Skip to Main content Skip to Navigation
Journal articles

Upscaled models for time-varying solute transport: Transient spatial-Markov dynamics

Abstract : Correlated velocity models (CVMs) have proven themselves to be effective tools for describing a wide range of solute transport behaviors in heterogeneous porous media. In particular, spatial Markov models (SMMs) are a class of CVMs where subsequent Lagrangian velocities along transport trajectories depend only on the current velocity, and not on past history. Such models provide a powerful tool for modeling transport in terms of a limited number of flow properties, such as the Eulerian point distribution of (flow) velocities, tortuosity, and the spatial scale of persistence of velocities. However, to date, all SMM modeling frameworks and applications have assumed that the underlying flow is steady-state. In this work, we extend SMMs to the case of time-varying flows. We propose, compare, and validate alternative numerical implementations, and we determine conditions for validity and efficiency based on standard physical quantities used to describe flow and transport at the Darcy scale. The models require additional information relative to a steady-state velocity SMM and we discuss the conditions under which this extra burden is warranted. We also provide clear, deterministic tests for the validity of the transient SMM, termed the “slow variation” and “fast propagation” criteria, which offer clear guidance on when transient, upscaled models are reasonable to employ. Our work forms the basis of a new framework allowing for the application of efficient upscaled models of transport to realistic transient flow conditions.
Complete list of metadata
Contributor : Isabelle Dubigeon Connect in order to contact the contributor
Submitted on : Wednesday, July 13, 2022 - 9:30:57 AM
Last modification on : Friday, August 5, 2022 - 3:04:59 PM


 Restricted access
To satisfy the distribution rights of the publisher, the document is embargoed until : 2023-01-13

Please log in to resquest access to the document



Nicholas B Engdahl, Tomás Aquino. Upscaled models for time-varying solute transport: Transient spatial-Markov dynamics. Advances in Water Resources, Elsevier, 2022, 166, pp.104271. ⟨10.1016/j.advwatres.2022.104271⟩. ⟨insu-03722000⟩



Record views