Tailing of the breakthrough curve in aquifer contaminant transport: The impact of permeability spatial variability

G. Dagan*, A. Fiori, I. Jankovic, V. Cvetkovic

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations

Abstract

A contaminant plume of mass Mo is inserted at time t = 0 at an injection plane at × = 0 in an aquifer of spatially variable conductivity K. The log-conductivity Y = InK is modelled as stationary and isotropic, of univariate distribution f(Y), and of finite integral scale I. The flow of water is uniform in the mean (natural gradient) and the plume is of large transverse extent relative to the integral scale. Advective transport and longitudinal spread are quantified by the solute mass arrival ("breakthrough curve", BTC) M(t,x) at a control plane at × > I. For a large plume (ergodic conditions) the relative mass flux μ(t,x) = (l/Mo)M/t is approximately equal to the probability density function of travel times of solute particles f(τx) and the latter is used to analyse transport. f(τx) is derived by adopting a structural model of the aquifer that contains spherical or cubic inclusions of uniform size and of independent Y that fill the space. Such a structure can represent any formation of given f(Y) and I. The flow and transport solutions are obtained by a simple semianalytical model and by accurate numerical simulations. The travel time distribution at few control planes is determined for a log-normal f(K) first. Under the assumption of weak heterogeneity, i.e. for small variance σy2 and for x»I, the travel time distribution is symmetrical and Gaussian. Subsequently, by using the semi-analytical model and numerical simulations we derive f(τx) for a highly heterogeneous formation of σ y2 = 2. The main finding is f(τx) is highly skewed due to the presence of a thin, but long tail, for large travel times. The tail is of significance to applications that deal with aquifer pollution and remediation. The tail is related to the large residence time of solute particles in blocks of low conductivity. A simple relationship is established between the tail of f(Y) for low K and that f(τx) for large τ. To further examine the impact of the log-conductivity distribution on BTC tailing, a non-Gaussian model, the subordinate model, is adopted for f(Y). This distribution depends on an additional parameter Is; travel time distribution tends to normal for Is→0, whereas the tails of the two distributions are different for Is > 0. This choice reflects the difficulty of identification of the tail of f(Y) based on field data. The relevance of results to applications is examined in terms of impact of conductivity spatial distribution, as well as influence of plume size (non-ergodic behaviour) and diffusion.

Original languageEnglish
Title of host publicationGroundwater Quality
Subtitle of host publicationSecuring Groundwater Quality in Urban and Industrial Environments, GQ'07
Pages335-341
Number of pages7
Edition324
StatePublished - 2008
EventGroundwater Quality 2007 Conference - Securing Groundwater Quality in Urban and Industrial Environments, GQ'07 - Fremantle, WA, Australia
Duration: 2 Dec 20087 Dec 2008

Publication series

NameIAHS-AISH Publication
Number324
ISSN (Print)0144-7815

Conference

ConferenceGroundwater Quality 2007 Conference - Securing Groundwater Quality in Urban and Industrial Environments, GQ'07
Country/TerritoryAustralia
CityFremantle, WA
Period2/12/087/12/08

Keywords

  • Contaminant transport
  • Groundwater hydrology
  • Random media
  • Stochastic processes

Fingerprint

Dive into the research topics of 'Tailing of the breakthrough curve in aquifer contaminant transport: The impact of permeability spatial variability'. Together they form a unique fingerprint.

Cite this