Author(s): Matteo Nicolini; Virgilio Fiorotto; Elpidio Caroni

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Abstract: Natural porous formations are inherently heterogeneous, and solute plumes transported by large-scale advection and pore-scale dispersion are characterized by very irregular shapes. Most of environmental regulations define water quality standards and acceptability in terms of concentration thresholds, thus the prediction in natural aquifers should be performed with reference to the concentration probability of excess relative to the relevant threshold value. Moreover, ergodicity for a solute plume is satisfied if its initial size is much larger than the characteristic size of the heterogeneity, which is rarely true in practice. In this work, an analytical procedure for the calculation of concentration pdf is presented, assuming small values of the log-conductivity variance, σ 2 Y. Under nonergodic transport, the uncertainty in the prediction of the barycenter of the plume may be described by a multi-normal random variate, as confirmed by a series of Monte Carlo analyses: this allows an estimate of the overall concentration pdf, which may be obtained by the analytical convolution between the two distributions, in which the covariances of the tra jectory of the center of mass of a given plume are calculated starting from the elements of the two-particle displacement covariance matrix.

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Year: 2007