10.4122/1.1000000410
Fiorotto, Virgilio
Virgilio
Fiorotto
virgilio@dic.univ.trieste.it
Caroni, Elpidio
Elpidio
Caroni
caroni@dic.univ.trieste.it
Nicolini, Matteo
Matteo
Nicolini
matteo.nicolini@uniud.it
Nicolini, Matteo
Matteo
Nicolini
matteo.nicolini@uniud.it
Analysis of concentration under non-ergodic transport as sampled in natural aquifers
XVI International Conference on Computational Methods in Water Resources
2006
2006
Groundwater is probably the major source of water supply in the world, and the
predictive ability in describing the fate of chemical contaminants in soils is of
great importance when performing risk assessment and designing effective and
efficient techniques to mitigate such problems.
Most of environmental regulations (e.g., U.S. EPA, 1988; European Union, Directive
80/778/EEC) define water quality standards and acceptability in terms of
concentration thresholds, and thus the prediction in natural aquifers must be
performed with reference to the concentration probability of excess relative to the
relevant threshold value.
Natural porous formation are inherently heterogeneous, and solute plumes transported
exhibit irregular shapes. Transport of an inert solute in heterogeneous porous
formation is determined by large-scale advection and pore-scale dispersion, the
relative importance given by the Péclet number. The first is mainly controlled by
the spatial variability of hydraulic conductivity while the second, acting at scales
lower than the heterogeneity characteristic length, is usually neglected.
The prediction of the concentration field, due to the irregular variation of
permeability, is affected by uncertainty, which has been set in a theoretical
framework by regarding the permeability as a random space function. Several
investigations have been conducted, for small values of the log-conductivity
variance, in order to define the first and second moment of concentration, both in
Eulerian and in Lagrangian framework.
These analyses have been carried out under the ergodic hypothesis (satisfied when
the solute initial characteristic lengths are much larger than the heterogeneity
correlation scale), in which case the position of the barycenter of the plume can be
regarded as deterministic. Moreover, these approaches give only an estimate of mean
concentration and variance, while no consideration has been made about the
underlying pdf.
Recently, Fiorotto and Caroni (Trans. Porous Media, 48, 2002), and Caroni and
Fiorotto (Trans. Porous Media, 59, 2005), analyzed, under ergodic conditions, the
statistical properties of solute concentration in natural aquifers as sampled in
observation wells.
The aim of the present paper is to extend such previous research, in particular
investigating to which extent the ergodic hypothesis may be assumed valid, and
analyzing the statistical properties of the position of the barycenters of the
solute plume, thus giving an estimate of the uncertainty in the prediction.
The calculations, in Lagrangian framework, take advantage of the reverse formulation
where, instead of considering the destination of the injected particles, the origin
of the particle being sampled is sought. The advantage is that the concentration can
be simulated using a reduced number of particles, while the accurate forward
computation of the concentration requires a large number of particles, increasing up
to prohibitive levels as long as the sampling area tends to shrink into a point.
The analyses, have considered different sizes of the solute initial plume, and have
been carried out varying the log-conductivity variance and the Péclet number, to
quantify the relative role of the macro and the pore scale dispersion processes.
In the case of small values of the log-conductivity variance, the methodology allows
the derivation of an analytical expression for concentration mean, variance and pdf,
while for high values, a Monte Carlo approach in a two-dimensional heterogeneous and
statistically isotropic aquifer, characterized by log-normally distributed
trasmissivity with an exponential covariance, has been developed.
In the last case, the adoption of the Beta function to fit the concentration pdf
proves valid for practical application, under the ergodic hypothesis (Caroni and
Fiorotto, Trans. Porous Media, 59, 2005). Simulations show that, under non-ergodic
transport, the uncertainty in the prediction of the barycenters of the plumes may be
described by a multinormal random variate: this allows an estimate of the overall
concentration pdf, which may be obtained by the convolution between the two
distributions (in this case reducing to the mere product, being the processes
uncorrelated).