Encyclopaedia Index

TITLE : LAMINAR FLOW OF NON-NEWTONIAN FLUIDS IN ECCENTRIC ANNULI

BY : CHAM Development Team - G.Garnier

FOR : Validation of Non-Newtonian Models

DATE : 1997 PHOENICS Version : 3.0

PURPOSE OF THE CALCULATIONS:

1. HERSCHEL-BULKLEY FLUID: FLOW CURVE
2. ECCENTRIC ANNULI:GRID

3. POWER-LAW FLUID :

The second step is to validate PHOENICS implementation on flow of Herschel-Bulkley fluid in eccentric annuli. There is no existing correlation. We have hence validated the computations with Haciislamoglu and Langlinais results [1] (finite difference coding).

The flow properties are:

  _ n = .7
  _ K = .25 kg/ (m sec**n)
  _ tauy = 2.394 N/m**2
  _ flow rate Q = 1.2618e-2 m**3/sec
  _ Din = 25.4 cm
  _ Dout = 12.7 cm

We first compare the PHOENICS pressure drops. We can notice the well- known effect: For a constant flow rate, frictionnal pressure losses are decreasing with increasing eccentricity. The results show good agreement with Haccislamoglu and Langlinais pressure losses.

PREDICTIONS VS CORRELATION

4. HERSCHEL-BULKLEY FLUID :

PRESSURE DROP vs ECCENTRICITY

Then, we check the velocity profiles by comparing two extremum velocities: the maximum velocity of the largest and the narrowest part of the annulus. The results are in good agreement (fig. 5) with Haccislamoglu and Langlinais works.

We can notice the effect of increasing eccentricity: The velocity in the narrowing part of the annulus is reduced, while the fluid is rushing into the widening part (fig. 6). For high eccentricities (greater than .5), there is a high velocity plug (flat velocity profile) in the wide part of the annulus, while a no-flow (stagnant) region is created in the narrow part.

A few velocity profiles are given for differents eccentricities (fig. 7,8,9,10,11)

5. HERSCHEL-BULKLEY FLUID : EXTREMUM VELOCITIES
6. HERSCHEL-BULKLEY FLUID : RADIAL VELOCITY DISTRIBUTION
7. HERSCHEL-BULKLEY FLUID : VELOCITY PROFILE (E=0)
8. HERSCHEL-BULKLEY FLUID : VELOCITY PROFILE (E=.25)
9. HERSCHEL-BULKLEY FLUID : VELOCITY PROFILE (E=.50)
10. HERSCHEL-BULKLEY FLUID : VELOCITY PROFILE (E=.75)
11. HERSCHEL-BULKLEY FLUID : VELOCITY PROFILE (E=.95)

References

[1] M. Haciislamoglu, J. Langlinais, 1990, "Non-Newtonian flow in eccentric annuli", Journal of Energy Ressources pp 163,169

[2] T.D. Reed, Conoco Inc, A.A. Pilehvari, U. of Tulsa, 1993, "A new model for laminar, transitionnal, and turbulent flow of Drilling muds", Society of Petroleum Engineers, SPE 25456, pp 39, 52

wbs