Solute concentration statistics in heterogeneous aquifers for finite Peclet values

A Lagrangian framework is used for analysing the concentration fields associated with transport of nonreactive solutes in heterogeneous aquifers. This is related to two components: advection by the random velocity field v(x) and pore-scale dispersion, characterized by the dispersion tensor D-d; the relative effect of the two components is quantified by the Peclet number. The principal aim of this paper is to define the probability density function (pdf) of a nonreactive solute concentration and its relevant moments and sigma(c)(2) as sampled on finite detection volumes. This problem could be relevant in technical applications such as risk analysis, field monitoring and pollution control. A method to compute the concentration statistical moments and pdf is developed in the paper on the basis of the reverse formulation widely adopted to study solute dispersion in turbulent flows. The main advantages of this approach are: (i) a closed form solution for concentration mean and variance is attained, in case of small size of the sampling volume; (ii) a numerically efficient estimate of the concentration pdf can be derived. The relative effects of injection and sampling volume size and Peclet number on concentration statistics are assessed. The analysis points out that the concentration pdf can be reasonably fitted by the beta function. These results are suitable to be employed in practical applications, when the estimate of probability related to concentration thresholds is required.