It is very common in hydrogeological analysis to require a single hydraulic conductivity (K) for all or part of a model domain. In fractured rock aquifers K commonly varies by at least several orders of magnitude, however the rock mass is modelled as an equivalent idealised porous medium. It is assumed that the rock is sufficiently homogeneously fractured and interconnected such that it can be considered "an equivalent porous medium” and that at a large enough scale the small scale variation of K is evened out. Usually, in fractured rock, the properties for this idealised large scale, homogeneous porous medium are derived from statistical analysis of small scale testing, typically packer tests. This presents the problem of what is the appropriate statistic to use from a data set for use in groundwater analysis and modelling?
There appears to be some difference in the hydrogeological community as to whether it is appropriate to use the geometric mean or arithmetic mean for this purpose. If variability in K is high, as is typical of fractured rock, the geometric mean can be several orders of magnitude lower than the arithmetic mean. This paper describes why the arithmetic mean is more appropriate, and use of the geometric mean can result in significant error. However in projects using packer test data, if the bias of not being able to reproduce high end K values is not corrected, then even the arithmetic mean may be invalid. The approach of Raymer and Maerz (2014) to derive a ‘reconstructed’ arithmetic mean to take account of this effect is described and is considered to be the most representative value.
Finally, this paper examines three additional factors that need to be considered in selecting a K value; the scale effect of hydraulic conductivity measurement, problem geometry and the analysis/modelling purpose.