Analytical Model for Solute Transport in Fracture Networks

Abstract:

Predicting solute transport in fracture networks using Random Walk -based models that consider adsorption, matrix diffusion, and decay is computationally intensive as they require the release of a large number of particles achieve accurate results. While analytical approaches are much less computationally intensive, solutions are not available at the network scale. A computationally efficient analytical model simulating solute transport in fracture networks is developed considering advection, hydrodynamic dispersion, matrix diffusion, sorption on the fracture walls and in the matrix, and first order decay.

The model was based on two previously developed analytical solutions for single, parallel plate fractures, and mass sharing at intersections was implemented using both the complete mixing and stream tube methods. The developed model was verified by comparing its results to those from numerical solutions (time domain random walk and random walk particle tracking) under a range of Peclet numbers to assess the efficiency of each mass sharing method.

The developed model showed excellent agreement with the numerical solutions. The results indicated that transport processes, in environments where matrix diffusion exists, are nearly independent of mass sharing approach employed, particularly when the spacing between fractures is large. Diffusion-dominated transport processes, however, are impacted by the mass sharing approach employed. The developed model can be used as a reference model to verify other numerical solutions that simulate solute transport in fracture networks with matrix diffusion and variable fracture spacings (dual porosity).