Stochastic evaluation of mixing-controlled steady-state plume lengths in two-dimensional heterogeneous domains

Olaf A. Cirpka, Massimo Rolle, Gabriele Chiogna, Felipe P. J. De Barros, Wolfgang Nowak

Research output: Contribution to journalJournal articleResearchpeer-review


We study plumes originating from continuous sources that require a dissolved reaction partner for their degradation. The length of such plumes is typically controlled by transverse mixing. While analytical expressions have been derived for homogeneous flow fields, incomplete characterization of the hydraulic conductivity field causes uncertainty in predicting plume lengths in heterogeneous domains. In this context, we analyze the effects of three sources of uncertainty: (i) The uncertainty of the effective mixing rate along the plume fringes due to spatially varying flow focusing, (ii) the uncertainty of the volumetric discharge through (and thus total mass flux leaving) the source area, and (iii) different parameterizations of the Darcy-scale transverse dispersion coefficient. The first two are directly related to heterogeneity of hydraulic conductivity. In this paper, we derive semi-analytical expressions for the probability distribution of plume lengths at different levels of complexity. The results are compared to numerical Monte Carlo simulations. Uncertainties in mixing and in the source strength result in a statistical distribution of possible plume lengths. For unconditional random hydraulic conductivity fields, plume lengths may vary by more than one order of magnitude even for moderate degrees of heterogeneity. Our results show that the uncertainty of volumetric flux through the source is the most relevant contribution to the variance of the plume length. The choice of different parameterizations for the local dispersion coefficient leads to differences in the mean estimated plume length. �� 2012 Elsevier B.V.
Original languageEnglish
JournalJournal of Contaminant Hydrology
Pages (from-to)22-39
Number of pages18
Publication statusPublished - 2012
Externally publishedYes


  • Water Science and Technology
  • Environmental Chemistry
  • Groundwater transport
  • Mixing-controlled reactions
  • Stochastic subsurface hydrology
  • Transverse dispersion
  • Analytical expressions
  • Flow focusing
  • Heterogeneous domains
  • Homogeneous flow
  • Local dispersion
  • Mixing rates
  • Mixing-controlled reaction
  • Monte Carlo Simulation
  • Parameterizations
  • Plume fringes
  • Plume length
  • Reaction partners
  • Semi-analytical expression
  • Source area
  • Source strength
  • Sources of uncertainty
  • Statistical distribution
  • Stochastic evaluations
  • Subsurface hydrology
  • Total mass flux
  • Transverse mixing
  • Volumetric flux
  • Degradation
  • Groundwater
  • Hydraulic conductivity
  • Mixing
  • Monte Carlo methods
  • Probability distributions
  • Stochastic systems
  • Uncertainty analysis
  • Darcy law
  • degradation
  • flow field
  • groundwater flow
  • hydraulic conductivity
  • mixing
  • Monte Carlo analysis
  • parameterization
  • probability
  • spatial variation
  • steady flow
  • transport process
  • two-dimensional modeling
  • uncertainty analysis
  • article
  • intermethod comparison
  • Monte Carlo method
  • plume
  • plume dispersion
  • priority journal
  • statistical analysis
  • steady state
  • volumetry
  • Computer Simulation
  • Models, Chemical
  • Monte Carlo Method
  • Stochastic Processes
  • Uncertainty
  • Water Movements
  • Water Pollutants


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