Effect of Drag-Reducing Polymers on a Vertical Multiphase ... · Effect of Drag-Reducing Polymers...

Effect of Drag-Reducing Polymers on aVertical Multiphase Flow

by

G.M.H. Nieuwenhuys

MEAH: 230

Supervisor: dr. ir. R. Fernandes

Period of work:February – August 2003

Afstudeerverslag voor het examen van Natuurkundig ingenieurAfdeling Technische Natuurkunde van de faculteitTechnische NatuurwetenschappenVakgroep Fysische Stromingsleer

Afstudeerproject uitgevoerd bijShell International Exploration and Production B.V.SIEP EPT ANE, RijswijkExploratory Research

Afstudeerhoogleraar: prof. dr. ir. G. Ooms

Afstudeercommissie: prof. dr. ir. G. Ooms prof. dr. ir. F.T.M. Nieuwstadt prof. dr. R.V.A. Oliemans dr.ir. R. Fernandes dr. R. Delfos

G.M.H.Nieuwenhuys - 1 - MEAH 230

SUMMARY

The effect of the addition of small amounts of drag-reducing polymers to a vertical water-gas flow has been experimentally investigated. The objective is to reduce the frictionalpressure drop in oil and gas wells. The pressure drop in a vertical flow is due to hydrostaticand frictional effects.

The effect of the polymer was studied in two experimental facilities at Shell in Rijswijk. Avertical perspex pipe with a length of 18 m and diameter of 72 mm was used at first. In thisset-up, the pressure drop was dominated by the hydrostatic head due to low flow rates.The Multiphase Plug & Play Gas-Lift (MPPGL) set-up was constructed during thisinvestigation to test vertical multiphase drag reduction for flows where frictional pressuredrop dominates. In this set-up, consisting in a vertical perspex pipe with a length of 3 mand diameter of 40 mm, high flow rates are obtained with mixture Reynolds numbers up to500,000. The flow patterns during the experiments were bubbly and slug flow.

The main conclusions of this investigation are:

• No strong conclusions can be made as to whether polymers can reduce friction invertical multiphase flow. We suggest that the MPPGL set-up did not allow the correctmixing of the polymers and the development of the flow.

• A coherent set of data obtained in both set-ups has shown that the addition ofpolymers to a water-air flow induces an increase in the hydrostatic pressure drop. Forflows having a void fraction between 36% and 83% and a negligible amount of friction,an absolute decrease in void fraction has been measured within a range of 2% to 12%.

• We argue that the polymers diminish the turbulence intensity in the flow and lessenthe break-up mechanism. This leads to larger bubbles and consequently a migration ofthe gas towards the center of the pipe. This effect has been calculated using the drift-fluxmodel and is responsible for higher actual gas velocities and a shorter residence time ofthe bubbles in the pipe. This is equivalent to lower void fractions and higher hydrostaticpressure drops.

• A change in flow regime due to the addition of polymer has been visualised:

o The size of the bubbles is increased.

o The bubble to slug flow transition occurs for lower superficial gas velocities.

Thus, it has been found that polymers have a negative effect on the hydrostatic pressuredrop. The effect of the polymers on the frictional pressure drop remains unknown andshould be subject to further investigation.


INDEX OF SYMBOLS

Roman symbols

Symbol Explanation [Dimension]

A Area [m2]

BHP bottom hole pressure [bar]

c0 distribution parameter [-]

CL net transferred lift coefficient [-]

D diameter [m]

g gravitational constant [m2/s]

f friction factor [-]

L tubing length [m]

M molecular weight kg/kmol

.

m mass flux [kg/s]

p pressure [bar]

Q volumetric flow rate [m3/s]

Re Reynolds number [-]

R universal gas constant J/kmol.K

u velocity [m/s]

T torque [N.cm]

We Weber number [-]

wppm weight parts per million [-]


Greek symbols

Symbol Explanation [Dimension]

α void fraction [-]

Ä difference [-]

å dissipation m2/s3

ϑ angle [rad]

ë volume fraction [-]

ì dynamic viscosity [Pa s]

ρ density [kg/m3]

σ surface tension [N/m]

Subscripts

Symbol Explanation

b bubble

DRA with DRA

c continuous

e equivalent

f friction

g gas

l liquid

m mixture

max maximum

r relative

sg superficial gas

sl superficial liquid

Field units

Unit Explanation (Conversion to SI unit)

bbl barrel (= 0.258987 m3)

bpd barrels per day (= 0.11 l/min)

sl standard liters

KEYWORDS

multiphase, drag reduction, friction, polymer, slug flow, bubbly flow, DRA, drag reducing agent,hydrostatic pressure drop, void fraction, drift-flux model, gas-lift, distribution parameter, risevelocity


TABLE OF CONTENTS

SUMMARY 1INDEX OF SYMBOLS 21. INTRODUCTION 5

1.1. Oil wells and gas-lift 51.2. Background of drag reduction 61.3. Objectives 61.4. Outline 7

2. THEORETICAL BACKGROUND 82.1. Multiphase flow 8

2.1.1. An overview 82.1.2. Multiphase flow patterns 92.1.3. Bubble sizes and rise velocities 112.1.4. Pressure gradient 122.1.5. Drift flux model 132.1.6. Bubble break-up theory 16

2.2. Multiphase drag reduction 162.2.1. Definition of the amount of drag reduction 162.2.2. Mechanisms for drag reduction 172.2.3. Drag-reducing polymers 18

3. EXPERIMENTAL SET-UP AND INSTRUMENTATION 193.1. 18m gas-lift set-up 193.2. Multiphase Plug & Play Gas-Lift set-up 20

3.2.1. Description 203.2.2. Liquid-gas separation 233.2.3. Hold-up and drag reduction measurement 24

3.3. Polymer DRA injection system 253.4. Polymer solutions 26

3.4.1. Description 263.4.2. Degradation 263.4.3. Drag reduction 26

4. RESULTS 284.1. Experimental results 28

4.1.1. Results in the 18m gas lift set-up 284.1.2. Results in the Multiphase Plug & Play Gas-Lift set-up 31

4.2. Theoretical results 394.2.1. Flow pattern 394.2.2. Hydrostatic pressure drop 404.2.3. Hinze theory 42

5. CONCLUSIONS AND RECOMMENDATIONS 465.1. Conclusions 46

5.1.1. Multiphase Plug and Play Gas-Lift set-up 465.1.2. Experimental results 46

5.2. Recommendations 475.2.1. Multiphase Plug & Play Gas-Left set-up 475.2.2. Vertical multiphase drag reduction 48

REFERENCES 49ACKNOWLEDGEMENTS 51


1. INTRODUCTION

Oil is a primary demand to modern society and is used all over the world for i.e. fuel,lubricant and plastics. Oil reserves are not infinite, and this has lead to an awareness of thedependence on the oil industry. This means we have to use existing oil reserves moreefficiently and that we have to explore new sources of energy. Drag reduction experimentsare a good example of research in efficient depletion of oil wells. It enables to produce oiland gas more efficiently.In this chapter a short introduction is given treating oil wells and the principle of gas-lift,which generates vertical two-phase flows. The background of drag reduction is thendiscussed followed by the objectives of this investigation and the outline of this report.

1.1. Oil wells and gas-lift

Oil and gas result from a long process. Producing oil starts with finding an oil-reservoir,defined as a porous layer in the ground, containing hydrocarbons and water. Reservoirsexploited in the industry are typically situated between 1 and 5 km depth with pressuresand temperatures up to respectively 200 bars and 180 �C.Natural flowing wells and gas-lift wells are two standard types of vertical oil wells, bothused in the industry. The installation that connects the reservoir to the flow line on thesurface is called the well completion and is depicted in Figure 1. A well is drilled and theborehole is secured by the casing down to the depth of the reservoir; this is the outer wallof the completion. A string of pipe called the production tubing is then installed from theproduction platform to the reservoir. The annulus is denominated as the space between thecasing and the tubing. A packer is placed to prevent the oil from flowing up the annulus atthe bottom of the casing. At the reservoir depth, perforations are shot into the tubing, toenable oil to flow from the reservoir into the tubing. The set of valves on top of thetubing is called the Christmas tree. When oil flows out of the well it enters the flow linethrough the production choke valve.

Figure 1: A natural flowing well (left) and a gas-lift well (middle)


The bottom hole pressure (BHP) is defined at the depth of the perforations and is equal tothe hydrostatic pressure drop of the column of oil, water and gas in the tubing. The tubingpressure head (TPH) is the pressure defined just upstream of the choke. The BHP dependson the height of the tubing and the density of the mixture. In natural flowing wells thereservoir pressure is much higher than the BHP, which enables the oil to flow to thesurface. When the oil has flown out of the reservoir causing a reservoir pressure lower thanthe BHP, the production ceases after having decreased significantly.In gas-lift wells, gas is injected into the tubing. Low gas densities cause mixture densityreduction, and thus a decrease in the hydrostatic head. The BHP decreases by consequenceand higher production rates can be reached. The injection of gas generates a two-phasevertical oil-gas flow in the tubing. This flow has different properties than a single phaseflow, as will be described in more detail in section 2.

1.2. Background of drag reduction

In a vertical well the pressure loss is dominated by hydrostatic and frictional pressure loss(see section 2.1.4). As we have seen in the previous section, it is key to minimise thepressure drop in the tubing. Gas-lift wells enable to decrease hydrostatic pressure drops;drag reduction with use of drag reducing additive agents (DRA) allows to reduce frictionalpressure losses. As stated in [2], the first large scale commercial use of drag reducingpolymers took place in the Trans Alaska Pipeline in 1979 [3]. An increase in throughput of200 M bbl/day to the 150 MM bbl/day level was attributed to the application of the dragreducing additive agent.

The application of DRA to crude and refined product (kerosene, diesel) pipelines hasbecome widespread from that moment onward. Both in academia as in the industry,numerous publications have treated the subject of single-phase drag reduction. However,the theory about the physical mechanism which causes drag reduction in single-phase flowsis still unclear and no generally excepted proposal exists. Drag reduction work is scarcewhen it comes to multiphase flow, compared to that achieved in single-phase flow [8]. Therare amount of work published is focussed on horizontal flows. Fernandes [2] hasdescribed multiphase drag reduction in a horizontal two-phase flow, and showed resultswith DRA giving up to 65% drag reduction.

Gas-lift wells create oil-gas flows in vertical production tubing. Vertical flows have thecomplication that the hydrostatic term generally has a significant contribution to thepressure drop. Since drag reducers change the flow regime, even if they decrease thefrictional component of the pressure gradient, they may inadvertly increase the hydrostaticcomponent. The effect of drag-reducing polymers on a vertical multiphase flow remainsuninvestigated, and forms the topic of the present research.

1.3. Objectives

The main objective of this report is to document the experiments performed in the 18mhigh gas-lift set-up and the Multiphase Plug and Play Gas-Lift (MPPGL) set-up of Shell inRijswijk. In the first facility the hydrostatic pressure effects of DRA are studied, togetherwith a visualisation of their influence on vertical two phase flow in bubbly and slug flowregime. An important part of this work consisted in the design and construction of theMPPGL set-up. This facility has been designed and set up to study vertical multiphase dragreduction for regimes in which friction dominates. In this set-up, the influence of DRA onhydrostatic pressure drop will be further tested and the effect on the frictional pressuredrop will equally be tested. This brings us to define the main objective of the investigation:


The objective of this research is to experimentally investigate the influence of drag-reducing polymers on a vertical two-phase (water-gas) flow.

The experiments described in this investigation will attempt to answer the followingquestions:

• Do drag-reducing polymers generate drag reduction in vertical multiphase flowsand if so in what kind of scale does this occur?

• Do drag-reducing polymers affect the hydrostatic pressure drop in verticalmultiphase flows, and if so in what kind of scale?

• Do drag-reducing polymers affect the flow regime in vertical multiphase flows?

1.4. Outline

The outline of this report is as follows. Section 2 contains the necessary theory onmultiphase flow and multiphase drag reduction. Section 3 describes the experimentalfacilities that were used to acquire the results for this investigation, which are presented insection 4. In section 5 the main conclusions of this investigation are summarized and arecommendation for further work is given.


2. THEORETICAL BACKGROUND

This section will describe the necessary theory concerning multiphase flow and dragreduction.

2.1. Multiphase flow

Multiphase flow is characterized by the existence of interfaces between the phases anddiscontinuities of associated properties. Multiphase flow is classified according to theinternal phase distributions or flow patterns and its properties differ from a single phaseflow. In an oil well different patterns can occur and these patterns can change from thebottom to the top of a well, which makes a good understanding of multiphase flow vital tothe oil industry. We will look at these patterns in more detail in section 2.1.2. At first, wewill go through basic definitions necessary to obtain an understanding of multiphase flow.Section 2.1.3 and 2.1.4 will respectively describe properties of gas bubbles in a multiphaseflow and the pressure gradient in such a flow. Finally, a model used in the oil industry isdescribed. Additional information can be found in the course on applied multiphase flows[7].

2.1.1. An overview

The gas density ρg is given by:

RTMp

g =ρ {1}

M is the molecular weight (kg/kmol), p the pressure (Pa), R the universal gas constant(J/kmol.K), and T is the temperature (K).

The liquid and gas flow rates, respectively Ql and Qg (m3/s), are given by:

l

ll

mQ

ρ&

= , g

gg

mQ

ρ

&= {2}

In this formula .

m designates the mass flux (kg/s).

The superficial velocity (usl and usg (m/s)) is the velocity a phase would have when flowingalone in a pipe:

A

m

A

Qu

l

llsl ρ

.

== , A

m

A

Qu

g

ggsg ρ

.

== {3}

A (m2) is the cross sectional area of the pipe. The mixture propagates at the velocity whichis the sum of the liquid- and gas velocities. This is called the mixture velocity um:

slsgm uuu += {4}

The hold-up is defined as the area of the pipe cross section which a certain phase (ággg and ál

for gas and liquid hold-up) occupies compared to the total area of the pipe cross section:

l

sll u

u=α ,

g

sgg u

u=α {5}


The gas hold-up is often referred to as void fraction (á), and we will do so throughout thisreport. The volume phase fraction (for liquid and gas respectively ël and ëg) is defined as:

m

sll u

u=λ ,

m

sgg u

u=λ {6}

When there is no slip between the phases, i.e. they move at the same velocity, the volumefractions and hold-ups are equal. This is called no-slip or homogenous flow. In reality, thephases often do not move at the same velocity because of slip which occurs between thephases. In this case, lα is larger than lλ , and the phases have relative velocities defined as:

l

sll

uu

α= ,

g

sgg

uu

α= {7}

Finally, the density of the mixture is defined:

( ) glm αρραρ +−= 1 {8}

In this equation, ñl denotes the liquid density (kg/m3).

2.1.2. Multiphase flow patterns

In gas/liquid flow both phases can adopt different geometric configurations, which arecalled flow patterns or flow regimes. In a vertical pipe with gas and liquid, four flowpatterns are commonly used. These are depicted in Figure 2, where from left to right, theamount of gas in the pipe is gradually increased.

Figure 2: Schematic representation of four different flow patterns

Bubbly flow occurs at low to moderate liquid and gas flows and low void fractions. The gasbubbles have approximately the same size and are homogeneously distributed in the pipecross-section.


Slug flow occurs at low to moderate liquid and gas flows and high void fractions. The flowconsists of large bullet shaped bubbles, so called Taylor bubbles, and small bubbles inintervening liquid cylinders.

Churn or froth flow occurs at high liquid and gas rates, when the flow is highly turbulent.It is a very unstable flow of oscillatory nature, whereby the liquid near the pipe wallcontinually pulses up and down.

Annular flow occurs at very high gas rates. The flow consists of gas with small droplets ofliquid in the centre of the tube, and an annular film of liquid on the wall. In annular flow, aphenomenon called entrainment can take place when liquid drops are carried along into thecore of the flow from the liquid film.

10

1

.1

.01

.1 1 10 100

Superficial gas velocity (m/s)

Annular dispersed

Intermittent/slug

Bubble

Dispersed bubble

Su

per

fici

al li

qu

id v

elo

city

(m

/s)

Figure 3: Flow pattern map for a vertical water gas flow. The pipe diameter is40 mm. The flow pattern is plotted as function of usg and usl

A so-called flow pattern map can be made using the computer code TWOPPI [28]. Such amap is plotted in Figure 3. Different flow patterns can occur depending on operationconditions, fluid properties, flow rates, orientation and geometry of the tubing. Thephysical parameters that play a major role in determining the flow pattern are surfacetension and gravity. The surface tension keeps pipe walls wet and tends to make smallliquid drops and small gas bubbles spherical. The rate of exchange of mass, momentumand energy between gas and liquid phases depends on the different internal flowgeometries, and so on the different flow patterns. For example, relationships for pressure


drop are more likely to be different for bubbly flow than for annular flow. This leads to theuse of flow-pattern dependent models and appropriate flow pattern transition criteria. Foroil production bubbly flow and slug flow are the most common regimes, but bubbly flow ispreferred above slug flow, because slug flow creates instabilities and undesired pressurefluctuations in the pipe. A recent paper by Guet et al. [10] describes the transition betweenbubbly flow and slug flow. This transition is important for the oil industry because itaffects the gas-lift efficiency. The amount of gas injected into the tubing increases until at acertain point the bubbly flow transitions to a slug flow. This transition can be seen inFigure 3. Because bubbly flow is preferred above slug flow, it is key to postpone thistransition as much as possible in terms of increasing gas rates. It is currently believed thatthe transition has a strong relation with the bubble size. Song et al. [5] experimentallyshowed that the critical void fraction at which the transition occurs is not a fixed value, buta value that increases with decreasing bubble size. The experimental results from Guet etal. [10] equally confirmed this for water. The critical void fraction depicts the critical valueabove which transition to slug flow takes place.

Gas wells commonly operate in annular flow. Much work has been done concerning thedifferent transitions between flow regimes. More information on flow pattern transitioncan also be found in [11].

2.1.3. Bubble sizes and rise velocities

The rise velocity of a bubble in a vertical pipe is not constant and interesting for the oilindustry. The lower the velocity of a gas bubble, the longer it’s residence time in the fluidand thus the more effective the gas-lift. The velocity of a bubble depends on the size andthe shape of the bubble. Two opposing mechanisms are responsible for the size and shapeof a bubble, namely surface tension and turbulence. The turbulence of the flow tends tobreak up the bubbles until a new dynamic equilibrium is reached. The break-up can occurby local viscous shearing or by dynamic pressure fluctuations. The vortices in a turbulentflow are responsible for the break-up of the bubbles. The smaller the vortices are, thelarger the pressure gradient is over the vortex. This is why vortices slightly larger than theKolmogorov scale [30] are held responsible for the break-up [24]. Break-up will be furtherdiscussed in 2.1.6. The surface tension allows the creation of spherical bubbles and thebalance of these two mechanisms results in the size and shape of a bubble. Clift et al. [12]showed a relation between the bubble size and the terminal rise velocity in water. This isdepicted in Figure 4.

In the graph, the equivalent diameter, the diameter of a non-spherical bubble if it would bespherical, is plotted on the x-axis and the terminal velocity is plotted on the y-axis. For apure liquid the rise velocity shows a peak, while for a contaminated liquid a peak is absent.For the water-based mixture used in these experiments, a partially contaminated liquid isassumed.

For bubbles with a diameter between 0.2 mm and 2 mm, the bubble rise velocity increaseswith the bubble diameter, up to typical values of 18 cm/s. Bubbles with a diameterbetween 2 and 20 mm have a rise velocity which is more or less constant around 20 cm/s.For slugs that have the same diameter as the pipe, the rise velocity is given by [7]:

( ) 2/135.0 gDub = {9}

In this equation, D denotes the pipe diameter.


Figure 4: Terminal velocity versus equivalent diameter in water according toClift et al. [12]

2.1.4. Pressure gradient

The pressure drop required to lift a fluid through the vertical production tubing at a givenflow rate is essential for the productivity of a well. It is key to minimize this pressure dropin the oil industry. With the use of a mass and momentum balance over a pipe segment anequation for the pressure gradient in a pipe segment can be derived:

( )

++++=−

l

sll

g

sggllgg

mmmm uu

dxd

gD

uuf

dxdp

αρ

αρθραρα

ρ 22

sin2

{10}

In this equation, fm is the friction factor and è is the angle between a horizontal plane andthe pipe. This pressure gradient consists of three parts:

• Frictional part, caused by the dissipation of energy by viscous forces in the liquid.This term depends strongly on the fluid properties, flow regime and the speed ofthe flow. We will go into more detail below.

• Gravitational part, caused by the gravity force acting on the oil in the productiontubing. In this report, the pipes are vertical and the angle è is 90º. The gravitationalpressure drop, also called the hydrostatic head, can also be written using themixture density defined in equation {8}:

gdxdp

mg ρ=− )( {11}

• Acceleration part, caused by the acceleration of the phases due to expansion. Inthis report, the acceleration term is neglected, since viscous and gravity effects aremore important in these situations.


With equation {11} the pressure loss in the tubing can be calculated, although thiscalculation is not always straightforward. The Fanning friction factor fm is calculated usingthe Moody diagram [7]. The Reynolds number of the mixture is computed as follows:

l

mmm

uD

µρ

=Re {12}

In this equation, µl (Pa.s) is the dynamic viscosity of the liquid. The hydrostatic head iscomputed using equation {11}. The mixture density is calculated using the void fraction. Insection 2.1.5 we will explain how the void fraction is calculated.

The frictional and gravitational pressure gradient dominate the acceleration pressuregradient. However, whether the pressure gradient is dominated by friction or gravitationdepends on the nature of the flow, i.e., operation conditions, fluid properties, flow rates,orientation and geometry of the tubing. The gravitational pressure depends only on themixture density. In most cases, gρ << ρl, and the hydrostatic head is important at low void

fractions. Friction becomes important when flow rates increase to high values and whenthe pipe diameter decreases. Using the computer code TWOPPI [28], it is possible tocompute the ratio between the frictional and hydrostatic pressure gradient in a pipe for ascale of different liquid and gas flow rates. Table 1 shows the output for a vertical flow ofwater and gas in a pipe of diameter 40 mm.

Table 1: Percentage of frictional pressure gradient over the total pressuregradient in a vertical pipe for different liquid- and gas flow rates. Thepipe has a 40 mm diameter and the fluids are water and air

Qg (sl/min) 0 30 50 80 110 140 170

Ql (l/min)

10 0% 0% 0% 1% 15% 28% 38%

20 2% 5% 12% 25% 38% 48% 56%

30 5% 14% 23% 37% 48% 57% 64%

40 8% 22% 41% 45% 56% 64% 70%

50 12% 28% 45% 51% 60% 68% 73%

60 16% 36% 48% 62% 64% 71% 76%

70 20% 40% 52% 65% 67% 73% 78%

80 25% 44% 55% 67% 70% 75% 80%

Equation {3} enables to compute the gas and liquid superficial velocities belonging to thedifferent flow rates in this table. This gives an idea of the flow regime belonging to theabove flow rates.

2.1.5. Drift flux model

In the oil industry, this model is widely used to calculate the void fraction in pipe flows. Itwas presented by Zuber and Findlay [13] in 1965 and incorporates two important aspects:


• Gravitational forces give bubbles a tendency to rise in a liquid. There is a differencebetween the velocities in the two phases, giving rise to the slip effect.

• The gas fraction is not uniformly distributed along the cross section of the pipe,which leads to different velocity profiles. According to these different profiles acorrection has to be made for the centerline velocity.

The basic assumption of the model is:

bmg uucu += 0 {13}

In this equation c0 is the distribution parameter and ub is the rise velocity of the bubbles. c0

will be described in the next section. The rise velocity takes care of the effect of the localrelative velocity and has been described in 2.1.3. c0 and ub are assumed to be known [13].When we equally know um, ug can be calculated from equation {13} and the void fractioncan be computed using equation {7}.

2.1.5.1. Distribution parameter

The distribution parameter takes into account the difference in mixture velocity betweenthe centerline and the average. If you would have a uniform flow of a homogeneous liquid,the distribution parameter would be equal to unity, since the centerline velocity and theaverage velocity are the same. If the concentration is not uniformly distributed two optionsare possible:

• Core peaking: the concentration of bubbles at the centerline is larger than at thewall. c0 can attain values op to 1.2.

o c0 > 1

• Wall peaking: the concentration of bubbles at the centerline is smaller than at thewall

o c0 < 1

The c0 parameter is assumed to be dependent on flow regime. The transition of the c0

parameter is not step wise, but gradually. In experiments conducted by Tomiyama et al.[21] a correlation is found between the net transverse lift coefficient CL and the bubblesize. The lift coefficient is responsible for the distribution profile of the bubbles. Threeregimes are distinguished. The graphical representation of the correlation is given in thefollowing Figure 5.

The experimental data has been obtained in a high viscosity system. Since the data yield thesame values for small bubbles in water-air systems, it can be applied to those systems aswell. For the region of bubbles smaller than 0.4 mm a uniform distribution profile isassumed, since bubbles with very small Reynolds numbers (Re< 300) rise in a straight line,stated by Iguchi et al. [27]. In the graph this implicates a net transferred lift coefficient ofzero, i.e. the neutral regime. The wall regime depicts a wall peaking flow, the core regime acore peaking flow.


Figure 5: Correlation between the net transferred lift coefficient and bubblediameter for an air water system. Also the three regimes of thedistribution are postulated

Guet et al. [31] experimentally investigated the effect of the bubble diameter on thedistribution parameter. He found that co depends on the bubble size, and was increasingfrom 0.95 to 1.2 with this bubble size. This effect is visible in Figure 6. For small bubbles,the well-known wall peaking is found, while for larger bubbles a core peaking flow isobtained. This is in agreement with the correlation proposed by Tomiyama. At wallpeaking conditions, the distribution parameter can be below 1 while at core peakingconditions co tends to a typical value of 1.2. This value is common for slug flow. Guetcompared the measured distribution parameters to the bubble size dependent relationrecently proposed by Hibiki et al. [32]. The qualitative effect measured by Guet andTomiyama seems to be in accordance with the relation proposed by Hibiki. Thiscorrelation is also plotted in Figure 6.

Figure 6: Distribution parameter c0 versus the bubble diameter experimentallydetermined by Guet et al. [31]. Also the correlation proposed byHibiki et al. [32] is plotted


2.1.6. Bubble break-up theory

The study of the break-up mechanisms for bubbles and drops originated in the 20th

diameter of a bubble in a turbulent two-phase flow. This balance states that a bubble willnot break if the ratio of the inertia force, which creates the deformation, and the opposingsurface force, which tries to keep bubbles spherical, does not exceed a critical value. Themodel of Hinze is relatively simple and therefore widely used. However, it is very difficultto determine the critical value for the force ratio and this makes the absolute values of theoutcome of the model discussable.

The ratio discussed above is the Weber (We) number:

σρ du

We rc2

= {14}

In this equation, ñc (kg/m3) is the density of the continuous phase and ur (m/s) is therelative velocity. A critical value for the We-number can be found by experiments, which isused to determine the maximum stable bubble diameter dmax.

4.0

6.0

max . −

= ε

ρσ

l

constd {15}

In this equation, å (m2/s3) is the turbulent rate of dissipation per unit mass and σ denotesthe interfacial surface tension (N/m). The constant in the equation for the maximum stablediameter has been determined experimentally for different flow configurations. Theconstant is approximately 2. Walstra [25] found the constant to be equal to 2.3, Vaessen[26] found a value of 1.9 and Hinze suggests a value of 0.725. The value to use is subject tomuch discussion. In this report, we will use the value 2.0 [29].

2.2. Multiphase drag reduction

2.2.1. Definition of the amount of drag reduction

Drag reduction is a flow phenomenon by which small amounts of additives, e.g. a fewweight parts per million (wppm), can greatly reduce the turbulent friction factor of a fluidor fluids. The aim for the drag reduction is to improve the fluid-mechanical efficiencyusing active agents, known as polymers. In a single-phase flow, drag reduction is defined asthe reduction of friction below that which would occur for the same flow without the drag-reducing additive. By consequence, we define drag reduction in a vertical multiphase flowas the reduction in the frictional pressure drop when the flow rates are held constant:

f

DRAff

P

PPDR

∆

∆−∆= {16}

ÄPf denotes the frictional pressure drop without the presence of DRA while ÄPf DRA standsfor the pressure drop with addition of drag reducing additives. A second definition for theamount of drag reduction is given using the friction factor introduced in equation {11}:

f

fDR DRA−= 1 {17}

f and f DRA are the frictional factors with and without the presence of DRA.


Finally, the amount of drag reduction can also be related to the reduction in the amount oftorque, T. This is expressed in the following equation:

T

TDR DRA−= 1 {18}

In this equation T and TDRA denote the amount of torque without and DRA. In a followingchapter we will use this expression to shown an example of drag reduction.

2.2.2. Mechanisms for drag reduction

Despite the extensive research in the area of drag reduction over the past decades, there isno universally accepted model that explains the mechanism by which macromolecules aspolymers reduce friction. A comprehensive mechanism would have to address the role ofthe polymer structure, composition and microstructure as well as polymer-solventinteractions in the drag reduction phenomena. An overview of important results achievedin both single phase and multiphase drag reduction will be given in the followingparagraphs.

During the last 50 years, numerous papers have been written, discussing severalexperimental, numerical and theoretical aspects of drag reduction of turbulent flows bypolymer additives. A general review of drag reduction is available in Lumley [18] and morerecent work can be found in Gyr & Bewersdorff [20].

Lumley came with a theory about drag reduction in 1969. He stated that the stretching ofrandomly coiled polymers increase the effective viscosity. By consequence, small eddies aredamped which leads to a thickening of the viscous sub layer and thus drag reduction. DeGennes [19] proposed a new theory which argues that drag reduction is caused by elasticproperties rather than viscous. He came to this hypothesis by observing drag reduction inexperiments where polymers were active at the centre of the pipe, where viscous forces donot play a role. He arguments that the elastic properties of polymers cause shear waves toprevent the production of turbulent velocity fluctuations at the small scales. Virk et al.[35]observed that the amount of drag reduction is limited by an empirical asymptote, called theVirk asymptote.

Single-phase drag reduction is still the subject of much research. As to multiphase flow,very little research has been published, and in all cases this research describes the reductionof friction in horizontal flows. A remarkable aspect of the addition of polymers tomultiphase flow is not only the drag reduction which can be measured, but also thechanges in the configurations of phases or flow patterns. For example, Al-Sarkhi andHanratty [17] found that the injection of a concentrated solution of polyacrylamide andsodium acrylate into an air-water flow in a horizontal pipe changed an annular pattern to astratified pattern by destroying the disturbance waves in the liquid film. Drag reduction of48% was measured for mean concentrations of 10-15 wppm.

Fernandes [2] tested high molecular weight poly-alpha-olefin DRA’s for gas-condensatetwo-phase flows and observed drag reductions up to 65%. These polymers are typicallyused for oil flows. The polymers modified the multiphase flow pattern. Annular entrainedflows changed into annular flows without entrainment or stratified flows; wavy stratifiedflows changed into smooth stratified flows; and slug flows changes into stratified flows. Inall cases the flow pattern affected by the addition of DRA’s had less mixing and interactionbetween the phases. This results in less momentum transfer between phases and lesskinetic energy to be dissipated due to interfacial effects, and thus drag reduction. The other


main mechanism of multiphase drag reduction described is turbulence suppression in theliquid phase, just as in a single-phase flow.

2.2.3. Drag-reducing polymers

The additives, which cause drag reduction, can be split into three groups: polymers,surfactants and fibres. Surfactants can reduce the surface tension of a liquid. Fibres arelong cylinder-like objects with high length to width ratio. They orient themselves in themain direction of the flow to reduce drag.

In their extended configuration, polymers have a size which is much smaller than thesmallest length scale of the turbulence. A well known effect is the increase of the shearviscosity of a fluid due to polymers, which gives reason to suspect that polymers can at themost affect the microscales of the turbulence. That polymers affect the macrostructure ofthe turbulence, which is responsible for the transport of momentum that results in drag,seems unlikely. However, the story is completely different. Polymers are primarily active onthe microscale of the turbulence but also influence the macroscales of the turbulence. Moreinformation to this subject can be found in [16].

Research on polymers originated with the development of the chemical industry in the 20th

century. Polymer solutions are now widely used for many applications, i.e. the oil, food,cosmetics and chemical industry.

General guidelines for the selection of a DRA for a given multiphase flow application donot exist. The most important requirement is that the DRA is soluble in the liquid. Inaqueous systems, hydrolysed polyacrylamide and polyacrylate are used. Polyacrylamide is along-chain synthetic polymer that acts as a strengthening agent, binding soil particlestogether. A chemical structure of polyacrylamide is given in Figure 7.

Figure 7: Chemical structure of polyacrylamide

Many polymers based on polyacrylamide are used to obtain drag reduction in the industry.In section 3.4, the different polymers tested in these experiments are described.

Upon the solubility of the chemical, it is known that the following properties influence theperformance of the polymer:

• High molecular weight (M> 106 g/mol)

• Shear degradation resistance (see section 3.4)

• Quick solubility in the pipeline fluid

• Heat, light, chemical, biological degradation resistant


3. EXPERIMENTAL SET-UP AND INSTRUMENTATION

In this chapter the experimental set-up and the corresponding instrumentation is discussed.During the first months of this research, the Multiphase Plug and Play Gas-Lift (MPPGL)set-up was under construction and preliminary measurements were achieved in an 18mhigh gas-lift set-up. This set-up is described before going into more detail concerning theMPPGL set-up. A polymer injection system is used in both experiments and will bedescribed in section 3.3. The different polymer solutions used in these experiments arepresented in section 3.4.

Pictures and videos of the set-up and experiments have been made using a SonyDCRTRV16 video digital camera.

3.1. 18m gas-lift set-up

A graphical representation of the set-up is given in the figure below.

Pump

Downcomer /

De-gassing

Magnetic liquid flow meter

Vessel Controllable valve

Bubble generator

Compressed air

Dp = 72 mm

Perspex riser

L = 18

2 m section

Controllable valve

P

P

P

P

P

P Gas mass flow meter

Polymer DRA injection system


Figure 8: Schematic representation of the experimental set-up. The perspextest pipe has a length of 18 meters and an inner diameter of 72 mm.The total length is divided in 9 sections of 2 meter

The 18-meter high perspex test pipe is made out of nine segments of 2 meter. Each sectionhas a 72 mm inner diameter. A Schmitt centrifugal pump in an open storage vesselgenerates the liquid flow; a control valve and a bypass valve can control the flow rate. Thepump is driven by a constant speed electric drive. The maximum head is 30 m and can beachieved at liquid rates from 15-70 l/min. At the top of the set-up the liquid is de-gassedand the liquid is returned to the open storage vessel by a large down-comer. The gas can beinjected using three different injectors. A flow controller controls the gas flow rate whichcan be set using the ROC, a Remote Operated Commander, which is the interface betweenPC and the set-up. The gas is supplied by the instrumental air supply at 7 bars. Gas flow ismeasured using two gas mass flow meters, Brooks 5861S. These gas mass flow metersprovide the volumetric flow rate at atmospheric pressure with an accuracy of less than0.5%. To measure the pressure differences in the set-up, 6 pressure transducers are placedat each section between 2 and 12 meters. These piezo transducers are flush mounted, sothey do not interfere with the flow. The measurement range is 0-2 bars and the pressuretransducers have an accuracy of 0.1% of the full range. The liquid flow is measured by anEndress & Hauser Promag50 magnetic flow meter. The meter has an accuracy of <0.5% ofthe full range for 5 to 70 l/min.

With liquid rates of 5-70 l/min and gas rates of 10-250 sl/min all obtainable flow regimeshave pressure drops dominated by hydrostatic head. This means frictional pressure dropsare negligible, and that polymer effects on friction cannot be observed in this set-up. But aswe shall see in 4.1.1 this set-up enables to learn effects of polymers on flow regime andhydrostatic pressure drops. The flow patterns observed are bubbly flow and slug flow.

A polymer DRA injection system is used to inject polymers into the 18m pipe, at 4 metresheight as illustrated in Figure 8. More information concerning this injection set-up is givenin section 3.3. The polymers are injected into the test pipe and flow to the top of the pipebefore being returned to the open storage vessel by the large down-comer. The liquid inthe storage vessel is pumped back into the set-up. Section 3.4.2 explains how the polymerchains are degraded by the pump’s shear stress. This means the solution which is pumpedbacked into the set-up does not contain any active drag reducers, because they have beendegraded by the pump. When measuring the effect of the polymers, we can constantlyinject polymers and run the experiment in steady state. By these means, the concentrationof the polymers is constant during the injection period. Measurements are done before andduring the injection to evaluate the effect of the polymers.

The liquid used in this system is tap water with 0.5-vol% ethanol. The addition of ethanolcauses a decrease in coalescence [4] compared to a pure water solution, due to surfacetension effects. Further on we will see that the addition of polymers does not affect thesurface tension.

3.2. Multiphase Plug & Play Gas-Lift set-up

3.2.1. Description

The MPPGL set-up was designed by Schrama [6] and the author of this report. Therational for this facility was primarily to enable new test facilities for multiphase flow


applications, which should be quick and simple to use. The set-up is titled “plug and play”because the lab can be used for multiple applications which should be easy to implement.

A main task of this work was to bring this experimental set-up from a design on paper to aworking facility. Selecting the measurement equipment, redesigning parts of the set-up,making the initial tests, solving initial problems are some of the aspects that came to lightduring the construction and implementation of this facility.

A flow diagram of the set-up is given in Figure 9 and Table 2 gives an overview of thedifferent components. Figure 10 shows a photograph of the lower side of the set-up.

Figure 9: Flow diagram of the MPPGL set-up

Table 2: Legend belonging to Figure 6

Position Count Description

1 1 Liquid pump (Grundfos)

2 2 Retaining valve

3 1 One-way valve

4 2 Check valve

5 1 Polymer DRA injection system (see section 3.3)

6 4 Pressure Transducers 0-2.5 bars

7 1 Test pipe

8 1 Reservoir


Figure 10: Photograph of the MPPGL set-up: at the front right, the liquid pumpis visible. The liquid reservoir is at the right, and on the left we seethe liquid flow meter (back), the gas flow meter and the polymerinjection pipes on both sides of the test pipe

The set-up primarily consists of a 3 m vertical perspex test pipe with inner diameter of 40mm, a liquid reservoir designed to function as liquid-gas phase separator, a polymerinjection system and diverse pipes to connect the test pipe and reservoir to each other. Inthe 40 mm test pipe, pressure measurements are made using four pressure transducers,each separated by 1 m of height. The flush-mounted pressure transducers measurepressures relative to 1 bar and have a range of 0-2.5 bars. The absolute inaccuracy of thetransmitters is 0.006 bars. The test pipe has a smaller diameter than the pipe in the 18mgas-lift set-up, to enable higher friction amounts in the test pipe. The liquid reservoir is twometers high and has an inner diameter of 15 cm. A Grundfoss centrifugal pump generatesthe liquid flow, pumping the liquid from the reservoir into the test pipe. A control valveand bypass valve control the flow rate, which is measured by a digital flow transmitter thatcommunicates with the data acquisition system. The pump delivers liquid flow rates from0-110 l/min and allows superficial liquid Reynolds numbers up to 160,000. The volumetricflow rate is measured with an accuracy of 0.5% of the full range. The gas is supplied by theinstrumental air supply at 7 bars. The gas flow rate can be set and is controlled by a flowcontroller. The range of possible gas flow rates is 0-240 sl/min and this corresponds tosuperficial gas Reynolds numbers as high as 42,000. The gas flow rate is measured with athermal mass flow meter with an accuracy 0.2% of the full scale and 0.8% of the reading.The mass flows are converted to standard volumetric flow rates. The polymers are injectedas described in section 3.3. To enable an efficient dispersion of the polymers into the flow,the polymer is injected on both sides of the tubing, 30 cm above the first pressuretransducer. This can be seen in Figure 10.


In this set-up the total pressure drop is of the order of 0.3 bars. Due to these pressurefluctuations the volumetric flow rate is not constant in the pipe. The volumetric flow ratedepends on the local pressure in the test pipe. Thus, at the bottom of the pipe thevolumetric gas flow rate and superficial gas velocities will differ from the values at the topof the test pipe. Because this effect is very small, we will constantly refer to the actualvolumetric gas flow rates and assume a constant value in the test pipe.

The liquid used in this system is pure tap water.

3.2.2. Liquid-gas separation

The liquid-gas mixture flows through the test pipe into the liquid reservoir. In thereservoir, the gas can escape to the environment by a small hole which has been drilled atthe top of the reservoir. The principle of the liquid-gas separation is based on the fact thatthe rise velocity of the gas enables the bubbles to reach the surface and thus to separatefrom the liquid phase in the reservoir. From the bottom of the reservoir, the liquid ispumped towards the test pipe.

Several problems were encountered concerning the liquid-gas separation. The high mixturevelocities flowing into the reservoir caused the jet to entrain gas into the liquid phase. Byconsequence, the velocity of the gas flowing downwards into the liquid becomes moreimportant than the rise velocity of the bubbles. Gas is then pumped into the test pipecausing negatives effects: the liquid flow meter loses its accuracy and an unknown amountof gas is added into the test pipe. To avoid this effect, several options were envisaged,trying to break up the mixture velocity and the impact of the jet. The solution had to beboth effective, and easy to implement due to the time schedule. The choice became thesystem depicted in Figure 11. Visible are table tennis balls at the surface of the liquid and atube projecting the mixture against the pipe wall, breaking up its kinetic energy. The table-tennis balls reduce the effect of the jet and disable the formation of a vortex in thereservoir.

Figure 11: Photograph of the liquid reservoir

The liquid-gas separation is only satisfactory for low liquid flow rates, i.e. lower than 30l/min. As the liquid flow rate is increased, the effectiveness of the separator decreases


quickly, which prevents accurate measurements for liquid flow rates above 30 l/min. Forhigher liquid flow rates, the effect of the liquid plunging downwards and entraining gas isstronger than the rise velocity of the gas bubbles in the reservoir. The time schedule didnot allow to implement a more efficient system, but in section 5.2.1 a durable solution tothis problem is proposed.

3.2.3. Hold-up and drag reduction measurement

This set-up has been built to study drag reduction in vertical two-phase flow using drag-reducing polymers. From equation {16} we can see that measuring drag reduction isequivalent to measuring a difference in frictional pressure drop. The four pressuretransducers measure the total pressure drop over the test pipe. To calculate the frictionalpressure drop, the hydrostatic pressure drop is subtracted from the total pressure drop. Aswe have seen in section 2.1.4, this makes it necessary to determine the void fraction in thetest pipe.

By adding gas into the test pipe during stationary conditions, the level in the reservoir willrise. The level with which the reservoir rises corresponds to the extra amount of waterpresent in the reservoir. This volume is equal to the amount of gas in the test pipe whichhas forced the extra liquid into the reservoir. Down flow of the reservoir, no gas is present,due to the liquid-gas separator. The volume of the section between the test pipe and thereservoir is negligible. By consequence, by reading off the liquid level in the reservoir, weknow the amount of gas in the test pipe. This enables us to compute the void fraction inthe test pipe.

A small tube connected to the bottom of the reservoir is visible in Figure 8. The tube isfilled with liquid only. The tape measure shown in Figure 11 next to the small tube enablesthe read-off of the difference in level with an accuracy of 0.5 cm. This makes it possible todetermine the void fraction with an accuracy of 2.3%, corresponding to an accuracy in thehydrostatic pressure of 0.007 bars. Combining this with the inaccuracy of the pressuretransducers leads to frictional pressure drop inaccuracies of 0.009 bars.

As will be explained in section 4.1.2.1, the polymer concentrations injected into this set-upbecame more diluted than expected beforehand. The suspicion of lack of mixing of thepolymers in the flow lead to the idea to use lower concentrations of polymer mastersolutions. While solutions of 5,000 wppm were correctly dispersed in the 18m gas-lift set-up, solutions of 1,000 wppm were used in this set-up. To compensate the lower injectionconcentrations, higher flow rates are injected to keep the concentration of the polymer inthe test pipe constant and at the wanted level. Volumes of approximately one litre areinjected into the system for typical times scales of two minutes. This affects the level in theliquid reservoir in a non-negligible way. Because the level in the reservoir has to be read offwith the eyes, it is not possible to accurately determine the change in level in the reservoir,because a polymer solution is constantly injected and thus affects the level. A change involume of one litre would correspond to a change in void fraction of approximately 25%.By consequence, it was not possible to determine the change in hold-up with an acceptableaccuracy while injecting polymers by this method. In section 5.2.1, an answer to thisproblem is given.

However, for regimes where friction plays no role, where the emphasis of the resultsachieved in this investigation lies, the void fraction measurement is independent of thelevel in the reservoir and depends only on the accuracy of the pressure transducers. Thepressure transducer measure the local pressure relative to atmospheric pressure. The meanvoid fraction can be calculated because the pressure drop is fully dominated by hydrostatic


head. The void fraction is measured with an accuracy of 2.0% in this case. As the frictionin the set-up becomes more important, this value rises significantly.

3.3. Polymer DRA injection system

For both the 18m gas-lift set-up and the MPPGL set-up the polymer DRA injectionsystem illustrated in Figure 12 is used. Visible are the pressure vessel polymer reservoirwith a volume of 1.4 litres, the coriolis mass flow meter with digital display and thepressure-regulating valve.

The polymer solutions are injected using a 200 bar nitrogen pressure cylinder. Instead ofusing a pump which would damage the polymers, this system minimizes any deteriorationduring the injection. The flow rate is controlled by using the pressure regulation valve. Anover-pressure of 5-20 bars is sufficient to give the master solutions of polymer flow ratesof 0.2-2.2 l/min. The flow rate is monitored using a coriolis mass flow meter.

A liquid polymer solution with known concentration is poured into the reservoir using afunnel. The pressure-regulating valves enable to set the mass flow of the solution thatleaves the injector. This mass flow can be read-out by the digital display of the coriolismeter. By these means, the polymer concentration in the test pipe can be set at aconcentration varying from 20-100 wppm.

The polymer reservoir enables injection times (and thus measurement times with polymers)of 1-5 minutes, for typical polymer concentration and liquid flow rate ranges in both set-ups.

Figure 12: Photograph of the polymer DRA injection system. Visible are thepressure vessel polymer reservoir, the coriolis mass flow meter withdigital display and the pressure-regulating valve


3.4. Polymer solutions

3.4.1. Description

The visco-elastic fluids used in these experiments are so-called dilute polymer solutions,consisting of polyacrylamide-based polymers dissolved in water. Polyacrylamide can bepurchased in dry granular, liquid or solid form. In these experiments, different industrialpolymers have been used, all in dry granular form. An overview of the polymers tested inthese experiments is given in the following table. The table shows the industrial name ofthe chemical as well as its composition and manufacturer.

The polymers in this table have all been tested in the MPPGL set-up and have shown dragreduction in previous experiments [17]. In section 3.4.3 an example of drag reduction withthe industrial Flopaam will be shown. All results reported in section 4.1.1.2 and 4.1.2.2have been achieved using the Flopaam polymer.

Table 3: Overview of the polymers tested in the experiments

Industrial name Composition Manufacturer

Flopaam 3630 S Aqueous polyacrylamide solution SNF Floerger

Unspecified Anionic emulsion of acrylamide Unspecified

Percol 721 Copolymer of sodium acrylamide Ciba Specialty Chemicals

Polyox WSR-301 Polyethylene oxide Dow Chemical Company

Before the actual experiments the solutions are prepared by creating a solution with a high,fixed concentration (500-5,000 wppm) of Flopaam. This is done by slowly adding Flopaamin powder form in stirred water so that a vortex originates. The stirring keeps on forapproximately 2 hours and then the solution is left alone for a day to enable the polymer tohydrate in the solution.

3.4.2. Degradation

Mechanical degradation is a process of rupture of the polymers into smaller molecules dueto mechanical forces. The two main forces involved in these set of experiments are theshear stress delivered by the pump and in less important matters, the flow through thepipe. Mechanical degradation leads to a strong reduction in molecular weight, and as wehave seen in section 2.2.3, this leads to important decreases in drag reduction.

In both set-ups, a shear pump is used which completely degrades the polymer solutionswhen they are pumped through. We will come back to this in more detail in section 4.1.1.1.

3.4.3. Drag reduction

Solutions of hydrolysed Flopaam polymer mixed by the author of this report have beentested on drag reduction in other experimental set-ups. Cuypers [15] experimentally testedthe solutions on a rotating disk apparatus and measured the difference in torque due to theaddition of polymer solution. In section 2.2.1 we saw that a reduction in the amount oftorque is equal to drag reduction. In Figure 13, the torque is plotted against the Reynoldsnumber for a solution of water and a polymer solution diluted to 40 wppm. FromReynolds numbers of 100,000 and higher the reduction in friction is visible in the graph.


For Reynolds numbers greater than 300,000, the drag reduction becomes significant andreaches values up to 40%. This proves that the polymer solutions used in theseexperiments are drag-reducers.

0

1

2

3

4

5

6

0.E+00 1.E+05 2.E+05 3.E+05 4.E+05 5.E+05 6.E+05 7.E+05

Reynolds

Tor

que

(N.c

m)

Water

Water @40wppm flopaam

Figure 13: Drag reduction in a rotating disk apparatus due to the addition of 40wppm of Flopaam polymer


4. RESULTS

In this chapter the results of the experiments will be discussed. In the first segment of thischapter, the results achieved in the 18m gas-lift set up will be discussed. Secondly theexperimental results of the MPPGL set-up are presented. Following the presentation of theexperimental results, we will make an interpretation of these results using theory onmultiphase flow.

4.1. Experimental results

4.1.1. Results in the 18m gas lift set-up

The results in the 18m gas lift set-up enabled to achieve results and to answer keyquestions which would help further investigation in the MPPGL set-up.

4.1.1.1. Implementation

The first test was to inject polymers into the set-up and try to learn about their dispersioninto a vertical multiphase flow in different regimes. A red water based dye was mixed intothe polymer solution to visualise the diffusion, as illustrated in Figure 14. The diffusionappeared to be effective, i.e. in all regimes (bubbly flow and slug flow) the polymer wouldbe dispersed less than one meter downstream of the injection point. It also appeared thatthe efficiency of the polymer diffusion increased with the turbulence in the pipe. However,using this experiment it is only possible to visualise the mixing of the polymers on themacroscale. The mixing at the smaller scales cannot be visualised and thus this effect hasnot been investigated. Due to a tight time schedule, we were obliged to be content withthis result.

Figure 14: Polymer injection visible up to 0.6 m above the injection point. Reddye was added to the solution to visualise the dispersion in theturbulent flow


A second test was to find out the effect of the shear stress created by the centrifugal liquidpump on the polymers. It is key to be sure that the pump totally breaks up the long-chainpolymers, so that the effects of the polymers do not persist in the flow loop. This isexplained in 3.4.2. The effects due to the polymers appeared to vanish shortly afterstopping the injection, as we shall see in the following section. This proved the shear stresscreated by the pump was effective in destroying the polymers.

4.1.1.2. Results

As discussed in section 3.1, friction is negligible at the conditions used in this set-up, andall visualisations and measurements were achieved in regimes dominated by hydrostaticpressure drop. Thus it was not possible to obtain results in frictional regimes butinteresting results were achieved concerning the effect of polymers on the hydrostaticpressure drop and the flow pattern.

The first important observation was that the addition of polymers causes an increase in thehydrostatic pressure drop. Figure 15 shows the pressure in the pipe at two pressuretransducers downstream of the polymer injection. The pressure is plotted as function oftime, and we can see a significant increase in pressure when the polymers are injected. Thetwo injection periods are delimited by the vertical red lines in the figure. The first injectionof polymers takes place at flow conditions of liquid and gas flow rates of 54 l/min and 25sl/min, the next injection takes place at the same liquid flow rate and at a gas rate of 70sl/min. At the end of the injection periods we can see a steep pressure drop. The polymerreservoir at that point is empty and contains only gas, which is injected into the test pipe,and causes the pressure drop to decrease. We can also see that the pressure almostimmediately returns to its pre-injection level, which proves the degradation of the polymersby the pump as discussed above.

0.6

0.7

0.8

0.9

1

1.1

0 60 121 182 244 305 366 425 486 547 609 670 731 790 851 912 974

Time (s)

Pre

ssu

re (

bar

s )

PT 11

PT 12Polymer injection: Ql = 54 l/minQg = 25 l/min

Polymer injection: Ql = 54 l/minQg = 70 l/min

Figure 15: Two pressure transducer signals downstream of the injection

Table 4 shows the pressure increase and hold-up decrease for different liquid and gas flowrates with the relevant void fractions. The pressure increase is measured using the pressuretransducer at 6m height, the first downstream of the polymer injection. The pressuretransducer measures the local pressure relative to atmospheric pressure, or in other words,the differential pressure between 6m and the top of the set-up. The mean void fraction can


be calculated for the remaining 12 meters because the pressure drop is fully dominated byhydrostatic head. The friction in the test pipe at the flow conditions in these experimentscontributes for less than 1% to the total pressure gradient. In the following table have thevoid fraction decreases with absolute values between 5.2% and 11.6%.

Table 4: Pressure increase and hold-up decrease due to injection of DRA

Ql (l/min) Qg (l/min) Äp (bar) ág (%) Decrease in ág (%) Accuracy

54 25 0.137 36.4 11.6 0.2%

54 70 0.058 55.7 5.0 0.2%

27 320 0.062 80.9 5.2 0.2%

A possible explanation for this effect will be given further on in this chapter.

In Figure 16 we can visualise the effect of the polymer addition on a bubbly flow. On theleft we observe a bubbly flow with respectively gas and liquid flow rates of 25 l/min and 54l/m, without polymers. To the right a flow with a polymer concentration of 25 wppm isshown, under the same conditions as the flow to the left. It is clear that the polymers causea change in the flow pattern but it is difficult to qualify the exact effects. To the left we cansee many bubbles in contrast to the picture on the right, where the bubbles are lessnumerous. The lack of time for these experiments due to the transfer of the 18m high gas-lift set-up made it impossible to obtain more experimental data and visualisation. In anycase, it is clear that the polymers do affect the flow pattern. Thankfully, results achieved inthe MPPGL set-up will provide more information.

Figure 16: The flow on the left shows a flow without polymers and on the rightpolymers are injected resulting in a concentration of 25 ppm in thetest pipe. Both flows are bubbly with liquid and gas flow rates ofrespectively 54 l/min and 25 sl/min.

These results and observations have given important insights for further investigation inthe MPPGL set-up. Primarily, we know that polymers can have a negative effect onhydrostatic pressure drops and that they affect the flow pattern. In the following section,these conclusions will be further investigated and the effect of polymers on the frictionalpressure gradient is investigated. In section 4.2 an interpretation of these results will be


given followed by an explanation as to how the polymers cause a decrease in the voidfraction.

4.1.2. Results in the Multiphase Plug & Play Gas-Lift set-up

4.1.2.1. Drag reduction

Drag reduction has not been measured in the MPPGL set-up. All polymers described insection 3.4 were used in a broad range of concentrations, varying from 25 to 150 wppm inthe test pipe. The polymer master solutions were evenly varied, from 500 to 10,000 wwpm.The following combinations of liquid and gas flow rates have been tested:

0< Ql < 100 l/min 0< Usl < 4 m/s 0< Resl < 160,000

0< Qg < 240 sl/min 0< Usg < 10.5 m/s 0< Resg < 30,000

As we can see from Table 1, the maximum values correspond to flow patterns which aredominated by frictional pressure drop. An important test was to measure single-phase dragreduction in the pipe. Literature is rich in examples showing drag reduction in verticalflows of water with addition of polymers. Several examples were discussed in section 2.2.2.Cuypers [15] experimentally tested the Flopaam polymer at a concentration of 40 ppm in arotating disk and measured drag reduction, as described in 3.4.3. The polymer solutionused was exactly the same as the ones used in these experiments. This proves the polymercan reduce drag and that the pre-mixing of the polymer did not influence this effect. Wecannot not determine why the drag reduction did not appear in these experiments. The factthat friction was not reduced for single-phase flow forbids us to make conclusionsconcerning vertical multiphase drag reduction with polymers. Two hypotheses as to whythe drag reduction did not appear can be given and should be tested in future work:

• The flow in the test pipe is not fully developed

• The polymers do not fully mix in the test pipe

We speculate that a combination of both of these effects has contributed to the lack ofdrag reduction. The mixing of concentrated solutions of polymers (500-2,000 wppm) into atwo-phase flow has not been subject to systematic research and is not well understood. Ingeneral, researchers have used long test pipes to ensure a correct mixing. In theseexperiments, the mixing of the polymer solution into the flow was visualised using a dyesolution. The conclusion of this test was that the polymer correctly mixed at themacroscales. The mixing at the smaller scales has not been monitored because thisphenomenon is not observable using visualisation. The correct mixing of the polymersrequires a certain inlet distance. The polymers are correctly mixed only after a certaindistance into the flow has been covered. In the experiments using the dye solution, thisdistance was estimated at half a meter. At that point, the polymers were correctly mixed atthe macroscales but uncertainty remains as how the polymers were mixed at themicroscales. In the following section we will see that the polymers did have an effect onthe flow pattern and that they diminished the turbulence intensity in the flow. Thissuggests that the polymers were active in the flow, which could make one assume that thepolymers were correctly mixed into the flow. Due to the lack of knowledge concerning themixing of drag-reducing additives, it remains difficult to draw a conclusion. Furtherinvestigation on this topic is required.

From the inlet of the test pipe, the properties of the flow change until a certain point isreached. From this point onwards, the flow is fully developed and the velocity profile is


constant and the pressure drops are linear. A certain inlet distance is needed for the flow tofully develop. A relation for the length necessary to attain full development of a flow isgiven by [33] for turbulent flows and computing this equation leads to an inlet distance ofabout 1.5 meters for these experiments. Taking into account a length of about half a meterfor the polymers to mix, the test pipe should be long enough to enable the fulldevelopment of the flow after the mixing of the polymers. This statement is subject to theassumption that the mixing of the polymer and the development of the flow no notinfluence each other. For inhomogeneous flows like slug flow, the inlet distance is knownto be much larger. Taitel, Barnea and Dukler [9] found a relation for the inlet distancenecessary for the development of a slug flow or churn flow. The equation describes thatthe necessary amount of diameters needed is proportional to the mixture velocity. For aflow with superficial liquid and gas velocity of 0.4 m/s, an inlet distance of 2.5 meters issufficient. For flow conditions where friction plays an important role, the velocities aremuch higher and this leads to much longer inlet distances. For a liquid flow rate of 50l/min and a gas flow rate of 80 sl/min, Table 1 shows that the frictional pressure gradientis of the same order as the hydrostatic pressure gradient. For these conditions the inletdistance is 300 diameters, i.e. approximately 12 meters. With a test pipe length of 3 meterssuch a flow will never fully develop in the MPPGL set-up. We can conclude that the flowswhere the frictional pressure drop plays an important role are not fully developed. Theinfluence of drag-reducing polymers to a undeveloped flow has not been subject toresearch. The pressure drop at the entrance of the pipe is usually larger than when the flowis fully developed [33]. This could make one assume that the polymers should reduce thefrictional pressure drop for undeveloped flows as well. Here again, further investigation isrequired.

It remains difficult to test these hypotheses and to conclude why the drag reduction did notappear. In section 5.2 we will discuss alternatives that bring the possibility to avoid theabove problems. The following section will describe the influence of the addition ofpolymers to a water-air flow for low flow rates.

4.1.2.2. Influence of polymers on hydrostatic pressure drop

As discussed in section 3.2.3, the void fraction measurement in flow regimes where frictionplays an important role has unacceptable accuracies. Therefore, we have tested the additionof polymers in regimes dominated by hydrostatic pressure drop. This has given theopportunity to compare the results that were obtained in the 18m set-up. In this section,the effect of the addition of drag reducing polymers on flows dominated by hydrostatichead has been tested for a low liquid flow rate (10 l/min) and increasing gas flow rates.

For the different flow rates the pressure in the test pipe is measured as explained in 3.2.1.The effect of the drag reducing polymers is tested by comparing the pressures measuredwith and without presence of drag reducers. For regimes in which friction is negligible, thepressure measurement functions as a void fraction measurement. The polymerconcentrations are diluted from 1000 wppm in the injection vessel to 25 wppm in the testpipe. An overview of the results is given in the following table:


Table 5: Effect of drag reducing polymers on the hydrostatic pressure andvoid fraction, for different gas flow rates

Ql (l/min) Qg (l/min) Friction Äp (bar) ág (%) Decrease in ág (%) Accuracy

10 0 0% -0.001 0.0 0.0% 2.0%

10 10 0% 0.012 48.9 3.9% 2.0%

10 30 0% 0.016 68.2 5.4% 2.0%

10 50 0% 0.017 74.9 5.7% 2.0%

10 80 1% 0.011 79.1 3.8% 2.0%

10 110 15% 0.006 81.2 2.0% >2.0%

10 140 28% 0.013 82.5 4.3% >2.0%

10 170 38% 0.008 83.3 2.8% >2.0%

For different sets of liquid and gas flow rates, the tables shows the estimated amount offriction present in the flow, the pressure increase at the first pressure transducer, the voidfraction in the flow without addition of polymer, and the decrease in void fraction due tothe addition of polymer, with the belonging accuracy. The amount of friction representsthe calculated ratio of the frictional pressure drop and the total pressure drop in the testpipe using the computer code TWOPPI [28]. The first row in the table shows a single-phase flow of water. The accuracy of the pressure transducers is 0.006 bars, and we can seethe polymers do not affect the pressure drop in the flow, which is an expected result due tothe absence of friction. For gas rates from 10 sl/min to 80 sl/min, friction is negligible andthe void fraction is given with an accuracy of 2.0%. The absolute changes in void fractionare of the order of 5%. In these cases, the mixture velocities are fairly low which enableslow inlet distances. However, according to Taitel, Barnea and Dukler [9] the flow is onlyfully developed for the case of a gas flow rate of 10 sl/min. For the following rows, theflow is only partially developed.

When friction becomes more important, i.e. for gas rates of 110 sl/min and higher, theaccuracy of the void fraction measurement is affected negatively. The effect of thepolymers on the friction cannot be measured, and by consequence we cannot split thehydrostatic and frictional pressure drop. However, the measurements in single-phase flowdid not show any effect on the frictional pressure drop, which could make one assume thatthe friction is not affected at the conditions shown in the lower part of Table 5. By makingthis assumption, the decrease in void fraction can be calculated for the lowest three rows ofthe table. The validity of this assumption is subject to discussion, which is why theinaccuracies of the measurements for high gas rates are higher than 2.0%. It is not possibleto compute the exact accuracy for these measurements with the available data. It shouldalso be noted that these flows are not fully developed.


1.0%

2.0%

3.0%

4.0%

5.0%

6.0%

7.0%

8.0%

0 20 40 60 80 100 120 140 160 180

Qg (sl/min)

Ab

solu

te v

oid

fra

ctio

n d

ecre

ase

Figure 17: Decrease in void fraction due to the addition of drag reducingpolymers at 25 wppm in the test pipe, for different gas flow rates

Figure 17 shows the absolute decrease in void fraction due to the polymers as function ofthe gas flow rate. Figure 18 shows the decrease in void fraction as function of the pre-injection void fraction. The error bars are shown for the cases where friction does not playa role.

1.0%

2.0%

3.0%

4.0%

5.0%

6.0%

7.0%

8.0%

40.0 45.0 50.0 55.0 60.0 65.0 70.0 75.0 80.0 85.0

Void fraction (%)

Ab

solu

te v

oid

fra

ctio

n d

ecre

ase

Figure 18: Absolute decrease in void fraction vs. void fraction due to polymeraddition at 25 wppm in the test pipe

Next to these quantitive results illustrational results have been achieved which show theeffect of the addition of polymers on the flow regime. This will be discussed in thefollowing section. Together with the quantitive results discussed above, this should help toexplain and qualify these results.


4.1.2.3. Visualisation

Both experimental facilities have given important insights on the effect of the addition ofdrag-reducing polymers on the flow regime in a vertical two phase-flow. The followingconclusions can be made:

• The effective diameter of the bubbles is enlarged. In further sections this subject willbe further discussed.

• The transition from bubbly flow to slug flow occurs for lower superficial gasvelocities. This will be addressed in the present section.

• The distribution of the bubbles in the pipe changes. With addition of polymers, thebubbles move towards the center of the pipe. This will be discussed in section 4.2.2.

The following pairs of photographs have been taken in the MPPGL set-up. Each pair ofphotographs shows a flow without polymer to the left and to the right a flow under thesame conditions but with a concentration of polymer of 25 wppm. These pictures show astriking difference induced by the addition of polymers. The above conclusions areillustrated by the following pictures and the belonging explanation.

Figures 19, 20 and 21 depict the difference between a flow with and without polymer forliquid and gas flow rates of 10 l/min. The flow without polymer is relatively uniformlydistributed with lots of small bubbles. When the polymers are added at 25 wppm, thebubbles gain in size and the size of the Taylor bubbles becomes more important. Thesebubbles can be recognized by their bullet-like shape and their large diameters, that are ofthe order of the pipe diameter. The diameter of the pipe is 40 mm, so these bubbles have adiameter of approximately 30-35 mm. Equation {10} enables to calculate that the risevelocity of such a bubble is around 22 cm/s. In Figure 19 the small bubbles present underthe Taylor bubble are not present above the bubble. Another example of this effect can beseen in the rightmost photograph of Figure 20. We suggest that the smaller bubbles have ahigher rise velocity than the Taylor bubble. The theory from Clift et. al [12] predicts thatthese small bubbles should have rise velocities of the order of 20-25 cm/s, which is inaccordance with the above statement. The smaller bubbles situated above a certain Taylorbubble rise faster than the Taylor bubble itself and therefore approach towards the nextTaylor bubble. If the smaller bubbles had lower velocities, the lower part of the interveningliquid cylinders between the Taylor bubbles would contain small bubbles. This is clearlynot the case. It can be noted that for a pipe with a larger diameter, the effect would bedifferent as the Taylor bubbles would have higher rise velocities.


Figure 19: Liquid and gas flow rate of 10 l/min. This pair of photographs showsa flow without polymers to the left and a flow with a concentration of25 wppm of polymer on the right

In the case of the flow with polymers, the effective transport of gas occurs via the largeTaylor bubbles. These bubbles have large diameters and are very long, which is why mostof the gas is conveyed in these bubbles. The Taylor bubbles are centered around the centerof the pipe, as can be seen from the photographs. By absence of the polymers, the bubblesseem to be uniformly distributed in the pipe. This suggests that with the addition ofpolymers, the distribution of the gas in the pipe changes. The gas migrates towards thecenter of the pipe. This assumption will be verified with the outcome of our experiments insection 4.2.2 and with a turbulent model in section 4.2.3.


Figure 20: Liquid and gas flow rate of 10 l/min. For both pairs of photographs,the picture to the left depicts a flow without polymer while the pictureto the right shows a flow with a polymer concentration of 25 wppm

Figure 21: Liquid and gas flow rate of 10 l/min. For both pairs of photographs,the picture to the left depicts a flow without polymer while the pictureto the right shows a flow with a polymer concentration of 25 wppm


The void fraction in the flow for the above pictures has been experimentally determined atapproximately 49%, a typical value for slug flow. In all cases shown above we are dealingwith slug flow. The development of a Taylor bubble is shown in the leftmost photographof Figure 21. However, the photographs of the flow without polymer show flows that alsohave bubbly flow aspects. The bubbles are smaller and uniformly distributed, unlike thecase when polymers are added to the flow. With addition of the polymers, the flow showsmuch clearer signs of slug flow. In the experiments performed in the 18m gas-lift set-up, itwas visualised that the addition of polymer caused a transition from bubbly flow to slugflow for lower superficial gas velocities. Due to the lack of experimental data obtained inthe 18m gas-lift set-up, it is not possible to quantify this effect. But it was noticed that forequal flow conditions around the transition area from bubble to slug flow, a bubbly flowwould transition to slug flow with addition of polymers. Without the addition of polymers,a transition would not occur. The photographs in this section strengthen the idea that thepolymers cause an earlier transition to slug flow. This effect is negative for the oil industry,where it is key to postpone this transition.

We discussed that a decreasing bubble size postpones the transition from bubbly flow toslug flow. We argue that in this case, the larger diameters of the bubbles are the cause forthe earlier transition to slug flow. This is in agreement with the experiments discussed insection 2.1.2 and the correlation proposed by Song [5].

Figure 22 shows three pairs of photographs for higher gas rates. The liquid flow rate is 10l/min and the gas flow rate is 30 sl/min, with a corresponding void fraction of 68%. Hereagain, the difference between the flows is striking. For each pair of photographs, the leftpicture corresponds to a flow without polymer while the right hand photograph shows aflow with polymer. For these higher gas rates, it is difficult to visualise the exact differencesbut the overall effect is clear. The conclusions made at the beginning of this section can beverified by these pictures as well. The diameters of the bubbles for the pictures on the rightis larger and a core distribution of the gas is perceptible.

The visualisation of these flows has given important insights. The transition from bubblyflow to slug flow was discussed in this section. In section 4.2.1 we will explain how theincrease in bubble diameter is caused by the polymers. Using our experimental results, wewill quantify the change in gas distribution in the pipe in section 4.2.2. A quantification ofboth these effects is given in 4.2.3 using the break-up theory of Hinze [24].


Figure 22: Liquid flow rate of 10 l/min and gas flow rate of 30 sl/min. For thethree pairs of photographs, the picture to the left depicts a flowwithout polymer while the picture to the right shows a flow with apolymer concentration of 25 wppm

4.2. Theoretical results

4.2.1. Flow pattern

The size of a gas bubble is affected by two prominent factors: surface tension andturbulence (see also section 2.1.3). Surface tension tends to enlarge bubbles and keep themspherical while turbulence tends to break-up bubbles into smaller ones. The surface tensionof the following solutions has been measured:

• Tap water solution with 0.5% ethanol, with and without addition of 25 ppm Flopaam

• Tap water, with and without addition of 25 ppm Flopaam

These are the fluid solutions that have been used in both experimental facilities. The resultsindicated that the polymers do not affect the surface tension of the liquid in both cases.This leads to the following hypothesis: the increase of the bubble diameter due to thepolymers is caused by a reduction of the turbulence intensity.

It is well known that polymers reduce the turbulence intensity in a single-phase flow. Thiseffect has been subject to much research. Lumley [18] stated that the smaller eddies in aflow are damped by the addition of polymers. De Gennes [19] showed that polymers


prevent the production of turbulent velocity fluctuations at the small scales. Equally wellknown is that the vortices slightly larger than the Kolmogorov scale are responsible for thebreak-up of bubbles in a turbulent flow. This effects has been discussed in section 2.1.3.We suggest the following conclusion: the addition of polymers leads to a decrease in theturbulence intensity. This causes the smaller vortices in the flow to vanish and byconsequence the break-up of the bubbles in the flow is diminished. This enables bubbles toattain larger diameters.

In these experiments it was not possible to measure the diameter of the bubbles. From thephotographs presented in section 4.1.2.3 it is visible that a flow with polymers containsbubbles that have a larger diameter than a flow without polymers. However, determiningthe absolute values of the diameters is difficult. Using the theory of Hinze we will try toquantify this effect in section 4.2.3.

4.2.2. Hydrostatic pressure drop

The results obtained in the 18m gas-lift set-up and the MPPGL set-up are consistent. Bothshow that when drag-reducing polymers are added to a vertical flow of water and gas, thehydrostatic pressure drop is increased. The associated void fraction decreases within arange of 2 to 12%. In this section we will give an explanation of this effect using the drift-flux model.

Equation {5} shows that the void fraction is proportional to the superficial gas velocity inthe pipe. The local gas flow rate and usg are proportional to the local pressure in the pipe,but this effect is negligible and therefore neglected in the following section. As weexplained in section 3.2, the gas volumetric flow rate and superficial gas velocity are takenas constant. Combining equations {5} and {13} leads to:

bmo

sgg uuc

u

+=α {19}

From this equation we can see the void fraction is affected by the two parametersintroduced in the drift flux model. The distribution distribution parameter c0 and thebubble rise velocity ub are described in section 2.1.5. We can conclude that the lower voidfractions due to the addition of polymers is caused by one or both of the two followingeffects:

• The bubbles have higher rise velocities.

• The distribution of the bubbles in the pipe changes.

To investigate which parameter dominates in decreasing the void fraction, the followinggraph is plotted:


0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Um (m/s)

Ug

(m

/s)

Ug (m/s)

Ug @ 25ppm (m/s)

Figure 23: Plot of the actual gas velocity versus mixture velocity for a flow withand without polymer

The actual gas velocity, defined in equation {7}, is plotted against the mixture velocity fordifferent liquid- and gas flow rates for a flow with and without polymer. The actual gasvelocity is the measured superficial gas velocity divided by the measured void fraction. Theaccuracy of the gas velocity is shown in the graph. The data points in the graph correspondto rows 2-5 in Table 5. At these conditions, friction is negligible and the void fractionmeasurement has an acceptable accuracy. Two lines have been drawn through the datapoints. The line with the lower gas velocities corresponds to the pure tap water solutionand has the following equation:

098.0*151.1 −= mg uu {20}

With the addition of polymers, the actual gas velocity increases and this leads to thefollowing equation:

034.0*198.1 −= mg uu {21}

The numbers in these equations correspond to an evaluation of c0 and ub. In fact, each datapoint in the graph has its own distribution parameter and rise velocity. To compare theseparameters for a flow with and without polymer we compute an average value of theseparameters over the different gas flow rates for both flows. This enables us to make thefollowing conclusions:

• The measurements offer an accurate scatter. The data points show a good fit and lieon the same line within the accuracy of the measurement.

• The distribution parameter of the flow with polymer is higher than for the flowcontaining pure water. The distribution parameter rises by 4.1%.


• The absolute values of the distribution parameter are in agreement with valuesobtained in the literature (discussed in section 2.1.5). For core peaking and slug flow, thedistribution parameter is known to have a value varying from 1.1 to 1.2.

• The bubble rise velocity is negative for both solutions. This value should be positiveand have a value of approximately 20 cm/s, as can be seen in Figure 4. In theseexperiments, the diameter of the bubbles is of the order of 4 to 20 mm. In this region, theterminal rise velocity of the bubbles is more or less constant around 18 - 25 cm/s. Forthe slug bubbles that have diameters of the order of the pipe diameter, equation {9}should be used to calculate the rise velocity. This leads to velocities of 22 cm/s. Indeed,an increase in the bubble diameter is not expected to lead to higher rise velocities in theseregimes. Also, the bubble rise velocity has values that are much smaller than the mixturevelocity. The ratio of the bubble rise velocity and mixture velocity has values between 5%and 25%. Thus, even if an increase in rise velocity would occur, these fluctuations wouldonly have a very small effect on the actual gas velocity in these conditions.

We can conclude that the decrease in void fraction due to the addition of polymers iscaused by a change in the distribution of the gas in the pipe. The bubbles migrate towardsthe center of the pipe and the so-called core peaking occurs. At the center of the pipe thevelocity is higher than near the wall and this causes the gas velocity to rise. The bubbleshave a shorter residence time in the pipe which leads to a decrease in void fraction. Theeffect of change of gas distribution in the pipe has also been visualised in section 4.1.2.3.The same conclusion was made using photographs of flows with and without polymer.

The distribution of the gas in the pipe depends on the diameter of these bubbles. This isshown in Figure 5 and Figure 6. In section 4.2.1 we have seen that the diameter of thebubbles is increased by the presence of the polymers. This leads to the hypothesis that thisincrease in diameter is responsible for the migration of the gas bubbles towards the centerof the pipe.

We have previously discussed that we are not able to determine the values of the bubblediameters accurately in these experiments. This prevents from evaluating the effect of theincrease in diameter on the gas distribution, using the figures proposed by Tomiyama et al.[21] and Guet et al. [31]. In the following section a turbulent model will be discussed andthe increase in diameter will be quantified. This will enable to identify the impact of thisincrease on the distribution of the gas in the pipe.

4.2.3. Hinze theory

In this section we will try to quantify the results achieved in these experiments using themodel described in section 2.1.6. The equation for the maximum stable diameter of the gasbubbles is calculated using:

4.0

6.0

max 2 −

= ε

ρσ

l

d {22}

This equation was introduced in 2.1.6. For a turbulent pipe flow, the amount of dissipationis related to the friction factor by the following equation [7]:

D

uf mm3

2=ε {23}


Equations {17} and {23} show that a reduction in the friction factor is equal to areduction in the amount of turbulent dissipation. Consequently, drag reduction can also bedefined as the amount of reduction of the turbulent dissipation. Neither the density nor thesurface tension of the fluids is affected by the addition of polymers into the flow. This hasbeen discussed in the previous sections.

In these experiments drag reduction has not been observed in the measurements.However, polymers are well known to reduce friction. We have no satisfaction as to whyreduction in friction has not been measured. At the flow conditions at which themeasurements concerning the influence of polymers on the hydrostatic pressure drop wereperformed, the frictional term was negligible. Taking into account the accuracy of thepressure transducers used in the MPPGL set-up, at these conditions, the effect of areduction in frictional pressure drop cannot be measured. Thus uncertainty remains as towhich effect the polymers have on the friction and by consequence on the turbulentdissipation. In a turbulent flow, the dissipation rate is proportional to the turbulenceintensity [30]. In section 4.2.1 we have discussed that the polymers reduce the turbulenceintensity in the flow. This leads to the idea that the amount of dissipation is reduced.Unfortunately, this assumption cannot be validated using our experimental data.

If we assume a reduction in the dissipation rate, a quantitive analysis can be given as tohow the polymer affects the bubble diameter and consequently the distribution in the pipe.Using this assumption and two estimates for the amount of decrease in turbulentdissipation, we can estimate the increase in bubble diameter and identify the effect this hason the distribution of the gas in the pipe.

Table 6 and 7 show the respective effect of a 40% and 20% decrease of the turbulentdissipation for the flow conditions at which measurements have been performed in theMPPGL set-up. The drag reduction estimates are based on previously achievedexperimental results in multiphase flow [2]. In these tables, the constant used for theequation of the maximum bubble diameter is 2.0. The table shows the computed maximumbubble diameter using the Hinze model for both the case with and without polymers.Figures 5 and 6 have been used to translate the effect of increase in diameter to thedistribution of gas in the pipe. Both the effect on the distribution parameter and the nettransferred lift coefficient are shown. The last column shows the regime transition.

Table 6: Effect of a 40% reduction in turbulent dissipation on the maximumbubble diameter, distribution parameter and net transferred liftcoefficient. The effect is shown for different liquid and gas flow rates.The constant in the equation for the maximum diameter is 2.0

Ql

(l/min)

Qg

(l/min)

dmax

(mm)

dmax (dra)

(mm) c0 c0(dra) Ä(c0) (%) CL CL(dra) Ä(CL)Regime

Transition

10 10 13.3 16.3 1.19 1.19 0.0% -0.29 -0.29 0.00 core : core

10 30 6.2 7.6 1.13 1.17 3.5% -0.12 -0.29 -0.17 neutral : core

10 50 4.1 5.0 1.00 1.06 6.0% 0.29 0.16 -0.13 wall: neutral

10 80 2.6 3.2 0.96 0.98 2.1% 0.29 0.29 0.00 wall: wall

In the first table, the maximum diameter is increased by 23% due to the decrease indissipation. The distribution parameter and lift coefficient are not affected in the top row.


For the higher gas rates both the lift coefficient according to Tomiyama et al. [21] and thedistribution parameter according to Guet et al. [31] are affected. This can be translated to amigration of the gas towards the center of the pipe. This is in agreement with thediscussion we had using the visualisation in section 4.1.2.3 and also with the experimentalresults discussed in the previous section.

In Table 7, the maximum diameter is increased by 9%. This table shows similar qualitativeresults. The changes in the distribution parameter and lift coefficient are less important butthe same flow regimes transitions take place. Figure 24 shows the effect of the reduction indissipation at the two different estimates for the different gas flow rates.


Ql

(l/min)

Qg

(l/min)

dmax

(mm)

dmax (dra)


Transition

10 10 13.3 14.6 1.19 1.19 0.0% -0.29 -0.29 0.00 core : core

10 30 6.2 6.8 1.13 1.15 1.8% -0.12 -0.24 -0.12 neutral : core

10 50 4.1 4.5 1.00 1.03 3.0% 0.29 0.25 -0.04 wall: neutral

10 80 2.6 2.8 0.96 0.97 1.0% 0.29 0.29 0.00 wall: wall

0.95

1.00

1.05

1.10

1.15

1.20

0 10 20 30 40 50 60 70 80

Qg (sl/min)

Co

Co

Co (dra 40%)

Co (dra 20%)

Figure 24: Effect of a reduction in the turbulent dissipation on the distributionparameter for different gas rates. The distribution parameter iscomputed using the experiments from Guet et al. [31] and the Hinze[24] model. The constant used in equation {15} is 2.0


The model of Hinze is widely used thanks to its simplicity. However, it remains verydifficult to determine an accurate value for the constant in equation {15} and a criticalvalue for the force ratio on which the equation is based. By consequence the absolutevalues shown in the above tables have a limited meaning. However, the qualitative effectshown in both cases is important. The model enables to conclude that the increase inbubble diameter visible in the experiments is responsible for the change in the distributionof the gas in the pipe, and thus for the decrease in void fraction observed.

If we compute the model using the constant proposed by Hinze in 1955 (0.725), we obtainsimilar results. The qualitative effect does not change. The outcome for a decrease indissipation of 40% is shown in table 8. The flow regime transition occurs for lower gasrates. For a gas rate of 10 sl/min, the flow regime changes from wall peaking to a neutralregime. The absolute values differ from those in tables 6 and 7 but the overall effect is thesame: the increase in diameter is responsible for a migration of the gas bubbles towards thecenter of the pipe.


Ql

(l/min)

Qg

(l/min)

dmax

(mm)

dmax (dra)


Transition

10 10 4.8 5.9 1.05 1.14 7.9% 0.16 -0.10 -0.26 wall : core

10 30 2.3 2.8 0.96 0.97 1.0% 0.29 0.29 0.00 wall: wall

10 50 1.5 1.8 0.95 0.95 0.0% 0.29 0.29 0.00 wall: wall

10 80 0.9 1.1 0.95 0.95 0.0% 0.29 0.29 0.00 wall: wall

The assumptions made on the decrease in turbulent dissipation cannot be justified byexperimental results. But an important conclusion can be taken without using an estimationfor the turbulent dissipation. The theory of Hinze has shown that the bubbles have typicalsizes where a change in the diameter leads to a change in the distribution of the gas in thepipe. This is visible in the figures shown in section 2.1.5.1. From the visualisation in section4.1.2.3 we know that the diameter of the bubbles is increased, and a rough visualestimation of the bubbles size confirms the calculations made with the theory of Hinze.Any increase in bubble size at these scales is responsible for a change in the gasdistribution. From figures 5 and 6 we can see the increase leads to a migration of the gastowards the center of the pipe.


5. CONCLUSIONS AND RECOMMENDATIONS

In the previous section we have discussed the experimental and theoretical results achievedin this investigation. In this final chapter we shall draw the conclusions appropriate for theresults achieved in our experiments and try to answer the questions set out in theintroduction of this report.

As a conclusion of this thesis, we will make several recommendations. Firstly, theserecommendations will concern the experimental facility. Secondly, we will giverecommendations for further investigation on vertical multiphase drag reduction.

5.1. Conclusions

5.1.1. Multiphase Plug and Play Gas-Lift set-up

A significant part of the work carried out during this thesis consisted in the constructionand design of a new experimental facility to test multiphase drag reduction in verticaltubing. The author of this report succeeded in completing the construction of the facilityand solving the numerous problems encountered during this period. Importantexperimental results have been obtained using this facility.

The MPPGL set-up was designed to enable new test facilities for multiphase flowapplications. One of these applications is to study the influence of drag-reducing polymersin a vertical two-phase flow in regimes where friction dominates. The test facility enabledto test the influence of DRA on water-gas flows in vertical tubing with mixture Reynoldsnumbers up to 500,000, i.e. regimes where the frictional pressure gradient is more thanthree times larger than the hydrostatic pressure gradient. The facility has proved to be easyto implement and to be “plug and play”. However, the original design of the set-updisabled to accurately measure the amount of friction and the void fraction in the flow.Also, the set-up did not allow the correct mixing of the injected polymer solutions and thefull development of the flow, and this has prevented us from testing the effect of theaddition of polymers on the frictional pressure drop in the pipe. In the next section, arecommendation is given on how to solve this problem.

5.1.2. Experimental results

The objective of this research was to experimentally investigate the influence of drag-reducing polymers on a vertical two-phase flow. This has been done by analysingexperimental results and flow visualisations.

It should be noted that the quantitative interpretation of the results is limited. Due to a lackof accuracy in the measurement facility and a tight time schedule, the set of data achievedin these experiments has to be strengthened by further work. However, the conclusions ofthis report have an important qualitative meaning based on experimental results. Theoutcome of these results points us to concrete and clear conclusions.

Looking back at the questions set out in the introduction of this report, the following canbe said:

• No strong conclusions can be made as to whether polymers can reduce friction invertical multiphase flow. We suggest that the MPPGL set-up did not allow the correctmixing of the polymers and the development of the flow.


• A coherent set of data obtained in both set-ups has shown that the addition ofpolymers to a water-air flow induces an increase in the hydrostatic pressure drop. Forflows having a void fraction between 36% and 83% and a negligible amount of friction,an absolute decrease in void fraction has been measured within a range of 2% to 12%.

• We argue that the polymers diminish the turbulence intensity in the flow and lessenthe break-up mechanism. This leads to larger bubbles and consequently a migration ofthe gas towards the center of the pipe. This effect has been calculated using the drift-fluxmodel and is responsible for higher actual gas velocities and a shorter residence time ofthe bubbles in the pipe. This is equivalent to lower void fractions and higher hydrostaticpressure drops.

• A change in flow regime due to the addition of polymer has been visualised:

o The size of the bubbles is increased.

o The bubble to slug flow transition occurs for lower superficial gas velocities.

Thus, it has been found that polymers have a negative effect on the hydrostatic pressuredrop. The effect of the polymers on the frictional pressure drop remains unknown andtopic this should be subject to further research.

5.2. Recommendations

5.2.1. Multiphase Plug & Play Gas-Left set-up

The first results in the MPPGL set-up have already been obtained. Severalrecommendations can be made as to how this facility can be used more efficiently.

The liquid-gas separation discussed in section 3.2.2 has to be improved. The effect of theliquid plunging down into the reservoir has to be completely compensated by the rise ofthe gas bubbles. By enlarging the diameter of the liquid reservoir, the bubbles will have thespace and time to rise to the surface. A new reservoir is currently being designed to thispurpose.

Measuring the void fraction accurately for flows in which friction have a non-negligiblecontribution was not possible during this investigation. Due to large volumes of polymersolution injected into the system, the read-off of the liquid level was too inaccurate. Thislead to inaccurate void fraction calculations. Installing a pressure transducer under thesmall tube connected to the reservoir which is visible in Figure 11, will significantlyincrease the accuracy of the hold-up measurement. The flow rate of the polymers injectedinto the system can be monitored by the coriolis mass flow meter and recorded on the PC-based data acquisition system. The values of the pressure transducer can equally be readout. This change is simple to implement and will allow accurate void fractionmeasurements. Fehmers [22] is currently developing a tomography system which will beinstalled on the MPPGL set-up. This system will also allow accurate void fractionmeasurements, that will be independent of the measurements using the level in thereservoir.

The pressure transducers used in this facility should be replaced by differential pressuregauges. To correctly and accurately measure frictional pressure drops, it is necessary todetect pressure differences that cannot be measured using absolute pressure measurements.

To test this new facility, experiments have to be performed to measure the drag in a single-phase flow for a set of turbulent Reynolds numbers. A so-called Moody diagram can be


obtained and the measured values should be compared to literature. This diagram plots adimensionless pressure drop as a function of a dimensionless flow rate.

Finally, this experiment should enable to measure drag reduction in single-phase flows.When this effect is measured and tested, more concrete measurements and conclusions canbe made on vertical multiphase drag reduction. The assumptions made as to why thefriction has not been reduced in these experiments have to be tested. A recommendation isto install a disk pump replacing the currently present centrifugal pump. A disk pumpminimizes the mechanical degradation of polymer solutions [23]. This change makes itpossible to recirculate pre-mixed polymer solutions in the set-up. By these means, thepolymer solutions can be mixed before arriving into the set-up, and the full developmentof the flow is facilitated. If this change appears not to be sufficient, a set-up with a highertest pipe should be envisaged.

Recent experiments performed by [34] have shown vertical multiphase drag reduction in arecirculatory facility with a test pipe of 25 meters height. In these experiments, a disk pumpwas used to minimize the degradation of the polymers and a very long test pipe is availablethat enables the correct mixing of the polymer and development of the flow. The fluidsused are water and gas and a Percol 721 polymer was added.

5.2.2. Vertical multiphase drag reduction

From these experiments we have learned that drag-reducing polymers can cause a decreasein the void fraction for vertical two-phase flows. These results have shown this negativeeffect for flows where hydrostatic pressure drop dominates the frictional pressure drop.Taking into account the qualitative aspect of these results, the focus for future work on thistopic should be dedicated to obtaining accurate measurements for a broad range of flowconditions. Especially, the effect of the polymers on the hydrostatic pressure drop forregimes where friction plays an important role should be investigated. We have seen thatthe increase in bubble diameter has caused a migration to the gas bubbles towards thecenter of the pipe. For different flow conditions, this effect might change.

The effect of the polymers on the friction in the flow remains unsolved and should formtopic for future research, using the recommendations set out above. In any case, results inhorizontal multiphase flow have shown reduction in friction factors up to 65%. Takinginto account the flow patterns which are common to oil wells and gas-condensate wells, ifthis improvement can be reached in vertical production tubing, even with the negativeeffect of the hydrostatic pressure drop, significant overall improvement can be achieved.This underlines the importance of future investigation on this topic.


REFERENCES

[1] Geest, S. van; Comparison of different air injection methods to improve gas-lift performance, StudentReport EP 2000-5514, Shell Rijswijk, 2000.

[2] Fernandes, R.L; Multiphase Drag Reduction. Part I: Proof-of-concept Experiments, Internal ShellReport EP 2003-5028, Shell Rijswijk, 2003.

[3] Wahl, H.A., Beaty, W.R., Dopper, J.G,. and Haas, G.R.; Drag Reducer Increases Oil Pipeline FlowRates, SPE 10446 presented at Offshore South East Asia 82 Conference, Singapore, 1982.

[4] Visser 't Hooft, M.; Efficiency improvement of the gas-lift technique by decreasing the bubblediameter into the micrometric regime. Student Report EP 2002-5479, Shell Rijswijk, 2002.

[5] Song, C.H., No, H.C. and Chung, M.K.; Investigation of bubble flow developments and its transitionbased on the instability of void fraction waves, Int. J. Multiphase flow 21, No. 3, 1995.

[6] Schrama, E.; Breaking up slug flow into small-dispersed bubbly flow using a passive mechanicaldevice, Student Report, EP 2002-5464, Shell Rijswijk, 2002.

[7] Oliemans, R.V.A.; Applied multiphase flows, Delft University of Technology, Delft, The Netherlands,1998.

[8] Mansfield, P.D., Lawrence, C.J., Hewitt, G.F.; Drag Reduction with additives in multiphase flow: Aliterature survey, Multiphase Science and Technology, 11, pp. 197-221, 1999.

[9] Taitel, Y., Barnea, D., Dukler, A.E.; Modelling flow pattern transition for steady upward gas-liquidflow in vertical tubes. A.I.Ch.E. Journal Vol.26 No.3, p.345-352, 1980.

[10] Guet, S., Ooms, G. and Oliemans, R.V.A.; Influence of bubble size on the transition from low-Rebubbly flow to slug flow in a vertical pipe, Experimental Thermal and Fluid Science, Vol. 26, Issues 6-7, pp. 635-641, August 2002.

[11] Barnea, D. and Taitel Y.; Flow Pattern Transition in Two-Phase Gas-Liquid Flows, A Chapter in theEncyclopedia of Fluid Mechanics, 3 , Gas Liquid Flows, Gulf Publishing, N.P. Cheremisinoff, Editor,403-474, 1986.

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[17] Al-Sarkhi, A., and Hanratty, T.J.; Effect of drag-reducing polymers on pseudo-slugs-interfacial dragand transition to slug flow, International Journal of Multiphase Flow, 28, pp. 1911-1927, 2002.

[18] Lumley, J.L; Drag reduction by additives. Ann. Rev. Fluid Mech. 1, 367-384, 1969.

[19] De Gennes, P.G; Introduction to polymer dynamics. Cambridge: Cambridge University Press, 1990.

[20] Gyr. A. & Bewersdorff, H.-W.; Drag reduction of turbulent flow by additives. Dordrecht: Kluwer,1995.

[21] Tomiyama, A., Tamai, H., Zun, I. and Hosokawa, S.; Transverse migration of single bubbles in simpleshear flows. Chemical engineering science 57, pp. 1849-1858, July 2002.

[22] Fehmers, G.; Volumetric flow rates from impedance tomography in oil-gas flows. Third worldcongress of an industrial tomography, Banff, Canada, 2003.

[23] Draad, A.A.; Laminar-turbulent transition in pipe flow for newtonian and non-newtonian fluids. PhDthesis, Delft University of Technology, The Netherlands, 1996.

[24] Hinze, J.O., AIChE Journal 1, 289-295, 1995.


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ACKNOWLEDGEMENTS

This thesis is based on six months of work within Shell Exploratory Research in Rijswijk.This report functions as the authors’ masters thesis in Applied Physics, within theLaboratory of Aero & Hydrodynamics of the Delft University of Technology.

During this period, many people have assisted and contributed to the work which has beenpresented throughout this report. I am very grateful to all and would like to give specialattention to some of these people.

Gijs Ooms and Frans Nieuwstadt for giving me the opportunity to perform my mastersinvestigation within a company as Shell International. They have given be great help insetting out my research and analysing my results. The independent manner of working Iadopted never seemed to be problem and I am very thankful that this was possible. Iwould like to thank René Delfos for his critical view which helped me ask the correctquestions to pursue my investigation. Especially in the final period of this work, René hasbeen a great help providing me with lots of useful information. I will really miss his criticalview in the future.

Richard Fernandes has been a great support throughout the entire period of my report.The freedom and confidence he has given me to direct my project is very muchappreciated. It has been a great pleasure and privilege to work with Richard. Hisstraightforward way of attacking problems has given me a great deal of inspiration.

Erik Schrama was a great help in the first few months of my investigation and he enabledme to obtain experimental data within the first months of this investigation. Erik’s insightsduring my research have been a great help. I also thank Erik for being able to use his digitalvideo camera during the experiments.

A special word of appreciation is in order of Boy Markus. Time and time again, he came upwith practical solutions to the large amount of problems that were encountered during thedesign and construction of the experimental facility. I also thank Maradona, René van derBruggen, Jos Beljaars, Sjon Vlasbom, Alex Schwing and others in the mechanicalengineering team.

My family has helped me out in more practical events. A special thanks also goes toMinnemijn, who has been a great support and her photoshop skills have been a great help.My residence, “Het Plateelkasteel” has equally been a great help. Especially in the finalweeks of this work, it was great to arrive home and to know I could always relax.

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