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1990

Drag reduction in pipe flows with polymeradditivesDaniel W. Grabowski

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Recommended CitationGrabowski, Daniel W., "Drag reduction in pipe flows with polymer additives" (1990). Thesis. Rochester Institute of Technology.Accessed from

DRAG REDUCTION IN PIPE FLOWS WITH POLYMER ADDITIVES

by

Daniel W. Grabowski

A Thesis Submitted

in

Partial Fulfillment

of the

Requirements for the Degree of

MASTERS OF SCIENCE

in

Mechanical Engineering

Approved by: Prof.__D_r_._A_I_i_O-=gu=-""t:--:-_---:- _(Advisor)

Robert A. ElIsonProf.-------------------

Prof. _-N-am-e--I-I-I-e-=g:....i_b_l_e ---..;.

Name IllegibleProf.-----_----::_-----------

DEPARTMENT OF MECHANICAL ENGINEERING

COLLEGE OF ENGINEERING

ROCHESTER INSTITUTE OF TECHNOLOGY

ROCHESTER, NEW YORK

FEBRUARY 1990

DRAG REDUCTION IN PIPE FLOWS WITH POLYMER ADDITIVES.

I Daniel W. Grabowski hereby grant permission to

the Wallace Memorial Library, of R.I.T., to reproduce

my thesis in whole or in part. Any reproduction will

not be for commercial use or profit.

February 1990

ACKNOWLEDGEMENT

I would like to dedicate this work to my family for

their loving support and encouragement.

To my advisor Dr. Ali Ogut for his continual guidance,

To my professors at R.I.T. for tneir instruction.

And finally to Dave Hathaway and the Machine shop for

all their help in setting up this experiment.

11

ABSTRACT

Polyethylene Oxides (PEO) with molecular weights

of 4 and 6 million and a Polyacrylamide (PAM) with a

molecular weight of 15 million, were added to a

turbulent pipe flow (15000 < Re < 50000) for drag

reduction. The polymer was injected directly into the

test section in one scenario, premixed in a tank and

then pumped through the test section in the second.

The injection addition method was found to be optimal

because it subjected the polymer to lower amounts of

shear stresses than the premixed addition method. A

maximum of 75% reduction in drag was obtained. Even

trace concentrations, as low as 2.5 WPPM (weight parts

per million) , resulted in as high as 37% reduction in

drag. Long thin high molecular weight polymers (PEO)

were more effective than coiled high molecular weight

polymer (PAM) . For the same molecular structure it was

found that the polymer with heavier molecules had

better drag reducing characteristics. The polymer with

coiled molecules, however, is more resistant to shear

stresses which break down the polymer into smaller less

effective molecules. It was found that there is a

critical concentration for the greatest drag reduction.

This concentration is approximately 375 WPPM (.0375% by

iii

weight) of PEO for the injection method, and 500 WPPM

of PEO for the premixed method. At greater

concentrations, the viscosity of the solution increases

such that the drag reduction characteristics of the

polymer can no longer compensate.

iv

TABLE OF CONTENTS

Page

List of Tables vii

List of Figures viii

List of Symbols ix

1.0 Introduction 2

2.0 Theory and Literature review 7

2.1 Friction Factor 7

2.2 Drag Reduction 11

2.2.1 Friction Factor 11

2.2.2 Mechanism 12

2.2.3 Onset of Drag Reduction 16

2.3 Polymer Degradation 16

3.0 Materials and Methods 19

3.1 Experimental Set-up 19

3.2 Determination of Flow Parameters 22

3.2.1 Reynolds Number 22

3.2.2 Pressure Drop 25

3.2.3 Friction Factor 26

3.2.4 Wall Shear Stress 26

3.2.5 Percent Drag Reduction 26

3.3 Drag Reduction Test Procedure 27

3.3.1 Premix Drag Reduction

Measurement Procedure 27

3.3.2 Injected Drag Reduction

Measurement Procedure 28

3.4 Viscosity measurement procedures

Using a Capillary Tube Viscometer .. 33

4.0 Results and Discussion 36

4.1 Friction Factor as a Function

of Reynolds Number 36

4.1.1 Effect of Polymer Addition

Method 36

4.1.2 Effect of Molecular Weight

and Structure 50

4.1.3 Maximum Drag Reduction 53

4.2 Friction Factor as a Function

of Concentration 55

4.3 Friction Factor as a Function of

Concentration and Vol. Flow Rate ... 57

5.0 Conclusion 63

References 65

Table of Contents (Continued)

Appendices

A. Data

Al. Calibration data 67

A2. Viscosity data 69

A3. Drag Reduction Data 73

A4. Regression Analysis Results 75

B. Data Analysis and Sample Calculations

Bl. Viscosity 76

B2. Injection Quantities 77

B3. Manometer and Pressure Drop 78

Bibliography 80

vi

LIST OF TABLES

Table Page

2.1 Comparison of Empirical Correlations

of Friction Factor for water in

smooth pipes 10

4.1 Regression Analysis Results

f = * (Re) 45

4.2 Test Results for Water and Polymer

Solutions at 250 WPPM 46

4.3 Regression Analysis Results

f = i (C.Q) 62

Al.l Flow Meter Calibration Data 67

A1.2 Injection flow Calibration Data 68

A2.1 Viscosity Measurement Data 69

A3.1 Pipe Flow Friction Data 70

A4.1 Regression Analysis Results

f = i (Re) 75

vii

LIST OF FIGURES

Figure Page

3.1 Experimental Setup 20

3.2 Polymer Injection Chamber 21

3.3 Manometer 23

3.4 Flow Meter Calibration Curve 24

3.5 Polymer Injection Flow Calibration

Curve 30

3.6 Static Pressure at Injection Location... 22

3.7 Effect of Polymer Concentration

on Solution Viscosity 34

4.1 Friction Factor For Water and

By Equations 2.4 and 2.5 37

4.2 Friction Factor For Premixed

PEO (WSR-301) 39

4.3 Friction Factor For Premixed

PEO (WSR-303) 40

4.4 Friction Factor For Premixed

PAM (N-300-HMW) 41

4.5 Friction Factor For Injected

PEO (WSR-301) 43

4.6 Friction Factor For Injected

PEO (WSR-303) 44

4.7 Comparison of Addition Methods

for 50 wppm of PEO (WSR-301) 48

4.8 Comparison of Addition Methods

for 50 wppm of PEO (WSR-303) 49

4.9 Friction Factor for Different

Molecular Weight Polymers

(WSR-301, 4 Million;

WSR-303, 6 Million) 51

4.10 -Friction Factor for Premixed

Polymers with Different Molecular

Structures (301 & 303 -

PEO;

300 -

PAM) 52

4.11 Maximum Drag Reduction

(WSR-303, 500 wppm, Premixed)

Compared to Virk's [10] Results 54

4.12 Effect of Polymer Concentration

on Friction Factor for Fluid

Velocity of 0.69 m/s 56

4.13 Effect of Polymer Concentration

on Friction Factor for Fluid

Velocity of 2.05 m/s 58

4.14 Comparison of Calculated

(Equation 4.3) and Measured

Friction Factor For

Premixed PEO (WSR-301)*

60

4.15 Comparison of Calculated

(Equation 4.3) and Measured

Friction Factor For

Injected PEO (WSR-303) 61

viii

LIST OF SYMBOLS

C Average Polymer Concentration in Test Section,wppm

CT Threshold Concentration, wppm

ccr Critical Concentration, wppm

Cp Concentration of injection Solution, wppm

D Pipe Diameter, m

f Friction Factor

fp Friction Factor of Polymer Solution

fw Friction Factor of Water

g Gravitational Constant, m/s2

h Height difference in Manometer, m

L Length of Test Section, m

MW Molecular Weight

P Pressure, kPa

Ptot Total Pressure needed to Inject, kPa

P . Static Pressure Due to Flow, kPa

P. Pressure needed to Inject Solution, kPa

Q Flow rate In Test Section, n\3/s

Qp Flow rate of Injection Solution, m^/s

r2 Coefficient of Correlation

u*

Friction velocity, m/s

Re Reynolds Number of Solution

V Average Flow Velocity in Test Section, m/s

W Polymer Onset Wave Number

y+ Dimensionless Distance From Wall

%DR Percentage of Drag

Constant

fi Constant

Y Constant

* Polymer Solution Parameter

r. Wall Shear Stress, Pa

ix

LIST OF SYMBOLS (cont'd)

r Onset Wall Shear Stress, Pa

p Fluid density, kg/m^

Degradation Delay Time, Sec

* Absolute Viscosity,N-sec/m2

Kinematic Viscosity, m2/s

Functional Relationship indication

V

1 . 0 INTRODUCTION

The phenomenon of drag reduction by using

additives in Newtonian and Non-Newtonian fluid flows

was discovered back in 1947 by Toms [1] , thus it is

sometimes calledToms'

phenomenon. Credit for the

first experiments with drag reduction, however, should

go to H. S. Hele-Shaw [2]. He was interested in the

skin friction of marine animals and tried to simulate

their soluble excretions by the addition of fresh bile

to water. Later, this phenomenon was described by

Lumley [3] as "The reduction of skin friction in

turbulent flow below that of the solvent alone". Drag

reduction with polymer additives has received a great

deal of attention recently because it suggests

practical benefits in many areas. The fields of fire

fighting, storm control, medicine, pipeline

transportation, scale flow testing, racing and military

sea going vessels have all taken an interest in the

discovery.

Under certain conditions of turbulent pipe flow,

dilute polymer solutions, as small as 1 weight parts

per million (WPPM) , require a smaller specific energy

expenditure than the pure solvent. Thus, with a

polymer solution, a lower pressure gradient is needed

to maintain the same flow rate or a higher flow rate

can be attained for the same pressure gradient.

The field of fire fighting can benefit

tremendously from the use of polymer additives. Fire

fighters can use polymers to get more water to a fire

in a shorter period of time. A sprinkler system would

also be able to pump more water. This would be an

economical way to increase capacity without having to

put in a larger system. In the same way storm drainage

systems can carry a larger capacity. This would be

very useful during severe storms. Pipeline

transportation and hydraulic transport of solids such

as coal slurries (Golda [4]) could be run more

efficiently if an inexpensive polymer injection system

was developed. Usually though, the cost of such a

system can be prohibitive.

Polymer additives can also be used for external

flows if the polymer concentration can be maintained in

the boundary layer. One way to do this is to

continuously inject polymer into the boundary layer.

The Navy has tested the use of polymer solutions

injected out the nose of sea vessels. They would be

able to move faster or with less power. The everyday

use of such a system would not be economically

feasible, but in an emergency a quick escape is

priceless. Racing boats have used polymer films

released over a period of time from their hulls to

increase their speed. A hydro-foil boat, which

requires more energy at the start, to lift off, could

benefit from a polymer drag reducing system. Drag

reducing polymer additives have been used to overcome

scale-up problems in the testing of ship models in

towing tanks. The polymer alters the viscous friction

in such a way that a small model can easily be used to

simulate the motion of a large ocean vessel. In the

medical world the use of polymer solutions as the

driving fluid in artificial hearts has been

investigated. Also the introduction of polymers

directly into the blood of animals with heart disease

or arteriosclerosis has been studied. The polymer will

decrease the hydrodynamic drag "in vitro". It has been

tested to be non-toxic in laboratory animals.

The actual use of polymer additives in these

applications have had limited success because of the

characteristics of polymers under high shear stresses,

such as in turbulent flow. Under high shear stresses,

these polymers degrade at very rapid rates. As time

5

progresses the drag of the solution approaches that of

the solvent. The degradation rate of polymers is also

affected by temperature, radiation, acidity, mechanical

stress, chemicals, ultraviolet light and ultrasonics.

In the past many investigations have been

conducted, however, there is still not a clear concept

of how drag reduction actually occurs. Before any

practical use of polymer additives can be implemented,

extensive work must be done to understand the

characteristics of additive induced drag reduction.

The objectives of this study were to:

1. Show that drag reduction in a pipe flow with

polymer additives does occur.

2. Compare the drag reducing characteristics of

different polymer types and different molecular

structures.

3. Find a minimum threshold concentration (Ct)

needed to start drag reduction.

4. Find a critical concentration (Ccr) at which

polymeric drag reduction is maximum.

5. Compare two types of polymer addition

methods:

A. Polymer additives are introduced into

6

the pipe-flow test loop as premixed.

B. A highly concentrated polymer solution

is introduced into the pipe-flow test

loop by injection.

6. Develop empirical correlations, and compare

these to previous works.

2.0 THEORY AND LITERATURE REVIEW

Turbulent flow (Reynolds Number (Re) >2300) is

characterized by random three dimensional motion of

fluid particles superimposed on the mean flow. There

is a macroscopic mixing of fluid layers. Consequently,

in turbulent flow there is a high momentum transfer in

the radial direction and a high energy loss in the

flow.

2.1 FRICTION FACTOR

The friction factor (f) is generally used to

characterize the drag in a flow. It can be defined as

a function of the following flow variables; pressure

drop (^P), pipe diameter (D) , length (L) , fluid density

( p ) , average fluid velocity (V) , and pipe roughness

(e) .

f * 4 ( JP,D,L, / ,V,e) 2.1

Applying the Buckingham Pi methods of dimensional

analysis an expression for f in terms of these

variables can be found. This equation is commonly

expressed as

f = 4_P D 1 2.2

L 2 p V2

In laminar flow the friction factor is expressed

by Poiseuille's Law.

f = 16 2.3

Re

For turbulent flow in smooth pipes the friction

factor is defined by Prandtl's universal Law of

friction:

1.= 1.2 Log(ReVf) - 0.8 2.4

Vf

Equation (2.4) agrees very closely with many

experimental studies [5-9] for a wide range of Re, from

500 to 10 million. Blasius offered a simpler equation

which is valid at a smaller range of Re from 3000 to

100,000.

-0.25

f = 0.0791 Re 2.5

Although many other equations have been developed for

the turbulent friction factor in smooth pipes,Blasius'

9

equation (2.5) is the most popular one because of its

simplicity and Prandtl's equation (2.4) is usually used

because of its accuracy. A comparison of friction

factors from these two equations at different Re is

given in Table 2.1

10

TABLE 2.1

COMPARISON OF EMPIRICAL CORRELATIONS

FOR FRICTION FACTOR

Re Blasius

f

Prandtl

f

%

Difference

5000 0.00940 0.00935 0.53

10000 0.00790 0.00773 2.20

20000 0.00665 0.00647 2.78

50000 0.00530 0.00522 1.53

100000 0.00445 0.00450 -1.11

200000 0.00375 0.00390 -3.85

500000 0.00297 0.00327 -9.17

1000000 0.00250 0.00290 -13.79

2000000 0.00210 0.00260 -19.23

5000000 0.00167 0.00225 -25.78

10000000 0.00140 0.00202 -30.69

11

2.2 DRAG REDUCTION

In turbulent flow a small concentration, as low as

0.003% by weight (30 WPPM), of certain polymers has

been shown to decrease the drag by as much as 8 0% [17] .

Often 1 to 500 WPPM is used to reduce drag. Drag

reduction in a turbulent pipe-flow is characterized by

a reduction in the friction factor.

2.2.1 Friction Factor

A regime with drag reduction, in which the

friction factor is a function of polymer

characteristics, was approximated by Virk [10] for PEO.

1 - (4+1) Log (ReVf) - 0.4 -

Log (V2 DW) 2.6

Vf

D - Pipe diameter.

W - Polymer onset wave number ( wTmP)l * ) .

I - Slope Increment

The slope increment is the change in slope between

the polymer solution and the solvent when plotted on =-

verses Re Vf coordinates.

Virk [10] pointed out that there is an "asymptotic

regime of maximum possible dragreduction"

inwhicfi*

the

12

friction factor is not a function of polymer solution.

The following non-polymer specific equation was

obtained for this condition.

1 = 19.0 Log (ReVf) - 32.4 2.7

He also derived an equation of the form ofBlasius'

for

a Re range of 4000 to 40000. This relationship is also

insensitive to the polymer solution being employed.

-0.58

f = 0.58 Re 2.8

Virk et al. [11] also obtained two equations of the

same form for maximum drag reduction using five

different molecular weights of PEO.

1= 23.0 Log (ReVf) -

43.0 2.9Vf

and

-0.55

f = 0.42 Re 2.10

2.2.2 Mechanism

Elongational flows such as pipe flows seemto"

13

allow polymers the most opportunity to reduce drag.

Lumley [3] suggests that macromolecular elongation

initiates a sequence of changes in mean and turbulent

flow structure. Fluid particle elongation of

significant magnitude has been studied in near-wall

flow visualizations by Grass [12] and Kim, Kline and

Reynolds [13] . However, the precise role of the

elongation of flows during turbulent bursts, or the

elongation of macromolecules is still under study.

Tandon, Kulshreshtha and Agarwal [14] summarized

five theories on Drag Reduction with polymer additives.

1. The effective wall layer theory states that

the pipe walls induce a preferred orientation of the

polymer molecules near the wall. Drag reduction can be

explained by effective slip velocities of the fluid at

the wall.

2. The anisotropic viscosity theory relies on

the expansion of random coils of the polymer molecules

to explain drag reduction.

3. The viscoelastic theory states that the

polymers can store kinetic energy given up by the flow

in the form of elongation and deformation which

decreases radial turbulent flow.

4. In the adsorption theory, the polymer along

14

the wall provides a thickened laminar sublayer which

has the effect of reducing drag.

5. The microcontinuum theory describes elongated

polymers in a shear flow to behave like micropolar

fluids, which explains the drag reduction.

Virk [10] has also explained this phenomenon. He

stated that the macromolecules of polymer in a

turbulent pipe flow near the wall hinders the transfer

of energy between the axial and transverse components

of turbulent kinetic energy. This reduces turbulent

diffusivity and retards turbulent transport thus

decreasing turbulent friction drag. This agrees with

the previously stated viscoelastic theory.

There are three distinct zones of the velocity

profile in a turbulent pipe flow. The laminar sublayer

(y+< 5) , buffer zone (5 <

y+

< 30) and the turbulent

core (30 < y+) . Wherey+ is a dimensionless parameter

to describe the distance from the wall of the pipe to

the axis.

y+ =y_u*

2.11

w

where is the Kinematic viscosity.u*

is the

friction velocity defined by

15

u*= V(rmlp) 2.12

where *. is the shear at the wall and p is the fluid

density.

When drag reduction is at a maximum, the buffer

zone extends all the way to the axis of the pipe. The

turbulent core does not exist. This is the zone in

which drag reduction occurs. Oldroyd [15] suggested

that polymers affect the flow most in a region near the

wall(y+ = 15) . This study is supported by many other

works. Wells and Spangler [16] confirmed this by

injecting polymer solutions into a flow at both the

wall and the pipe axis. The former started reducing

drag almost instantly after injection. The latter

reduced drag after the solution diffused via turbulence

towards the wall. This also suggests that if the

polymer could be kept in a small annulus near the wall

greater amounts of drag reduction could be attained.

This was also confirmed by McComb and Rabie [17].

McComb and Rabie [18] later concluded that drag

reduction occurred in an effective annulus bounded by

15 <_y+

< 100 for Polyox WSR-301, a Polyethylene Oxide

(PEO) and Separan AP30, a Polyacrylimide (PAM).

16

2.2.3 Onset of Drag Reduction

It has been found that for laminar flow, polymers

do not affect the drag. Even in turbulent flows at

small Re, drag reduction can not be obtained. Virk

[10] has shown that for Re < 12000 the drag of a PEO

solution is the same as that of the solvent alone.

Only after Re > 12000 does a polymer solution have the

effect of reducing drag. He states that regardless of

pipe size, the given polymer solution only reduces drag

after a certain onset wall shear stress ( r,= 7.0 Pa

for PEO) . This onset shear stress is the threshold

shear needed to induce drag reduction and is

independent of polymer concentration but corresponds to

a Reynolds number of 12000. Virk et al. [11] found

that the onset wall shear stress was related to the

random coiling effective diameter of the polymer.

2.3 POLYMER DEGRADATION

Polymers break down and lose their effectiveness

when subjected to shear, this is termed degradation.

Degradation manifests itself as a decrease in polymer

molecular weight with time of shear. The applied shear

causes ruptures of covalent molecular bonds due to

17

severe deformation of the polymer. It has been found

by Weissler [19] that cavitation in turbulent flow can

cause a violent collapse and expansion of bubbles in

solution as a result of pressure changes that occur due

to turbulent bursts. This, Weissler owes, can also be

responsible for polymer degradation.

There is a certain initial time ( 9 ) when the

polymer is not affected by the shear stress. Sylvester

and Kumar [20] have defined three distinct regions of

polymer degradation. At 0<t< 9 there is constant drag

reduction. The polymer does not deteriorate at all.

For # <t< oe the polymer degrades in a linear fashion

with time. As a result there is a linear decrease in

polymer effectiveness or drag reduction. In the third

region as time approaches infinity, the drag of the

polymer solution approaches asymptotically that of the

solvent. White [21] has shown that under high shear

stresses, the polymer solutions degrade at very rapid

rates. Significant degradation can occur in a matter

of a few seconds. This suggests that 9 is very small

at high Re.

Although the theories behind turbulent flow are

precise and well documented, those that describe

additive induced drag reduction are many and varied.

This study does not attempt to critique the theories

18

previously stated. It is more of an analysis of

Polymer drag reducing characteristics.

19

3.0 MATERIALS AND METHODS

3.1 EXPERIMENTAL SETUP

The experimental apparatus consisted of a closed

loop pipe flow system in which water was circulated.

There were eight major components in this system as

shown in Figure 3.1. These components are:

1. Centrifugal pump and motor.

2. Flow rate control valve.

3. Flow meter.

4. Settling tank. At the top was a relief valve

to let the air escape during start up.

5. Polymer injection chamber (Figure 3.2). This

was a vessel with a pressure gage and an inlet and

outlet valve. This chamber used air pressure to

overcome the static pressure in the pipe to inject

polymer solution into the pipe flow. It held

approximately one half gallon.

6. The test section. The test section was made

of one inch diameter drawn copper tubing. There were

flow trip rods at the beginning to assure turbulent

flow. Two static pressure taps, spaced 4 meters apart,

were used to measure static pressure drop along the

pipe.

20

21

PR55UC. G*6-&

u, To Tksr

Figure 3.2 Polymer Injection Chamber

22

7. Manometer. A manometer (Figure 3.3) was used

to measure pressure difference between the pressure

taps. Equations for determining the pressure drop from

the manometer measurements are in Appendix B3.

8. Reserve tank. This contained drain and tap

water refill capabilities.

3.2 DETERMINATION OF FLOW PARAMETERS

3.2.1 Reynolds Number

The flow meter was calibrated by collecting water

in a graduated container over a period of time. Figure

3.4 shows the flow meter calibration curve. From this

flow rate the average velocity (V) was calculated as:

V = Q/A 3.1

Where:

Q = Volumetric Flow Rate, m^/s

A = cross sectional area,m2

23

/To Pressure Ta^j

Ai R

vS </

VJ*TR

Figure 3.3 Manometer

24

0)

>u

3

U

c

oH

^^ P

*(0

^^ ja

oz (0

o

5<Ul -U

ocs

SB sUl 01- rH

Ul b

1*

* oo

o-1

(1)

Ik M-i

b

s%

4-m-

) aivu Moid aaunsvaw

25

The solution Reynolds Number was calculated by

Re = JUi 3.2

M

where:

p =solution density, kg/m3.

V = mean velocity, m/s.

D = pipe diameter, m.

f =solution viscosity, N-sec/m2.

It was assumed that the density of the solution

was the same as that of the solvent. This is a valid

assumption because at such low concentrations the

density change is minuscule.

3.2.2 Pressure Drop

The pressure drop (AT?) was calculated using the

height difference (h) from the manometer, by using the

following equation.

P =

p gh 3.3

where g is gravitational constant, m/s2.

The density and compressibility of air in the manometer

were assumed negligible in these calculations. This

assumption was validated and is shown in Appendix B3 .

26

3.2.3 Friction factor

The friction factor was calculated using:

f - JP D 1 3.4

L 2 ,V2

3.2.4 Wall Shear Stress

The wall shear stress was calculated by:

r- = D Jp 3.5

4 ~L

Where, L is length between pressure taps. This was

developed assuming fully developed flow (the test

section started 1.5 meters from polymer addition

location), incompressible, steady flow, in a horizontal

pipe.

3.2.5 Percent Drag Reduction

The percent drag reduction (%DR) can be expressed

in terms of the friction factors for pure water (fw)

and that with polymer solutions (fp) as:

27

%DR = (1 - f ) 100 3.6

f.-w

3.3 DRAG REDUCTION TEST PROCEDURE

Two different types of tests were run.

1. The polymer was premixed in the reserve tank

while the system was off. This did not affect the

calibration of the flow meter.

2. The polymer was injected through the

injection chamber, directly into the pipe flow. The

injection was made at the wall of the pipe normal to

the flow.

3.3.1 Premix Drag Reduction Measurement Procedure

The procedure for conducting premixed drag

reduction measurements was as follows.

1. The weight of water in the system was

measured. It was made sure that at every run of the

test the water was at the same level.

2. The desired weight of polymer was measured to

obtain the correct concentration in weight parts per

million (WPPM) . The entire system weight was used as

the solvent.

28

3. The system was turned on with fresh water and

the flow rate control valve was set to get the desired

flow rate. The system was turned off with the flow

control valve left at the same level.

4. The polymer was slowly mixed in the reserve

tank until it was fully dissolved into a solution.

Different polymers dissolve at different rates, and

some, if mixing is not done carefully can form a gel

structure, which will increase the mixing time.

5. The pump was turned on, and the flow rate

readjusted.

6. After all the air was out of the system the

pressure drop reading was taken with the manometer.

The time it took between turning on the system and

taking the pressure drop reading was kept constant from

test to test to maintain similarity in data readings.

This was needed because of polymer degradation.

3.3.2 Injection Drag Reduction Measurement Procedure

The polymer injection flow rate was calibrated by

timing how long it takes to empty the injection chamber

under different pressures with different polymer

concentrations. From this information the polymer flow

rate can be calculated. Figure 3.5 shows calibration

29

curves for the injection chamber. Note that the

pressure to achieve a given injection flow rate for

concentrations less than 1000 WPPM is constant. At

less than 1000 WPPM, the increase in viscosity due to

polymer concentration does not affect the flow rate

significantly. The injection method was conducted only

with PEO because PAM showed poor results with the

premixed method.

The following is a step by step procedure for the

injection method.

1. The system was drained and fresh tap water

was added. In this case the amount of water in the

system is not critical.

2. The equation below was used to find the

injection polymer concentration and flow rate needed to

obtain the desired average concentration and fluid flow

rate in the test section.

c_

c/ *r 1 3.7

I Q wp

Where:

C = Pipe flow average concentration, wppm.

CD= Polymer injection concentration, wppm.

Qp= Polymer injection flow rate, m3/sec.

Q = Pipe flow rate, m3/sec.

30

o

oo

3a.a.

o

o_Cv

o

oo

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8:

o

omC\|

I I

O <

r

a>

>

M

3

U

a

0H

<4J

as

a u

tt J3

H

rH

u IB

a U

3 3

CO 0

COrH

Ul

K c

BUoH

(C4J

<0)

r-i

zCM

ou

p 0)

oUl rH

^ 0

z CU

in

0)

M3

H

1X4

-i- aiVU MOld NOI103PNI

t

31

Qp and Cp must be chosen such that, with a half gallon

of injection solution, the solution will not run out

before the pressure drop reading is taken.

Approximately 25-30 seconds is needed, therefore, the

injected flow rate should not be much greater than

7.5 71 xio~ 3 m3/s. Because the injection flow rate was driven

by air pressure and controlled by a pressure gage, for

accuracy the pressure should not be required to be

below 34.5 kPa. The injection flow rate, therefore,

should not be below 5.678 x 10~5m3/s. Sample

calculations of injection quantities are shown in

Appendix B2.

3. Figure 3.5 was used to find the required

injection pressure to push a certain concentration out

of the injection chamber at the correct flow rate. The

total pressure (Ptot) required for an injection is the

sum of the static pressure (Pst) at the injection

locations and the injection pressure (Pin^) for a given

flow rate.

tot st inj

Static pressure is shown in Figure 3.6, for different

flow velocities. This was measured with a mercury

manometer.

32

0H

Q -P

*(0

o

0

1-5

c

0 0-H

N-p

T

u0)

<* |

E cM

e P

^ (0

0)

M

Ul 3

25CO

CQ

0

cc M

(k

:* O

oOH

IL

-P

(0

-P

CO

V

d)

P.

3

tP

H

b

(Yd)*) aunssaud ouvis

33

4. The polymer solution was mixed and poured

into the injection chamber. The air hose was hooked up

and set at the desired injection pressure.

5. The pump was started and the system flow rate

was set as desired.

6. The top valve of the injection chamber was

opened to pressurize the injection solution, then after

all the air was out of the system the bottom valve was

opened to allow the solution to flow into the test

section.

7. The pressure drop reading was taken at the

manometer before the injection chamber was emptied.

3.4 VISCOSITY MEASUREMENT PROCEDURES USING A CAPILLARY

TUBE VISCOMETER.

A capillary tube viscometer was used to measure

the viscosity of polymer solutions. Figure 3.7

displays the absolute viscosity as a function of the

polymer concentration. These values were used in

calculations of Re.

34

* * z >.p

? rH

CO

0CJ

e W

r -H

w >

C

o-H

P

3r-1

0CO

O

-o ^^ c* z o

& c

& o

5H

p^^

(0

zM

-p

o-o

ft

o C

CJ

< c

B0

CJHZ u

Ul g

O >i

-o

z

o

r-i

o

a,

Mo

MH

cc0

HI p

2 cj

>2H-l

i

eo w

*

ro

a)

p

3Oi

H

By

JW-i (8-Vd) aiisoosia aimossv

35

The procedure to measure the viscosity is listed in a

step by step form as follows.

1. The desired solution concentration of polymer

was mixed.

2. The capillary tube viscometer's bottom bulb

was filled with solution and set in the temperature

bath for approximately 5 minutes to allow it to come to

a constant temperature.

3. A suction device was used to pull solution to

the top bulb above the two hash marks.

4. A stop watch was used to measure the time it

takes for the solution to drop from the first to the

second hash mark.

5. The viscosity can be calculated using either

the given viscometer constant or by knowing the time

for a known standard such as water. The latter method

was used. Sample calculations of viscosity from

measurements are shown in Appendix Bl.

36

4.0 RESULTS AND DISCUSSION

4.1 FRICTION FACTOR AS A FUNCTION OF REYNOLDS NUMBER

In order to show the relationship between the

friction factor, f, and Reynolds number, Re, friction

factors were calculated from Equation 3.4 and plotted

against Re for pure water. This is shown in Figure

4.1, along with the relationships obtained from

Prandtl's universal friction law for smooth pipes

(Equation 2.4) andBlasius'

Equation (Equation 2.5).

Prandtl's andBlasius'

equations were developed

for turbulent flow of water in"smooth"

pipes. The

drawn copper tubing used in this experimentation has a

very low relative roughness and can be considered

"smooth". The friction factor for water in this study

is in the same range as that of Prandtl's and Blasius',

this indicates a smooth pipe.

The following equation was developed from

experimental data for Re of 20,000 to 60,000.

f = 0.107 Re*2935

4.1

This equation has a correlation coefficient of 0.984.

Equation 4.1 does not deviate from those of

37

K Om m

ai

Ul

CO

o

Ul

in

CM

T)

C

(0

CM

CO

c

o1-1

p

(0

3

er

w

>.

CQ

c

(0

p

0)

P

(0

p

o

p

o4-1

CJ

(0

Cu

c

oH

P

OH

P

Cu

s

0)

p

3

cn

-H

Cu

UOlOVd NOIlOIUd

38

Prandtl and Blasius by more than 20% in the range of Re

tested.

When drag reducing polymer additives were

introduced into the pipe-flow the friction dropped

significantly as shown in Figure 4.2. This figure is a

plot of f vs. Re and shows the progressive decrease in

friction factor with increase of polymer concentration

for PEO (WSR-301) as premixed. The drag is reduced

from that of water (0 wppm) by up to 61.9% with 500

wppm polymer concentration. Also seen in this figure

is the decrease in friction factor with increased Re as

predicted by theory.

Figure 4.3 shows similar results for PEO (WSR-303)

as premixed. Up to 70.4% drag reduction is seen for

500 wppm. This figure also shows that at very small

concentrations (2.5 wppm) of polymer, there is a

significant amount of drag reduction, up to 16.7%.

Figure 4.4 shows results for PAM (N-300-HMW) as

premixed which are similar the the premixed results for

PEOs. The reduction of f for the PAM is much more

gradual as seen by only a slight decrease in f at 50

wppm compared to water (0 wppm). The maximum

obtainable drag reduction was 21.2% for PAM at 500

wppm.

39

? o. - "OZ & a. Ok a.

a. a > > >

O w?v e e p m n

^^o o <

o

ro|1

OS

CO

5"-'

owcu

T3

dl

X-1-1

CCs

Ul P

aCU

2 P

3

Z

OCu

(0P

0

a p

^ o

o(0

Cu

z

111

c

oHI

H

CC p

CJ

H

p

Cu

<N

**

CD

P3

CP

HOXOVJ NOI13IUJ

40

oa 5- 2 5 | 1 |'

a. * a. o, cl o.

O'^^ooeiftK

n

o

CCu

CO

a-i

oz>Ul

cc

8

i

CO

Ow

a>

X

H

e<D

p

a.

p

oCu

P

Op

o

(0

Cu

c

oH

p

oH

P

Cu

ro

^

0)

P

3

CP

H

Cu

UOXOVd NOI13IUJ

41

oz

oo

_ Z a. a o.a S o. a.

fc s * * **

o^o

o id *- ei w>

Ul

>

Ul

sX

Io

o

ro

IZ

<Oi

c

0)

Xr-l

E

p

04

p

oCu

P

op

CJ

(0

Cu

c

oH

P

o

H

P

Cu

CD

P3D

H

Cu

UOlOVd NOI10IHJ

42

Figure 4.5 shows f versus Re for PEO (WSR-301) as

injected directly into the test section. This shows

that similar results are obtainable for injection

addition method as for premixed (Figure 4.2).

Figure 4.6 shows results for injected PEO (WSR-303).

As seen in this figure, the maximum reduction in drag

is 71.7% at 375 wppm. This figure also shows that with

the injection method, significant amount of drag

reduction can be obtained at low concentrations of

polymers. At 2.5 wppm the friction factor was reduced

by 37.7%.

All polymers with varying concentrations and

addition methods showed a general decrease in friction

factor with increasing Reynolds number and polymer

concentration. Many previous works [10,11,20] have

shown the same characteristics.

43

oz

oo

Ul

>Ul

cc

o

ro

I

CO

ow04

CDP

O

CD

P

0Cu

P

0P

CJ(0

Cu

c

oH

p

CJH

p

Cu

^<

<D

P

3

H

Cu

ts

UOXOVd NOI13IUJ

. _ f s 2 i i |

S *1252

44

Ul

CO

2

>

Ul

ro

O

ro

I

CC

CO

s

ow

0)

P

O

CD

P

OCu

P

op

CJ

ro

Cu

c

oH

p

CJH

P

Cu

VD

0)

p

3o>

H

Cu

H013VJ NOLLOIHJ

45

The relationship between the friction factor, f,

and Reynolds Number, Re, for polymer solutions can be

shown in the form of empirical equations.

f =

Re 4.2

Table 4.1 gives the ranges of constants for the range

of Re of each polymer, addition method and

concentration ( 12000 < Re < 60000).

TABLE 4.1

REGRESSION ANALYSIS FOR f" (Re)

fi

Water 0.107 -0.2935

PEO (WSR-301) Premixed 0.0102 to 0.1230 -0.1160 to -0..4040

PEO (WSR 303) Premixed 0.0112 to 0.0972 -0.1451 to -0. 3798

PAM (N300-HMW) Premixed 0.1185 to 0.3681 -0.3080 to -0 .4412

PEO (WSR-301) Injected 0.0309 to 0.1417 -0.0385 to -0 .4070

PEO (WSR-303) Injected 0.0318 to 0.1653 -0.2783 to -0 .4280

These equations are similar to equations 2.8 and 2.10.

Also a sample of reduced data is shown in Table

4.2 for water and concentration of 250 wppm for both

addition methods and all polymers. A complete set of

results is found in Appendix A3, Table A3.1 and

Appendix A4 , Table A4.1.

46

TABLE 4.2

TEST RESULTS FOR WATER AND POLYMER SOLUTIONS AT 250 WPPM

V 4P f T- %DR

Re (/s) (kPa) Pa]

WATER STANDARD

19683 0.69 0.88 0.00594 1.35

32520 1.14 2.03 0.00494 3.10

45642 1.60 3.68 0.00459 5.63

58479 2.05 5.70 0.00430 8.72

PEO (WSR-301) PREMIXED

16852 0.69 0.45 0.00302 0.69 49.2

27842 1.14 0.95 0.00231 1.45 53.2

39076 1.60 1.69 0.00211 2.59 54.0

50067 2.05 2.67 0.00201 4.08 53.2

PEO (WSR-303) PREMIXED

15109 0.69 0.29 0.00193 0.44 67.5

24963 1.14 0.75 0.00182 1.14 63.1

35036 1.60 1.26 0.00157 1.93 65.8

49173 2.05 2.04 0.00154 3.13 64.2

PAM (N-300) PREMIXED

16079 0.69 0.82 0.00554 1.26 6.7

26565 1.14 1.94 0.00474 2.97 4.0

37284 1.60 3.34 0.00416 5.11 9.4

47771 2.05 4.63 0.00350 7.09 18.6

PEO (WSR-301) INJECTED

16852 0.69 0.30 0.00201 0.46 66.2

27842 1.14 0.77 0.00188 1.18 61.9

39076 1.60 1.35 0.00168 2.06 63.4

50067 2.05 1.94 0.00147 2.97 65.8

PEO (WSR-303) INJECTED

15109 0.69 0.30 0.00201 0.46 66.2

24963 1.14 0.77 0.00188 1.18 61.9

35036 1.60 1.30 0.00126 1.98 64.7

49173 2.05 1.92 0.00145 2.94 66.3

47

4.1.1 Effect of Polymer Addition Method

The premixed and injection polymer addition

methods gave different levels of drag reduction. In

the injection case the solution only passed through one

valve and the test section. In the case of the

premixed, the solution passed through the pump before

it enters the test section. As a result, the premixed

solution was exposed to greater amounts of shear

compared to the injected solution before the test

section. Therefore, it can be expected that the

premixed method would be less effective than the

injection method because of partial polymer

degradation. Inspection of Figure 4.7 confirms this

point for PEO (WSR-301) polymer solution of 50 wppm.

This is a result of polymer break down where long

polymer chains are severed into shorter ones, making

them less effective. This agrees with the results of

Sylvester and Kumar [20]. Figure 4.8 shows similar

results with PEO (WSR-303) for 50 wppm where higher

drag reduction is obtained with the injection method.

It can be concluded that any addition method which

minimizes the shear exerted on the polymer solution

will maximize the effectiveness of the polymer in

48

Ul

E * 3(das

Ml W W

w w o

ro

Oi

CO

3

oH04

Ul

CO

0

a

oz

ui

Ea

o

m

p

o

CO

'V

o

p

(D

s

c

o

o

a

<

o

c

o(0

H

P

ro

a

EOu

I 1 r

U0JL9VJ HOI10IBJ

p

3a>

H

Cu

49

i

a

ro

O

ro

Ioi

co

Ul

CO

&

ow04

M-l

o

Ea

a

o

ir>

p

0

in

-o

0sz

p

<D

2

C

O

a

<

<4-4

o

c

ow

H

P

ro

aEOo

co

<D

P3

UOlOVd NOI19IIM Cu

50

reducing drag. In this study, the injection method was

found to give consistently higher reduction of drag.

4.1.2 Effect of Molecular Weight and Structure

The molecular weight and structure of polymer also

influence the level of drag reduction. In general for

the same structure of polymer, with an increase in

molecular weight an increase in drag reduction is

expected. Figure 4.9 confirms this for PEOs as

injected at 500 wppm. WSR-303 (molecular weight of 6

million) has a greater effectiveness than WSR-301 (with

molecular weight of 4 million) .

The molecular weight alone does not control the

effectiveness of a polymer solution as shown in Figure

4.10. Premixed PAM (N-300) has the highest molecular

weight (15 million) but the lowest drag reducing

characteristics at 50 WPPM. The two PEOs (WSR-301 and

WSR-30 3) are both lighter but are better at reducing

drag because of their structures. It has been shown

that a polymer with longer and thinner molecular

structure (PEO) is more effective than a bulkier coiled

molecule (PAM) of the same molecular weight. The PAM

is heavier and has more side chains than PEOs. This

51

Z 2

D

CO

p

0)

E>

r-l

004

p

^o>

-P

<D

3

P ,^

ro ci-H 03 H

CJ H

0) -I

l-l H

o ss

vo

cc p

Ul

CO

c

CD

P

ro

O

2 (D ro

3M-l

M-t

1

0.

Z H CO

Q 2CO

3o

P

0 c

0H

z p H

X* 0P

rH

P

Ul o s

cc ro

Cu ^<

c ^

0 l-l

H o

P ro

o 1r-l 05P CO

Cu s

ON

>*

<D

P

3o>

Cu

U019VJ N0ML9IH4

52

eU Bl Ul

c OC CC

a a. o.

1- > oooow w w

s

Ul

CO

9e

c

0)

p ,^

0)

M-l *:U-l 04p

Q 1

J= o

P o

P ro

3#^

CQ O

P wCD 04

E>. 1iH

0 ro

04 o

ro

o

0) cS

X

p H

E O

0) ro

p*-*

04CO

p <D

o P

U-l 3P

p CJ

0 3

p P

o P

ro CO

CuP

c ro

0 r-i

H 3P O

0 0)

l-l r-l

p 0

Cu z

?s

0)

p

30^

H

Cu

UOIOW NOLLOIU4

53

concept is verified by Virk [10]. On the other hand,

PAM is more resistant to shear because of its bulk per

unit length and does not degrade as easily as PEOs.

Tandon, Kulshreshtha and Agarwal [14] confirmed that

thinner molecules degrade at a much more rapid rate.

Molecular structure and weight, therefore, have direct

affects on the polymer drag reducing effectiveness.

4.1.3 Maximum Drag Reduction

It has been discovered that there is a

concentration at which the drag reduction is maximum

(minimum friction factor) . The maximum drag reduction

for premixed PEO (WSR-30 3) at 500 wppm is compared with

Virk's premixed results as shown in Figure 4.11. If

the first experimental point is eliminated the results

are very similar. The fact that the drag is reduced by

70% is most important. This is equivalent to a 70%

decrease in pressure drop along a given length of pipe

or in power to move a fluid over a surface or a surface

through a fluid.

The same critical concentration was reached by the

injection method at about 375 wppm for both PEOs. Virk

54

z =>:

T3Ul

3 UJi

c JV(/!

<d n^i

QCEI

>,'

Ul

CO

>

Ul

'O

CDXH

ECDP

04

Ea

a

3

o

o

in

ro

o

ro

I

OS

CO

s

4J

CJ3

>o

CD

OS

E3

EH

X

ro

co

p

H

3

(0

CD

OS

o

CQ

P

cn >

"*r.

P

CDP

ro

a

EO

U

U0JL3VJ N0U9IMJ

CD

P

3

Cu

55

[10] found the critical concentration to be 450 wppm

for Injected PEO (WSR-301). No critical concentration

was found for the PAM in this work.

4.2 FRICTION FACTOR AS A FUNCTION OF CONCENTRATION

In order to see the direct influence of polymer

concentration on the amount of drag reduction, the

friction factor was correlated to the polymer

concentration as shown in Figure 4.12 for different

polymers and addition methods at a constant average

fluid velocity of 0.69 m/s. The friction factor drops

sharply at low concentrations and then levels off at

higher ones for the PEOs. This happens more rapidly

for the injection method than the premixed method. For

the PAM the friction factor drops very gradually

showing the ineffectiveness of PAM as a drag reducing

additives. The friction factor for the premixed

solutions seems to have reached a minimum (maximum drag

reduction) at approximately 500 WPPM. For the

injection addtion method the minimum friction factor is

reached at 375 WPPM. A concentration at which drag

reduction is maximum can be found, after which the drag

of the system increases. It is at this point that the

56

2 Ul u u. .

C ce ue cc 3 3a & a 5 s

o9 99

a

O T-

W C^ C9

o <

p

0p

u

ro

Cu

c

0p

^^ p

of0 Ck

0p

p

Cu0.

* c^*

0

z c

0 0 CO

-p \

p p E

< ro

ap

p

e t c

z CD 0

*UIOC M-l

0 0 0

z u>.

0 p p

0 CD

E

-H

O

a iH

0r4

Ul O CD

2 04 >

0

>j M-l TJ

0 P

O 3

aP

OCD

Cu

U P

<P 0

w M-l

-*< aoiovj nouoiuj

CM

CD

P3

o>

P

Cu

57

viscosity increase can no longer be compensated for by

the drag reducing characteristics of the polymer.

Figure 4.13 shows the same relationship (f vs.

polymer concentration) at a higher average fluid

velocity (2.05 m/s). Compared to the results for a

fluid velocity of 0.69 m/s lower friction factors were

obtained. This is due to the friction factor being

proportional to the inverse of the square of the

velocity-

A threshold concentration which would produce a

measurable amount of drag reduction was also sought.

It was found that even with a 2.5 wppm (0.00025% by

weight) concentration of premixed and injected PEO

solutions, drag reduction of 17% and 38% can be

obtained respectively. This leads to the conclusion

that any trace concentration of PEO will cause drag

reduction above the critical wall shear. McComb and

Rabie [17] used as low as 0.9 wppm of PEO (WSR-3 01) to

obtain up to 40% drag reduction.

4.3 FRICTION FACTOR AS A FUNCTION OF CONCENTRATION AND

VOLUMETRIC FLOW RATE.

In Published works [4,10,11,17,18,20] no general

correlations are offered for drag reduction. Usually

58

TlB Ul Ul

e

0CC CC CC

a i iO)

* v-

0>o o o

ff 9 4 4r

JD o <

p

0p

CJ

ro

Cu

c

or

P

oH

p

Cu

Z

O

C

o

sc

0p

CO

cc p E

H ro

Zp

p o

Ul c .

o CD <N

zCJc M-l

o o o

oCJ

>.

ccUl

p

CD

E

p

p

CJ

2>. 0

5o

o04

rp

CD

>

a M-l TJ0 H

3p iH

o CuCDM-l

PM-l 0

.014

aOXOVd NOIlOIUi

W M-l

ro

CDP

3

cn

p

Cu

59

drag reduction is correlated to specific variables such

as polymer concentration, pressure drop or Reynolds

number. It is desired to have a single equation for a

polymer which will give the friction factor for a pipe

flow for a range of concentrations and flow rates. For

each polymer and addition method empirical equations of

the following form were developed.

f "C Q 4.3

Where, Q is the volumetric flow rate in m^/s and C is

the average polymer concentration in wppm. To show the

fit of this equation, the calculated friction factors

from Equation (4.3) were plotted against the

experimentally measured friction factors. This is

shown in Figure 4.14 for the premixed PEO (WSR-301).

The agreement between these two is very good. Figure

4.15 shows the same relationship for the injected PEO

(WSR-303) . Again the friction factors calculated from

Equation (4.3) are in good agreement with the measured

friction factors. This shows the applicability of

Equation (4.3) in practical situations. Table 4.3

shows the results of multivariable regression analysis

for Equation (4.3).

60

TJ

C

ro

o

ro

l

OS

co

Ow

~. 04

ro

TJ-3< CD

X

P

ECD

P P

ro 043

cr p

w oCu

c

o

TJ

CDP

P

OP

ro o

ih ro

3

o

ro

CJ

c

o

M-l O

O -H

p

C Cu

o10 TJ

CDP

3

P

ro

a co

E0

ro

CD

u s

CD

p3

Cn

r-l

Cu

w

JDfc uoiovd Nouoiud aaivinoivo

61

TJ

C

ro

ro

o

ro

I

OS

co

ow04

ro

TJ

P

c oO CDP -ro

P C

(0 rH

3O1

P

w o*-~

Cu

TJ

CDP

ror-l

3

or-l

ro

u

p

op

o

ro

Cu

c

op

p

CJ

c Cu0CQ TJH CDP P

ro 3

a CQ

E ro

o CD

CJ 2

in

CD

p3

Cn

H

Cu

ft

,.o-, HOlOVd NOIXOIUal daiVMOIVO

62

TABLE 4.3

REGRESSION ANALYSIS RESULTS

Equation Form:P y

f =C Q

C = Concentration (wppm)

Q = Volumetric flow rate (m^/s)

P r r*

WSR-301 (PRE) 0.564 x10"3

-0.1765 -0.3215 0.917

WSR-3 03 (PRE) 0.977 x10"3

-0.2078 -0.2334 0.870

N-300 (PRE) 0.291 x10"3

-0.0246 -0.3866 0.931

WSR-301 (INJ) 0.279 x10~3

-0.0394 -0.2699 0.689

WSR-3 03 (INJ) 0.304 x10"3

-0.1321 -0.3265 0.922

63

5.0 CONCLUSIONS

Introducing polymer additives into turbulent pipe

flow (15000 < Re < 50000) does in fact reduce the drag

of the system below that of the solvent alone. The

following major conclusions can be cited.

1. As much as 7 5% reduction in drag can be

obtained by using Polyethylene Oxides (PEOs) . This

corresponds to a 75% decrease in the pressure drop

along a pipe flow.

2. Significant drag reduction can occur with

trace amounts of PEO. Concentrations as small as 2.5

WPPM injected PEO (WSR-303) produced 37% drag

reduction.

3. There is a critical concentration at which

drag reduction is maximum. This critical concentration

was approximately 375 WPPM for the injected PEO and 500

WPPM for the premixed PEO.

4. In general for the same structure, higher

molecular weight polymers (PEO (WSR-303)) reduce drag

more effectively than lower molecular weight polymers

(PEO (WSR-301)).

5. Molecular structure also influences drag

reduction. Long thin molecules with no side chains,

such as PEOs, are more effective than the coiled,

64

heavier Polyacrylamide (PAM) molecules, which have many

side chains. This suggests that molecular structure

also has an effect on the drag reduction attainable by

a polymer.

6. The effectiveness of a polymer also depends on

the method of addition. The injection method proved to

be more effective because the flow experienced less shear

than in the premixed method.

Further investigation in the area of the critical

wall shear being a clue to the mechanism of drag

reduction is warranted. Also the use of a Laser Doppler

Anamometer to study the nature of velocity profiles can

give further insight into the mechanism of drag reduction.

65

REFERENCES

1. Toms, B. A., "Some Observation on the Flow of

linear Polymer Solutions Through Straight

Tubes at Large Reynolds Numbers", Proc. First

Intern. Congr. on Rheology, Vol II, pp

135-141, North Holland, Amsterdam (1948).

2. Hele-Shaw, H. S., "Experiments on the Nature of

Surface Resistance in Pipes and on Ships",

Trans. Inst. Naval Arch. 39, p 145 (1897).

3. Lumley, J. L. , Annual Rev. Fluid Mech. , Annual

Reviews, Palo Alto, Calif., 1, 367 (1965).

4. Golda, J., "Hydrolic Transport of Coal in Pipes with

Drag Reducing Additives", Chem. Eng. Commun. ,

Vol 43, 53 (1986) .

5. Stanton, T.E., and R. J. Pannell, Trans. Roy. Soc.

(London), 214A, 199 (1914).

6. Nikuradse, J., VDI-Forschungshef t , 365 (1932).

7. Karman, T. Von, NACA TM, 611 (1931) .

8. Drew, T. B. , E. C. Koo, and W. H. McAdams, Trans.

AIChE J. 28, 56 (1932) .

9. Saph. V., and E. H. Schoder, "An Experimental Studyof the resistance to the flow of water in

pipes", Trans. Amer. Soc. Civ. Eng., 51,944 (1903).

10. Virk, P- S. , "Drag Reduction Fundamentals", AIChE

J. , 21, 4 (1975) .

11. Virk, P. S., E. W. Merrill, H. S. Mickley, K. A.

Smith, and E. L. Mollo-Christenson, "The Toms

Phenomenom: Turbulent Pipe Flow of Dilute

Polymer Solutions", J. Fluid Mech., 30, 2

(1967) .

12. Grass, A. J., J. Fluid Mech., 50, 233 (1971).

13. Kim, H.T. , S. J. Kline, and W. C. Reynolds, J.

Fluid Mech., 50, 133 (1971).

66

14. Tandon, P. N., Kulshreshtha, A. K., and Agarwal,

R. , "Rheological Study of Laminar-Turbulent

Transition in Drag-Reducing Polymeric

Solutions". Slippage and Drag Phenomena, pp

460-1 (1988) .

15. Oldroyd, J. G. , "A Suggested Method of DetectingWall Effects in Turbulent Flow Through

Pipes", Proc. First Intern. Congr. on

Rheology, Vol II, pp130-

134, North Holland,

Amsterdam (1948) .

16. Wells, C. S., and J. G. Spangler, "Injection of a

Drag-Reducing Fluid into Turbulent Pipe Flow

of a Newtonian Fluid", Phys. Fluids, 10, 1890

(1967) .

17. McComb, W. D. , and L. H. Rabie, "Development of

Local Turbulent Drag Reduction Due to

Nonuniform Polymer Concentrations", Phys.

Fluids, 22, 1 (1979) .

18. ., "Local Drag Reduction Due to Injection of

Polymer Solutions into Turbulent Flow in a

Pipe", AIChE J., Vol 28, 4 (JY 1982).

19. Weissler, A., J. Appl. Phys., 21, 171 (1950).

20. Sylvestor, N. D., and S. M. Kumor, "Degradation of

Dilute Polymer Solutions in Turbulent Tube

Flow", AIChE Symp. Series, 130, 69.

21. White, P- A., Chem. Eng. Sci., 25, 1255 (1970).

67

APPENDIX Al

CALIBRATION DATA

TABLE Al.l Flow Meter Calibration Data

READING ON

FLOWMETER

(%)

TIME FOR FLOW RATE

. 01 m3 m^/s

11.46 sec 2.328 x 10

8.36 4.183 x 10

6.26 4.580 x 10

5.06 5.623 x 10

4.22 6.788 x 10

3.57 8.0 25 x 10

3.13 9.161 x 10

2.79 1.0 27 x 10

2.47 1.174 x 10

2.25 1.275 x 10

15.0

20.0-4

-4

-4

-4

-4

-4

-3

55.0 2.47 1.174 x iU~3

60.0~ "" ' """ " ,ft

25.0

30.0

35.0

40.0

45.0

50.0

TABLE A1.2 Injection Flow Calibration Data

68

PRESSURE TIME TO FLOW RATE

( kPa) EMPTY TANK

(sec)

(m3/s)

FOR 0 wppm

27.58 40.64 4.67 X 10-5

34.47 35.00 5.42 X 10-5

51.71 29.60 6.43 X 10-5

55.16 26.00 7.32 X 10-5

68.95 25.25 7.51 X 10-5

86.18 21.90 8.71 X 10-5

-596.53 20.6 0 9.15 X 10

103.42 19.50 9.72 X 10-5

-5

-4

120.66 19.00 9.97 X 10

137.90 16.00 1.19 X 10

FOR 1000 wppm

-5

-5

-4

-4

-4

-4

34.47 36.35 5.24 X 10

68.95 25.40 7.44 X 10

103.42 18.90 1.00 X 10

137.90 15.60 1.21 X 10

172.37 14.0 5 1.34 X 10

206.84 12.40 1.53 X 10

FOR 2500 wppm-5

-5

-5

-4

-4

-4

34.47 42.30 4.48 X 10

68.95 29.90 6.89 X 10

103.42 19.85 9.53 X 10

137.90 18.02 1.05 X 10

172.37 14.90 1.27 X 10

206.84 13.50 1.40 X 10

FOR 40 00 wppm-5

-5

-5

-5

-4

-4

34.47 75.30 2.52 X 10

68.95 46.40 4.10 X 10

103.42 27.90 6.57 X 10

137.90 24.3 0 7.76 X 10

172.37 17.10 1.10 X 10

206.84 16.70 1.13 X 10

FOR 7500 wppm-5

-5

-5

-5

-5

-5

34.47 110.90 1.70 X 10

68.95 66.00 1.70 X 10

103.42 42.88 4.42 X 10

137.90 31.10 6.12 X 10

172.37 27.74 6.81 X 10

206.84 23.10 8.20 X 10

69

APPENDIX A 2

TABLE A2.1

VISCOSITY DATA

Viscosity (Pa-s)

c

wppm WSR-3 01 WSR-3 03 N-3 00 HMW

0 0.89 x 10-3

0.89 x 10-3

0.89 x 10-3

50

100 0.96 x 10-3

0.99 x 10-3

0.93 x 10

0.97 x 10

-3

-3

250 1.03 x 10-3

1.21 x 10-3

1.09 x 10-3

500 1.20 x 10-3

1.39 x 10-3

1.29 x 10-3

EQUATIONS:

WSR-301 (PEO)

WSR-303 (PEO)

N-3 00-HMW (PAM)

r = 0.601 x10"6

C + 0.8916 x 10"3

M = 1.024 x10"6

C + 0.9036 x 10"3

. = 0.985 x10"6

C + 0.8972 x 10"3

70

APPENDIX A3

Drag Reduction Data

Table A3.1 Pipe Flow Friction Data

V JP f *. %DRRe (m/s) (kPa) f CALC. (Pa)

WATER STANDARD.

19683 0.69 0.88 0.00594 1.35

32520 1.14 2.03 0.00494 3.10

45642 1.60 3.68 0.00459 5.63

58479 2.05 5.70 0.00430 8.72

PREMIXED POLYMER SOLUTION FRICTION DATA WSR-301

FOR 50wppm

19050 0.69 0.49 0.00327 0.00365 0.74 44.9

31474 1.14 1.25 0.00304 0.00311 1.91 38.5

44174 1.60 2.37 0.00295 0.00279 3.62 35.7

56598 2.05 3.81 0.00288 0.00257 5.83 33.0

FOR 100wppm

18448 0.69 0.47 0.00319 0.0 03 21 0.72 46.3

30479 1.14 1.10 0.00267 0.00275 1.68 45.9

42777 1.60 1.89 0.00236 0.00247 2.90 48.6

54809 2.05 3.09 0.00233 0.00234 4.73 45.8

FOR 250wppm

16852 0.69 0.45 0.00302 0.00275 0.69 49.2

27842 1.14 0.95 0.00231 0.00234 1.45 53.2

39076 1.60 1.69 0.00211 0.00210 2.59 54.0

50067 2.05 2.67 0.00201 0.00199 4.08 53.2

FOR 500wppm

14728 0.69 0.40 0.00268 0.00234 0.61 54.9

24333 1.14 0.77 0.00188 0.00199 1.18 61.9

34152 1.60 1.42 0.00177 0.00179 2.17 61.4

43757 2.05 2.29 0.00173 0.00169 3.51 59.7

71

TABLE A3.1 (Cont)

PREMIXED POLYMER SOLUTION FRICTION DATA WSR-3 03

V 4.P f T. %DR

Re (/s) (kPa) CALC. (Pa)

FOR 2.5 wppm

19259 0.69 0.74 0.00495 0.00517 1.12 16.7

31820 1.14 1.69 0.00413 0.00460 2.59 16.4

45659 1.60 3.24 0.00404 0.00425 4.96 12.0

57220 2.05 5.41 0.00408 0.0 04 01 8.27 5.1

FOR 5 wppm

19259 0.69 0.71 0.00478 0.00448 1.09 19.5

31820 1.14 1.66 0.00404 0.00398 2.54 18.2

44659 1.60 3.09 0.00385 0.00367 4.73 16.1

57220 2.05 5.18 0.00392 0.00347 7.93 8.8

FOR 10 wppm

19529 0.69 0.62 0.00419 0.00387 0.95 29.5

31820 1.14 1.50 0.00364 0.00344 2.29 26.3

44659 1.60 2.77 0.00345 0.00319 4.23 24.8

57220 2.05 4.83 0.00365 0.00300 7.40 15.1

FOR 50 wppm

18448 0.69 0.39 0.00260 0.00276 0.59 56.2

30480 1.14 0.9 5 0.00231 0.00246 1.45 53.2

42779 1.60 1.81 0.00225 0.00228 2.76 51.0

54811 2.05 2.92 0.00220 0.00214 4.46 48.8

FOR 100 wppm

17526 0.69 0.36 0.00243 0.00239 0.55 59.1

28956 1.14 0.78 0.00191 0.00313 1.20 61.3

40640 1.60 1.33 0.00166 0.00197 2.04 63.8

52070 2.05 2.17 0.00164 0.00185 3.32 61.8

FOR 250 wppm

15109 0.69 0.29 0.00193 0.00197 0.44 67.5

24963 1.14 0.75 0.00182 0.00176 1.14 63.1

35036 1.60 1.26 0.00157 0.00163 1.93 65.8

49173 2.05 2.04 0.00154 0.00153 3.13 64.2

FOR 37 5 wppm

13586 0.69 0.29 0.00193 0.00181 0.44 67.5

22446 1.14 0.74 0.00179 0.00162 1.12 63.7

31504 1.60 1.20 0.00149 0.00150 1.83 67.5

40364 2.05 1.97 0.00149 0.00141 3.01 65.3

FOR 5 00 wppm

12342 0.69 0.26 0.00176 0.00170 0.40 70.4

20391 1.14 0.70 0.00170 0.00153 1.07 65.6

28619 1.60 1.18 0.00148 0.00141 1.81 67.7

36668 2.05 1.92 0.00145 0.00133 2.94 66.3

72

TABLE A3.1 (Con't)

PREMIXED POLYMER SOLUTION FRICTION DATA N-300-HMW

Re

V

(/s)

4.P

(kPa) f CALC. (Pa)

%DR

FOR 50 wppm

18845

31136

43699

55989

0.69

1.14

1.60

2.05

0.85

2.01

3.58

5.36

0.00570

0.00489

0.00446

0.00405

0.00572

0.00470

0.00414

0.00376

1.30

3.07

5.47

8.20

4.1

1.0

2.8

5.8

FOR 100 wppm

18068 0.69

29852 1.14

41897 1.60

53680 2.05

0.83

1.97

3.46

5.28

0.00562

0.00480

0.00432

0.00399

0.00562

0.00462

0.00407

0.00370

1.28

3.01

5.30

8.08

5.4

2.8

5.9

7.2

FOR 250 wppm

16079 0.69

26565 1.14

37284 1.60

47771 2.05

0.82

1.94

3.34

4.63

0.00554

0.00474

0.00416

0.00350

0.00549

0.00451

0.00398

0.00362

1.26

2.97

5.11

7.09

6.7

4.0

9.4

18.6

FOR 500 wppm

13586 0.69

22446 1.14

31504 1.60

40364 2.05

0.82

1.79

3.11

4.49

0.00554

0.00437

0.00388

0.00339

0.00539

0.00443

0.00391

0.00356

1.26

2.74

4.77

6.68

6.7

11.5

15.5

21.2

73

TABLE A3.1 (Con't)

INJECTED POLYMER SOLUTION FRICTION DATA WSR-3 01

Re

V

(/8)

4P

(kPa)

0.37

0.87

1.50

2.12

f

CALC. (Pa)

%DR

FOR 50 wppm

19050

31474

44174

56598

0.69

1.14

1.60

2.05

0.00252

0.00213

0.00186

0.00160

0.00205

0.00179

0.00163

0.00153

0.57

1.33

2.29

3.24

57.6

56.9

59.5

62.8

FOR 100 wppm

18448 0.69

30479 1.14

42777 1.60

52809 2.05

0.32

0.82

1.40

2.02

0.00218

0.00200

0.00174

0.00152

0.00199

0.00174

0.00159

0.00149

0.50

1.26

2.13

3.09

63.3

59.5

62.1

64.6

FOR 2 50 wppm

16852 0.69

27842 1.14

39076 1.60

50067 2.05

0.30

0.77

1.35

1.94

0.00201

0.00188

0.00168

0.00147

0.00192

0.00167

0.00153

0.00144

0.46

1.18

2.06

2.97

66.2

61.9

63.4

65.8

FOR 375 wppm

15648 0.69

25854 1.14

36286 1.60

46491 2.05

0.22

0.75

1.30

1.92

0.00151

0.00182

0.00162

0.00145

0.00189

0.00164

0.00151

0.00142

0.34

1.14

1.98

2.94

74.6

63.1

64.7

66.3

FOR 500 wppm

14728 0.69

24333 1.14

34152 1.60

43757 2.05

0.35

0.87

1.42

2.37

0.00235

0.00213

0.00177

0.00179

0.53

1.33

2.17

3.62

60.4

56.9

61.4

58.4

74

TABLE A3.1 (Con't)

INJECTED POLYMER SOLUTION FRICTION DATA WSR-3 03

V JP r. %DR

Re (/s) (kPa) CALC. (Pa)

FOR 2.5 wppm

19259 0.69 0.57 0.00386 0.00408 0.88 35.0

31820 1.14 1.37 0.00334 0.00307 2.10 32.4

44659 1.60 2.29 0.00286 0.00275 3.51 37.7

57220 2.05 3.89 0.00294 0.00254 5.95 31.6

FOR 10 wppm

19259 0.69 0.45 0.00302 0.00340 0.69 49.1

31820 1.14 1.07 0.00261 0.00256 1.64 47.2

44659 1.60 1.77 0.00221 0.00229 2.71 51.8

57220 2.05 2.72 0.00205 0.00211 4.16 52.3

FOR 50 wppm

18448 0.69 0.37 0.00252 0.00275 0.57 57.6

30480 1.14 0.80 0.00194 0.00207 1.22 60.7

42779 1.60 1.35 0.00168 0.00185 2.06 63.4

54811 2.05 2.19 0.00160 0.00171 3.24 62.8

FOR 100 wppm

17526 0.69 0.32 0.00218 0.00251 0.50 63.3

28956 1.14 0.81 0.00197 0.00189 1.24 60.1

40640 1.60 1.35 0.00168 0.00169 2.06 63.4

52070 2.05 1.97 0.00149 0.00156 3.01 65.3

FOR 250 wppm

15109 0.69 0.30 0.00201 0.00222 0.46 66.2

24963 1.14 0.77 0.00188 0.00167 1.18 61.9

35036 1.60 1.30 0.00126 0.00150 1.98 64.7

49173 2.05 1.92 0.00145 0.00138 2.94 66.3

FOR 375 wppm

13586 0.69 0.25 0.00168 0.00210 0.38 71.7

22446 1.14 0.75 0.00182 0.00158 1.14 63.1

31504 1.60 1.27 0.00158 0.00142 1.94 65.6

40364 2.05 1.92 0.00145 0.00131 2.94 66.3

FOR 500 wppm

12342 0.69 0.34 0.00226 0.51 61.9

20391 1.14 0.85 0.00207 1.30 58.1

28619 1.60 1.35 0.00168 2.06 63.4

36668 2.05 2.22 0.00168 3.39 60.9

75

APPENDIX A4

REGRESSION ANALYSIS RESULTS

TABLE A4.1

EQUATION FORM:

Pf =

Re

WATER 0.107 -0.2935 0.984

WSR-301 (Pre)50 wppm 0.0102 -0.1160 0.984

100 0.0622 -0.3030 0.964

250 0.1140 -0.3770 0.954

500 0.1230 -0.4040 0.872

WSR-303 (Pre)"

2.5 wppm 0.0287 -0.1817 0.785

5 0.0309 -0.1920 0.833

10 0.0170 -0.1450 0.679

50 0.0114 -0.1523 0.932

100 0.0972 -0.3798 0.953

250 0.0147 -0.2102 0.913

375 0.0244 -0.2652 0.906

500 0.0112 -0.1949 0.890

N-300 (Pre)

50 wppm 0.1185 -0.3080 0.996

100 0.1221 -0.3141 1.000

250 0.2910 -0.4067 0.966

500 0.3681 -0.4412 0.996

WSR-301 (Inj)

50 wppm 0.1417 -0.4070 0.983

100 0.0549 -0.3250 0.937

250 0.0309 -0.2778 0.912

375 0.0911 -0.0385 0.994

500 0.0347 -0.2799 0.913

WSR-303 (Inj)

2.5 wppm 0.0595 -0.2783 0.913

10 0.1124 -0.3655 0.988

50 0.1653 -0.4280 0.978

100 0.0339 -0.2800 0.974

250 0.0318 -0.2842 0.947

375 0.0895 -0.3890 0.998

500 0.0401 -0.3037 0.908

76

APPENDIX Bl

DATA ANALYSIS & SAMPLE CALCULATIONS

Viscosity

f< - Polymer Solution Viscosity (Pa-s)

*w - Water Standard Viscosity (Pa-s)

tp- Time for Water (Sec)

tw- Time for Polymer Solution (Sec)

STANDARDS

0.8 904 x 10"3

Pa-s at 30 degrees C

M

tw= 250.63 Sec. at 30 degrees C

tw w

tp= 395.6 Sec

(395.6 Sec ) (0.8904 x 10"3

Pa-s)

(250.63 Sec)

m = 1.404 x 10"

Pa-s

77

APPENDIX B2

DATA ANALYSIS AND SAMPLE EQUATIONS

Injection Quantities

NEED: C 25 0 WPPM

Q

Equation 4.1:

0.58 x 10"3 m3/s

c = ( Qy ) CpQp + Q

250 = ( Qp

~Qp + 0.58 x 10 3

CP

This is an iterative method to find a Cp which results in a

Qp which is between 0.057 x 10"3

and 0.075 x 10"3 m /s.

Choose Cp= 2500 WPPM

Qp= 1.0 2 GPM

To get Qp= 0.064 m3/s with a Cp

= 2500 WPPM the pressure in

the injection chamber needs to be:

p = p + P. .

*tot st in]

= 4.83 kPa + 119.97 kPa

P^ t

= 124.80 kPatot

78

APPENDIX B3

DATA ANALYSIS AND SAMPLE EQUATIONS

MANOMETER AND PRESSURE DROP

JP = p gh ( rw-

ra )

JP = Pressure Drop (Pa)

g= Gravity (m/s2)

h = Manometer Deflection (m)

*w = Specific gravity water

yg= Specific gravity air

* = Density water (k9/m2)

Example: g- 9-81 m/s2

*w= 1000

kg/m3

Yw - 1

ra=

.001

h =.25 m

JP = (1000) (9.81) (.25) (1-.001)

JP = 2.4500 KPa

If the density of air is neglected,

JP - 'gh

JP = 2.4525 kPa

Percent Error = 0.1%

79

In the calculation of pressure drop from the manometer the

compressibility of air is neglected. This can be done

because the pressure of the air in the manometer does not

fluctuate a great amount between the highest and the lowest

flow rates.

Ideal gas law: p= P

mRT

The density is proportional to the pressure at constant

temperature. Taking the extreme pressures from Figure 4.4

(Static Pressure at Injection location) .

Plow* 1 atm

PHigh" 1'35 atm

therefore the density of air at these pressures is

'low- l k9''3

'High- i"35 IC9/*3

if the density of air increases by 35%

Y%=

.00135

JP = 2.4492 kPa

Percent error = 0.3%

JP (kPa) % Error

Taking into account air

compressibility and density

Neglecting air compressibility

Neglecting air density

2.4492

2.4500 .03%

2.4525 .1%

80

BIBLIOGRAPHY

Cyanamer, Polvacrylamides For the ProcessingIndustries. American Cyanamide Company.

Fox, R. w., and A. T. McDonald, Introduction to Fluid

Mechanics. Third Edition, John Wiley and Sons,Inc. 1985, pp 360-365.

How To Dissolve Polyox Water-Soluble Resins, Union

Carbide Corporation, USA.

Knudsen, J. G., and D. L. Katz, Fluid Dynamics and Heat

Transfer, McGraw-Hill Book Company, 1958, pp171-171.

Kumor, S. M. , and N. D. Sylvester, "Effects of aDrag-

Reducing Polymer on the Turbulent Boundary Layer",AIChE Symp. Series, 130, 69.

Schlichting, H. , Boundary-Layer Theory, McGraw Hill

Book Company (1979) .

Using Polyox Water-Soluble Resins to Reduce

Hydrodynamic Drag, Union Carbide Corporation, USA.

Water-Soluble Resins Are Unique, Union Carbide

Corporation, USA.

Wilkinson, W. L. , Non-Newtonian Fluids: Fluid

Mechanics, Mixing and Heat Transfer, Pergamon

Press (1960).