Transp Porous Med (2012) 93:127–145
DOI 10.1007/s11242-012-9947-6
Anomalous Reactive Transport in the Framework
of the Theory of Chromatography
Valentina Prigiobbe · Marc A. Hesse · Steven L. Bryant
Received: 28 September 2011 / Accepted: 23 January 2012 / Published online: 10 February 2012
© Springer Science+Business Media B.V. 2012
Abstract The anomalous reactive transport considered here is the migration of contami-
nants through strongly sorbing permeable media without significant retardation. It has been
observed in the case of heavy metals, organic compounds, and radionuclides, and it has
critical implications on the spreading of contaminant plumes and on the design of remedia-
tion strategies. Even in the absence of the well-known fast migration pathways, associated
with fractures and colloids, anomalous reactive transport arises in numerical simulations of
reactive flow. It is due to the presence of highly pH-dependent adsorption and the broad-
ening of the concentration front by hydrodynamic dispersion. This leads to the emergence
of an isolated pulse or wave of a contaminant traveling at the average flow velocity ahead
of the retarded main contamination front. This wave is considered anomalous because it is
not predicted by the classical theory of chromatography, unlike the retardation of the main
contamination front. In this study, we use the theory of chromatography to study a simple
pH-dependent surface complexation model to derive the mathematical framework for the
anomalous transport. We analyze the particular case of strontium (Sr
2+
) transport and define
the conditions under which the anomalous transport arises. We model incompressible one-
dimensional (1D) flow through a reactive porous medium for a fluid containing four aqueous
species: H
+
, Sr
2+
, Na
+
, and Cl
-
. The mathematical problem reduces to a strictly hyperbolic
2 × 2 system of conservation laws for effective anions and Sr
2+
, coupled through a compet-
itive Langmuir isotherm. One characteristic field is linearly degenerate while the other is not
V. Prigiobbe (B ) · S. L. Bryant
Department of Petroleum and Geosystems Engineering, University of Texas at Austin,
1 University Station, Austin, TX 78712, USA
e-mail: valentina.prigiobbe@mail.utexas.edu
M. A. Hesse
Department of Geological Sciences, University of Texas at Austin, 1 University Station, Austin,
TX 78712, USA
M. A. Hesse · S. L. Bryant
Institute for Computational Engineering and Sciences, University of Texas at Austin,
1 University Station, Austin, TX 78712, USA
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