Next Article in Journal
Development and Evaluation of the Combined Machine Learning Models for the Prediction of Dam Inflow
Previous Article in Journal
Environmental Benefits and Economical Sustainability of Urban Wastewater Reuse for Irrigation—A Cost-Benefit Analysis of an Existing Reuse Project in Puglia, Italy
Open AccessArticle

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

School of Engineering, University of Basilicata, 85100 Potenza, Italy
Water 2020, 12(10), 2929; https://doi.org/10.3390/w12102929
Received: 31 August 2020 / Revised: 4 October 2020 / Accepted: 17 October 2020 / Published: 20 October 2020
(This article belongs to the Section Hydrology and Hydrogeology)
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. View Full-Text
Keywords: subsurface flow and transport; stochastic analytical approach; tracer concentration prediction subsurface flow and transport; stochastic analytical approach; tracer concentration prediction
Show Figures

Figure 1

MDPI and ACS Style

Pannone, M. A Theoretical Study about Ergodicity Issues in Predicting Contaminant Plume Evolution in Aquifers. Water 2020, 12, 2929.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Search more from Scilit
 
Search
Back to TopTop