ANNUAL TRANSACTIONS OF THE NORDIC RHEOLOGY SOCIETY, VOL. 20, 2012

ABSTRACT We present results of a primarily

experimental study of buoyant miscible displacement flows of a yield stress fluid by a higher density Newtonian fluid along a long inclined pipe. We focus on the industrially interesting case where the yield stress is significantly larger than a typical viscous stress in the displacing fluid, but where buoyancy forces may be significant. We identify distinct flow regimes and observe exotic behaviours due to the large yield stress of the displaced fluid. We present the phenomenology of the flow regimes observed. We also find non-uniform static residual layers.

INTRODUCTION

There are many industrial processes in which it is necessary to remove a gelled material or soft-solid from a duct. Examples include bio-medical applications (mucus1, biofilms2), cleaning of equipment and food processing3, oil well cementing4 and waxy crude oil pipeline restarts5. A wide range of material models are used to describe residual deposits in these situations. Some of these flows are turbulent, but equally often process limitations dictate that the flows be laminar. It is this case that we study here. Our industrial motivation comes from the oil industry, (both mud removal and waxy crude oil restarts), and we assume that the residual fluids in each case have a

yield stress. We study downward displacement flows along inclined pipes. We have recently studied in detail such displacement flows, in the iso-viscous Newtonian fluid setting6,7,8,9, for viscosity ratios and shear-thinning fluids10, and for yield stress fluids11. Each of these studies is targeted at pipe/duct inclinations close to horizontal.

Here we present results of a primarily experimental study of buoyant miscible displacement flows of a yield stress fluid by a higher density Newtonian fluid along a long inclined pipe. We focus on the industrially interesting case where the yield stress is significantly larger than a typical viscous stress in the displacing fluid, but where buoyancy forces may be significant. EXPERIMENTAL SETUP

Our experimental study was performed in a 4m long, 19.05mm diameter, transparent pipe with a gate valve located 80cm from one end, see Fig. 1. The pipe was mounted on a frame which could be tilted to any angle. Initially, the lower part of the pipe is filled with a less dense fluid (fluid 2) coloured with a small amount of ink. The upper part of the pipe, above the gate valve, is filled by the denser fluid 1. To avoid pump disturbances, the displacing upper fluid was fed by an imposed over-pressure. The flow rate was controlled by a valve and measured by both a rotameter and

Displacement of Yield Stress Fluids in Inclined Pipes

Kamran Alba1, Seyed Mohammad Taghavi2, Ian A. Frigaard1,2

1Department of Mechanical Engineering, University of British Columbia, Canada.

2Department of Mathematics, University of British Columbia, Canada

71

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r range for tents.

range 0, 15, 30, 450, 75, 83, 8.001, 0.00350.01, 0.014,

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72

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Figure 3. Cent = 4x10-3 a

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btained fromgate valve. velocity val

oiseuille proe superimpolines show t

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acing fluid long the bpassing th

bove it. We which a sinng the pipe.

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Contours of m the UDV Assuming alues from a

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mm long secers below thvelocity prat 80cm be

a symmetricsimple two

nded by stathis plot. Then of the symd from the mation.

ment the n a layer the pipe, ry yield

xample in face/layer

= 85o,

mages of 7s after of pipe

ction, he gate ofiles

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73

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hots showingpipe a few cat t = 30, 60te valve; b) UDV at 80c

xample show, in compartype displac

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cm below th

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Figure 5. S45o, At=

mm/s. a) Ima12, 13,..., 2

alve. b) Spadisplaceme

distance meaDV plot of t

probe is lo

Slump-type =0.01, Y =7ages of the d6, 27s aftertiotemporal

ent. Note x iasured fromthe same ex

ocated 156cmvalve)

e displaceme7.9Pa , V0 =displacemenr opening thl image of tis the stream

m the gate vaxperiment (tm down the).

ent at = 81.5 nt at t =

he gate he same

mwise alve. c) the UDV e gate

74

many displacements a thin front advances very rapidly along the bottom of the pipe, sometimes with unsteady ruptures of the gel above, believed to be related to transition to turbulence in the narrow channel. Effects of inclination:

As pipe inclinations are reduced towards vertical, we continue to see both slump and central type displacements, but also observe other interesting behaviours.

Fig. 5 shows an example of a slump type displacement in which, as at high inclinations, an initially fast moving front advances, followed by a slower second trailing front.

Figure 6. Slump-type displacement for 60o At=0.016, Y=14.9Pa, V0 = 26.8

mm/s. a) Images of the displacement at t = 22.5, 25,..., 62.5, 65s after opening the gate valve. b) Spatiotemporal image of the same

displacement.

The UDV results (Fig. 5c) show that before the trailing front reaches the UDV position, the plug flow exists in the upper part of the pipe with a fast front moving beneath. After the trailing front passes by (t ~ 9s) there is static layer formed at upper and lower walls, and presumably all around the pipe walls. The thickness of the static layer is very small close to the lower wall. Also note that the velocity magnitudes within the displacing layer are larger as we get closer to the wall due to the existence of the fast front of displacing liquid11.

A prevalent feature at inclinations away from horizontal is that the displacing fluid has a stronger axial buoyancy component and appears to by-pass the displaced fluid much more easily. Together with the unsteady flows common in slump-type displacements it is common to observe the development of slugging along the pipe, so that the yield stress fluid is displaced in a number of discontinuous stages. Examples are shown in Figs. 6 and 7, at slightly different inclinations and Atwood numbers.

Whereas for near-horizontal displacements unsteadiness was often caused by high speeds in a relatively narrow basal channel, here we may also begin to have interfacial type instabilities due to the increasingly strong axial buoyancy forces, which lead to regions of counter-current flow. Whatever the cause, we commonly observe pieces of yield stress fluid in the UDV graph (in this case at t~20 and t~82s) and are advected downstream by the mean flow.

Finally, at inclinations close to vertical and for stronger yield stresses, we see the development of interesting helical structures during the displacement; see Fig. 8. The UDV results clearly show a highly unsteady streamwise velocity component. This type of mode does occur in Rayleigh-Taylor type instabilities and it is not clear if this is the underlying instability mechanism here. Alternatively, one could view this as a

0 0.10.20.30.40.50.60.70.80.91

a)

75

helical configu

Figu4

mm/s.22.5, 2valve;

disp

instabilituration.

ure 7. Slump5o At=0.016. a) images 25,..., 62.5, b) Spatiotelacement. c

ex

ty of a

p-type displ6, Y =16.4Pof the displ65s after opmporal ima

c) UDV plotxperiment.

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mages of th48, 52 s aft

Spatiotemdisplaceme

In either celd stresses

the displaeak up the uid. For th

Helical instaY =19.7Pa, Vhe displacemer opening tmporal imaent. c) UDV

experime

case it is likin this expcing fluid helical colu

he experim

ability for V0 = 61.3 m

ment at t= 7the gate val

age of the saV plot of theent.

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are insuffiumn of yie

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15o

mm/s a) , 10,..., lve; b) ame e same

the large e stresses ficient to eld stress nted two

76

unstable pieces of yield stress fluid pass by the UDV location, at t~20s and t~33s respectively. This can be confirmed through the UDV results as well (see the enhanced jump in velocity around the given time).

At lower imposed flow rates, closer to an exchange flow regime, we have also observed helical backflows of the yield stress fluid, although here the yield stress fluid is displaced. SUMMARY

We have presented experimental results in which a heavy Newtonian fluid displaces a lighter yield stress fluid in the downwards (density unstable) direction. We have focused on the industrially interesting case where the yield stress is significantly larger than a typical viscous stress in the displacing fluid, but where buoyancy forces may be significant.

A number of distinct flow regimes and exotic behaviours have been observed, due to the large yield stress of the displaced fluid. We have mostly presented the phenomenology of these flow regimes. ACKNOWLEDGMENTS

This research has been carried out at the University of British Columbia, supported financially by NSERC and Schlumberger through CRD project 354716-07. The authors also thank Messrs Hady Abou Jaoude and George Hatzikiriakos for assisting in running the experiments.

REFERENCES 1. P.D. Howell, S.L. Waters, and J.B. Grotberg. J. Fluid Mech., 406:309–335, 2000.

2. O. Wanner, H.J. Eberl, E. Morgenroth, D. Noguera, C. Picioreanu, B.E. Rittmann, & M.C.M. Van Loosdrecht. IWA Scientific and Technical Report Series,, volume 18, pages 1–199. IWA Publishing, ISBN 1843390876., 2006.

3. G.K. Christian and P.J. Fryer. Trans. IChemE C, 84:320–328, 2006.

4. E.B. Nelson & D. Guillot. Well Cementing, 2nd Edition. Schlumberger Educational Services, 2006.

5. G. Vinay, PhD thesis, These de l’Ecole des Mines de Paris, Paris, France, 2005.

6. S.M. Taghavi, T. Seon, D.M. Martinez, and I.A. Frigaard. J. Fluid. Mech., 639:1–35, 2009.

7. S.M. Taghavi, T. Seon, D.M. Martinez, and I.A. Frigaard. Phys. Fluids, 22:031702, 2010.

8. S.M. Taghavi, T. Seon, K.Wielage-Burchard, D.M. Martinez, & I.A. Frigaard. Phys. Fluids, 23:044105, 2011.

9. S.M. Taghavi, K. Alba, T. Seon, K.Wielage-Burchard, D.M. Martinez, & I.A. Frigaard. J. Fluid Mech, to appear in 2012.

10. S.M. Taghavi, K. Alba, and I.A. Frigaard. Chem. Eng. Sci., 69:404–418, 2012.

11. S.M. Taghavi, K. Alba, M.A. Moyers-Gonzalez, & I.A. Frigaard. J. Non-Newt. Fluid Mech., 167:59–74, 2012.

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