Effects of Local Dispersion and Kinetic Sorption on Evolution of Concentration Variance in a Heterogeneous Aquifer
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Effects of Local Dispersion and Kinetic Sorption on Evolution of Concentration Variance in a Heterogeneous Aquifer1 Bill X. Hu2 and Changming He3 A Eulerian stochastic method is applied to develop a theory of concentration variance for solute transport in a heterogeneous medium. The study focuses on the effects of kinetic sorption and local dispersion on solute dissipation. Spatial distribution of the concentration variance is obtained by scaling the zero local dispersion form of σc2 . The scaling function resulting from the local dispersion and kinetic sorption is derived in a closed integral form. It satisfies the measurement of total concentration variance resulting from the Eulerian mass balance using spatially integrated concentration moments. The spatially integrated moments bypass the need for classical closures applied to joint moments between concentration and velocity fields. The study results indicate that kinetic sorption reduces the total development of concentration variance in comparison with non-reactive solute transport. Kinetic sorption acts as a reduction mechanism, but not as a dissipating mechanism like the local dispersion. Kinetic sorption and local dispersion are not additive processes and their effects on the concentration variance depend on the stage of transport time. KEY WORDS: reactive transport; heterogeneity; concentration variance; local dispersion; kinetic sorption.
INTRODUCTION Predicting solute concentration within the context of a subsurface transport process is a problem of describing a random field in statistical terms. Mean concentration is the simplest and the most studied property of a concentration field. Concentration variance is the next most important property that represents the measure of concentration fluctuations around the means. Concentration fluctuations around means are the quantities usually measured in fields, subject to the sampling volumes used. Thus, the difference between the commonly modeled mean concentration 1Received
17 February 2003; accepted 2 August 2005; Published online: 27 May 2006. of Geological Sciences, Florida State University, 108 Carraway Building, Tallahassee, Florida 32306-4100; e-mail: [email protected]. 3Desert Research Institute, Division of Hydrologic Sciences, University and Community College System of Nevada, Las Vegas, Nevada 89119. 2Department
327 C 2006 International Association for Mathematical Geology 0882-8121/06/0400-0327/1
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and measured concentration is not small, and the concentration variance is a statistical quantity that measures such difference. Contrary to the mean concentration, the concentration variance is more sensitive to physical and chemical reactions in a transport process. Local dispersion as a physical process of mixing was the first process analyzed for its influence on the concentration variance (e.g., Kapoor and Gelhar, 1994a,b; Kitanidis, 1988; Dagan and Fiori, 1997; Fiori and Dagan, 1999; Zhang and Neuman, 1996; Andricevic, 1998). Besides local dispersion, the sampling volume is another
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