Derivation of macroscopic filtration law for transient linear viscoelastic fluid flow in porous media

Khuzhayorov, B. Kh.; Auriault, Jean‐Louis; Royer, Pascale

doi:10.1016/s0020-7225(99)00048-8

Cited by 78 publications

(42 citation statements)

References 10 publications

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“…See [37] for an efficient numerical method and [23] for an analytic study of the filtration laws, corresponding to the power and Carreau law viscosities. (b) For the (formal) homogenization of a linear Oldroyd fluid in a bundle of capillary tubes at low Reynolds and Deborah numbers see [43] . Very little is known concerning filtration laws for non-Newtonian fluids, which are more complicated than the quasi-Newtonian ones discussed in this chapter.…”

Section: Concluding Remarks On Filtration Laws For Non-newtonian Fluidsmentioning

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: Concluding Remarks On Filtration Laws For Non-newtonian Fluidsmentioning

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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“…Under the assumption of low Reynolds number based on the pore dimension, the generalized Darcy's law (7) is also derived by [20] using a homogenization theory.…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…Therefore, the neutral temporal stability curve is obtained for ω i = 0, which selects dominant modes at the onset of convection. Substituting Equations (20), (21) into (12)- (15), linearizing the equations and applying the curl twice to the momentum balance equation, one can obtain:…”

Section: Infinite Aspect Ratiosmentioning

confidence: 99%

Onset of Primary and Secondary Instabilities of Viscoelastic Fluids Saturating a Porous Layer Heated from below by a Constant Flux

Gueye

Ouarzazi

Hirata

et al. 2017

Fluids

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Abstract:We analyze the thermal convection thresholds and linear characteristics of the primary and secondary instabilities for viscoelastic fluids saturating a porous horizontal layer heated from below by a constant flux. The Galerkin method is used to solve the eigenvalue problem by taking into account the elasticity of the fluid, the ratio between the viscosity of the solvent and the total viscosity of the fluid and the lateral confinement of the medium. For the primary instability, we found out that depending on the rheological parameters, two types of convective structures may appear when the basic conductive solution loses its stability: stationary long wavelength instability as for Newtonian fluids and oscillatory convection. The effect of the lateral confinement of the porous medium by adiabatic walls is to stabilize the oblique and longitudinal rolls and therefore selects transverse rolls at the onset of convection. In the range of the rheological parameters where stationary long wave instability develops first, we use a parallel flow approximation to determine analytically the velocity and temperature fields associated with the monocellular convective flow. The linear stability analysis of the monocellular flow is performed, and the critical conditions above which the flow becomes unstable are determined. The combined influence of the viscoelastic parameters and the lateral confinement on the characteristics of the secondary instability is quantified. The major new findings concerning the secondary instabilities may be summarized as follows: (i) For concentrated viscoelastic fluids, computations showed that the most amplified mode of convection corresponds to oscillatory transverse rolls, which appears via a Hopf bifurcation. This pattern selection is independent of both the fluid elasticity and the lateral confinement of the porous medium; (ii) For diluted viscoelastic fluids, the preferred mode of convection is found to be oscillatory transverse rolls for a very laterally-confined medium. Otherwise, stationary or oscillatory longitudinal rolls may develop depending on the fluid elasticity. Results also showed the destabilizing effect of the relaxation fluid elasticity and the stabilizing effect of the viscosity ratio for the onset of both primary and secondary instabilities.

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“…Koshiba et al [120] investigated the viscoelastic flow through an undulating channel as a model for flow paths in porous media and concluded that the stress in the flow through the undulating channel should rapidly increase with increasing flow rate because of the stretch-thickening elongational viscosity. Khuzhayorov et al [121] applied a homogenization technique to derive a macroscopic filtration law for describing transient linear viscoelastic fluid flow in porous media. The results obtained in the particular case of the flow of an Oldroyd fluid in a bundle of capillary tubes show that viscoelastic behavior strongly differs from Newtonian behavior.…”

Section: Dilatancy At High Flow Ratesmentioning

confidence: 99%

Flow of non‐newtonian fluids in porous media

Sochi

2010

J Polym Sci B Polym Phys

124

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The study of flow of non‐Newtonian fluids in porous media is very important and serves a wide variety of practical applications in processes such as enhanced oil recovery from underground reservoirs, filtration of polymer solutions and soil remediation through the removal of liquid pollutants. These fluids occur in diverse natural and synthetic forms and can be regarded as the rule rather than the exception. They show very complex strain and time dependent behavior and may have initial yield‐stress. Their common feature is that they do not obey the simple Newtonian relation of proportionality between stress and rate of deformation. Non‐Newtonian fluids are generally classified into three main categories: time‐independent whose strain rate solely depends on the instantaneous stress, time‐dependent whose strain rate is a function of both magnitude and duration of the applied stress and viscoelastic which shows partial elastic recovery on removal of the deforming stress and usually demonstrates both time and strain dependency. In this article, the key aspects of these fluids are reviewed with particular emphasis on single‐phase flow through porous media. The four main approaches for describing the flow in porous media are examined and assessed. These are: continuum models, bundle of tubes models, numerical methods and pore‐scale network modeling. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2010

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Derivation of macroscopic filtration law for transient linear viscoelastic fluid flow in porous media

Cited by 78 publications

References 10 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

Onset of Primary and Secondary Instabilities of Viscoelastic Fluids Saturating a Porous Layer Heated from below by a Constant Flux

Flow of non‐newtonian fluids in porous media

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