Issues in Single‐Fracture Transport Modeling: Scales, Algorithms, and Grid Types

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Abstract
Transport in single fractures has recently been intensely examined. Potential applications of these studies include nuclear waste storage and infiltration of rainwater into soil desiccation cracks. We modeled hydrodynamic dispersion in single fractures, using a variable‐aperture model and particle‐tracking techniques. We examined issues of scale of heterogeneity, particle‐tracking method, and grid topology. Hydrodynamic dispersion tends to zero as the scale of the transport path increases in relation to the scale of heterogeneity. Since this is not observed in nature, it implies either that fractures have fractal structure or that hydrodynamic dispersion alone does not account for all the dispersion that occurs in fractures. Dispersion and retardation as simulated using a node‐to‐node or mixing type algorithm are greater than when they are simulated using an interpolation algorithm, and the difference cannot be attributed to molecular diffusion. Differences in conductivity and dispersion between different grid types (serial, parallel, square, and random field) are related to the coordination number (degree of connectedness) of the grid, with lower coordination number grids having higher dispersion.

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