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A semi-analytical method for simulating matrix diffusion in numerical transport models.

Ronald W Falta1, Wenwen Wang1

  • 1Department of Environmental Engineering and Earth Sciences, Clemson University, SC 29634-0919, United States.

Journal of Contaminant Hydrology
|January 22, 2017
PubMed
Summary
This summary is machine-generated.

A new semi-analytical method improves contaminant transport simulations by efficiently modeling matrix diffusion. This approach enhances numerical models by representing low-permeability zones, reducing computational costs and increasing accuracy.

Keywords:
Matrix diffusionNumerical modelingSemi-analytical

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Area of Science:

  • Environmental Science
  • Hydrogeology
  • Numerical Modeling

Background:

  • Contaminant transport in heterogeneous media often involves diffusion in low-permeability zones (matrix diffusion), which is computationally intensive.
  • Traditional numerical methods require discretizing both high and low permeability zones, leading to significant computational demands.
  • Efficient simulation of matrix diffusion is crucial for accurate predictions of contaminant fate and transport.

Purpose of the Study:

  • To develop a computationally efficient semi-analytical approximation for transient matrix diffusion.
  • To integrate this method into numerical contaminant transport simulators.
  • To reduce the computational burden associated with simulating contaminant transport in fractured porous media.

Main Methods:

  • Adaptation and extension of the heat conduction method (Vinsome and Westerveld, 1980).
  • Representation of concentration profiles in low-permeability materials using a time-step adjusted fitting function.
  • Inclusion of matrix diffusion fluxes as linear, concentration-dependent source/sink terms in numerical models.
  • Discretization limited to high-permeability zones only.

Main Results:

  • The semi-analytical method significantly enhances computational efficiency by avoiding discretization of low-permeability zones.
  • The method demonstrates favorable comparisons with analytical solutions for various diffusion and decay scenarios.
  • Validation against a fully numerical solution for a complex thin sand zone bounded by clay confirms accuracy.

Conclusions:

  • The developed semi-analytical approximation provides an efficient and accurate alternative for simulating transient matrix diffusion in contaminant transport models.
  • This method offers a practical solution for reducing computational costs in complex hydrogeological simulations.
  • The approach is broadly applicable to various scenarios involving fractured porous media and contaminant transport.