Estimates of effective permeability for non-Newtonian fluid flow in randomly heterogeneous porous media

Federico, Vittorio Di; Pinelli, Marco; Ugarelli, Rita Maria

doi:10.1007/s00477-010-0397-9

Cited by 36 publications

(19 citation statements)

References 35 publications

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“…Cross, Ellis and Carreau models Yun [29] Fractal porous media Power law Balhoff et al [1] Network modeling Power law and Ellis model Tang and Lu [23] Packed bed Power law Di Federico et al [7] Randomly heterogeneous porous domain…”

Section: Power Lawmentioning

confidence: 99%

On Laminar Flow of Non-Newtonian Fluids in Porous Media

2015

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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 [5] is used to determine the effective viscosity as a function of the shear strain rate. Carreau model can predict accurately variation of 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 of 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 generalize Newtonian fluid flows in porous media.

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Section: Power Lawmentioning

confidence: 99%

On Laminar Flow of Non-Newtonian Fluids in Porous Media

2015

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“…In fact the condition on the spatial derivative of h at the front arises by the governing function (see Eq. (18) in Section 3). Akin to viscous gravity currents (see [30] for a detailed description) if the limits on Reynolds and/or Bond number are not satisfied, the solution should be totally controlled by the conditions at the front, that must be experimentally detected.…”

Section: Formulationmentioning

confidence: 95%

“…(where s is the shear stress, _ c the shear rate, m the fluid consistency index [ML À1 T nÀ2 ] and n the flow behavior index), the modified Darcy's law takes in the literature the two equivalent forms (for a list of references see [18]). …”

Section: Formulationmentioning

confidence: 99%

Spreading of axisymmetric non-Newtonian power-law gravity currents in porous media

Federico

Archetti

Longo

2012

Journal of Non-Newtonian Fluid Mechanics

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“…After solving the fluid equation, the permeability can be computed following the general Darcy's law [27,28] as follows:…”

Section: Numerical Approach and Validationmentioning

confidence: 99%

The Effect of Heat Transfer and Polymer Concentration on Non-Newtonian Fluid from Pore-Scale Simulation of Rock X-ray Micro-CT

et al. 2017

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Most of the pore-scale imaging and simulations of non-Newtonian fluid are based on the simplifying geometry of network modeling and overlook the fluid rheology and heat transfer. In the present paper, we developed a non-isothermal and non-Newtonian numerical model of the flow properties at pore-scale by simulation of the 3D micro-CT images using a Finite Volume Method (FVM). The numerical model is based on the resolution of the momentum and energy conservation equations. Owing to an adaptive mesh generation technique and appropriate boundary conditions, rock permeability and mobility are accurately computed. A temperature and concentration-dependent power-law viscosity model in line with the experimental measurement of the fluid rheology is adopted. The model is first applied at isothermal condition to 2 benchmark samples, namely Fontainebleau sandstone and Grosmont carbonate, and is found to be in good agreement with the Lattice Boltzmann method (LBM). Finally, at non-isothermal conditions, an effective mobility is introduced that enables to perform a numerical sensitivity study to fluid rheology, heat transfer, and operating conditions. While the mobility seems to evolve linearly with polymer concentration in agreement with a derived theoretical model, the effect of the temperature seems negligible by comparison. However, a sharp contrast is found between carbonate and sandstone under the effect of a constant temperature gradient. Besides concerning the flow index and consistency factor, a master curve is derived when normalizing the mobility for both the carbonate and the sandstone.

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Estimates of effective permeability for non-Newtonian fluid flow in randomly heterogeneous porous media

Cited by 36 publications

References 35 publications

On Laminar Flow of Non-Newtonian Fluids in Porous Media

On Laminar Flow of Non-Newtonian Fluids in Porous Media

Spreading of axisymmetric non-Newtonian power-law gravity currents in porous media

The Effect of Heat Transfer and Polymer Concentration on Non-Newtonian Fluid from Pore-Scale Simulation of Rock X-ray Micro-CT

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