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

Thomas Sherman, Amir Paster, Giovanni Porta, Diogo Bolster*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


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.

Original languageEnglish
Pages (from-to)31-40
Number of pages10
JournalJournal of Contaminant Hydrology
StatePublished - Apr 2019
Externally publishedYes


FundersFunder number
US Army Research Office
National Science FoundationEAR-1417264, CBET-1705770, EAR-1446236, EAR-1351623, 1705770
Army Research OfficeW911NF-18-1-0338


    • Sorption desorption
    • Spatial Markov model
    • Upscaling


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