A spatial Markov model for upscaling transport of adsorbing-desorbing solutes

Journal of Contaminant Hydrology
Thomas ShermanDiogo Bolster

Abstract

The Spatial Markov Model (SMM) is an upscaled model with a strong track record in predicting upscaled behavior of conservative solute transport across hydrologic systems. Here we propose an SMM that can account for reactive linear adsorption and desorption processes and test it on a simple benchmark problem: flow and transport through an idealized periodic wavy channel. The methodology is built using trajectories that are obtained from a single high resolution random walk simulation of conservative transport across one periodic element. Our approach encodes information about where a particle starts at the inlet, where it leaves at the outlet, how long it takes to cross the domain and one additional piece of information, the number of times a particle strikes the boundary, with the objective of predicting large scale transport with arbitrary linear adsorption and desorption rates. Our benchmark problem demonstrates that predictions made with our proposed SMM agree favorably with results from direct numerical simulations, which resolve the full transport problem.

References

Oct 15, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Tanguy Le BorgneJesus Carrera
Oct 15, 2008·Physical Review Letters·Tanguy Le BorgneJesus Carrera
Mar 9, 2010·Journal of Contaminant Hydrology·Diogo BolsterJesus Carrera
Jul 6, 2010·Journal of Contaminant Hydrology·I Battiato, D M Tartakovsky
Nov 24, 2011·Physical Review Letters·Peter K KangRuben Juanes
Oct 4, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Maximilien LevesqueBenjamin Rotenberg
May 21, 2013·Physical Review Letters·Pietro de AnnaPhilippe Davy
Jul 6, 2014·Journal of Contaminant Hydrology·N SeethaAmir Raoof
Jan 24, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·D R LesterM G Trefry
Oct 3, 2017·Journal of Contaminant Hydrology·Gianluca BoccardoMatteo Icardi
Mar 27, 2018·Journal of Contaminant Hydrology·T BaharC Lorgeoux

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