On the statistics of concentration fluctuations in aquifers

This paper describes a procedure allowing computation of relevant statistics of non-reactive solute concentration as sampled in detection volumes larger than the pore-scale dimension. This problem could be relevant in technical applications such as risk analysis, field monitoring and pollution control. In the case of low conductivity heterogeneity level, the concentration statistical moments could be obtained by integration of the multivariate normal pdf of the relative displacement of a number of particles equal to the moment order. Despite the theoretical simplicity, these methods do not allow the concentration frequency distribution to be defined. Hence, a novel Monte Carlo procedure is developed, able to define the concentration statistics in general. A comprehensive analysis of concentration statistical moments and frequency is performed as a function of the relevant parameters. The meaning of the statistical elaboration of experimental concentration data by Fitts (1996) is consequently highlighted.