Models for flow of non-Newtonian and complex fluids through porous media

Pearson, J. R. A.; Tardy, Philippe Michel Jacques

doi:10.1016/s0377-0257(01)00191-4

Cited by 201 publications

(142 citation statements)

References 7 publications

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“…After our two-scale expansions, it makes sense to link the effective shear rate (21)- (23) is not of Darcy law type and generally does not lead to the usual filtration law used in standard engineering treatment (e.g. as in [28], [81] and [68]):…”

Section: Remarkmentioning

confidence: 99%

An Introduction to the Homogenization Modeling of Non-Newtonian and Electrokinetic Flows in Porous Media

Mikelić

2018

Lecture Notes in Mathematics

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Section: Remarkmentioning

confidence: 99%

An Introduction to the Homogenization Modeling of Non-Newtonian and Electrokinetic Flows in Porous Media

Mikelić

2018

Lecture Notes in Mathematics

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“…Many of the fluids used in the oil industry and simulate reservoirs are significantly non-Newtonian. In different degree, they display shear-dependent of viscosity, thixotropy and elasticity (Pearson and Tardy 2002;Ellahi and Afza 2009;Ellahi 2009). …”

Section: Introductionmentioning

confidence: 99%

Numerical solution of non-Newtonian nanofluid flow over a stretching sheet

2013

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The steady flow of a Jeffrey fluid model in the presence of nano particles is studied. Similarity transformation is used to convert the governing partial differential equations to a set of coupled nonlinear ordinary differential equations which are solved numerically. Behavior of emerging parameters is presented graphically and discussed for velocity, temperature and nanoparticles fraction. Variation of the reduced Nusselt and Sherwood number against physical parameters is presented graphically. It was found that reduced Nusselt number is decreasing function and reduced Sherwood number is increasing function of Brownian parameter N b and thermophoresis parameter N t .

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“…Earlier work on this filtration problem focused only on the flow in the porous, or Darcy, region [1,21,25,29,30], but analysis of the fully coupled problem is essential to accurately simulate the transport of the suspended particles into the filter. The fully coupled problem for non-Newtonian Stokes and Darcy flows was initially analyzed in [11].…”

Section: Introductionmentioning

confidence: 99%

Coupling nonlinear Stokes and Darcy flow using mortar finite elements

Ervin

Jenkins

Sun

2011

Applied Numerical Mathematics

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We study a system composed of a non-linear Stokes flow in one subdomain coupled with a nonlinear porous medium flow in another subdomain. Special attention is paid to the mathematical consequence of the shear-dependent fluid viscosity for the Stokes flow and the velocity-dependent effective viscosity for the Darcy flow. Motivated by the physical setting, we consider the case where only flow rates are specified on the inflow and outflow boundaries in both subdomains. We recast the coupled Stokes-Darcy system as a reduced matching problem on the interface using a mortar space approach. We prove a number of properties of the nonlinear interface operator associated with the reduced problem, which directly yield the existence, uniqueness and regularity of a variational solution to the system. We further propose and analyze a numerical algorithm based on mortar finite elements for the interface problem and conforming finite elements for the subdomain problems. Optimal a priori error estimates are established for the interface and subdomain problems, and a number of compatibility conditions for the finite element spaces used are discussed. Numerical simulations are presented to illustrate the algorithm and to compare two treatments of the defective boundary conditions.

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Models for flow of non-Newtonian and complex fluids through porous media

Cited by 201 publications

References 7 publications

An Introduction to the Homogenization Modeling of Non-Newtonian and Electrokinetic Flows in Porous Media

An Introduction to the Homogenization Modeling of Non-Newtonian and Electrokinetic Flows in Porous Media

Numerical solution of non-Newtonian nanofluid flow over a stretching sheet

Coupling nonlinear Stokes and Darcy flow using mortar finite elements

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