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Applied Stochastic Hydrogeology$
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Yoram Rubin

Print publication date: 2003

Print ISBN-13: 9780195138047

Published to Oxford Scholarship Online:

DOI: 10.1093/oso/9780195138047.001.0001

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An Overview of Stochastic Tools for Modeling Transport of Tracers in Heterogeneous Media

An Overview of Stochastic Tools for Modeling Transport of Tracers in Heterogeneous Media

Chapter:
7 (p.161) An Overview of Stochastic Tools for Modeling Transport of Tracers in Heterogeneous Media
Source:
Applied Stochastic Hydrogeology
Author(s):

Yoram Rubin

Publisher:
Oxford University Press
DOI:10.1093/oso/9780195138047.003.0012

Spatial variability and the uncertainty in characterizing the flow domain play an important role in the transport of contaminants in porous media: they affect the pathlines followed by solute particles, the spread of solute bodies, the shape of breakthrough curves, the spatial variability of the concentration, and the ability to quantify any of these accurately. This chapter briefly reviews some basic concepts which we shall later employ for the analysis of solute transport in heterogeneous media, and also points out some issues we shall address in the subsequent chapters. Our exposition in chapters 8-10 on contaminant transport is built around the Lagrangian and the Eulerian approaches for analyzing transport. The Eulerian approach is a statement of mass conservation in control volumes of arbitrary dimensions, in the form of the advection-dispersion equation. As such, it is well suited for numerical modeling in complex flow configurations. Its main difficulties, however, are in the assignment of parameters, both hydrogeological and geochemical, to the numerical grid blocks such that the effects of subgrid-scale heterogeneity are accounted for, and in the numerical dispersion that occurs in advection-dominated flow situations. Another difficulty is in the disparity between the scale of the numerical elements and the scale of the samples collected in the field, which makes the interpretation of field data difficult. The Lagrangian approach focuses on the displacements and travel times of solute bodies of arbitrary dimensions, using the displacements of small solute particles along streamlines as its basic building block. Tracking such displacements requires that the solute particles do not transfer across streamlines. Since such mass transfer may only occur due to pore-scale dispersion, Lagrangian approaches are ideally suited for advection-dominated situations. Let us start by considering the displacement of a small solute body, a particle, as a function of time. “Small” here implies that the solute body is much smaller than the characteristic scale of heterogeneity. At the same time, to qualify for a description of its movement using Darcy’s law, the solute body also needs to be larger than a few pores. The small dimension of the solute body ensures that it moves along a single streamline and that it does not disintegrate due to velocity shear.

Keywords:   Concentration variance, Diffusion equation, Gas kinetic theory, Lagrangian, Macrodispersion, Particle tracking, Solute flux, Travel times, Uncertainty

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