A Theoretical Study about Ergodicity Issues in Predicting Contaminant Plume Evolution in Aquifers

A large-time Eulerian–Lagrangian stochastic approach is employed to: (1) estimate centroid position uncertainty of contaminant plumes that originate from instantaneous point sources in statistically stationary and isotropic porous formations; (2) assess the time needed for achieving ergodic conditio...

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Bibliographic Details
Published in:Water (Basel) 2020-10, Vol.12 (10), p.2929
Main Author: Pannone, Marilena
Format: Article
Language:English
Subjects:
Aquifers
Centroids
Coefficient of variation
Contaminants
Dilution
Dispersion
Ergodic processes
Fluid dynamics
Fluid flow
Heterogeneity
Plumes
Power law
Random variables
Reynolds number
Stochasticity
Turbulent flow
Uncertainty
Velocity
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Summary:A large-time Eulerian–Lagrangian stochastic approach is employed to: (1) estimate centroid position uncertainty of contaminant plumes that originate from instantaneous point sources in statistically stationary and isotropic porous formations; (2) assess the time needed for achieving ergodic conditions, which would allow for the evaluation of local concentration values based on the only ensemble mean distribution; (3) derive the concentration coefficient of variation (CV) as a function of asymptotic macro-dispersion coefficients and centroid trajectory variances. The results indicate that the decay time of plume position uncertainty is so large that there is practically no chance for effective ergodicity. The concentration coefficient of variation is zero at the centroid but rapidly increases when moving away from it. The dissipative effect of local dispersion in the presence of relatively high Péclet numbers is considerably exalted by marked flow field heterogeneity, which confirms the previously postulated synergic, non-additive effect of advection and local dispersion in passive solute dilution. A further result from this study is the derivation of the power law that relates dimensionless concentration micro-scale to dimensionless local dispersive area. The exponent of this power law is the same that appears in the relationship between dimensionless Kolmogorov turbulent micro-scale and flow Reynolds number.
ISSN:2073-4441
2073-4441
DOI:10.3390/w12102929