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Titel |
Pore scale simulations for the extension of the Darcy-Forchheimer law to shear thinning fluids |
VerfasserIn |
Tiziana Tosco, Daniele Marchisio, Federica Lince, Gianluca Boccardo, Rajandrea Sethi |
Konferenz |
EGU General Assembly 2014
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Medientyp |
Artikel
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Sprache |
Englisch
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Digitales Dokument |
PDF |
Erschienen |
In: GRA - Volume 16 (2014) |
Datensatznummer |
250095088
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Publikation (Nr.) |
EGU/EGU2014-10529.pdf |
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Zusammenfassung |
Flow of non-Newtonian fluids through porous media at high Reynolds numbers is often
encountered in chemical, pharmaceutical and food as well as petroleum and groundwater
engineering and in many other industrial applications (1 - 2). In particular, the use of
shear thinning polymeric solutions has been recently proposed to improve colloidal
stability of micro- and nanoscale zerovalent iron particles (MZVI and NZVI) for
groundwater remediation. In all abovementioned applications, it is of paramount
importance to correctly predict the pressure drop resulting from non-Newtonian
fluid flow through the porous medium. For small Reynolds numbers, usually up
to 1, typical of laboratory column tests, the extended Darcy law is known to be
applicable also to non Newtonian fluids, provided that all non-Newtonian effects
are lumped together into a proper viscosity parameter (1,3). For higher Reynolds
numbers (eg. close to the injection wells) non linearities between pressure drop
and flow rate arise, and the Darcy-Forchheimer law holds for Newtonian fluids,
while for non-Newtonian fluids, it has been demonstrated that, at least for simple
rheological models (eg. power law fluids) a generalized Forchheimer law can be
applied, even if the determination of the flow parameters (permeability K, inertial
coefficient β, and equivalent viscosity) is not straightforward. This work (co-funded
by European Union project AQUAREHAB FP7 - Grant Agreement Nr. 226565)
aims at proposing an extended formulation of the Darcy-Forchheimer law also for
shear-thinning fluids, and validating it against results of pore-scale simulations via
computational fluid dynamics (4). Flow simulations were performed using Fluent 12.0
on four different 2D porous domains for Newtonian and non-Newtonian fluids
(Cross, Ellis and Carreau models). The micro-scale flow simulation results are
analyzed in terms of “macroscale” pressure drop between inlet and outlet of the
model domain as a function of flow rate. The results of flow simulations show the
superposition of two contributions to pressure drops: one, strictly related to the
non-Newtonian properties of the fluid, dominates at low Reynolds numbers, while a quadratic
one, arising at higher Reynolds numbers, is dependent only on the porous medium
properties.
The results suggest that, for Newtonian flow, the porous medium can be fully described
by two macroscopic parameters, namely permeability K and inertial coefficient β.
Conversely, for non-Newtonian flow, an additional parameter is required, represented by the
shift factor α, which depends on the properties of both porous medium and fluid, which is not
easy to be determined in laboratory tests, but can be in turn calculated from 2D or 3D
pore-scale flow simulations, following the approach which was adopted in this
work.
References
1. Sorbie, K.S. Polymer-improved oil recovery; Blackie ; CRC Press: Glasgow, Boca
Raton, Fla., 1991.
2. Xue, D.; Sethi, R. Viscoelastic gels of guar and xanthan gum mixtures provide
long-term stabilization of iron micro- and nanoparticles. J Nanopart Res 2012,
14(11).
3. Bird, R.B.; Armstrong, R.C.; Hassager, O. Dynamics of polymeric liquids. Volume 1.
Fluid mechanics; John Wiley and Sons Inc.: New York - NY, 1977.
4. Tosco, T.; Marchisio, D.L.; Lince, F.; Sethi, R. Extension of the Darcy-Forchheimer
Law for Shear-Thinning Fluids and Validation via Pore-Scale Flow Simulations. Transport in
Porous Media 2013, 96(1), 1-20. |
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