore geometries used are shown left to right: Voronoi polygons, Perlin noise, and Fractal noise based topographies. White regions belong to the void space $\Omega_{\text{void}}$, and black regions belong to the solid inclusions $\Omega_{\text{solid}}$.
  • Figure 2: A depiction of the various volumes used while performing a volume averaging of flow and transport at the pore scale. In \ref{['fig:UnitAvg']}, the full domain, $\Omega$, and its split void-solid regions, $\Omega_{\text{void}}$ and $\Omega_{\text{solid}}$, are shown. In \ref{['fig:ConvAvg']}, the extended domain, $\Omega_{\text{Extended}}$, and the volumes related to convolutional and unit averaging, $\text{V}_{\text{Conv}}$ and $\text{V}_{ \text{Average}}$, are shown.
  • Figure 3: The development of $\alpha_L$ and $\alpha_T$ for symmetrical cases. Considered are circular and rectangular solid inclusions of increasing length ratio ${\text{r}}/{\text{L}}$.
  • Figure 4: The development of $\alpha_L$ and $\alpha_T$ for asymmetrical ellipsoid cases. The aspect ratio and the pitch rotation $\Theta$ are varied.
  • Figure 5: The development of $\alpha_L$ and $\alpha_T$ for asymmetrical triangular cases. The face orientation, $\Theta$, is varied.
  • ...and 15 more figures