Heterogeneity of the permeability field and permeability structures of low-permeability geologic units is critical to fluid flow and contaminant transport studies. Analysis of density-driven flow where denser fluids, such as brines or DNAPLs, overlie less dense fluids and the two fluids are separated by a low permeability unit illustrates how heterogeneity affects solute transport. For the above model scenario, we generated a number of numerical realizations to simulate the distributions of permeability in a shale layer. The thirty two-dimensional distributions of permeabilities have identical geometric means (log k=-13.0 and k=10^-13 m² ) and variances. The standard deviation of permeability is about log 1.2. Arbitrary maximum and minimum permeabilities were set at 10^-10 m² and 10^-20 m², respectively. The simulated permeability data were analyzed by using patch analysis method to delineate and outline high permeability zones within the shale layer. Percolation theory was used in defining these patches. Area, vertical and horizontal connectivity indices of these high permeability patches were calculated. Weighted arithmetic mean was also calculated to analyze the structure of a permeability field. Results from modeling solute transport through the shale layer show that higher weighted arithmetic means correspond to deeper penetration depths of the plume, and permeability structure determines plume development in the shale layer.