Two-dimensional concentration distribution for mixing-controlled bioreactive transport in steady state

Olaf A. Cirpka, Albert J. Valocchi

Research output: Contribution to journalArticlepeer-review


Under steady-state conditions, the degradation of contaminant plumes introduced continuously into an aquifer is controlled by transverse dispersion when the other reacting compound is provided from ambient groundwater. Given that the reaction is instantaneous and longitudinal dispersion can be neglected, the length of the plume is inversely proportional to the transverse dispersion coefficient. In typical scenarios of natural attenuation, however, the considered reaction is biotic and kinetic. The standard model of bioreactive transport relies on double-Monod kinetics and pseudo first-order biomass decay. Under these conditions, a fraction of the injected mass flux remains beyond the length of the plume determined for the instantaneous reaction. We present an analytical framework to derive the steady-state concentration distributions of the dissolved compounds and the biomass from the concentration distribution of a conservative compound, assuming double-Monod kinetics and two different models describing biomass decay. The first biomass-decay model assumes a constant first-order decay coefficient, while the second assumes that the decay coefficient depends upon the electron-acceptor concentration. We apply the method to the case of a line-injection in two-dimensional uniform flow. In general, the bioreactive concentration distributions are similar to the distributions computed for an instantaneous reaction. The similarity is greater when the biomass decay coefficient is assumed to depend on the electron-acceptor concentration rather than being constant.

Original languageEnglish (US)
Pages (from-to)1668-1679
Number of pages12
JournalAdvances in Water Resources
Issue number6-7
StatePublished - Jun 2007


  • Analytical solution
  • Bioreactive transport
  • Monod kinetics
  • Transverse dispersion

ASJC Scopus subject areas

  • Water Science and Technology


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