Local Equilibrium and Retardation Revisited

Hansen, Scott K.; Vesselinov, Velimir Valentinov

doi:10.1111/gwat.12566

Title: Local Equilibrium and Retardation Revisited

Journal Article · 19 July 2017 · Ground Water

DOI: https://doi.org/10.1111/gwat.12566 · OSTI ID:1477643

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Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

We present that in modeling solute transport with mobile-immobile mass transfer (MIMT), it is common to use an advection-dispersion equation (ADE) with a retardation factor, or retarded ADE. This is commonly referred to as making the local equilibrium assumption (LEA). Assuming local equilibrium, Eulerian textbook treatments derive the retarded ADE, ostensibly exactly. However, other authors have presented rigorous mathematical derivations of the dispersive effect of MIMT, applicable even in the case of arbitrarily fast mass transfer. We resolve the apparent contradiction between these seemingly exact derivations by adopting a Lagrangian point of view. We show that local equilibrium constrains the expected time immobile, whereas the retarded ADE actually embeds a stronger, nonphysical, constraint: that all particles spend the same amount of every time increment immobile. Eulerian derivations of the retarded ADE thus silently commit the gambler's fallacy, leading them to ignore dispersion due to mass transfer that is correctly modeled by other approaches. We then present a particle tracking simulation illustrating how poor an approximation the retarded ADE may be, even when mobile and immobile plumes are continually near local equilibrium. Finally, we note that classic “LEA” (actually, retarded ADE validity) criteria test for insignificance of MIMT-driven dispersion relative to hydrodynamic dispersion, rather than for local equilibrium.

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Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE Office of Science (SC); USDOE

Grant/Contract Number:: AC52-06NA25396; 89233218CNA000001

OSTI ID:: 1477643

Alternate ID(s):: OSTI ID: 1418694; OSTI ID: 1495158

Report Number(s):: LA-UR-16-22097; LA-UR-18-28969

Journal Information:: Ground Water, Vol. 56, Issue 1; ISSN 0017-467X

Publisher:: Wiley - NGWACopyright Statement

Country of Publication:: United States

Language:: English

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