Flow and transport in highly heterogeneous formations: Conceptual uncertainty and solution for multi-indicator permeability structure

Flow of water and transport of a solute take place in a heterogeneous aquifer of spatially variable, random, permeability. Solutions are sought for formations of large logconductivity variance σ²_y. The formation is modeled as a collection of blocks (Fig. 1) of different conductivity and size that are implanted at random and independently in space. By adopting simple shapes (circle, spheres for isotropic formations), approximate analytical solutions are obtained for the velocity field in terms of the permeability distribution. The solute particle trajectories are determined by particle tracking. The asymptotic, large travel time macrodispersivity is computed for large permeability contrasts and the validity of first-order approximations is discussed.