Tailing of the breakthrough curve in aquifer contaminant transport: The impact of permeability spatial variability
2008 (English)Conference paper (Refereed)
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 σy 2 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 y 2 = 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.
Place, publisher, year, edition, pages
2008. no 324, 335-341 p.
, IAHS-AISH Publication, ISSN 0144-7815
Contaminant transport, Groundwater hydrology, Random media, Stochastic processes, Advective transports, Break through curves, Conductivity distributions, Contaminant plumes, Control planes, Ergodic, Ergodic conditions, Field datum, Flow and transports, Gaussian, Heterogeneous formations, Large travels, Log normals, Long tails, Low conductivities, Natural gradients, Non-gaussian models, Numerical simulations, Plume sizes, Probability densities, Relative mass, Residence time, Semi-analytical models, Spatial distributions, Spatial variabilities, Structural models, Travel time, Uniform sizes, Univariate distributions, Aquifers, Computer simulation, Contamination, Groundwater resources, Hydrogeology, Model structures, Molybdenum, Normal distribution, Probability density function, Random processes, Trellis codes, Underground reservoirs, Water injection, Water quality, Yttrium alloys, Groundwater pollution, advection, aquifer pollution, Gaussian method, groundwater, hydrology, numerical model, permeability, pollutant transport, spatial variation, stochasticity
Oceanography, Hydrology, Water Resources
IdentifiersURN: urn:nbn:se:kth:diva-154096ScopusID: 2-s2.0-62949163759ISBN: 9781901502794OAI: oai:DiVA.org:kth-154096DiVA: diva2:759773
Groundwater Quality 2007 Conference - Securing Groundwater Quality in Urban and Industrial Environments, GQ'07; Fremantle, WA; Australia; 2 December 2008 through 7 December 2008
QC 201410312014-10-312014-10-142014-10-31Bibliographically approved