Development of Ultrasonic Techniques for Multiphase Systems

by

Valeriu Stolojanu

Department of Chernical and Biochemical Engineering Faculty of Engineering Science

Thesis submitted in partial hlfillment of the requirements for the degree of

Master of Engineering Science

Faculty of Engineering Science The University of Western Ontario

London Ontario, Canada August, 1999

Q Valeriu Stolojanu, 1999

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Abstract

Ultrasonic techniques have been developed to rneasure local phase holdups and variations

in particle size distribution in dense two-phase (liquid-solid) and three-phase (gas-liquid-

solid) suspensions. The measurements are based on variations in velocity, attenuation and

mean frequency of the acoustic pulse traveling through suspension. Solids concentrations

of up to 43 vol. % and particle sizes of 35, 70 and 180 pm have been used in liquid-solid

system. In gas-liquid-solid system, g l a s beads of 35 pm only were used. The solids

concentration and the gas holdup were varied up to 21 vol.% and 30 vol.% respectively.

Available theoretical approaches have been reviewed and their applicabilities and

limitations have been pointed out. Approaches for determining particle size variations in

suspensions are presented. A procedure has been developed for local phase holdup

measurements in sluny bubble colurnn based on variations of acoustic velocity and signal

attenuation.

Ke-wvords: slurry bubble column; phase holdup; ultrasound; ultrasound velocity; solids concentration; gas holdup; pulse frequency

Acknowledgments

The author wishes to express his gratitude to Dr. Anand Prakash for his constructive

suggestions and help during this work. I am also thankful to Dr. Maurice Bergougnou for

being a constant source of encouragement and constructive discussions.

The professors and staff of the Department of Chemical and Biochemical Engineering are

also thanked for their support and assistance

Thanks to Sujit Bhattacharya for his valuable help in various aspects of the study,

JingJing Li for her support, as well as to fellow graduate students in the department.

Last but not least, 1 would like to thank my parents!

Table of Contents

. . CERTIFICATE OF EXAMINATION ............................................................................. 11

ACKNOWLEDGMENTS . . . . .. .. ...... .. . .. . . . . . . . .. .. . . . . .. . . . . . . . . . . . . . . . . . ... . . . . --.. . . . . . . ... . . . . . . . . . . . . . . . . . . . . .. . . iv

TABLE OF CONTENTS ..... ... ............... ... ........................................................................... v

LIST OF TABLES ............................................................................................................ ix

LIST OF FIGURES .................................... ... ..............,....................................................+.. x

NOMENCLATURE ...........................................+....................................................... xiv

CHAPTER 1 Introduction ...............................,..........++.....,..........,..................~.................... 1

1 . 1 Objective of the Study .............................................. .... ........ ... . . ..... . .............. . . ..... .... 4

CHAPTER 2 Literature Review ......................................................................................... 6

2.1 Classi fication of the Analyzed Systems ... ........... ....... ....... .... .... .... . . . .. ........ ..... . ........ 6

2.1.1 Miiltiphase Reactors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6 2.1.1.1 Flow Regimes of Gas Bubbles in Bubble and Sluny-Bubble Columns ....... 8

2.1.1.2 Bubble Flow Regime.. ..................... .......................... ......... ... .. ..... ............. .... 8 2.1 .1.3 Churn Turbulent Flow Regime .......... ................ ......... .... ... ............. ......... ... I O

2.1 .1.4 SIug Flow Regime ... ... .. . . . . . .. .. .. .. . . . . .. . . .. .. ... .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 0 . .

2.1.1.5 Flow Regime Transition ............... .......................... . . ........ .............. 1 0

2.12 Stirred Reactors ......................................................... . . ... ...... . ...... .. ... .. ........ 1 1

2.1.2.1 Liquid -Solid Suspension in Agitated Systems .......................................... 1 1

....................................................................................... 2.2 Fractional Phase Hold-up -14

.............................................................................................. 2.2.1 Physical Methods 1 5

2.2.1.1 Weighing Technique .................................................................................. 15

................................................................ 2.2.1.2 Measurement of Bed Expansion 1 5

2.2.1.2.1 Simultaneous Closure of Gas and Liquid Flow .................................... 15

................................................... 2.2.1.2.2 Dynamic Disengagement Technique 1 6

................................................................................... 2.2.1.3 Sampling Technique 1 7

2 2.1.4 Quic k Closing Valves Technique ................................................................ 17

................................................... 2.2.1.5 Pressure Drop Measurements Technique 1 8

......................................... 2.2.2 Electrical Conductance and Capacitance Meihods -20

.................................................................. 2.2.2.1 Electroconductivity Technique - 2 0

................................................................................. . 2.2.1.1 1 Measuring System 2 0

................................................ 2.2.2.1.2 Measurements in Liquid-Solid S ystems 22

......................................... 2.2.2.1.3 Measurements in Gas-Liquid-Solid Systems 24 . . . ............................................................................ 2.2.2.2 Electroresistivity Methods 27

................................................................................ 2.2.2.2.1 Measurïng System - 2 7

..................................................... 2.2.2.2.2 Measurements in Gas-Solid Systems 28

......................................... 2.2.2.2.3 Measurements in Gas-Liquid-Solid Systems 28

................................................................................... 2.2.2.3 Capacitance Methods 29

................................................................................................ 2.2.3 Optical Methods 31

....................................................................................... 2.2.3.1 Measuring System 31

.......................................................... 2.2.3.2 Measurements in Gas-Solid S ystems 32

............................................. 2.2.3.3 Measurements in Gas-Liquid-Solid Systems -33

...................................................................................... 2.2.4 Gomma Ray Technique 38

....................................................................................... 2.2.4.1 Measuring System 40

2.2.4.2 Measurements in Gas-Liquid, Gas-Solid and Liquid-Solid Systems .......... 41

...................................................... 2.2.4.3 Measurements in Three-Phase S ystems 44

...................................................................................... 2.2.5 Ultrasound Technique -46

....................................................................................... 2.2.5.1 Transmission Loss 46

2.2.5.2 Measwing S ystems ..................................................................................... 48

2.2.5.3 Measurements in Liquid-Solid (Liquid-Liquid) Systems ........................... 50

2.2.5.3.1 Ultrasound Velocity as a Function of Solids Concentration ................. 50

2.2.5.3.2 Ultrasound Velocity as a Function of Temperature .............................. 57

2.2.5.3.3 Ultrasound Velocity as a Function of Frequency and Particle Size ...... 58

2.2.5.3.4 Ultrasound Attenuation as a Function of Solids Concentration ............ 59

2.2.5.3.5 Ultrasound Attenuation as a Function of Temperature ......................... 61

2.2.5.3.5 Ultrasound Attenua . as a Function of Frequency and Particle Size ...... 62

2.2.5.3.6 Viscosity E ffect on the Propagation of Ultrasound .............................. 63

2.2.5.4 Measurements in Gas-Liquid System ......................................................... 64

2.2.5.4.1 Ultrasound Velocity as a Function of Gas Holdup in G-L System ....... 64

2.2.5.4.2 Ultrasound Attenua . as a Function of Gas Holdup in G-L System ...... 68

2.2.5.5 Measurements in a Three-Phase System ..................................................... 71

............................................................................................... 2.2.6 Other Techniques 74

2.2.5.1 Real -Tirne Neutron Radiography Technique .............................................. 74

2.2.5.2 Particle Image Velocimetry Technique ........................................................ 74

2.3.5.3 Laser Holography Technique ....................................................................... 75

CHAPTER Experimental .............................................................................................. 76

3.1 Experimental Setup ................................................................................................. 76

3.2 Experimental Technique ........................................................................................ -87

3.2.1 Measurement Procedure for Liquid - Solid System ........................................... 87

3.2.2 Memurement Procedure for Gas - Liquid System ............................................. 88

3.2.3 Measztrement Procedure for Gas - Liquid - Solid System ................................. 89

................................................................................ CHAPTER 4 Resuits and Discussion 90

4.1 Liquid . Solid System ............................................................................................. 90

4.2 Gas - Liquid System ............................................................................................. 1 4

4.3 Gas - Liquid - Solid System ................................................................................. 135

vii

C W T E R 5 Conclusions and Recommendations ......................................................... 1 5 2

......................................................................................................... 5.1 Conclusions 1 52

............................................................................................... 5 -2 Recomendations 1 53

APPENDIX A . Bubble Size. Pore Size and Stirrer Speed Calculations ........................ 154

APPENDU B . Liquid Manometers ............................................................................... 160

APPENDIX C . Solids Properties .................................................................................... 163

APPENDIX D . Ultrasonic Equipment Calibration and Characteristics ......................... 168

REFERENCES ................................................................................................................ 171

VITAE .............................................................................................................................. 187

List of Tables

Table 2.1 M(u) . expressions from several authors .................................................. 54

Table 4.2.1 Gas holdups from results of Beinhauer (197 1) and this study ................ 130

Table 4.2.2 Interfacial area given by both small and large bubbles ........................... 132

Table A . 1 Wet pressure drop rneasurements for porous plate characterization ...... -157

Table A.7 Bubble size distribution lrom photographie technique (exp . 1 ) ............... 157

Table A.3 Bubble size distribution fiom photographic technique (exp.2) ............... 157

Table A.4 Stirrer speed calculated with Zwietenng equation ................................. 159

Table C . 1 Glass beads properties as given by the manufacturing Company ............ 164

Table C.2 Sieve analysis of larger glass beads particles ......................................... 167

Table D . 1 Characteristics of ultrasonic equipment ............................................. 170

List of Figures

Figure 1 . 1

Figure 2.1.1

Figure 2.1.2

Figure 2.1.3

Figure 3.1.1

Figure 3.1.2

Figure 3.1.3

Figure 3.1.4

Figure 3.1.5

Figure 3.1.6

Figure 3.1.7

Figure 4.1.1

Figure 4.1.2

Figure 4.1.3

Figure 4.1.4

Figure 4.1.5

.......................................... Schernatic diagrarn of a slurry bubble column 2

Common operating ranges for three-phase fluidized bed and slurry bubble colurnn systems (Fan et al.. 1987a) ...................................... 7

Flow regime map for a liquid-batch bubble colurnn considering a low viscosity liquid phase (Fan. 1989) .................................................... 9

Correlation for complete suspension with stirrer diarnetedwidth ratio of 4 (Zwietering. 1958) ..................................................................... 13

...................... Schematic of the slurry bubble column used in this study 77

Typical photograph obtained for bubble size characterization .................. 79

................ Effect of stirrer speed on ultrasound velocity in water at 25 "C 81

Effect of stirrer speed on ultrasound attenuation in water at 25 "C ........... 82

.............. Schematic of Plexiglass cell used in liquid-solid measurements 83

Schematic of ultrasound transducers ......................................................... 85

Block diagram of experimental setup ........................................................ 86

Ultrasound velocity versus solids concentration for different particle sizes (3 MHz) ............................................................................................. 91

Cornparison of measured ultrasound velocity with theoretical models ..... 92

Cornparison of ultrasound velocity at two ultrasound ................................................................................................ Frequencies -95

Calibration c w e s of ultrasound velocity versus solids ................................... concentration for different particle sizes (3 MHz) 97

.................. Ultrasound velocity variation in mixed particle sizes system 99

Figure 4.1 h a Ultrasound attenuation variation in mixed particle sizes system X

Figure 4.2.6 Ultrasound amplitude ratio versus superficial gas velocity for different distances between transducers .,,,... .. .... .., ......... ... ... ......... 12 1

Figure 4.2.7 Attenuation coefficient (experimental versus predicted). . . . . .... . . . . . . . . . . .l23

Figure 4.2.8 Ultrasound velocity variations with superficial gas velocity for different distances between transducers ....................................... 124

Figure 4.2.9 Standard deviation of velocity measurements at a larger superficial gas velocity ....... ..................................... ........................... .. 1 25

Figure 4.2.10 Attenuation coefficient versus gas holdup in air-water system ..... . ..... .l26

Figure 4.2.1 1 Interfacial area in gas-liquid system fiom attenuation measurements ............ ...... ........................................ ........... . ...... ......... .. 129

Figure 4.2.12 Attenuation coefficient in gas-liquid system. cornparison between experirnental and predicted values (3.9 MHz) ...... . . . .. . . . . . . . . . . . . . . . . . . . . . . . .133

Figure 4.3.1 Ultrasound velocity versus solids concentration in G-L-S system (Vg = 0.017 m/s) ....................................................................... 137

Figure 4.3.2 Comparison of ultrasound velocity in G-L-S system with L-S system (Vg = 0.01 7 m/s) .................................. ..................... 138

Figure 4.3.3 Ultrasound velocity versus solids concentration in G-L-S system (Vg = 0.033 m/s) ............................................. ................... ...... ,139

Figure 4.3.4 Ultrasound velocity versus solids concentration in G-L-S system (Vg = 0.056 d s ) ........ . . .. . . . . . . . . . .. .. . . . .. . .. . .. . .. . .... ... . . . . .. . .... . ... . . . . . . . -140

Figure 4.3.5 Cornparison between ultrasound velocity in G-L-S system . and Iiquid-solid system ....... .. ............................ .. ........ ..... .... .......... .. ... . -14 1

Figure 4.3.6 Comparison of ultrasound attenuation from three-phase system with liquid-solid system .......................................... ... ....... ...... ..... .... . .... 143

Figure 4.3.7 Axial variation of solids concentration in G-L-S system (sedimentation- dispersion model) ......... .. . .. . . . .. . . .. .. . .. .. . . ... .... .. . . . .. .. .. .. . .. -144

Figure 4.3.8 Ultrasound attenuation variation with solids concentration in three-phase system minus solids attenuation at Vg = 0.0 127 rn/s ......... 145

xii

Figure 4.3.9 Attenuation variation with solids concentration in G-L-S ................. system compared to L-S system for different gas velocities 147

Figure 4.3.10 Ultrasound attenuation variation with solids concentration in three-phase and the resulting gas holdup ......................................... 148

Figure 4.3.1 1 Cornparison between gas holdup given by ultrasound .................... attenuation and the gas holdup fiom level measurements 149

............................... . Figure A 1 Wet pressure &op venus supetficial gas velocity 155

Figure A.2 Calibration of Dweyer rotameter at 34.5 kPa backpressure and 22 OC ...................................................................... 156

Figure B . I Schematic of liquid manometers .......................................................... 162

. ............................. Figure C 1 Particle size analysis for glass beads of 35 microns 165

............................. Figure C.2 Particle size analysis for g l a s beads of 70 microns 166

Figure D . 1 Ultrasound velocity variation as a function of temperature in water only ................................................................ 169

xiii

Nomenclature

A =ultraSound signal amplitude (%)

A, =initial ultrasound signal amplitude (%)

A,, = ultrasound signal amplitude before addition of solids or bubbles (%)

A, = ultrasound signal amplitude after addition of solids or bubbles (%)

A, = coefficients determined experimentally

B = weight of solids in suspension per weight of liquid times 100 ( O h )

C = solids concentration (w%)

CD = drag coefficient

C, = bubble density (number of bubbleshnit volume)

C, = heat capacity at constant pressure (I K" mol-')

Cs = average solids concentration in gas-tee solid-liquid system (kg/m3)

C, = heat capacity at constant volume (J R' mol-')

d, = bubble diameter (m) - Dg = mean bubble diameter at height h (m)

Dc = colurnn diameter (m)

d, = particle diarneter (m)

$or= average pore size diameter (m)

D, = stirrer diameter (m)

dSM =Sauter mean diameter (m)

dT = transducer diameter (m)

f = frequency (Hz)

f,, = resonant Frequency (Hz)

Fr (Froude number) = v & ~ ~ $ , ~ g = gravitational acceleration (m2/s)

h = longitudinal distance fiom gas distributor (rn)

h' = height at point of pressure p, (m)

xiv

H, = height of the mixture (m)

HL= height of the liquid phase only (m)

I = intensity at a given point

1, = initial intensity

j = mode of oscillation

k = wavenumber. 2n/h (m")

K = conductance ( S )

K, = coefficient defined by < = K , ( ~ & )"' k, = conductivity in phase i (S/m)

k r,,,, = dimensionless wave nurnber as defined in equation (4.1.1 )

L = length between transmitter and receiver (m)

Ib = bubble length (m)

In = distance between neighbouring contact points on optical fibers (m)

m = m a s fraction of particles used in equation (4.1.1)

n =number of particles or bubbles

N,, =stirrer speed for just suspension (rotationdminute)

No = Avogadro's number

N(x,) = total number of bubbles in the colurnn of length x, and unit cross section

n' = mean probability density function of bubbles in the layer

n(x,) - number of gas bubbles varying with layer thickness x,

P = pressure (~ /m' )

Po= static pressure (~lm')

p* = atrnospheric pressure (N/rn2)

p' = pressure at a reference point wm2) p,, p2 = pressure at manometer 1 and 2 (Pa)

q = 3 / ( d p L ( r A

QG = volumetric gas flow rate (m3/s)

QL = volurnetnc liquid flow rate (rn31s)

r = radius (m)

rb = bubble radius (m)

Re ( Reynolds nurnber ) = ,/purp / 2q

rOb = resonant bubble radius (m)

r,, = resonant particle radius (m)

r, = particle radius (m)

s = constant for a given system geometry

S = cross sectional area of the column (m2)

s,,= scattering coefficient (m-')

%,,,=apparent scattering coefficient (m*')

Sk = expression for hydrodyoamic interactions between particles and fluid

T= temperature ( O C )

t = time (s)

& = delay time of two signals detected by neighbouring light receiver (s)

Ue =mean bubble rise velocity ( d s )

Umi = minimum fluidization velocity (m/s)

U, = terminal velocity of the particle (m/s)

V = velocity of ultrasound (mls)

V b = bubble rise velocity (m/s) - Vb = mean bubble rise velocity (mis)

V,= superficial gas velocity (m/s)

V, = velocity of ultrasound in phase i ( d s )

v, = complex wave vector

V, = ultrasound velocity in liquid phase (m/s)

Vp = particle velocity (mis)

x = distance from source (m)

x, = bubble layer thickness (m)

yl , yz = manomenter readings (m)

vu= ratio of the circumference of the bubble to the ultrasound wavelength 2rr r&

We (Weber number) = V , ? $ ~ ~ ~ ~ I E ' G ,

W, = solids wheight (kg)

Z = acoustic impedance (kg/m2s)

Zi = atomic rnass number

z, , z2 = height of manometer 1 and 2 (m)

Greek Ietters

a = total attenuation coefficient (m")

a, ,a2,%,ab = experimentally determineci coefficients in equations (2.2.58), (2.2.5 1 )

a,, = attenuation due to turbulent fnction in irnrnediate vicinity of the obstacle (rn")

azz = attenuation due to Stream flow fnction (m'l)

a,, = attenuation due to scattering (m-')

a, = attenuation coefficient due to phase i (m.')

a, = attenuation coefficient due to bubble presence (m-')

a, = attenuation coefficient given by liquid phase (rn-')

a, = rittenuation coefficient given by particles (rn*')

a, = attenuation due to scattering (rd)

a, = attenuation due to viscosity loss (m-')

PCrr = effective compressibiiity ( ~ a - ' )

p, = compressibility of phase i ( ~ a " )

pf = cornpressibility of fluid (pi')

PL = compressibility of liquid (~a-' )

p, = mixture compressibility ( ~ a " )

Ps = compressibility of solids ( ~ a - ' )

xI. = complex compressibility of the liquid

xb = complex compressibility of bubbles

s = 4(2qr/op3

h= PL /PS

xvii

E = porosity of the porous plate

E~ = dispersed phase holdup

eG = gas phase holdup

egL = gas phase holdup given by the large bubbles

= local gas phase holdup

cg, = gas phase holdup given by the srnaIl bubbles

cL = liquid phase holdup

cso= solids holdup at the bed center

esw= solids holdup near the wall

E~ = solids holdup

@ = dimensionless radial coordinate MD,

y = ratio of conductivity between two different medium

y, = specific heat ratio C&

qi = viscosity of phase i (Pas)

qcrr = effective viscosity (Pa.s)

qo = gas viscosity (Pa.s)

qL = liquid viscosity (Pa.s)

cp = solids volume fraction

cp, = volume fraction of phase i

cp,,, = solids volume fraction corresponding to the velocity (scattenng theory)

cp,,,, = solids volume Fraction corresponding to the velocity V in the dispersion

h = wavelength of ultrasound signal (m)

p = absorption coefficient (m-')

K = absorption coefficient of phase 1 (m")

p- = absorption coefficient of a mixture (m") - pmix = averaged absorption coefficient of a mixture (m")

pc = kinematic viscosity, qL/pL (m'ls)

0 = direction of particle motion (degree)

p = density (kg/m3)

xviii

perr = effective density (kg/m3)

p,= fluid density (kg/m3)

pG = gas density (kg/m3)

pi = density of the phase i (kg/m3)

p, = liquid density (kg/rn3)

p, = mixture density (kg/rn3)

p, = solids density (ke/rn3)

O = surface tension (Nlm)

oc = atornic absorption cross section (mm')

o, = total extinction cross section (m2)

O, = extinction cross section caused by absorbed energy (m2)

O, = extinction cross section caused by scattered energy (m2)

q, = extinction cross section caused by absorbed energy at resonance (m')

O=, = extinction cross section caused by absorbed energy at resonance (ml)

os, = extinction cross section caused by scattered energy at resonance (m2)

t = tortuosity

o = angular Frequency, 2nf (s")

j = angle between horizontal and the line defined by contact points of an optical fiber

(degee)

5 = shape factor equal to 2.5 for spheres

r = volumetric interfacial area (m'lm3)

i ~ , 9 = Lame elastic constants of the particle

0 = mass absorption coefficient (m2/kg)

a, = mass absorption coefficient for phase i (m'/kg)

K = bulk modulus (Pa)

Q = bubble damping constant

ha, = correction absorption term for Iarger kr, (r i ' )

Ap = difference in compressibility between phases ( ~ a - ' )

Ap = difference in density between phases (Kg/m3)

Ai = intensity variation

hp = pressure difference between hvo points (Pa)

AP, = excess pressure required to generate bubbles on porous plate distributor (Pa)

At = transmission time di fference (s)

hx = layer thickness (m)

Ay = diference between readings at manometers (m)

hz = height difference between two point (m)

Subscripts

i = L,G,S

L = liquid phase

G = gas phase

S = solid phase

rn = mixture

b = bubble

d = dispersion

p = particle

Abreviations

Atenua. = atenuation

Chapter 1 Introduction

Particulate suspension systems are used in a number of applications in chemical and

biochemical processes. Examples of liquid-solid suspension are crystallization,

clarification and sedimentation while examples of gas-liquid-solid suspension systems

inc lude sluny- bubble columns and three-phase fluidized beds. Some O f the applications

of gas-liquid-solid suspension reactors are syngas conversion to fuels and chemicals,

hydrotreatment of petroleum residues, polymerization, fermentation, and waste water

treatment. Specific applications of bubble or slurry-bubble columns have been listed in

literature (Shah et al., 1982; Fan, 1989). For optimum operation and control of these

systems, it is often necessary to measure phase holdups Le. fraction of gas and solid

phases.

The schematic of a typical sluny-bubble column is s h o w in Figure 1.1. The gas enters

the reactor bottom through a gas distributor and rises in the fom of bubbles through a

continuous sluny phase. The column can be operated in continuous mode (when the

liquid/slurry phase enters at the bottom and exits from the side) or in a batch mode when

liquid phase is stationary. To maintain a constant temperature, a heat exchanger is often

necessary. The efficient operation of these reactors depends on hydrodynarnics, heat and

mass transfer as well as idrnposition and distribution of phases. Several techniques have

been reported in literature for phase holdup measurements in multiphase suspensions.

These inc lude static-pressure technique (Hikita et al., 1 980; Hwang and Fan, 1 986),

electncal-probe technique (Dhanuka and Stepanek, 1987; Begovich and Watson, 1978),

shutter technique (Kato et al., 1985; Fan et al., 1987) and optical-probe techniques (Lee

and de Lasa, 1987). However, the static-pressure method suffers from some difficulties

when the solids and liquid densities are close, while optical and electrical methods require

specific properties of the medium such as transparency or electrical conductivity.

Figure 1.1 Schernatic of slurry bubble colurnn

Also, none of these techniques provides a non-invasive method of instantaneously

monitoring the local phase holdups over the range of operating conditions of interest in

reactor operation.

Although relatively new, the ultrasonic techniques are already well established in a

variety of industrial applications such as materials testing, flow and level rneasurements,

particle size analysis (Kuttmff. 1991). Given its ability to penetrate through reactor walls.

this method offers the advantage of a tmly non-invasive and non-intrusive technique. As

a consequence, this technique could be used at high pressure and temperature operating

conditions or even for reacton with radioactive content (Grenwood et al., 1993). Highly

concentrated or optically opaque systems could also be analyzed. Other advantages of

ultrasonic techniques are their relatively low cost and fast response, which rnakes tbem

compatible with on-line measurements and incorporation with control systems.

An ultrasonic pulse of certain energy emitted from a vibrator (transducer) into a medium

propagates through this medium and reaches the receiver ai a lower energy after a certain

amount of tirne. The variations of solids and/or gas bubble concentration ia liquid will

change the density as well as the compressibility of the medium and thus the speed and

the attenuation of acoustic signal. An accurate rneasurement of the variations in velocity

and attenuation of the acoustic wave will indicate the nature of the mixture. When the

particle sizes are smaller cornpared to the wavelength of the signal or the non-

dimensional acoustic wavenumber k'r, «1, a simple phenomenological approach by

Urick (1947) may be successfully applied. The speed of ultrasound is calculated with

averaged values of density and cornpressibility of the medium components.

Compared to acoustic speed, which is mainly dependent on density and cornpressibility

of the medium, the loss of energy or transmission loss is caused by many other factors i.e.

scattering, absorption, reflection, re fraction, di fiaction or interference. For particles

smaller than pulse wavelength, scattering phenornenon predominates while for larger

particles, reflection and refraction phenornenon at the liquid/solid interface need to be

considered,

The application of ultrasonic techniques as a new measuing method in multiphase

systems was investigated recently by several tearns of researchers (Uchida et al., 1989;

Okarnura et al., 1989; Maezawa et al., 1993; Wenge et al., 1995; Warsito et al., 1995;

Soong et al.. 1995; Wanito et al.. 1997: Stolojanu and Prakash. 1997). The results show

the possibility of sirnultaneously measuring both solids and gas holdup in three-phase

system.

1 .l Objective of the Study

For optimum design and operation of multiphase reacton as well as for a cornprehensive

understanding of the mixing, hydrodynamics or heat and mass transfer; a key parameter is

the spatial distribution of phase holdups in the reactor. This study presents experimental

measurements on hydrodynamics in liquid-solid, gas-liquid as well as in gas-liquid-solid

systems with the help of ultrasonic technique. The investigated hydrodynamic parameters

are gas holdup and solids concentration. The continuous phase is water while air and

glass beads (351701180 pm) are used as gas and solid phase respectively. The measured

parameters are the velocity, the attenuation and the mean frequency of the transmitted

acoustic pulse. The sluny-bubble column operates with solids concentration of up to 21

vol. % (glass beads of 3 5 pm) and gas holdup of up to 30 vol. %. Some measurements are

conducted in a separate stirred cell for sluny system characterization. The results are used

to study the effect of the solids concentration and particle size over the measured

parameters as well as for calibration purposes.

While most literature studies have measured velocity and attenuation variations in dilute

suspensions (< 20 vol. %), this study investigates variations in velocity and attenuation of

ultrasonic signal for solids concentration of up to 43 vol.% and high gas holdups (up to

30 vol. %). It is ofien desired to detennine the particle concentration and composition at

different locations in a reactor. Measurements have been made at different axiai and

radial locations in both rnechanically agitated and gas agitated systems. Calibration

curves and procedures have been presented to detennine particle concentration and size

distribution in suspensions of mixed particles. A procedure is developed for simultaneous

measurements of gas and solids holdups in a slurry-bubble column.

Chapter 2 Literature Review

2.1 Classification of the Analyzed Systems

2.1.1 Multiphase Reactors

Multiphase reactors are conveniently classified according to the state of particle motion.

Three major operating regimes have been identified. First regime is fixed bed regime,

when the drag force on the particles induced by the flow of a gas-liquid mixture is smailer

than the particle weight (or the particles are immobilized by mechanical means). Second

regime is the fluidized bed regime when an increase in gas anaor liquid velocity

counterbalances the weight of the particle in the system. In this case the bed is increasing

in volume and the operation in this mode is also known as the expanded bed operation

mode. The fluid velocity where the operation in packed bed is changing into expanded

bed is known as the minimum fluidization velocity. If the fluid (gas or liquid) velocity is

increased iurther up to the point when the terminal velocity of the particle is reached. the

transport operation regime will occur. In this regime, the particles will be entrained.

The operating regimes of interest in this work are the fluidized and the transport regime.

Multiphase reactors operating in these regimes have been customady categorized into

two reactor types, namely slurry-bubble column reactor and three-phase fluidized bed

reactor. The distinction however, is a little fuzzy fiom the scientific point of view. It is

based mainly on the solids concentration and the particle size or, as some researchers are

considering, whether there exist a solid fiee layer in the upper part of the column

(Ostergaard, K., 1968; Shah, 1978; Fan, 1985; Deckwer, 1980). These differences are

though giving di fferent operating ranges as seen in Figure 2.1.10. Three-phase fluidized

beds usually operate in the expanded bed regime (0.03 to 0.50 mls) while sluny-bubble

colurnns may operate in both expanded and transport regimes (0.03 - 0.07 m/s).

Figure 2.1.1 Operating ranges for three-phase fluidized bed and slurry bubble column systems (Fan et al., 1987a)

2.1.1.1 Flow Regimes of Gas Bubbles in Bubble and Slurry-Bubble Columns

In bubble or slurry-bubble columns, the hydrodynamics are greatly affected by the nature

of the flow pattern. Figure 2. l .2 (Deckwer et al., 1980) shows a map of the flow regime

for a liquid-batch bubble column with a low viscosity liquid phase (i.e water). As it can

be seen, three types of flow regimes have been observed. These are dispersed bubble

regime, the coalesced bubble regime and the slug flow regime. For bubble columns, the

dispersed bubble regime is usually referred to as homogeneous flow regime and the

coalesced bubble regime as heterogeneous regime. The above delimitation is not though

very precise while most of the observations were visual and targeted a specific system

(Darton and Harrison, 1974; Hills, 1976; Fan, 1985). Other approaches for flow regime

identification were also considered. Theîe are, the pressure fluctuation analysis (Zheng et

al., 1988). particle image velocimetry (Tzeng et al., 1993; Chen et al., 1994), computer

automated radioactive particle tracking (Devanathan et al, 1995) and radioactive tracer

gas (Hyndman and Guy, 1995 a, b). As a consequence a more accurate description of the

flow regirnes in bubble and slurry bubble columns is given.

2.1.1.2 Bubble Flow Regime

This regime is charactenzed by a distribution of bubbles of relatively unifom s i x over

the entire cross sectional area of the bubble column. The gas velocities at which this

regime has been reported to exist are less than 0.05 m/s for liquid-batch columns (Hills,

1974; Fan, 1989). Cheng et al. (1994) observed also a vertical-spiral flow regirne at gas

velocities between 0.021 and 0.049 m/s, however, this regime is considered to be part of

the transition process to the heterogeneous flow when hole diameter of the gas distnbutor

is small. The relation between gas holdup and superftcial gas velocity is found to be a

straight Iine in the homogeneous flow regime (Mamcci, 1965; Kawagoe et al., 1976). In

sluny-bubble columns the homogeneous fiow regime is rarely observed. This is due to

the coalescence of the bubbles induced by the solid particles.

Coalesced bubble mgi ( he teroqeneous ,

o o * O .

2.5 S 1 O 20 50 100 0, (cm)

Figure 2.1.2 Flow regime map for a liquid-batch bubble column with a low viscosity liquid phase (Fan et al., 1989)

2.1 .l.3 Churn-Turbulent Flow Regime

With increasing gas velocity the uniform dispersion of relatively unifom bubble sizes is

no longer maintained and an unsteady flow pattern with turbulent motion is generated by

the larger bubbles. This flow regime is charactenzed by the phenomenon of bubble

coalescence and break up. A wider bubble size distribution is generated as a result.

Bubble sizes with diameters ranging From a few millimeters to a few centimeten were

observed (Matsuura and Fan, 1984). Akita and Yoshida (1973), Hikita et al. (1980)

analyzed the heterogeneous flow and developed equations for gas holdup calculations.

For liquid-batch bubble columns this flow regime was seen to exist at superficial gas

velocities higher than 0.05 d s .

2.1.1.4 Slug Flow Regime

This flow regime is seen to exist ai high superficial gas velocities and small column

diameters. The small colurnn diameter helps stabilize larger bubbles when the increase in

superficial gas velocity leads to formation of bubble slugs. Hills ( 1 976) and Miller ( 1980)

reported slugs in colurnns of diarneter up to 0.15 m. A detailed discussion on this flow

regime will not be carried out here, since this type of flow regime is not of interest in this

study.

2.1.1.5 Flow Regime Transition

Particle size and density, gas and liquid flowrates, column diameter, liquid and gas

properties are just a Few of the parameters which affect the transition between flow

regimes. Hikita et al. (1980) and Oztumk et al. (1987) observed that the gas holdup

increases with increasing gas density. Krishna et al. (1991) noted that an increase in

pressure causes a delay in the transition to Chum-turbulent regime, while dominating

mechanism is bubble break up. Wilkinson et al. (1992) observed that higher liquid

viscosity favors bubble coalescence phenomenon. Tlus in tum causes a transition to the

coalesced bubble regime at lower gas velocities. The solids addition to liquid in a bubble

column reduces the gas holdup (Koide et al., 1984; Koide, 1996). Kara et al. (1982)

observed that an increase in solids concentration or particle size resulted in an early

transition fiorn dispersed regime to coalesced bubble regime.

2.1-2 Stirred Reactors

2.1.2.1 Liquid So l id Suspension in Agitated Systems

The suspension of solid particles in agitated vessels is a process encountered in many

industrial applications. A suspension can have two main States: complete suspension

when al1 particles are in suspension or homogeneous suspension when particle

concentration is uniform throughout the stirred reactor. In a complete suspension, if the

solid particles are small and light, the distribution of solid particles is fairly

homogeneous. Ilcoarse and heavy solid particles are present, they will tend to remain in

the lower part of the vessel. In expenments canied in agitated vessels with sand particles

in water. it was observed that particles with a diameter of 800 Fm do not reach the upper

level of the liquid while particles under 200 pm form a fairly uniform suspension when

they are completely suspended (Zwietering, 195 8).

The most commonly used critenon to study solid suspension is the stirrer speed for jusi

suspension (NJs) when al1 the solid particles are in motion. This is not the point where the

suspension becomes homogeneous. A suspension is considered to be complete if no

particles are at rest on the bonom of the stirred tank for more than 1 or 2 seconds

(Zwietering, 1958). The use of the stirrer speed for just suspension to characterize a

suspension of solid particles is considered more important than the speed for

homogeneous suspension. This is due to the fact that, while the particles are in motion,

their entire surface is exposed to the fluid, thereby the maximum surface area is available

for heat and mass transfers. An increase in stirrer speed above this point does not pay

unless there is a clear justification, while from this point onwards the mass transfer from

solids to liquid increases very slowly with increasing agitation. The first extensive work

of the conditions for complete suspension is due to Zwietering (1958). Oyama and Endoh

(1955) developed also equations for the minimum stirrer speed for complete suspension,

but Zwietering's empirical equation developed on the b a i s of a dimensional analysis

using an extensive range of variables is still the most popular. It is especially useful for

labotatory work or scale up procedures when no data is available. The equation is:

where s = constant for a given system geometry, d, = particle diameter, q, = liquid

viscosity, p, = liquid density, Ap = density difference between solid particles and liquid

phase, B = weight of the solids in suspension per weight of liquid. times 100 (%), and Ds

= stirrer diameter.

The equation was verified by Nienow (1968) and found to be reasonably accurate.

Narayanan et ai. (1 969) proposed expressions considering theoretical considerations such

as energy or force balances. Their results do not agree with Zwietering formula, however

some of their assumptions are questionable. Baldi et al. (1 978) proposed a new mode1 for

detennining the minimum stimer speed for complete suspension based on energy

balances. Their equation is almost identical to that of Zwietering. Other researchers

supporting Zwietering equation with slight improvements to fit their experimental data

are Chapman et al. (1983), Guerci et al. (1986). The value of constants for Zwietenng

equation has been determined experimentally for different impeller types, tanWstirrer

diameter ratios, and tankklearance ratio and vesse1 geometry. Diagrarns like the one

presented in Figure 2.1.3 (Zwietenng, 195 8), were developed for di fferent impeller types.

Figure 2.1 -3 Correlation for complete suspension with stirreldiameter ratio of 4 (Zwietering , 1 958)

2.2 Fractional Phase Hold-up

In a three-phase system the holdup of each phase will be given by the volume fraction

occupied by that phase in a unit volume of mixture (fractional holdup). The importance of

holdup as a parameter related to the hydrodynamics and kinetics of a process was

underlined by Shah et al (1982). A large range of methods exists for the phase holdup

measurernents. A cornmon classification of these methods would be afier different

properties of the analyzed medium. A few of the classibng methods are:

physical methods

electrical conductance and capacitance

optical rnethods

radiation attenuation methods

ultrasonic methods

The holdup measurements c m be carried over the analyzed system regardless of the local

variations or it cm be carried locally and instantaneously for a better undentanding of the

reacting system. In both cases while the method involved will be same, only the probe

design or measuring setup will be different.

2.2.1 Physical Methods

2.2.1.1 Weighing Technique

This technique involves the weighing of the whole column before and after the operation

is started. Dynarnic and static holdups can be measured with suficient accuracy

especially since very precise electronic balances can be used. Unfortunately this

technique can not be used for local holdup measurements and it is difficult to apply to

large colurnns.

2.2.1.2 Measuremen t of Bed Expansion

This method is one of the simplest used for overall holdup measurements. By measuring

the bed height before and afier the dispersed phase iç present. an estimation of an average

value of Fractional phase holdup can be obtained using the following formula:

where cd, Hd and HL are the dispersed phase holdup, the height of the mixture and the

height of the liquid phase only. Although simple, the accuracy of this method decreases

when large fluctuations of bed level are present, or when foaming occurs.

2.2.1.2.1 Simultaneous Closure of Gas and Liquid Flow

In two or three-phase systems where gas is one of the phases, the measurement of gas

holdup can be done by simultaneous closure of gas and liquid flow. The volume fraction

of the gas will be given by the difference between the height before and after the closure

as seen in the above equation (2.2.1). The technique has been successfully applied by

several researchers (Akita and Yoshida, 1 973; Grover et al., 1986; Trudell, 1995). Some

of the difficulties encountered are when the foam is present or large fluctuations of the

level are occumng. In these cases it is difficult to measure an accurate height of the

mixture. An assumption where the dispersion height is equal to the column height such as

in continuous bubble columns is also not acceptable because of the weir effects (Prakash,

1991). Other errors may be present from the design of the gas and solids distributors,

when liquid or solids can drain into the gas sparger or into the gas line (Schurnpe and

Grund, 1986). Also, some gas bubbles may remain trapped between defluidized solid

particles. By recirculating the remaining liquid (refluidizing the bed) the bubbles are

dislocated and the error eliminated (Prakash, 199 1 ).

2.2.1 2 . 2 Dynamic Disengagement Technique

The measurernents of the bed height can be also camed dynamically after the gas flow is

stopped. These measurements in the bed height drop can give also information over the

bubble size distribution (Snrarn and Mann, 1977). Large bubbles will disengage first

when the gas flow is initially shut off, while the transient gas holdup will be due to small

bubbles (Guy et al., 1986). The technique is based on the assumption that there are no

bubble interactions after shutting off the gas. Snrarn and Mann (1977) were the first to

record the change in the gas-liquid dispersion height by filming the drop after the gas

flow was intempted. One major problem of the dynamic disengagement technique is the

poor measurement accuracy. An important role in improving the accuracy is played by

the sensors used for level measurements. Lee et al. (1985) proposed a novel digital sensor

consisting of a buoy, an encoded rod and a light emitter-receiver pair, connected to a

computer to record the real time dynarnic gas disengagement profile. The sensor used,

worked very well by dampening out radial and temporal fluctuations in the gaslliquid

level. Unfortunately this technique c m not be applied to opaque systems. For opaque

systems other types of senson c m be used. Daly et al. (1982) used five pressure

transducers placed at various heights along the column wall to measure the steady state

axial profiles and the level fluctuations during bubble disengagement. Their results for

the bubble Sauter mean diarneter are shown to be in excellent agreement with those

obtained with optical technique.

2.2.1.3 Sampling Technique

Withdrawal of samples from any point of the analyzed medium is another holdup

measurement technique. A trap of some sort, typical piston like, is used to capture a

specific volume From the analyzed medium (Joshi et al., 1990). The sample is then

transferred to a graduated cylinder when the volume is analyzed. In case of an existing

dispersed phase the concentration and size distribution are also analyzed. Nienow ( 1985)

showed that it is extremely difficult to obtain representative samples from a mixing tank

due to inertia di fferences between the fluid and particles of di fferent size and density.

With increasing pressure and temperature of the analyzed medium sealing of the

sampling probe is difficult and problems are encountered. For local measurements, care

has to be exercised while the probe may disturb the flow pattern.

2.2.1.4 Quick CIosing Valves Technique

Quick closing valves c m be placed at the beginning and the end of the section to be

analyzed. Both valves can be quickly and simultaneously manipulated to entrap the flow

in it (Joshi et al., 1990). This technique can be used in high pressure and high temperature

systems when solenoid valves actuated from a single switch are employed. The solenoid

valves with a closure time of 10-30 milliseconds cm be used up to 10-15 M N I ~ ' and 350

OC (Hewitt, 1982a,b). Of course, for higher degree of accuracy, several samples m u t be

taken and the average is used.

A major limitation of using this technique is that it is inapplicable for dynarnic

measurements or where flow can not be intempted. Also, finite time is required to close

the valves and this leads in principle to inaccuracies (Joshi et al., 1990).

2.2.1.5 Pressure Drop Measurements Technique

The pressure profile technique is one of the most widely used to determine the fiactional

phase holdup. The method uses the measurement of the static pressure profile along the

length of the column uçing manometers (Hikita et al., 1980; Fan et al., 1985; Reilly et al.,

1 986; Wachi et al., 1987; Del Pozo, 1 992). The pressure profile plotted as a hinction of

pressure tap heights will give the bed height. The technique is especially usehl when

used for three-phase systems. For three phases, obviously three equations would be

needed. Conventionally these equations were derived frorn rnass/volume balances and

measurements of static pressure gradients at two or more locations along the vertical mis

of the column. First equation cornes From a total volume balance:

The second, for a liquid-batch system, comes from the total volume of solids present in

the mixture divided by the volume of the mixture.

where Ws= total amount of solids in the mixture, S= cross-sectional area of the column.

The third equation comes usually From the consideration that under steady-state

condition. the static pressure at any point on the vertical axis of the reactor is given by the

total weight of the three-phase system.

For continuous operation or systems in which static pressure measurements are not

sensitive enough, equations (2.2.3) and (2.2.4) will be replaced by results obtained with

other methods. Dhanuka and Stepanek (1987) and Begovich and Watson (1 978) using

electroconductivity methods have shown that their results are within 5% of those

obtained with pressure profile technique.

The pressure profile technique proved to be very accurate at low gas flowrates, however,

with increasing superficial gas velocity the fluctuations fiom manometers are amplified

and the readings become corrupted with noise. Also. in sluny systerns. small particles

tend to enter the manometer lines disturbing the measurements. To solve these problems,

Prakash (199 1 ) inserted capillaries in the manometer lines. The use of capillaries proved

to be a good approach in eliminating pressure fluctuations, however care has to be

exercised the response time being longer.

2.2.2 Electrical Conductance and Capacitance Methods

Electrical methods are among the most widely used for medium characterization. For

these methods to work it is desirable that the phases have significant different electncal

properties. Most of the electrical methods are based on impedance measurements. These

measurernents cm include measurements of the conductance or of the capacitance or both

at the same time.

2.2.2.1 Electroconductivity Technique

The electncal conductivity technique is based on the difference between the

electroconductivity of a mixture of a solid ancilor a gas phase dispersed in a liquid phase

and that of the liquid phase alone. Maxwell (1892), as far as is known, was the first to

investigate this technique. He found that, the measured conductivity depends upon the

conductivity of the pure phases and their volume fraction. Since then, the technique was

continuously developed and has become an efficient method for measuring the cross-

sectional average and local gas or solids holdups.

2.2.2.1.1 Measuring System

Measurernent of electncal conductivity requires a pair of probes and an electrical

conductivity meter. The probes c m be constructed from different highly conductive or

electrochemically stable materials such as copper, platinum, tungsten or other metals. The

shape and size of these probes differs greatly. Altemating current (AC) of sufficiently

high frequency (-1000 Hz) and low voltage ( 4 . 5 V) is used to avoid the polarkation of

the electrodes. Very oflen the electncal conductivity of electrolytes is measured by using

a rectangular ce11 with two electrodes covering the entire cross-sectional area of the cell.

Under these conditions of uniform electrical fields, the conductivity of the electrolyte is

directly proportional with cross-sectional area (S) of the conducting material and

inversely proportional to the length (L) of the path between two electrodes (or probes):

S The - ratio is often referred as the ce11 constant. Uribe-Salas (1994) show that the

L

geometry of the ce11 used for electroconductivity rneasurements in both two and three

phase systems appears to be critical. Achwal and Stepanek (1975,1976), Turner (1976).

Dhanuka and S tepanek ( 1 987), Uribe-Salas ( 199 1,1994) and Marchese et al. ( 1 992) used

either coi1 or "grids" tungsten or copper wire electrodes separated by a set distance and

covering the entire cross-sectional area of a column. This design conserves the basic

geometry to provide conditions for uniform electrical field generation. Other

configurations were used by Begovich and Watson (1978) and Kato et al. (1981) who

attached several pairs of stainless steel sheets (0.025 X 0.100 m) to the inside wall of the

column and along the axial direction or Nasr-El-Din et a1.(1987), who used an L-shaped

probe configuration made From stainless steel tubing terminated with a conical stainless

steel tip to minimize the effect of flow disturbance. Nasr-El-Din et al. used two pain of

electrodes inside the L-shaped probe. First pair, two field electrodes, is flush with the

surface of the tubing and completely isolated from each other. The second pair. two

sensor electrodes (0.001 m apart), were also flush with the surface of the tubing and

located between field electrodes. These sensors were also insuiated from each other and

fiom the field electrodes. One general disadvantage of using electrode plates is the non-

uni fomity of electrical field.

2.2.2.1.2 Measurements in Liquid-Solid S ystems

Maxwell (1892) derived an expression for calculating the suspension conductivity as a

function of each of the phase conductivity and solids concentration:

km, k, and k, being the conductivity of the mixture, dispersed and continuous phase

respectively and C the solids concentration. The equation was said to be valid only for

low concentrations and for spherical particles of unifom size. For a mixture of non-

conducting solids (k=O) the above equation becomes:

Turner ( 1973,1976), and Neale and Nader (1973) extended the validity of the Maxwell's

equation and found it to be true for fractions of fluidized non-conducting spheres up to

packed bed values given the ratio k,k, is smaller than about 10. The equation can still be

used for higher values of kJk, but lower solids volume fraction less than 0.2 (Turner,

1976). Other models based on distribution of unifom spheres in a conducting liquid have

since been denved (Rayleigh, 1892; Meredith and Tobias, 1961 ; Neale and Nader, 1973;

Yianatos et al., 1985).

Bruggeman (1935) extended Maxwell's work to the case of random distribution of

spheres of various sizes. The result is the following equation, claimed to be valid for a

wide size distribution:

I \ - I

(km - k 3 = ( 1 - ~ ) ( k , k , )

Nasr-El-Din et al. (1987) and De la Rue and Tobias (1959) confirmed Bruggeman's

equation with their experirnental results. Tang and Fan (1989) found that both

Bruggeman and Maxwell models were suitable for particles of diameter less than 1.5 mm

in a liquid-solid fluidized bed.

Other equations were developed for estimating solids concentration in liquid-solid

systems with particles of non-spherical shape by Keller and Sachs ( 1964). for particles of

cylindrical shape and Fricke (1 924) for ellipsoid particles.

A cornparison of some of the above expressions is made by Nasr-El-Din et al. (1987) for

a slurry system. For different particles and particle sizes, Maxwell and Bruggeman

equations give very similar results at low concentrations. As the slurry resistance or the

concentration increases, Bruggeman's equation deviates significantly. As a conclusion. in

spite of the numerous equations proposed, the Maxwell equation remains adequate, and

its simplicity is attractive.

Achwal and Stepanek (1975) studied the gas-liquid system by electroconductivity

technique in a three-phase system. They used a glass column filled with II4" Rashig rings

and 0.006 m ceramic cylinders. As is well known, the electroconductivity of a liquid

system is proportional to the cross-sectional area of the conducting liquid and inversely

proportional to the length of the path between the electrodes. If the tortuosity factor

remains almost constant, the electroconductivity should be proportional to the liquid

holdup in the bed:

kL-S-G -- - E~ ( E ~ is on a solid-free basis) k L - s

A linear dependence of gas holdup versus conductivity was noted. The fit is given as very

close with the correlation coefficient 0.9857 and a standard deviation of 4.07 %, Dhanuka

and Stepanek (1987) found a similar equation for a gas-liquid system using g las spheres

(0.002-0.006 rn).

Yianatos et al. (1 985) and Uribe-Salas et al. (1994) found that Maxwell's mode1 gave a

good fit in a gas-liquid system for a measured gas holdups of up to 30 vol.% in a water-

air bubbles mixture (bubbles smaller than 0.002 m). A good prediction of their

experirnental results was obtained by using Maxwell and Bruggernan equations, however

this was true only for the case when a surface-active reagent was used. It was established

that the surface reagent did not affect the conductivity of the water solution, however it

did affect the bubble size distribution causing a decrease in bubble sizes (<0.002 rn). As a

conclusion, Maxwell and Bruggeman equations give a good fit only for bubble sizes

smaller than 0.002 rn and for gas holdup up to 30 vol.%.

2.2.2.1.3 Measurements in Gas-Liquid-Solid Systems

Begovich and Watson (1978), applied a modified rnethod of' Achwal and Stepanek

(1975,1976) to a three-phase fluidized bed for high fluid flow rates (gas and liquid) when

a visual observation of the bed height is no longer possible:

Begovich and Watson calculated the phase holdups by substituting equation (2.2.3) with

the equation (2.2.10). This equation (2.2.10) is said to fit their experimental results better

than the one (eq.2.2.6) developed by Maxwell (1892) for non-conducting uniform

spheres. The experimental results are compared with those obtained by using equations

(2.2.2), (2.2.3) and (2.2.4). An almost identical result was obtained by using both

approaches (within 5% deviation). Kato et al. (1981) used a similar form of the above

equation, to fit their experimental data for 0.4 - 2.2 pm glass bead particles:

Buyevich (1974) denved another equation for non-uniform sized spheres, applicable for

both solid-liquid and gas-solid systems:

The applicability of this equation for both the liquid-solid and gas-liquid systems rnakes

it useful in calculations of local liquid holdup from measured conductivity of gas-liquid-

solid system. Buyevich's equation was found to fit closely the data of Nasr-El-Din et al.

(1987) and Kato et al. (1981). Both Maxwell and Buyevich equations were tested by

Tang and Fm (1987) for pas-liquid system and found to be accurate up to 0.13 volume

gas fraction. Sarne researchen found that the Buyevich equation works well in three-

phase fluidized beds of low-density particles with size greater than 0.001 m for liquid

holdup measurements.

More recently Uribe-Salas (1991) estimated the gas holdup in a three-phase system by

substituting km and kL with kLS, and kL.s into Maxwell's equation for two-phase systems.

He also noted that both Begovich and Watson (1978) and Kato et al. (1981) used facing

electrodes (plates) which may lead to an incorrect empirical mode1 when there is no

uniformity of the generated electncal field.

Unbe-Salas et al. (1994) confirmed again that Maxwell's equation could be used with

sufficient accuracy for different granular solids with diarneter c 0.3 pim and for bubbles <

0.002 m. They also proposed two equations replacing the third equation (2.2.3) for

complete holdup estimation in three-phase systems. The first relates the gas and solids

concentration (non-conductive phases) to conductivity measurements perfonned in three-

phase system and in the liquid alone, and the second equation relates only the gas holdup

to conductivity measurements camed in three-phase system and liquid-solid system:

Equation (2.2.15) suggests that the liquid-solid mixture can be treated as a pseudo-

homogeneous system. This is in accordance with the findings of Tang and Fan (1989) in

their study on three-phase fluidized beds with batch solids. The selection of either

equation will depend on the facilities available to perform the conductivity

measurements. Achwal and Stepanek (1975) empirical model was also found to fit the

experimental data while Begovich and Watson (1978) and Kato et al. (1981) did not.

Marchese et al.. (1992) found the Uribe-Salas model to be applicable up to concentrations

of 60 vol.% gas holdup in a slurry-air system.

Some of the limitations of this technique are that the liquid phase has to be electrically

conductive. Also, the measurements depend strongly upon the flow pattem, which will

produce different results for dispersed and separated flows. A homogeneous flow field

between electrodes is desired but it is difficult to rneet these requirements. The presence

of the probes themselves disturbs the flow pattem and the transient response is relatively

slow. Other problems are caused by the polarization, electrochemical attack and deposits,

which will age and damage the probes.

2.2.2.2 Electroresistivity Methods

Similar to conductivity measurements, this technique is based on the measurement of the

local resistivity of the flow. Fundamental properties of gas bubbles such as gas holdup,

bubble frequency, bubbles size distribution and bubble nsing velocity distribution c m be

studied.

2.2.2.2.1 Measuring Equipment

The main difference between electroconductivity and electroresistivity methods lays in

the probe design. The electroresistivity probe is usually made from two insulated wires

(except the tips) placed equidistant in a tube with a diameter less than 5-6 mm. The parts

of the wires coming out of the tube are aligned vertically at a fixed distance apart,

depending on the bubble sizes investigated (Figure 2.2.1). The probe is placed inside the

analyzed system with its tips facing a reference electrode. The reference electrode is made

usually From a sheet of thin highly conductive material with a surface of a few cm2

attached to the colurnn's wall, following its curvature. Both the electroresistivity probe

and the reference electrode will be c o ~ e c t e d to the measuring equipment. This

equipment will sense any voltage drop when the probe will be activated. When any of the

probe's tips is in contact with the liquid phase the circuit is closed, but when a gas

bubbles interfere the circuit is open and a square wave can be generated. The fraction of

time over which the circuit is open can be determined, recorded and analyzed generating

information over the bubble size and other related parameters.

2.2.2.2.2 Measurements in Gas-Solid Systems

Considerable attention has been given to the behavior of bubbles in gas-fluidized systems

for a better understanding of such systems. Park et al. (1969) used a dual electroresistivity

probe irnmersed in a conductive coke bed to measure the bubble properties. Two

independent measuring systems were used for each tip of the probe and the results

compared. The results were initially conditioned generating two sets of square waves

with the upper part given by the bubble passing and the lower part by the dense phase.

The bubble size and velocity were calculated kom the length of the upper square wave

and also from the displacement of the same square wave read by the second tip. The

results showed that bubbles formed at distributor coalesce as they rise through the bed

and as a result they grow in size and diminish in frequency. The radial distribution of

bubble frequency and void Fraction occupied by bubbles has a maximum at about 1/2 to

% from the column radius in the lower levels of the bed while at higher levels it shi As

toward the center of the bed. Similar probes but with a single tip were used by Neal and

Bankolf (1 963) for two-phase flow studies and by Goldschmidt and Le Goff ( 1967) to

study the texture of a fluidized bed as shown by Park et al. (1 969).

2.2.2.2.3 Measurements in Gas-Liquid-Solid Systems

Rigby et al. (1970) using an electroresistivity probe similar to that of Park et al. (1969)

investigated the bubble properties and local volume fraction occupied by gas bubbles in a

three phase (water-air-glas beads) fluidized bed. They used a similar calculation

procedure and found similar results. A peak in the bubble fiequency distribution at 0.4-

0.75 radial position for the lower regions of the bed (D,=O. 1 m) was seen, while at higher

levels in the bed the peak moved toward center of the bed. An increase in bubble size

caused by the coalescence phenornenon was observed with increasing height above

distributor and a satisfactory correlation was found for bubble velocity and gas holdup as

a h c t i o n of gas and liquid flowrates:

Where Vb = bubble velocity; QG = volumetric gas flow rate; S s o l u m n cross-sectional

area; QL= liquid flow rate; E = bed porosity (gas and liquid); 1, = bubble length

Yasunishi et al. (1986) investigated also bubble properties in a slurry-bubble column

(Dc= 0.1 5 m) by a dual electroresistivity probe. They investigated a system of water-air-

glas beads and found a radial parabolic distribution of the local gas holdup in the range

where the mean solids holdup was less than 0.2 for di fkrent particle sizes (0.56~ 1 04, 1.6

x 1 04, 2.3 x 1 O-', 4.6 x 10-I rn). For higher solids concentration the gas holdup was seen to

decrease considerably in the region of dimensionless radius between 0.4 to 0.8 caused by

a significant increase of bubble concentration in the central region of the column. The

expenmental results for the cross-sectional averaged gas holdup were seen to agree fairly

well with the values predicted by Koide et al. (1984).

Similar limitations, as in the case of conductivity technique, apply in the case of

electroresistivity methods also.

2.2.2.3 Capacitance Methods

The pnnciple of this method is based on measunng the electncal irnpedance of the

medium (two or three phase system). The electrical impedance will change along with the

changes in dielectnc properties of the measured system. Several researchen (Rigby et al.,

1970; Hardy and Hylton, 1984; Hu et al., 1986; Wolff et al., 1990) used this technique for

phase concentration rneasurements. Hewitt (1978, 1982) made a review of this technique.

Depending on the system on which the technique is applied the impedance could be

governed by the conductance or capacitance or both. It is recornmended to operate at

conditions where the capacitance dominates while the liquid conductivity c m be easily

affected by the presence of dissolved salts.

Although the irnpedance method provides rapid response, the accuracy is sornewhat

doubthl due to uncertainties in data interpretation (Prakash, 199 1 ). Its potential

sensitivity io flow patterns is one of the major disadvantages. For a given void fraction, a

wide range of impedance values might be expected due to flow configurations. Other

problems may be encountered when cables are too long (high noise). Also. careful

calibrations are needed while these calibrations are strongly depended on bed material or

reactor temperature and pressure.

2.2.3 Optical Methods

The optical technique is based on measurements of the intensity of transmitted light

through a transparent medium or the refiected light From that medium. Either way, for

this technique to work, the continuous phase has to be transparent. Unlike the

electroconductivity technique it isn't limited to conductive fluids only. The usage of the

reflected light technique has been reported for measuring local phase holdups and bubble

properties in three-phase fluidized beds (e.g. Abuaf et al., 1978, Ishida and Tanaka, 1982,

De Lasa et al., 1984, Ishida et al., 1980, Hu et al., 1986). The transmitted light technique

was also used by other researchen (e.g. Kitano and Fan, 1988).

2.2.3.1 Measuring System

Different researchers proposed different fiber optic geornetry and matenals as a function

of the analyzed medium. Abuaf et al. (1978), Ishida et al. (1980) and Hatano and Ishida

(1983) proposed optical fibers in the fom of a single-fiber, a bundle or of two opposed

fiben For gas-solid fluidized beds. De Lasa et al. (1984) proposed a new type of fiber

probe for measuring the gas holdup in a three-phase system. This probe has a U-shaped

iorm and allows an appropriate control of the light projected and received through the

adequate selection of fiber materials or changes in its geometry. This is a unique

advantage over the other probes while strong light absorbing media require an

optimization of the amounts of light collected or emitted by the probe. Usually the optical

fiber probes were made of quartz or similar materials and were connected to a photo

multiplier. nie photo multiplier converts the light into electrical signal. This signal is

recorded on a data recorder and converted again From analog to digital. Finally the digital

signal is collected and examined by a cornputer.

2.2.3.2 Measurements in Gas-Solid Systems

Most of the optical measurements ftom NO-phase systems were carried in gas-solid

systems. Oki et al (1977,1980) studied the effect of the particles over the discharged gas

near the grid region in a three-dimensional fluidized bed. They developed an optical-fiber

m a y probe that provided the cross-sectional images of jets and bubbles fomed above the

center orifice of the multiple-orifice gas distributor. Another probe was also developed

for measuring the direction and velocity of rapid particle motion near the distributor. This

time a bundle of 7 optical fiben was used. The center fiber illuminated the rnoving

particles while the surounding six fibers detected the reflected light. Each of the

surrounding fibers was comected to a photo multiplier. The photo multiplier converted

light variations into electrical signals. For velocity and direction measurements the

following correlation between neighboring probes was used:

where V,= particle velocity, 1, = distance between neighbouring contact points of fibers,

&=30, 90 or 150 degree for n=l-2, 1-3 or 3-4; 8 = direction of particle movement as

sbown in Figure 2.2.2 and t, = delay time of two signals detected by light receivers, 2

and 3 when s 2 - 3 . AAer measuring the delay times between neighbouring fibers two

equations (2.2.17) are sufficient to determine the velocity and direction of the particles. A

dependence of the bubble diameter over the gas velocity through the orifices of the plate

was also studied. It was concluded that the orifice spacing played an important role in the

discharge mode of the gas phase, which in turn affected the gas holdup in the gas-solid

system.

in a similar experiment Ishida et al. (1980) measured the movement of solid particles

around bubbles in a fluidized bed at high temperatures using a bundle of 7 quartz-fiber

optic sensors. Another bundle of 3 fiben was used to detect bubbles. By comparing the

signals of both probes (bundles), the rising velocity of bubbles was obtained. The nsing

bubble velocity could also be obtained fiom fint probe (7 quartz-fiber) only, when the

wake showed vertical movement and the velocity of particles at the top of the wake could

be equal to bubble velocity.

In interpreting the experimental results, the bubble diarneter was taken as 1.5 times the

bubble height. The velocity of bubbles was found to be almost proportional to the square

root of bubble diameters. These results followed quite closely the equation for mean

bubble diameter developed by Hirama et al. (1975) at normal temperatures:

where D, = mean bubble diarneter at height h, V, = superficial gas velocity, U,,=

minimum fluidization velocity and K, = coefficient defined by yb=~, (g D,)"' with

K=rnean bubble rise velocity at height h above the gas distributor. Ishida et a1.(1980)

found also a correlation between particle velocity and mean bubble nse velocity or (Vg-

Vm# yb . The parameter (Vg-U,J Yb was seen to play an important role as a coalescence

index. Measuring the bubble velocity, size or frequency along the radial or axial distance

of the investigated two-phase medium led to calculations of the local and averaged gas

holdup.

2.2.3.3 Measuremeots in Gas-Liquid-Solid Systems

Ishida and Tanaka (1982) developed a new optical probe suitable for investigations of the

three-phase medium. Typical optical probes used in two-phase systems were made by

fusing two fibers together, one of which working as a light projector and the other one as

a receiver. The new probes were made of a single optical fiber, which in tum is

comected, with two others. The pnnciple is quite similar, but this time same optical fiber

acts as both trammitter and receiver. This makes the probe more "powerfùl" while the

traveling light distance h m the source to the medium and Crom the medium to the source

is minimized. Also, the probe's surface is slightly increased which in turn may be one of

the causes why the reflected light cornes also from particles and not only from the fluid

medium. Ishida and Tanaka used the newly developed probes in a three-phase medium of

g l a s beads ( 0 . 5 ~ 1 0 ~ mm), fluidized by water (0.015 m/s) and air (0.02 m/s). The

cornparison between the different types of probes (quartz fiber 180 and 350 Pm diameter)

show that the typical probes are lcss suitable for detecting bubbles in a dispersed zone,

but they can detect the reflected light fiom the moving particles over the tip of the probe.

The new probe is seen to detect both particles and bubbles at the same time. This proved

that this type of probe is more suitable for measurements in three phase systems.

De Lasa et al. (1984) proposed a new type of optical probe for high pressure and

temperatures. This new probe had a different constmction characteristic having a U-shape

profile, which allows some control over the light projected and received. Aiso the

adequate selection of fiber material was considered not only for mechanical resistance

properties but also for controlling the light transmission. The probe was tested in a

fluidized bed of g l a s b e d s (335 pm) where the fluidizing media were water and air. The

newly designed optical fiber was based on the difference of refractive indexes between

the gas phase and the liquid phase. Knowing that the angle of total reflection is iarger in

the liquid than in the air (Snell's law), the probes' curvature was chosen such that the

radius of the cwature is large enough. The angle of incidence at the iuming point is

larger than the angle of total reflection when the sarne fiber is exposed to air. On the other

hand, the curvature radius has to be small enough to secure an angle of incidence at the

tuming point srnaller than the angle of total reflection for the same fiber in water. This

design wil1 determine the probe to act as a light keeper in the air while in water medium

the same light will be lost.

The curvature radius was found to be about 0 . 5 ~ 1 0 ~ m at the tip of the probe for the

studied system and the diameter of the fiber was 400 Fm. Superficial liquid velocities of

0.007 to 0.022 m/s and superficial gas velocities of 0.019 rn/s were used to test this probe.

A correlation between the bubble velocity and the axial bubble length was obtained at

different liquid flow rates From experimental data:

where 1, = measured axial bubble length. However the standard deviation was quite high

(about 0.17 m/s) and the regression coefficient was also small (about 0.75). A

classification of the bubble types was also discussed taking into consideration the

measured axial length.

Same type OF probe was used again by Lee and De Lasa ( 1987) in a three-phase fluidized

bed of 250 pm narrow cut g l a s bead particles where liquid and air were the fluidizing

media. This time though, the time-averaged local gas holdup was measured. A local gas

holdup was obtained in the above expenments at different radial and a i a l positions. The

cross-sectional average gas holdup at a fixed height was calculated with the following

equation:

1 = y G r 2 m d r KR-

Using this equation along with the general volurnetric balance and local pressure

measurements, the gas, liquid and solids concentration could be completely determined.

Hu et al. (1986) investigated the solid and the gas holdups in a three-phase fluidized bed

with the help of two techniques. The phases used were air, water and giass beads (0.001

m)*

The solids concentration was measured with an optical probe while the gas holdup was

measured with an electncal probe. The measurement of the solids concentration had a

major difficulty in the fact that the gas bubbles reflect light as well. This pmblern was

solved through a set of experiments carried in both liquid-solid and gas-liquid-solid

fluidized beds. By subtracting the measured reflected signals in liquid-solid system from

those measured in three-phase system, the corresponding value for the gas holdup was

found. An expression for the radial profile of solids concentration was proposed from the

experimental data:

where = solids concentration at the bed center, E,,= solids concentration near the wall

and 4 = r/R dimensionless radial coordinate. The proposed equation matched the

experimental data quite well. Moreover the equation also gave a better fit for the data of

Linneweber, (1983).

Kubota et al. (1986) measured the concentration profile in a concurrent-flow gas-slurry

bubble column. The suspended solids were glass beads of about 45 Pm in diameter.

Calibration curves with known concentrations of g l a s bead particles were initially

produced for liquid-solid system. The relationship b e ~ e e n the concentration of the sluny

and the light absorbency was linear up to a concentration of 2 kgim3. The experirnental

results from the three-phase system are compared with those from liquid-solid system for

different gas flow rates and sarne solids concentration or for different concentrations and

sarne gas flow rate. The results are generally satisfactory but a consistent difference exists

suggesting that some additional phenomenon might be present.

The methods based on optical measurements require the transparency of the medium.

This c m be a major limitation for using this method. Also, in industrial applications for

highly viscous liquids or high pressure and temperature the mechanical resistance of the

optical fiber has to be taken into consideration. Improvements on signal to noise ratio are

still required. Finally. while most of the reacton do not have transparent walls. intrusive

placement of the optical fiber has to be carried out.

2.2.4 Gamma Ray Technique

Measurements with gamma ray radiation have been used since 195 1 to determine density

patterns in transverse sections of fluidized systems (Bartholomew and Casagrande, 1957).

This technique has become particularly attractive because the measunng equipment does

not interfere with the studied system and it can be used on vessels up to 40 feet in

diameter. The technique is based on the use of a beam of gamma radiation passing

through the analyzed medium and received on the other side by a radiation detector. A

part of the collimated beam is absorbed or redirected while the rest of the bearn penetrates

through the medium being detected. The intensity of the received gamma radiation is

proportional to the thickness of the matenal and the incident intensity as seen in the

following equation:

where p = absorption coefficient, Ax = thickness of the material, I and Io = intensity of

the measured and incident radiation. For a homogeneous medium and a mono-energetic

radiation, upon integration, the above equation cm be written as (Leipunski et al., 1965):

I = Io exp (-p x) (2.2.23)

The numerical value of p will depend on both the physical and chernical state of the

absorber. Using p/p (absorbency/density) ratio another coefficient is obtained (CD). This

coefficient 0 is called mass absorption coefficient and is independent of state but not

composition of absorber. As shown also by Bartholomew and Casagrande (1957)

equation (2.2.23) becomes:

1 = 1, exp (4 p x)

Abouelwafa and Kendall, (1979), analyzed the absorption of gamma radiation through a

homogeneous mixture with single narrow beams. They noted that the absorption

phenornenon could be described with the help of a mean absorption coefficient defined

as:

where No = Avogadro's number, 2, = atomic rnass number, oc = atomic absorption cross

section, p,,, = ptp, , <pi = volume fraction of component i. An averaged absorption

coefficient can be written also for a multiphase sysiem as:

- Pm, = CPA (2.2.26)

1

Knowing that the volume fraction <p, is actually x,/L where x, is the thickness of the phase

layer and L is the total distance between the source and the receiver of the gamma

radiation, the equation for a multiple absorption medium becomes:

where, pl = absorption coefficient for medium i and n is the number of absorben or

phases. In using these equations as a starting point For determining the phase holdups in a

two or three phase system, a discussion has to be conducted over the alignment of the

phases with respect to the beam of radiation. Two possible alignments can be considered

lrom theoretical point of view. Case I when the cylindrical beam of radiation is

perpendicular on the phases. The phases are represented in this case, by circula. slices of

certain thickness of the cylinder. Case II when the phases are aligned in parallel with

respect to the beam of radiation. In this case the phases are parallel in the longitudinal

plane and circular slices of the cylinder will include d l the phases.

The actual phase alignment will be sornewhere in between the two cases described above

though most of the studied cases (Bematowicz et al., 1987; Seo and Gidaspow, 1987;

Abouelwafa and Kendall, 1979) assurned that the majority of the gamma radiation will be

attenuated according to Case 1 alignment. This approach should be considered only when

the column reactor operates outside the slug flow regime when there is considered to be a

considerable arnount of homogeneity in the flow patterns.

2.2.4.1 Measuring Systern

An ideal gamma ray source for density measurements should emit mono-energetic

radiation in the range 0.5 to 1.5 MeV, and have a long half-life for avoiding the repeated

calibrations of the empty test sections. Sources of radiation as co60. CS'^', ~ a " ) . ~ m " "

with a half-life time between approximately 1 and 458 years were used (Bartholornew

and Casagrande, 1957; Gidaspow et al.. 1983; Seo et al, 1987; Abouelwafa and Kendal,

1980; Heywood and Richardson, 1978). For measurements in three phase systems two

sources have to be used. In case of a large reactor or pipe diameter it may not be possible

to use a low energy source while most of the radiation will be absorbed by the medium.

In this case a medium energy source and a very high energy source ( N O MeV) have to be

used. In this case senous safety problems would appear. Usually the source will be

encapsulated in a welded stainless steel capsule filled with lead. The capsule is provided

with a shutter to tum off the source.

The transmitted radiation intensity is measued by any practicable means. Scintillation

crystals (NaI), lithium-drified germanium detectors as well as Geiger-Muller tubes can be

used depending on the application considered. The scintillation crystals like Nd have

much higher gamma sensitivity than Geiger-Muller tubes, which in turn have the

advantage of simplicity. However, other factors such as, sensitivity to temperature,

voltage fluctuations and vibrations as well as initial cost or usehl life had to be

considered.

2.2.4.2 Measurements in Gas-Liquid, Gas-Solid and Liquid-Solid Systems

Bartholomew and Casagrande (1 957) presented a general equation for a mixture density

in any two-phase system (gas-liquid, liquid-solid or gas-solid):

where p, a, G, and L are the subscripts for particles, air, gas and liquid respectively and

the other symbols have been defined before. For a gas-solid system Bartholomew and

Casagrande (1957) neglected the absorbency by the gas phase thus simplifying the above

equation to a satisfactory forrn for their experimental work:

1, is measured as the intensity of the beam through empty vessel. In their study

Bartholomew and Casagrande used four sources of radiation co60 and eleven Geiger-

Muller detector tubes in a vertical riser of a fluid catalytic cracker unit (0.52 m diameter)

to study cross-sectional density patterns. The gas velocity was about 12 m/s. The

experimental results were compared with the calculated values from the above equation.

Separate experiments were carried out for determining the absorption coefficient. The

standard error for estimation of path densities through gas entrained solids calculated

From experimental measurements was found to be quite high (+ 13 %). Also, a general

finding was that the solids concentration increased in radial direction From the center to

the wall. Other researchers have reported similar results (Hunt et al., 1957; El Halwagi

and Gomezplata, 1 967).

Abouelwafa and Kendall (1979) showed that for a two-phase system, using equation

(2.2.27) and writing the volume Fraction of each component as q+=x ,/L and cp2=x2/L, the

following equations can be used for the calculation of each phase volume fraction:

where I l and I2 are for cases when only component 1 or component 2 are present in the

measured system. These equations can be used only in a senes of homogeneous media

(Case 1). A heterogeneous system may be treated as a series of homogeneous media if a

highly collimated (narrow bearn) source of mono-energetic radiation is used. In the

extreme case where the gas and Iiquid flow in layers parallel to the radiation bearn (slug

flow) the holdup of discontinuous phase will be given by the following equation (Wentz

et al., 1968):

Equations 2.2.3 1 and 2.2.32 are representing the above extreme studied cases, Case 1 and

Case 2. In practice, however, most of the situations are close to Case 1 as mentioned

earlier. Abouelwafa and Kendall (1979) successfully analyzed static configurations of

different two-phase systems such as oil-water oil-air and water-air. The results showed a

linear dependence between the attenuation coefficient and oil or water concentration. The

radiation sources used in their study were CO" (1 22 KeV, 270 days), ~ a ' ~ ' (365 KeV, 7.2

years). Stronger sources would be needed for a turbulent medium. A stronger source wiil

increase the measurernent precision, but at the sarne time will create more safety

problems. Also, if the source is too strong (N.5 MeV) the absorption will be too small to

be detected (Bartholomew and Casagrande, 1957).

Fan et al. (1962) and Weimer et al. (1985) measured the axial density profiles in a gas -

solid fluidized systems. They reported two distinct density zones, one of relatively

constant density in the lower part of the column, and one of rapidly decreasing density at

the top portion of the column. Weimer et al. (1985) using a rnovable gamma radiation

source CS"^. 500 rnCi) studied the dense phase voidage. centerline bubble phase volume

Fraction, bubble diarneter and bubble frequency. While accurate results were obtained for

dense phase voidage, centerline bubble phase volume fraction and bubble frequency, the

measurements of bubble sizes were considered approximate at best. Bubble shape.

shadowing of bubbles and the diarneter of the collimated bearn were just few of the

parameters affecting the measurements. The error in bubble size measurements is seen to

decrease with increasing bubble size. Instruments with collimated beams as small as

possible should be employed in bubble size measurements (Weimer et al.. 1985).

Orcutt and Carpenter (1985) reported similar studies on bubble sizes and bubble

Frequency. They used two gamma-radiation density gauges (cob0, 4000 mCi and CS"',

1715 mCi) sources to study the steady state bubble coalescence. The reported results

allowed the measurernent of individual bubble diameters directly, but it was also noted

that bubbles under 0.01 rn in diameter were not distinguished clearly.

Other studies in two-phase systems were carried in air-water slug flow in horizontal pipe

(Heywood and Richardson, 1 978) and jet penetration length in fluidized gas-solid system

(Cidaspow et al.. 1983). Heywood and Richardson (1978), by rapid scanning of the pipe

test section with a ~ r n ~ ' ' (60 KeV, 458 years) line source obtained estimation of the

actual holdup profiles in good agreement with existing theoretical rnodels. Gidaspow et

al. (1983) using a CS')' source (0.667 MeV, 30 years) consmicted calibration curves by

measuring the absorption of the radiation through several transversal sections of the

column filled with sand particles. Profiles of the porosity over the radial and axial

directions of the fluidized bed were found.

2.2.4.3 Measurements in Three-Phase Systems

In the case of' a three-phase system equation (2.2.27). considering Case 1. will have three

unknown variables:

Therefore three equations will be required for the solutions as s h o w by Abouelwafa and

Kendall (1979). The most obvious approach for finding these solutions is to consider

using two sources of radiation of different energies. Because the absorption of gamma ray

is dependent on the energy of the radiation, two sets of coefficients can be obtained for

each unknown holdup or layer thickness. A third equation c m be written as a sum of the

holdups (equal to l ) , or as a surn of the layer thickness equal to L.

This system of equations can be solved considenng the attenuation thmugh the gas phase

negligible at atmosphenc pressure when and p ~ ~ & ~ are omitted fiom the above first

two equations. in this case:

E, can be calculated also by replacing the numerical value of E, in one of the equations

(2.2.35), (2.2.36). Finally EG can be calculated From the third equation.

Abouelwafa and Kendal (1980) tested various mixtures of oil-water-air in a O.lm thick

section. The sources used were CO'' (122 KeV and 270 days), (365 KeV and 7.2

years). The measured oil-water-air ratios were calculated from attenuation measurements

as s h o w above. A good reproducibility (within 3 %) was found up to 40wt%

concentration. but it decreased (40%) for higher concentrations. The errors are mainly

due to the relative weakness of the sources used in this study.

Seo and Gidaspow (1987) studied binary solids concentrations and voids in a Ruidized

bed. They used two radiation sources, CS')' and X-ray source CU? A novel

experimental technique was reported for measurements of the volume fractions of binary

particles. Calibration curves were constructed by measwing the radiation absorption

through several transversal sections of known thickness filled with particles of either of

the types. The calibration was found to give a reasonable resolution with an error less

than a volume fraction of 0.015. Profiles of the time-averaged volume fractions over the

radial and axial directions of the fluidized bed were plotted using the calibration curves

and the experimentally measured attenuation.

Sorne of the most obvious problems with gamma ray technique are the safety problems

given the fact that higher radiation sources are needed to produce a given accuracy. Other

problems are the void orientation (case 1 and case 2) as seen above, which gives the

correlation used to determine gas holdup. This correlation generates a certain amount of

error while the real case is somewhere in between the two cases. Using two widely

different energy gamma radiation sources can eliminate rnany problems but the

equipment will be expensive and large with connected safety problems. Last but not least,

the radiation sources are usually not mono-energetic. This complicates even more the

rneasurements while photons of reduced energy are generated leading to an erroneous

interpretation of the signals.

2.2.5 Ultrasound Technique

An ultrasonic burst of certain energy emitted From a vibrator into a medium propagates

with a certain speed through this medium and reaches the receiver after a certain amount

of time, of course, with a lower energy. The ultrasound speed is dependent on the density

and cornpressibility of the medium. Generally, sound speed (or for that matter, ultrasound

speed) is higher in solid than liquid or gas. Liquids are in turn better carrier of sound than

gases. The presence of solids o r h d gas bubbles in liquid will change the density as well

as the compressibility of the mixture and thus the speed of ultrasound. An accurate

measurement of change in speed will indicate the make of the mixture.

2.2.5.1 Transmission Loss

The loss of energy or transmission loss of the transmitted signal is caused by several

factors. however. only one causes a direct loss of energy, and this is the absorption

phenomenon. The loss is due to the viscosity, heat transfer and perhaps moleculas

processes fiom media. The absorption increases with increasing viscosity or increasing

frequency of ultrasound (Asher, 1997). Other factors such as refiaction, retlection,

scattering, difkaction and interference will also diminish the energy of the transmitted

signal, but mostly through a reonentation of the ultrasound signal.

The reflection takes place at the boundary between hhro media, such as gas-liquid, liquid-

liquid or liquid-solid. The intensity of the reflection is dependent of the acoustic

impedance (2) of the two media given by:

where p = density of the medium and V= velocity of ultrasound in the medium. A high

mismatch of acoustic impedance may cause an almost complete reflection of the acoustic

wave at the boundary as in water and bubbling air systems. The mismatch of acoustic

impedance for this case is over 99.97 % at 20 OC (Cracknell, 1980).

The refractioo phenomenon or bending of acoustic wave at the boundary appears

between two media of lower impedance mismatch. The Snell's law gives the direction of

the retiacted wave as a hnction of both velocities From the two media:

The mle is that the beam bends away from the normal to the boundary if the velocity

increases in the second medium and bends toward the normal if the velocity decreases in

the second medium.

The scattering phenomenon takes precedence over the reflectionirefraction effects when

particle sizes are smaller than the wavelength of the ultrasound signal. The presence of

small objects in the path of the acoustic wave will cause a loss in the energy of the

transmitted signal through removal of a small amount of energy from the directed beam

and then, radiation in al1 directions. A scattering effect can also be caused by the

irregularities fiom a solid surface (Cracknell, 1980).

The diffraction is dependent mainly on the source characteristics. A beam generated by a

large diarneter ultrasound emitter will be less dimacted near a beam generated by a small

source. The distance from the source where the difiaction phenomenon is not visible for

an ultrasound beam is called the near-field zone and its length is given by the formula

dT2/4h where dT = source diarneter and h= wavelength of the signal.

Finally the interference can occur by overlapping of the transmitted signals with

reflections from the reactor walls, or with scattered ultrasonic waves fiom solid particles

or gas bubbles present in the dispersed phase.

It should be also mentioned that acoustic wave can travel in a variety of ways, usually

called modes of propagation. The two most common modes are longitudinal and shear

wave (charactenstic for solids). Liquids and gases transmit only longitudinal acoustic

waves.

2.2.5.2 Measuring Systems

Unfortunately there is no standard configuration for a measuring system of ultrasound

transmission through dispersed media. The researchers have to develop their own

instruments and data interpretation. Usually, the configuration is composed fiom a pulser

(and/or receiver board) designated for a fiequency range and a corresponding power. one

or two ultrasonic transducers, an oscilloscope, and a penonal computer equipped with a

data acquisition board (for example RS 232).

The block diagram could be one of the following:

i Pulse generator

I

Digital scilloscope ,y J1~l

[ Rilserireceiver 1

Figure 2.4 (a, b)

The generator will send a voltage pulse train to the transducer. The transducer produces

the ultrasonic bunts by converting the electric pulse of a certain amplitude, duration and

fkequency into a mechanical vibration through a piezoelectric crystal (in MHz range). In

pitch-catch mode (Figure 2.4 b) the RF signal is captured by the receiving transducer

connected to an amplifier with different gains (for ex: O - 80 dB) and transformed fiom

mechanical energy into elecûical energy which is finally quantified either from the

oscilloscope or from the receiver board. In pulse-echo mode (Figure 2.4 a) the reflected

pulse is received after some waiting period and converted back into an electrical signal by

the same transducer. The pitch-catch and pulse-echo modes are also sometimes called as

monostatic and bistatic modes (Asher, 1997).

There are many characteristics of the pulsedreceiver such as available pulse width. pulse

energy, rise time, PRF = pulse rate frequency, gate delay range and width, attenuation and

gain, R F phase (Asher, 1997). The pulse energy and width features allow the increase in

the extent of mechanical excitation of the transducer. The rise time shows the time

necessary for the signal to reach the maximum amplitude. The interface gate mode is

rnost useful. It allows the researcher to eliminate the unwanted interface echoes and

background noise caused by scattered ultrasound. Most of the ultrasonic systems require

the addition of a separate preamplifier unit to provide the additional gain or broadband

signal-to-noise enhancement necessary for optimum signal acquisition. Resistance values

are also available for attenuating the emitted signal when it is too strong (saturated

signal).

The transducers used in ultrasonic measurements are made from piezoelectric materials at

high Frequency such as polymer PVDF, lithium niobate, barium titanate, LMN ceramic.

The alignment of the transducers is a very important factor, especially when focused

transducers are used. The energy of the received signal can be greatly reduced by an

improper alignrnent between the emitter and receiver (Povey, 1 997). One way to increase

the power of the ultrasound system is by increasing the transducer diarneters.

The digital oscilloscope used in different experimental setups is used either for reading

the transmission time and amplitude of the received signal or, in the case of the integrated

pulserfreceiver system, for visualization purposes in fixing the gate delay. Remote control

is typically accomplished using a persona1 computer Iinked to the pulsedreceiver by a

serial RS232 connection or by the GPIB bus.

2.2.5.3 Measurements in Liquid-Solid (Liquid-Liquid) Systems

Extensive studies were conducted over the propagation of ultrasound signal in two-phase

systems. The methods of investigation were different involving either measurement of the

transmitted signal or of the backscattered signal. The main parameters measured are the

velocity and the attenuation of either the transmitted or backscattered signal. The

correlation between different frequencies and amplitude or velocity variation is also

shown.

2.2.5.3.1 Ultrasound Velocity as a Function of Solids Concentration

A simple approach to calculate the speed of ultrasound in suspensions is by making the

assumption that the suspended particles are infinitesimally srna11 compared to the wave-

length of the acoustic wave, and that accordingly the effects of scattering on the acoustic

wave may be neglected. This assurnption is not unreasonable as long as the frequency is

of the MHz order and the particle sizes (pm) are less than a hundredth of the wavelength

of acoustic wave in water. As a consequence the velocity of ultrasound may be calculated

by using Wood's equation and considering the suspension as an ideal mixture (Urick,

1947):

where pmpm are the density and cornpressibility of the mixture. The equation uses

averaged values of density and cornpressibility:

where cp is the volume Fraction of particles. Unck (1947) demonstrated the validity of the

above formula by conducting measurements for a suspension of kaolin particles (1 to 10

pm) in water at a dnving frequency of I MHz. The results were in good agreement with

the theoretical predictions, up to concentrations of 40 %. It should be mentioned that a

deflocculant (sodium pyrophosphate) was used for improving the charactenstics of their

suspension. Urick also tested the applicability of the formula in some emulsions of

xylene-in-water and water-in-xylene. The emulsions were prepared with the help of

emulsifiers such as sodium oleate and sorbitan rnonooleate respectively.

Same acoustic frequency was used and the median globule size. measured with a

microscope, was found to be 5 Fm. The measured velocities are s h o w over a wide range

of concentration for the two types of emulsions. The results show a very good correlation

between the emulsion concentration fiom both cases and the ultrasound ve locity

indicating that the ultrasound velocity is determined by the composition of the emulsion.

Ament (1953) reported improvements on Urick's expression by including the effect of

fluid viscosity and particle size in the density expression:

with r, = particle radius, 6=d(2tlL/opL), q ~ = viscosity of liquid, o = angular frequency of

the ultrasound. Substituting this pen in Urick's equation has not been used too much, but

according to McClements and Povey (1987, 1977) and Asher (1977) it is very useful in

descnbing the real behavior.

Given the initial assumption of homogeneous medium, Urick's equation does not take

into account the particulate nature of the mixture. The theory was developed further to

explain the obvious heterogeneity for higher solid volume Fractions. Biot (1956)

developed a theory for the propagation of acoustic waves through a porous solid saturated

with a compressible. viscous liquid. Using Biot's theory, Johnson and Plona (1982) found

another expression for effective density :

where r = tortuosity, denved for isolated spherical particles by Berryman (1980):

Another approach in deriving the equations for ultrasound propagation was proposed by

Harker and Temple (1987). They used the hydrodynarnic equations balancing momentum

and continuity of the phases with the drag of one phase on another. An equation

describing the complex wave vector, v,, of wave propagation in the mixture was obtained

ignonng the gravitational effects and heat and mass transfer between the phases, but

taking into account the intrinsic viscosity of the host fluid (Harker and Temple, 1987).

where p, p = density and compressibility of the liquid (,) or suspended particles (,) and

the term Sk represents the hydrodynamic interactions between particles and fluid:

In deriving the above expression Harker and Temple assumed that the viscous drag on a

particle could be taken to be that for an isolated particle in an infinite fluid (however,

mutual interactions will enhance the effective viscosity). Assuming that each particle is

making its own independent contribution to the local resistance to motion Einstein ( 1906)

ignored mutuai effects when the effective viscosity is given by:

where 5 = shape factor which For spheres becornes 2.5. Another form of writing the

effective viscosity cm be used:

Harker and Temple used the above expression in their calculations. The expression for

effective viscosity is said to be valid only for 6 < r,&"*. Harker and Temple (1 987) also

showed a cornparison between several approaches for characterizing the propagation of

ultrasound in suspensions or emulsions by writing the complex wave vector as:

w here

with M(o) is given in Table 2.1 frorn several authors:

Table 2.1

1 Authors :

Urick ( 1 947)

Arnent (1953) r-- Biot (1962) 1 Schwartz and Plona

(1984)

Harker and Temple

( 1987)

M(o) expression

The complex wave vector vk=V(o)+ia will give both the velocity and the attenuation of

ultrasound signal.

Harker and Temple (1987) conducted a series of expenments to test the validity of the

above equations. A suspension of kaolin particles (0.55 pm) in water was considered in

order to compare the results with those obtained by Urick (1947) and Ament (1953).

Good agreement between the experimental data and their theoretical prediction was

found. Even better results were obtained for al1 the above equations in a suspension of' 2

Fm radius globules of pentane in water.

Other researchers have also investigated the above expressions. Gibson and Toksoz

(1989) found results similar with those obtained from rnodified Biot's theory for a kaolin

suspension (1 pm radius particles) at 100 kHz. Anson and Chivers (1988) analyzed the

variation of the relative velocity with concentration for polystyrene spheres ( 140 pm)

suspended in oil. Atkinson and Kytomaa (1993) studied also the ultrasound speed in a

fluidized bed of 1.0 mm g l a s beads in water as a Function of solids concentration

comparing the results with Unck's predictions. There was no minimum velocity in their

results. Many other studies were conducted for liquid-solid or liquid-liquid systems such

as those by Bonnet and Sorrentino, 1994; Tsourk et al, 1990; Bonnet and Tavlarides,

1987; Tsouris et al, 1995, etc., showing more or less accordance with the developed

theory.

Trying to improve the existing theoretical models multiple scattenng theories were

developed, but these theories are too complicated and also require many physical details

of the system. Particle size distribution, densities of phases and thermal properties of the

phases are just few of the required parameters. Sometimes these properties are not very

well known or may change in an unknown manner, such as the particle size distribution.

In addition finding data for physical properties of many components is a difficult task.

That is why the Urick's equation is greatly appreciated for its simplicity.

Pinfield et al. (1995) tried to find simplified expressions for ultrasound velocity versus

solids concentration from Urick's equation including the effects of scattenng, but

avoiding the complexities associated with multiple scattering theory. They show that a

reproducible relationship exists between the ultrasound velocity and the volume fraction,

even when scattering is significant if the frequency and the particle size distribution are

constant. This relationship can be determined experimentally and applied as an

appropriate conversion to the Urick equation. When the volume Fraction is the unknown

parameter, the Urick's equation is best written as:

where

with V,= velocity of sound in the pure continuous phase,(o,,, = volume fraction

corresponding to the velocity V in the dispersion, AP=Ps - PL and Ap=ps - p , the

differences in compressibility and density between phases. In multiple scattenng

approach same equation c m be written as:

where <p,,, = volume fraction corresponding to the velocity according to scattering

theory. The above two equations are quite similar and the expenmental determination of a

calibration cuve of 1~~ versus <p would consist in finding the scattering coefficients as

and cq. The above coefficients c m be considered to be identical with Unck's coefficients

(a, and a?). While Urick's coefficients were expressed as functions of compressibility

and densities, after determining the coefficients as and a, expenmentally we can also

calculate:

As a conclusion finding the parameters for the calibration curve may be interpreted as

finding the effective fiactional compressibility and density difference between the two

phases.

2.2.5.3.2 Ultrasound Velocity as a Function of Temperature

For solids, the variation of the speed with increasing temperature is almost invariably

negative (eg. alurnina, magnesia, and stainless steel). There is however one exception for

fused quartz when the variation of the ultrasound speed is positive up to temperatures of

1000 O C (Asher, 1997).

For liquids the trend is sirnilar, almost d l the liquids showing a negative variation of the

ultrasound velocity with increasing temperature (Schaaffs, 1967). There are though again

exceptions, for liquids also. Water shows a steady increase in ultrasound speed with

increasing temperature of roughly 3.5 m/s°C. The increase is becoming smaller until a

maximum is reached at 74 O C . After this temperature the variation of the speed becomes

negative. A thorough investigation of the sound speed in pure water was carried by Del

Grosso and Mader(1972) at temperatures between O and 100 "C. After a respectable

number of experiments they found a sound-speed equation of fifth order in temperature

with a standard deviation of 0.003 m/s for the fit. The above data is considered reference

for ultrasound measurements also, given the velocity of sound in water is independent of

the frequency (non-dispenive). Most of the aqueous solutions show sirnilar behavior.

2.2.5.3.3 Ultrasound Velocity as a Function of Frequency and Particle Size

The ultrasound velocity depends also on Frequency amongst other ihings in a velocity

dispersive medium. Asher (1997) shows that in suspensions where Urick's equation is no

longer applicable, e.g. larger particles compared to the wavelength or larger density

difference, elastic or inelastic scattering will occur. This will cause a significant increase

in attenuation and consequently a velocity dispersion effect. Harker and Temple (1987)

showed some theoretical predictions for a suspension of Fe,O, particles in water.

Frequencies between 10 kHz and 10 MHz and particle radius 1, 10, 100 pm were

considered. The velocity of ultrasound was seen to increase for higher frequencies as well

as for larger particle size. Of course, the properties of the solid and liquid phase such as

density and compression wave speed have to be known. These predictions were

confirmed by Harker et al. (1991) with few experiments for a suspension of silicone

carbide in water when a variation in attenuation with ultrasound Frequency and particle

size was observed. Same experiment was repeated in ethylene glycol instead of water

showing clearer these variations. It was seen that velocity meastuement as a function of

fiequency is capable, in principle, of giving both the rnean particle size and the

concentration.

2.2.5.3.4 Ultrasound Attenuation as a Function of Solids Concentration

The decrease in the energy (amplitude) of the ultrasound signal is also important in

characterizing the investigated medium. Some of the attenuation factors responsible For

energy loss were already discussed above. Al1 the attenuation factors c m be cumulated

into an attenuation coefficient (a) which for a plane wave is given by the following

equation:

where L = traveling distance of the ultrasound signal and 1 and 1, the values of the

ultrasound intensity after a distance L and initially respectively.

According to Stakutis et al., (1955) the attenuation coefficient cm be written as a sum of

two contribution. the attenuation coefficient of suspending liquid and the attenuation

coefficient for the suspended particles (a = a,+ a,). This study is concemed with

measurements of ap. SeweIl(19 10) in his study of aerosols provided an expression for a,

assuming that the highest energy loss is in the neighborhood of the obstacle due to a

fnctional dissipation and due to the scattenng of a secondary wave.

where a

60

.,, are the losses due to turbulent Friction in immediate vicinity of the

obstacle, due to stream flow friction and due to scattering respectively, r, =particle radius,

n =number of particles, o= angular frequency and pc = kinematic viscosity. The above

equation shows that for a fiequency below 1 MHz a, is dominant and for a Eequency

above 10 MHz a,, dominates. Between 1 and 10 MHz a11 three tems have roughly the

same contribution. Epstein (1941) derived also an expression for a,. assuming that the

ratio of particle circumference to wavelength was small, and also that (kt,)' « 1 where

k= wavenurnber of the suspending medium. As in Sewell's study Epstein considered three

ternis a, a tme absorption terni, Aa, the correction to this absorption for larger k'r,, and

a, a scattering tenn, al1 of these tems being cumulated in the attenuation coefficient ap.

iw fi 2

rhcre 5 = (?) 5 ; b,= fluid density/particle density; S = bulk rnudulus; iy,9=

Lame elastic constants of the particle. In the developed expression the oscillations of the

particles in the sound field have been considered. but the darnping due to thermal

conductivity has been neglected.

A complete description of the ultrasound absorption in emulsions and suspensions due to

viscous and thermal transport processes occurring at the interface of the particles as well

as the inûinsic absorption in the systems components may be investigated in the work of

Epstein and Carhart (1953). A series of expenments were camied out to test the provided

theory by Stakutis et al. (1955). Two different systems lycopodium particles (30 pm

diameter and 1070 kg/m3 density) in water and fine quartz sand (0.5 to 5.0 pm diameter

and 2640 kg/m3 density) in water were investigated. The measurements were camied at

different temperatures and frequencies, for low concentrations (0-1.3 by volume). The

concentrations were expressed as number of particles per cubic centimeter and the results

show that the attenuation coefficient depends linearly on the concentration of the

suspended particles in the range of concentration investigated. As a conclusion the

experiments confirmed Epstein and Carhart (1 953) theoretical approach.

Other researchers conducted experiments for measunng the attenuation coefficient in

suspension of particles and much more complicated equations were developed as shown

in the work of Allegra and Hawley (1971). The observed attenuation with increasing

concentration for latex DC 586 (0.1 1 pm) at 20 O C by Allegra and Hawley (1971). was

seen to be linear up 20 wt % solids concentration. The linear dependency was also

observed for other four latex suspensions with particle radii of 0.044, 0.178, 0.504 and

0.653 microns up to 10 wt %. More recently Greenwood et al. (1 993) conducted a senes

of experiments in kaolin-water slumes of known composition with a particle mean

diarneter of 1 .O4 pm (median 0.85 pm) trying to assess the feasibility of using ultrasonic

attenuation to determine the concentration of a slurry. A linear dependence was also

found for volume Fraction up to 0.4 and for di fferent applied frequencies.

2.2.5.3.5 Ultrasound Attenuation as a Function of Temperature

Temperature variations are causing changes in the physical properties of the medium.

Stakutis et al. (1955) showed that the attenuation (for a lycopodiurn suspension)

decreases with increasing temperature and this could be either due to a decrease in

Rayleigh scattering, or due to the decrease in viscous absorption (lower shear viscosity at

higher temperatures). An expression, which shows the attenuation coefficient versus

temperature variations. was proposed as:

where a,, a, are the absorption and scattering terms from Epstein and Carhart (1953)

expression.

7.7.5.3.5 Ultrasound Attenuation as a Function of Frequency and Particle Size

As already rnentioned at the beginning of this chapter the attenuation is usually

determined by a sum of factors. While for pure phases the main factor is absorption

phenomenon, in two-phase systems the nature of the heterogeneity as well as the size,

shape and relation to the ultrasound frequency are al1 important in determining the level

of attenuation.

Stakutis et al. (1955) showed that the attenuation coefficient ap varies nearly with f ' ' in

suspension of lycopodiurn (30 pm diameter and 1070 kg/m3 density) and with f ' in

suspension of quartz sand (2.15 prn diameter and 2600 kg/m3 density) at approxirnately

15 MHz. For higher frequencies (about 30 MHz) the dependence is seen to Vary nearly

with the fourth power of the fiequency. These results c m be explained by the presence of

a viscous absorption at low frequencies (proportional with f " 2 ) and a Rayleigh scattering

(proportional with f ') at higher ftequencies. For quartz-sand suspension the attenuation

dependence o f f is said to be an equal contribution of viscous absorption and scattering

phenomenon caused by larger particles. The calculated attenuation coefficient was seen to

veri@ also the expenmental results obtained by Unck (1948) with suspensions of kaolin,

lycopodiurn and sand (1-2 pm) for the fiequency range of 1 to 15 MHz when viscous

absorption predominates.

Davis (1978) analyzing a coal sluny system (100 pm radius) with fiequencies up to 1

MHz, showed that the frequency dependence is roughly f' for attenuation in pure liquid,

f' for viscous attenuation and f ' for acoustic scattenng in suspensions of solid particles.

Atkinson and Kytomaa (1993) show that the measured attenuation for silica beads (0.001

m) in water depends almost linearly on fkequency for 0.1< kt, c0.75 and quadratically for

k.r, >0.75.

Harker et al. ( 199 1) conducted also measurements of variations in ultrasonic attenuation

with fiequency, particle size and volume fraction for silicon carbide (1.5 and 3.25 pm) in

water. The expenments show that the attenuation increases with increasing frequency and

with increasing particle size. Studies on the influence of the fiequency and particle radius

over the attenuation phenornenon are usually conducted by showing the correlation

between attenuation and the multiple factor k'r, (k =2r 1 h and r, = particle radius). In this

way both, the frequency and particle radius are accounted for versus attenuation.

2.2.5.3.6 Viscosity Effect on the Propagation of Ultrasound

For higher solids concentration where fluid is saturated in granular material, many of the

above theoretical predictions are no longer accurate. Other theories on the propagation of

acoustic waves are available such as the theory developed by Biot (19524962). Biot

worked on the propagation of acoustic waves through a porous elastic material saturated

by a compressible fluid. Stol1 (1974) extended Biot's work analyzing unconsolidated

granular sediments. The Biot's theory cornes with a new feature allowing the possibility

of a viscous fluid loss. This loss will increase with increasing frequency proportional to/

for lower frequencies and withp" for higher frequencies. The practical applicability of

Biot's theory was discovered later by Stol1 (1974). He came with a new approach taking

into account losses at grain to grain contacts, modeling the solid matenal as a viscoelastic

porous solid.

Costley and Bedford (1988) verified the above two theones by measuring the velocity

and attenuation variations versus viscosity in a laboratory tank containine glass beads

saturated with a mixture of water and glycenn. The viscosity of the supporting fluid was

changed by varying the proportion of glycenn. The agreement between the expenmental

results and the calculated values for both velocity and attenuation are very good. The

increase in velocity with increasing viscosity was seen to be more powerful than the

attenuation increase.

2.2.5.4 Measuremeots in Gas-Liquid System

2.2.5.4.1 Ultrasound Velocity as a Function of Gas Holdup in Gas-Liquid System

The research done on the acoustical properties of the gas-liquid system is less irnpressive

than that of liquid-solid systems. However, an adequately treatment of the theory has

been done by Meyer and Skudqk (1 953) and Carstensen and Foldy (1947). Sarne simple

Wood's equation c m be used again. At a small content of bubbles in liquid. the density of

liquid is little changed, however the compressibility is greatly affected. Bubbles can

radiate themselves sound waves when under a certain frequency of an acoustic wave

(Strasberg, 1955). The phenornenon appears as a result of oscillatory motion of the

bubble wall and the frequency at which it occurs is called "natural fkequency". The

bubble volume pulsation can take place in different modes (0,1,2,3) along different axes.

If the amplitude of oscillation is relatively mal1 the various modes are independent of

each other. Each of these modes has a natural fkquency of oscillation. Minnaret (1933)

calculated the natural frequency of O order (sphencal pulsation) and Lamb (1945)

calculated it for higher modes of shape oscillation:

where Po= static pressure, y,= specific heat ratio CdC, of the gas; CF surface tension, fi and r.6 =the resonant Frequency and radius, y = mode of oscillation. As it c m be seen for

y = l (transitional oscillation) there is no natural Frequency, since no restonng Force is

associated with a free bubble in a transitional oscillation. For spherical air bubbles in

water the natural Frequency or resonance radius is given by:

/, x r,, = 3.26 Hz. m (2.2.70)

The presence of resonance bubbles do not in general affect the velocity of ultrasound

propagation but greatly affect the attenuation of the acoustic wave. The compressibility of

a liquid containing gas bubbles of equal size was studied by Meyer and Skudrzyk (1953)

which have identified bubbles vibrating with small amplitude of a zero-order radiator and

derived the following expression for complex compressibility of the mixture.

where XL,Xb are the complex compressibility of the liquid and bubbles respectively, V, =

velocity of ultrasound in water only, R = bubble damping constant, q = 31(4n2p,(ro,f,)2)

which for air bubbles in water becomes 7.05~10-~, rd = bubble radius having the

resonance frequencyf;. Using this complex compressibility in Wood's equation we have:

PL X and the phase velocity becomes:

for f «/,

and for the particular case of air bubbles in water:

As it can be seen from the above Formula the velocity of ultrasound is lower in air bubble

-water system for frequencies smaller than the resonance frequency. In case of bubbles of

various sizes the component 5 is determined by the sum of the compressibility of the

individual bubbles:

The contribution of the imaginary component (bubble-induced absorption) can be

neglected at off-resonance frequencies and the above expression can be reduced to:

For the case of air bubbles in water and considering the velocity in the liquid phase being

1500 m/s, the previous equation for air bubbles of equal size can be written as:

Fox et al. (1954) measured the variation of ultrasound velocity at different air bubble

concentrations in water. The bubble sizes were between 0.03 and O. 15 mm in diameter

and the frequencies used between 10 kHz and 1 MHz. For these bubbles sizes the

resonance frequency should be around 60 kHz. The results are in good agreement with

the theoretical values calculated fiom Wood's equation using the cornplex

cornpressibility. The velocity variation is accompanied by a large attenuation variation at

resonant frequency (60 kHz) up to about 200 kHz when the acoustic velocity is

approaching asymptotically the value in water phase only and the attenuation is

decreasing substantially. The precision of phase velocity measurements is estimated to be

within 5% and for attenuation within 2 dB/m.

For frequencies higher than resonance frequency, Davids and Thurston (1950) showed

also that while the acoustic velocity exceeds the velocity in liquid phase irnmediately

after resonance, at higher frequency values f >>/a the acoustic velocity is not affected but

the bubbles, approaching asymptotically the value in liquid only.

Greenspan and Tschiegg (1958) using a very high precision laboratory velocimeter

reported that the influence of dissolved gas on the acoustic velocity need not to be taken

into account while the variation of velocity in water saturated with air between 10% and

1 00% is less than 0.00 1 %.

2.2.5.4.2 Attenuation as a Function of Gas Holdup in Ga-Liquid System

Similarly with the attenuation caused by solid particles, the attenuation of acoustic wave

caused by the presence of gas bubbles c m be expressed through an attenuation coefficient

called effective extinction cross section a,, which is interpreted as the area of the cross

section perpendicular on the incident acoustic wave such that the transmitted acoustic

energy equals the sum of the energies absorbed (GA and scattered (a,) by the bubble:

The expressions for the above three coefficients given by Myasischev (1955) are as

foilows:

where f, = resonance frequency, rb= bubble radius, f = frequency of the acoustic wave, R

= damping constant of the bubble, w=lrrr,,ih is the ratio of the circumference of the

bubble to the wavelength A. At resonance, there is a strong increase in ultrasound

attenuation. Heating of the bubble, withdrawal of heat into the liquid during the periodic

volume variations experienced by the bubble and dissipation of part of the acoustic

energy due to the role of the vibrating bubble as a spherical sound source are just few of

the causes. Also energy losses due to the formation of currents in the liquid about the

vibrating bubble could occur. The quantity w in the above equation is almost constant for

resonance bubbles of any radius when small-amplitude vibrations are occumng.

As seen From the above expressions the effective cross section is maximal for a given

bubble radius when f =j, (the fiequency of the acoustic wave is in resonance with the

bubble vibrations). An obsei-vation to be made is that the resonance values of effective

cross sections O,, ,G,, , and os, are much more higher than the geometric cross section of

the bubble nrb2. For the regular case of an acoustic bearn entering a bubble region. al1 of

the same size. the energy attenuated by each bubble is given by 0,I. If [(O) and I(x) are

the intensities of the ultrasound beam at the bubble entry region and at the distance r

inside the bubble region:

f,

I(r) = ~ ( o ) e - " ~ ~ ' ' ~ ' and N ( x , ) = [n(x)dr O

N(x,) is the total number of bubbles in the column of length xi and unit cross section. In

decibels the above equation can be written as:

w here

where n' = mean probability density function of bubbles in the layer and a, = ultrasound

attenuation factor. Finally the attenuation factor for a sheet of bubbles al1 of the sarne size

c m be written as:

Carstensen and Foldy (1947) conducted expenments for air bubbles in water system at

the lower limit of ultrasound range (20 kHz). A short burst of different bubble sizes was

emitted causing the bubbles of varying sizes to rise to the surface with different

velocities. The theoretical values matched quite well the experimental results showing

that the main attenuation was introduced by bubbles whose radii are close to the

resonance value (0.16~ 10" m). In a second experiment Carstensen and Foldy injected air

into water continuously, when the volume concentration of bubbles of al1 sizes increased

and the experimental values of the attenuation (25 dB) tumed out to be much lower than

the calculated values (50 to 200 dB). This is said to be mainly because of the mutual

influence of the closely spaced bubbles as discussed previously. Fox et al. (1954)

obtained sirnilar results for air bubbles ( 0 . 15~ 1 O" m) in water.

Macpherson (1 957) however, obtained excellent agreement between theoretical values of

the attenuation and the experimental results. The results for air bubbles (0.16 to 0.5~10"

m) in water at a bubble density (4 bubbleskc) was only slightly higher than the limiting

value above which it is required to take into account the overlapping effect.

The developed rnodels have been successfully applied to describe the propagation of both

infinitesimal and finite amplitude one-dimensionai disturbances through liquid containing

small gas bubbles.

More recent investigations dfAgostino and Brennen (1988) show that the acoustical

absorption and scattering cross sections of a bubble cloud are very significantly different

in both amplitude and fiequency distribution From the acoustical absorption and

scattering cross section of individual bubbles in the cloud. Also, the natural frequencies

of the cloud are always lower than the natural ftequency of the individual bubbles.

2.2.5.5 Measurements in Three-Phase System

Okamura et al. (1988) in a short communication initiated the measurement of ultrasound

velocity in three-phase fluidized bed by ultrasonic technique. They showed that if an

ultrasonic burst is emitted in a three-phase slurry which contains gas bubbles, as well as

solid particles, a part of the signal is transmitted through the liquid phase without

encountering any bubbles, showing the same phase lead and amplitude as that in the

liquid-solid system. Another part of the signal is accelerated by fluid currents (caused by

bubble motion) showing a phase lead and of course sorne part of the signal is completeiy

blocked by the bubbles when a zero-amplitude output is received. The experiments were

conducted at 1.7 MHz with two types of solids, activated carbon (1.58 x10" m) and glass

beads (0.194 x 10-' m). Air was used as gas phase and water as liquid phase. No effect

over the time ratio was observed.

A similar study was conducted by Uchida et al. (1989) with glass beads (194 pm) in

water and air as the gas phase (O - 0.03 16 rnls) using sarne fiequency (1.7 MHz). In this

case the phase lead was quantified versus the gas holdup (up to 0.1), however the phase

lead was considerably smaller than that caused by the solids concentration and the

expenmental error was quite large. It was concluded that it was difticult to measure the

gas holdup in this way. Another diagram shows the profile of the axial solids

concentration distribution. The solids concentration was represented by the following

empincal equation:

with A, = coefficients determined experimentally and h = longitudinal distance from

distributor.

.4n interesting approach was by Warsito et al. (1995). They proposed the following

equation for the transmission time in a three-phase system:

=(Tls +(FIG G- L-S

where A t L are the time di fference caused by solid particles (,) and by gas b u b b I e ~ ( ~ ) and

L the distance between transducen. While a linear relationship was observed for two-

phase system in both liquid-solid and gas-liquid system it was assurned that the linear

relationship between the holdup and the transmission time difference is also valid in the

gas-liquid-solid system, when:

For a high enough ultrasound Eiequency the micro-bubbles pulsation does not affect the

velocity of ultrasound and the contributions of gas bubbles and solid particles to the

change in transmission time of acoustic wave can be Witten as:

Using the above two equations and measuring the transmission time at two different

frequencies, the solids concentration and the gas holdup can be rneasured instantaneously

in the three-phase fluidization systems. it should be noted that the value of k, has to be

investigated in three-phase system while it is not the sarne as in two-phase system. The

experimental results for gas-holdup dependence of transmission time in three-phase

system compared to WO-phase system are quite similar. In case of solids concentration

measurements, the method is said to give about 15 % error.

Warsito et al. ( 1997) conducted another series of experiments using the sarne theoretical

mode1 as in their previous work, to study the radial distribution of solids concentration in

the hilly developed flow region of a slurry bubble colurnn. The particles used were glass

beads of radius 0.100, 0.228 and 0.454 ~ 1 0 ' ~ m at 0.9 MHz, and the liquid and gas phase

were tap water and air. The trends of the solids concentration distributions were similar to

those in gas-solid down-flows (Zhu et al., 1995).

Soong et al. (1 995,1996,1997) conducted numerous experiments in three-phase slumes.

Some of the systems investigated were paraffin wax, nitrogen bubbles and g las beads

(80 pm). The effect of temperature on ultrasound propagation was found to be large. The

attenuation increased with increasing nitrogen flow which was expectable and the results

were found to be follow the developed theory by Bensler et al. (1987) given by the

following equation:

where i- = volumetnc interfacial area, a, =scattering coefficient, k =wavenumber , d,,

=Sauter mean bubble diameter, x = travelling distance. For three-phase measurements,

the presence of gas bubbles was found to have no effect on transmission time of

ultrasound.

2.2.6 Other Techniques

2.2.5.1 Real -Tirne Neutron Radiography Technique

This real-time technique is based on the usage of a collimated beam of thermal neutrons.

The beam penetrates the medium and it is detected on the other side by a neutron to

photon converter in a camera head. This technique is very similar to the gamma ray

technique. Several researchers (Fairholm et al., 1991; Harvel et al., 1992) showed that the

real-time neutron radiography (RTNR) technique can be used to visualize two-phase flow

through aluminium and steel pipes. Flow regime, void fraction and interfacial area could

be studied. Chang and Harvel (1992) used this technique for determination of gas-liquid

bubble column instantaneous interfacial area and void fraction. A thermal neutron flux of

approxirnately 10' n/cm2s was used. Void fraction measurernents at approximately every

0.001 m in a 0.30x0.30 m imaging area could be studied. The camera designed for RTNR

applications detected the photons generated by the neutron to photon converter. and

images of the analyzed medium were obtained. The void Fractions were calculated using

the relative intensities of the neutron radiographie images. The interfacial area was

caIculated fiom the void fiaction and the mean bubbte diameter. The results were

compared with those obtained by level measurements or by an ultrasonic technique

(Chang and Morala, 1990). The experimental results are seen to agree well for the

measured systems. The agreement is seen to be better with the ultrasonic technique than

with the liquid level rneasurement technique. One of the main disadvantages of this

technique is the cost and availability of the equipment.

*

2.2.5.2 Particle Image Velocimetry Technique

This is a relatively new non-intrusive digital technique based on digital analysis of

successive captured images fiom a transparent medium. The technique is not suitable for

sluny systems because of the opacity of the medium. The measuring system is usually a

video carnera, which snaps image -es of the analyzed medium. The images are then

digitized and stored on a computer when using specialized software the differences

behveen successive h m e s are analyzed.

Several researchers (Chen and Fan. 1992: Chen et a\.. 1994; Lin et al.. 1996) showed that

this technique is capable of giving information not only on the phases holdup or bubble

sizes and their distributions, but also on instantaneous velocity distribution of different

phases or other statistical flow information.

In spite of its advantage of operation without affecting the flow charactenstics, the

particle image velocimetry technique may be more dificult to adapt to an industrial

application. This is mainly due to the medium transparency requirements.

2.3.5.3 Laser Holography Technique

Although expensive and hard to setup this technique is capable of providing the diameter,

shape and position of every gas bubble at a certain time (Peterson, 1984). The

requirement that liquid and solids have sarne refractive index, limits though its

applicability. Also, at higher gas velocities it becomes difficult to use given the turbulent

nature of the medium. However, when used in proper conditions good results are

obtained. Peterson (1 984) showed a good correspondence between the measurements for

phase holdups over a range of gas flow rates obtained with this technique when compared

with those From the pressure gradient measurements.

Chapter 3 Experimental

3.1 Experimental Setup

Experiments were conducted in a plexiglas colurnn and a plexiglass cell. The column was

used for measurements in gas-liquid and gas-liquid-solid systems while the ce11 was used

only for liquid-solid rneasurements. The results from the ce11 measurements were

compared with those from the column in liquid-gas-solid system.

The column had an inner diarneter of 0.101 m and it consisted of three flanged sections

(each section 0.101 m and 0.457 m high) connected with bolts and sealed with O rings.

The base and the middle section of the column were firmly fixed to the building structure.

Ports were installed for manometers along the column height. The bottom section of the

column worked as the windbox. Compressed oil-free air was introduced through a porous

polyethylene plate (5-mm thickness with 75 pm pores), sandwiched between the first and

second sections of the column and its flow rate was measured with a rotarneter. A

backpressure of 34.5 kPa, monitored with a pressure gauge, was kept constant through the

rotameter by adjusting the airflow with a pressure regulator installed on the compressed

air line and a valve installed between rotarneter and colurnn. A schematic of the above

column is shown in Figure 3.1.1.

The calibration of the rotameter for the above pressure and temperature was carried with

the help of a wet testmeter. The results are shown in Appendix A (Figure A.2) for three

experiments. A correction factor of 1.15 was used to multiply the rotarneter readings at

working conditions (22 O C and 34.5 kPa backpressure). An error of less than 2% was

observed which is in cornpliance with manufacturer specifications.

I I

Pressure

0,457 m

sect. c

Uttrasontc transducers Manome~ers

Pressure W"g= Porous

polyethytene I

Rotameter JI ! A l r J Water

Intet outlet

Figure 3.1.1 Schematic of slurry bubble column

The porous sparger provided high gas holdup and relatively unifonn bubble size

distribution. The properties of the porous plate used for liquid-gas measurements were

characterized by pressure drop measurements, which provided the average pore diameter.

The plate material is said to be of little importance for bubble generation as long as the

plate is wetted with liquid (Koide et al., 1968). The given characteristics for the porous

polyethylene plate were $,,=75pm pore size and 0.005 m thickness. A larger pore size

was found by using the approach by Houghton et al. (1957), as seen in Appendix A. The

new pore size ($,,;100 pm) was used in further calculations of the bubble sizes

generated by the porous plate.

The bubble size distribution was measured by taking photographs of a delimited volume

from inside the column. A thin square panel of 0.09x0.09x0.002 m made From opaque

plastic was attached at the end of a long rod (2 m length and 0.005 rn diameter). Mettic

scales were attached on the sides of the plastic panel for reference proposes. The panel,

kept in vertical position, was introduced fiom the top of the column so as to touch the

colurnn wail facing the photo camera. A plexiglass square box of O. lx0.3x0.3 m made

fiom two identical pieces was attached and sealed on the outside wall of the column in

between photo camera and measured section. The square box was filled with water. This

procedures helps eliminate the column curvature. The opaque plastic panel delimited an

inside volume of about 170 cm' close to the column wall. Pictures were taken for

different flow rates. The pictures were magnified (scale 1: 4) and projected on a large

drawing surface where the circumference of each bubble was underlined. Most of the

bubbles were of spherkal form, however some of the bubbles were ellipsoid when an

average between the x and y-axis was taken as the bubble radius. The results are

summarized in Table A.2 and A.3 s h o w in Appendix A. Figure 3.1.2 shows a typical

photograph used for bubble size measurements.

Figure 3.1.2 Typical photograph used for bubble size measurements

The superficial gas velocity was varied between O and 0.05 rn /sec. The continuous phase

(batch mode) was tap water. For installation of the transducer and receiver diametrically

opposite ports were located 0.150 m from the gas distributor plate. The ports allowed

radial movement of the transducers. A small Plexiglas flanged section 0.01 m high with

two similar ports was also used for measurements. This section could be interco~ected

between first and second or second and third section of the column, allowing

measurements in the axial direction. The radial distance between transducers was Lept at

0.0254 m in three-phase system due to higher attenuation in presence of gas bubbles and

0.0508 m in liquid-solid system. The solids used were glass beads of average diameter 35

Fm and density 2450 kg/m3. A Brinkmann analyzer w u used for particle size analysis

and a pycnometric technique for particle density measurements. The results are s h o w in

Appendix C. Technical data given by the manufacturing Company are also shown.

The ce11 used for liquid-solid measurements had a construction similar to any one section

of the above colurnn. It was made from Plexiglas with same inner diameter of 0.101m

and almost same height (0.5 m), the ce11 had also two diametrically opposite pons, but

their placement was slightly off center (0.02 m) to allow the presence of a mechanical

stirrer. The mechanical stirrer maintained a hornogeneous suspension with the help of a

six-blade propeller (45 degrees pitch with a diameter of 0.051 m). Tap water was again

used as the liquid phase while the solids used were glass beads of 35. 70 and 180 Pm. The

stirrer rpm used for different particle sizes and concentrations was 10 % in excess of the

value calculated with the Zwietering (1957) correlation for this type of setup. Because of

the high stirrer rpm required for complete suspension four baffles (0.008m width) were

also installed inside the ce11 to brake the vortex. The baffles were slightly distanced from

the ce11 wall (0.002 rn) to allow for suspension circulation. The effect of stimng over the

measured parameten was studied in water only for different stirrer rpm and the results are

s h o w in Figure 3.1.3 and 3.1.4 for both attenuation and acoustic velocity.

As seen the e ffect of stimng is negligible for ultrasound velocity measurernents (standard

deviation < 0.005 d s ) and small for ulhasound attenuation rneasurements

O 200 400 600 800 1000 1200 1400

Stirrer speed (RPM)

Figure 3.1.3 Effect of stirrer speed on ultrasound velocity

Stirrer speed (rpm)

Figure 3.1.4 Effect of stirrer speed on measured attenuation

Figure 3.1 S Sketch of cell used for liquid-solid measurernents

(standard deviation < 1%). This also shows the robustness of the ultrasound velocity

measurements. The temperature for measurements was maintained at 254 0.1 " C by

circulating cold and hot water through a coi1 installed near the bottom of the cell. A

simplified sketch of the cell is s h o w in Figure 3.1 S.

The ultrasonic system consisted of two 0.01 m diameter (LMN ceramic) ultrasonic

bansducers with a center Frequency at 3 and 3.9 MHz (50 % bandwidth) and a two

channel ultrasonic pulser-receiver system designed For the frequency range of 0.1 - 100

MHz. The transducer was made from a cylindrical stainless steel tube 0.2 m in length and

0.1 rn in diameter. At the end of the tube a piezoelectrical crystal was installed. A

protective layer of epoxy was poured over the crystal to avoid excessive erosion. A wire

crossed the empty stainless steel tube up to the crystal where it was connected to the

surfaces of the crystal through a special technique. Figure 3.1.6 shows a simplified sketch

of the transducer. Both transducers the trmsmitter and the receiver were identical. The

system could be used either in pulse-echo mode or pitch-catch mode. In this study only

pitch-catch mode was used. The system was modified to generate a higher energy pulse

(800 pJ) for measurements in dense suspensions used in this study. Al1 the system

parameters Le. gain, pulse voltage, gate, energy were controlled via RS232 interface with

the cornputer. The characteristics of the equipment are presented in Table D.1 as seen in

Appendix D.

A digital oscilloscope (TDS 210 from Tektronics) was used to visualize and analyze the

received signal. In a typical experirnent, afier visualizing the signal on oscilloscope

(avoiding signal saturation) a gate position and a gate width were selected according to

the position of the signal. When an ultrasonic pulse was emitted by one of the

transducers, the receiving transducer was activated at a tirne fixed by the gate delay and

for duration of selected gate width. During the time the gate was open the transmission

time and the amplitude of the ultrasonic signal were measured. This process was repeated

electrical wire

piezoelectric crystal

/ Shell tube

protective material

Figure 3.1.6 Schematic of ultrasonic transducer

Cell

~ernperature control

Osci~loscope Ultrasonic system Personal Corn puter

i

Figure 3.1.7 Block diagram of experimental setup

at a rate of 1 kHz and a mean value was recorded at a rate of 1 per second. Each ploned

point is an average of 200 readings. The equipment was already pre-calibrated by the

supplier (Fallon Utrasonics inc.), however an initial calibration was also caried as

s h o w in Appendix D (Figure D. 1). Figure 3.1.7 shows an integrated simplified block

diagrarn of the overall experimental setup.

3.2 Experirnental Technique

3.2.1 Measurement Procedure for Liquid - Solid S ystem

Given the dependency of the stirrer rpm on the suspension density and viscosity. the

measurements of the rpm were carried in loading conditions with the help of a

stroboscope, for each measured concentration. The values of the rpm used were those

calculated in Table A.4 as seen in Appendix A. A study on the rpm effect over the

ultrasound propagation was carried in water only at constant temperature (25 OC). No

significant effect on the velocity or attenuation of the ultrasound signal was observed,

providing the formation of gas bubbles was avoided.

The temperature effect was quite significant as seen in Appendix D (Figure D.1) and

extra care was taken for keeping a constant temperature (25 O C 2 0.1). The hot and cold

water flows were regulated through two needle valves. An immersion themorneter was

placed inside the ce11 close to the investigated zone. The mercury themorneter (0-50 "c) had an accuracy of 0.1 OC.

The distance between transducers was selected at about 0.0508 m (half the colurnn

diameter). Several reasons were considered to rnake the selection. At maximum

separation, equal to colurnn diameter, the attenuation in liquid-solid system is very high

for largest particles used (180 pm). In these conditions the equipment generates multiple

misreadings and the accuracy of the measurement decreases. Choosing a too small

distance between transducers would affect the system's hydrodynarnics, though, a

compromise had to be made. Another consideration was also taken into account. The

transducers used are Bat and the near field length (dT2/4h) gives the distance after which

the diffraction effect becomes significant. In our case the near field length is about 0.05

m. Increasing the distance between transducers above this limit will cause a loss of

energy caused not only by the analyzed medium, but also due to diffraction phenornenon.

The distance 0.0508 m was chosen for measurements in liquid-solid system based on the

above considerations.

For each data point 300 readings were taken and averaged. A study of the average and

standard deviation for different number of readings (up to 1000) showed that at steady

state in liquid-solid system both the average and standard deviation were not changing

significantly above a number of readings of about 50. However. at higher solids

concentration and particle size or at higher gas holdup, when there was often complete

blockage of the signal, a significant number of readings were not useful and had to be

elirninated. This caused a reduction of the number of readings f'rom 100 to about 100. still

sufficient to give an accurate average.

3.2.2 Measurement Procedure for Gas - Liquid System

Gas holdup measurements were camied both through measurements of pressure profiles

and expanded bed height. The results obtained through level measurements were not

reliable given the difficulty in localizing the expanded bed height level due to presence of

foam layer and transparency of the medium.

The static pressure profiles were measured with liquid filled manorneters, this being a

common technique for gas holdup measurements. Three taps dong the axial length of the

colurnn at 0.05, 0.2 and 0.35 m above the porous plate gas distributor were comected to

liquid filled manometer. A capillary connection was used to avoid liquid manometer levrl

fluctuations. For a higher sensitivity the manometers tubes were inclined at 26 degree

from horizontal plane. Given the slow response tirne there was a waiting penod of 20

minutes for each manorneter reading at steady state.

3.2.3 Measurement Procedure for Gas - Liquid - Solid System

In three-phase system the gas holdup measurements were carried only fiom level

measurements. The manometen were easily plugged by 35 pm glass beads particles and

iheir usage was not feasible. The level readings were carried without taking into account

the foam layer. The interface between expanded bed and foarn layer could be easily

localized especially at low superficial gas velocities. The height of the foam layer varied

with both superficial gas velocity and solids concentration from 0.02-0.05 m at V, = 0.01

m/s and low solids concentration to about 0.20 m at 0.05 m/s and 40wt% solids

concentration. A period of time of at least one hour was considered to achieve steady

state and also a decrease in foarn layer. The static bed height varied also from 0.25 m to

about 0.35 m with addition of the solid particles.

The attenuation of ultrasound signal increased significantly with increasing gas holdup.

This made collecting of useful data more and more difficult. A decrease in distance

between tramducers had to be considered in gas-liquid-solid system compared to liquid-

solid system. Several separations were tested (0.0127, 0.0254 and 0.0508 m) and the

results were presented in section (4.2). A separation of 0.0254 m proved to be a good

choice for three-phase systems as a balance between gas holdup and solids concentration

measurements.

Chapter 4 Results and Discussion

The results and discussion are stnictured in three sections (4.1.4.2 and 4.3). Section (4.1)

presents the expenmental results fiom liquid-solid system, section (4.2) shows the data

obtained in gas-liquid system and section (4.3) presents data from gas-liquid-solid

system.

4.1 Liquid- Solid System

The effect of particle concentration was measured up to about 43 vol. %. The variations

of acoustic velocity with particle size and concentration are presented in Figure 4.1.1

based on average of up to six replicates. The standard deviation From replicates was less

than 0.1 % indicating a good repeatability of the results. The change in velocity is

generally less significant bellow solids concentration of about 5 vol.% but increases for

higher solids concentration. Figure 4.1.1 also shows that for the same solids

concentration, acoustic velocity decreased with increasing particle size. Figure 4.1.2

compares the data of this study for 35 Fm particles with the results of Atkinson and

Kytomaa (1991) obtained with particles at similar kt,. It can be seen that there is good

agreement between the two sets of data from these independent studies.

In suspensions of fine particles with small k.r, (k'r,<<l) the medium cari be treated as

homogeneous and the phenomenological approach by Urick (1947) would prove usehl as

discussed in section (2.2.5.3):

O glass beads 35 pm

1 0 glass beads 70 prn 1 a g las beads 180 prn / I

1460 ! I I

0.00 0.1 O 0.20 0.30 O .40

Solids volume fraction

Figure 4.1.1 Ultrasound velocity versus solids concentration for different particle sizes (f = 3 MHz)

Solids volume fraction

1700

Figure 4.1.2 Cornparison of measured acoustic velocity with theoretical models

1680 4 O experimental (glass beads 35 pm) Ament(l953)

1660 4 / - - Urick(1947) 1

I

Harker and Temple(1987) ,' /

/ --- Atkinson and Kytomaa(l991) ,f

1 /

1620 I - ,/'

i ' 0

/= / - 1600 7

I

/ V)

where p,, p, are the mixture density and compressibility:

The data fkom this study does not follow Urick's predictions. This can be attnbuted to the

fact that, the condition k'r, << 1 required in Urick's equation is not satisfied, while in our

case kt, is in between 0.2 and 1.2.

Improvements to Urick equation have been proposed (Ament, 1953) and found useful in

descnbing the observed behavior of acoustic velocity by several investigators (Harker and

Temple, L 988; McClements and Povey, 1987). The improvements have been obtained by

including the effects of fluid viscosity and particle size in the effective density expression

and thus taking into account the heterogeneous nature of the medium. Harker and Temple

(1987) analyzed the propagation of an acoustic wave through a mixture of two phases

using the hydrodynamic equations to balance mornentgm and continuity of the phases

with the drag of one phase on another. They assurned that there was no heat or mass

transfer between phases and no gravitational field. Their final equaiion c m be rewritten

as a cornplex wave vector v, of the fom:

where

Harker and Temple (1987) compared several existing theoretical models by replacing

M(o) with the corresponding expressions developed by other researchers.

The expressions by Ament (1953) and Harker and Temple (1988) were tested against the

data of this study. As shown in Figure 4.1 2, the Ament's equation is fitting quite close

the expenmental data from this study over the whole range of solids concentration. while

the approach by Harker and Temple deviates quite significantly above 12 vol. %. The

effect of particle diarneter was not properly predicted by these equations though. A

decrease in acoustic velocity with increasing particle size at same solids concentration

was observed while the theoretical predictions show the reverse. The same phenornenon

occurs when a different Frequency is used, for exarnple 3.9 MHz instead of 3 MHz when

a decrease in acoustic velocity is seen with increasing ultrasound fkequency at same

solids concentration for al1 particle sizes used in this study (Figure 4.1.3). Although these

equations take into account the particulate nature of the medium they are still valid only

For kt, < 0.1. Again the particle wave number For the smallest particles used in this study

is about 0.2 which is close to the theoretical limit where the predictions are reasonable.

For practical purposes, the variation of acoustic velocity with particle concentration can

be correlated by modified Form of Urick's equation as proposed by (Pin field et al. 1995)

and seen in the literature review:

where a, and a, are experimentally detemined values which are hnction of particle size.

Providing, good temperature and mixing controls are ensured calibration lines can

O glassbeads35pm(3.9MHz) 0 glass beads 70 pm (3.9 MHz)

glass beads 70 pm (3 MHz) glass beads l80pm (3 MHz) 1

n

1480 1 1 i l

1460 I I

0.00 0.10 0.20 0.30 0.40

Solids volume fraction

Figure 4.1.3 Comparison between ultrasound velocity at two frequencies (3 MHz and 3.9 MHz)

be constnicted in this manner for different industriai setups. Figure 4.1.4 shows

calibration lines for the three particle sizes used in the present study.

35 pm particles

70 Fm particles

180 pm particles

1 - = 4.46 - 0 . 6 5 6 ~ - 1.95~' v'

Such calibration curves cm be used to determine sluny concentration from measurement

of ultrmund velocity in suspensions of known particle sizes.

Measurements were also conducted in mixed particle sizes glass beads - water system.

Two sets of expenments were conducted by adding g las beads of 70 or 180 pm in a 15

vol.% suspension of 35 pm particles. The objective was to observe the sensitivity as well

test the additive effect of the velocity measurements with increasing Craction of larger

O glass beads 35 pm

i glass beads 70 pm ,

1

I I * l

I 1

Sol ids volume fraction

Figure 4.1.4 Calibration curves of ultrasound velocity versus solids volume fraction for different particle sizes

particle sizes. As seen in Figure 4.1.5, the velocity deviations fiom the curve described by

the presence of the 35 pm particles can be observed for both larger particle sizes. A larger

effect was seen for attenuation measurements (Figure 4.1.6a and 4.1.6b).

A series of experiments were conducted to cover a wider range of mixed pmicle sizes.

By defining a k'r,,,, as:

where m = mass fraction of larger particle size it cm be seen in Figure 4.1.7 that for the

same overall solids concentration the kr,,, values are lying in between the values given

by the particles of one size. This shows an additive effect of the particle size and can be a

ba i s to determine fraction of each particle in a mixture of known total concentration and

particle sizes. This appmach, however, is restncted to the range in which the ultrasound

velocity varies with particle size.

Attenuation of an acoustic wave passing through a medium provides additional

information about the composition of the medium. The attenuation coefficient defined by

equation (2.2.64) was calculated for each new incremental addition of particles:

where A,, represents the amplitude level before incremental solid addition and Ai after

addition. The attenuation for a given total solids concentration was calculated by

summing the incremental addition. This procedure was adopted to avoid saturation of

signal at low solids concentration and to account for the increase in gain required at

higher solids concentration for the signal to be received.

1640 -

0 glass beads 35 pm 1620 4 1 glass beads 35 (<p=0.15)+70 prn

1 3 glas beads 35 (cp=0.15)+180 prn

1600 4'

Solids volume fraction

Figure 4.1.5 Ultrasound velocity variation in mixed particle sizes system

glass beads 35 ((p=O.Og)+I 80 Pm

160 -' 0 glass beads 35 prn glass beads 180 Fm

140 -. n F

'E

200 - glass beads 35(<p=O. 1 5) +18O pm 1 180 + A glass beads 35 ((p=O.O4)+18O pm 1

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35

Solids volume fraction

Figure 4.l.6a Ultrasound attenuation in mixed particle sizes system (3 MHz)

100 - glass beads 35 ((p=O. 1 5)+70 pm

A glass beads 35 ((p=0.04)+70 pm glass beads 35 ((p=0.09)+70 prn

- O gass beads 35 prn glassbeads70pm

Solids volume fraction

Figure 4.1.6b Ultrasound attenuation in mixed particle sizes system (3 MHz)

glass beads 35+70 pm glass beads 35+180 prn glass beads 35 pm

m glass beads 70 pm

A glass beads 180 pm

lids volume fraction

Figure 4.1.7 Ultrasound velocity as a function of kr,,, in mixed particle sizes system (3 MHz)

The results presented in Figure 4.1.8 show almost linear and monotonie increase in

attenuation with increasing solids volume fraction for different particle sizes at low solids

concentration ( < 10 vol.%). Such variation of attenuation with increasing solids

concentration was confirmed by several researchers (Stakutis et al., 1955; Allegra and

Hawley, 1971; Atkinson and Kytomaa, 1992) up to about 30% volume solids

concentration at low values of kt,, or for higher solids concentration and kr, < 0.5

(Atkinson and Kytornaa. 1992). As kt, increases at same applied Frequency, (Le as the

particle size increases) the multiple scattering phenomenon become significant. This

effect is causing a deviation of the overall attenuation from linear behavior as seen in

Figure 4.1.8 for larger particle sizes when the change in attenuation coefficient with

increasing solids concentration becomes less significant above about 15 vol. %. Figure

4.1.8 shows also the repeatability of attenuation measurements for a number of 5

expenments for each particle size. As seen the repeatability decreases with increasing

particle size. Figure 4.1.9 shows how an increase in Frequency from 3.0 to 3.9 MHz

affects the attenuation measurements. As seen the attenuation increases drastically with

increasing ultrasound frequency.

Attenuation in liquid-solid suspensions could be estimated by the approach onginally

developed by Epstein (1953) and subsequently verified by Stakutis et al(1955) for other

types of solids. The total attenuation coefficient as derived by Epstein consisted of three

terms.

where a, = attenuation caused by scattering phenomenon, a, = absorption caused by

viscous drag at the particle surface and AaV = correction of the absorption for larger kr,.

Epstein and Carhart (1953) used also a thermal absorption term for hlly characterizing

the absorption of the acoustic wave. Urick (1948), Urick and Ament (1948), Allegra and

Hawley (1 971) show that for suspensions where the particle density is more than twice

that of the suspending medium, thermal conduction losses are very small compared to

-/ C

glassbeads70pm 1 0 glass beads 35 Pm 1

200 -

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35

Solids volume fraction

glass beadsl80 pm

Figure 4.1.8 Ultrasound attenuation versus solids concentration for different particle sizes (3 Mhz)

O glass beads 35 pm (3.9 MHz) glas bssbs I O pm (3.9 MHz) 260 i

a glassbeads180p(3.9MHz) 240 1 A glass beads 180 pm (3 MHz)

220 -1 i glass beads 70 pm (3 MHz) 1 1 glass beads35 Fm(3MHz)

200 -,

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35

Solids volume fraction

Figure 4.1.9 Cornparison between ultrasound attenuation at two ultrasound frequencies

viscous drag losses. Indeed, the calculated thermal conduction from the theoretical

equations of Allegra and Hawley (1971) were very small. That is why this term will not

be accounted for in this work.

The Epstein coefficient a, was calculated from:

1

iwp where b = ( ) r,, , 8, = pLips., k = ultrasound wavenumber (Zn/A), X bulk modulus

and iv.9 = Lame' constants and the rest of the symbols have the significance from above.

The predictions given by the above equation are s h o w in Figure 4.1.10. A good fit of the

experimental values is Sound for 35 pm particles over the whole range of solids volume

fkaction and reasonable for 180 pm bellow solids volume Fraction of about 0.15. By

analyzing the contribution of the viscous and scattering term in the overall calculated

attenuation, a highly dominating viscous term is seen for 35 pm particles while for 180

pm particles a highly dominating scattering term is obsewed. For 70 pm particles both

terms seem to have comparable values. This is particularly interesting while it is in

accordance with the observations of Atkinson and Kytomaa (1992). In their work

Atkinson and Kytomaa used a Re nurnber for oscillatory motion of a particle of radius r,

1 glass beads 180 prn 260 1 a glass beads 70 prn

240 i (3 glass beads 35 Fm 1 I

Solids volume fraction

Figure 4.1.1 0 Cornparison between experimental ultrasound attenuation and theoretical models

to describe the importance of the above effects.

It is s h o w that inertial effects dorninate the interface drag for particles at hi& values of

Re numbers while for low Re numbers, viscous effects are dominant. Re number equal to

100 is given as the demarcation between the two regirnes. By calculating Re nurnber in

this study we obtain 58, 1 O6 and 242 for glass bead particles of 35, 70 respectively 180

Fm. As clearly seen, 70 Fm particles are at the interface between the two regimes were

both viscous and drag effects are important. For this case the theory doesn't match

reasonably the experimental data. Attenuation measurements can be used to veriQ the

composition of the suspension obtained From velocity measurements. This will be

signi ficant especially for low slurry concentration (C 1 0 vol.%) where the variation of

attenuation is linear (multiscattering effect is low). The rate of increase is higher at lower

slurry concentrations and slows d o m at higher concentrations for larger particle sizes.

Figure 4.1.1 1 shows the variation of the averaged dimensionless wavenumber as a

function of attenuation with slurry concentration as a parameter in mixed particle sizes

system. The average value of k'r, for binary mixtures of solids was calculated using

equation (4.1.1). This type of plot cm be used to veriQ the velocity measurement

deductions. An increase in mass fraction of larger particles in suspension at same overal

concentration can be traced along the curves of known slurry concentration.

The liquid-soiid suspensions were further characterized by analyzing the captured wave

form. The mean pulse frequency obtained from oscilloscope was plotted as a Function of

solids volume fraction. The mean frequency was caiculated by averaging 10 values given

by the oscilloscope ( TDS 210, Tektronics, Inc.) over a penod of time (10 minutes). The

Figure 4.1.1 1 Ultrasound attenuation as a function of krpaVg in mixed particle sizes system (3 MHz)

standard deviation of these readings was less than 2 %. A change in mean pulse

frequency was observed for larger particles (70 pm and 180 pm) while for the smallest

particles (35 pm) there was no significant effect (aproximatelly sarne as in water). There

is a direct proportionality between solids concentration and the measured mean Frequency

of the acoustic pulse for both 70 and 180 pm glass beads particles (Figure 4.1.12). From

the analysis of the attenuation measurements, it was observed that the scattenng

phenomenon become significantly important with increasing particle size. It cm be

concluded that when scattering effect is becoming important the mean pulse frequency

gets altered significantly. When the viscous loss dominates (kt, ~ 0 . 1 ) no significant

effect on the collected wave form is seen. This property can be used again for particle size

distribution measurements in suspensions. Based on these observations some expenments

were conducted to measure the fiaction of particle of larger size (70 pm or 180 pm) in a

suspension where the solid phase was a mixture of 35-70 and 35- 180 prn glass beads. The

results are shown in figure 4.1.13. These results are compared with those when only one

particle size was suspended in water ai corresponding concentrations (Figure 4.1.1 4). It

can be seen that the results overlap well indicating that the presence of 35 Fm particles

did not affect significantly the mean pulse Frequency of ultrasound signal. The rariation

of this frequency is caused mainly by larger particles present in the system.

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35

Solids volume fraction

Figure 4.1.12 Mean frequency variation with solids volume fraction for different particle sizes

2.0 4 O glass beads 35 pm 1 / c giass beads 35 pm(<p=0.15)+70 prn \

*8 - A glasç beads 35 prn(q=O. 15)+180 pm

Solids volume fraction

Figure 4.1.1 3 Mean signal frequency variation with solids fraction for mixed particle sizes

r 1.4 -: l

1.2 -1 0 glass beads 35 pm I I c I glass beads 70 pm ' 1 A glass beads 35(p = 0.1 5)+7O prn o glass beads 180 pm I I

O glass beads 35((p = 0.1 5)+180 pm 1 I

Solids volume fraction

Figure 4.1 . l4 Comparison between mean signal frequency variation in single particle size system with

mixed particle sizes system

4.2 Gas-Liquid system

The gas-liquid system was characterized by studying the variation of the gas holdup and

bubble size with increasing superficial gas velocity. The gas hold-up was measured by

using inclined manometers. These manometers, were placed at 0.06, 0.22 and 0.36 m

above the porous plate. Gas holdup measurements were carried between first and second

manometers (lower section), second and third (upper section) and first and third (whole

section), as shown in Figure 3.1 in expenmental setup section. A number of five

experiments were averaged and repeatability was found to be good. The manometer

readings show a standard deviation of less than 1 % for superficial gas velocity up to 0.05

mls and less than 6% for higher gas velocities.

Figure 4.2.1 shows the gas holdup variation fiom al1 three sections as a function of

superficial gas velocity. As seen the increase in gas holdup is linear up to a gas velocity

of 0.05 m/s. At higher superficial gas velocities a lower increase is encountered and a

distinction could be seen between the gas holdup in lower and upper sections. The higher

gas holdup in the lower section can be explained by considering the coalescence

phenornenon. The gas holdup in the whole section shows as predicted an average between

the lower and upper sections (Figure 4.2.1). Deckwer (1992) reported that in bubble

columns a uniform bubble size distribution would result at low gas velocity rates (0.01-

0.02 m/s). This flow region is called homogeneous, or bubble flow region, when bubbles

rise at almost constant rate and the radial profile of gas holdup is nearly flat. When the

gas rate is increased, larger bubbles form by coalescence at a certain distance above

distributor. These bubbles coexist with smaller bubbles defining a new flow region called

heterogeneous or Churn-turbulent. The transition from one flow regime to another is also

dependent on the column diarneter or gas distributor. A general mle of thurnb is given

that for a superficial gas velocity below 0.04 m/s the flow regime is homogeneous.

0.02 0.04 0.06 0.08

Superficial gas velocity (mis)

Figure 4.2.1 Gas holdup as a function of superficial gas velocity in different sections of column

This will explain the above experimental results for gas velocities higher than about 0.4

m/s. A larger bubble diameter in the upper section of the colurnn will produce a lower gas

holdup at the s m e gas velocity. The gas holdups obtained in this study where compared

with gas holdup data for air-water systems from literature. The work of Prakash (1991)

and Beinhauer (1971) was considered while both used porous plates (35 pm and 75 pm

respectively) as gas distributors and similar column diameten (0.080 and 0.092 m).

Fisure 1.2.2 shows that the results fiom this study are comparable to those by Prakash

(1 99 1 ) or Beinhauer (1 972) for the range of superficial gas velocity investigated.

Several measurements were made to determine the gas holdup and interfacial area in air-

water systems with the help of ultrasonic technique. The measurements were taken at

constant temperature ( 2 5 ' ~ ) and for different distances between transducers. Two

parameters were measured, the attenuation and velocity of the wave pack as descx-ibed in

experimental section. A typical measured signal s p e c t m for gas-liquid system will look

as shown in Figure 4.2.3. It is seen that there are large amplitude variations with passing

of bubbles. A simple statistical method of moving average (100 moving data points) was

applied on each period of 200 s when the signal was collected at same superficial gas

velocity. The moving average was fed with one new value per second and it purged the

oldest accumulated value at same rate. Figure 4.2.4 shows that using a moving average

from 100 values the signal fluctuations were almost completely eliminated and a linear

behavior was obtained on each interval. This shows that the average of 200 collected

values for each measurement used in this study is reasonable accurate. Figure 4.2.5

presents the moving average for different superficial gas velocities at a separation of

0.0127 m between transducers. This simple statistical approach can be usehl for online

measurements camed in reacton where slow reactions take place and where a delay time

of 100 s is not of concem. Three sets of measwements were conducted for each

separation distance of 0.0127, 0.0254 and 0.0508m between transducers. Good

repeatability of the results is seen (Figure 4.2.6) for al1 measured distances. Strong

attenuation produced by bubbles makes the measurements increasingly difficult with

O experimental n Beinhauer (1971) a Prakash (1991) 1

Superifcial gas velocity (cmls)

Figure 4.2.2 Comparison of experirnental gas holdup with literature

0-1 00s water only 1 300-500s Vg=0.016 mls 500-700s Vg=0.022 mls

100 200 300 400 500 600 700

Tirne (s)

Figure 4.2.3 Typical attenuation signal spectrum at different superficial gas velocities

200 y

! - moving average (1 00 values) 1 I

1 water oniy

Vg=0.016 mls - O i 1 I 1 1

O 1 O0 200 300 400 500 600 700

Time (s)

Figure 4.2.4 Moving average of 100 values for amplitude measurements

O V~=O.OII~~/S / O Vg=O.O167m/s 1

Vg = 0.0223 mls / I o Vg = 0.0335 mls 1

O Vg=O.O447mIs / O Vg = 0.0558 mls i

120 140 160

Time series (s)

Figure 4.2.5 Moving average of 100 values for amplitude rneasurements

Superficial gas velocity (mls)

Figure 4.2.6 Amplitude ratio versus superficial gas velocity for different distances between transducers

increasing distance between transducers. The repeatability of these experiments is shown

in Figure 4.2.7 for L=0.0254 m. Calibration curves c m be generated using this data.

Lowest standard deviation is obtained for smallest separation (0.01 27m) between

bansducers (< 5%). However, for this small separation the velocity measurements for

solid particles are no longer very accurate. At 0.0254 m separation between transducers

the standard deviation between averaged expenments was less than IO %. This generated

an error of l e s than 0.01 volume fraction for gas holdup measurements. This error was

considered acceptable and 0.0254 rn separation between transducers was considered for

three phase measurements.

Very little effect on ultrasound velocity was seen in al1 the expenments (Figure 4.2.8).

Slight variations from the value for water only were observed. These variations are

considered to be due to several reasons: the effect of the fluid vortex originated by the

bubble nsing ahead of the wave as s h o w by Okarnura et al. (1988) and Maezawa et.al.

(1993), very mal1 bubbles ( < 0.001 m) present in small concentration causing small

changes of compressibility and density of the gas-liquid mixture or minor temperature

variations. Figure 4.2.9 shows that for a given distance between transducers the standard

deviation increases with increasing superficial gas velocity. Similar results are obtained at

al1 distances. However, higher variations are seen only for gas velocities larger than 0.05

m/s, which suggests that velocity measurements in three-phase system can provide solids

volume Fraction if gas holdup is noi very high.

The attenuation coefficients calculated for al1 expenments with equation (4.1 2) are

surnrnarized in Figure 4.2.10. A good correspondence is seen ai al1 distances between

transducers. An attempt was made to calculate the attenuation coefficient From theoretical

considerations as well using the approach by Stravs and Stockar (1985). These authors

showed that the attenuation coefficient is related to the scattering cross-section of

obstacles such as gas bubbles. Assuming that the individual scatterers are independent of

each other, an equation for attenuation coefficient related to the scattenng cross-section

0.00 0.05 0.10 0.1 5 0.20 0.25 0.30

Gas holdup (-)

Figure 4.2.7 Attenuation versus gas holdup for different distances between transducers

l 1 1 - + 2 m/s (3.9 MHz)

0.00 0.01 0.02 0.03 0.04 0.05 O .O6

Superficial gas velocity (mis)

Figure 4.2.8 Acoustic velocity variations with superficial gas velocity for different distances between transducers

Superficial gas velocity (mis)

Figure 4.2.9 Standard deviation of velocity measurements at higher superficial gas velocity

0.2 0.3

Gas holdup (-)

Figure 4.2.1 0 Attenuation coefficient versus gas holdup in air-water system

was proposed:

where c, = bubble density, s,,,, = apparent scattering coefficient which depends on

s,,(krb) = scattering coefficient, and the geometry of the expenmental apparatus, f(r,) =

bubble size distribution and nrb2 = projection area of the bubble. The absorption cross

section was neglected due to almost total reflection at the gas-liquid interface given the

high impedance mismatch. The value of scattering coefficient was seen to reach a value

of 2 for both light and ultrasound For values of higher than about 50. It is also

mentioned that the bubble removes an arnount of energy from the incident bearn as if it

were a completely absorbing disk of twice its projection area. This energy is actually

partly reflected backwards (one halo, and partly (the other haln diffracted forward

around the bubble. For a very narrow angle of difiaction, as in the case of light, the

apparent scattering coefficient becomes 1 and the attenuation coefficient will become

equal to the projection area of the bubble thus:

Interfacial area a is four times larger (4rrrb2) than the projection area of the bubble. In the

case of ultrasound the scattering coefficient was calculated and given by the following

equation for kq, values between 1 and 10:

For the case of sphencal bubbles Stravs and Stockar (1985), developed the following

equation for ultrasound attenuation:

The apparent scattering coefficient (s , ,~~, ) is taken as equal to the scattenng coefficient

(s,,) if the emitting transducer is piaced far enough from the measuring section so that the

wave is planar and if the receiving transducer is small enough and also Far fiom

measunng section. None of these conditions are met in this study. Both transducers are

0.01 rn in diarneter and the distance between them (0.0254m) is smaller than the near

field distance to avoid energy loss. In this case, the receiver will rneasure the diffracted

part of the signal along with the undisturbed signal and the projected area of the bubble

will be approximately 1. Stravs and Stockar (1985) using 12.7 mm transducers (5 MHz)

separated by 0.03m. showed that the measured interfacial area fiom ultrasound

attenuation calculated with equation (4.2.2) differs only by 5% compared to the light

measurements. The results for the interfacial area From this study, taking into account the

above considerations, are shown in Figure 4.2.1 1.

An attempt was also made to compare the interfacial area obtained from ultrasound

attenuation with the one estimated from gas holdup and bubble size measurements. The

cornparison is at best approximate due to limited data especially for bubble size

rneasurements. The photographie technique used to measure the bubble size is discussed

in the experimental section. Two sets of photographs were taken for different superficial

gas velocities in a delimited volume near the column wall (Appendix A). The Sauter

mean diameter was found to Vary between 2.6 and 4.7 mm for superficial gas velocity

between 0.005 and 0.042 mis. The bubble size was also calculated using an empirical

equation developed by Koide et al. (1968) as s h o w in Appendix A. The results show an

average bubble size of about 2.4 to 3.2 mm for superficial gas velocities between 0.01 to

0.05 m/s at porous plate level. Schumpe (1981) using a sulphite oxidation method found a

Sauter mean diarneter of 3 mm at 0.03 m/s superficial gas velocity in a sirnilar

0.00 0.05 0.1 O 0.15 0.20 0.25 0.30

Gas holdup (-)

Figure 4.2.1 1 lnterfacial area in gas-liquid system from attenuation measurements

experimental setup. An increase in bubble size c m be considered at some distance above

the porous plate. Grienberger and Hofinam (1991) reported that in air-water system the

coalescence occurs mainly in the region near the distributor (porous plate). From same

published results, at 0.20 m above the gas distributor, an increase of about 15 to 20 % in

bubble diameter for gas superficial velocity between 0.02 to 0.05 m/s can be observed.

Considering this increase in our study, the calculated bubble diameters will become about

2.8 mm and 3.8 mm for superficial gas velociiy between 0.01 and 0.05 m/s. This will

account for some of the increase in experimentally measured values. by photographic

technique.

At superficial gas velocities higher than 0.02 m/s a fraction of larger bubbles is generated

due tu coalescence. The contribution of larger bubbles to the total gas holdup increases

with increasing superficial gas velocity. Beinhauer (1971) quantified the gas holdups

given by smaller and larger bubbles in air-water system using X-ray absorption and gas

disengagernent techniques in an experimental setup similar to the one used in this study.

The results are shown in Table 4.2.1. The Fractional gas holdup, given by larger bubbles,

can be used as a percentage in our calculations since the gas holdup results fiom this

study are very similar to those of Beinhauer ( 197 1 ) up to about 0.05m/s.

Table 4.2.1 Gas holdups fiom results of Beinhauer (197 1) and this study:

where E,, = gas holdup of large bubbles and E, = gas holdup of srnall bubbles.

The division of gas holdup in two classes, larger and smaller bubbles can help us to

calculate the contribution to interfacial area of larger bubble sizes. Beinhauer (1971),

Hills (1974) and Warsito et al. (1999) showed through different measurement techniques

that for low gas velocity (c 0.02 mis) the bubble Frequency and gas hold-up are

approximately constant over the whole cross section area. For higher than 0.02 m/s gas

velocity, a parabolic gas hold-up and bubble fiequency was shown. As a consequence a

bubble size distribution will be more and more evident with increasing superficial

velocity. O'Dowd et al. (1987) reported an averaged bubble dimeter in the center of the

column about 1.25, 1.5 and 2 times the value of the bubble diameter near the column wall

for gas velocities of 0.03, 0.04 and 0.05 rn/s respectively. Hills (1974) found also a

parabolic gas hold-up radial profile for superficial gas velocities larger than 0.025 mis.

Using the above measured Sauter mean diarneter (averaged and interpolated), and

considering the radial profile as discussed above, the bubble diameter for larger bubbles

Fraction was taken 125, 1 50 and 200% higher than the size of the bubble near the column

wall. This corresponds to 0.03, 0.04 and 0.05 mis superficial gas velocity respectively.

The interfacial area of both small and large bubbles was calculated with the well known

formula:

The results are summarized in the following Table 4.2.2:

Table 4.2.2 Interfacial area given by both srna11 and large bubbles

It can be seen that larger bubbles have a small contribution (less than 8%) to the

interfacial area as expected. Not the sarne conclusion can be drawn for very small

bubbles. While in this work the bubbles smaller than 0.001-0.002 m were not accounted

for, but observed to be present in a small proportion, it is expected that the values of total

interfacial area be sornewhat higher than the above results. Finally the calculated values

of interfacial area from ultrasound attenuation measurements are compared with those

obtained from gas holdup and photographic measurements in Figure 4.2.1 2. Interfacial

area for air-water system at similar superficial gas velocities were shown also by Wolff et

al. ( 1990) with optical and conductivity techniques. Akita and Yoshida (1974) developed

an equation for interfacial area calculations through a photographic technique. The range

of application for this equation (Vg 50.07 rnls and 0.077 5 R 0 . 1 5 rn) covers our

parameters. The equation given by:

where Dc = reactor diameter and the other symbols the meaning from before. Both the

1 1 O experirnental interfacial area 1 1 fi photographic technique 700 7 i l 1 1 - Akita and Yoshida (1 974) - modified 1 1 I

0.00 0.01 0.02 0.03 0.04 0.05 0 .O6

Superficial gas velocity (mis)

Figure 4.2.1 2 Interfacial area in gas-liquid system (experimental versus predicted)

results of Wolff et al. (1990) and Akita and Yoshida (1974) equation give lower values of

interfacial area for superficial gas velocities in our range (V, c 0.05 mls). This is due to

the simple gas supply equipment used (e.g. sparger, O ring, perforated plate). For more

effective gas distribution equipment ( e.g. porous plate) Greenhalgh et al. (1975) shows

that the constant 0.23 fiom equation (4.2.6) is no longer accurate and a higher value is

needed. In this study a value of 0.52 fitted the experirnental results obtained with

ultrasound measurements.

4.3 Gas-LiquidSolid system

Measurements in three-phase systems were canied at two axial locations of the column

(0.055 m and 0.165 m). The distance between the transducers, placed in central position

was maintained at 0.0254 m for al1 expenments. The temperature was maintained

constant at 25 O C and the liquid level was 2.5 times the column diameter. The solids used

were 35pm g l a s beads and their concentration was varied from O to 40 wt% (O to 0.21

volume fraction) for each superficial gas velocity used. Three superficial gas velocities

were used (0.017,0.033 and 0.056 mls).

A verification was made to ensure that at lowest gas velocity we have complete

suspension. The critical gas velocity. required for complete suspension of solid particles,

was calculated using the equations proposed by Koide et al. (1984) for slurry bubble

columns. The column diameter and properties of phases used in this study are covered in

the proposed equation given below:

where Dc = reactor diameter; Cs = average solids concentration in gas-fiee liquid-solid

system (kg/mJ), and Ut = terminal velocity of a single particle in stagnant liquid (rn/s).

The unhindered terminal velocity for 35 pm g l a s beads particles in water was calculated

to be 0.001 m/s. The maximum concentration of solids in this study for three-phase

measurements was 40 wt% and the critical gas velocity was found to be 0.005 m/s with a

maximum error of 20%. The lowest gas velocity used was 0.01 7 m/s in our case, which is

about three times the minimum gas velocity for complete suspension. This ensured that

the solids particles were completely suspended.

The ultrasound velocity measurements for low superficial gas velocity of Vg = 0.01 7 m/s

are shown in Figure 4.3.1. Figure 4.3.2 compares the measured ultrasound velocity

(average of four experiments) in the slurry bubble column with similar measurements

made in liquid-solid suspension. The results show that the variations in ultrasound

velocity are mainly due to the presence of solid particles. At higher gas velocity (0.033

m/s) the ultrasound velocity rneasurements give same results as at lower Vg (Figure

1.3.3). For highest gas velocity (0.056 m/s) used in this study, a series of three

expenments were made (Figure 4.3.4). The scatter of the data is seen to increase with

increasing gas velocity. This is not surprising and it is considered to be due to reasons

already discussed in gas-liquid section caused by by the bubble presence (Figure 4.2.8).

However, as seen in Figure 4.3.4 one of the experiments shows a considerable low

ultrasound velocity compared to the other two. In this expenment a strong foaming effect

was observed. It cm be assumed, that the main components of the foarn layer are the very

fine particles, srnaller than 35 Fm. This will cause a slight change in particle size

distribution fiom the slurry as well as a decrease in slurry concentration, which would

lead to lower acoustic velocities. Also, with increasing solids concentration the foam

layer decreases when, as seen in Figure 4.3.4. the measured ultrasound velocity increases

again to the expected values. The large bubble sizes generated at higher gas velocity have

very strong attenuating properties. In these conditions the equipment gives an increasing

number of misreadings which need to be removed from collecied data. This makes

increasingly difficult to account for this type of error through signal corrections. Figure

4.3.5 shows a summary of al1 measured acoustic velocities fiom gas-liquid-solid system.

Only one expenment causes a higher standard deviation when strong foaming effect was

observed. A cornparison of al1 measured velocities in three-phase system with ultrasound

velocity in liquid-solid system is made in same figure and a good correspondence is

observed. These results show that ultrasound velocity variation in gas-liquid-system can

be used to obtain solids volume fiaction.

0.00 0.05 0.1 0 0.1 5 0.20 0.25

Solids volume fraction

Figure 4.3.1 Ultrasound velocity versus solids fraction in G-L-S system (Vg =O .O 1 7mls)

-- -- - - -

gas-liquid-solid

I ! I

Solids volume fraction

Figure 4.3.2 Cornparison of ultrasound velocity in G-LS system with L-S system (Vg=O.O17 mis)

O gas-liquid-solid 1 . liquid-solid 1 ' 1540 i t 1 / P

Solids volume fraction

Figure 4.3.3 Ultrasound velocity versus solids fraction in G-L-S system (Vg=0.033 mls)

0.00 0.05 0.1 0 0.15 0.20 0.25

Solids volume fraction

Figure 4.3.4 Ultrasound velocity versus solids fraction in G-L-S system (@=0.056 mls )

Solids volume fraction

Figure 4.3.5 Cornparison between ultrasound velocity in G-L-S system and L-S system

Measurements were also made on the attenuation of ultrasound signal. For lowest

superficial gas velocity used (0.0 17mIs) the increase in attenuation with increasing solids

concentration for three-phase systern is same as in liquid-solid system (Figure 4.3.6). The

repeatability is s h o w between five expenments and the variation is belived to be due to

dynamic nature of bubble size distribution at a given location. These results indicate that

the presence of solids does not significantly affect the gas holdup for this low gas

velocity. Similar observations were made by Ying et.al. (1980) who found that at low gas

velocity (Vg ~ 0 . 0 3 mls), the presence of solids did not change the gas holdup. Fan (1989)

shows that both solids concentration and particle size may affect the bubble size in slurry

bubble columns. However, for particles smaller than 50 Fm at low solids concentration

and superficial gas velocity, no significant effect is observed over the gas holdup (Sauer

and Hempel, 1987; Wolflet al., 1990).

Another observation was that measrirements carried at both axial positions (0.055 and

0.165m) are seen to show similar results in Figure 4.3.6. Murray and Fan (1989) show

that for glass beads of 19 pm the variation of the solids concentration with axial length is

small due to fast decrease in settling velocity with decreasing particle size. Also, a

sedimentation-dispersion mode1 was employed io calculate the axial solids concentration

distribution. Several approaches, (Kato et al., 1972; Smith and Reuter, 1985; O'Dowd et

al., 1987) were considered. The results showed that indeed for 35pm particles, at low gas

velocity and low bed height (-O.Sm). The variation of solids concentration with axial

length is minimum (Figure 4.3.7). This shows that the solids concentration c m be taken

as equal to the average concentration at any axial point. The experimental measurements

fiom lowest gas velocity confinn the above observations.

For higher superficial gas velocity (0.033 m/s) the variation of attenuation with solids

concentration changes. Figure 4.3.8 shows the repeatability between four experimrnts. A

decrease in attenuation with increasing solids concentration is seen up to about 0.1 solids

volume fraction. This can be attributed due to decrease in gas holdup caused by increase

--

l 7

O gas-liquid-solid (Vg=0.017 mis ) liquid-solid suspension I I

l I

0.05 0.10 0.15 0.20

Solids volume fraction

Figure 4.3.6 Cornparison of ultrasound attenuation in G-L-S system with L-S systern

O Smith and Ruether(1985) 0 Kato et al. (1 972) a O'Dowdetal. (1987)

measured values 1 l

Figure 4.3.7 Axial variation of solids concentration in G-L-S system (sedimentation-dispersion model)

0.00 0.05 0.1 O 0.1 5 0.20 0.25

Solids volume fraction

180

Figure 4.3.8 Ultrasound attenuation from three-phase system and the resulting attenuation in gas-liquid system

O gas-liquid-solid I I

*Oo 1 - gas-liquid (subtracted) 1 / CI liquid-solid I '

~ I

160 3 Vg=0.033 mls i

1

in bubble size. At higher solids concentrations the attenuation caused by the presence of

solids takes over and an increase in attenuation is seen with increasing solids

concentration. This cornes as a confirmation of the observations by Sauer and Hempel

(1989) and Wolff et. al. (1990) who used other measurements techniques (e.g

conductivity, optical) to study the hydrodynamics of bubble coiumns in presence of

solids. A large increase in bubble size and consequently a decrease in gas holdup was

reported when solids of higher density and concentration are present at gas velocities

higher than 0.02 m/s. Many studies have been conducted, using different measurement

techniques, for sluny concentration ranges up to 0.2 solids volume fraction (Kato et al.,

1973; Deckwer et. al., 1980; Yasunishi et.al., 1986; Kara et-al.. 1982; Koide et. al., 1984;

Sauer and Hempel, 1987; Ying et.ai., 1980; Bimal, 1997). Most of the researchen

concluded that an increase in solids concentration usually reduces the gas holdup for gas

velocities higher than 0.02 m/s. Figure 4 3 . 8 shows also the attenuation given by gas

holdup alone in gas-liquid-solid system obtained by subtracting the attenuation given by

the solid particles (liquid-solid system) from overall attenuation. The result clearly show

a decrease in attenuation due to gas bubbles with lower gas holdup.

The attenuation measurements at Vg = 0.056 m/s are shown in Figure 4.3.9 along with a

comparkon of the averaged data ftom attenuation measurements for al1 superficial gas

velocities used in this study. By subtracting the attenuation given by solid particles we

obtain a profile of the gas phase attenuation in the center of the column with increasing

gas velocity and solids concentration as shown in Figure 4.3.10. The drop in attenuation

is seen to increase with increasing gas velocity for gas velocities higher than 0.01 7 mis.

These attenuation values can be used in Figure 4.2.7 or substituted in the tegression

equation fiom sarne figure, when gas holdup can be quantified.

The results are shown in Figure 4.3.1 1. A cornparison between the gas holdup measured

through ultrasound attenuation and the gas holdup nom level measurements is also made.

Reasonably good agreement is seen up to 0.1 solids volume fraction. For higher solids

0 .O0 0.05 0.10 0.1 5 0.20 0.25

Solids volume fraction

Figure 4.3.9 Ultrasound attenuation versus solids volume fraction in G-L-S system compared to L-S system

Solids volume fraction

Figure 4.3.1 0 Attenuation variation with solids fraction in G-L-S system minus solids attenuation from L-S systern

Solids volume fraction

Figure 4.3.11 Comparison between gas holdup given by ultrasound attenuation and gas holdup

from level measurements

concentration level measurements indicate a lower gas holdup at al1 superficial gas

velocities used in this study. This is not surprising since the level readings give an

average gas holdup while ultrasound attenuation give a local gas holdup in column center.

Although, the gas holdup in this region is lower with increasing solids concentration than

in gas-liquid system it is still higher compared to the average gas holdup from level

readings. It should be pointed out also, that a systematic error may be present in level

readings for higher solids concentrations due to level fluctuations and foam layer. Fisure

4.3.1 1 also shows that standard deviations for each data point calculated as an average of

gas holdups between several experirnents are quite small.

The experimental results fiom three-phase system are confirmed by results from

literature. Warsito et al. (1995,1999) showed that at low solids concentration for particles

of 200 Fm, the radial profile of gas holdup is flatter than the corresponding gas-liquid

system. Wolff et al (1990) studied the effect of solids concentration and particle size for

different particle densities over the bubble coalescence phenornenon in a three-phase

Auidized bed. It was concluded that the largest Sauter mean bubble diameters were

observed in suspension with the higher solids concentration. Consequently the lowest gas

holdup was seen at highest solids concentration.

Based on the investigations in this study, a procedure for phase holdup measurements in

L-S and G-LS systems can be recommended using ultrasonic technique.

Step 1

Generate calibration curves for variation of ultrasound velocity and attenuation with

particle size and concentration in liquid-solid suspensions over the solids concentration

used.

ln gas-liquid system generate calibration c w e s based on attenuation measurernents. For

a good repeatability a proper distance between transducers and location inside the column

has to be chosen. Also an average from a sufficient number of data point has to be

considered.

For computation of phase holdups in three-phase gas-liquid-system the following steps

wouId be recommended:

1) Make measurements of ultrasound velocity and attenuation in the analyzed three-phase

medium

2) Use calibration cuve (or regression equation) for ultrasound velocity variations from

L-S system to estimate slurry concentration.

3) Use calibration curve (or regression equation) from attenuation measurements in L-S

system to estimate attenuation due to solid particles only.

4) Subtract the attenuation due to solids particles From the total attenuation in three phase

suspension and get an attenuation value.

5) Read gas holdup fiom calibration curve for attenuation in G-L system at corresponding

attenuation.

Chapter 5 Conclusions and Recornmendations

5.1 Conclusions

1. An increase in acoustic velocity with increasing solids concentration was observed for

al1 particle sizes used in this study. The increase is small below 10 vol.% solids and

quite significant in the range 10 to 50 vol.%. A decrease in ultrasound velocity with

increasing particle size was also observed for same solids concentration. A reversed

effect was seen in ultrasound attenuation measurements. The attenuation increased

significantly up to 10-15 vol.% and less at higher solids concentrations for larger

particles. For smaller particles a linear increase was observed.

2. The variations in acoustic velocity and attenuation could be used to detemine rnean

particle size in a suspension. A suspension consisting of two particle sizes was

success full y anal yzed.

3. The liquid-solid system was fùrther charactenzed by measuring the mean pulse

frequency of ultrasonic signal. It was observed that for smaller particles the mean

Frequency of the ultrasound pulse is not changing significantly with increasing solids

concentration. However, for larger particles there is a large increase in mean

Frequency of the pulse. The increase was quantified and seen to be linear with

increasing solids concentration.

4. In gas-liquid system it is shown that the acoustic velocity is not affected by bubble

presence. The attenuation, however, increased strongly with increasing superficial gas

velocity. By using a simple statistical approach of moving average (100 values) the

noise caused by the bubbles passing between transducers was reduced and

reproducible results of gas holdup were obtained showing the possibility for on-line

rneasurements.

5. In gas-liquid-solid system ultrasonic velocity variations were similar to those

obtained in liquid-solid systems. However, attenuation measurernents had a different

trend depending on the gas velocity used. By subtracting the attenuation due to solids

alone the attenuation due to gas bubbles c m be obtained. Therefore local gas holdup

could be obtained simultaneously from measurements of acoustic velocity and

attenuation in a three-phase system.

5.2 Recommendations

A detailed investigation of the three-phase system should be conducted for

quantification of the measurernent errors especially at high gas holdups.

A Frequency scanning ultrasonic system would be highly recommended especially

when the analyzed medium is a suspension or slus, with unknown particle size.

The alignrnent between transducers was found to be important. A system which

allows for transducers orientation would geatly improve the measuring system.

A very precise temperature control is highly desirable given the high sensitivity of the

ultrasonic velocity to temperature changes.

Calibration of the ultrasonic equipment is recommended on a regular basis.

For measurements in gas-liquid or gas-liquid-solid systems measurement of the

backscattered signal would also prove usehil.

For measurements in three phase systems two pairs of transducers will be strongly

recommended. One can be suited to solids concentration measurements whiIe the

other to gas holdup rneasurements.

The transducer diarneter can be chosen such as to fit a given purpose. For a study of

gas holdup a large surface transducer may be considered while for bubble size or

velocity measurements a punctiform transducer will be useful.

. The use of a faster data acquisition system would give more insight into dynamic

variations of the system.

Appendix A - Bubble size, Pore size and Stirrer Speed Calculations

Pore size measurements

Several experiments were done tu detemine the pore size using the method proposed by

Houghton et al. (1957). -4 liquid height of 0.3 m was kept above the porous plate and a

manometer was comected to the windbox for pressure measurements reading. The air-

flow rate was varied and readings were taken first for initial bubble generation and then at

different flow rates. A number of four experiments were averaged and the repeatability

was found to be good (standard deviation less than 1%). The equation used for pore size

calculation was:

where o = surface tension and AP, = excess pressure required to generate bubbles on

distnbutor. AP, is obtained from the extrapolation of AP to zero gas flow rate. where AP

is the pressure &op on and through the distributor at any gas flow rate (Figure A.1). The

results are tabled (Table A.l). A larger pore size than the producer's reported size =

70 prn) was found. This newly found pore size (100 pm) was used in further calculations

of the bubble sizes generated by the porous plate.

Superificial gas velocity (mls)

Figure A.l Wet pressure drop versus superficial gas velocity

O 5 10 15 20 25 30 35 40

Readings at rotameter corrected for T and P (LPM)

Figure A.2 Calibration of Dweyer rotameter at 34.5 KPa backpressure and 22 OC

Table A.l Wet pressure drop measurernents for porous plate characterization

ubble size measurements

Table A.2 Bubble size distribution from photographie technique (exp. I )

Rota meter

10

Exp4

0.560

Table A.3 Bubble size distribution From photograp hic technique (exp.2)

Vg (rn/s)

0.005

0.0 15

[ Vg (mh) [ Bubble size (mm) 1 % From total 1 Sauter diam. (mm) ]

Average h (ml

0.549

Vg(m1s )

0.01

Exp2 hm)

0.545

Expl h(m)

0,548

BubbIe size (mm)

1 .O, 2 . 0 3.0, 4.0,5.0

2.0, 3.0,4.0, 5.0

Exp3 h(m)

0.543

Static pressure (Pa) 2937.11

OeltaP

(Pa) 2437

% from total

4%,45%,36%,10%,3%

1 4%,45%,29%, 1 1 %

Sauter diam. (mm)

2.4

3.2

ons for bubble sizes

The bubble size was calculated using the equation developed by Koide et al. (1968) for

liquids belonging to group A of liquids (e.g. water):

where Fr (Froude number) = ~,? /~ '~cb , , , We (Weber number) = ~,'ci,,~,~,!~'o, V, = gas

flow rate per unit area of porous plate, E = porosity of porous plate, = average pore

diameter, o = liquid surface tension, p, = liquid density and g = gravitational acceleration

and & = average bubble diameter. The porosity of the porous plate was taken as an

average value of 0.35. The results show an average bubble size of 2.4 to 3.1 mm for

superficial gas velocities between 0.01 to 0.05 mh. A study of the pore sizr effect over

the calculated bubble size was initiated. Using a smaller pore size value (e.g. 35 pm) the

calculated bubble size will Vary between 2.2 mm and 2.8 mm For the corresponding gas

velocities.

The stirrer rpm was calculated with equation (2.1.1) as given by Zwietenng (1958) for

different solids concentrations. A value of the constant s of 6.8 was considered From the

work of Nienow (1968) for a similar type of impeller.

Table A.4 Stirrer speed in rpm for different solids concentrations

Conc. (wt%) O

rpm -35 pm O

rpm- 70pm O

rprn 180prn i

n

Appendix B - Liquid Manometers

A schematic for liquid filled manometers is shown in Figure B. 1 . If we consider z1 and z2

as the height from which the manometers 1 and 2 are taking readings and y, and y? the

actual level readings a correlation can be proposed for a pressure difference p2-pi.

Let: Az = z2-z,

AY = Y--YI

AP = PTP1

p* = atmosphenc pressure

pi = pressure at reference point

h' = height at point of pressure p2

as shown in Figure B. 1 . We cm write then a balance of pressure at the reference point:

If we subtract first equation (B.2) kom (B. 1) we get:

By rearranging the above equation we get:

Assuming that ~ p , is negligible and substituting equation (B.6) into (B.5) we get:

Replacing E~ with (hg) in equation (B.7) we obtain the final equation (B.8) for gas

holdup calculation from ratio of differential pressure (cm HzO) to the height difference

between the pressure taps.

Column Wall

Figure B.l Schematic of liquid manometers

Appeodix C - Solids Properties

The g l a s beads were purchased from Flex-O-Lite Ltd., St.Thomas, Ontario. Three

average particle sizes were chosen for experimental work. The supplying Company gave

the physical and chemical characteristics of g l a s beads. A table with these properties is

shown (Table C. 1 ). A check of the above properties was made (e.g. density and particle

size distribution).

For density measurements, a pycnometric technique was used. A known mass of solids

was placed inside a volumetric cylinder and then gradually the cylinder was filled up to

the 1 L mark. By rneasuring the cylinder mass before and after filling the exact density of

the solids can be obtained. The average density obtained was close to the one found in

Table C. 1 and equal to 2450 kg/m3. This is the value used in Our calculations throughoit

this study.

For particle size analyses, permission from Dr. Inculet was obtained to use the

Brinkrnann particle size analyzer. Several independent samples were analyzed and the

results were compared. For smallest particle size an average of 35 Fm was found (e.g

Figure C.l). For medium size particles an average of about 70 pm was obtained (e.g.

Figure C.2) . For largest particle size a reconfiguration of Brinkrnann analyzer would have

been needed given the upper limit of usage (150 pm), case in which a sieve analyses was

carried with the results from Table C.2. A 180 pm average particle size was found to be

significant for the largest particle size.

The arnounts of g l a s beads used in this study were eventually not very large. That is why

a careful mixing of the g l a s beads sort was carried each time an amount was collected

(chute splitter and table sampler). For the samples used in particle size analyzer a particle

riffling machine was employed to collect the glass beads samples.

. . . . . . . . . . . . . . . . . . YWHG'S HOûUWS. 72 GPa

. . . . . . . . . . . . . . . . . . . #)XSSON'S RATIO 0.25

Table C.1 Properties of glass beads particles

Figure C.1 Brinkmann analysis of glass beads particles (35 pm)

B r i n k r n a n n

P a r t i c l e S i z e Analyzer

Sb (ir iiapnt)

tiw Sule

Figure C.2 Brinkmann analysis of glass beads particles (70 pm)

Table C.2 - Sieve analysis of glas beads particles

' Size opening Trial 2 (kg)

x 10"

Trial 1 (kg)

10"

Trial 3 (kg)

10''

Average (kg)

10'~

168

Appendix D - Ultrasound Equipment Calibration and Characteristics

Calibration

The calibration of ultrasound equipment was carried by measuring the variation of the

ultrasound velocity in water only with increasing temperature. Five experiments were

carried and a comparison of the results with reference data from literature was done. The

results are s h o w in Figure D.1 and a good agreement is observed. Ultrasound velocity

deviations of less than 0.05 % are observed which is considered to be acceptable.

The comparison data was taken from Del'Grosso and Mader (1972) who conducted

measurements of ultrasound velocity in pure water as a function of temperature with an

accuracy of 0.0 15 m/s.

The deviation of the velocity variations from Our experirnents, can be caused by a less

accurate temperature control + 0.1 O C compared to 2 0.00 1 O C in the measurements by

Del'Grosso and Mader. Also, tap water was used instead of pure water. However, as

mentioned above the differences are small and the results are considered to be good.

. . ment charactensm

The equipment characteristics are given by the manufacturing Company (Fallon

Lntrasonic Inc.) and presented in following Table D. 1.

1 1 - Del'Grosso and Mader (1 972) 1530 !

1525 I 1520 1

1515 1 I

1510 - I

1505

1500 1 !

1495 4 I /

# a"

20 22 24 26 28 30 32 34 36 38 40

Temperature (OC)

Figure D.l Calibration of ultrasonic equipment with temperature variations in water only

Table D. 1 Characteristics of ultrasonic equipment

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Vitae

NAME:

ADDRESS:

Valeriu Stolojanu

1003- 190 Chenyhill Circle London, Ontano Canada N6H 2M3

POST-SECOM>ARY The University of Tirnisoara EDUCATION AND Timisoara Romania DEGREES: 1984- 1990 B.Eng.Sc.

PUBLICATIONS: Stolojanu V. and A. Prakash, ( 1 997) "Hydrodynamic Maisuremenu in a Slu- Bubbie Colurnn using Ultrasonic Technique" ('hem. Eng. Sci.. 52.42254230

RELATED WORK Anal- Programmer EXFERENCE: West S hoes Industxy~ Arad/ Romania

1 990- 1992

Chernical Engineer Petroleum Exploatation / Arad/ Romanta 1992-1995 -

-

Researc h Assis tant University of Western Ontano 1 997-1 998

TeachingReasearch Assistant Univeaitv of Western Ontano 1997- 1999