{
"@context": "http://schema.org",
"@type": "ScholarlyArticle",
"@id": "https://doi.org/10.4122/1.1000000410",
"url": "https://zenodo.org/record/3536722",
"name": "Analysis of concentration under non-ergodic transport as sampled in natural aquifers",
"author": [
{
"name": "Virgilio Fiorotto",
"givenName": "Virgilio",
"familyName": "Fiorotto",
"@type": "Person",
"@id": "virgilio@dic.univ.trieste.it"
},
{
"name": "Elpidio Caroni",
"givenName": "Elpidio",
"familyName": "Caroni",
"@type": "Person",
"@id": "caroni@dic.univ.trieste.it"
},
{
"name": "Matteo Nicolini",
"givenName": "Matteo",
"familyName": "Nicolini",
"@type": "Person",
"@id": "matteo.nicolini@uniud.it"
},
{
"name": "Matteo Nicolini",
"givenName": "Matteo",
"familyName": "Nicolini",
"@type": "Person",
"@id": "matteo.nicolini@uniud.it"
}
],
"description": "Groundwater is probably the major source of water supply in the world, and the \npredictive ability in describing the fate of chemical contaminants in soils is of \ngreat importance when performing risk assessment and designing effective and \nefficient techniques to mitigate such problems.\n\nMost of environmental regulations (e.g., U.S. EPA, 1988; European Union, Directive \n80/778/EEC) define water quality standards and acceptability in terms of \nconcentration thresholds, and thus the prediction in natural aquifers must be \nperformed with reference to the concentration probability of excess relative to the \nrelevant threshold value.\n\nNatural porous formation are inherently heterogeneous, and solute plumes transported \nexhibit irregular shapes. Transport of an inert solute in heterogeneous porous \nformation is determined by large-scale advection and pore-scale dispersion, the \nrelative importance given by the Péclet number. The first is mainly controlled by \nthe spatial variability of hydraulic conductivity while the second, acting at scales \nlower than the heterogeneity characteristic length, is usually neglected.\n\nThe prediction of the concentration field, due to the irregular variation of \npermeability, is affected by uncertainty, which has been set in a theoretical \nframework by regarding the permeability as a random space function. Several \ninvestigations have been conducted, for small values of the log-conductivity \nvariance, in order to define the first and second moment of concentration, both in \nEulerian and in Lagrangian framework. \n\nThese analyses have been carried out under the ergodic hypothesis (satisfied when \nthe solute initial characteristic lengths are much larger than the heterogeneity \ncorrelation scale), in which case the position of the barycenter of the plume can be \nregarded as deterministic. Moreover, these approaches give only an estimate of mean \nconcentration and variance, while no consideration has been made about the \nunderlying pdf.\n\nRecently, Fiorotto and Caroni (Trans. Porous Media, 48, 2002), and Caroni and \nFiorotto (Trans. Porous Media, 59, 2005), analyzed, under ergodic conditions, the \nstatistical properties of solute concentration in natural aquifers as sampled in \nobservation wells.\n\nThe aim of the present paper is to extend such previous research, in particular \ninvestigating to which extent the ergodic hypothesis may be assumed valid, and \nanalyzing the statistical properties of the position of the barycenters of the \nsolute plume, thus giving an estimate of the uncertainty in the prediction.\n\nThe calculations, in Lagrangian framework, take advantage of the reverse formulation \nwhere, instead of considering the destination of the injected particles, the origin \nof the particle being sampled is sought. The advantage is that the concentration can \nbe simulated using a reduced number of particles, while the accurate forward \ncomputation of the concentration requires a large number of particles, increasing up \nto prohibitive levels as long as the sampling area tends to shrink into a point.\n\nThe analyses, have considered different sizes of the solute initial plume, and have \nbeen carried out varying the log-conductivity variance and the Péclet number, to \nquantify the relative role of the macro and the pore scale dispersion processes.\n\nIn the case of small values of the log-conductivity variance, the methodology allows \nthe derivation of an analytical expression for concentration mean, variance and pdf, \nwhile for high values, a Monte Carlo approach in a two-dimensional heterogeneous and \nstatistically isotropic aquifer, characterized by log-normally distributed \ntrasmissivity with an exponential covariance, has been developed.\n\nIn the last case, the adoption of the Beta function to fit the concentration pdf \nproves valid for practical application, under the ergodic hypothesis (Caroni and \nFiorotto, Trans. Porous Media, 59, 2005). Simulations show that, under non-ergodic \ntransport, the uncertainty in the prediction of the barycenters of the plumes may be \ndescribed by a multinormal random variate: this allows an estimate of the overall \nconcentration pdf, which may be obtained by the convolution between the two \ndistributions (in this case reducing to the mere product, being the processes \nuncorrelated).",
"inLanguage": "en",
"datePublished": "2006",
"publisher": {
"@type": "Organization",
"name": "XVI International Conference on Computational Methods in Water Resources"
},
"provider": {
"@type": "Organization",
"name": "datacite"
}
}