Digital simulation of the scale effect in hydraulic conductivity

Measured hydraulic conductivity increases with the scale of testing, but the reason for this increase is not clear. Possibly, high-conductivity heterogeneities are more effective in raising hydraulic conductivity over the regional scale than at the local scale. Alternatively, borehole skin and storage effects, among others, can systematically bias the results of small-scale tests; thus, the increase may simply be an artifact of the test method. Radial-flow tests were simulated at various scales in digital models of fractured double-porosity media. The mean hydraulic conductivity increases until the radius of influence in the test exceeds the fracture spacing. Therefore, under radial flow, hydraulic conductivity is indeed dependent on measurement scale. The increase in hydraulic conductivity with scale is a natural consequence of heterogeneity. Over short distances, water converging toward a borehole must generally flow across heterogeneities. Therefore, small-scale tests tend to measure a weighted harmonic mean of the hydraulic-conductivity field. Over a large area, however, flow is primarily along high-conductivity heterogeneities. Therefore, large-scale tests approach a weighted arithmetic mean where high-conductivity heterogeneities have a greater influence.[PUBLICATION ABSTRACT]