On Laminar Flow of Non-Newtonian Fluids in Porous Media

Handle URI:
http://hdl.handle.net/10754/582859
Title:
On Laminar Flow of Non-Newtonian Fluids in Porous Media
Authors:
Fayed, Hassan E. ( 0000-0003-2082-3269 ) ; Sheikh, Nadeem A.; Iliev, Oleg ( 0000-0002-9691-4100 )
Abstract:
Flow of generalized Newtonian fluids in porous media can be modeled as a bundle of capillary tubes or a pore-scale network. In general, both approaches rely on the solution of Hagen–Poiseuille equation using power law to estimate the variations in the fluid viscosity due to the applied shear rate. Despite the effectiveness and simplicity, power law tends to provide unrealistic values for the effective viscosity especially in the limits of zero and infinite shear rates. Here, instead of using power law, Carreau model (bubbles, drops, and particles in non-Newtonian fluids. Taylor & Francis Group, New York, 2007) is used to determine the effective viscosity as a function of the shear strain rate. Carreau model can predict accurately the variation in the viscosity at all shear rates and provide more accurate solution for the flow physics in a single pore. Using the results for a single pore, normalized Fanning friction coefficient has been calculated and plotted as a function of the newly defined Reynolds number based on pressure gradient. For laminar flow, the variation in the friction coefficient with Reynolds number has been plotted and scaled. It is observed that generalized Newtonian fluid flows show Newtonian nature up to a certain Reynolds number. At high Reynolds number, deviation from the Newtonian behavior is observed. The main contribution of this paper is to present a closed-form solution for the flow in a single pore using Carreau model, which allows for fast evaluation of the relationship between flux and pressure gradient in an arbitrary pore diameter. In this way, we believe that our development will open the perspectives for using Carreau models in pore-network simulations at low computational costs to obtain more accurate prediction for generalized Newtonian fluid flows in porous media.
KAUST Department:
Numerical Porous Media SRI Center (NumPor)
Citation:
On Laminar Flow of Non-Newtonian Fluids in Porous Media 2015 Transport in Porous Media
Publisher:
Springer Science + Business Media
Journal:
Transport in Porous Media
Issue Date:
20-Oct-2015
DOI:
10.1007/s11242-015-0592-8
Type:
Article
ISSN:
0169-3913; 1573-1634
Additional Links:
http://link.springer.com/10.1007/s11242-015-0592-8
Appears in Collections:
Articles

Full metadata record

DC FieldValue Language
dc.contributor.authorFayed, Hassan E.en
dc.contributor.authorSheikh, Nadeem A.en
dc.contributor.authorIliev, Olegen
dc.date.accessioned2015-11-29T08:31:27Zen
dc.date.available2015-11-29T08:31:27Zen
dc.date.issued2015-10-20en
dc.identifier.citationOn Laminar Flow of Non-Newtonian Fluids in Porous Media 2015 Transport in Porous Mediaen
dc.identifier.issn0169-3913en
dc.identifier.issn1573-1634en
dc.identifier.doi10.1007/s11242-015-0592-8en
dc.identifier.urihttp://hdl.handle.net/10754/582859en
dc.description.abstractFlow of generalized Newtonian fluids in porous media can be modeled as a bundle of capillary tubes or a pore-scale network. In general, both approaches rely on the solution of Hagen–Poiseuille equation using power law to estimate the variations in the fluid viscosity due to the applied shear rate. Despite the effectiveness and simplicity, power law tends to provide unrealistic values for the effective viscosity especially in the limits of zero and infinite shear rates. Here, instead of using power law, Carreau model (bubbles, drops, and particles in non-Newtonian fluids. Taylor & Francis Group, New York, 2007) is used to determine the effective viscosity as a function of the shear strain rate. Carreau model can predict accurately the variation in the viscosity at all shear rates and provide more accurate solution for the flow physics in a single pore. Using the results for a single pore, normalized Fanning friction coefficient has been calculated and plotted as a function of the newly defined Reynolds number based on pressure gradient. For laminar flow, the variation in the friction coefficient with Reynolds number has been plotted and scaled. It is observed that generalized Newtonian fluid flows show Newtonian nature up to a certain Reynolds number. At high Reynolds number, deviation from the Newtonian behavior is observed. The main contribution of this paper is to present a closed-form solution for the flow in a single pore using Carreau model, which allows for fast evaluation of the relationship between flux and pressure gradient in an arbitrary pore diameter. In this way, we believe that our development will open the perspectives for using Carreau models in pore-network simulations at low computational costs to obtain more accurate prediction for generalized Newtonian fluid flows in porous media.en
dc.language.isoenen
dc.publisherSpringer Science + Business Mediaen
dc.relation.urlhttp://link.springer.com/10.1007/s11242-015-0592-8en
dc.rightsArchived with thanks to Transport in Porous Media. The final publication is available at Springer via http://dx.doi.org/10.1007/s11242-015-0592-8en
dc.subjectLaminar flowen
dc.subjectNon-Newtonianen
dc.subjectPower lawen
dc.subjectCarreau modelen
dc.subjectFriction factoren
dc.titleOn Laminar Flow of Non-Newtonian Fluids in Porous Mediaen
dc.typeArticleen
dc.contributor.departmentNumerical Porous Media SRI Center (NumPor)en
dc.identifier.journalTransport in Porous Mediaen
dc.eprint.versionPost-printen
dc.contributor.institutionDepartment of Flows and Materials Simulation, Fraunhofer Institute for Industrial Mathematics (ITWM), Kaiserslautern, Germanyen
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)en
kaust.authorFayed, Hassan E.en
kaust.authorSheikh, Nadeem A.en
kaust.authorIliev, Olegen
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