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Rheologica Acta

, Volume 58, Issue 11–12, pp 755–769 | Cite as

On the miscible thermo-viscous fingering instability of non-Newtonian fluids in heterogeneous porous media

  • Hosna Shokri
  • Mohammad Hassan Kayhani
  • Mahmood NorouziEmail author
Original Contribution
  • 45 Downloads

Abstract

In this paper, the thermo-viscous fingering instability in the displacement of Newtonian fluid by a shear-thinning non-Newtonian fluid in the heterogeneous porous media is studied. Here, the heterogeneity of medium is assumed to be layered. Two different types of displacements are considered: a cold low viscous fluid displaces a hot high viscous one and vice versa. The numerical solution is obtained using a spectral method based on Hartley transforms and fourth-order Adams–Bashforth technique. By interoperation of concentration and temperature contours, transversely averaged profiles, mixing length, and sweep efficiency, it is shown that heterogeneity of porous media has a significant effect on the thermo-viscous fingering instability. The decreasing thermal-lag coefficient leads to more unstable flow and Lewis number has different effects on displacements. When a cold less viscous fluid is displacing fluid, this parameter has destabilizing effect while for displacing hot more viscous fluid, and it acts in favor of stability.

Keywords

Thermo-viscous fingering instability Non-Newtonian fluid Heterogeneous porous media Spectral method 

Nomenclature

A

Sspect ratio of Hele–Shaw cell

b

Size of gap in the Hele–Shaw (m)

c

Concentration

D

Dispersion tensor (m2/s)

k

Wave number of the disturbances

K

Permeability of the porous medium (m2)

K0

Average permeability of the medium (m2)

L

Length of the Hele–Shaw cell (m)

Le

Lewis number

n

Power law index

p

Pressure (Pa)

Pe

Peclect number

q

Frequency of layers in y direction

S

Variance of permeability

T

Temperature (°C)

t

Time (s)

U

Average velocity of fluid injection (m/s)

u

Velocity (m/s)

u

Streamwise component of the velocity field (m/s)

V

Magnitude of the velocity vector (m/s)

W

Width of the Hele–Shaw cell (m)

x

Coordinate in the streamwise direction (m)

y

Coordinate in the transverse direction (m)

Greek symbols

β

Natural logarithm of the viscosity ratio

\( \dot{\gamma} \)

Generalized shear rate (1/s)

ζ

Characteristic time of Careau model (s)

η

Apparent viscosity (Pa s)

η

Infinite shear rate viscosity (Pa s)

η0

Zero shear rate viscosity (Pa s)

θ

Dimensionless temperature

λ

Thermal lag coefficient

σ

Growth rate of the disturbance

ϕ

Porosity

ψ

Stream function (m2/s)

ω

Vorticity (1/s)

Superscript

*

Dimensionless parameter

'

Perturbation

Subscripts

1

Displacing fluid

2

Displaced fluid

0

Base state profile

C

Concentration

T

Temperature

Notes

Supplementary material

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Hosna Shokri
    • 1
  • Mohammad Hassan Kayhani
    • 1
  • Mahmood Norouzi
    • 1
    Email author
  1. 1.Faculty of Mechanical EngineeringShahrood University of TechnologyShahroodIran

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