TY - JOUR

T1 - Two-dimensional concentration distribution for mixing-controlled bioreactive transport in steady state

AU - Cirpka, Olaf A.

AU - Valocchi, Albert J.

N1 - Funding Information:
This research was supported in part by the National Science Foundation through Grant BES-496714. We thank the reviewers, Erick Burns and Min-Ying Chu, for their constructive remarks.

PY - 2007/6

Y1 - 2007/6

N2 - 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.

AB - 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.

KW - Analytical solution

KW - Bioreactive transport

KW - Monod kinetics

KW - Transverse dispersion

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U2 - 10.1016/j.advwatres.2006.05.022

DO - 10.1016/j.advwatres.2006.05.022

M3 - Article

AN - SCOPUS:34247117269

VL - 30

SP - 1668

EP - 1679

JO - Advances in Water Resources

JF - Advances in Water Resources

SN - 0309-1708

IS - 6-7

ER -