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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: November 2020

DOI: 10.1093/oso/9780195138047.001.0001

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The Lagrangian Picture, Part I : Fundamentals of the Lagrangian Approach to Solute Transport

The Lagrangian Picture, Part I : Fundamentals of the Lagrangian Approach to Solute Transport

9 (p.200) The Lagrangian Picture, Part I : Fundamentals of the Lagrangian Approach to Solute Transport
Applied Stochastic Hydrogeology

Yoram Rubin

Oxford University Press

This chapter explores the principles of the Lagrangian approach to solute transport, with an emphasis on the dispersive action of the spatial variability of the velocity field. We start by developing the tools for characterizing the displacement of a single, small solute particle that will subsequently be used for characterization of the concentration’s variability and uncertainty, and we continue with a discussion of the stochastic description of solute travel times and fluxes. The principles presented in this chapter will be employed in chapter 10 to derive tools for applications such as macrodispersion coefficients, solute travel time moments, the moments of the solute fluxes and breakthrough curves, and transport of reactive solutes. As has been observed in many field studies and numerical simulations, the motion of solute bodies in geological media is complex, making the geometry of the solute bodies hard to predict. Furthermore, the concentration varies erratically, sometimes by orders of magnitude, over very short distances. The variability of the velocity field plays a significant role in shaping this complex geometry, and makes it impossible to characterize the concentration field deterministically. The alternatives we will pursue include characterizing the concentration through its moments such as the expected value and variance, and other descriptors of transport such as solute fluxes and travel times. This line was pursued in chapter 8 using the Eulerian framework. In this chapter we pursue this line from the Lagrangian perspective. Applications of these concepts are presented in chapter 10. Let us consider the displacement of a marked solute particle over time.

Keywords:   Breakthrough curves, Central limit theorem, Dirac delta, Gas kinetic theory, Particle tracking, Solute flux, Travel times, Uncertainty

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