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

ABSTRACT This paper describes initial experiments

that are done at the University of Stavanger in a new flow rig for study of gas lift under static and flowing conditions. Lift efficiency is determined from lift of a liquid column under various experimental conditions, while bubble rise velocity and bubble sizes are determined using high speed video recordings. For the experiments water, and also PAC (polyanionic cellulose) are used as fluids. Both static lift and air-circulation experiments involving polymers is found to be more time dependent than with water, due to different accumulation of gas bubbles.

INTRODUCTION

Gas-lift techniques are based on injection of gas into fluids to be transported in vertical upward flows in pipes and circulation systems. Gas reduces the mixture density and lowers the hydrostatic pressure gradient. It is used as a pumping technique often also for enhancement of chemical reactions via interfacial mass transfer and turbulence. It is used in a variety of engineering applications, as well as environmental cleaning and bioreactor systems, which generally involves non-Newtonian fluids 1,3,4.

Gas lift is also very important in oil production. A substantial fraction of drilled

oil wells worldwide are “helped” by gas lift, and may increase production rates very much. Basically two applications are well known for petroleum. One is “gas lift production”, where usually produced natural gas is injected through gas-lift valves into the production tubing at the bottom of the well. The bottom-hole pressure (BHP) is reduced and thereby the inflow from the producing reservoir is increased. In this case the liquid is usually oil which is predominantly Newtonian, or an oil-water mixture which has a complex rheological nature not easily described by common non-Newtonian models. Another application is the addition of gas into drilling mud for so-called “underbalanced drilling”. The aim is to reduce the pressure at the bottom of the well to slightly below the reservoir pressure. The purpose is to avoid reservoir fracture and loss of lubrication drilling fluid into the reservoir formation. Drilling mud is usually non-Newtonian.

The gas-lift efficiency depends on the in-situ gas fraction for a given amount of injected gas. The lift process leads to increase in liquid flow-rate and thus the total flow-rate and mixture velocity will increase. However a number of parameters play a role in the overall process, where the rise velocity or “slip” is one of the most important. Additional factors involve solubility of the gas into the liquid, and also the total mixture velocity. Solubility is

An Experimental Study of Gas Lift Efficiency in Polymer Systems

Rune W. Time and A.H. Rabenjafimanantsoa

University of Stavanger, Norway

59

difficult to know in petroleum systems since the produced natural gas is most often used as gas source, and this aspect is not covered here since air and water based systems are used, with only minor interfacial mass transfer.

Rheology of the liquid is likely to have a major impact on the lift efficiency, in particular in conjunction with the suspended bubbles. The power-law behavior of the polymer solutions will not necessarily be the same in a gas-liquid system, like with shear rate versus shear stress in a vertical pipe. The rise velocity is closely connected to the bubble size but in non-Newtonian flows this is not a simple connection. It depends very much on the rheological parameters of the fluid. Furthermore it is found1 that even for the same fluid the rise velocity depend in a more non-linear way on bubble size than in Newtonian flows. Finally, the bubble size in multiphase flow is in general a “self-organized” quantity. It is influenced by upstream injection or mixing history, and also by the turbulence intensity. The latter is a challenge to determine in polymer liquids with dispersed gas bubbles.

THEORY

The gas-lift efficiency is basically determined by the in-situ gas fraction which controls the hydrostatic pressure gradient. The gas fraction is for a given flow rate of gas directly connected to the slip velocity or the slip ratio S = uG/uL. Here uG and uL are the gas and liquid phase velocities respectively.

For low mixture velocity systems like in a bubbling column, it is more convenient to use the bubble rise velocity instead of the slip ratio, since uL is practically zero and S would become very large. This is a common parameter to use also in drift-flux models for numerical simulation. In the drift-flux formulation the gas fraction can be determined theoretically by equating the two equations for the “drift flux” (Zuber and Findlay, 1965 and Wallis, 1969):

(1 )nGM G G Tj U (1)

and

(1 )GM G GS G LSj U U (2)

Eq. (1) is referred to as the “dynamical

equation” since fluid flow dynamics controls the rise velocity uT while n is a system dependent parameter. The equation also includes effective rise velocity in a system of bubbles with gas fraction G as compared to terminal velocity for the bubbles. UT is the stabilized rise velocity for one single bubble in a large tank. Equation (2) called the “kinematic equation” is theoretically just a connection between the superficial velocities in a fixed reference frame to the so-called “drift–flux” jGM. This is the superficial velocity in a system following the mixture velocity, which again is the sum of the superficial velocities

mix GS LSU U U (3)

For pure bubble column mode with

liquid circulation ULS=0, and the equations simplify to solving

n 1 GS

G GT

U(1 )

U (4)

Alternatively if the gas fraction is

known, it possible to derive the average bubble terminal velocity UT using

GST n 1

G G

UU

(1 )

(5)

However the rise velocity may be very

different for single bubbles in a big tank compared to in pipes with high gas fraction and complex velocity profiles. One objective of this study is to investigate also the effect of non-Newtonian liquids on the

60

bubble velocity

Goocan beexperimmore comput EXPER

Themotivatdynamiapplica“productransposurfacedrillingtranspothe dril

It wflow ri“Riser”two hoas showalso a applica

Figurdefini

flow patty. od survey ae found6,9.mental issu

focus ontational mod

RIMENTALe particulated by neics for

ations. Gas-ction” will

ort from “e “wellheag it may invort. Gas is thll pipe. was decidedg with two

” and “Doorizontal crown in Fig. very gener

ations.

re 1. Sketchitions of “R

cross

tern and n

articles of g. The firs

ues, while n mass dels.

L SETUP ar setup weed to dete

petroleum-lift assistedl normally “bottom-holad”. For volve also dhen injected

d to build o 5 m high wncomer”, ossover pip1. In this w

ral rig for

h of the gas-Riser”, “Dowsover “Legs

net bubble

gas-lift systst focuses the other transfer

was originermine gas

m engineed flow in wbe a one-

le” up to underbalan

downwards d from top

the laboravertical legconnected

pes 1.5 m loway it wouldmany diffe

lift loop, wiwncomer” as”.

rise

tems on

has and

nally s-lift ering wells -way

the nced gas into

atory gs; a d by ong, d be erent

ith and

chereccrome

(aiFigin onofusesinele

“pahaninfdiaou

inoth

miobbubthebub

tobas

It is quite emical reacirculation ossover pipeans of valv

Gas liftingir) bubbles ag. 1. A clothe insert oly partly coinjectors o

ed a porountered metaectron micro

A problemassive” spang on to tflation stagameters largtlet.

Figure

nserted into f the surfache image wi

However

icroscopic,tain smallerbbles clinge inflation, bbles beforAlternativ

generate smsed on app

similar to wactors or

flow is des can be o

ves. g is obtainedat the bottomose up of thof Fig. 2. ontrollable wr “spargers”us injector al particles,oscope pictu

m with this targers is ththe pore op

ges and mager than the

2. Picture oan electrone. Magnificidth is appro

even if the10-100 mr bubbles thing to the or by coal

e they are ree spargers a

maller bubbplying a sh

what is usedbioreactors

desirable. Topened or c

d by injectiom of the rig

he injector iThe bubbl

with differe”. In this w

made from, as shownure in Fig. type and m

hat bubblespenings duay becomeopenings o

of the gas injn microscopcation is 100oximately 3

e pore openm, it is difhan 1-2 mmpore outletlescence weleased. are planned

bles. These hearing forc

d also for s where The two closed by

on of gas ght leg in is shown le size is ent types

work was m small n in the 2. ost other tend to

uring the e several of the gas

njector e image 0X, and 3.8 mm.

nings are fficult to m, due to ts during ith other

d in order could be

ce to the

61

bubbles either by a strong cross flow, or by using a fast mechanical scraper mechanism to wipe the bubbles off the surface. EXPERIMENTS

Experiments were planned and carried out to determine the following issues: 1) flow regimes in the riser, crossovers and downcomer pipe, 2) gas-liquid fractions as a function of superficial gas velocity, 3) flooding limit for gas bubbles in the downcomer pipe in terms injected gas, 4) bubble size for given gas sparging unit as a function of gas flow rate, 5) pressure gradients versus flowrates for different configurations of valve openings, and finally 6) velocity profiles of liquid and gas in riser and downcomer. Determination of the velocity profile in the downcomer could also enable calculation of the liquid flow-rate.

There are already quite a lot of data generated from these initial experiments. They have been acquired during a very busy experimental campaign the last month. This has left less time to carry out all the planned analysis, so only some few examples will be presented and discussed here. More will be presented at the conference and in later papers.

Experimental program

The different tests were grouped as i) Static column bubbling ii) Gas-lifted circulation Static bubbling was used to determine

liquid height as a function of gas flow rate. The goal was to determine gas fraction. This was done both for water and PAC. Flow regime determination and a feasibility study to find bubble sizes gas fraction distributions was also part of this study.

Circulation with fully opened valves was carried out to study dynamic lift, both in Newtonian and non-Newtonian flow. As described later a direct comparison between the experimental modes was influenced by the gradual entrainment of bubbles especially in the non-Newtonian case.

The lift efficiency can be measured from the pressure gradient in the riser, but it is representative only in the initial period when gas bubbles still have not reached the downcomer pipe. On the measurement program was also the flooding limit for gas bubbles in the downcomer, both for water and PAC

Flow aspects regarding the tests

The “static 1” experiments were carried out with the crossover pipes closed These tests reveal the potential lift properties of a full circulating the gas-lift system. It is also possible to close just the upper valve to aloe inflow from the bottom into the riser. These tests mainly shift the column level to a slightly higher level, but do in principle not add much more information.

The circulating fully dynamic tests also involve flow friction. Both in two-phase flow, and in single-phase non-Newtonian system this is important to determine. A comment on the static versus circulating test regards the analogous equivalent when measuring the voltage difference between the poles of a battery when not loaded. The circulation tests give the corresponding voltage when current flows in an external circuit. In his case the voltage is reduced due to internal losses in the battery. The friction in the left downcomer leg corresponds to the internal loss.

Instrumentation

The flow loop has been set up to give a best possible access to vital information to determine lift dynamics and efficiency. Transparent pipes give excellent information about flow regimes, bubble size and velocities, and also liquid rise levels. Pressure is measured at the gas flowmeter with a Honeywell sensor. Also the pressure difference P between the two locations shown in Fig. 1 was measured, using a Rosemount transmitter 3051C. It has a range of 62 mbar and time resolution 100ms. Finally the gauge pressure is measured at

62

the lowP sensensor used. Pfast dat12 bit)profilesspeed vthat reresolutirecord resolutifor 82ImagesGigaBidedicat(“Motio

Fluids

Basused; concen(PAC) of distiPAC 20PAC rheomecone pl

PACtranspapower-in Fig. RESUL

Vidof flowand gaas a refon whmeasurliquid l

Static e

Forclosed, more ithe bub

west positionsor. A “

(Crystal Pressures artalogging ca). Phase ds are measuvideo camerecords up ion 512x5

up to 1ion. The cam

223 full frs are downlit Ethernetted comonBlitz”, by

sically thretap wate

ntrations owith 2g anilled water.00 and PACsolutions

eter of typelate configuC is chosenarency. The law fluids 3.

LTS AND Ddeo recordinw regime, gas-liquid disference techhat can berements liklift heights.

experimentsr static expthe flow r

nhomogenebble size inc

on of the tw“Gauge DiEngineeringre recorded ard (brand Ndistributionsured by mera (SpeedCato 2500

12 pixels. 120.000 fpmera has onrames at floaded to ct cable bymmunicatioy Mikrotron

ee differener, and

of polyaniond 4g dry po. These areC 400. The was mease Physica U

uration. n because o

PAC solutwith param

DISCUSSIOngs allowedgas bubble stribution, ahnique. Thie obtained ke pressure

s periments wregime becoeous at thecreases with

wo used forigital Testig, XP2I) to PC usin

NIDAQ 602s and veloeans of a ham MiniVisfps using

It may eps at redunboard memfull resolutcomputer vy means on prog

n).

nt fluids wtwo diffeonic celluowder per Le referred toviscosity ofured usingUDS 200 w

of good opttions behav

meters as g

ON d determina

rise velocand this ses paper focu

from ovee gradient

with both vaomes more same time

h the gas flo

r the ting” was

ng a 24E, ocity high s e2)

full even uced mory tion.

via a of a gram

were erent ulose Liter o as f the g a with

tical ve as iven

ation cities erves uses erall and

alves and

e as ow

F

rat4.

dissompacoftBacridis

Figure 3. Rh

te. Transitio

For Newtospersed bumetimes dcking” modten referredarne and Ditical gas stinct and

heology of P

on to slug fl

onian flowsbble (DB)

described wdel. This is d to as the Dukler mofraction th

dispersed

PAC 200 an

low is show

s the transit) to slug with a “mone part ofmechanistic

odel”12. Bhe bubblesd. Exceedi

nd 400.

wn in Fig.

ion from flow is

maximum f what is c “Taitel Below a remain ing this

63

fractioncoalescNewtonmaximufluids iturbuleover 50

Figure moderand s

The

currentpresentmode) experimbubble change

Thiand woto slugg

Howwhere pathwa

n the dencence into nian liquidum gas frs approximnt flows it

0%.

4. Flow regrate gas inflslug flow. T

with 2 s

e model12 it upwards t static expe

the liquidments reve

flow with continuouss enhances

ould for a noging at lowewever it i

the bubbays resembli

se bubble larger b

ds, at low raction for

mately 25%, t may stay

gime in watelux varies beThe two imaseconds inte

is validatedNewtonian

eriments (“bd flow is eal a veryh recirculasly. the bubbleon-Newtonier gas fractis also seebles set ing transpor

cloud caububbles. flow rates low visco

while at higy bubbly up

er-filled riseetween bub

ages are takeerval.

d only for flows. In

bubble columstagnant.

y compliction cells

e collision ian system ions. en other c

up collecrt veines.

auses For the

osity ghly p to

er at bbly en

co-the

umn” The

cated that

rate lead

cases ctive

calinc

fraprerel

Ffuo

Ffu

In Fig. 5 lculated dicrease.

However, action can essure gradlation

G g (

Figure 5. Gafunction of son volumetr

Figure 6. Gafunction of s

on pre

the gas frarectly from

in the stalso be ca

dient in th

L G 12

P

) h

as fraction wsuperficial gic increase o

used.

as fraction wsuperficial gessure gradi

action in them the liqu

tatic case alculated fhe pipe us

with PAC 4gas velocityof liquid in .

with PAC 4gas velocityient in riser

e riser is uid level

the gas from the sing the

(6)

00 as a y, based

riser is

00 as a y, based .

64

since thand 2 tfractionwater apipe (1Fig. 7.given tIt is althougpressurfractionvolumeto the rconnec

Thipressurhigher pressurexpecteof a frmixturepipelineis also (gauge)Fig. 8.

Figu

vo

he differencto the DP sen. Using thand air at th.5 bar), we Ideally the

the same requite obvi

gh there ire method n compareetric, whichreal value sted to the frs comparisre sensors i

DP, equivre drop ued. This coriction come. This seeme pressure isupported b) versus ga

ure 7. Gas frolumetric me

ce between tensor then i

he densities he ambient e get the rele two methoesult, followious from s a good

overestimed to whh must be asince volumractions. son showsindicate movalent to supwards isuld be exp

mponent in ms plausibleincreases. Tby the variaas flow rat

fraction withethod versu

the two inles due to theof PAC aspressure in

lation showods should hwing a 450 l

the plot linearity,

mates the en using assumed cl

mes are dire

that the ore gas froaying that

s higher tlained in tethe multiphe since also

This assumption in preste as shown

h PAC 400 –us pressure.

ets 1 e gas s for n the

wn in have line. that the gas the

loser ectly

DP om a

the than erms hase

o the ption ssure n in

–

b

0.0couSinFignuhigfloof neiric

calpremavelvelThexpqu

Figure 8. Gbottom of ris

r

Fig. 8 sh012 m/s anuld be attrince only thg. 8, a detmber mustgh-speed viowmeter cou

the convenither electro

ch flows. Finally, th

lculated uesented earlay be seelocities ovelocity is fai

his is a reapected sincite complex

Gauge pressser as a funcrate for PAC

hows a linnd then a ibuted to ine gas flowrtailed calcu

await the ideo systemuld be used,ntional techomagnetic n

he bubble risusing the lier. This is en that foer 0.008 mirly constan

asonable vace the bubx for the hig

sure (in mbction of gasC 400.

near increassharper ris

ncreased turrate is measulation of R

analysis um. A fullbo, but very fe

hniques are nor acoustic

se velocitiedrift-flux

shown in For superfic

m/s the bubnt around 0alue, and sobble intera

gher gas flow

ar) at s inflow

se up to se which rbulence. sured for Reynolds using the re liquid ew if any feasible; c for gas

s may be model

Fig. 9. It cial gas bble rise 0.15 m/s. omewhat action is wrates.

65

Figure

PAC 4

At bubble becauseand in trains opipe wvisibly of the Coanda

For kind ofviscousdecreasshear deformmore su

Finastatic cFig. 10for the0.012 mseems t

Experim

Whallowedlevels seem toin this ngas todownco

e 9. Averag400, based o

gas flow lrise velo

e the bubblefairly stra

of bubbles wall, where

much highpipe. This

a effect. the shear

f dynamics s dampingses the col

thinning mation, and

usceptible tally conside

cases, all th0. From the e superficim/s. For hto be slightl

ments with hen the vad to circulais reached.

o the same anew situatioo the cromer. Impo

ge bubble rison drift-flux

lower than ocities are es move wi

aight paths. were devel

e the bubbher than in t

is very lik

thinning PAis modified

g of the llision stren

also incrthus mak

o coalescenering the co

he tests are graph thereial gas vehigher flowly higher fo

open valveslves are o

ate until a n. At first as the staticon the liquidrossover prtant new re

se velocity fx model (Eq

0.007 m/s much hig

thout collisIn some t

oped alongble speed the central kely a kind

AC system d due to hig

liquid whngth. Howreases bub

kes the bubnce. olumn lift in

summarizee is clear treelocities be

w rates, the r water.

s - circulatioopen, liquidnew equilibrsight this m case. Howd may transpipe and egimes occu

for q.5).

the gher, sions tests

g the was part

d of

this gher hich ever bble

ubble

n the ed in ends elow lift

on d is rium may ever

sport the

ur

whas

infratpipgraredgascirgasdo(diin De

accanalarbehpipforgra

detvaldopipbub

Figure 10. C

static bub

hen the liquin the examThe diffe

fluence thete. The equipes reflect adient. Gasduce the mis-lift effect rculation ves to ventiwncomer.ifference inthe riser wh

ensity variatWith PA

cumulation alysis somerger bubblhavior maype. This pipr the liquadually redu

To some termined anlves and cwncomer wpe which bbles.

Column liftbling - with

uid start to mple Fig. 11

rent flow gas fracti

librium liquthe diffe

s bubbles ixture densiis lost. This

elocity and ilate out aIt is only gas fractio

hich sets up

tions with tiAC, over

in the liquewhat, in ples with y continue ipe is supposuid densityuced.

extent thnd accountecomparing with the levecontains on

t for all the hout circula

flood the g1. regimes th

ion and ciruid levels inerence in in the dowity and mucs in turn redallows mor

at the topy the “exceon in the tw a lift effect

ime time t

uid complicparticular si

unpredictabinto the dowsed to be a ry, which

his effect ed for usinliquid leveel in a thirdnly liquid

fluids, ation.

gas down

hat arise rculation n the two pressure

wncomer ch of the duces the re of the

of the ess gas”

wo pipes) t.

he gas cates the ince also ble rise wncomer reference is then

can be ng closed el in the d thinner

without

66

Figuredow

bubbleconstan

In separatdowncoin the changephase) counterspecificpolymesmall blarge briding”the wvariatioscale imflow co Floodin

In teffects the wavelocityforces amiddle

e 11. Floodiwncomer wits agglomerantly varying

fr

circulation tion effectomer pipe. Triser. The of flow rand flow dyrcurrent floc and diffeer flows. Ibubbles flobubbles cau effect - th

wake of thons in Fig. mpact of thonditions in

ng dynamicthe downcopresent; 1)

all decreasy. For noa higher do(“core”) pa

ng of gas buth PAC 400ate, rotate ag patterns. Irom video.

mode als

ts takes This is diffeimmediate

regimes (siynamics in ows. This erent effectsn the riser

ow side by uses a type he small bubhe larger 12 mainly

he pressurethe riser an

s in downcoomer pipe bubbles inse the neaon-Newtoniownward liqart of the pip

ubbles into 0 liquid. Theand rearrangImage snaps

so bubble place in erent from fe reason is ingle and tconcurrent again sets

s in water both large sides, and of “piggyb

bbles followbubbles. show the l

e gradients nd downcom

omer there are

n the vicinitar wall liqan flows

quid flow inpe. 2) This

the e

ge in shot

size the

flow the

two-and

s up and and

d the back w in The arge and

mer.

two ty of quid this

n the

Fr

floo

Lift

hei

ght

(mm

)Li

ft h

eigh

t (m

m)

Lift

hei

ght

(mm

)

Figure 12. Driser and dowow rate. Circopened valv

(middle

0 0.000

100

200

300

400

500

600Liqui

Sup

R

D

0 0.000

100

200

300

400

500

600P20

Sup

R

D

0 0.000

100

200

300

400

500P40

Sup

R

D

Difference iwncomer asculation expes using wa

e) and PAC4

05 0.01 0

d (water) rise vers

perficial gas veloc

iser

owncomer

05 0.01 0

00 Liquid rise vers

perficial gas veloc

iser

owncomer

05 0.01 0

00 Liquid rise vers

perficial gas veloc

iser

owncomer

in liquid hes a functionperiments water (top), P400 (bottom

0.015 0.02

sus gas flowrate

city UGS (m/s)

0.015 0.02

us gas flowrate

city UGS (m/s)

0.015 0.02

us gas flowrate

city UGS (m/s)

ight in n of gas with fully AC200

m).

0.025

0.025

0.025

67

causes a “pinch” effect so that there is higher shear further away from the wall than for water. Since PAC is shear thinning this causes a reduction of apparent viscosity in the main flow of the pipe. So even though the downflow is stronger in the core, the reduced liquid viscosity in some cases may cause enhanced counter current upwards bubble flow compared to with water circulation.

Similar phenomena are seen in the riser, but with opposite effect. Bubbles rise faster close to the wall causing a positive feedback with increased wall shear stress and reduced apparent viscosity. As an example, this is as reflected in Fig. 9.

The high speed camera is particularly useful for this study. It enables both calculation of the liquid phase velocity with the addition of small tracer particles. It also visualizes the velocity profile, bubble size and bubble fractions profile, as well as bubble shape. CONCLUSIONS

Two different modes of operation were used, with and without external circulation, often referred in literatures to as bubble column and gas-lift mode. In this work the bubble column mode is mainly used as an indicator of the gas rise velocity as reflected in the gas fraction.

It was found that gas-lift with Newtonian and non-Newtonian liquids differ in several ways. Fig. 10 and 12 illustrate the overall behavior in various ways. These are not conclusive until a more detailed analysis from high-speed recordings is done. The lift in the non-Newtonian PAC 200 case is slightly higher for low gas flow rates than the corresponding Newtonian case, even though the overall viscosity of water is lower.

The interpretation is therefore not straightforward, since the lift process dynamics involves both the liquid viscosity and the density. The main mechanisms seems to be the reduced rise velocity of the

gas bubbles which increases gas fraction as seen in the “static” experiments where both of the crossovers valves were closed. Reduced density should in the case of equal viscosity lead to higher flow. However for PAC the viscosity is higher and friction increases. The flowing case (circulation mode) is in accordance with this conclusion, but is complicated by the gradual saturation of small and microscopic bubbles over time.

The effect of gas bubble size is for the present initial study difficult to estimate, since bubble size was not easily controllable. Similar conclusions are given in most publications too; that diameter of gas sparger orifices has small effect on the overall gas fraction and pressure drop. We conclude this from a theoretical point of view; the bubble rise velocity approaches zero for small bubbles, and thus the gas fraction would increase with smaller diameter. This would be even more pronounced with shear thinning fluids like PAC.

For the bubble column mode this would lead to accumulation of time until the gas creates a foamy mixture at the sparger, eventually leading to slugging when the foam breaks. For the gas-lift mode a similar effect is expected, although taking much longer time and leading to a more even gas distribution.

Friction is modified by the bubbly flow as compared to single phase flow for both the Newtonian and the non-Newtonian case, in accordance with the general conclusion in most published works8. ACKNOWLEDGMENTS

We greatly acknowledge the work of bachelor students Bjørn Holien and Knut Jørgen Brodahl. They have contributed very much experimentally to this work, with flow loop building, pictures and data recording.

68

REFERENCES 1. Chhabra, R.P. and Richardson, J.F.(1999), “Non-Newtonian Flow in the Process Industries - Fundamentals and Engineering Applications”, Butterworth-Heinemann. 2. Clift, R., Grace, J.R, and Weber, M.E. (1978) “Bubbles, Drops and Particles”, Academic Press. 3. Gavrilescu, M., and Tudose, R.Z. (1997), “Hydrodynamics of non-Newtonian liquids in external-loop airlift bioreactors. Part 1: Study of the gas holdup”, Bioprocess and Biosystems Engineering, 18, 17-26. 4. Gavrilescu, M., and Tudose, R.Z. (1997), “Hydrodynamics of non-Newtonian liquids in external-loop airlift bioreactors – Part 2: Study of the liquid circulation velocity”, Bioprocess and Biosystems Engineering, 18, 83-89. 5. Li, H. Z. (2001): “Towards the understanding of bubble interactions and coalescence in non-Newtonian fluids- a cognitive approach”, Chemical Engineering Science, 56, 6419–6425. 6. Merchuk, J.C. (1986), “Hydrodynamics and Hold-up in Air-Lift Reactors”, In Encyclopedia of Fluid Mechanics, Vol 3; Gas-Liquid Flows, pp.1485- 1511, Gulf Publishing. 7. Merchuk, J.C. (1986), “Gas Hold-Up and Liquid Velocity in a Two-Dimensional Air Lift Reactor”, Chemical Engineering Science, 41, 11-16. 8. Pauli, J., Menzel, T, and Onken, U. (1989), “Directional Specific Shear-Rate Measurements in Gas-Liquid Two-Phase Flow”, Chem. Eng. Technology, 12, 374-378.

9. Smita, S.L. and Joshi, J.B. (1993), “Hydro dynamics and Mass Transfer in Air-Lift Loop Reactors”, In Encyclopedia of Fluid Mechanics, Supplement 2; Advances in Multiphase Flow, Gulf Publishing, pp.405 - 510. 10. Sivakumar,V., Akilamudhan, P., Senthilkuma, K., Kannan, K. (2011), “Prediction of Gas Hold-Up in a Combined Loop Air Lift Fluidized Bed Reactor Using Newtonian and Non-Newtonian Liquids”, Chem. Ind. Chem. Eng. Q., 17, 375−383. 11. Sivakumar, V., Kannan, K, Akilamudhan, P. (2010), “Prediction of Riser Gas Holdup in Three- Phase External Loop Air Lift Fluidized Bed Reactor”, Modern Applied Science, 4, 75-87. 12. Taitel,Y., Barnea, D. and Dukler, A.E. (1980), "Modelling Flow Pattern Transitions for Steady Upward Gas - Liquid Flow in Vertical Tubes", AIChE J., 26, 345-354.

69