title: Upscaling transport of a reacting solute through a peridocially converging-diverging channel at pre-asymptotic times.
abstract: In this study we extend the Spatial Markov model, which has been successfully used to upscale conservative transport across a diverse range of porous media flows, to test if it can accurately upscale reactive transport, defined by a spatially heterogeneous first order degradation rate. We test the model in a well known highly simplified geometry, commonly considered as an idealized pore or fracture structure, a periodic channel with wavy boundaries. The edges of the flow domain have a layer through which there is no flow, but in which diffusion of a solute still occurs. Reactions are confined to this region. We demonstrate that the Spatial Markov model, an upscaled random walk model that enforces correlation between successive jumps, can reproduce breakthrough curves measured from microscale simulations that explicitly resolve all pertinent processes. We also demonstrate that a similar random walk model that does not enforce successive correlations is unable to reproduce all features of the measured breakthrough curves.
authors: Environmental Fluid Dynamics Laboratories, Department of Civil and Environmental Engineering and Earth Sciences, University of Notre Dame, IN, USA.
authors: Nicole L
authors: NL
authors: Sund
authors: Environmental Fluid Dynamics Laboratories, Department of Civil and Environmental Engineering and Earth Sciences, University of Notre Dame, IN, USA. Electronic address: dbolster@nd.edu.
authors: Diogo
authors: D
authors: Bolster
authors: The Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX 78712, USA.
authors: Clint
authors: C
authors: Dawson
mesh_terms: D003198:Computer Simulation; D004058:Diffusion; D062070:Hydrology / Q000379:methods; D008390:Markov Chains; D008962:Models, Theoretical; D016062:Porosity; D014872:Water Movements
keywords: Reactive transport; Spatial Markov model; Upscaling