BY : CHAM Development Team - G.Garnier
FOR : Validation of Non-Newtonian Models
DATE : 1997 PHOENICS Version : 3.0
e= delta / (Rin - Rout)wherein delta is the distance between the two centers, Rin the inner radius, Rout the outer radius.
(dP/dZ)ecc=(dP/dZ)conc * Rwherein
R= 1 - .0072(r**.8454)(e/n) -1.5(r**.1852)(e*e)(n**.5) + .96(e**3)(n**.5)(r**.2527)This correlation accuracy is within +/- 5 percent. The PHOENICS predicted pressure drops are compared with this correlation in the range of parameters this one is valid. The differences are within the same accuracy.
r = Din/Dout
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
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)
 M. Haciislamoglu, J. Langlinais, 1990, "Non-Newtonian flow in eccentric annuli", Journal of Energy Ressources pp 163,169
 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