The Effect of Crack Geometry on Hydrodynamic Dispersion in Cracked Media

Abstract

ABSTRACT A theoretical as well as a numerical study has been carried out with special emphasis on developing a basic understanding of how crack geometry influences hydraulic phenomena such as permeability and hydrodynamic dispersion in cracked bodies. The permeability tensor Kij is formulated in terms of length, aperture and orientation of cracks plus one more non-dimensional scalar λ depending on connectivity among cracks. By extending the Robinson's formula, a general expression for λ is given as a function of density and anisotropy of existing cracks. Dispersion tensor Dij con-sists of two different sources. The first comes from the fact that each tracer is forced to move along cracks the directions of which deviate from the mean path. The second comes from non-uniform distribution of hydraulic head throughout a cracked body. The second source has increasing importance not only when crack density is low, but also when crack arrangement is highly anisotropic. The distribution of head becomes extremely non-uniform, especially when overall hydraulic head gradient is parallel to the preferred orientation of cracks. The permeability tensor Kij is isotropic so long as the related crack tensor Nij is isotropic. Dispersion tensor Dij is anisotropic unless the fourth-rank crack tensor Nijkl is isotropic. Accordingly, any crack body characterized by an isotropic permeability tensor is not necessarily isotropic in dispersion.