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Modelling the Flow of Yield-Stress Fluids in Porous Media

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Abstract

Yield-stress is a problematic and controversial non-Newtonian flow phenomenon. In this article, we investigate the flow of yield-stress substances through porous media within the framework of pore-scale network modelling. We also investigate the validity of the Minimum Threshold Path (MTP) algorithms to predict the pressure yield point of a network depicting random or regular porous media. Percolation theory as a basis for predicting the yield point of a network is briefly presented and assessed. In the course of this study, a yield-stress flow simulation model alongside several numerical algorithms related to yield-stress in porous media were developed, implemented and assessed. The general conclusion is that modelling the flow of yield-stress fluids in porous media is too difficult and problematic. More fundamental modelling strategies are required to tackle this problem in the future.

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Abbreviations

\({\dot{\gamma}}\) :

Strain rate (s−1)

τ :

Stress (Pa)

τ o :

Yield-stress (Pa)

τ w :

Stress at tube wall (Pa)

\({\phi}\) :

Porosity

C :

Consistency factor in Herschel–Bulkley model (Pa.sn)

K :

Absolute permeability (m2)

L :

Tube length (m)

n :

Flow behavior index

P :

Pressure (Pa)

P y :

Yield pressure (Pa)

ΔP :

Pressure drop (Pa)

ΔP th :

Threshold pressure drop (Pa)

Q :

Volumetric flow rate (m3.s−1)

R :

Tube radius (m)

T :

Temperature (K, °C)

IPM:

Invasion percolation with memory algorithm

MTP:

Minimum threshold path

PMP:

Path of minimum pressure algorithm

TYP:

Threshold yield pressure

x l :

Lower boundary of the network model

x u :

Upper boundary of the network model

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  1. Department of Physics and Astronomy, University College London, Gower Street, London, WC1E 6BT, UK

    Taha Sochi

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Sochi, T. Modelling the Flow of Yield-Stress Fluids in Porous Media. Transp Porous Med 85, 489–503 (2010). https://doi.org/10.1007/s11242-010-9574-z

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