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Flow instabilities during annular displacement of one non-Newtonian fluid by another

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Abstract

This paper describes an experimental setup for axial laminar flow of liquids in the annulus between two eccentered cylinders. The design uses a conductivity method for measuring peak axial velocities around the annulus, and for the determination of displacement efficiency when displacing one fluid by another (displacement efficiency being defined as the ratio of volume of displaced fluid removed from the annulus, to the volume of the annulus, after a given number of annular volumes have been pumped). In an eccentric annulus, lower axial velocity in the narrow side produces “channeling” of the displacing fluid in the wide side and reduces the displacement efficiency. A positive density contrast between the two fluids can increase the efficiency by promoting azimuthal flow of the (denser) displacing fluid towards the narrow side. In this paper we report that gravity driven azimuthal flow is prone to severe instabilities which accelerate the displacement process but may leave behind an immobile strip of the displaced fluid in the narrow side.

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Abbreviations

C m :

mean tracer concentration in exit stream

C 0 :

tracer concentration in displacing fluid

d m:

distance between centres of inner and outer pipes

E :

circulation or displacement efficiency

e :

non-dimensional eccentricity [= d/(R 0-R i)]

g m s−2 :

gravitational acceleration

h m:

typical annular gap ( = R 0-R i)

k Pa sn :

consistency index in Herschel-Bulkley equation

L m:

hydrostatic head between wide and narrow sides of annulus

n :

flow behaviour index in Herschel-Bulkley equation

p Pa:

pressure

Q m3 s−1 :

volume flow rate

R i m:

inner radius of annulus

R 0 m:

outer radius of annulus

r m:

radial distance in annulus

T s:

time

T b s:

breakthrough time

V m3 :

volume of annulus

w m s−1 :

axial velocity

w max m s−1 :

peak axial velocity

w m s−1 :

mean flow velocity

z m:

length in direction of flow

ġg s−1 :

shear rate

θ :

angular position around annulus

μ Pa s:

shear viscosity

ρ Kg m−3 :

fluid density

τ Pa:

shear stress

τ y Pa:

Herschel-Bulkley yield-stress

φ :

angle of deviation from vertical

*:

denotes non-dimensionalized quantities such as time, etc.

S:

specifies value of variable at position S along the annulus

References

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Authors and Affiliations

  1. Schlumberger Cambridge Research, Madingley Road, CB3 0EL, Cambridge

    M. A. Tehrani, S. H. Bittleston & P. J. G. Long

Authors
  1. M. A. Tehrani
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  2. S. H. Bittleston
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  3. P. J. G. Long
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Tehrani, M.A., Bittleston, S.H. & Long, P.J.G. Flow instabilities during annular displacement of one non-Newtonian fluid by another. Experiments in Fluids 14, 246–256 (1993). https://doi.org/10.1007/BF00194015

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  • DOI: https://doi.org/10.1007/BF00194015

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