Tracer dispersion in two-dimensional rough fractures - art. no. 056104

Tracer diffusion and hydrodynamic dispersion in two-dimensional fractures w ith serf-affine roughness are studied by analytic and numerical methods. Nu merical simulations were performed via the lattice-Boltzmann approach, usin g a boundary condition for tracer particles that improves the accuracy of t he method. The reduction in the diffusive transport, due to the fractal geo metry of the fracture surfaces, is analyzed for different fracture aperture s. In the limit of small aperture fluctuations we derive the correction to the diffusive coefficient in terms of the tortuosity, which accounts for th e irregular geometry of the fractures. Dispersion is studied when the two f racture surfaces are simply displaced normally to the mean fracture plane a nd when there is a lateral shift as well. Numerical results are analyzed us ing the Lambda parameter, related to convective transport within the fractu re, and simple arguments based on lubrication approximation. At very low Pe clet number, in the case where fracture surfaces are laterally shifted, we show using several different methods that convective transport reduces disp ersion.