Scale Dependency of Hydraulic Conductivity in Heterogeneous Media

Abstract

Various types of sediments and rocks were analyzed for the relationship between hydraulic conductivity (K) and scale of measurement No variations of K with scale were observed for homogeneous media such as quartz‐arenites (quartz sandstones). However, hydraulic conductivity increased with scale of measurement in heterogeneous media. The scaling behavior can be described with the equation K = c (V)m, where c is a parameter characteristic of the geological medium that relates to geological variables such as average pore size and pore interconnectivity in porous media, and probably fracture opening and fracture interconnectivity in fractured media. V is the volume of tested material (used as scale measure), and m is the exponent of the relationship (slope of the line on a log‐log plot). The value of the exponent depends on the type or types of flow present. Porous flow media have an exponent of 0.5, multiple flow media an exponent between 0.5 and 1.0, and fracture and conduit flow controlled media an exponent of about 1.0. The more dominant fracture/conduit flow is relative to porous flow, the closer the exponent 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 larger scale in karstic media (if encountered at all) than in nonkarstic and more homogeneous media. Both confined and unconfined aquifers exhibit a similar scale dependence.

Measuring methods for groundwater – surface water interactions: a review

“…Therefore, they concluded that scale-dependency of hydraulic conductivity is not related to the measurement method, but to the existence of high-conductivity zones within a low-conductivity matrix. Schulze-Makuch et al (1999) observed no scaling effects for homogeneous media, whereas for heterogeneous media they found an empirical relation for the scaling behavior. The relationship is a function of the type of flow present (porous flow, fracture flow, conduit flow, doubleporosity media) and the degree of heterogeneity, associated with pore size and pore interconnectivity.…”

“…The relationship was found to be valid up to an upper boundary value, representing the scale above which a medium can be considered quasi-homogeneous. In many of the test results included in the study by Schulze-Makuch et al (1999), hydraulic conductivities obtained by pumping tests were close to the upper boundary.…”

Method of Relating Grain Size Distribution to Hydraulic Conductivity in Dune Sands to Assist in Assessing Managed Aquifer Recharge Projects: Wadi Khulays Dune Field, Western Saudi Arabia

“…This approach may be used in large dune areas to determine the appropriate locations for water infiltration or can be correlated with the infiltration rate in dune recharge studies. Since the samples used to develop the equation were relativity small in volume compared to the full dimensions of the dunes, the issue of scale needs to be addressed in that small samples commonly tend to underestimate the bulk hydraulic conductivity of an aquifer [54]. Larger scale measurement methods used to assess saturated aquifer systems, such as standard aquifer performance tests or tracer tests, almost always yield higher average hydraulic conductivity values based on the occurrence of bedding or diagenetic enhancement of hydraulic conductivity within an aquifer.…”

Comportement hydraulique des milieux faillés /

“…L'importance de celle-ci ne peut être évaluée que par une bonne connaissance 32 des caractéristiques du réseau, notamment en termes de hiérarchisation des discontinuités. Cette approche permet théoriquement une appréciation correcte des transmissivités, cependant un biais apparaît lors du passage en conductivités du fait de la concentration des écoulements dans une portion restreinte de l'espace d'intégration Niemann et Rovey, 2000 (Clauser, 1992 ;Garven, 1995 ;Schulzemakuch et Cherkauer, 1997 ;Schulze-Makuch et al, 1999). Il est cependant difficile de déterminer la taille minimale du VER et de montrer qu'elle vérifie le critère de validité de l'approche.…”