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 (mucus 1 , biofilms 2 ), cleaning of equipment and food processing 3 , oil well cementing 4 and waxy crude oil pipeline restarts 5 . 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 setting 6,7,8,9 , for viscosity ratios and shear-thinning fluids 10 , and for yield stress fluids 11 . 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 Alba 1 , Seyed Mohammad Taghavi 2 , Ian A. Frigaard 1,2 1 Department of Mechanical Engineering, University of British Columbia, Canada. 2 Department of Mathematics, University of British Columbia, Canada 71
7
Embed
Displacement of Yield Stress Fluids in Inclined Pipes
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
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
a magnof the the gatdisplaccameracharactVelocitcentral downstUltraso
Figureset
The
Newtonalways of CarbCarbopstabilizrheologby the Once man acidyield ston neucase Nfairly tas wate
PARM
Ourof pipebetweestress odenoted BN = Y
netic flowmpipe. At thte valve ising fluid ar
as, and suterize differty is also
plane of tream of thonic Dopple
e 1. Schemat-up (the sh
illust
e displacingnian salt-waa yield stre
bopol® EZ-pol® is wizer and gy of Carboconcentratimixed withdic solutiontress is dev
utralising wNaOH). Thtransparent er (for low c
ETER RANr experimen inclinationn the yieldof the Newd by BN, def
YD/V0
meter, locatehe start of s opened. re recorded ubsequentlyrent aspect
o measuredthe pipe
he gate vaer Velocime
atic view ofhape of the itrative only
g fluid 1 ater solutioess fluid, na-2 polymer idely used suspendingopol® is laron and pH
h water, Can with no yiveloped at inwith a basehe neutralis
and has thconcentratio
NGE STUDnts coveredns and flow d stress an
wtonian dispfined as:
ed downstrthe experimImages of using 2 dig
y analyzedts of the fld through
at a posialve, using
eter (UDV).
f experimeninterface is y).
was alwayon. Fluid 2 mely a solu(Noveon Ias thicke
agent. rgely controof the solut
arbopol® maield stress. ntermediate agent (in
sed solutione same den
ons).
DIED d a broad ra
rates. The rnd the viscplacing flui
ream ment f the gital
d to flow.
the ition g an
ntal
ys a was
ution Inc). ener, The
olled tion. akes The
e pH our
n is nsity
ange ratio cous id is
(1)
andarewenu Re whrel At Fr Thexp
RE
maresas difinc
essoccas delas
d typically e designed te consider tmber:
e = V0D/
here = (levant dime
= (1-2)/(
= (At g D)1
he ranges wperiments a
Table 1
Para
β d
A
VRFB
ESULTS
We will ain sectionsults for neaalready rep
fferences thclined.
For near-hsentially twcurred: cen
described lineated excshown in F
we have Bto be in lamthe Newton
1+2)/2. Tensionless g
1+2)
1/2
we have care given in
. Parameterexperime
meter
deg 06
At0.
0
V0 0Y
ReFrBN
describe ouns. Firstly, ar horizontaported11. Thhat arise wh
horizontal piwo types
ntral and slubelow. Th
clusively byig. 2.
BN >>1. Ominar regimnian fluid R
The other twgroups are
considered table 1.
r range for tents.
range 0, 15, 30, 450, 75, 83, 8.001, 0.00350.01, 0.014,
0.016 0-120 mm/s
0-26 Pa 0-2300 0.1-6
600-72000
ur results we descr
al pipe inclhereafter wehen the pipe
ipes11 we foof displa
ump displahese regimy the value o
ur flows me, when Reynolds
(2)
wo most
(3)
(4)
for our
the
5, 5 5, ,
s
in three ribe our linations, e discuss e is more
ound that acements cements,
mes were of Re/Fr,
72
CentralAn
displacsequencadvancfront shpipe, wthe tip/lead to the scamean cdarker pipe, bpipe. Ta residuimagesand furwavele
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
elow the c flow, o-layer tic layers e broken
mmetric mean
73
The
4a is interfacconcenbroken from thupper displacincreasvelocity
Figure = 10-2
snapshof the pvalve the gat
the U
The exsimple,slump t
e UDV proshown in ce height in
ntration andwhite line
he measurelayer is
ement proges and sincy in the disp
4. Slump d2 and V0 = 2
hots showingpipe a few cat t = 30, 60te valve; b) UDV at 80c
xample show, in compartype displac
file correspFig. 4b, a
nferred fromd superim
e on Fig. 4ed velocity
largely sgresses the ie the flow rplacing fluid
displacemen26mm/s: a) g a 990 (mmcentimeters 0, 570, 600scontours of
cm below th
wn in Fig. rison to somcements obs
ponding to again with m the measu
mposed as b. We can that the th
tatic. As interface herate is fixedd reduces.
nt for = 85o
a sequence m) long sectbelow the g
s after openf velocity fr
he gate valve
4 is relativme of the oserved11. Fo
Fig. the
ured the
n see thick
the eight d the
o, At of tion gate
ning rom e.
vely other or
m
va
dUD
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.
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.
core-ann
lacement foPa, V0 = 61lacement at pening the gage of the sat of the sam
nular
or .3 t =
gate ame
me
Ai
yiein breflu
Figure 8. HAt=0.016, Y
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.
kely that at periment the
are insuffiumn of yie
ment presen
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.