Scale dependency of hydraulic conductivity in heterogeneous media

Various types of sediments and rocks were analyzed for the relationship bet ween hydraulic conductivity (K) and scale of measurement. No variations of K with scale were observed for homogeneous media such as quartz-arenites (q uartz sandstones). However, hydraulic conductivity increased with scale of measurement in heterogeneous media. The scaling behavior can be described w ith the equation K = c (V)(m), where c is a parameter characteristic of the geological medium that relates to geological variables such as average por e size and pore interconnectivity in porous media, and probably fracture op ening and fracture interconnectivity in fractured media. V is the volume of tested material (used as scale measure), and m is the exponent of the rela tionship (slope of the line on a log-log plot). The value of the exponent d epends on the type or types of flow present. Porous flow media have an expo nent of 0.5, multiple flow media an exponent between 0.5 and 1.0, and fract ure and conduit flow controlled media an exponent of about 1.0, The more do minant fracture/conduit now is relative to porous flow, the closer the expo nent is to 1.0, K increases with scale up to a rock volume after which the aquifer approaches the properties of an equivalent homogeneous medium and K remains constant with scale. This volume (upper bound of the relationship) is related to the degree of heterogeneity in a medium. It is at a much lar ger scale in karstic media (if encountered at all) than in nonkarstic and m ore homogeneous media, Both confined and unconfined aquifers exhibit a simi lar scale dependence.