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Effective Behavior Near Clogging in Upscaled Equations for Non-isothermal Reactive Porous Media Flow
Univ Bergen, Geophys Inst, POB 7803, N-5020 Bergen, Norway.;Univ Hasselt, Fac Sci, Campus Diepenbeek,Agoralaan Bldg D, BE-3590 Diepenbeek, Belgium..ORCID iD: 0000-0003-0495-2634
Univ Bergen, Dept Math, POB 7803, N-5020 Bergen, Norway..
2017 (English)In: Transport in Porous Media, ISSN 0169-3913, E-ISSN 1573-1634, Vol. 120, no 3, p. 553-577Article in journal (Refereed) Published
Abstract [en]

For a non-isothermal reactive flow process, effective properties such as permeability and heat conductivity change as the underlying pore structure evolves. We investigate changes of the effective properties for a two-dimensional periodic porous medium as the grain geometry changes. We consider specific grain shapes and study the evolution by solving the cell problems numerically for an upscaled model derived in Bringedal et al. (Transp Porous Media 114(2):371-393, 2016. doi 10.1007/s11242-015-0530-9). In particular, we focus on the limit behavior near clogging. The effective heat conductivities are compared to common porosity-weighted volume averaging approximations, and we find that geometric averages perform better than arithmetic and harmonic for isotropic media, while the optimal choice for anisotropic media depends on the degree and direction of the anisotropy. An approximate analytical expression is found to perform well for the isotropic effective heat conductivity. The permeability is compared to some commonly used approaches focusing on the limiting behavior near clogging, where a fitted power law is found to behave reasonably well. The resulting macroscale equations are tested on a case where the geochemical reactions cause pore clogging and a corresponding change in the flow and transport behavior at Darcy scale. As pores clog the flow paths shift away, while heat conduction increases in regions with lower porosity.

Place, publisher, year, edition, pages
2017. Vol. 120, no 3, p. 553-577
Keywords [en]
Upscaling, Homogenization, Free boundary, Periodic porous medium, Clogging, Reactive flow
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:kau:diva-69246DOI: 10.1007/s11242-017-0940-yISI: 000415280400006OAI: oai:DiVA.org:kau-69246DiVA, id: diva2:1255369
Available from: 2018-10-12 Created: 2018-10-12 Last updated: 2018-10-18Bibliographically approved

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Kumar, Kundan

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