Tracer dispersion in twodimensional rough fractures
Abstract
Tracer diffusion and hydrodynamic dispersion in twodimensional fractures with selfaffine roughness are studied by analytic and numerical methods. Numerical simulations were performed via the latticeBoltzmann approach, using a boundary condition for tracer particles that improves the accuracy of the method. The reduction in the diffusive transport, due to the fractal geometry of the fracture surfaces, is analyzed for different fracture apertures. In the limit of small aperture fluctuations we derive the correction to the diffusive coefficient in terms of the tortuosity, which accounts for the irregular geometry of the fractures. Dispersion is studied when the two fracture surfaces are simply displaced normally to the mean fracture plane and when there is a lateral shift as well. Numerical results are analyzed using the Λ parameter, related to convective transport within the fracture, and simple arguments based on lubrication approximation. At very low Péclet number, in the case where fracture surfaces are laterally shifted, we show using several different methods that convective transport reduces dispersion.
 Publication:

Physical Review E
 Pub Date:
 May 2001
 DOI:
 10.1103/PhysRevE.63.056104
 arXiv:
 arXiv:condmat/0010369
 Bibcode:
 2001PhRvE..63e6104D
 Keywords:

 02.50.r;
 05.40.a;
 47.11.+j;
 47.55.Mh;
 Probability theory stochastic processes and statistics;
 Fluctuation phenomena random processes noise and Brownian motion;
 Condensed Matter  Statistical Mechanics;
 Nonlinear Sciences  Cellular Automata and Lattice Gases;
 Physics  Computational Physics;
 Physics  Fluid Dynamics;
 Physics  Geophysics
 EPrint:
 Phys. Rev. E, 63, 056104 (2001)