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WASHINGTON UNIVERSITY

SEVER INSTITUTE

DEPARTMENT OF ENERGY, ENVIRONMENTAL AND CHEMICAL ENGINEERING

___________________________________________________________________

Bubble and Slurry Bubble Column Reactors: Mixing, Flow Regime Transition and

Scaleup

by

Ashfaq Shaikh

Prepared under the direction of

Professor Muthanna H. Al-Dahhan

___________________________________________________________________

A dissertation presented to the Sever Institute of Washington University

in partial fulfillment of the requirements for the degree of

DOCTOR OF SCIENCE

August 2007

Saint Louis, Missouri, USA

WASHINGTON UNIVERSITY

SEVER INSTITUTE

DEPARTMENT OF ENERGY, ENVIRONMENTAL AND CHEMICAL ENGINEERING _________________________________________________________________________

ABSTRACT _____________________________________________________________

Bubble and Slurry Bubble Column Reactors: Mixing, Flow Regime Transition and Scaleup

by

Ashfaq Shaikh

ADVISOR: Professor Muthanna H. Al-Dahhan _____________________________________________________________

August 2007

Saint Louis, Missouri, USA _____________________________________________________________

Bubble and slurry bubble column reactors are used for a wide range of applications in the

chemical, petrochemical, and biochemical industries. A thorough understanding of their

complex flow structure is crucial for design and scale-up of these reactors.

This study used a multi-pronged approach to advance the state of knowledge of the

hydrodynamics of high pressure bubble and slurry bubble column reactors. First, the

effect of liquid phase physical properties and solids loading on the flow structure of

slurry bubble column reactors was studied, with particular emphasis on the churn-

turbulent flow regime. This study was performed in a system using a liquid phase which

at room temperature mimics Fischer-Tropsch (FT) wax at FT synthesis conditions and a

gas at a pressure that mimics syngas density. Computer Automated Radioactive Particle

Tracking (CARPT) and single source γ-ray Computed Tomography (CT) were utilized to

compute the time-averaged solids velocity fields, turbulent parameters’ profiles, and

time-averaged solids and gas holdup profiles.

The second part of this study included the development of non-invasive techniques, such

as CT and Nuclear Gauge Densitometry (NGD), for delineation of flow regimes in

bubble column reactors. The capability of these techniques to identify flow regime

transition was evaluated and compared against conventional methods of flow regime

demarcations, such as the change in the slope of the gas holdup curve and the drift flux

plot. Special attention was given to NGD to develop a non-invasive and online flow

regime measurement and monitoring technique. Hence, the guidelines and rules were set

up for these techniques (CT and NGD) by developing its ‘flow regime identifiers’. Both

of these techniques are ‘active’, i.e., involve penetration of γ-rays through the column,

and therefore are expected to represent the prevailing hydrodynamics with fidelity, even

in industrial scale columns.

The last part tackled the challenging task of extrapolating small diameter behavior to

large diameters, a task that essentially needs criteria for hydrodynamic similarity. Based

on a comprehensive review of the reported scaleup procedures, this work proposed a new

hypothesis for hydrodynamic similarity and subsequently for scale-up of bubble column

reactors operating in the regime of industrial interest, i.e., the churn-turbulent regime.

This task was performed in two stages: first, the proposed hypothesis was experimentally

evaluated for hydrodynamic similarity using existing CT and CARPT; second, for a

priori prediction of hydrodynamic parameters to maintain such similarity, state-of-the-art

correlations were developed using an Artificial Neural Network (ANN). The current

study showed that the similarity of overall gas holdup and its radial profile is pertinent for

similar recirculation and mixing in two systems. The similarity based only on global

hydrodynamics should be exercised with prudence.

The work accomplished in this study, and in particular the concepts developed in last two

parts, are, in retrospect, generic for multiphase reactors with bubble columns as an

example. Hence it presents promising avenues to explore them in other configurations of

multiphase reactors.

To my Ammiji, Abbaji, and Didi

Copyright by

Ashfaq Shaikh

2007

Contents Page No. Tables …………………………………………………………………. ix Figures ………………………………………………………………... x Nomenclature ………………………………………………………… xix Acknowledgements …………………………………………………... xxiv 1. Introduction…………………………………………………………… 1

1.1 Motivation …………………………………………………………. 8 1.2 Objectives …………………………………………………………. 10 1.3 Thesis Organization ………………………………………………. 12 2. Literature Review ……………………………………………………

15

2.1 Mixing of liquid/slurry phase ……………………………………. 15 2.2 Flow Regime Transition …………………………………………. 18 2.2.1 Flow Regime Types and Characteristics …………………… 19 2.2.2 Methods for Flow Regime Identification ………………….. 21 2.2.3 Prediction of Flow Regime Transition ……………………..

26

2.2.4 Remarks ……………………………………………………. 26 2.3 Scaleup of Bubble Column Reactors ……………………………… 28 2.3.1 Reported status of scaleup in literature …………………….. 28 2.3.2 Reported status of scaleup in industry ……………………… 37 3. Experimental Investigation of the Hydrodynamics of Slurry

Bubble Column: Phase Holdups Distribution via Computed Tomography ………………………………………………………….

39 3.1 Choice of Phases ………………………………………………….. 40 3.2 Experimental Details ……………………………………………… 42 3.3 Single Source Computed Tomography (CT) ……………………… 45

v

3.4 Results and Discussion…………………………………………….

47

3.4.1 Overall gas holdup …………………………………………... 47 3.4.2 Drift Flux Model ………………………………………….…. 49 3.4.3 Cross-sectional Distribution of Gas Holdup ………………… 51 3.4.4 Time averaged gas and solids holdup radial profile ………… 53 3.4.5 Effect of liquid phase physical properties on gas and solids

holdup radial profile ……………………………………………………………….

55

3.4.6 Effect of solids loading on gas and solids holdup radial

profile ……………………………………………………….

63 3.4.8 Normalized gas holdup radial profile ………………………. 67 3.4.9 Normalized solids holdup radial profile ……………………. 67 3.4.7 Comparison with predictions of Sedimentation-Dispersion

Model (SDM) …………………………………………………………..

68

3.5 Remarks …………………………………………………………… 70 4. Experimental Investigation of the Hydrodynamics of Slurry

Bubble Column: Solids Flow Pattern via CARPT …………………

73 4.1 Experimental ………………………………………………………. 73 4.2 Computer Automated Radioactive Particle Tracking (CARPT) ….. 74 4.3 Results and Discussion ……………………………………………. 75 4.3.1 Time averaged solids velocities …………………………….. 75 4.3.2 Turbulent stresses and kinetic energy ……………………….. 81 4.3.3 Effect of liquid phase physical properties on solids axial

velocity and turbulent parameters parameters……………….

84 4.3.4 Effect of solids loading on solids axial velocity and turbulent

parameters …………………………………………………..

89

vi

4.3.5 Cross-sectional averaged turbulent stresses …………………. 93 4.3.6 Turbulent eddy viscosity …………………………………… 93 4.3.7 Eddy diffusivities ……………………………………………. 93

4.4 Remarks …………………………………………………………… 94 5. Flow Regime Transition ……………………………………………... 95 5.1 Flow Regime Transition using CT ………………………………... 95 5.1.1 Experimental setup and conditions ………………………… 96 5.1.2 Results and Discussion ……………………………………... 96 5.1.3 Evaluation of the empirical correlations ……………………. 103 5.2 Flow Regime Transition using NGD ……………………………… 105 5.2.1 Nuclear Gauge Densitometry (NGD) ……………………… 106 5.2.2 Results and Discussion ……………………………………... 109 5.2.3 Evaluation of the ‘flow regime identifiers’ developed for

NGD …………………………………….…………………..

130 5.2.4 Evaluation of literature correlations………………………… 142 5.3 Remarks …………………………………………………………… 144 6. Scaleup of Bubble Column Reactors ………………………………... 147 6.1 Hypothesis for hydrodynamic similarity ………………………….. 147 6.2 Experimental conditions …………………………………………... 149 6.3 Results ……………………………………………………………... 151 6.3a Discussion …………………………………………………… 162 6.4 Development of correlations for ‘a priori’ prediction of

hydrodynamic parameters…………………………………………

166

vii

6.5 Remarks …………………………………………………………… 167 7. Summary and Recommendations …………………………………... 168 7.1 Summary and Conclusions ………………………………………... 168 7.2 Recommendations …………………………………………………. 172

Appendix-A. Phase Distribution in Three Dynamic Phase Systems via Combination of Computed Tomography (CT) and Electrical Capacitance Tomography (ECT) ……………………………. 175

Appendix -B. Experimental Investigation of Hydrodynamics of Slurry

Bubble Column Reactors via CT ……………………………… 186 Appendix -C. Experimental Investigation of Hydrodynamics of Slurry Bubble Column Reactors via CARPT…………………………. 203 Appendix -D. Sedimentation-Dispersion Model ……………………………… 231 Appendix -E. Material Safety Data Sheet for Therminol LT …………………. 236 Appendix –F. Development of Artificial Neural Network (ANN)

Correlations for Hydrodynamic Parameters …………………. 244 References ………………………………………………………………………… 269 Vita………………………………………………………………………………… 279

viii

Tables 3-1 Physical properties of Sasol wax and Therminol LT

40

3-2 Experimental conditions employed in this study

45

3-3 The values of drift flux parameters at the studied experimental conditions

50

4-1 CARPT experimental conditions

73

5-1 Comparison of experimental and predicted transition velocities from the available correlations in an air-Therminol LT system at various operating pressures

105

5-2 Characteristics frequencies in bubble column (Drahos et al., 1991)

109

5-3 Slope of power spectra at studied operating conditions 128

5-4 Experimental conditions for evaluation of ‘flow regime identifiers

131

5-5 Statistical comparisons of prediction of correlations with experimental data

144

6-1 List of similarity conditions in a 6” diameter stainless steel column

151

6-2 List of experimental conditions of mismatch gas holdup radial profile in a 6” diameter stainless steel column

152

ix

Figures 1-1 Schematic diagram of bubble/slurry bubble column 2

1-2 Projected US energy and oil production and consumption [Source:

National Energy Policy, White House Report, 2001]

3

1-3 US vulnerability to oil disruption (Williams and AlHajji, 2003) 4

1-4 a) M. King Hubbert at 1956 API Spring Meeting proposing peak theory b) Popular Hubbert-peak curve.

5

1-5 Relationship between fuel economy and urban air benefits (Koelmel, 2005)

6

1-6 CAPEX cost for GTL (Rahmim, 2003) 6

1-7 Projected economies of scale for GTL-FT process (Brown, 2003)

7

2-1 Various flow regimes in bubble column reactors

20

2-2 Flow regime map for air-water system at ambient pressure a) Shah et al., 1982 and b) Zhang et al., 1997

21

2-3 Photographs of bubbly and churn-turbulent flow in 2-D column

22

2-4 Typical overall gas holdup curve a) Shaikh and Al-Dahhan, 2005; and b) Rados, 2003

23

2-5 Typical drift flux plot using Wallis (1969) approach (Deckwer et al., 1981)

24

2-6 Average bubble-swarm velocity in air-ethanol-Co (van Baten et al., 2003)

35

3-1 Bubble column reactor of 6” diameter used for CARPT/CT measurements. CT1, CT2, and CT3 represent the scan levels used in this investigation.

44

3-2 Configuration of the CT experimental setup (Kumar, 1994) 46

3-3 Effect of solids loading on a) overall gas holdup curve and b) drift flux plot in air-Therminol LT-glass beads system at ambient conditions in 6” steel column

48

x

3-4 Effect of operating pressure on overall gas holdup at various solids

loading in air-Therminol LT –glass beads system in 6” steel column

49

3-5 Cross-sectional distribution of gas holdup in 6” diameter stainless steel column using air-Therminol LT-glass beads system at different superficial gas velocities, solids loading of 9.1 % vol. and P = a) 0.1, and b) 1 MPa.

51

3-6 Cross-sectional distribution of gas holdup in 6” diameter stainless steel column using air-Therminol LT-glass beads system at superficial gas velocity of 30 cm/s, operating pressure of 1 MPa, and solids loading of a) 9.1 and b) 25 % volume.

52

3-7 a)Gas holdup and b) solids holdup radial profile in air-Therminol LT-glass beads system using 9.1 % vol. solids loading at superficial gas velocity of 8 cm/s and ambient pressure

54

3-8 a) Gas holdup and b) solids holdup radial profile in air-Therminol LT-glass beads system using 25 % vol. solids loading at superficial gas velocity of 30 cm/s and operating pressure of 1 MPa

54

3-9 Overall gas holdup curve using air-water-glass beads (Rados, 2003) and air-Therminol LT-glass beads system at ambient conditions, solids loading of 9.1 % vol. in a 6” diameter column.

55

3-10 Effect of physical properties on a) gas holdup, and b) solids holdup radial profile at P = 0.1 MPa, z/D = 5.5, solids loading of 9.1 % vol. and Ug = a) 8, b) 14, and c) 30 cm/s in 6” diameter steel column

58

3-11 Overall gas holdup curve using air-water-glass beads (Rados, 2003) and air-Therminol LT-glass beads system at operating pressure of 1 MPa, solids loading of 9.1 % vol. in a 6” diameter column..

60

3-12 Effect of physical properties on a) gas holdup, and b) solids holdup radial profile at P = 1 MPa, z/D = 5.5 and solids loading of 9.1 % vol. at Ug = a) 8, b) 14, and c) 30 cm/s in 6” diameter steel column

61

3-13 Effect of solids loading on gas and solids holdup radial profile in air-Therminol LT-glass beads system at ambient pressure at Ug = a) 20 and b) 30 cm/s 6” diameter steel column

64

3-14 Effect of solids loading on gas and solids holdup radial profile in air-Therminol LT-glass beads system at Ug = a) 20 and b) 30 cm/s and P = 1 MPa in 6” steel column

66

xi

3-15 Predictions of the SDM in air-Therminol LT-glass beads system at ambient pressure and solids loading of a) 9.1 and b) 25 % vol. in 6” diameter column

68

3-16 Comparison of the SDM predictions with experimental data in air-Therminol LT-glass beads system at ambient pressure, solids loading of 9.1 % vol., and Ug = a) 8 and b) 30 cm/s in 6” diameter column

69

3-17 Comparison of the SDM predictions with experimental data in air-Therminol LT-glass beads system at ambient pressure. a) effect of superficial gas velocity at solids loading of 25 % vol. and b) effect of solids loading at Ug = 30 cm/s in 6” diameter column

70

4-1 Configuration of the CARPT experimental setup (Degaleesan, 1997)

75

4-2 Time and azimuthally averaged solids velocity in air-Therminol LT-glass beads system at Ug = 30 cm/s, P = 0.1 MPa, and solids loading = 9.1 % volume a) uz-ur vector map, b) axial, and c) radial velocity components

77

4-3 Radial profile of solids a) axial, b) radial, and c) tangential velocity in air-Therminol LT-glass beads system at Ug = 30 cm/s, P = 0.1 MPa, and solids loading = 9.1 % volume

77

4-4 Probability distribution function of solids axial velocities at L/D = 2.5 at various dimensional radius positions of r/R = 0.063, 0.44, and 0.96 at Ug = 30 cm/s, P = 0.1 MPa, and solids loading of 9.1 % volume

78

4-5 Probability distribution function of solids axial velocities at L/D = 2.5, 5.5, and 9 along the column radius at r/R = 0.063, 0.44, 0.69, and 0.96 at Ug = 30 cm/s, P = 0.1 MPa, and solids loading of 9.1 % volume

79

4-6 Probability distribution function of solids axial velocities in fully developed flow in the column center and near the wall at a) 30 cm/s, 9.1 % vol., and 0.1 MPa, b) 30 cm/s, 9.1 % vol., and 1.0 MPa, and c) 30 cm/s, 25 % vol., and 1.0 MP in 6” diameter stainless steel column.

80

4-7 Radial profile of solids a) turbulent kinetic energy, and b) axial, b) radial, and c) tangential normal stresses in air-Therminol LT-glass beads system at Ug = 30 cm/s, P = 0.1 MPa, and solids loading = 9.1 % volume.

82

4-8 Radial profile of solids shear stress components in an air-Therminol LT-glass beads system at Ug = 30 cm/s, P = 0.1 MPa, and solids loading = 9.1 % volume

84

xii

4-9 Comparison of radial profile of a) gas holdup, b) solids axial velocity c) solids TKE, and d) solids shear stress in air-water- glass beads and air-Therminol LT-glass beads system at Ug = 30 cm/s, P = 0.1 MPa, and solids loading of 9.1 % vol.

86

4-10 Comparison of radial profile of a) gas holdup, b) solids axial velocity c) solids TKE, and d) solids shear stress in air-water-glass beads and air-Therminol LT-glass beads system at Ug = 30 cm/s, P = 1 MPa, and solids loading of 9.1 % vol.

87

4-11 Effect of solids loading on radial profile of solids a) axial velocity, b) turbulent kinetic energy, c) axial normal stress, and d) shear stress in air-Therminol LT-glass beads system at Ug = 20 cm/s, and P = 0.1 MPa.

89

4-12 Effect of solids loading on radial profile of solids a) axial velocity, b) turbulent kinetic energy, c) axial normal stress, and d) shear stress in air-Therminol LT-glass beads system at Ug = 30 cm/s, and P = 0.1 MPa

90

4-13 Effect of solids loading on radial profile of solids a) axial velocity, b) turbulent kinetic energy, c) axial normal stress, and d) shear stress in air-Therminol LT-glass beads system at Ug = 20 cm/s, and P = 1 MPa

91

4-14 Effect of solids loading on radial profile of solids a) axial velocity, b) turbulent kinetic energy, c) axial normal stress, and d) shear stress in

air-Therminol LT-glass beads system at Ug = 30 cm/s, and P = 1 MPa.

92

5-1 Gas holdup radial profile at various superficial gas velocities in an air-Therminol LT system at ambient condition in a 0.162 m steel column.

97

5-2 a) Cross-sectional averaged gas holdup versus superficial gas velocity and b) Drift flux plot based on cross-sectional averaged gas holdup in an air-Therminol LT system at ambient conditions in a 0.162 m steel column.

99

5-3 Evolution of steepness parameter with superficial gas velocity in an air-Therminol LT system at ambient conditions in a 0.162 m steel column.

100

5-4 Gas holdup radial profile at various superficial gas velocities in an air-Therminol LT system at operating pressure of 0.4 MPa in a 0.162 m steel column.

100

5-5 a) Gas holdup curve based on cross-sectional averaged gas holdup and b) Flux plot based on cross-sectional averaged gas holdup in an air-

101

xiii

Therminol LT system at operating pressure of 0.4 MPa in a 0.162 m steel column.

5-6 a) Gas holdup curve based on cross-sectional averaged gas holdup and b) Drift flux plot based on cross-sectional averaged gas holdup in an air-Therminol LT system at operating pressure of 1.0 MPa in a 0.162 m steel column.

102

5-7 Evolution of steepness parameter with superficial gas velocity in an air-Therminol LT system at operating pressures of 0.4 and 1 MPa in a 0.162 m steel column

103

5-8 Experimental setup of Nuclear Gauge Densitometry (NGD)

108

5-9 Overall gas holdup curve using an air-water system at ambient conditions in 0.1012 m diameter column

110

5-10 Drift flux plot using an air-water system at ambient conditions in 0.1012 m diameter column

110

5-11 Time-series of photon count fluctuations in 0.1012 m diameter column in a) empty column and b) water (no gas flow).

111

5-12 Time-series of photon count fluctuations in 0.1012 m diameter column using air-water system at superficial gas velocity of in a) 1, b) 3, c) 7, and d) 11 cm/s at ambient conditions.

112

5-13 Variation of variance of photon counts fluctuations with superficial gas velocity in 0.1012 m diameter column using air-water system at ambient conditions.

114

5-14 Variation of variance of pressure drop fluctuations with superficial gas velocity in 0.1012 m diameter column using air-water system at ambient conditions (Reproduced from Lin et al., 1999).

115

5-15 The coefficient of departure from Poisson distribution versus superficial gas velocity in 0.1012 m diameter column using an air-water system at ambient conditions.

117

5-16 Autocorrelation curve at superficial gas velocities of a) 1, b) 3, and c) 4 cm/s using an air-water system in 0.1012 m diameter column at ambient conditions.

118

5-17 Autocorrelation curve at superficial gas velocities of a) 7, b) 9, and c) 11 cm/s using an air-water system in 0.1012 m diameter column at ambient conditions.

119

xiv

5-18 Typical log-log plot of normalized psdf at superficial gas velocities of

a) 1, b) 3, c) 4, d) 6, e) 9, and f) 11 cm/s using an air-water system in 0.1012 m diameter column at ambient conditions.

122

5-19 Power spectra of liquid velocity fluctuations in a bubble column by Zarzewski et al. (1981).

124

5-20 LDA axial velocity signal power spectra a) D = 15 cm, Ug = 2.7 cm/s, z/D = 5.5, b) D = 23 cm, Ug = 1.2 cm/s, z/D = 6, and c) D = 40 cm, Ug = 5.5 cm/s, z/D = 5 (Groen, 2004)

125

5-21 Log-log plot of normalized psdf of photon counts history obtained in a) empty column and b) water (with no gas flow).

127

5-22 Log-log plot of normalized psdf with fitted slope line at superficial gas velocities of a) 4, b) 6, c) 9, and d) 11 cm/s using an air-water system in 0.1012 m diameter column at ambient conditions

127

5-23 a) Overall gas holdup curve and b) drift flux plot in an air-water system at ambient pressure in 6” diameter stainless steel column

132

5-24 Variation of coefficient of departure, Dp with superficial gas velocity in an air-water system at ambient pressure in 6” diameter stainless steel column

132

5-25 Autocorrelation curve in a) bubbly flow (Ug = 2 cm/s) and b) churn-turbulent flow (Ug = 20 cm/s) at ambient pressure using an air-water system.

133

5-26 Psdf plot at superficial gas velocity of a) 2 cm/s, b) 7 cm/s, and c) 20 cm/s and ambient pressure using an air-water system in 6” diameter stainless steel column.

133

5-27 a) Overall gas holdup curve and b) drift flux plot in an air-water system at operating pressure of 1 MPa in 6” diameter stainless steel column

134

5-28 Variation of coefficient of departure, Dp, with superficial gas velocity in an air-water system at operating pressure of 1 MPa in 6” diameter stainless steel column

135

5-29 Autocorrelation curve in a) bubbly flow (Ug = 2 cm/s) and b) churn-turbulent flow (Ug = 20 cm/s) at operating pressure of 1 MPa using an air-water system.

135

xv

5-30 Psdf plot at superficial gas velocity of a) 2 cm/s, b) 10 cm/s, and c) 20 cm/s and operating pressure of 1 MPa using an air-water system in 6” diameter stainless steel column.

135

5-31 a) Overall gas holdup curve and b) drift flux plot in an air-C9-C11 system at operating pressure of 0.1 MPa in 6” diameter stainless steel column

136

5-32 Variation of coefficient of departure, Dp, with superficial gas velocity using an air-C9-C11 system at operating pressure of 0.1 MPa in 6” diameter stainless steel column

137

5-33 Autocorrelation curve in a) bubbly flow (Ug = 2 cm/s) and b) churn-turbulent flow (Ug = 20 cm/s) at ambient pressure using an air-C9-C11 system.

137

5-34 Psdf plot at superficial gas velocity of a) 2 cm/s, b) 12 cm/s, and c) 20 cm/s and ambient pressure using an air- C9-C11 system in 6” diameter stainless steel column.

138

5-35 a) Overall gas holdup curve and b) drift flux plot in an air-C9-C11 system at operating pressure of 1 MPa in 6” diameter stainless steel column

138

5-36 Variation of coefficient of departure, Dp with superficial gas velocity using an air-C9-C11 system at operating pressure of 1 MPa in 6” diameter stainless steel column

139

5-37 Autocorrelation curve in a) bubbly flow (Ug = 2 cm/s) and b) churn-turbulent flow (Ug = 20 cm/s) at operating pressure of 1 MPa using an air-C9-C11 system.

139

5-38 Psdf plot at superficial gas velocity of a) 2 cm/s, b) 14 cm/s, and c) 20 cm/s and operating pressure of 1 MPa using an air- C9-C11 system in 6” diameter stainless steel column.

140

5-39 Comparison of reported correlations with transition velocities obtained based on variation in Dp of photon counts history in a) an air-water system b) an air- C9-C11 system at ambient and high pressure.

143

6-1 Comparison of gas holdup radial profile in 6” column using an air-water system at two different operating conditions [D6U12P7Water: 7 bar, 12 cm/s, air-water (Kemoun et al., 2001); D6U60P1Water: 1 bar, 60 cm/s, and air-water (Ong, 2003)] with similar overall gas holdup (~ 0.41).

148

xvi

6-2 a) Gas holdup and b) Axial liquid velocity radial profile in 6” diameter

stainless steel column using an air-water system [D6P4U45: 6 inch diameter, 4 bar, and 45 cm/s (Ong, 2003), D6P10U30: 6 inch diameter, 10 bar and 30 cm/s] (Overall gas holdup ~ 0.41).

152

6-3 Variation of AARD in liquid axial velocities between similarity conditions [D6P4U45Water (Ong, 2003) and D6P10U30Water] along the column radius in 6” diameter stainless steel column using an air-water system.

153

6-4 TKE profile in 6” diameter stainless steel column using an air-watesystem [D6P4U45: 6 inch diameter column, 4 bar and 45 cm/s (Ong2003), D6P10U30: 6 inch diameter column, 10 bar and 30 cm/s(Overall gas holdup ~ 0.41).

153

6-5 a) Gas holdup and b) Axial liquid velocity radial profile in 6” diameter stainless steel column using an air-water system (D6P1U45Water: 6 inch diameter column, 1 bar and 45 cm/s, D6P4U30Water: 6 inch diameter column, 4 bar and 30 cm/s) [Overall gas holdup ~ 0.35].

154

6-6 Variation of AARD in liquid axial velocities between similarity conditions (D6P1U45water and D6P4U30water) along the column radius in 6” diameter stainless steel column using an air-water system.

155

6-7 TKE radial profile in 6” diameter stainless steel column using an air-water system (D6P1U45Water: 6 inch diameter column, 1 bar and 45 cm/s, D6P4U30Water: 6 inch diameter column, 4 bar and 30 cm/s) [Overall gas holdup ~ 0.35].

155

6-8 a) Gas holdup and b) Axial liquid velocity radial profile in 6” diameter stainless steel column [D6P1U30 C9-C11: 6 inch diameter column, 1 bar, 30 cm/s (Han, 2006), and air- C9-C11 fluid system, D6P4U30water: 6 inch diameter column, 4 bar, 30 cm/s, and an air-water system] [Overall gas holdup ~ 0.35].

156

6-9 Variation of AARD in liquid axial velocities between similarity conditions [D6P1U30C9-C11 (Han, 2006) and D6P4U30water] along the column radius in 6” diameter stainless steel column.

157

6-10 TKE radial profile in 6” diameter stainless steel column (D6P1U30 C9-C11: 6 inch diameter column, 1 bar, 30 cm/s, and air- C9-C11 fluid system, D6P4U30water: 6 inch diameter column, 4 bar, 30 cm/s, and an air-water system) [Overall gas holdup ~ 0.35].

157

6-11 a) Gas holdup and b) Axial liquid velocity radial profile in 6” diameter 159

xvii

stainless steel column (D6P4U30water: 6 inch diameter column, 4 bar and 30 cm/s, air-water; D6P4U16C9-C11: 6 inch diameter column, 4 bar and 16 cm/s, air- C9-C11) [Overall gas holdup ~ 0.35].

6-12 Variation of AARD in liquid axial velocities between similarity conditions (D6P4U30water and D6P4U16C9-C11) along the column radius in 6” diameter stainless steel column.

159

6-13 TKE radial profile in 6” diameter stainless steel column (D6P4U30water: 6 inch diameter column, 4 bar and 30 cm/s, an air-water; D6P4U16C9-C11: 6 inch diameter column, 4 bar and 16 cm/s, air- C9-C11) [Overall gas holdup ~ 0.35].

160

6-14 a) Gas holdup and b) Axial liquid velocity radial profile in 6” diameter stainless steel column (D6P4U30water: 6 inch diameter column, 4 bar and 30 cm/s, an air-water; D6P10U8C9-C11: 6 inch diameter column, 10 bar and 8 cm/s, air- C9-C11) [Overall gas holdup ~ 0.35].

161

6-15 Variation of AARD in liquid axial velocities between similarity conditions (D6P4U30water and D6P10U8C9-C11) along the column radius in 6” diameter stainless steel column.

161

6-16 TKE radial profile in 6” diameter stainless steel column (D6P4U30water: 6 inch diameter column, 4 bar and 30 cm/s, an air-water; D6P10U8C9-C11: 6 inch diameter column, 10 bar and 8 cm/s, air- C9-C11) [Overall gas holdup ~ 0.35].

162

6-17 Gas holdup radial profile in 6” diameter stainless steel column (D6U2P1water: 1 bar and 2 cm/s, an air-water; D6U3P1TherminolLT: 1 bar and 3 cm/s, air- Therminol LT) [Overall gas holdup ~ 0.1].

165

6-18 Gas holdup radial profile in 6” diameter stainless steel column (D6U5P4TherminolLT: 4 bar and 5 cm/s, air-Therminol LT; D6U3.5P10Therminol: 10 bar and 3.5 cm/s, air- Therminol LT) [Overall gas holdup ~ 0.22].

165

xviii

Nomenclature BBO Bodenstein number, dimensionless c Wall holdup parameter (equation 3-2), dimensionless c’ Wall holdup parameter (equation 3-4), dimensionless C0 Distribution parameter in drift flux model, dimensionless C1 Weighted average drift velocity, m.s-1

CD Drag coefficient, dimensionless CV Volumetric solids loading (equation 2-3), dimensionless Cxx Autocorrelation function, dimensionless D Column diameter, m dB Bubble diameter, cm d’B Dimensionless bubble diameter, dimensionless DG Gas dispersion coefficient, m2.s-1

DL Liquid dispersion coefficient, m2.s-1

DP Coefficient of departure from Poisson distribution, dimensionless Drr Radial eddy diffusivity, m2.s-1

DR Ratio of gas and liquid phase densities, dimensionless Dzz Axial eddy diffusivity, m2.s-1

e Permittivity, F.m-1

Eo Etovos number, dimensionless f Frequency, Hz F(x) Fourier transform of x Frg Gas Froude number, dimensionless

xix

g Gravity constant, m.s-2

Hd Dynamic height, m HS Static height, m I Number of input nodes j drift flux, m.s-1

J Number of hidden layers k0 Pseudo-first order rate constant, s-1

kLa Volumetric mass transfer coefficient, s-1

K Turbulent kinetic energy, cm2.s-2

Number of output nodes L Column length, m Mo Morton number, dimensionless n Slope of gas holdup curve (equation 2-1), dimensionless Steepness parameter of gas holdup radial profile (equation 3-2), dimensionless n’ Steepness parameter of solids holdup radial profile (equation 3-4), dimensionless N Length of time series, dimensionless r Radial location in the column, m rk Relative permittivity, dimensionless R Cross-correlation coefficient Relative volumetric attenuation coefficient Re Reynolds number, dimensionless Sk Normalized output variable T length of time series, min u’i Fluctuation velocity in ith direction (i = r, θ, z) ub0 Terminal velocity of an isolated bubble, m.s-1

xx

UB∞ Terminal bubble rise velocity, m.s-1

UG Superficial gas velocity, m.s-1

UGtrans Superficial gas velocity at flow regime transition, m.s-1

Ui Normalized input variable UL Superficial liquid velocity, m.s-1

Ulb Large bubble rise velocity, m.s-1

umax Rise velocity of maximum stable bubble size, m.s-1

ur Solids radial velocity, m.s-1

recu Liquid recirculation velocity, m.s-1

Usb Small bubble rise velocity, m.s-1

uslip Slip velocity, m.s-1

uz Solids/liquid axial velocity, m.s-1

uθ Solids azimuthal velocity, m.s-1

Vb0 Bubble rise velocity at vanishingly small velocity, m.s-1

wij,wjk ANN fitting parameters Greek Letters −

Gε Cross-sectionally averaged gas holdup, dimensionless

transGε Overall gas hold up at transition point, dimensionless

Gε Overall gas hold up, dimensionless −

sε Cross-sectionally averaged solids holdup, dimensionless

sε Overall solids hold up, dimensionless

xxi

SLε Solids loading, dimensionless

ξ Constant (equation 2-17), dimensionless νeff Effective turbulent eddy viscosity, cm2.s-1

νBIT Turbulent eddy viscosity due to bubble-induced turbulence, cm2.s-1

νSIT Turbulent eddy viscosity due to shear-induced turbulence, cm2.s-1

νm Molecular viscosity, cm2.s-1

νS Solids loading, (% vol/ %vol), dimensionless

νSC Critical solids loading, (% vol/ %vol), dimensionless

μ Mean of a time-series, dimension of time-series

θ Phase angle of cross-spectral density function, rad σ Standard deviation of a time series, dimension of time-series

Surface tension, dyne.cm-1

τ Time lag, sec

β0 Drag interaction parameter, dimensionless βd Particle to liquid density ratio, dimensionless βu Drag interaction parameter, dimensionless

ρg Gas phase density, kg m-3

ρL Liquid phase density, kg m-3

ρS Solids phase density, kg m-3

ρSL Slurry phase density, kg m-3

σL Liquid surface tension, N m-1

μL Liquid viscosity, kg m-1 s-1

ϕxx Power spectral density function β Correction factor, dimensionless

xxii

τ Time lag, sec

Abbrevations

AARD Average Absolute Relative Difference AARE Average Absolute Relative Error ANN Artificial Neural Network ARD Absolute Relative Difference CARPT Computer Automated Radioactive Particle Tracking CFD Computational Fluid Dynamics CT Computed Tomography

DGD Dynamic Gas Disengagement ECT Electrical Capacitance Tomography FT Fischer-Tropsch GTL Gas-to-Liquids LDV Laser Doppler Velocimetry PBM Population Balance Model PDF Probability Density Function PIV Particle Image Velocimetry PSDF Power Spectral Density Function SDM Sedimentation Dispersion Model

xxiii

Acknowledgements First and foremost, thanks are due to the One God for His kindness and blessings, for

they sailed me through the ups and downs, and ecstasies and agonies during this time. It

is divinity we tend to believe in during such times, however, per JFK’s famous quote

“...here on earth, God's work must truly be our own”, for better or worse we tend to rely

on people around us. As I am writing this acknowledgement, I see a fine ray of hope of

getting some name to the work and efforts of these peak years of my youth and also feel a

sense of gratitude to all those who have influenced it in some or other way during these

years.

I express a deep sense of gratitude to my advisor, Prof. M. H. Al-Dahhan, for giving me

an opportunity to work on this project. I wish to thank him for his encouragement and

support throughout my doctoral work which helped me overcome many obstacles. The

load of enthusiasm and intensity he brings to the work is simply amazing. The times

spent helping him on different reports, presentations, and short courses on bubble

columns were unforgettable.

I would like to thank Prof. M. P. Dudukovic for his comments on some parts of my work

and for being on my committee. It was indeed an experience to see him working so

closely which was and will be useful in future. I am thankful to my committee members,

Prof. P. A. Ramachandran, Prof. John Kardos, Prof. R. A. Gardner, and Dr. Jiangping

Zhang (Chevron) for investing their time and providing valuable comments. I also want

to thank my thesis committee members Prof. Ramesh Agarwal and Dr. Ralph Goodwin

(ConocoPhillips, USA) for agreeing to be on my committee and investing their valuable

time on relatively short notice. Thanks to Prof. Ramachandran for teaching me as well as

discussing facets of multiphase reactor modeling and to Prof. Kardos for being supportive

during different stages.

I would like to acknowledge the financial support of the High Pressure Slurry Bubble

Column Reactor Consortium (HPSBRC) [ConocoPhillips, USA; EniTech, Italy; Sasol,

xxiv

South Africa; Statoil, Norway] and the U.S. Department of Energy-University Coal

Research (DOE-UCR) grant (DE-FG26-99FT40594) that made this work possible. The

interactions with scientists and engineers from these industries during bi-annual review

meetings were a rewarding experience. The discussions with Drs. Alex Vogel and

Bremann Berthold of Sasol and Christina Marretto of EniTech provided me much needed

industrial perspective on parts of my research. During these years, I worked on various

bubble column related projects of Syntroleum Corporation and Snamprogetti that

certainly helped in looking at things from different angles. For the sake of my fancy of

undergraduate days, I had gone through Fischer-Tropsch (FT) synthesis and in general

Gas-to-Liquid (GTL) literature, most of it made sense after those long discussions with

Dr. Steve LeViness from Schlumberger. The discussions with him were invaluable and

further enhanced my interest in the field of energy. Thanks to Dr. Kym Arcuri from

Syntroleum for those valuable suggestions and advice, they were timely and will

certainly be useful.

I wish to acknowledge Professor K. Krishnaiah of the Indian Institute of Technology

(IIT), Madras for encouraging me to pursue doctoral studies. His reaction engineering

classes and surprise tests were certainly an enjoyable and memorable experience during

IIT-days. I am also thankful to my masters research advisors Drs. Abhijit Deshpande and

Susy Varughese of IIT, Madras.

Apart from CREL’s abundant and high quality literature on bubble column reactors, I

immensely benefited from the works of Prof. J. B. Joshi of MUICT, Prof. R. Krishna of

University of Amsterdam, and Prof. L. S. Fan of OSU. Prof. Krishna’s creative

descriptions of complex phenomena have been always a pleasure to read.

I am thankful to Mr. Pat Harkins, Mr. Jim Linders, and Mr. John Krietler for helping me

in various technical issues and fabrication of equipments. The experience of Mr. Steve

Picker was useful, particularly during crunch times. Mr. Edward Lau and Mrs. Susan

Tucker (MIT Nuclear Reactor) were extremely helpful during irradiation of tracer

radioactive particles.

xxv

Numerous people at CREL were of immense help during these years. I thank Dr. Novica

Rados, with whom I started my research day-1 at CREL. He introduced me to CARPT,

CT, and experimental issues related to radioactive materials and bubble columns. I am

thankful to Dr. Muhammad Rafique for discussions on general research in multiphase

flows and also on different topics in my initial days. I am also thankful to Drs. Peter

Spicka and Stoyan Nedeltchev, who helped me understand various aspects of bubble

columns in the first year. The several useful discussions with Stoyan on regime transition

and chaos theory along with my own literature survey on regime transition convinced me

to work on flow regime transition in my thesis (although not using pressure fluctuations).

The long conversations with Dr. W. Warsito (OSU) on tomography were enlightening

and extremely useful. I wish to acknowledge Mr. Klass Koop for those daily insightful

discussions on hydrodynamics and mass transfer in bubble columns while we were

sharing an office. I am thankful to Mr. Lu Han and Mr. Chengtian Wu for helping me

during CARPT and other experimental work. Working together on the consortium project

with Novica, Lu, and Chengtian was an experience to remember. I am also thankful Dr.

Liu, a visiting scholar from China, and Mr. Saurabh Agarwala for being a timely help on

countless occasions when I was working late nights on CARPT/CT with Therminol LT. I

wish to acknowledge the help I received from Mr. Rajneesh Varma with a new CT setup

and experiments during joint work with OSU. I am thankful to Dr. Satish Bhusarapu for

his timely help at numerous occasions during my experimental work. The help I received

from Mr. Z. Kuzeljevic’ and Mr. S. Nayak during CT and CARPT experiments is highly

appreciated.

I wish to acknowledge the help of the secretaries of the Department of Chemical

Engineering in numerous administrative issues. I wish to thank Dr. Y. Yamashita for his

prompt help in computer and network related issues. The discussions on chaos theory,

symbolic dynamics, and S-statistics with Dr. Miryan Cassanello from University of

Buenous Aires were helpful in improving my knowledge regarding time-series analysis.

Thanks to Mr. Jim Ballard from the Engineering Technical Writing Center for going

through the manuscripts and helping to improve their language. Discussions with him on

nuances of technical English to various topics were amazing. I must also thank the

xxvi

personnel of InterLibraryLoan (ILL) services for providing the needed references on

time. Thanks to all those unknown faces behind Google and Wikipedia, for without them

my research life would not have been complete. However, I must mention that these were

not used as the scholarly references during this work.

During these years, I have made numerous friends who were of immense help time and

time and also made my stay enjoyable. Thanks to Dr. R. Ramaswamy for all those

agreements and disagreements over wide ranging issues during Sub-way lunches. I

assume they will continue. I wish to acknowledge all my roommates over these years

namely, Dennis Thomas, Keshav Ruthiya, Wisam Khudayar, and Ahmed Youssef. The

discussions with Keshav, ranging from the economy of chemical industries to economy

of India, to fancy business plans certainly diversified my interests. Thanks, Ahmed for

being a co-operative roommate during my last few months. Time spent with Ahmed and

Keshav was indeed a learning experience for me. I am thankful to many other people who

made a difference in one way or other: Shaibal, Pubs, Kartik, Subu, Karim, Mehul,,

Salim, Huping, Rajneesh, Radmila, Kaps, Saurabh, RC, DG, Ert, Nicola, Prashant.

Thanks to Abdul Rehman, Rehan, and Jaani for Eid dinners and to Chachi and Dr. Zakir

Sabry for making the environment during fasting far lighter and fun. I am thankful to

Jaani and Vikram for those weekend movie and biryani times in last years. Thanks to Mr.

Farhan Majid for discussing those lofty and fancy ideas related to economics.

I express a deep sense of gratitude to my parents and my younger sister for unconditional

support, patience, and belief in me. My father is my strength, and I forever appreciate the

courage of my mother in allowing her only son to go to the other side of the globe for

further education. In school days, out of guilt, I would pretend studying seeing my

younger sister studying so hard. I guess those times helped me when I actually started

studying. Words are just not enough to thank them. I owe everything that I have achieved

to them. I am thankful to my grandfathers and grandmothers, who, out of their affection

for my parents, wanted me to have some education. I wish to thank my Mumaani and

Mamu and also my other relatives for being a moral support to my family during these

years.

xxvii

Robert Frost ended his poem “Stopping by Woods on Snowy Evening” as,

The woods are lovely, dark and deep, But I have promises to keep, And miles to go before I sleep, And miles to go before I sleep.

As I end my walk through this portion of the woods and hope to enter a new one, I thank,

from the bottom of my heart, all those who directly and indirectly helped me over the

years during this journey.

Ashfaq Shaikh Washington University, St. Louis

xxviii

1

Chapter 1.

Introduction Bubble columns are two-phase gas-liquid systems in which a gas is dispersed through a

sparger and bubbles through a liquid in a vertical cylindrical column (Figure 1-1), with or

without internals. When suspended fine solids are present in liquid, they form a slurry

phase. Accordingly, they can be called either two-phase or three-phase (slurry) bubble

column. The liquid/slurry phase flow can be either co-current, counter-current, or in

batch mode with respect to the gas flow. The size of the solid particles ranges from 5 to

150 μm, with solids loading up to 50 % volume (Krishna et al., 1997). The gas phase

contains one or more reactants, while the liquid phase usually contains product and/or

reactants (or is sometimes inert). The solid particles are typically catalyst. In these

reactors, momentum is transferred from the faster, upward moving gas phase to the

slower liquid/slurry phase. Generally, the operating liquid superficial velocity (in the

range of 0 to 2 cm/s) is an order of magnitude smaller than the superficial gas velocity (1

to 50 cm/s). Hence, the hydrodynamics of such reactors are controlled mainly by the gas

flow.

Bubble columns offer numerous advantages such as good heat and mass transfer

characteristics, no moving parts and thus reduced wear and tear, higher catalyst

durability, ease of operation, and low operating and maintenance cost. One of the main

disadvantages of bubble column reactors is significant back-mixing, which can reduce

product conversion. The excessive back-mixing can be overcome by modifying the

design of bubble column reactors. Such modifications include the addition of internals,

baffles (Deckwer, 1991), or sieve plates (Maretto and Krishna, 2001). Bubble column

reactors have been used in chemical, petrochemical, biochemical, and pharmaceutical

industries for various processes (Carra and Morbidelli, 1987; Deckwer, 1992; Fan, 1989).

2

Solids

Sparger

.. . .

.

.

.

. .

..

.

.

Liquid

Liquid

Gas Inlet

Gas Outlet

Figure 1-1: Schematic diagram of bubble/slurry bubble column

Examples of such chemical and petrochemical processes are the partial oxidation of

ethylene to acetaldehyde, wet-air oxidation (Deckwer, 1992), liquid phase methanol

synthesis (LPMeOH), Fischer-Tropsch (FT) synthesis (Wender, 1996), and

hydrogenation of maleic acid (MAC). In biochemical industries, bubble columns are used

for cultivation of bacteria, cultivation of mold fungi, production of single cell proteins,

animal cell culture (Lehmann et al., 1978), and treatment of sewage (Diesterweg, 1978).

In metallurgical industries, they can be used for leaching of ores. The most popular

3

present day application of bubble columns is for energy conversion process where

‘stranded gas’ is converted to liquids. The popularity of such a conversion is a response

to the postulated future energy crisis.

Albert Einstein once wrote, “I never think of the future, it comes soon enough”. Einstein’s

convenient approach to the future is a luxury that is denied to governments and energy

companies. These days of global economy and increased energy demands, coupled with

complex international relationships and interdependence, demand an understanding of the

probable trends and the drivers for future energy use. Figure 1-2 shows the projected gap

between oil production and consumption in USA. Currently, North America imports 65

% of their crude oil. With the economic growth of China, India, and other developing

countries, the demand for oil in these countries has risen significantly. Currently, Asia

imports approximately 65 % of their crude oil, while Western Europe imports 55 % of its

crude oil (Koelmel, 2005). These countries depend on the oil producing countries to meet

their energy demands. With current scenarios, it is clear that such dependence possibly

makes an existence of their own and subsequently of other nations vulnerable.

Figure 1-2: Projected US energy and oil production and consumption [Source: National

Energy Policy, White House Report, 2001]

Figure 1-3 shows the vulnerability of the US to oil supply disruption. The percentage of

the vulnerability depends on the oil supply from ‘secure’ and ‘nonsecure’ sources.

4

Presently, US vulnerability is at its peak, and is higher than during the first and second

energy shocks (Williams and Alhajji, 2003). Such scenarios are the motivation to come

up with a solution to meet the future energy challenges. The energy business is

characterized by large-scale, long-term investment and there is an urgent need to

understand potential future energy solutions. Because the latter half of Albert Einstein’s

approach is not a luxury but a universal fact. It is said that the single biggest shift in

global demand for oil over the past decade has not been the rise of China but the rise of

SUVs (Zakaria, 2006). Hence, the solution to problems regarding energy demands a

multidimensional approach that involves politicians, policy makers, scientists,

technologists, and consumers of energy.

Figure 1-3: US vulnerability to oil disruption (Williams and AlHajji, 2003)

Shell geologist M. King Hubbert analyzed oil production utilizing the concept used by

population biologists to examine population growth. Hubbert (1956) predicted that US oil

production would peak in the early 1970s (Figure 1-4), which proved correct. He

predicted in 1969 that world oil production would peak around the year 2000, which is

supposedly also coming true (Deffeyes, 2004). In addition, the assessment of Simmons

(2005) of key oil fields in the world calls for heavy investment in alternative energy

5

strategies. Such strategies should give priority to proven technologies rather than those

still in initial stages.

(a) (b)

Figure 1-4: a) M. King Hubbert at the 1956 API Spring Meeting where he proposed the

peak theory b) Popular Hubbert-peak curve.

The development of Gas-to-Liquid (GTL) conversion provides one piece of a more

complex solution. The development of GTL worldwide today suggests that it has the

potential to supply 10 % of the global diesel fuel market within the next 15 years. The use

of GTL fuel, in addition to utilizing flared and stranded gas, can aid energy conservation.

US economies are dominated by petrol fuels and thus, spark ignition engines, which are

less efficient than diesel engines. As shown in Figure 1-5, compared to the conventional

refinery fuels, GTL fuel can improve transportation fuel economy and carbon dioxide

efficiency while also augmenting urban air quality benefits. Hence, the combination of

efficient engines and clean fuels allows economies to reduce fuel consumption, reduce

greenhouse emissions, and improve air quality (Koelmel, 2005).

While GTL is a marginally commercial proposition today, it is a proven technology

compared to most other alternative energy technologies such as hydrogen and biomass.

6

Figure 1-5: Relationship between fuel economy and urban air benefits (Koelmel, 2005)

Since Franz Fischer and Hans Tropsch developed the process to convert CO/H2 mixture

into hydrocarbons and oxygenated compounds back in 1922, the obvious question is why

was its potential not un-locked before now? The answer lies in the Capital Expenditure

cost (CAPEX) of the GTL process, which has remained above $ 20,000/per specific

barrel of installed GTL capacity. The early pioneers of this process, specifically Sasol,

built plants at more like $ 120,000/bpd. As shown in Figure 1-6, the current CAPEX

remains close to $ 25,000/bpd (Brown, 2003). However below $ 20,000/bpd, one can

reach a watershed where GTL becomes attractive. At this cost, the resource holders have

enough margin to compete with refinery products.

Figure 1-6: CAPEX cost for GTL (Rahmim, 2003).

7

An improvement in efficiency of the GTL industry can be realized through economies of

scale, reduced costs from technology improvements in all areas of the processes, and

process efficiency gains from de-bottlenecking (Koelmel, 2005). As far as multiphase

reaction engineering domain is concerned, the solution lies in improving catalyst

efficiency and economies of scale. Espinoza et al. (1999) recommended that an ideal

catalyst, apart from its high selectivity, should have the activity of cobalt and robustness

of iron towards changing conditions. As shown in Figure 1-7, an economy of scale

suggests that GTL can become economically viable if high capacity plants are built.

Figure 1-7: Projected economies of scale for GTL-FT process (Brown, 2003).

Based on Figure 1-7, it is clear that to reach below the $ 20,000/bpd mark from the

current level, the plant capacity need to be increased by at least double. The high capacity

plants will need efficient catalysts and, more importantly, larger reactors. The different

reactor configurations utilized for FT processes are divided into two types, depending

upon the types and quantities of FT products required.

1. High temperature FT (HTFT): This process, with an iron based catalyst and

temperature in a range of 300 – 3500 C, is used for production of gasoline and low

molecular weight olefin (C3 – C11). The reactors are circulating fluidized beds (CFBs)

and fixed fluidized beds (FFBs).

8

2. Low temperature FT (LTFT): This process, with either an iron or cobalt based

catalyst and temperature in a range of 200 – 2400 C, is used for the production of high

molecular weight linear waxes (> C20). The reactors are fixed beds and slurry bubble

columns.

The design of bubble columns has been considered for low temperature FT processes

since Kolbel’s pioneering work in 1950s. According to Krishna and Sie (2000), with the

present state of knowledge, it can be expected that a bubble column reactor may achieve

productivity a thousand times higher than that of the classical FT reactors (such as fixed

beds and multibed reactors) used in industry. However, there are considerable reactor

design and scale-up problems associated with such energy conversion processes

involving bubble columns. In order to achieve economically high space-time yields, a

high slurry concentration (typically 30 – 50 % vol) needs to be employed. To suspend

such a large amount of catalyst, a high energy input is needed, which can be provided by

high superficial gas velocities. The process operates under high-pressure conditions

(typically 10 – 80 bar). The high exothermic heat of reaction requires an efficient means

of heat removal that can operate in the churn-turbulent flow regime. Finally, the large gas

throughputs necessitate the use of large diameter reactors (typically 5 – 8 m), and to

obtain high conversion levels, large reactor heights, typically 20 – 30 m tall, are required.

Successful commercialization of bubble column reactors is crucially dependent on proper

understanding of their hydrodynamics and scale-up principles.

1-1 Motivation

Although bubble column reactors are simple in construction, proper design and scale-up

of such reactors require a thorough understanding of the prevailing hydrodynamic and

mixing characteristics at conditions similar to the targeted process. The hydrodynamics of

such reactors affect the mixing intensity and gas-liquid interfacial area, which affect the

transport coefficients, and hence the conversion and selectivity of the reactor.

Hydrodynamic behavior in a bubble column reactor is complex, since the fluid phases

involved are characterized by very different masses, and one is more compressible than

9

the other. Various design parameters (e.g., reactor geometry, internals, sparger design,

etc.) and operating variables (e.g., reactor pressure and temperature, gas and liquid/slurry

flow rates, catalyst size and loading, etc.) along with phase properties and kinetics, affect

the reactor hydrodynamic and transport rates in bubble/slurry bubble column reactors.

These, in turn, impact the reactor performance, operation, and its design and scale-up.

However, due to the complex interaction among the various phases, the flow field and

hydrodynamics of these reactors have not yet been well understood. In slurry bubble

column reactors, the ability to achieve complete catalyst suspension and the desired flow

pattern of the liquid/solid phase is critical to the targeted reactor performance.

Accordingly, in order to accomplish the desired flow pattern, an improved understanding

and quantification of the key hydrodynamic phenomena are required.

As mentioned earlier, industrial processes such as FT synthesis and liquid phase

methanol synthesis need to be carried out at high superficial gas velocity, high pressure,

high temperature, high catalyst loading, and in large diameter reactors. The literature

studies performed under such conditions are limited to global parameters such as overall

gas holdup and overall mass transfer coefficient (Wilkinson, 1991, Letzel, 1997).

Detailed studies of hydrodynamic parameters, such as phase holdup distribution and

velocity and turbulent parameter profiles, have been performed at high superficial gas

velocity and pressure only in air-water (Ong, 2003) and air-water-glass beads systems

(Rados, 2003) via advanced diagnostic techniques such as CT and CARPT. They found

that the effect of the sparger on hydrodynamics at high superficial gas velocities is

relatively insignificant. The pressure tends to increase the gas holdup and flatten gas

holdup radial profile. It was observed that an increase in pressure increases liquid

recirculation and reduces turbulent kinetic energy. In the literature, no work has been

reported regarding detailed hydrodynamic studies of slurry bubble columns at the

conditions of industrial interest. Such studies can be performed either by using a real

system or by mimicking the system of interest at laboratory operating conditions.

Therefore, the lack of hydrodynamic studies at the conditions of industrial interest

motivates the present work, which seeks to fill this gap by investigating the

hydrodynamics of a slurry bubble column using a liquid phase that at room temperature

10

mimics the FT synthetic wax at low temperature FT reaction conditions. In addition, such

work will be useful in gaining insight into the effect of physical properties on the flow

dynamics by comparing the findings with those obtained using air-water-glass beads

(Rados, 2003). The work will further extend the benchmark data for evaluation and

validation of Computational Fluid Dynamics (CFD) models and closures predictions.

The demarcation of the flow regime in bubble columns is an important task because

different hydrodynamic characteristics exist in different flow regimes, and result in

different mixing and heat and mass transfer. It is very possible that the laboratory column

may operate in a heterogeneous regime, while industrial columns, due to their high

operating pressure and temperature and large diameters, may operate in a homogeneous

regime under similar conditions. The current state of empirical correlations, semi-

analytical models, and analytical models to predict transition in bubble columns is not yet

complete (Shaikh and Al-Dahhan, 2007a). The experimental techniques used to measure

flow regime transition are either visual or probe based. Apart from being intrusive,

probing techniques provide only point information or hydrodynamic information at the

wall. In large diameter industrial scale columns, such hydrodynamic information

transmitted from large distances can be questionable. Also, the implementation of a

probing technique for flow regime transition requires modification of existing reactors

and/or shut-down of the operation. Therefore, this work attempts to develop and

demonstrate non-invasive techniques for flow regime transition identification and its

‘objective flow regime identifiers’ that can be implemented on industrial scale bubble

columns without disturbing the operation to pinpoint the flow regime at the reactor

operating conditions. Noninvasive techniques such as γ-ray CT and Nuclear Gauge

Densitometry (NGD) will be considered for this purpose. NGD is commercially available

and used widely in industries for liquid/slurry level monitoring and control. Hence, the

successful development and demonstration of these techniques can be utilized for online

flow regime monitoring in commercial as well as laboratory applications.

Extrapolating the behavior of laboratory scale columns to industrial scale columns is

always a difficult and challenging task. Because the dispersion and interfacial heat and

11

mass transfer fluxes, which often limit the chemical reaction rates (and in turn

conversion, selectivity, and yield), are closely related to hydrodynamics of the system

through the gas-liquid contact area and the turbulence properties of the flow, the scaleup

criteria need a reliable hydrodynamic similarity rule. The available scale up

methodologies for bubble columns depend on the similarity of overall gas holdup in the

two systems. It will be shown later that such an approach could be exclusively applicable

in bubbly flow, where gas holdup radial profiles are flat, but it cannot be extended to the

churn-turbulent regime, where parabolic profiles are present. Hence, the development of

a hydrodynamic similarity hypothesis in the regime of industrial interest motivates this

work to propose and evaluate a new methodology for scale up of bubble columns

operated in the churn-turbulent flow regime, with the aid of existing CT, CARPT, and

state-of-the-art modeling tool. An ideal choice of modeling tool for scaleup would be

CFD. However, due to the lack of universal closures, CFD has not yet been developed for

scaleup purposes. Hence, in this work, we have resorted to Artificial Neural Network

(ANN) correlations.

In summary, this work aims at advancing the state of knowledge of key hydrodynamic

parameters of bubble and slurry bubble column reactors at mimic industrial conditions. It

develops an experimental technique and flow regime identifiers for flow pattern

delineation that can be useful for online monitoring. Also, it proposes and demonstrates a

new scaleup methodology with the aid of state-of-the-art experimental and modeling

tools.

12

1-2 Objectives

The primary objective of the work is to improve the fundamental understanding of the

hydrodynamics of bubble/slurry bubble column reactors at industrially relevant

conditions. The specific goals of the work are as follows:

1-2.1 Hydrodynamic Parameters

• Study the hydrodynamic characteristics of a slurry bubble column reactor using a

liquid, which, at room temperature, mimics FT wax at FT reaction conditions.

Investigate the effects of liquid phase physical properties and solids loading on the

phase distribution via a single source γ-ray CT.

• Investigate the effects of liquid phase physical properties and solids loading on solids

axial velocity and turbulent parameters radial profile via CARPT.

1-2.2 Flow Regime Transition

This part of work includes the evaluation of single source γ-ray CT and NGD for

identification of regime transition. It comprises the following:

• Evaluate CT for flow regime delineation and propose its ‘flow regime identifiers’.

• Develop NGD for flow regime identification by analyzing obtained photon counts

history via various signal processing methods such as statistical analysis,

autocorrelation function analysis, and spectral analysis. The emphasis will be to study

the deviation of system behavior from a Poisson distribution and to develop “flow

regime identifiers”. This exercise will be useful for generalization of the proposed

‘flow regime identifiers’. A successful development and demonstration should lead to

the implementation of Nuclear Gauge Densitometry (NGD) as a tool for online flow

13

regime identification in industrial scale bubble/slurry bubble column reactors in

particular and multiphase flow systems in general.

1-2.3 Scale-up and hydrodynamic similarity

• Develop a scale-up methodology for bubble columns by proposing a hypothesis that

to be hydrodynamically similar, the two reactors should have the same overall gas

holdup and its radial profile or cross-sectional distribution. The development of the

scaleup methodology consists of two steps:

I. Experimental evaluation of the proposed hypothesis, using CT and CARPT.

II. Development of state-of-the-art correlations based on ANN for prediction of

the overall gas holdup, the radial profiles of the gas holdup and liquid axial

velocity, and the center-line liquid velocity using available database and

including the findings of this work. Development of such correlations will

facilitate implementation of the developed scaleup methodology by a priori

prediction of the needed hydrodynamic parameters.

1-3 Thesis Organization

A general review of mixing of liquid/solids phase, flow regime transition studies, and

available scaleup methodologies is provided in Chapter 2. The experimental studies

regarding flow behavior of slurry bubble column reactors are divided into two chapters

(Chapters 3 and 4). Chapter 3 provides the discussion on choice of fluid, experimental

setup, techniques used, and results related to the effect of operating parameters on phase

distribution. Chapter 4 discusses the effect of operating parameters on the solids axial

velocity and turbulent parameters at operating conditions similar to the studies in Chapter

3. The development of flow regime monitoring techniques and its flow regime identifiers

will be discussed in Chapter 5, while Chapter 6 presents the development of the new

scaleup methodology for hydrodynamic similarity and its experimental evaluation using

14

CT and CARPT. ANN correlations of the needed hydrodynamic parameters that can be

useful in implementing the developed scaleup methodology are presented in Appendix-F.

Chapter 7 provides the conclusions and recommendations, and outlines possible future

efforts.

15

Chapter 2. Literature Review

In this chapter, a literature review pertinent to this thesis is presented. It is divided into

three parts as per the structure of thesis mentioned in Chapter 1. In the first part, mixing

of liquid/slurry phase is briefly reviewed. The second part reviews flow regime transition

studies in bubble column. The detailed review on this subject has been submitted for

publication [Shaikh and Al-Dahhan (2007a). A Review on Flow Regime Transition in

Bubble Columns. Accepted in International Journal of Chemical Reactor Engineering].

The third part deals with scaleup studies in bubble column reactors. The detailed review

on this part [Shaikh and Al-Dahhan. (2007b) Scaleup of Bubble Column Reactors: A

Review of Current State of the Art] is being prepared and will be submitted for

publication.

2.1 Mixing and velocity profiles of liquid/slurry phase

Mixing and velocity profiles in two- and three-phase bubble columns have been reviewed

in detail by Ong (2003) and Rados (2003). In addition, Joshi et al. (1998) and Wild et al.

(2004) discussed mixing and velocity profiles in bubble columns in great detail, and

hence, these will not be repeated here.

Several studies have examined the hydrodynamics of bubble column reactors (Franz,

1984; Devanathan 1991; Yao, 1991; Degaleesan, 1997). These studies have been

performed at atmospheric pressure and/or at superficial gas velocities up to 15 cm/s.

Though high pressure operations are preferred operating conditions, very little is known

about the flow structure of bubble and slurry bubble columns at high pressure.

Information available at high pressure is limited mainly to global parameters such as

overall gas holdup, and overall mass transfer coefficient. There have been few efforts to

study mixing in bubble columns at high pressure.

16

Yang and Fan (2003) measured the axial dispersion coefficient in bubble columns using

the thermal dispersion technique at operating pressures up to 10.3 MPa and superficial

gas velocities upto 40 cm/s. The axial dispersion coefficient increases with an increase in

superficial gas velocity and decreases with an increase in pressure. Axial dispersion was

found to increase with liquid velocity due to enhanced liquid phase turbulence. The

scaleup effect on liquid mixing reduces as the operating pressure increases. Wei et al.

(2003) investigated local bubble behavior using an optical fiber probe in different column

diameters (20, 40, and 80 cm). They confirmed the presence of a coherent gross

circulation structure spanning the entire column diameter in the larger column rather than

a pair of symmetrical circulation cells.

Cui and Fan (2004) applied Laser Doppler Velocimetry (LDV) and Particle Image

Velocimetry (PIV) techniques to measure turbulent properties in two- and three-phase

bubble columns and fluidized beds. They have performed experiments up to 7.5 cm/s of

superficial gas velocity. Bubble induced turbulence was found to be dominant in

turbulence generation under the studied operating conditions. They found that the effect

of solids on the turbulence in the liquid phase is complex and depends upon the solids

properties and superficial gas velocity. They proposed a criterion based on, local gas

velocity/minimum fluidization velocity, to account for the effect of solid particles on

turbulence in the liquid phase in three-phase fluidized beds.

Pohorecki et al. (2001) performed experimental studies in a nitrogen-cyclohexane system

to investigate the hydrodynamics in a pilot plant bubble column at high pressure (up to

1.1 MPa) and high temperature (up to 1600 C). They found that the current state of

prediction of hydrodynamics gives highly divergent results when applied to conditions of

industrial interest.

The only studies that have investigated detailed hydrodynamics at high superficial gas

velocity and operating pressure, in terms of instantaneous and time averaged velocity,

turbulent parameters profiles, and time averaged phase holdup distributions have been

performed by Ong (2003) and Rados (2003). They utilized advanced diagnostic

17

techniques such as CARPT and CT to study the effect of superficial gas velocity,

operating pressure, and sparger design on the bubble column hydrodynamics using air-

water and air-water-150 μm glass beads. In general, some of their significant findings are:

i) At atmospheric pressure, the effect of distributor was observed even at

superficial gas velocity of 14 cm/s, although the flow is generally be

considered in churn-turbulent flow at this gas velocity.

ii) Gas holdup in churn-turbulent flow increases with an increase in pressure and

radial profile of gas holdup becomes flatter with an increase in pressure.

iii) The strength of axial liquid recirculation increases with both increase in

superficial gas velocity and pressure which is directly related to gas holdup

and its radial profile which increases with these parameters.

iv) At ambient pressure, the liquid recirculation was independent of type of

distributor at Ug = 30 cm/s. However, differences were observed in turbulent

quantities with cross-sparger exhibiting higher turbulent kinetic energy

compared perforated plate distributors.

v) At P = 0.4 MPa, the effect of distributor on liquid recirculation was found to

be insignificant.

vi) While liquid recirulcation increases with an increase in pressure, turbulent

kinetic energy and eddy diffusivities were found to decrease.

vii) The contribution of bubble induced turbulence to eddy viscosity was found to

be less than 10 %.

viii) An addition of solids, in general, tends to decrease gas holdup. However, an

addition of solids from 0 to 9.1 % vol. does not appear to have significant

effect on gas holdup and liquid axial velocity profile.

There is little known about the turbulent characteristics in three phase systems. Except for

Rados (2003) and Cui and Fan (2004), no studies have investigated the turbulent

characteristics of three dynamic phase flow. Cui and Fan (2004) performed their studies

in a two dimensional bubble column and at low superficial gas velocities up to 7.5 cm/s.

Although Rados (2003) has studied the turbulent behavior of slurry bubble columns at

18

high superficial gas velocity and high pressure, his studies are limited only to water as the

liquid phase. Hence, it is necessary to study the effect of physical properties on the

detailed flow behavior in such systems as the industrial systems consists of liquid phases

that has properties vastly different than water. It is important to know whether using the

liquid other than water will affect the trend and/or the magnitude of flow behavior.

In addition, Rados (2003) studies were conducted at relatively low solids loading (9.1 %

vol.) and have not investigated the effect of solids loading on hydrodynamic

characteristics of slurry bubble columns. The effect of solids loading is of particular

interest because the flow behavior of solids that are used as catalyst in industrial

processes will have significant effect on the performance of slurry bubble column

reactors. Such investigations will be extremely useful in determining the optimum

amount of catalyst for maximum reactor performance. Hence the brief review shows that,

there is a need to study the effect of physical properties and solids loading on

hydrodynamic characteristics of bubble/slurry bubble column reactors.

Also, as shown by Pohorecki et al. (2001) hydrodynamics at conditions of industrial

interest may show different behavior than at laboratory conditions. Therefore, one needs

to know in detail the fluid dynamics and mixing characteristics at the conditions of

industrial interest. This can be achieved either by performing experiments at the

industrial conditions using the real system or by mimicking the industrial system at

laboratory operating conditions. With the limitations encountered in laboratory studies,

the later option is more attractive. Such an option needs to be utilized to study the

hydrodynamic behavior of bubble column reactors.

2.2 Flow Regime Transition Due to varied flow behavior, the demarcation of hydrodynamic flow regimes is an

important task in the design and scaleup of bubble column reactors. This section reviews

the studies performed for flow regime identification in bubble columns. The detailed

review article dealing with flow regime transition studies in bubble column has been

accepted for publication [Shaikh and Al-Dahhan (2007a). A Review on Flow Regime

19

Transition in Bubble Columns. accepted International Journal of Chemical Reactor

Engineering]. Hence, it is briefly reviewed in the following sections.

2.2.1 Flow Regime Types and Characteristics

In bubble columns, four types of flow patterns have been observed, viz., homogeneous

(bubbly), heterogeneous (churn-turbulent), slug, and annular flow. Researchers have

reported the occurrence of a slug flow regime only in small diameter columns. In these

different flow regimes, the interaction of the dispersed gas phase with the continuous

liquid phase varies considerably. Figure 2-1 shows the various flow regimes in bubble

columns. However, bubbly and churn-turbulent flow regimes are most frequently

encountered. Depending upon the operating conditions, these two regimes can be

separated by a transition regime.

The homogeneous flow regime generally occurs at low to moderate superficial gas

velocities. It is characterized by uniformly sized small bubbles traveling vertically with

minor transverse and axial oscillations. There is practically no coalescence and break-up,

hence there is a narrow bubble size distribution. The gas holdup distribution is radially

uniform; therefore bulk liquid circulation is insignificant. The size of the bubbles depends

mainly on the nature of the gas distribution and the physical properties of the liquid.

Heterogeneous flow occurs at high gas superficial velocities. Due to intense coalescence

and break-up, small as well large bubbles appear in this regime, leading to wide bubble

size distribution. The large bubbles churn through the liquid, and thus, it is called as

churn-turbulent flow. The non-uniform gas holdup distribution across the radial direction

causes bulk liquid circulation in this flow regime.

20

Figure 2-1: Various flow regimes in bubble column reactors

As one can see, homogeneous and heterogeneous flow regimes have entirely different

hydrodynamic characteristics. Such different hydrodynamic characteristics result in

different mixing as well as heat and mass transfer rates in these flow regimes. Therefore,

the demarcation of flow regimes becomes an important task in the design and scale up of

such reactors and has led to considerable research efforts which have resulted into

various experimental methods and empirical, semi-empirical, and mechanistic models to

identify flow regime transition.

The flow regime transition from bubbly to churn-turbulent flow or from churn-turbulent

to slug flow depends simultaneously on parameters such as superficial gas velocity,

column diameter, liquid and gas phase properties, and distributor design (Urseanu, 2000).

No flow regime map is available that covers a wide range of industrial conditions. Figure

2-2a shows one of the few approximate flow regime maps of transition velocity versus

column diameter that distinguishes among bubbly, transition, churn-turbulent, and slug

flow (Shah et al., 1982). However, it is limited to low viscosity systems at ambient

conditions. Figure 2-2b shows another flow regime map of superficial gas velocity versus

superficial liquid velocity which distinguishes discrete bubble, dispersed bubble, slug,

churn, bridging, and annular flow (Zhang et al., 1997). This map was proposed based on

data collected using air-water system at ambient conditions in a small diameter column

(0.0826 m).

21

(a)

(b)

Figure 2-2: Flow regime map for air-water system at ambient pressure a) Shah et al.,

1982 and b) Zhang et al., 1997.

2.2.2 Methods for Flow Regime Identification

The experimental methods used for regime transition identification can be broadly

classified in the following groups:

• Visual observation

• Evolution of global hydrodynamic parameter

• Temporal signatures of quantity related to hydrodynamics

• Advanced measurement techniques

22

Visual Observation

Visual observation is the simplest method to study the flow pattern in bubble columns.

The slow, vertically rising bubbles can be observed in the homogeneous regime.

However, in the heterogeneous regime there is an intense interaction of bubbles, leading

to gross circulation (Figure 2-3). It is difficult to pinpoint the exact transition velocity by

visual observation. Moreover, this method can be useful only when the column is

transparent.

Figure 2-3: Photographs of bubbly and churn-turbulent flow in 2-D column

Evolution of global hydrodynamic parameter

Because the global hydrodynamic parameters are manifestations of the prevailing flow

patterns, they vary with the regimes. This fact has generally been utilized to identify flow

regime transition point. Typically, the global hydrodynamics have been quantified based

on overall gas holdup. The relationship between overall gas holdup and superficial gas

velocity can be expressed as

Gε α . (2-1) nGU

The overall gas holdup increases with an increase in superficial gas velocity. As can be

seen in Figure 2-4a (Shaikh and Al-Dahhan, 2005), the relationship between overall gas

holdup and superficial gas velocity varies over a range of velocities. The relationship is

almost linear (n ~ 0.8-1) at low gas velocities, but with an intense non-linear interaction

of bubbles at high gas velocities, the relationship between overall gas holdup and

superficial gas velocity deviates from linearity. The value of n is less than 1 (n ~ 0.4 –

0.6). Hence, the change in slope of the gas holdup curve can be identified as a regime

23

transition point. Sometimes, gas holdup shows an S-shaped curve, depending upon

operating and design conditions (Figure2-4b) [Rados, 2003]. In such cases, the superficial

gas velocity at which maximum gas holdup has been attained is identified as the

transition velocity.

0 10 20 300

0.1

0.2

0.3

0.4

0.5

Superficial gas velocity (cm/s)

Cro

ss-s

ectio

nal g

as h

oldu

p

(a) (b)

Figure 2-4: Typical overall gas holdup curve a) Shaikh and Al-Dahhan, 2005; and b)

Rados, 2003.

However, when the change in slope is gradual or the gas holdup curve does not show a

maximum in gas holdup, it is difficult to identify the transition point. In such cases, the

drift flux method proposed by Wallis (1969) has been used extensively.

In this method, the drift flux, jGL (the volumetric flux of either phase relative to a surface

moving at the volumetric average velocity) is plotted against the superficial gas velocity,

UG. The drift flux velocity is given by:

(1 )GL G G L Gj U Uε ε= − ± , …(2-2)

where εG is gas holdup and UL is superficial liquid velocity. The positive or negative sign

indicates counter-current or co-current flow of liquid relative to the gas phase,

respectively. Figure 2-5 shows a typical plot of the drift flux versus gas holdup. The

change in the slope of the curve represents the transition from homogeneous to

24

heterogeneous flow. The change in slope of the drift flux plot is generally sharper than

the change in slope of gas holdup curve.

Figure 2-5: Typical drift flux plot using Wallis (1969) apporach (Deckwer et al., 1981)

Temporal signatures of quantity related to hydrodynamics

The global parameters represent macroscopic phenomena that are result of prevailing

microscopic phenomena. Several attempts have been made to capture the instantaneous

flow behavior through an energetic parameter.

The following temporal signatures have been utilized for flow regime transition:

- Pressure fluctuations [Nishikawa, 1969; Matsui, 1984; Drahos et al., 1991; Letzel

et al., 1997; Vial et al., 2001, Park and Kim, 2003]

- Local holdup fluctuations using resistive or optical probes [Bakshi et al., 1995;

Briens et al., 1997]

- Temperature fluctuations using a heat transfer probe [Thimmapuram et al., 1991]

- Local bubble frequency measured using an optical transmittance probe [Kikuchi

et al., 1997]

- Conductivity probe [Zhang et al., 1997]

- Sound fluctuations using an acoustic probe [Holler et al., 2003; Al-Masry, 2004]

25

Various time-series analyses have been used to interpret the fluctuations of these

parameters and to identify flow regimes and their transition. The commonly used time-

series analyses are statistical analysis, autocorrelation analysis, stochastic modeling,

spectral analysis, chaos analysis, and wavelet analysis.

Amongst these techniques, pressure fluctuations are supposed to be an attractive option.

However, the relationship between pressure and flow structure is not straightforward.

Although in gas-solid flows pressure fluctuations are mainly due to bubbles, in gas-liquid

flows more complex phenomena exist as shown by Drahos et al. (1991) and Letzel et al.

(1997). Hence, these fluctuations need careful analysis when applying novel time-series

techniques to interpret the data.

Advanced measurement techniques

With advances in measurement techniques, various imaging and velocimetric techniques

have been used in flow regime transition studies.

- Particle Image Velocimetry (PIV) [Chen et al., 1994; Lin et al., 1996]

- Electrical Capacitance Tomography (ECT) [Bennett et al., 1999]

- Electrical Resistance Tomography (ERT) [Dong et al., 2001; Murugaian et al.,

2005]

- Laser Doppler Anemometry (LDA) [Olmos et al., 2003]

- Computer Automated Radioactive Particle Tracking (CARPT) [Cassanello et al.,

2001; Nedeltchev et al., 2003]

Although the implementation of advanced measurement techniques is relatively difficult,

they provide detailed flow information and are useful in understanding prevailing

phenomena.

Table summarizing most of the flow regime transition studies along with operating and

design conditions and significant remarks is provided in Shaikh and Al-Dahhan (2007a).

26

The details of few important studies as well as the effects of operating and design

parameters can be found in Shaikh and Al-Dahhan (2007a).

2.2.3 Prediction of Flow Regime Transition The objectives of the experimental studies, apart from achieving a fundamental

understanding of the prevailing phenomena, are to evaluate theoretical criteria. To design

bubble column reactors, one needs to know ‘a priori’ the prevailing flow regime at the

design and operating conditions. Predictions of flow regime transition have been

achieved by the development of various models and approaches that include pure

empirical correlations, semi- empirical and phenomenological (or mechanistic) models,

linear stability theory, and Computational Fluid Dynamics (CFD). The brief discussion

on this topic can be found in Shaikh and Al-Dahhan (2007a).

2.2.4 Remarks

The methods to determine regime transition have progressed from visual observation, to

the measurement of time-averaged global hydrodynamic parameters, to more quantitative

analysis based on examination of temporal signatures related to hydrodynamics. Various

linear and non-linear time-series techniques have been applied to the temporal signatures.

The simpler techniques, such as statistical analysis, spectral analysis, do identify the flow

regime transition point. Advanced non-linear techniques such as chaos analysis,

stochastic modeling, and multiresolution analyses provide tools to extract additional

features of the flow, apart from regime transition. However, these techniques can be

computationally intensive. Hence, the choice of time-series techniques appears to be a

compromise between what and how fast the information is needed. In this regard, the

comments made by Drahos (2003) need consideration.

Shaikh and Al-Dahhan (2007a) showed that empirical correlations exhibit large

discrepancies in their predictions at the same operating and design conditions. All of

these studies calculated transition velocities from the gas holdup curve, however, the

method of treatment to predict transition point from gas holdup curve differs in each case.

27

The prediction of transition using stability theory and CFD still needs substantial

improvement.

Energy conversion processes such as Fischer-Tropsch synthesis and methanol synthesis

operate in large diameter columns at high temperature, pressure, and solids loading.

Increased diameter, pressure, temperature (and thereby reduced viscosity) increases the

transition velocity, while solids loading reduces the transition velocity. Therefore,

experiments performed in lab scale columns and operating conditions (i.e., using air-

water system or conditions of no interest to industry) may be very much in the

heterogeneous regime, but quite possibly that in the homogeneous regime in industrial

columns. The state-of-the-art of empirical correlation, stability theory and CFD is not yet

sophisticated enough to a priori predict transition velocities in real systems. Hence, the

only option remains is to measure the transition velocity using a reliable experimental

technique. As discussed above, the available experimental techniques are based on either

visual observation or are probe based. Visual observation is often not possible due to the

opaque nature of the flows in bubble columns while probe based techniques are intrusive

and can provide unreliable hydrodynamic information in large diameter industrial scale

columns. By using probes flush to the wall, some researchers claim the probing

techniques to be non-invasive. However, in large diameter columns, one can not be sure

that fluctuations transmitted over great distances up to the wall can represent the

underlying hydrodynamics with fidelity. In addition, the probe-based techniques provide

point information that may not necessarily describe hydrodynamic information across

that cross-section. Also, Ellis et al. (2004) have shown that the probe dimensions can

influence the obtained hydrodynamic information and subsequently its interpretation. To

diagnose the flow in an industrial reactor which is in operation, probing techniques

require modification in the reactor and also shut-down of the operation to implement it,

which is not economical. Therefore, there is a need to develop a technique that is

noninvasive, can be easily implemented on an industrial scale without disturbing the

operation, and can provide hydrodynamic information that is reliable in lab scale and

industrial scale reactors.

28

2.3 Scaleup of Bubble Column Reactors

The following is a brief review of the current state of the scale up of bubble column

reactors reported in literature. The detailed review regarding this topic [Shaikh and Al-

Dahhan. (2007b) Scaleup of Bubble Column Reactors: A Review of Current State of the

Art] will be submitted for publication and hence is briefly reviewed here.

2.3.1 Reported status of scaleup in literature

Wilkinson et al. (1992)

Wilkinson et al. (1992) performed experiments for scaleup purposes in two different

column diameters (15 and 23 cm) at operating pressures varying between 0.1 to 2 MPa

using three different liquids. Based on these experimental observations, they proposed

criteria for scaleup of high pressure bubble column reactors. It was argued that, the gas

holdup is virtually independent of the column dimensions and the sparger layout (for low

as well as high pressures) provided following criteria are fulfilled:

1) The column diameter has to be larger than 15 cm.

2) The column height to diameter ratio has to be in excess of 5.

3) The hole diameter of the sparger has to be larger than 1-2 mm.A correlation was

proposed based on their own and literature data that accounts the effect of gas density

and incorporates the flow regime transition.

A correlation was proposed for overall gas holdup based on their own and literature data

that accounts the effect of gas density and incorporates the flow regime transition.

Wilkinson et al. (1991) recommended using this correlation for scaleup purposes.

29

Degaleesan (1997)

Degaleesan (1997) proposed a scaleup method that was based on the assumption that any

gas-liquid/slurry would exhibit the similar hydrodynamic behavior as air-water system if

both the systems have the same overall gas holdup. The procedure involves measuring (or

evaluating based on the suitable correlation) the overall gas holdup in scaled up unit at its

operating conditions and then calculating the equivalent superficial gas velocity, uGe that

results in the same overall gas holdup in an atmospheric air-water system as in the scaled

up unit. Hence, it was suggested that hydrodynamics and mixing at the equivalent

superficial gas velocity, uGe in an atmospheric air-water system would represent the

hydrodynamics and mixing in scaled up unit. The value of uGe can then be used to predict

recirculation velocity and other turbulent parameters using correlations proposed based

on CARPT data in an air-water system. The liquid velocity profile has been estimated

using a 1-D model (Kumar, 1994), with a known mean recirculation velocity and gas

holdup radial profile.

Degaleesan (1997) developed a two-dimensional convection-diffusion model for liquid

mixing to interpret the tracer response in 18-inch diameter slurry bubble column reactor

for liquid phase methanol synthesis at La Porte, Texas. The convection-diffusion model

needs knowledge of liquid axial velocity profile, eddy diffusivities profile, and gas

holdup profile to predict the tracer responses. The available fluid dynamic measurements

in industrial unit were gas holdup radial profile measured using Nuclear Gauge

Densitometry (NGD). The liquid axial velocity profile and eddy diffusivities profile were

not available in industrial scale unit at reaction conditions. The experimental

measurements of these fluid dynamic parameters were available only in laboratory scale

bubble column (diameter = 14, 19, 44 cm) at ambient conditions in air-water system.

Degaleesan (1997) developed scaling rules to extrapolate available laboratory scale data

to industrial unit, to predict the needed fluid dynamic parameters,

It provides a systematic approach to characterize recirculation and mixing in an industrial

scale bubble column using an atmospheric air-water data. However, similarity based on

30

only overall gas holdup may not be sufficient. This method needs a priori knowledge of

gas holdup and its distribution.

Inga and Morsi (1998)

Inga and Morsi (1998) have demonstrated their scaleup/scaledown methodology for FT

synthesis where it was shown that how the experimental results obtained in laboratory

scale stirred tank reactor could be extrapolated to design industrial scale slurry bubble

column. It is based on similarity of the relative importance of mass transfer resistance in

the overall reaction resistances, defined in terms of a dimensionless parameter, βi which

represents the balance between kLa (mass transfer coefficient) and k0 (rate of

consumption, pseudo kinetic constant for first order). Accordingly, maintaining the same

β in two reactors will result in the same reactant concentration and catalyst activity and

thereby the conversion and selectivity in two reactors.

Inga and Morsi (1998) demonstrated their proposed method for FT synthesis using a

laboratory scale 4-litre stirred tank reactor operating at 20 Hz and 5 % wt which was

simulated to a conceptual industrial scale slurry bubble column reactor. The conceptual

slurry bubble column reactor with 7 m diameter and 30 m height operating at 30 bars,

523 K and 20 cm/s was modeled using Axial Dispersion Model (ADM). The simulations

were performed to maintain similar βi as in stirred tank reactor. The authors found the

same productivity in both the reactors when the values of βi were the same.

The method proposed by these authors shows that, maintaining relative contribution of

transport parameter the same in two systems results into the same performance even if

one system is impeller-agitated (CSTR) and the other one is gas-agitated (slurry bubble

column). Although Inga and Morsi (1998) procedure combines transport and reaction

kinetics, the use of overall mass transfer coefficient is not enough to describe the mixing

as it represents global transport parameter. The authors described phase mixing using

ADM that needs reliable prediction of axial dispersion coefficient in both gas and slurry

phase.

31

Fan et al. (1999)

Fan et al. (1999) proposed a criterion for hydrodynamic similarity in bubble and slurry

bubble columns based on the overall gas holdup. Using the vast range of data collected

from literature and their own data, an empirical correlation was proposed to estimate the

gas holdup in terms of three dimensionless numbers,

4

0.054 0.41

2.9( ) ( )

(1 ) [cosh( )]

G G G

G L L

G SL

ug

Mo

α βρ ρε σ ρε

=−

…(2-3)

where,

0.0079 0.0110.21 ; 0.096SL SLMo Moα β −= =

4

2 3

( )(SL G LSL

SL L

gMo ρ ρ ξμρ σ−

=)

+0.58 0.22ln( ) 4.6 {5.7 sinh[ 0.71exp( 5.8 ) ln ] 1}V V VC C C Moξ = − −

It was argued that maintaining these numbers the same in two systems would lead to

similar overall gas holdup and hence mixing and hydrodynamics. However, this proposed

similarity rule has not been evaluated experimentally. The suggested dimensionless

numbers does not account the effect of column diameter on gas holdup. The reason for

not accounting column diameter lies in the reported studies which found that, above 15

cm, column diameter has negligible effect on overall gas holdup. However, such studies

were performed mostly but not exclusively in air-water system. Recently, van Baten and

Krishna (2004) reported that, in concentrated slurries such an observation does not quiet

hold. Additionally, similarity criteria based only on overall gas holdup may not be

sufficient in churn-turbulent flow regime.

32

Safonuik et al. (1999) and Macchi et al. (2001)

Safonuik et al. (1999) presented a scale-up method for three phase fluidized beds with the

aid of the Buckingham pi theorem, which yielded five dimensionless numbers that have a

profound effect on overall gas holdup. These dimensionless groups are Morton number,

Mo; Etovos number, Eo; Reynolds number, Re; Density ratio; Superficial gas and liquid

velocity ratio.The methodology was evaluated by maintaining these dimensionless groups

the same in 0.91 m (hydrogen-kerosene-ceramic particles) and 0.0826 m (air-magnesium

sulphate solution-cylindrical alumina particles) diameter columns. Whenever the

dimensionless numbers were close in these systems, the dimensionless hydrodynamic

parameter, viz., overall gas holdup was found to be close to each other.

Later, Macchi et al. (2001) have tested the scaling approach of Safounik et al. (1999) in

three phase fluidized beds where the liquid phase was an aqueous solution of glycerol (a

liquid mixture) in one column and silicone oil (a pure liquid) in the other. The

experiments were performed in an acrylic column of 0.127 m diameter and 2.58 m long.

It was observed that, whenever five dimensionless numbers were the same in these

systems, the overall gas holdups were within 11 % of root mean standard deviations.

Hence, it provided a reasonable basis for hydrodynamic similarity in two systems.

However, the pressure fluctuations studies revealed that the power spectra in the two

systems are different. Macchi et al. (2001) concluded that, the mismatch is likely due to

the difference between coalescence in monocomponent and multicomponent liquid that

results into different bubble distribution. Hence, they suggested that more than five

dimensionless groups are needed to fully characterize the system.

Krishna et al. (2001)

Krishna et al. (2001) developed a strategy for scaling laboratory reactors to commercial

ones based on the fundamental understanding of hydrodynamics. The developed

understanding in terms of correlations of various hydrodynamic parameters was

33

incorporated into Computational Fluid Dynamics (CFD) to design commercial size

bubble column reactor.

Based on Dynamic Gas Disengagement (DGD) experiments in different systems and

different column diameters, they proposed correlations to predict bubble diameter, rise

velocity, and small and large bubble holdups. These models have been incorporated into

a fundamental model based on CFD in an Eulerian framework. The overall gas holdup

and velocity profiles predicted from CFD were compared to experimental values for three

different column diameters and found to be in a good agreement. Based on this

confirmation, they studied hydrodynamics in a 6 m diameter bubble column using CFD.

However, no comparison of CFD predictions with experimental data was shown at these

conditions.

The correlations for prediction of bubble diameter, rise velocity, and holdups were

developed based on Dynamic Gas Disengagement (DGD) studies. These reported studies

suggest that, the small bubble holdup remains constant in heterogeneous flow regime.

However, Jordan et al. (2003) performed DGD experiments at atmospheric as well as

high pressure and analyzed the obtained results using independent disengagement,

sequential disengagement, and constant slip velocity assumptions. In contradiction to

previous findings, they observed that, the small bubble holdup increases with an increase

in superficial gas velocity. In addition, Xue (2004) studied bubble dynamics in air-water

system at atmospheric and high pressure using newly developed four point optical probe

and found that small bubble holdup increases with an increase in superficial gas velocity.

In addition, Lee et al. (1999) studied the assumptions of DGD technique in two-

dimensional bubble column and slurry bubble column with the help of Particle Image

Velocimetry (PIV). They found that the assumptions in DGD that there is no bubble-

bubble coalescence and breakup during disengagement and disengagement of bubble

classes are not affected by each other are not valid particularly in heterogeneous regime.

However, such limitations shown by Lee et al. (1999) have to be checked in three-

dimensional bubble column.

34

van Baten et al. (2003)

van Baten et al. (2003) proposed a new method for scale up of bubble columns where

they have demonstrated how the hydrodynamic behavior in 1 m. diameter column can be

estimated using the experimental data in 5.1 cm diameter column. They developed a

procedure to study the flow behavior in commercial scale bubble columns based on CFD

in Eulerian framework by considering only momentum exchange term. A method was

devised to replace the need for closure equation that may mar the predictions of CFD.

The drag coefficient and bubble diameter were calculated utilizing only overall gas

holdup data in small diameter column (5.1 cm).

van Baten et al. (2003) developed a CFD model in Eulerian framework for three phase

system (16.4 % wt. solids loading) assuming pseudo-homogeneity. Based on the work of

Sanyal et al. (1999) and Sokolichin and Eigenberger (1999), the added mass and lift force

terms were neglected. The momentum exchange term was written following the work of

Pan et al. (1999) as,

( ) LGLGLGLb

DGL uuuu

dC

M −−= εερ ]43[, …(2-4)

For a bubble swarm rising in a gravitational field, drag force balances the difference

between weight and buoyancy so that the bracketed term in equation 2-4 can be

substituted as,

20,

1)(43

bGLL

b

D

Vg

dC

ρρρ −= …(2-5)

where, Vb,0 is the rise velocity of bubble swarms at low superficial gas velocities.

Equation 2-5 clearly shows that, the knowledge of the bubble rise velocity in infinite

volume of liquid is the only unknown parameter in the model. The authors proposed a

following method to calculate bubble rise velocity

35

G

i) Perform overall gas holdup experiments in small diameter column (5.1 cm, in

current case).

ii) Calculate average bubble swarm velocity, Vb as

/b GV u ε= ..(2-6)

iii) Plot average bubble swarm velocity, Vb versus superficial gas velocity (Figure 2-

6).

iv) Extrapolate Vb data to low superficial gas velocity as shown in Figure 2-6.

v) The value of bubble swarm velocity at vanishingly small superficial gas velocity

is Vb,0. Substitute this value in equation 2-5.

This way, one does not need to know the bubble size in the momentum exchange term to

predict drag coefficient. The overall gas holdups predicted from CFD along with the

developed approach was compared to the one obtained from experiments and were found

to be in a good agreement. Based on this comparison, van Baten et al. (2003) estimated

the behavior of 1 m diameter bubble column.

The authors proposed an elegant approach and it appears to be promising and robust to

study and design the flow behavior in large diameter bubble columns, as it does not

require a priori knowledge of bubble diameter and also it does not need drag force

coefficient closure. The only knowledge needed is simple overall gas holdup

Figure 2-6: Average bubble-swarm velocity in air-ethanol-Co (van Baten et al., 2003)

36

experimental data in laboratory scale column. However, the validation of CFD simulation

results with experiments in large diameter columns need to be established. This method

can be applicable in cases where the bubble size does not increase significantly with

superficial gas velocity. Vermeer and Krishna (1981) showed that, ratio of kLa / εG is

constant (~ 0.5) in churn-turbulent flow regime in air-Turpentine 5 system. Godbole et al.

(1984) reached the similar conclusions in air-water and air-Soltrol -130 systems. Vandu

and Krishna (2004) also found the similar results in three different diameter columns (10,

15, and 38 cm) using air-water system and concluded that the constant value of ratio of

kLa / εG is due to the fact that the effective bubble diameter is independent of superficial

gas velocity. Based on these findings, van Baten and Krishna (2004) rationalized the

application of the developed approach for scaleup of bubble columns. Recently, Chaumat

et al. (2005) developed a gas tracer technique to study Residence Time Distribution

(RTD) and mass transfer in 0.2 m diameter and 1.6 m long bubble column. Various gases

(nitrogen, carbon dioxide) and liquids (water, cyclohexane) were used at ambient

pressure. However, they concluded that, the relation between mass transfer and

hydrodynamics appears to be more complex than simplified linear relation. In the light of

conflicting results, such an approach may need to be revisited.

Zhang and Zhao (2006)

Recently, Zhang and Zhao (2006) proposed a scale up strategy for low temperature

methanol synthesis in a continuous slurry bubble column reactor. It involved studying

hydrodynamics in cold flow units, catalyst performance evaluation in an autoclave, and

process investigation in pilot-scale continuous slurry bubble column reactor.Overall the

study was performed in following three steps,

1) Hydrodynamics in a cold flow unit with different column structure using the

different three-phase systems

2) Catalyst preparation and performance evaluation in an autoclave

3) Process exploration in continuous slurry bubble column reactor with a capacity of

2 tons per year.

37

The authors provided a comprehensive roadmap for development of the low-temperature

methanol synthesis in circulating slurry bubble column reactor. The strategy tied flow

behavior and catalysis studies with that of process engineering. However, neither any

guidelines were provided regarding hydrodynamic similarity in cold and hot unit nor any

results with successful scaleup were shown.

2.3.2 Reported status of scaleup in industry

The status of scaleup of bubble column reactors in industry is not widely reported in

literature. Tarmy and Coulaloglou (1992) discussed fundamental development and

scaleup issues and related them through example of coal liquefaction process and

mentioned that understanding of hydrodynamics and related issues to be the most critical

element in development and scaleup of these reactors. The industrial example of scaleup

demonstrated by them involves hydrodynamic studies based on overall phase holdups

and liquid backmixing in terms of Peclet number measured using pressure transducers

and radioactive tracers, respectively. The highest superficial gas velocity in the pilot

reactor at process conditions was 8 cm/s. Based on Tarmy et al. (1984) studies; this

condition appears to be in bubbly flow.

Espinoza et al. (1999) discussed gas holdup prediction and scaleup for Sasol slurry phase

reactor. Espinoza et al. (1999) modified gas distribution theory proposed by Toomey and

Johnstone (1952) for slurry bubble column reactors where it was divided into dense and

dilute phases. The minimum fluidization velocity was replaced by transition velocity

from homogeneous to heterogeneous flow regime. Using the modified two-phase theory,

they developed an approach similar to the one proposed by Krishna and Ellenberger

(1992). Espinoza et al. (1999) mentioned that during scaleup of 1 m diameter FT reactor

to 5 m diameter one, such an approach was not used. However, an importance of gas and

slurry mixing characteristics in a slurry bubble column was emphasized.

The reported scaleup procedures so far utilize the similarity of global parameter such as

overall gas holdup in two columns for hydrodynamic similarity. Such similarity based on

38

global parameters is not surprising because over the years bubble column hydrodynamics

have been quantified mostly based on the global parameters such as overall gas holdup

and mass transfer coefficient. Based on the studies reported by Macchi et al. (2001), it is

clear that the close overall gas holdup in two systems does not necessarily result in

similar local hydrodynamics. Hence, there is a need to evaluate and update the

generalization of hydrodynamic similarity based on global parameter such as overall gas

holdup and a new approach needs to be sought.

39

Chapter 3. Experimental Investigation of the Hydrodynamics of Slurry Bubble Column: Phase Holdups Distribution via Computed Tomography

As mentioned in Chapter 2, although there have been numerous efforts to study the

hydrodynamics of bubble/slurry bubble column reactors, most of these studies provide

information regarding global hydrodynamics. The only investigations to study the

detailed hydrodynamics of bubble and slurry bubble column reactors at high superficial

gas velocities and/or pressures of industrial interest were performed using air-water and

air-water-150 μm glass beads systems (Kumar, 1994; Degaleesan, 1997; Ong, 2003;

Rados, 2003). No work has been reported that studies the detailed hydrodynamics (the

radial profiles of axial velocity, turbulent kinetic energy, normal stress, shear stress, and

eddy diffusivities) of slurry bubble column reactors at high superficial gas velocity and

pressure using a liquid other than water. That motivates us to study the detailed fluid

dynamics and mixing characteristics at the operating conditions of pressure and

superficial gas velocity using a gas-liquid-solids system of industrial interest. There are

two ways to proceed: either perform experiments using real industrial conditions or

mimic a industrial system and operating conditions in the laboratory. Due to the general

limitations encountered in laboratory studies, we have chosen the second option. As

mentioned earlier, one of the most popular applications of slurry bubble column reactors

in the present day is the conversion of syngas to liquid fuels called as Fischer-Tropsch

(FT) synthesis. Based on this, one of the primary objectives of this chapter is to

investigate and study the effect of operating parameters on the flow behavior of slurry

bubble columns using a liquid that at room temperature mimics FT wax at FT reaction

conditions. This study will thus provide an idea about how the change in liquid phase

would affect the qualitative and quantitative behavior of these flows. In addition to

providing detailed insights into the flow microstructure of slurry bubble columns, this

40

study will extend a database that can be utilized as a benchmarking tool for CFD and

phenomenological modeling.

This study of the flow behavior of slurry bubble columns is divided into two chapters.

This chapter discusses the choice of phases employed, experimental setup, and

techniques, and then presents results, acquired via CT, related to the effect of operating

parameters on phase distribution in the selected system. Chapter 4 discusses the effect of

these operating parameters on the solids axial velocity and turbulent parameters at similar

conditions.

3.1 Choice of Phases

3.1.1 Choice of Liquid Phase

The physical properties of various liquids at ambient conditions were compared with

those of Sasol FT wax at FT reaction conditions, i.e., P = 3.1 MPa and T = 2400 C. The

physical properties of Sasol wax were measured at the Multiphase Flow and Powder

Reaction Laboratory, The Ohio State University, Columbus, utilizing a technique

developed for insitu measurement of fluid properties at high pressure and high

temperature. Based on the comparison, a heat transfer fluid popularly known as

Therminol LT was identified (the Material Safety Data Sheet is provided in Appendix-E),

which has the properties close to those of Sasol wax. Table 3-1 shows the physical

properties of Sasol wax and Theminol LT.

Table 3-1: Physical properties of Sasol wax and Therminol LT

Fluid Pressure

(MPa)

Temperature

(0C)

Density

(g/cc)

Viscosity

(cP)

Surface Tension

(dyne/cm) Sasol Wax 3.1 240 0.69 0.81 16.6

Therminol LT 0.1 25 0.866 0.88 17

41

The viscosity and surface tension of Sasol wax and Therminol LT are similar, while there

is a difference in their density values. Based on previous studies, it is known that the

effecst of viscosity and surface tension on flow behavior are dominant over that of fluid

density (Wilkinson, 1991). Hence, Therminol LT was used as the FT mimic liquid due to

its relatively close values of viscosity and surface tension.

3.1.2 Choice of Gas Phase

Air was used as the gas phase in this study. At an operating pressure of 1 MPa, the

density of air (12 kg.m-3) is close to the density of syngas at FT synthesis conditions.

Hence, the experimental investigations were planned at 1 MPa, in addition to an ambient

pressure to study the effect of pressure (i.e., gas density). The experimental conditions at

high pressure and ambient temperature enabled us to mimic gas and liquid phases at FT

synthesis conditions.

3.1.3 Choice of Solids Phase

FT catalyst/carrier would have been an ideal choice to mimic FT conditions. However,

glass beads with an average diameter of 150 μm and particle density of 2500 kg/m3 were

selected as the solids phase, for two reasons. The first reason is related to the limitations

on the radioactive tracer particle used in CARPT experiments. A 150 μm radioactive

particle has previously been successfully manufactured and irradiated and safely used in a

slurry bubble column using an air-water-glass beads system (Rados, 2003). Furthermore,

due to the limitations of the MIT Nuclear Reactor used for irradiation, it was not possible

or economical to irradiate a particle smaller than 150 μm. The second reason is to

complement Rados (2003) studies and provide proper experimental comparison to study

the effect of physical properties on the flow structure of slurry bubble column reactors

using a radioactive particle that matched properly in size and density of the solids used.

Moreover, the glass beads (range: 125 to 175 μm, with 85 % and above in the range of

145-155 μm) used in Rados (2003) and the current studies have a density of 2.5 gm.cc-1.

This value is close to the apparent density (density of solids filled with liquid in its pores)

42

of FT catalyst, i.e., 2.2 gm.cc-1, which has a mean size of 70-90 μm, with 45 % of the

solids 90 μm and above. These glass beads present an opportunity to study the effect of

non-porous solids that can provide a benchmark for future studies on porous FT catalyst.

3.2 Experimental Details

3.2.1 Experimental Setup

The experiments were carried out in a stainless steel column with an inner diameter of

0.162 m and a height of 2.5 m. Figure 3-1 is a schematic of the high pressure stainless

steel column without ports used for noninvasive measurements. The column with ports

and staggered windows was used for overall gas holdup measurements and is shown in

Figure B-1. Both columns are designed to support a maximum operating pressure of 300

psi. The air as a gas phase was supplied from two compressors connected in parallel, with

a working pressure of 1.45 MPa and a maximum corresponding rated flow rate of 8.8

m3/min. The compressed atmospheric air was purified by passing it through a dryer and

several air filter units. The air flow rate was regulated by a pressure regulator and

rotameter setup, which consisted of four rotameters of increasing range connected in

parallel. Air exited the column through a demister, passed through a back pressure

regulator that controlled the column operating pressure, and was vented to the

atmosphere. The column design enabled easy removal of the distributor chamber and

replacement of the sparger. The sparger used in this study has a porosity of 1.09 %. It

consists of 163 holes of 1.32 mm diameter with triangular pitch of 1 cm. Ong (2003)

studied the effect of the distributor on the hydrodynamics of bubble columns and showed

that the effect of the distributor is insignificant, particularly in the churn-turbulent flow

regime. Hence, only one type of sparger was employed in this study (Figure B-2). In all

experiments, the dynamic height of slurry was maintained at 1.8 m (z/D ~ 11) from the

distributor by varying the initial static height of the slurry based on the operating

condition.

43

3.2.2 Experimental Conditions

The selection of experimental conditions enabled a systematic comparison with Rados’

(2003) studies. In the literature, no studies regarding detailed flow behavior are reported

at the high solids loading typically employed in industrial processes. Hence, the effect of

solids loading is studied using both low (similar to Rados, 2003), and high solids loading.

Additionally, CT experiments were performed without solids. Table 3-2 lists the

experimental conditions employed in this work. It covers the study of the effect of

parameters of interest, superficial gas velocity, operating pressure, and solids loading. In

addition, the comparison of the performed experiments with those of Rados (2003)

provides information regarding the effect of liquid phase physical properties on the

hydrodynamics of such systems.

44

Gas Outlet

Top Cover

Batch Drain

21 1/2”

Bottom

LiquidDrain

1” Probe

8”

4 1/2”

GasInlet

4 3/4”

90”

Demister

8 3/4”

21 1/2”

28 1/2”

CT 2

CT 3

CT 1

6 3/8”

13”

Figure 3-1: Bubble/slurry bubble column reactor of 6” diameter used for CARPT/CT

measurements. CT1, CT2, and CT3 represent the scan levels used in this investigation.

45

Table 3-2: Experimental conditions employed in this study

Run Superficial gas

velocity

(cm/s)

Operating pressure (MPa)

Solids loading (% vol.)

1 8 0.1 9.1 2 14 0.1 9.1 3 20 0.1 9.1 4 30 0.1 9.1 5 8 1 9.1 6 14 1 9.1 7 20 1 9.1 8 30 1 9.1 9 20 0.1 25 10 30 0.1 25 11 20 1 25 12 30 1 25 13 20 0.1 0 14 30 0.1 0 15 20 1 0 16 30 1 0

3.3 Single Source Computed Tomography (CT)

CT has been extensively implemented on various multiphase flow systems at the CREL,

Washington University (Kumar, 1994; Roy, 2001; Rados, 2003; Ong, 2003). Software

and hardware details of the single source γ-ray CT have been explained elsewhere in

detail (Kumar, 1994). Hence only a brief description is provided here. The CT setup

(Figure 3-2) consists of an array of detectors with an opposing source, which rotate

together around the object to be scanned. The scanner uses a Cesium (Cs-137)

encapsulated γ−ray source with activity of ~ 85 mCi. The array of detectors and the

source are mounted on a gantry which can be rotated 3600 around the object to be

scanned, using a step motor. Also, the source-detector setup can be moved up and down

to scan cross-sections at any axial position of the column. In the present study, 5 NaI

scintillation detectors were used that cover the reactor diameter. Each detector consists of

a cylindrical 2 × 2 inch NaI crystal, a photo multiplier (PM), and electronics, forming a

46

0.054 × 0.26 m cylindrical assembly. In each view, every detector acquires 7 projections

covering the total angular span of 2.72o of the detector face. The total 99 views were

acquired with 3.6o of angular shift after every view. Hence, 3645 (5 x 7 x 9) projections

were used to reconstruct the phase holdup distribution at each cross-sectional plane. The

entire system is completely automated to acquire the data needed for the reconstruction of

the phase distribution in a given cross-section. After detailed analysis of various

algorithms, Kumar (1994) implemented the Estimation-Maximization (EM) Algorithm

for image reconstruction. It is based on maximum likelihood principles and takes into

account the stochastic nature of the γ-ray beam projection measurements.

Figure 3-2: Configuration of the CT experimental setup (Kumar, 1994).

While single source CT is used to reconstruct two-phase and three-phase (with stationary

solids phase) holdup distributions, the dynamic three-phase system under investigation

requires additional information to completely resolve phase holdup profiles. In the

absence of a dual energy/source CT technique, Rados (2003) proposed a methodology,

viz., CT/Overall gas holdup, to calculate phase holdup profiles in a slurry system using a

single γ-ray source. The details of this methodology are available elsewhere (Rados,

2003; Rados et al., 2005). This methodology utilized the following two assumptions,

which are sound at the range of employed operating conditions,

47

a) Axially invariant gas holdup.

b) Uniform cross-sectional solids loading (solids concentration). That is, the ratio of the

volume of solids to the volume of slurry (liquid+solids), [ ] is constant

along the cross-section of the column.

)/( Lss VVV +

Although the method facilitates reconstruction of three dynamic phases using single

source CT, it needs a prior’ knowledge of the overall gas holdup of the system under

study.

This work also initiated an effort to evaluate these assumptions and their range of

validity by combining two single modal tomographic techniques, viz., CT and Electrical

Capacitance Tomography (ECT). CT measurements were performed at Washington

University, while ECT measurements were to be performed at The Ohio State University

at identical operating and design conditions. The CT experiments and the development

of an algorithm for combination were completed at Washington University. The details

of this work can be referred to Appendix-A.

3.4 Results and Discussion

3.4.1 Overall gas holdup

Overall gas holdup measurements were performed at the conditions of interest. The

overall gas holdup was obtained by measuring the change in liquid/slurry height. The

experiments were performed using different solids loadings, viz. 9.1, 18, 25 vol.% over

the range of superficial gas velocities, and two pressures, 0.1 and 1 MPa. The

experiments were repeated three times and were found to be reproducible within ± 2 % of

relative error.

Figure 3-3a shows the effect of solids loading on the overall gas holdup in the air-

Therminol LT-glass beads system. With an increase in solids loading, overall gas holdup

decreases, which is consistent with the previous literature findings (Krishna et al., 1997).

48

An increase in solids loading increases pseudo-viscosity, which promotes coalescence of

large bubbles (Crabtree and Bridgewater, 1971), whereas the bubble break-up rate

decreases due to dampening of instabilities at interface. As a result more large bubbles

form in the system with an addition of solids, resulting in a decrease in transition

velocity. These large bubbles have high rise velocity, which results in lower gas holdup.

It can be observed that the point at which the change in the slope of the gas holdup curve

occurs shifts towards lower superficial gas velocity with an addition of solids. This can

be confirmed by plotting the drift flux (equation 2-2) against the overall gas holdup as

shown in Figure 3-3b. The drift flux plot also indicates an advance of the flow regime

transition to a lower superficial gas velocity with an increase in the solids loading, due to

the relatively early appearance of large bubble at increased solids loading. Hence, these

observations confirm that most of the planned experimental conditions appear to be in the

churn-turbulent flow regime.

Figure 3-4 shows the effect of operating pressure on overall gas holdup at various solids

loadings in the air-Therminol LT-glass beads system. An increase in pressure results in

(a) (b) Figure 3-3: Effect of solids loading on a) overall gas holdup curve and b) drift flux plot in

the air-Therminol LT-glass beads system at ambient conditions in a 6” diameter steel

column

an increase in overall gas holdup at the same superficial gas velocity. Increased gas

density at high pressure promotes bubble break-up, which counteracts the formation of

49

Figure 3-4: Effect of operating pressure on overall gas holdup at various solids loading in

air-Therminol LT –glass beads system in a 6” diameter steel column

larger bubbles due to coalescence (Wilkinson et al., 1993). The higher number of

relatively smaller bubbles at high pressure results in higher overall gas holdup.

3.4.2 Drift Flux Model

The drift flux is defined as the volumetric flux of either phase relative to a surface

moving at the volumetric average velocity. Zuber and Findlay (1964) presented the

detailed derivation for the drift-flux model based on an argument that gas holdup in two-

phase flow depends on two phenomena: the gas rises locally relative to liquid due to

phase density differences, and the gas holdup and velocity distribution across the column

diameter cause gas to concentrate in a faster or slower region of flow, thereby affecting

the average gas holdup. Their model has been represented as follows,

10 )( CUUCU

LGG

G +±=ε

, (3-1)

where,

)()(

0LGG

LGG

UUUU

C±

±=

εε

(3-1a)

and

G

GLjC

ε=1 . (3-1b)

50

The symbol represents averaging over the column cross-sectional area. In equation

(3-1), C0 is a distribution parameter and is a measure of the interaction of the holdup and

velocity distribution. The value of C0 is close to unity for flatter phase holdup profiles

and increases as the phase holdup profiles become steeper. C1 is the weighted average

drift velocity, accounting for the local slip. Generally, it is assumed to be similar to the

rise velocity of a bubble in an infinite medium.

Table 3-3: The values of drift flux parameters at the studied experimental conditions

Operating

Pressure

(MPa)

Solids loading

(% vol.)

C0 C1 R-squared

value

0.1 0 1.9 0.26 0.9910

0.1 9.1 1.8 0.36 0.9963

0.1 18 2.2 0.39 0.9837

0.1 25 3 0.44 0.9946

1 9.1 1.6 0.22 0.99

1 18 1.7 0.25 0.9893

1 25 1.9 0.36 0.9914

The overall gas holdup data was analyzed using equation 3-1. In the current study the

system is in batch mode, hence, UL = 0. Hence, equation 3-1 can be written as,

0 1( )GG

G

U C U Cε

= + . (3-1c)

Table 3-3 shows the values of C0 and C1 for different solids loading and operating

pressures. It can be observed that an increase in pressure decreases the value of C0, while

an increase in solids loading increases the value of C0. This result indicates that an

increase in pressure results in relatively flat profiles, while an addition of solids results in

51

steeper phase holdup profiles. The value of C1 decreases with an increase in pressure,

indicating that the value of bubble rise velocity decreases with pressure. An increase in

pressure reduces the mean bubble size due to an increase in the break-up rate and a

decrease in the coalescence rate, which results in a decrease in bubble rise velocity. An

increase in solids loading increases C1, resulting in higher bubble rise velocity with an

increase in solids loading. Increased solids loading produces larger bubbles that have

relatively higher rise velocities.

3.4.3 Cross-sectional distribution of gas holdup

Figure 3-5 shows the cross-sectional distribution of gas holdup at different superficial gas

velocities, solids loading of 9.1 % volume, and operating pressures of 0.1 and 1 MPa. The

red color shows higher gas holdup, while the blue indicates lower gas holdup. In general,

it can be observed that gas holdup is higher in the center and lower near the wall. At

lower superficial gas velocity, relatively uniform distribution of gas holdup can be

observed. Increases in superficial gas velocity and operating pressure tend to increase the

magnitude of gas holdup, while an increase in solids loading decreases gas holdup.

Generally, the cross-sectional distribution gives a qualitative picture of the way gas is

distributed across the column. The cross-sectional distribution of gas holdup observed in

this study is qualitatively similar to the one obtained in an air-water-glass beads system

(Rados, 2003), with differences in its magnitude that will be explained in the succeeding

section. The differences in magnitude and the trend observed in this study due to the

change in the liquid phase are pertinent to a fundamental understanding of the flow

behavior in a FT system.

52

a) P = 0.1 MPa b) P = 1 MPa Figure 3-5: Cross-sectional distribution of gas holdup in 6” diameter stainless steel

column using air-Therminol LT-glass beads system at different superficial gas velocities,

solids loading of 9.1 % vol., and P = a) 0.1, and b) 1 MPa.

a) 9.1 % volume b) 25 % volume

Figure 3-6: Cross-sectional distribution of gas holdup in 6” diameter stainless steel

column using air-Therminol LT-glass beads system at superficial gas velocity of 30 cm/s,

operating pressure of 1 MPa, and solids loading of a) 9.1, and b) 25 % volume.

53

They show symmetry in gas holdup distribution using air-Therminol LT-glass beads

systems similar to the air-water and air-water-glass beads systems, as observed

previously by Kumar (1994), Chen et al. (1999), Ong (2003), and Rados (2003). Such

symmetry exists at high pressure and even at high solids loading, as is evident from

Figure 3-6. However, for quantitative analysis, azimuthally averaged gas holdup along

the column radius has been studied and will be discussed in the remaining part of the

chapter. Selected experimental conditions were repeated, and the reproducibility of phase

holdup profiles was found to be reasonable. The results are presented in Appendix B

(Section B-2).

3.4.4 Time-averaged gas and solids holdup radial profile

Figures 3-7 and 3-8 show the gas and solids holdup radial profile obtained using the

CT/Overall gas holdup methodology at all axial locations (2.1D, 5.5D, and 9D) in air-

Therminol LT-glass beads at 8 cm/s, 0.1 MPa, and 9.1 % vol. and 30 cm/s, 1 MPa, and

25 % vol., respectively. The gas holdup profiles in the slurry systems look much like the

ones obtained in gas-liquid systems (Kemoun et al., 2001; Ong 2003). There are

insignificant differences between gas holdup profiles at various axial levels, which is due

to the assumption of axially invariant gas holdup stated earlier. The solids holdups are

higher at the wall than the center due to presence of high gas holdup in the center region

of the column. These findings are consistent with those reported in the literature (Rados

et al., 2005). The solids holdup profile along the radius shows two zones, one where it

remains almost uniform (0 ≤ r/R ≥ 0.6) and a second where there is a relatively sharp

increase in solids holdup towards the wall. A decrease in cross-sectionally averaged

solids holdup was found along the length of the column. At operating conditions of 8

cm/s, 0.1 MPa, and 9.1 % vol., the cross-sectionally averaged solids holdups at axial

locations of 2.1D, 5.5D, and 9D are close to 0.12, 0.074, and 0.044, respectively.

54

(a) (b)

Figure 3-7: a) Gas holdup and b) solids holdup radial profile in an air-Therminol LT-

glass beads system using 9.1 % vol. solids loading at a superficial gas velocity of 8 cm/s

and ambient pressure.

(a) (b) Figure 3-8: a) Gas holdup and b) solids holdup radial profile in an air-Therminol LT-

glass beads system using 25 % vol. solids loading at a superficial gas velocity of 30 cm/s

and operating pressure of 1 MPa.

This corresponds to solids loadings of 13.6, 8.9, and 4.5 % vol. at these axial locations.

The axial average of these estimated solids loadings at the three axial locations is 9 %

vol., which is close to the employed solids loading at this condition (i.e., 9.1 % vol.). At

operating conditions of 30 cm/s, 1 MPa, and 25 % vol., the cross-sectionally averaged

solids holdups are 0.24, 0.17, and 0.11, which correspond to solids loadings of 34.9, 24.5,

and 15.8, respectively. The axially averaged estimated solids loading at this condition is

25.4 % vol., which is close to the employed solids loading of 25 % vol.

55

3.4.5 Effect of liquid phase physical properties on gas and solids holdup radial profiles

The effect of liquid phase physical properties were studied by comparing the gas and

solids holdup radial profile in an air-Therminol LT-glass beads system obtained in this

work with that of an air-water-glass beads system using 9.1 % vol. solids loading (Rados,

20030). The experiments were performed with all other conditions the same, except the

employed liquid. Figure 3-9 shows the overall gas holdup curve in air-water-glass beads

and air-Therminol LT-glass beads systems at ambient conditions and solids loading of

9.1 % vol. in 0.1615 m diameter column.

Figure 3-9: Overall gas holdup curve using air-water-glass beads (Rados, 2003) and air-

Therminol LT-glass beads system at ambient conditions and solids loading of 9.1 % vol.

in a 6” diameter column.

The overall gas holdup curve in air-water-glass beads shows a familiar S-shaped curve in

transition regime that starts around 5 cm/s and is extended up to 12 cm/s. It is worth

mentioning that the S-shaped curve is not unique characteristic of air-water systems.

Based on the reported studies, it appears to be a strong function of the type of distributor

and operating conditions. The maximum gas holdup value was found at a superficial gas

velocity of 8 cm/s. No such S-shaped behavior was observed in an air-Therminol LT-

glass beads system. The increase in gas holdup with superficial gas velocity is gradual in

Therminol LT. Thimmapuram and Saxena (1992) provided the following explanation for

such different behavior in water and oil systems. They performed overall gas holdup and

heat transfer studies in nitrogen-water and nitrogen-Therminol 66 systems. They

56

observed S-shaped behavior in water, but not in Therminol 66. Based on the studies of

Saxena and Rao (1991), they concluded that for water systems, bubble size almost

remains constant in the bubbly flow regime, while in Therminol systems, it keeps

growing steadily. Hence, the increase in gas holdup with superficial gas velocity in water

is higher in this regime. In the transition and churn-turbulent flow regimes, bubble

coalescence sets in abruptly, resulting in rapid growth of coalesced bubbles, which

initially decreases the gas holdup, then keeps its magnitude constant in the churn-

turbulent flow regime. In Therminol 66, bubble coalescence occurs in the transition and

churn-turbulent flow regime, but the number of bubbles also increases with an increase in

superficial gas velocity. Hence, variation in gas holdup with superficial gas velocity is

different in these two systems. In addition, various authors (e.g., Yamashita and Inoue,

1975; Maruyama et al. 1986) explained the peak in gas holdup as being based on

‘structure collapse’ near transition.

The comparison of overall gas holdup in water and Therminol LT shows that in the

bubbly flow regime, overall gas holdup in water is higher than in Therminol LT, while in

churn-turbulent flow regime, it is higher in the Therminol LT. In the transition regime (5-

13 cm/s), gas holdup in water is higher than in the Therminol LT system. The higher gas

holdup in water in the bubbly flow regime and also near the transition regime due to S-

shaped behavior has been discussed above. The higher gas holdup in Therminol LT

(viscosity, µL = 0.88 cP, density, ρL = 886 kg.m-3

, surface tension, σL = 17 dyne.cm-1

)

compared to water ((viscosity, µL = 1 cP, density, ρL = 998 kg.m-3

, surface tension, σL =

72 dyne.cm-1

) in churn-turbulent flow can be attributed to the physical properties.

Therminol LT has lower viscosity and surface tension than water. When the surface

tension decreases, the bubble breakup rate increases and the coalescence rate decreases,

resulting in a relatively large number of small bubbles (Walter and Blanch, 1986). Also,

the lower viscosity promotes bubble break-up (because of the instabilities at the bubble

interface) and decreases bubble coalescence rate (Wilkinson, 1991), increasing the small

bubble population. Hence, the combination of lower viscosity and surface tension results

57

in relatively lower occurrences of larger bubbles in Therminol LT, which reduces bubble

rise velocity and thereby increases overall gas holdup.

The overall gas holdups at superficial gas velocities of 8, 14, and 30 cm/s at ambient

pressure and solids loading of 9.1 % vol. in the water system are 0.23, 0.22, and 0.27,

while in the Therminol LT system, they are 0.16, 0.23, and 0.33, respectively. The

absolute relative differences in gas holdup values at 8, 14, and 20 cm/s are 29, 5, and 19

%, respectively. Hence, it is obvious that the magnitude of gas holdup profiles in water

will be higher at Ug = 8 cm/s, while it will be higher in Therminol LT at Ug = 30 cm/s.

Also, the magnitude of the gas holdup profiles will be closer at Ug = 14 cm/s.

Figure 3-10 shows the comparison of gas and solids holdup radial profiles in air-water-

glass beads and air-Therminol LT-glass beads systems at ambient pressure and solids

loading of 9.1 % vol. in a 6” diameter column. At Ug = 8 cm/s, as discussed earlier,

overall gas holdup is higher in water than in Therminol LT, which results in a higher

magnitude of the gas holdup radial profile in water. The higher gas holdup in water

results in a lower magnitude of the solids holdup radial profile in water. The solids

holdup profile is higher in Therminol LT due to lower gas holdup in this system.

However, in both the systems, the solids holdup profiles are relatively flat. At Ug = 14

cm/s, the overall gas holdup values are close to each other. Hence, the magnitude of gas

holdup radial profiles is similar in both the systems. The holdup profiles in both the

systems almost match. The similar gas holdup profiles in water and Therminol LT results

in close solids holdup radial profiles in these systems. As discussed earlier, at Ug = 30

cm/s, the magnitude of gas holdup in Therminol LT was found to be higher than in water,

and hence higher magnitude of gas holdup radial profiles were observed in Therminol

LT. The higher gas holdup radial profiles result in slightly lower solids holdup radial

profiles

58

(a)

(b)

0 0.2 0.4 0.6 0.8 1

0

0.05

0.1

Dimensionless radius (-)

Sol

ids

hold

up (-

) air-water-glass beadsair-Therminol LT-glass beads

P = 0.1 MPa

(c) Figure 3-10: Effect of physical properties on a) gas holdup, and b) solids holdup radial

profile at P = 0.1 MPa, z/D = 5.5, solids loading of 9.1 % vol., and Ug = a) 8, b) 14, and

c) 30 cm/s in 6” diameter steel column

in Therminol LT. The close observation of gas holdup radial profiles in these systems

shows that the shape of the profile is relatively flatter in Therminol LT, which is due to

the presence of more small bubbles than in water. Also, the lower viscosity and surface

tension in Therminol LT tend to delay flow regime transition to the churn-turbulent flow

regime.

0 0.2 0.4 0.6 0.8 10

0.7

0.1

0.2

0.3

0.4

0.5

P = 0.1 MPa0.6

D )imensionless radius (-

Gas

hol

dup

(-)

air-water-glass beadsair-Therminol LT-glass beads

59

Figure 3-10 also shows the effect of superficial gas velocity on the radial profiles of gas

and solids holdup in an air-Therminol LT-glass beads system at ambient pressure and

solids loading of 9.1 % vol. in a 6” diameter column. An increase in superficial gas

velocity from 8 to 30 cm/s increases overall gas holdup from 0.16 to 0.33, and hence the

magnitude of gas holdup radial profile increases. With an increase in superficial gas

velocity, the system tends to be in the churn-turbulent flow regime. An increase in

superficial gas velocity results in more large bubbles that give rise to a wider bubble size

distribution. This subsequently results in a steeper gas holdup radial profile. An increase

in superficial gas velocity from 8 to 14 cm/s increases overall gas holdup by 28 %, while

increases in superficial gas velocity from 14 to 20 cm/s and from 20 to 30 cm/s increase

overall gas holdup by 17 and 15 %. As discussed in Section 3.4.1, the transition velocity

at this condition is around 5-6 cm/s. Accordingly, Ug = 8 cm/s which, is close to bubbly

flow and/or in the transition region, while other operating conditions fall in churn-

turbulent flow regime. Hence, a relatively larger change in overall gas holdup was

observed when superficial gas velocity was increased from 8 to 14 cm/s. As the system

enters the churn-turbulent flow regime, the rate of increase in gas holdup reduces with an

increase in superficial gas velocity, due to non-linear and intense interaction between

bubbles. An increase in superficial gas velocity at a given operating pressure and solids

loading does not seem to have a noticeable effect on gas holdup near the wall.

It can be observed that with an increase in superficial gas velocity, the magnitude of the

solids holdup profile decreases due to an increase in gas holdup. The solids holdup

profile tends to become steeper with an increase in superficial gas velocity as the system

tends to be in the churn-turbulent flow regime, which results in increased solids mixing.

This was reflected when Ug increased from 14 to 20 cm/s and 20 to 30 cm/s. At Ug = 8

cm/s, the solids holdup profile is relatively flatter, and gradually becomes steeper with an

increase in superficial gas velocity. The effect of superficial gas velocity on the gas

holdup profile is stronger than on the solids holdup profile. The effect of superficial gas

velocity on the solids holdup profile decreases with an increase in superficial gas

velocity. The stronger effect of superficial gas velocity on the solids holdup was found

when Ug was changed from 8 to 14 cm/s. The change in Ug from 8 to 14 cm/s reduces

60

the averaged solids holdup from by 8 %, while changes in Ug from 14 to 20 cm/s and 20

to 30 cm/s reduced the averaged solids holdup by 6.5 and 5 %, respectively.

Figure 3-11: Overall gas holdup curve using air-water-glass beads (Rados, 2003) and air-

Therminol LT-glass beads system at operating pressure of 1 MPa, and solids loading of

9.1 % vol. in a 6” diameter column.

Figure 3-11 shows the variation of overall gas holdup with superficial gas velocity at an

operating pressure of 1 MPa and solids loading of 9.1 % vol. in a 6” diameter column. At

high operating pressure, no S-shaped curve was observed in air-water-glass beads

systems, as was observed at ambient pressure. This observation is in line with the results

of Wilkinson (1991) and Letzel et al. (1997) who observed a gradual change in the

overall gas holdup at high pressure, as opposed to the S-shaped curve observed at

ambient pressure. Hence at high pressure, overall gas holdup in Therminol LT is

consistently higher than in water. The reason for this lies in the lower viscosity and

surface tension of Therminol LT. The combination of lower viscosity and surface tension

reduces the coalescence rate and increases the breakup rate, leading to more small

bubbles and a higher overall gas holdup in Therminol LT.

Figure 3-12 shows the effect of liquid phase physical properties on the gas and solids

holdup radial profiles at an operating pressure of 1 MPa and solids loading of 9.1 % vol.

at superficial gas velocities of 8, 14, and 30 cm/s. As explained above, based on the

61

(a)

(b)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7


Gas

hol

dup

(-)


P = 1 MPa

0 0.2 0.4 0.6 0.8 10

0.05

0.1


Sol

ids

hold

up (-

)

air-water-glass beads

air-Therminol LT-glass beads

P = 1 MPa

(c) Figure 3-12: Effect of physical properties on a) gas holdup, and b) solids holdup radial

profile at P = 1 MPa, z/D = 5.5 and solids loading of 9.1 % vol. at Ug = a) 8, b) 14, and c)

30 cm/s in a 6” diameter steel column

overall gas holdup curve at high pressure, the overall gas holdup is consistently higher in

Therminol LT than water at all the studied superficial gas velocities at high pressure. Due

to high overall gas holdup in Therminol LT system, the magnitude of the gas holdup

radial profiles is higher in Therminol LT. Similar to the ambient conditions, an increase

in gas holdup profile in Therminol LT resulted in a subsequent decrease in the solids

holdup radial profile. At high operating pressure, the gas holdup radial profiles at Ug = 8

62

cm/s look qualitatively similar in shape, while at Ug = 14 and 30 cm/s, the shapes of the

gas holdup radial profiles in Therminol LT are relatively flatter. The probable reason for

the similar shape at Ug = 8 cm/s can be due to existence of either the bubbly or transition

flow at these conditions. The comparison of gas holdup radial profiles in Therminol LT at

ambient and high pressure shows that an increased in pressure increases overall gas

holdup (Letzel et al., 1997; Kemoun et al., 2001) and hence the magnitude of the gas

holdup radial profile. An increase in pressure at the same superficial gas velocity

increased the gas density, which increased the rate of bubble break-up especially for large

bubbles. Such higher bubble break-up counters the formation of larger bubbles by

coalescence and generates small bubbles. The higher small bubble population in the

system results in an increase in overall gas holdup and therefore, the magnitude of the gas

holdup radial profile. An increase in pressure from 0.1 to 1 MPa at Ug = 8, 14, 20, and 30

cm/s increased gas holdup from 0.16 to 0.25, 0.22 to 0.33, 0.28 to 0.4 and 0.33 to 0.45,

almost relative increase of 36, 33, 30 and 27 % for solids loading of 9.1 % vol.,

respectively. The effect of pressure tends to decrease with an increase in superficial gas

velocity, which adds larger bubbles to the system with an increase superficial gas velocity

that counters the formation of smaller bubbles due to higher pressure. However, the effect

of operating pressure on gas holdup appears to be stronger than that of superficial gas

velocity. For example, at solids loading of 9.1 % vol., an increase in superficial gas

velocity from 14 to 20 and 20 to 30 cm/s increases gas holdup by 21 and 14 %,

respectively while an increase in operating pressure from 0.1 to 1 MPa at Ug = 14, 20,

and 30 cm/s increases gas holdup by 33, 30 and 27 %, respectively.

Due to generation of smaller bubbles at increased pressure, the shape of the gas holdup

radial profile becomes relatively flatter. An increase in pressure, in general, increases the

gas holdup in the center as well as close to the wall. An increase in gas holdup at higher

pressure results in reduction of solids holdup with an increase in operating pressure. In

addition, close observation of the solids holdup profile shows a relatively flatter profile at

higher operating pressure. The effect of pressure on the solids holdup profile is not as

strong as its effect on the gas holdup profile.

63

At ambient pressure and Ug = 30 cm/s, the gas holdup in Therminol LT was 0.33, while

in water it was 0.28, almost an increase of 19 %. At high pressure, the gas holdup in

Therminol LT was 0.44 while in water it was 0.39, almost an increase of 13 %. The

difference in liquid appears to have stronger effect at ambient pressure. In water, gas

holdup increased by 33 %, while in Therminol LT it increased by 28 % with the change

in operating pressure from 0.1 to 1 MPa.

The effect of physical properties on the solids holdup profile was observed to be less

significant than on the gas holdup radial profile. At Ug = 8 cm/s, the cross-sectional

averaged solids holdup in Therminol LT increased by 12 %, while gas holdup in

Therminol LT was reduced by 29 %. At Ug = 14 cm/s, the changes in cross-sectional

solids and gas holdups were 2.5 and 5 %, respectively. At Ug = 30 cm/s, the change in

cross-sectional solids and gas holdup is 6.5 and 18 %, respectively, while at P = 1 MPa,

the solids holdup was reduced by about 3.6 %. It should be noted that the reduction in

cross-sectional averaged solids holdup is higher at atmospheric pressure, and the increase

in gas holdup is also higher at ambient pressure.

3.4.6 Effect of solids loading on gas and solids holdup radial profiles The effect of solids loading on gas and solids holdup radial profiles at ambient pressure

and Ug = 20 and 30 cm/s is illustrated in Figure 3-13. An increased solids loading

reduces gas holdup and hence the magnitude of gas holdup radial profile. With an

addition of solids loading, the coalescence rate increases, while the break-up rate

decreases, which generates larger bubbles. The large bubbles have a high bubble rise

velocity that results in lower gas holdup at increased solids loading. An increase in solids

loading from 0 to 9.1 % vol. decreased the magnitude of the gas holdup radial profile.

However, the effect of addition of solids from 0 to 9.1 % vol. was weaker than the

addition of solids from 9.1 to 25 % vol. This observation is in line with the previous

studies of Rados (2003) who observed a weak effect of the addition of solids on the gas

holdup radial profile by changing the solids loading from 0 to 9.1 % vol. in air-water- 150

μm glass beads system. This weak effect is evident from the change in overall gas holdup

with an addition of solids. Increasing solids loading from 0 to 9.1 % vol, reduced overall

64

gas holdup by close to 9 % at Ug = 20 and 30 cm/s, while increasing solids loading from

9.1 to 25 % vol. reduced overall gas holdup by close to 34 % at Ug = 20 and 30 cm/s.

Similar trend was observed by Behkish (2005) in a He-Isopar M-alumina system at Ug =

15.4 cm/s and T = 400 K in a 0.3 m diameter column. An increase in solids loading from

0 to 10 % vol. reduced gas holdup by 10 %, while increasing solids loading from 10 to 20

% vol. reduced gas holdup by 60 %.

As mentioned earlier, the addition of solids increased the large bubble population in the

system. An increased larger bubble population, along with trapped small bubbles,

concentrates at the center of the column, pushing small bubbles towards the wall. The

bubble size distribution becomes wider with the addition of solids to the system. The

(a)

(b)

Figure 3-13: Effect of solids loading on gas and solids holdup radial profile in air-

Therminol LT-glass beads system at ambient pressure at Ug = a) 20, and b) 30 cm/s 6”

diameter steel column

reasoning is in line with the study of Lau (2004) who, based on 2-point optical probe

studies, observed wide bubble size distribution with an addition of solids. Due to this

reason, the gas holdup radial profile becomes relatively steeper at higher solids loading.

65

The system tends towards the churn-turbulent flow regime at higher solids loading when

operating at the same superficial gas velocity. The transition velocity calculated based on

the overall gas holdup curve and the drift flux plot also shows that an addition of solids

advances the flow regime transition. Additionally, gas holdup close to the wall is found to

be higher in the gas-liquid system compared to the slurry system. Also, it was found that

gas holdup close to the wall reduces as solids loading increases.

Obviously, an increase in solids loading increases the solids holdup at all axial locations.

The effect of superficial gas velocity and operating pressure on the solids holdup profile

was weaker than on the gas holdup profile. However, solids loading has a stronger effect

on the solids holdup profile than on the gas holdup profile. At Ug = 20 and 30 cm/s, an

increase in solids loading from 9.1 to 25 % vol. (change of 63.6 %) increased the cross-

sectional solids holdup by 68 and 66 % at ambient pressure.

Figure 3-14 shows the effect of solids loading on the gas and solids holdup radial profile

at superficial gas velocities of 20 and 30 cm/s and an operating pressure of 1 MPa.

Similar to the ambient pressure, increased solids loading decreased the magnitude of the

gas holdup radial profile. Similar to ambient pressure, the effect of addition of solids

from 0 to 9.1 % vol. was weaker (10 %) compared to an addition of solids from 9.1 to 25

% vol. At Ug = 20 and 30 cm/s, the gas holdup was reduced by 31 and 29 % at an

operating pressure of 1 MPa. The shape of the gas holdup radial profile became steeper

with an addition of solids. It is worth mentioning here that, although an increase in

operating pressure results in relatively flatter profiles, it cannot necessarily hold in the

case of high solids loading. As shown in Figure 3-14, at low solids loading and high

operating pressure, the profiles are relatively flat until r/R = 0.7, and then show a steep

decrease in gas holdup value in the region near the wall. However, at high solids loading

and high operating pressure, such behavior was not observed, and the gas holdup profiles

were found to be consistently steeper across the column radius. Although the shape of the

profile is steeper, it does show two different regions. However, both of these regions

show relatively steep behavior. The observation of such steep profiles at high operating

pressure (as opposed to flat ones at low solids loading and high pressure) is important for

66

FT reactor design, as these processes are generally operated at high pressure and high

solids loading. The importance of this finding is significant since the gas holdup profiles

studied at high pressure but low solids loading could be misleading. One should note here

that pressure and solids loading tend to have the favorable effect on FT reaction kinetics.

An increase in pressure increases the solubility of reactant gases in the liquid, while an

addition of solids increases the number of active sites in the reactor.

(a)

(b) Figure 3-14: Effect of solids loading on gas and solids holdup radial profile in an air-

Therminol LT-glass beads system at Ug = a) 20, and b) 30 cm/s and P = 1 MPa in a 6”

steel column

Hence, the knowledge of true behavior of the gas holdup profile at high pressure and

solids loading is pertinent in designing such reactors. An increase in solids loading from

9.1 to 25 % vol. (change of 63.6 %) increased solids holdup in the system by 70 and 71 %

at Ug = 20 and 30 cm/s, respectively.

67

The effect of solids loading on the gas holdup profile was stronger than the effect of

superficial gas velocity. At a superficial gas velocity of 20 cm/s, an increase in solids

loading from 9.1 to 25 % vol. at P = 0.1 and 1 MPa changed gas holdup by 35 and 30 %,

respectively. While the change in operating pressure from P = 0.1 to 1 MPa at solids

loading of 9.1 and 25 % vol. shows the change in gas holdup by 30 and 35 %,

respectively. At superficial gas velocity of 30 cm/s, an increase in solids loading from 9.1

to 25 % vol. at P = 0.1 and 1 MPa changes gas holdup by 34 and 30 %, respectively.

While the change in operating pressure from P = 0.1 to 1 MPa at solids loading of 9.1 and

25 % vol. shows the change in gas holdup by 28 and 32 %, respectively. This shows that,

pressure affects more at high solids loading while the solids loading has relatively more

effect at low pressure. However, the effect of solids loading at lower pressure is stronger

than the effect of pressure at higher solids loading.

3.4.7 Normalized gas holdup radial profile

The normalized gas holdup radial profile is the ratio of gas holdup at a certain radial

location to the cross-sectional averaged gas holdup. The analysis detailed discussion of

the normalized gas holdup radial profile is included in Appendix B (Section B-6).

3.4.8 Normalized solids holdup radial profile

The normalized solids holdup radial profile is the ratio of solids holdup at a certain radial

location to the cross-sectional averaged solids holdup. The analysis detailed discussion of

the normalized solids holdup radial profile is included in Appendix B (Section B-7).

3.4.9 Comparison with predictions of Sedimentation-Dispersion Model (SDM) The solids holdup axial gradient obtained in the current experimental studies was

compared with Sedimentation-Dispersion Model (SDM). SDM is currently the only

model available to predict the solids distribution over the column length in a batch slurry

68

reactor,. SDM predicts the exponential solids distribution profile in the following form

(for details, see Appendix-D),

][exp1

][exp

S

S

SSS BoLzBo

Bo−−

−=

−

εε , (3-5)

where BoS is a Bodenstein number.

(a) (b)

Figure 3-15: Predictions of the SDM in air-Therminol LT-glass beads system at ambient

pressure and solids loading of a) 9.1 and b) 25 % vol. in 6” diameter column

Figures 3-15a and b show the SDM predictions in air-Therminol LT-glass beads at P =

0.1 MPa and solids loading of 9.1 and 25 % vol., respectively. As expected, there is an

exponential solids distribution over the column length. At a given solids loading, the

SDM predicts more uniform solids distribution at higher superficial gas velocities. At

lower superficial gas velocities, it shows a higher solids holdup gradient and at lower

solids loading, it shows the relatively steeper solids distribution over the column length.

The correlations used to predict the solids axial dispersion coefficient do not account for

the effect of gas density, hence the comparison of the SDM predictions with the

experimental data was restricted to ambient pressure.

Figures 3-16a and b show the comparison of the SDM predictions with the experimental

data obtained in this study at superficial gas velocities of 8 and 30 cm/s, respectively. At

a superficial gas velocity of 8 cm/s, the experimental data is close to the SDM

predictions, while at a superficial gas velocity of 30 cm/s, the experimental data do not

69

match with the SDM predictions. However, the experimental data and SDM predictions

at z/D = 5.5 match well. The differences can be found only at z/D = 2.1 and 9. At Ug =

30 cm/s, the % average absolute errors between the experimental data and the SDM

prediction at z/D = 2.1 and 9 are 18 and 28 %, respectively.

(a) (b)

Figure 3-16: Comparison of the SDM predictions with experimental data in air-

Therminol LT-glass beads system at ambient pressure, solids loading of 9.1 % vol., and

Ug = a) 8 and b) 30 cm/s in 6” diameter column

Figure 3-17a shows the SDM predictions with the experimental data at superficial gas

velocities of 20 and 30 cm/s. The experimental data shows a higher normalized solids

holdup gradient at higher superficial gas velocity. This is in contradiction to the SDM

predictions, as shown in Figure 3-15. However, at high superficial gas velocities such as

20 and 30 cm/s, the solids holdup gradient appears to be linear, rather than exponential as

predicted by the SDM. The experimental data at these conditions also do not match with

the SDM predictions at z/D = 2.1 and 9, while at z/D = 5.5, the SDM and experimental

data match well.

Figure 3-17b compares the effect of solids loading on solids distribution using the SDM

predictions and experimental data at a superficial gas velocity of 30 cm/s and ambient

pressure. The predictions of the SDM do not match with the experimental data obtained

70

(a) (b)

Figure 3-17: Comparison of the SDM predictions with experimental data in air-

Therminol LT-glass beads system at ambient pressure. a) effect of superficial gas

velocity at solids loading of 25 % vol. and b) effect of solids loading at Ug = 30 cm/s in

6” diameter column

in this study. At a solids loading of 9.1 % vol., the average absolute errors between the

SDM prediction and experimental data are 18 and 28 %, while at a solids loading of 25 %

vol., the differences are 24 and 33 % at z/D = 2.1 and 9, respectively. However the trend

of the effect of solids loading predicted using the SDM is similar to the experimental

observation.

3.5 Remarks

The significant findings of this study are as follows.

1) At ambient pressure, the comparison of gas and solids radial profiles in air-

Therminol LT-glass beads and air-water-glass beads reveals that in bubbly flow the

magnitude of the gas holdup profile is higher in water; in churn turbulent flow, it is

higher in Therminol LT. In transition flow, the close gas holdup radial profiles were

observed in water and Therminol LT. The increased gas holdup in water in bubbly flow

71

accords with the S-shaped behavior of the overall gas holdup curve at the studied

conditions. An opposite effect of superficial gas velocity was observed on the solids

holdup radial profile.

2) At high operating pressure (1 MPa), the Therminol LT liquid phase consistently

increased the magnitude of the gas holdup radial profile due to an increased bubble

breakup rate and decreased coalescence rate that together produce more small bubbles.

This results in a relatively flatter profile in Therminol LT. The solids holdup radial

profile decreased with an increase in superficial gas velocity.

3) An addition of solids in the slurry reduced the magnitude of the gas holdup radial

profile due to a higher coalescence rate that produces more large bubbles in the system.

The higher population of large bubbles concentrated at the center and resulted in a steeper

profile at increased solids loading, and thereby advancing flow regime transition. An

addition of solids linearly increased the solids holdup profile at both pressures. At high

operating pressure and high solids loading, the gas holdup radial profile showed a

consistently steeper profile. The shape of the profile at this condition is qualitatively

similar to the one observed at low solids loading and ambient pressure.

4) Within the studied experimental conditions, the effect of superficial gas velocity

on overall gas holdup is weaker than that of operating pressure and solids loading.

5) Changes in the studied operating parameters consistently affected the gas holdup

radial profile more than they affected the solids holdup profile.

6) The cross-sectional averaged solids holdup increased with solids loading, but

decreased with superficial gas velocity and operating pressure.

7) The normalized solids holdup profiles at all the axial locations show a similar

shape and fall on each other for a given operating condition. The normalized solids

holdup at low superficial gas velocities show a similar shape and also fall on each other,

while the normalized solids holdup at higher superficial gas velocities show a similar and

relatively steeper shape and fall on each other within a band of relative error of ± 10 %.

8) The normalized solids holdup radial profile in water and Therminol LT shows

similar shapes and fall on each other at all the studied conditions except in bubbly flow at

ambient pressure. This shows that the solids flow behavior in these systems is

72

qualitatively similar. However, the differences are due to the different liquid phase

physical properties.

73

Chapter 4. Experimental Investigation of the Hydrodynamics of Slurry Bubble Column: Solids Flow Pattern via CARPT

This second part of the experimental investigation of the hydrodynamics of a slurry

bubble column focused on the effect of various operating parameters on the solids axial

velocity and turbulent parameters’ [turbulent kinetic energy, normal and shear stresses,

and eddy diffusivities] profiles using a liquid that at room temperature mimics FT wax at

FT reaction conditions. This chapter discusses the experimental setup, technique, and

results related to the solids axial velocity and turbulent parameters profiles.

4.1 Experimental

The choice of fluid and experimental setups is discussed in Chapter 3 and will not be

repeated here. Table 4-1 shows the CARPT experimental conditions used in this study.

Due to difficulties in performing CARPT experiments at severe conditions such as high

superficial gas velocity, high operating pressure, and solids loading along, with an

aromatic liquid, the experiments were planned only in fully churn-turbulent flow.

Table 4-1: CARPT Experimental conditions

Run Superficial gas

velocity

(cm/s)

Operating pressure (MPa)

Solids loading (% vol.)

1 20 0.1 9.1 2 30 0.1 9.1 3 20 1 9.1 4 30 1 9.1 5 20 0.1 25 6 30 0.1 25 7 20 1 25 8 30 1 25

74

4.2 Computer Automated Radioactive Particle Tracking (CARPT)

The computer Automated Radioactive Particle Tracking (CARPT) technique was first used

by Kondukov et al. (1964) to study particle motion in a fluidized bed. This technique has

been used extensively at Washington University in the CREL to measure the flow pattern

and turbulent parameters of different multiphase flow reactors in a non-invasive manner. A

CARPT experiment comprises two steps:

a) CARPT calibration (a ‘static’ experiment),

b) CARPT experiment (a ‘dynamic’ experiment).

The dynamic experiment involves tracking of a single radioactive tracer particle by

detecting the intensity distribution of emitted γ-rays. The γ-ray intensity distribution is

detected using an array of NaI scintillating detectors strategically placed around the studied

region of the column (Figure 4-1). In the ‘static’ experiment, the photon count rate obtained

at each detector is related to the distance between the source and the detector. The

instantaneous position of the tracer is then accurately calculated from the distances using an

optimized regression scheme. The time differentiation of the displacement yields local

velocities. The ensemble averaged velocity profiles and ‘turbulent’ parameters can then be

computed with the aid of an improved particle reconstruction algorithm proposed by Rados

(2003).

Due to various advantages, Scandium 46 with an activity of about 200 – 300 μCi was used

in this work (Rados, 2003). The objective was to compute solids instantaneous velocities,

the radial profile of the axial solids velocity, and turbulent parameters. Therefore a

radioactive particle of the same size and density as the solids was essential to monitor the

motion of the solids. A tracer scandium Sc46 particle of the required diameter was protected

with a thin coating of Parylene N. The resulting radioactive scandium Sc46 particle (with a

strength of up to 300 μCi and a half-life of 83 days) had a total diameter of 150 μm, which

was equal to the average particle size of the glass beads used in this study. The density of

Paralyne N is 1.11 g/cm3, so the application of a 7 μm coating lowered the overall particle

density from 2.99 g/cm3 (of pure scandium) to about 2.5 g/cm3.

75

The detailed experimental setup and calculation procedure for the CARPT experiments is

given in Degaleesan (1997) and Rados (2003). In-situ calibration of detectors was

performed under the desired operating conditions at high pressure. CARPT data (tracer

particle position in time) was acquired over a sufficiently long time to ensure enough

particle occurrences in each column cell and good time/ensemble averaging and was used

for calculation of the time averaged solids

a) velocities

b) “Reynolds” stresses

c) “turbulent” kinetic energy, and

d) eddy diffusivities

Figure 4-1: Configuration of the CARPT experimental setup (Degaleesan, 1997)

4.3 Results and Discussion

4.3.1 Time-averaged solids velocities

Before elaborating on the effect of liquid phase physical properties and solids loading, the

sample CARPT results at a superficial gas velocity of 30 cm/s, a solids loading of 9.1 %

vol,. and ambient pressure will be discussed (Figure 4-2). It should be noted that similar

qualitative flow behavior was observed at all the studied conditions. Based on CT studies

performed in the same system, it is known that the gas holdup is high in the center and

low at the wall, leading to buoyancy driven gross recirculation, which results in slurry

76

flowing up in the center (positive axial velocity) and down in the annular region, near the

column wall (negative axial velocity). Figure 4-2a is a two-dimensional vector plot at a

superficial gas velocity of 30 cm/s, solids loading of 9.1 % vol., and ambient pressure. It

is clear from the vector plot that there exists only one slurry recirculation cell in the time-

averaged sense, with slurry upflow in the center and downflow near the wall. The fully

developed flow extends axially between approximately 2D (0.32 m) and HD-D (1.63 m)

(2D < z < HD-D), where HD is the dynamic height and z is the total column height from

the distributor. From the plot, it is evident that everywhere in the column the time

averaged solids radial velocity is lower than the axial solids velocity. The highest upward

and downward axial velocities were found to be 140 and –135 cm/s. The highest value of

radial velocity was found be around 1.5 cm/s.

The axial and radial velocity components across the radius of the column are presented at

three axial locations, i.e., z = 2.5D, 5.5D, and 9D in Figure 4-2b and c. The averaged

velocity in these figures is averaged axially from z = 2D to HD – D, which represents the

fully developed flow region. One can see that the solids axial velocities at all axial

locations are similar to the averaged velocity. As mentioned earlier, this familiar

recirculation pattern has been observed earlier by many investigators: in bubble columns

(Franz, 1984; Devanathan, 1990; Degaleesan, 1997), in slurry bubble columns (Rados,

2003), and in liquid fluidized beds (Limtrakul, 1996). The inversion point where the

solids velocity becomes zero was found to be around a dimensionless radius (r/R =) 0.7

for all the studied experimental conditions. In CT studies, close inspection of the solids

holdup radial profile revealed two zones with different slopes. One region was from 0 ≥

r/R ≤ 0.6 – 0.7 and other was close to wall region and characterized by a larger slope. In

the core region (0 ≥ r/R ≤ 0.6 – 0.7) where the slope was relatively uniform, the solids are

moving up while in the higher slope region, as well as in high solids holdup region near

the wall, they move downward. Figure 4-3 shows the radial profiles of time- and

azimuthally- averaged axial, radial, and tangential solids velocities at these operating

conditions, with error bars. The error bars in these figures represent one standard

deviation from the averaged velocities along the axial coordinate at every radial location.

77

(b)

0 0.2 0.4 0.6 0.8 12

3

4

5

6

7

8

9

r/R

z/D

(a) (c) Figure 4-2: Time and azimuthally averaged solids velocity in air-Therminol LT-glass

beads system at Ug = 30 cm/s, P = 0.1 MPa, and solids loading = 9.1 % volume a) uz-ur

vector map, b) axial, and c) radial velocity components

(a) (b) (c)

Figure 4-3: Radial profile of solids a) axial, b) radial, and c) tangential velocity in air-

Therminol LT-glass beads system at Ug = 30 cm/s, P = 0.1 MPa, and solids loading = 9.1

% volume

78

Clearly, the radial and tangential solids velocities are much lower than axial velocities

indicating advectionless radial and tangential flow.

Figure 4-4 shows a PDF plot of the axial solids velocity at three different radial positions

(r/R = 0.063, 0.44, and 0.96) at an axial level of L/D = 2.5 at Ug = 30 cm/s, P = 0.1 MPa,

and a solids loading of 9.1 % vol. The alternating vortices appear to dominate the PDF of

solids axial velocity. As expected, the resultant solids axial velocity in the center is

positive, while near the wall, it is negative. Although the mean of the PDF in the center is

positive, it shows a few negative velocities. Figure 4-5 shows the PDF plot of solids axial

velocity at three different radial positions (r/R = 0.063, 0.44, 0.69, and 0.94) and at three

axial levels (L/D = 2.5, 5.5, and 9). Very small axial variation in PDFs was observed in

the studied region. As one moves from the column center to the column wall, the

contribution of negative velocities starts increasing. The mean of solids axial velocities at

r/R = 0.063, 0.44, and 0.69 are positive while at r/R = 0.94, it is negative. The negative

Figure 4-4: Probability distribution function of solids axial velocities at L/D = 2.5 at

various dimensional radius positions of r/R = 0.063, 0.44, and 0.96 at Ug = 30 cm/s, P =

0.1 MPa, and solids loading of 9.1 % volume.

solids velocities in the center are possibly due to downward moving small bubbles in the

wake of large bubbles. This fact can be corroborated based on the experimental studies

performed by Chen et al. (1994). Based on Particle Image Velocimetry (PIV), Chen et al.

(1994) showed that a significant number of small bubbles are trapped with large bubbles

moving in the center of the column. As seen from Figure 4.5, the presence of positive

79

Axial solids velocity (cm/s)

pdf

Column WallColumn Center

L/D

Figure 4-5: Probability distribution function of solids axial velocities at L/D = 2.5, 5.5,

and 9 along the column radius at r/R = 0.063, 0.44, 0.69, and 0.96 at Ug = 30 cm/s, P =

0.1 MPa, and solids loading of 9.1 % volume.

and negative velocities at all the radial locations indicates high fluctuations and the

dynamic nature of flow in the column. In addition, it can be observed that at a radial

location of r/R = 0.69, the contribution of both positive and negative velocities is equal.

Such comparable positive and negative velocities can possibly generate larger, and

vigorous fluctuations in the vortical region.

Figure 4-6 shows the effect of pressure as well as solids loading on the PDF of solids

axial velocity. The comparison of 4-6 a and b shows the effect of operating pressure at a

superficial gas velocity of 30 cm/s and 9.1 % vol. solids loading, while comparison of

Figures 4-6 b and c show the effect of solids loading at a superficial gas velocity of 30

80

r/R = 0.063 r/R = 0.96

(a)

(b)

(c)

Figure 4-6: Probability distribution function of solids axial velocities in fully developed

flow in the column center and near the wall at a) 30 cm/s, 9.1 % vol., and 0.1 MPa, b) 30

cm/s, 9.1 % vol., and 1.0 MPa, and c) 30 cm/s, 25 % vol., and 1.0 MP in 6” diameter

stainless steel column.

cm/s and an operating pressure of 1 MPa. It can be observed that an increase in pressure

results in a narrow PDF, while increasing the mean of the PDF both in the center and at

the wall. An addition of solids broadens the PDF and decreases its magnitude. However,

the general qualitative behavior at all the studied operating conditions is similar. It shows

averaged positive velocity in the center, with few negative velocities, and the contribution

of negative velocities increases as one move towards the wall.

81

4.3.2 Turbulent stresses and kinetic energy

When a gas is bubbled through slurry, large scale eddies are created. The turbulent

interaction between these eddies can be characterized by studying the auto-/cross-

correlation of the fluctuating velocity components (Degaleesan, 1997). The second order

velocity correlations, ' 'i ju u , represent the turbulent momentum transport along ith direction

due to the instantaneous flow in the jth direction. The turbulent stress tensors can be

defined by the following symmetric matrix in a cylindrical system,

' ' ' ' ' '

' ' ' ' ' '

' ' ' ' ' '

r r r r z

s r z

z r z z z

u u u u u u

u u u u u u

u u u u u u

θ

θ θ θ θ

θ

τ ρ

⎛ ⎞⎜ ⎟⎜ ⎟=⎜ ⎟⎜ ⎟⎝ ⎠

, (4-1)

where, ' 'i ju u = ' '

j iu u .

The above tensor consists of following quantities,

Normal stress in the axial direction = ' 's z zu uρ (4-2a)

Normal stress in the radial direction = ' 's r ru uρ (4-2b)

Normal ' 's u uθ θρ stress in the tangential direction = (4-2c)

Shear stress = ' 's r z

he solids phase turbulence can also be characterized in terms of turbulent kinetic

u uρ (4-2d)

T

energy, which is defined as

]'''[21 222

−−−

++= uuuk ρ . zrS θ (4-3)

here is considerable evidence that the time averaged turbulence in bubble columns is T

not isotropic (Franz et al., 1984; Chen et al., 1994; Degaleesan, 1997; Mudde et al.,

1997). The normal stresses in the axial direction are much larger than in the radial and

82

tangential direction. Hence, the characteristic length scale in the axial direction is

significantly larger than in the other two directions.

Figure 4-6a, b, c, d shows the radial profile of the solids turbulent kinetic energy, and of

the axial, radial, and tangential normal stresses at Ug = 30 cm/s and P = 0.1 MPa at a

solids loading of 9.1 % vol. using the air-Therminol LT-glass beads system. It is evident

that as in bubble column reactors, the solids axial normal stress is much higher in

magnitude than the radial and tangential normal stresses. Hence, it is not quite surprising

that the radial profile of the solids turbulent kinetic energy follows the behavior of the

solids axial normal stress.

(a) ` (b) (c) (d) Figure 4-7: Radial profile of solids a) turbulent kinetic energy, and b) axial, b) radial, and

c) tangential normal stresses in air-Therminol LT-glass beads system Ug = 30 cm/s, P =

0.1 MPa, and solids loading = 9.1 % volume.

Compared to the axial normal stress, the radial and tangential normal stresses are uniform

along the column radius. The magnitude of the radial and tangential stresses is

83

approximately 1/3rd of the axial normal stress. Although the axial velocities are higher in

the center, the axial normal stress shows a peak closer to the vortical region. Based on

Figure 4-5, it is clear that in the vortical region, both positive and negative velocities are

comparable. Hence the flow dynamically changes from upward to downward in this

region, based on the location of the central large bubble stream and its swirling motion.

The flow in this region, therefore, experiences larger and more vigorous fluctuations

leading to a peak in axial normal stress closer to the vortical region rather than in the

center, where flow is mostly upward.

The nature of the turbulence developed in a bubble column can be deduced from the

nature of these normal stresses. An isotropic turbulence, frequently used in modeling

such flows, does not exist in a slurry bubble column as the normal stresses in three

directions are of different magnitudes.

Figure 4-8a, b, c shows the radial profile of the solids shear stresses in an air-Therminol

LT-glass beads system at Ug = 30 cm/s, P = 0.1 MPa, and a solids loading of 9.1 % vol.

It is evident that the shear stresses are less than the normal stresses. A similar

phenomenon was observed in bubble columns, where the magnitude of the liquid shear

stress is much lower than that of normal stresses (Degaleesan, 1997; Ong 2003). This

implies that the cross-correlations (shear stresses) between the solids velocities are not as

strong as the auto-correlations (normal stresses). Between various shear stresses, the

value of rzτ is the most significant, hence will be used in further analysis. The radial

profile of rzτ shows the minimum value in the center and near the wall. It exhibits a

maximum value at r/R = 0.4 - 0.6. The peak in shear stress can be related to the inversion

point in the axial solids velocity near this region. In addition, the radial profile of

normalized solids holdup shows a change in its slope in this region as shown in

Appendix-B.

In the following analysis, only the axial normal stress and the shear stress in the axial and

radial directions are presented, since they are frequently used in the modeling of slurry

bubble columns. The effect of operating parameters on axial and radial eddy diffusivities

84

is provided in Appendix-C. The data pertinent to study the effect of operating parameters

is presented here, and the remaining data is provided in Appendix-C.

Now the effect of various operating parameters on the radial profiles of solids velocities

and of turbulent parameters will be studied.

(a) (b) (c) Figure 4-8: Radial profiles of solids shear stress components in an air-Therminol LT-

glass beads system Ug = 30 cm/s, P = 0.1 MPa, and solids loading = 9.1 % volume

4.3.3 Effect of liquid phase physical properties on the solids axial velocity and

turbulent parameters

Figure 4-9 compares the solids axial velocity and turbulent parameters in an air-

Therminol LT-glass beads and air-water-glass beads system at a superficial gas velocity

of 30 cm/s, ambient pressure, and a solids loading of 9.1 % vol. Due to low surface

tension and viscosity, the gas holdup radial profile in air-Therminol LT-glass beads is

higher than that of the air-water-glass beads system. The higher gas holdup radial profile

results in a higher solids axial velocity in the air-Therminol LT-glass beads system. The

center line velocity, as well as negative wall velocity, are higher in Therminol LT than in

water. Although, the solids axial velocity is higher in the air-Therminol LT-glass beads

system, the turbulent kinetic energy and normal stresses were found to be lower than

those of the air-water-glass beads system. The combination of low surface tension and

viscosity in the Therminol LT system generates more small bubbles that impart a low

level of fluctuations to the solids phase and result in the lower TKE and normal stresses.

On the other hand, due to higher radial gradient of solids axial velocity, the shear stresses

are higher in the air-Therminol LT-glass beads system. The change in physical properties

θτ r

θτ z

rzτ

85

of the liquid phase does not alter the location of the inversion point and maximum in

shear stress. Figure 4-10 shows the effect of change in liquid phase at a superficial gas

velocity of 30 cm/s, P = 1 MPa, and solids loading of 9.1 % vol. From the CT studies it is

known that, at a high operating pressure, the gas holdup profiles are higher in Therminol

LT. Such higher gas holdup profiles give rise to a higher solids axial velocity profile in

Therminol LT, even at high operating pressure. As with ambient pressure in Therminol

LT, the TKE is lower while the solids shear stress is higher.

With the change in operating pressure from 0.1 to 1 MPa, the centerline velocity

increased by 50 % in the water system, while it increased by 35 % in the Therminol LT

system. One should note here that a similar change in pressure resulted in 34 and 28 %

increase in overall gas holdup in water and Therminol LT, respectively. The comparison

between water and Therminol LT at ambient and high pressure shows that at ambient

pressure the center-line velocity is higher in Therminol LT by 33 %, ande at 1 MPa, it is

higher by 19 %. The change in center-line velocity between water and Therminol LT

appears to be higher at ambient pressure. It should be recalled here that the change in

liquid phase at ambient pressure increased overall gas holdup in Therminol LT by 19 %,

while at high pressure, it increased by 12 %. Thus the behavior of the solids velocity is in

accordance with the behavior of the gas holdup and its radial profile.

The change in liquid phase, i.e. physical properties does not appear to have any effect on

the location of the inversion point and maximum in shear stress. These two systems show

only quantitative differences in solids axial velocity and turbulent parameters. The

qualitative flow behavior in these systems remains the same indicating the same,

hydrodynamics in the two systems, differing only in magnitude due to the change in


86

(a) (b) (c) (d) Figure 4-9: Comparison of radial profile of a) gas holdup, b) solids axial velocity c)

solids TKE, and d) solids shear stress in air-water- glass beads and air-Therminol LT-

glass beads system at Ug = 30 cm/s, P = 0.1 MPa, and solids loading of 9.1 % vol.

The comparison of solids axial velocity profiles in Therminol LT in Figure 4-9 and

Figure 4-10 also shows the effect of operating pressure on solids axial velocity and

turbulent parameters at Ug = 30 cm/s and solids loading of 9.1 % vol. An increase in

operating pressure at the same superficial gas velocity results in an increased magnitude

of the gas holdup profile. Because the gas holdup profile drives the solids circulation in

slurry columns, higher pressure results in higher solids axial velocity due to increased gas

holdup. The reason for this behavior can be rationalized by drawing an analogy to bubble

dynamics studies performed in a two-phase bubble column. Xue (2004) developed a four-

point optical probe for bubble velocity, bubble size, and interfacial area measurement in

bubble columns. The experiments were conducted in an air-water system at atmospheric

87

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7


Gas

hol

dup

(-)


P = 1 MPa

0 0.2 0.4 0.6 0.8 1-60

-40

-20

0

20

40

60

80

100


Sol

ids

axia

l vel

ocity

(cm

/s)


(a) (b) (c) (d) Figure 4-10: Comparison of radial profile of a) gas holdup, b) solids axial velocity c)

solids TKE, and d) solids shear stress in air-water-glass beads and air-Therminol LT-

glass beads system at Ug = 30 cm/s, P = 1 MPa, and solids loading of 9.1 % vol.

and high pressure (0.4 and 1 MPa). It was observed that in the center the percentage of

bubbles moving downwards was reduced, while near the wall the percentage of bubbles

moving downwards increased greatly. Xue (2004) also noticed that in the center the mean

velocity of bubbles moving upwards increased, while downward movement was

enhanced near the wall due to an increase in negative velocity of the downward moving

bubbles. In addition, Xue (2004) observed that the bubble frequency increases greatly

with an increase in operating pressure. This results in higher solids/slurry recirculation

with an enhancement in pressure, as the solids/ slurry moves along with the bubbles. An

increase in pressure from 0.1 to 1 MPa at Ug = 30 cm/s increased the gas holdup by 27

%, and the centerline velocity increases from 60 to 90 cm/s, almost by 34 % while at

0 0.2 0.4 0.6 0.8 10

500

1000

1500

3500

2000

2500

3000


T2 )

KE

(cm

2 /s

0 0.2 0.4 0.6 0.8 10

100

400

200

300


Trz

) (c

m2 /s

2

air-water-glass beads

air-Therminol LT-glass beads

88

superficial gas velocity of 20 cm/s, gas holdup and centerline velocity increased by 30

and 35 %. At higher pressure, the negative velocity also increased from –28 to –35 cm/s

at Ug = 30 cm/s and from -23 to -27 cm/s at Ug = 20 cm/s, thereby increasing the

recirculation in the system. The effect of operating pressure at the remaining superficial

gas velocities is shown in Appendix-C.

The effect of pressure observed in this study is in line with previous studies in bubble

columns (Ong, 2003) and slurry bubble columns (Rados, 2003). However, Lee et al.

(2001) performed Laser Doppler Velocimetry (LDV) studies using nitrogen-water and

nitrogen-Paratherm NF and found that an increase in pressure resulted in reduced liquid

axial velocity. It is worth mentioning here that the experimental conditions of Lee et al.

(2001) appear to be in the bubbly flow regime (particularly at high pressure), while those

of Ong (2003) and Rados (2003) were in the churn-turbulent flow regime, similar to the

current study.

Although operating pressure increased solids axial velocity, the effect of pressure on

TKE was the opposite. It showed reduced turbulence in the system at higher operating

pressure. An increase in operating pressure increased the gas density and destabilized the

large bubbles. The maximum stable bubble size was reduced with an increase operating

pressure (Wilikinson, 1991; Lin et al., 1998; Xue, 2005). The high pressure resulted in a

narrow bubble size distribution with a smaller mean bubble size. Although at elevated

pressure the gas phase momentum is higher, due to the small mean bubble size, the

fluctuations of the solids/slurry phase are dampened out. As the population of the large

bubbles decreased with pressure, it results in relatively reduced swirling motion caused

by such structures. The lower intensity of fluctuations of smaller bubbles therefore leads

to a lower level of turbulence at high pressure. An increase in pressure reduces TKE by

close to 20 % at 20 and 30 cm/s.

The effect of pressure on the radial-axial shear stress is similar to its effect on the solids

axial velocity. An increase in operating pressure increases the shear stress due to the

89

higher radial gradient of solids axial velocity. The shear stress increased by 19 and 22 %

with an increase in pressure from 0.1 to 1 MPa at Ug = 20 and 30 cm/s, respectively.

4.3.4 Effect of solids loading on solids axial velocity and turbulent parameters

The effect of solids loading on the solids axial velocity and turbulence parameter at

ambient pressure in the air-Therminol LT-glass beads system at superficial gas velocities

of 20 and 30 cm/s is shown in Figures 4-11 and 4-12. The addition of solids reduced the

gas holdup and hence solids axial velocity. The reduction of gas holdup radial profile at

higher solids loading is translated into the lower solids axial velocity profile. An increase

in solids loading reduces centerline as well as negative velocity near the wall. The

centerline velocity decreased by 16 and 14 % at Ug = 20 and 30 cm/s, respectively. The

negative velocities changed from -27 to -21 cm/s at Ug = 30 cm/s, while at Ug = 20 cm/s,

it changed from -22 to -18 cm/s at ambient pressure.

(a) (b)

(c) (d) Figure 4-11: Effect of solids loading on the radial profile of solids a) axial velocity, b)

turbulent kinetic energy, c) axial normal stress, and d) shear stress in air-Therminol LT-

glass beads system at Ug = 20 cm/s and P = 0.1 MPa.

90

0 0.2 0.4 0.6 0.8 10

500

1000

1500

2000

2500

3000

3500


TK

E (c

m2 /s

2 )

Vs = 9.1 % volVs = 25 % vol

(a) (b) (c) (d) Figure 4-12: Effect of solids loading on the radial profile of solids a) axial velocity, b)


glass beads system at Ug = 30 cm/s, and P = 0.1 MPa

Figures 4-13 and 4-14 illustrate the effect of solids loading on the solids axial velocity

and turbulence parameters in the air-Therminol LT-glass beads system at high pressure

and superficial gas velocities of 20 and 30 cm/s, respectively. The addition of solids at

high pressure resulted in a decrease in gas holdup and subsequently in the solids axial

velocity and its profile. The addition of solids at higher pressure decreased gas holdup by

close to 30 %, while the centerline velocity decreased by 13 and 10 % at Ug = 20 and 30

cm/s.

0 0.2 0.4 0.6 0.8 1-40

-30

-20

-10

70

0

10

20

30

40

50

Vs = 9.1 % vol60Vs = 25 % vol


Sol

ids

axia

l vel

ocity

(cm

/s)

0 0.2 0.4 0.6 0.8 10

1000

2000

3000

4000


Axi

al n

orm

al s

tress

(cm2 /s

2 )

Vs = 9.1 % voldata2

0 0.2 0.4 0.6 0.8 10

50

100

150

200

250

300

350

400


Trz

(cm

2 /s2 )

Vs = 9.1 % volVs = 25 % vol

91

(a) (b) (c ) (d) Figure 4-13: Effect of solids loading on the radial profile of solids a) axial velocity, b)


glass beads system at Ug = 20 cm/s and P = 1 MPa

At both ambient and high pressure, the addition of solids resulted in an increase in TKE

and axial normal stress. At superficial gas velocities of 20 and 30 cm/s, the addition of

solids increased TKE by 22 and 18 % at ambient pressure, and by 20 and 15 % at P = 1

MPa, respectively. The addition of solids increased the pseudo-viscosity of the slurry,

thereby results in a stable interface that promoted coalescence and reduced bubble

breakup. The combination of these phenomena generated more large bubbles. Based on a

2- point optical probe, Lau (2003) also observed that an addition of particles led to

significantly larger bubble sizes in the system. Based on PIV studies, Chen et al. (1994)

92

showed that the large bubbles that accumulate at the center move in a rocking spiral

manner in the churn- turbulent flow regime. Hence the fluctuations of the solid/slurry

0 0.2 0.4 0.6 0.8 1-40

-20

0

20

40

60

80

100


Sol

ids

axia

l vel

ocity

(cm

/s)

Vs = 9.1 % volVs = 25 % vol

0 0.2 0.4 0.6 0.8 10

1000

2000

3000


TK

E (c

m2 /s

2 )

Vs = 9.1 % volVs = 25 % vol

(a) (b)

0 0.2 0.4 0.6 0.8 10

1000

2000

3000

4000


Axi

al n

orm

al s

tress

(cm2 /s

2 )

Vs = 9.1 % volVs = 25 % vol

0 0.2 0.4 0.6 0.8 10

50

100

150

200

250

300

350

400

450


Trz

(cm

2 /s2 )

Vs = 9.1 % volVs = 25 % vol

(c ) (d) Figure 4-14: Effect of solids loading on radial profile of solids a) axial velocity, b)


glass beads system at Ug = 30 cm/s, and P = 1 MPa

phase induced by gas phase become higher at increased solids loading due to the higher

large bubble population. The observation of increased turbulence at higher solids loading

is in line with the recent findings by Cui and Fan (2005). Their studies were performed in

a 2-D column using low solids loading (4 % vol.) at superficial gas velocities ranging

from 0.025 to 7.5 cm/s, covering bubbly and churn-turbulent flow. In general, Cui and

Fan (2005) observed enhancement in turbulence with an addition of particles, however

the effect of solids loading on the turbulence was found to be function of the solids

properties and the operating flow regime.

93

As shear stress is a radial gradient of the solids axial velocity, an addition of solids results

in reduction in the radial gradient of axial velocity; hence, axial-radial shear stress is

reduced at high solids loading. The reduction of shear stress at ambient pressure is 15 %,

while, at high pressure it is close to 12 %.

In Chapter 3, it was observed that pressure affects overall gas holdup more at high solids

loading, while solids loading affects overall gas holdup relatively more at low pressure. A

similar trend in the effect of the combination of solids loading and operating pressure was

observed on the solids axial velocity and turbulent parameters.

4.3.5 Cross-sectional averaged turbulent stresses

The values of the cross-sectional average of the turbulent stresses were obtained from

CARPT data. The effects of the studied parameters on the cross-sectional average of the

turbulent stresses are provided in Appendix-C.

4.3.6 Turbulent eddy viscosity

In this section, turbulent eddy viscosity, which signifies the turbulent transfer of

momentum by eddies giving rise to an internal fluid friction, is calculated from the

CARPT experimental data. Next the turbulent eddy viscosity is predicted using the

approach proposed by Ohnuki and Akimoto (2001) in gas-liquid systems and is compared

with the experimental values. In the next section, the available correlations for turbulent

viscosity are presented. The predictions of these correlations are also compared with the

ones obtained from CARPT data. The details are provided in Appendix-C.

4.3.7 Eddy diffusivities

In this section, eddy diffusivity, which is the exchange coefficient for the diffusion of a

conservative property by eddies in a turbulent flow, is calculated, and the effects of the

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94

liquid phase physical properties and solids loading are discussed. The details of this part

are provided in Appendix-C.

4.4 Remarks

The significant findings of this part are as follows:

1) As found in air-water and air-water-glass beads systems, this work also exhibits a

single circulation cell in fully developed flow in a time-averaged sense. The solids

move upward at the center and downward near the wall. The pdf of the solids

axial velocity reveals that although the net flow in the center is upward, there are

few negative velocities, net flow near the wall is downward, and there are few

positive velocities. Near the vortical region, comparable positive and negative

velocities are present, causing vigorous fluctuations. The axial solids velocity

shows an inversion point around a dimensionless radius of 0.7 while shear stress

shows maximum in the center of the column radius.

2) Comparison with an air-water-glass beads systems shows an increased solids axial

velocity and shear stresses in the air-Therminol LT-glass beads system. However,

due to the presence of smaller bubbles in the air-Therminol LT-glass beads, it

shows less TKE and normal stresses. The qualitative flow behavior in both

systems is similar; the quantitative differences exist due to differences in physical

properties.

3) An addition of solids reduces the solids axial velocity and shear stress, due to a

decrease in gas holdup, while TKE and normal stresses are higher at high solids

loading, due to an increased large bubble population.

4) The effect of superficial gas velocity is not as strong as the effect of operating

pressure. The operating pressure has a significant effect at high solids loading,

while the solids loading exhibits more effect at ambient conditions.

95

Chapter 5.

Flow Regime Transition

As discussed in Chapter 2, for lab scale and industrial scale reactors, there is a need to

develop a technique for flow regime diagnosis that is noninvasive, that can be easily

implemented on an industrial scale without disturbing the operation, and that provides

reliable information regarding the prevailing flow regime. The primary objective of this

chapter is to develop and demonstrate a non-invasive technique for online flow regime

demarcation and its corresponding ‘flow regime identifiers’. The developed technique

will then be utilized to study the effect of operating parameters on flow regime transition.

Stitt et al. (2003) summarized various tomographic systems and concluded that γ-ray

based techniques meet all essential requirements for field use. For this purpose, the

available non-invasive techniques, such as γ-ray CT and Nuclear Gauge Densitometry

(NGD), were evaluated for flow regime identification. This chapter is divided into two

parts. The first part evaluates CT for flow regime demarcation, while the second part

deals with the more robust NGD.

5.1 Flow Regime Transition using CT

Darwood et al. (2003) discussed in detail the commercial practicability of γ-ray CT

system as a process diagnostic tool. They developed a proprietary method to deliver an

economic, portable, and commercial product that can measure tomograms of equipment

at manufacturing sites.

Based on this development, in the first part of this work the following tasks were focused

on:

i) Explore the potential of CT for delineation of hydrodynamic flow regime

ii) Develop “flow regime identifiers” for CT

iii) Study the effect of operating pressure on flow regime transition

96

As we know, single source γ-ray CT has been used for phase holdup reconstruction in two

phase systems. Based on the published studies on gas holdup radial profiles, it is well

known that the homogeneous regime is characterized by a close to flat holdup profile,

while the heterogeneous regime has a parabolic profile. Therefore, the actual measurement

of either the holdup profiles or/and the liquid flow pattern across the column should

conclusively indicate the prevailing flow regime (Joshi et al., 1998).

5.1.1 Experimental setup and conditions The details of the experimental setup and CT used in this part of the work were given in

Chapter 3. Air was used as a gas phase, while Therminol LT was the liquid phase. The

obtained experimental data was processed using the EM algorithm implemented by Kumar

(1994). As mentioned earlier, the available studies show that the shape of gas holdup radial

profiles is different in both regimes. Therefore, based on the obtained results, the parameter

that defines the shape of the gas holdup radial profile will be studied for identification of

flow regime transition. The behavior of such a parameter will be explored in the context of

the knowledge of flow regime transition obtained from the gas holdup curve and Drift Flux

plot, based on the cross-sectional averaged gas holdup calculated from the obtained radial

profiles. Systematic experiments were performed where the superficial gas velocities were

varied from 1 to 20 cm/s with an interval of 1 cm/s and at 30 cm/s. The operating pressures

were 0.1, 0.4, and 1 MPa.

5.1.2 Results and Discussion

Figure 5-1 shows the plot of the gas holdup radial profile at superficial gas velocities

ranging from 1 to 20 and 30 cm/s with an interval of 1 cm/s, at ambient conditions using an

air-Therminol LT system. With an increase in superficial gas velocity, the magnitude of the

gas holdup profile increases. In addition, one can observe that an increase in superficial gas

velocity results in a change in the shape of the gas holdup radial profile, from flatter at low

superficial gas velocities to steeper, i.e. parabolic, at high superficial gas velocities.

Particularly, there is a distinct change in the shape of the gas holdup radial profile around

97

superficial gas velocities of 6 – 7 cm/s. To evaluate whether this is due to change in the

flow regime, the evolution of the cross-sectional averaged gas holdup with superficial gas

velocity was assessed.

Figure 5-1: Gas holdup radial profile at various superficial gas velocities in an air-

Therminol LT system at ambient conditions in a 0.162 m steel column.

Once the gas holdup radial profile was obtained by azimuthally averaging the cross-

sectional gas holdup distribution, the cross-sectional averaged gas holdup was then

estimated as follows,

, (5-1) ∫=− 1

0

)(2 ηηηεε dGG

where η = r/R.

The fact that bubbly and churn-turbulent flow exhibit different slopes in the gas holdup

curve will be utilized to identify the transition point. The commonly used drift flux

method proposed by Wallis was also used to determine the regime transition point. The

drift flux can be written as (Wallis, 1969)

GLGGGL UUj εε ±−= )1( , (5-2)

98

where the positive or negative sign indicates counter-current or co-current flow of liquid

relative to the gas phase, respectively. The change in the slope of the drift flux curve (jGL

v/s εG) represents the transition from homogeneous to heterogeneous flow. The change in

slope in the drift flux plot is generally sharper than the change in slope in the gas holdup

curve.

For the batch liquid, equation (5-2) will become

)1( GGGL Uj ε−= . (5-2a)

Figure 5-2a shows the evolution of the cross-sectional averaged gas holdup with superficial

gas velocity in an air-Therminol LT system at ambient conditions. The gas holdup curve

shows a change in slope around superficial gas velocities of 6 – 7 cm/s, indicating a regime

transition point.

In addition, the drift flux based on the cross-sectional gas holdup was plotted and is shown

in Figure 5-2b. The drift flux was calculated from equation (5-2a). The drift flux plot also

shows a sharp change in slope around 6 – 7 cm/s, confirming the regime transition point

around these velocities.

The shape of the obtained gas holdup radial profile data was analyzed further to identify the

flow regime transition. From traditional analysis (gas holdup curve and drift flux plot), it is

clear that regime transition occurs around 6 – 7 cm/s. This is consistent with Figure 5-1,

which shows a noticeable change in the shape of the profile around superficial gas

velocities of 6 – 7 cm/s. Therefore, the shape parameter of the profile and its evolution over

the studied superficial gas velocities can reveal information regarding the flow regime

transition.

To include the possibility of finite gas holdup close to the wall, Luo and Svendsen (1991)

modified the proposed form of Nassos and Bankoff (1967) for the gas holdup radial profile

as follows:

99

])(1)[22

2( n

G

G

Rrc

cnn

−−++

=−

ε

ε, (5-3)

where is the cross-sectional averaged gas holdup and r/R is the dimensionless radial

position. The exponent n is a parameter that indicates the steepness of the gas holdup radial

profile. The value of n is large for a flat profile (as observed in bubbly flow) and

−

Gε

(a) (b)

Figure 5-2: a) Cross-sectional averaged gas holdup versus superficial gas velocity and b)

Drift flux plot based on cross-sectional averaged gas holdup in an air-Therminol LT

system at ambient conditions in a 0.162 m steel column.

small for a steep profile (as observed in churn-turbulent flow). In the above equation, the

parameter c indicates the value of gas holdup near the wall. If c = 1, there is zero holdup

close to the wall, while for c = 0, the holdup is constant with changing r/R.

The obtained gas holdup radial profile has been fitted to the equation proposed by Luo and

Svendsen (1991) to calculate the steepness parameter. Figure 5-3 shows the evolution of

the steepness parameter, n, against superficial gas velocity. A break-point in the steepness

parameter curve has been observed around 6 – 7 cm/s, which matches with the one

obtained in the drift flux plot. Hence, the ‘break-point’ in the steepness parameter curve

100

Figure 5-3: Evolution of steepness parameter with superficial gas velocity in an air-

Therminol LT system at ambient conditions in a 0.162 m steel column.

can be utilized as the regime transition identifier. Using this identifier, the effect of

operating pressure on the flow regime transition was further studied.

Figures 5-4a and b show the gas holdup radial profile at superficial gas velocities of 1 to 20

cm/s, with an interval of 1 cm/s, and at 30 cm/s in an air-Therminol LT system at operating

(a) (b)

Figure 5-4: Gas holdup radial profile at various superficial gas velocities in an air-

Therminol LT system at operating pressure of 0.4 MPa in a 0.162 m steel column.

101

pressures of 0.4 and 1 MPa, respectively. The behavior of the profiles is similar to that at

ambient conditions, but the shape of the profiles is much flatter than at the ambient

conditions, which is consistent with the earlier literature findings (Kemoun et al., 2001;

Ong, 2003). This flatter profile is due to an increase in breakup rate and a decrease in the

coalescence rate at higher pressure. The distinct change in the shape of the profile observed

at ambient conditions was not observed at higher pressures. From the obtained gas holdup

radial profiles, cross-sectional gas holdups were estimated from equation 5-1. The gas

holdup curve and drift flux plot based on the estimated cross-sectional gas holdups are

shown in Figures 5-5a and b for an operating pressure of 0.4 MPa, while Figures 5-6a and b

show the gas holdup curve and drift flux plot at operating pressure of 1 MPa. The change of

slope in the gas holdup curve and drift flux starts at 7 cm/s for an operating pressure of 0.4

MPa, and at 9 cm/s for 1 MPa. To quantify the observed phenomena based on the obtained

gas holdup radial profiles, the steepness parameter n was plotted against superficial gas

velocities at operating pressures of 0.4 and 1 MPa (Figure 5-7). A gradual change, contrary

0 10 20 300

0.1

0.2

0.3

0.4

0.5


Cro

ss-s

ectio

nal g

as h

oldu

p

0 0.2 0.40

10

20

Cross-sectional gas holdup

Drif

t-flu

x, j

(a) (b)

Figure 5-5: a) Gas holdup curve based on cross-sectional averaged gas holdup and b)

Flux plot based on cross-sectional averaged gas holdup in an air-Therminol LT system at

operating pressure of 0.4 MPa in a 0.162 m steel column.

102

0 10 20 300

0.2

0.4

0.6


Cro

ss-s

ectio

nal g

as h

oldu

p

0 0.2 0.40

5

10

15

Cross-sectional gas holdup

Drif

t-flu

x, j

(a) (b)

Figure 5-6: a) Gas holdup curve based on cross-sectional averaged gas holdup and b) Flux

plot based on cross-sectional averaged gas holdup in an air-Therminol LT system at

operating pressure of 1.0 MPa in a 0.162 m steel column.

to the distinct one observed at ambient conditions, was observed in the steepness parameter

curve at increased pressure. Figure 5-7 shows that at an operating pressure of 0.4 MPa, a

noticeable change in the steepness parameter occurs at a superficial gas velocity of 7 – 8

cm/s. Also, at 1 MPa the change in the steepness parameter can be observed around 8 – 9

cm/s. Such a noticeable change in the steepness parameter curve has been observed at a

velocity similar to the transition velocity point obtained from the gas holdup curve and drift

flux plot based on cross-sectional gas holdup, thereby confirming the utilization of the

‘break-point’ in the steepness parameter for regime transition identification. In addition,

one can observe that, at increased pressure, the change in the steepness parameter near the

‘break-point’ is gradual, rather than distinct as observed at atmospheric pressure. In

general, the steepness parameter, n, decreases with an increase in superficial gas velocity

and reaches a constant value close to 2.

At atmospheric pressure, the change in the steepness parameter that starts at a superficial

gas velocity of 6 cm/s becomes smaller around 8 cm/s. At 0.4 MPa, the change in the

steepness parameter starts around 7 cm/s and extends up to 11 cm/s, while at 1 MPa, such

a change starts around 8 cm/s and extends up to 13 cm/s. In general, the ‘break-point’ in

steepness parameter curve, which is similar to the transition velocity, increases with an

103

increase in operating pressure. Although the change in the steepness parameter curve is

sudden at ambient conditions, it extends over the region of superficial gas velocities at

Figure 5-7: Evolution of steepness parameter with superficial gas velocity in an air-

Therminol LT system at operating pressures of 0.4 and 1 MPa in a 0.162 m steel column.

higher pressures. The extension of such a zone depends upon the operating pressure, and it

increases with an increase in pressure. Based on Deterministic Chaos Analysis of pressure

fluctuations, Letzel et al. (1997) found a sharp dip in Kolomogorov entropy at the transition

point, while at higher pressure, such a dip has not been observed. They observed a region

of low Kolomogorov entropy at higher pressure, and the length of the region increased with

an increase in pressure, similar to the observations made in this work. The increased

pressure delays the formation of larger bubbles and thereby postpones the ‘break-point’

velocity. The presence of an extended transition zone at higher pressure has been linked to

the appearance of ‘swirl’ and ‘large bubbles’ at different superficial gas velocities, whereas

at atmospheric pressure these two phenomena coincide (van den Bleek et al., 2002).

5.1.3 Evaluation of the empirical correlations

In the literature, the following two correlations have been utilized to predict transition

velocity,:

104

i) Wilkinson (1991)

Wilkinson (1991) developed a model for gas holdup prediction that is similar to but slightly

different from the one proposed by Krishna et al. (1991). They incorporated their own

experimental data along with the literature data in their model and proposed the following

correlation for prediction of regime transition velocity.

(5-4) 03.0273.0

4

3, [][23.2

G

L

L

LLbs

gU

ρρ

ηρσ

ση −= ]

(5-5) )0 00 σμρεU −−== 193exp(5. 11.5.61.0

,LGtrans

bs

trans

U

ii) Reilly et al. (1994)

Reilly et al. conducted experiments in 15 cm diameter column using water and non-

aqueous liquids. They used helium, nitrogen, air, argon and CO2 to study the effect of gas

density on regime transition. Using their own experimental data, they proposed the

following correlation based on the change in gas phase momentum,

(5-6) 5.012.096.05.1 ]/[)(59.0 LGtrans B ρσρε =

(5-7) )1(184.21 12.0

04.0 transtransG

transU εεσρ

−= where B = 3.85.

Table 5-1 shows the predicted transition velocities using the above correlations in

comparison with the experimental transition velocities at various operating pressures.

Quite surprisingly, both correlations show maximum relative error at atmospheric

pressure. Within the studied range of operating conditions, Wilkinson (1991) correlation

105

tends to underpredict the transition velocities compared to the correlation of Reilly et al.

(1991). The average relative errors using the correlations of Wilkinson and Reilly et al.

are 70 and 49 %, respectively. Clearly, the state of prediction of flow regime transition

velocities based on the correlations needs to be further improved.

Table 5-1: Comparison of experimental and predicted transition velocities from the

available correlations in an air-Therminol LT system at various operating pressures.

Operating Pressure (MPa)

Experimental Utrans(cm/s)

Wilkinson (1991) Utrans(cm/s) % Relative

Error

Reilly et al. (1994) Utrans(cm/s) % Relative

Error 0.1 6 - 7 0.4 93 2.5 58 0.4 7 - 11 2.4 66 4 43 1 9 - 14 4.3 52 4.8 47

5.2 Flow Regime Transition using Nuclear Gauge Densitometry (NGD)

The objective of this part of the chapter is to develop NGD for demarcation of

hydrodynamic flow regimes in bubble column reactors. The γ-ray CT was first attempted

because it provides a detailed time averaged cross-sectional distribution of underlying

hydrodynamics. However, NGD appeared to be more robust from an experimental point

of view, both on the laboratory as well as the industrial scale. Of particular industrial

interest is the fact that NGD can be implemented without disturbing the running

operation. Also, it is being currently used in industry for liquid/slurry level monitoring

and control.

Based on this development, this part of the work focused on the following tasks:

i) Explore the potential of NGD for demarcation of hydrodynamic flow regime

ii) Propose “flow regime identifiers” for NGD

iii) Evaluate the applicability of the proposed identifiers in different systems and at

high operating pressure.

106

5.2.1 Nuclear Gauge Densitometry (NGD)

Nuclear gauge densitometry (NGD) consists of a sealed source in a source holder and a

scintillation detector in front of the source. The source holder is mounted on one side of a

column, with the detector on the opposite side. A focused beam of radiation is transmitted

from the source, through the column and process material, to the detector. As the density

of the material in the column changes, the amount of radiation reaching the detector

changes. It is generally believed that the amount of radiation that reaches the detector

through the process material is reflective of its flow behavior and properties. Figure 5-8

shows the schematics of NGD with a source and a detector in front of it.

NGD is used extensively in industry for such applications as level control, density

measurement, interface identification, and weight measurements in conveyors. It is

widely used in the following industries: chemicals, petrochemicals, off shore oil and gas,

pharmaceuticals, cement, quarrying, solids handling, paper and food. The major

advantages of NGD that make it attractive in everyday industrial use are

(www.vegacontrols.com),

i) Totally non-contact: Because the sources and detectors are mounted externally

from the column or process, they are completely unaffected by the conditions

inside, however extreme, providing reliable solutions when other technologies

fail. They can be easily accessed, installed or removed without the process

being affected or interrupted.

ii) High integrity: A non-invasive system mounted outside the vessel means no

exposure or wear by corrosive or abrasive products, and no need for

construction to resist high pressure, high temperature process conditions. This

means less risk of leaks or emissions, protecting processes, people and the

environment.

iii) High reliability and low maintenance: NGD measurements offer reliability

and long term performance. In addition, source checking is routine, simple

and can be planned well in advance.

107

iv) Low installation costs: NGD can often be installed and commissioned without

process shutdown. Also, on most applications, no alterations to the

reactors/columns are needed, which means no expensive design changes for

such implementation of NGD.

5.2.1a Experimental Setup

The experimental setup consists of a laboratory scale plexi-glass column (diameter = a

0.1012 m, height = 1.2 m) as shown in Figure 5-8. Air from the in-house utility line was

fed through a sparger located at the bottom of the column. The gas flow rate was

measured and adjusted by a rotameter (Dwyer Intruments Inc., model Rate Master). The

sparger used in this study consists of 64 holes of 0.052” diameter with an open area (%

OA) of 1.09. This sparger is equivalent to the one used in the 6” stainless steel column

for slurry bubble column hydrodynamics experiments. The equivalent sparger was

designed such that the hole size and % OA remain the same in the two spargers, therefore

the number of holes differ in these spargers. In this study, an existing CT setup was

converted to NGD (Figure 5-8) by placing a detector in front of an encapsulated γ-ray Cs-

137 source (~ 100 mCi). The source and detector were mounted on a plate that can move

in axial direction. The detector consists of a cylindrical 2 × 2 inch NaI crystal, a photo

multiplicator (PM), and electronics, forming a 0.054 × 0.26 m cylindrical assembly. The

collimator (1/16” X 3/16”) was placed in front of the detector. The photon count rate that

was converted from the output voltage was collected through an automated data

acquisition system. The superficial gas velocity was varied from 1 to 12 cm/s, with an

interval of 0.5 cm/s, near the transition region. Air was used as the gas phase, while water

(μ = 1 cP, ρ = 998 kg.m-3, σ = 72 dyne.cm-1) was the liquid phase.

108

35

35

0.62

35

Ø 4”

3.6” ¼"

γ-ray Source Detector

Figure 5-8: Experimental setup for Nuclear Gauge Densitometry (NGD)

Drahos et al. (1991) systematically examined the effect of various operating parameters

on axial and radial profiles of the basic characteristics of pressure fluctuations. The signal

measured in the bubble column is a complex function of the effects connected with

formation, coalescence and passage of bubbles and their mutual interactions with the

liquid phase eddies of various scales. Based on the cross-spectral studies, they showed

that the characteristic frequencies are different, depending on the source as shown in

Table 5-2. Drahos et al. (1991) found that the interesting frequencies range from 0 to 20

109

Hz for bubble columns. Hence, the photon counts history was obtained at an acquisition

frequency of 50 Hz. In order to minimize statistical error in the various time-series

analysis, a time-series with a total number of points, N = 15,000, was collected (Smith,

1999, van Ommen, 2001). This requires a total acquisition time of 5 minutes. To check

the consistency of the obtained data, the experiments were repeated three times.

Table 5-2: Characteristic frequencies in bubble column (Drahos et al., 1991)

Source Order of characteristic frequencies (Hz)

Formation of bubbles > 101

Passage of bubbles 100 – 101

Coalescence of bubbles 100

Large-scale eddies 10-1

Medium-size eddies 100

Liquid level fluctuations 10-2 – 10-1

5.2.2 Results and Discussion

5.2.2a Traditional analysis of flow regime transition

The flow regimes were first defined using traditional methods such as the change in the

slope of the gas holdup curve and the change in the slope of the drift flux plot. The

overall gas holdup was calculated by measuring the change in dynamic liquid height.

Figure 5-9 shows the evolution of overall gas holdup with superficial gas velocity. The

overall gas holdup curve shows a change in slope around 3-4 cm/s, indicating flow

regime transition.

Figure 5-10 shows the drift flux plot in an air-water system at ambient conditions in a a

0.1012 m diameter column. The drift flux curve also exhibits a change in the slope

around 3 – 4 cm/s, confirming it to be the transition velocity.

110

Figure 5-9: Overall gas holdup curve using an air-water system at ambient conditions in a

0.1012 m diameter column

0

2

4

6

8

0 0.1 0.2

Gas holdup

Drif

t Flu

x

Figure 5-10: Drift flux plot using an air-water system at ambient conditions in a 0.1012 m

diameter column

Once the flow regime boundaries were defined using conventional methods, the obtained

photon counts history was analyzed to propose new “flow regime identifiers” for NGD.

The characteristic behavior of photon counts history and also the derived information

from the obtained time-series around the transition velocities, i.e., 3-4 cm/s will be

utilized to propose such identifiers.

111

5.2.2b Analysis of photon counts history Figure 5-11 shows the photon counts history over 20 sec. of acquisition length for: a) an

empty column (air) and b) water (without gas flow). The photon emission inherently

shows Poisson distribution, where the mean and the variance of the obtained photon

counts is the same. The photon counts history obtained in air and water (without gas

flow) in the current study also shows Poisson distribution. In case of an empty column,

the mean ≈ the variance = 265 while in water (no gas flow), the mean ≈ the variance =

130.

Figure 5-12 shows the photon counts history received by the detector at various

superficial gas velocities, a) 1, b) 3, c) 7, and d) 11 cm/s using air-water system at

ambient conditions in a 0.1012 m diameter column. It clearly shows an increase in

amplitude as well as oscillations in photon counts with an increase in superficial gas

velocity. The photon counts fluctuations at low superficial gas velocities are relatively

uniform, while at higher velocities, intense fluctuations can be observed, due to wide

bubble size distribution. At higher velocities, large peaks can also be observed which are

due to the presence of large bubbles in the path of γ-rays. The photon counts history

appears to show the signature of the prevailing flow regime.

(a) (b) Figure 5-11: Time-series of photon count fluctuations in a 0.1012 m diameter column in

a) empty column and b) water (no gas flow).

112

(a) (b)

(c) (d) Figure 5-12: Time-series of photon count fluctuations in a 0.1012 m diameter column

using air-water system at superficial gas velocities of a) 1, b) 3, c) 7, and d) 11 cm/s at

ambient conditions.

The obtained photon counts history was subjected to various time-series analyses.

i) Statistical analysis

Statistical analysis is one of the obvious methods to study a time-series. The mean, μ is

given by

N

xN

ii∑

== 1μ . (5-8)

113

The average deviation of a signal can be then written as

Average deviation = N

xN

ii∑

=

−1

μ. (5-9)

Although it is straightforward, the average deviation is almost never used in statistical

analysis. The important parameter is not average deviation but the power represented by

deviation from mean, called as the standard deviation, σ, or the the variance, σ2, and

given as

)1(

)(2

12

−

−=∑=

N

xN

ii μ

σ . (5-10)

Figure 5-13 shows the change in the second moment (i.e. the variance) of the photon

counts history with superficial gas velocity. An increase in superficial gas velocity

increases the variance of photon counts fluctuations. Around a superficial gas velocity of

3–4 cm/s, a noticeable increase in the variance with superficial gas velocity was

observed. The variance versus superficial gas velocity relationship shows two distinct

slopes. The change in the slope of the variance of the photons counts history was

observed at 3-4 cm/s. Based on the conventional methods, the transition from

homogeneous to heterogeneous flow also occurs at the same superficial gas velocities.

Hence, a change in slope of the variance of photon counts history can be used to identify

flow regime transition.

In the bubbly flow regime, the value of the slope of the variance is less, while in churn-

turbulent flow a rapid increase in the variance with superficial gas velocity was observed.

Apart from a Poisson distribution, the fluctuations in photon counts history are imparted

by the passage of bubbles in the system. The value of the variance is low in bubbly flow,

as small non-interacting bubbles with uniform sizes are present that result into lower

photon counts fluctuations and less the variance. However in churn-turbulent flow, both

small and large bubbles are present, resulting in a wide bubble size distribution. In

addition, there is an intense bubble-bubble interaction in this regime. In churn-turbulent

114

flow, the γ-rays are frequently intercepted by bubbles of different sizes and intensity

giving rise to higher fluctuations that result in higher value of the variance of the photon

counts history. The two distinct slopes in the variance are mainly due to the different

nature of bubble interactions and bubble size distribution in the two flow regimes. Hence,

the change in the variance indicates the flow regime transition point.

Lin et al. (1999) performed flow regime transition studies using pressure drop fluctuation

measurements. Figure 5-14 shows the transition velocity obtained in Lin et al. (1999) at

the same operating and design conditions used in the present work, based on the standard

deviation of the pressure fluctuation measurements. They performed experiments in a

0.1012 m diameter plexi-glass column using an air-water system to corroborate the

transition velocity obtained by pressure drop fluctuations with those of visual observation

and conventional methods such as the drift flux plot. Based on such evaluation, they

further implemented pressure drop fluctuations measurements for regime transition

identification at high pressure and temperature. The transition velocity obtained from the

change in the slope of the standard deviation of the pressure fluctuations (3.5 cm/s) is

close to the one obtained in the current study (3-4 cm/s).

Figure 5-13: Variation of the variance of photon counts fluctuations with superficial gas

velocity in a 0.1012 m diameter column using air-water system at ambient conditions.

115

Figure 5-14: Variation of the variance of pressure drop fluctuations with superficial gas

velocity in a 0.1012 m diameter column using air-water system at ambient conditions

(Reproduced from Lin et al., 1999).

ii) Deviation from Poisson distribution

γ-rays inherently show Poisson distribution (i.e. the mean = the variance) in empty

column as well as in water (no gas flow). Due to the introduction of gas in static water,

the photon counts history deviates from a Poisson distribution because the photon counts

obtained in a dynamic system have additional information characterizing the flow

behavior. Hence, the deviation from Poisson distribution might be able to decipher

information regarding the flow behavior and subsequently about the underlying flow

regime. It was observed that with an increase in superficial gas velocity, the mean and the

variance increase. In addition, the difference between the mean and the variance also

appears to increase with an increase in superficial gas velocity. To account for such a

deviation of the time-series from a Poisson distribution, a new coefficient was proposed,

called the coefficient of departure from Poisson distribution, DP, and defined as

pd

iP Variance

VarianceD

)()(

= , (5-11)

where (variance)i is the variance of the obtained photon counts history at a certain

superficial gas velocity, and (variance)pd is the variance of the obtained photon counts

history at that velocity, if it had been a Poisson distribution, i.e., the mean.

116

This reduces equation (5-11) to

i

iP Mean

VarianceD

)()(

= . (5-12)

Hence, it is the ratio of the variance and the mean of the obtained photon counts history at

a certain superficial gas velocity.

The value of DP in an empty scan and in water (no gas flow) was found to be, as

expected, unity. With an increase in superficial gas velocity, the value of DP departs from

unity. Figure 5-15 shows the change in the coefficient of departure from a Poisson

distribution with superficial gas velocity in a 0.1012 m diameter column using an air-

water system. The value of DP increases with an increase in superficial gas velocity. The

rate of change in the value of DP is less at low superficial gas velocities, but at higher

superficial gas velocities it increases significantly with the change in superficial gas

velocity. Only small bubbles are present in the system at low superficial gas velocities (in

bubbly flow) that imparts fewer fluctuations around the mean, and hence the deviation

with respect to the mean is less. However, in churn-turbulent flow, both small and large

bubbles come in the path of γ-rays, which imparts intense fluctuations around the mean.

Hence, the deviation of photon counts from the mean is significant at high superficial gas

velocities.

It was observed that for superficial gas velocities above 3 cm/s, the value of DP is greater

than 1.4. Based on the conventional methods, the transition velocity was found to be

around 3 – 4 cm/s; hence the behavior of the departure coefficient can be generalized

based on the flow regime. It was found that in the churn-turbulent flow regime the value

of DP was greater than 1.4. It should be noted that, although the coefficient of departure

from Poisson distribution has been defined based on the physics of γ-rays, its value for

flow regime demarcation is purely empirical.

117

Figure 5-15: The coefficient of departure from Poisson distribution versus superficial gas

velocity in a 0.1012 m diameter column using an air-water system at ambient conditions.

The proposed coefficient facilitates identification of the underlying flow regime at the

operating superficial gas velocity and promises to be a robust flow regime identifier in

bubble columns.

i) Autocorrelation Analysis

The autocorrelation function expresses the linear relationship between signal values at

two different times and can be mathematically written as

∫+∞

∞−

−= dttxtxT

Cxx ).()(1)( ττ , (5-13)

where τ is time lag, and μ and σ are the first and second moments of the distribution.

The autocorrelation function is used to estimate how well future values of a signal can be

predicted from knowledge of the signal history. It provides information regarding the

repetitiveness of a given signal. As long term processes do not appear in autocorrelation

curves, they are generally evaluated over the time lag of 0-2 sec without loss of any

important information (Smith, 1999).

118

The obtained photon counts histories were subjected to autocorrelation analysis. Figure 5-

16 shows the autocorrelation curve, i.e., the autocorrelation coefficient versus time lag in

bubbly flow at superficial gas velocities of a) 1, b) 3, and c) 4 cm/s. The autocorrelation

curves in bubbly flow exhibit the behavior of a typically random process and show a

shape close to an exponential curve. In homogeneous flow, as the name suggests, due to

the presence of uniform bubble sizes, the system is virtually similar everywhere. The

events evolving over the time are similar in nature in bubbly flow. Hence, the time-series

obtained in this regime is well correlated, as reflected in the autocorrelation curve.

(a)

(b) (c)

Figure 5-16: Autocorrelation curve at superficial gas velocities of a) 1, b) 3, and c) 4 cm/s

using an air-water system in a 0.1012 m diameter column at ambient conditions.

119

Figure 5-17 shows the autocorrelation curve in churn turbulent flows at superficial gas

velocities of a) 7, b) 9, and c) 11 cm/s. As the system enters into heterogeneous flow, the

coalescence of small bubbles results in the appearance of larger bubbles, which in turn

results into wider bubble size distribution. Hence, γ-rays encounter both small and large

bubbles. Due to interception by bubbles of different sizes and characteristics, the

probability of the same events evolving over time is relatively less, and hence the

obtained series is not well correlated. This reflects in a characteristic anti-correlation

superimposed on the exponential behavior in the autocorrelation curve in the churn-

turbulent flow regime.

(a)

(b) (c)

Figure 5-17: Autocorrelation curve at superficial gas velocities of a) 7, b) 9, and c) 11

cm/s using an air-water system in a 0.1012 m diameter column at ambient conditions.

The autocorrelation curve shows close to exponential behavior in bubbly flows, while in

churn-turbulent flows it exhibits characteristic anti-correlation behavior where cosine

120

behavior is superimposed on an exponential curve. The visibly different behavior of the

autocorrelation curves in the two regimes provides a means to demarcate them based on

the shape of the autocorrelation curve at the operating condition.

The behavior of the autocorrelation curves is a reflection of the nature of the time-series,

irrespective of its operating and design conditions. Based on the inherent nature of the

flow, the bubbly regime should exhibit correlated curve, while the churn-turbulent regime

should exhibit an uncorrelated curve. This fact can be utilized for online flow regime

identification in industrial reactors.

iv) Spectral Analysis The goal of spectral analysis is to describe the distribution of the power contained in a

signal over a frequency, based on a finite set of data. It converts information available in

the time-domain into the frequency-domain.

Spectral analysis is performed using Fourier transform, which is named after the French

mathematician and physicist Jean Baptiste Joseph Fourier. Fourier presented a paper in

1807 to the Institut de France on the use of sinusoids to represent temperature

distributions. The paper contained the (then) controversial claim that any continuous

periodic signal could be represented as the sum of properly chosen sinusoidal waves.

Among the reviewers were two of history's most famous mathematicians, Joseph Louis

Lagrange and Pierre Simon de Laplace.

While Laplace and the other reviewers voted to publish the paper, Lagrange adamantly

protested. For nearly decades, Lagrange had insisted that such an approach could not be

used to represent signals with corners, i.e., discontinuous slopes, such as in square waves.

The Institut de France bowed to the prestige of Lagrange, and rejected Fourier's work.

Luckily, Fourier had other things to keep him busy: political activities, expeditions to

Egypt with Napolean, and trying to avoid the guillotine after the French revolution. It

121

was only after Lagrange died that the paper was finally published (Smith, 1999).

Afterwards, it has been used abundantly to analyze time-series in various fields.

Fourier transform, F, of a time series x(t) can be given as

∫+∞

∞−

−= dttfjtxxF ).2exp()()( π , (5-15)

where, f, is frequency.

The power spectral density (PSD), xxϕ , is the square of the magnitude of the continuous

Fourier transform

)(*).( xFxFxx =ϕ , (5-16)

where F*(x) is the complex conjugate of Fourier transform.

Figure 5-18 shows the log-log normalized psdf plots at superficial gas velocities of a) 1,

b) 3, c) 4, d) 6, e) 9, and f) 11 cm/s. The normalized psdf is calculated by substracting the

original time-series from its mean. At 1 and 3 cm/s, i.e., in bubbly flow, the psdf plot did

not show any power law fall off, while at higher superficial gas velocities, i.e., in the

transition and churn-turbulent flow regimes, a distinct the power-law fall off was

observed. An analogy can be drawn between power-law fall off observed in the current

study with that observed in single phase turbulent flow.

The general picture of energy distribution in a single phase turbulent flow can be

explained as follows (Hinze, 1975). There exist large primary eddies, which originate

during the formation of the flow or as a result of disturbances. These eddies cause large

fluctuations of low frequency. Their size is comparable to the characteristic geometrical

dimension of the flow system.

122

(a) (b)

(c) (d)

(e) (f)

Figure 5-18: Typical log-log plot of normalized psdf at superficial gas velocities of a) 1,

b) 3, c) 4, d) 6, e) 9, and f) 11 cm/s, using an air-water system in a 0.1012 m diameter

column at ambient conditions.

123

The eddies in the range of the peak in spectral energy can be regarded as large. They

contain most of the energy and contribute little to energy dissipation by internal friction.

These eddies dissipate energy through fine-scale eddies. The process, by which energy

travels from large to fine scale in an energy cascade, is one-way street where counterflow

of energy from small to large scale has previously considered insignificant compared to

energy transfer in the opposite direction. It is now better understood that the energy flow

in both directions is significant, with just a net excess of energy moving to the fine scale

to be dissipated. The flow of energy transfers from large scale to fine scale through

vortex stretching and folding, and transfers from fine scale to large when vortices

compress, recombine, or reconnect into larger vortices. Energy dissipation by friction

occurs in the small eddies of high frequency.

Hence, one can divide the flow into three scales: the mesoscale, macroscale, and

microscale. Mesoscale eddies fluctuate at low frequency and have a size comparable to

the diameter of the column. Macroscale eddies contain most of the energy, microscale

eddies dissipates energy at the finer scale.

The famous Russian mathematician Kolmogorov pioneered a scale analysis that has had a

profound influence on the way in which the energy spectrum in turbulence is understood.

The general picture of energy transfer explained above in a single phase turbulent flow

forms the basis of the theory of isotropic turbulence. This theory is based on the

following two assumptions.

1) While the stirring force (i.e. the mechanism causing turbulence production) that

creates turbulence varies from flow to flow and affects the turbulence characteristics,

the small-scale motions at which dissipation takes place develop a common form for

all flows. For sufficiently great Reynolds numbers, the turbulence is in a universal

equilibrium that is entirely determined by the kinematic viscosity and the rate of

energy dissipation per unit mass.

124

2) In the so-called ‘inertial subrange’, the energy spectrum becomes independent of

viscosity and is solely determined by energy dissipation per unit mass. The following

distribution law of Kolomogorov applies:

E α k-5/3, (5-17)

where, k is the wavenumber and is proportional to frequency.

In the bubble column literature, attempts have been made to apply the theory of isotropic

turbulence. The ideas of Kolmogorov have proved to be of great value, and the past

experimental studies suggest and to some extent justify the applicability of this theory to

bubble columns. However, it should be noted here that the current study attempts neither

to justify/evaluate the applicability of Kolmogorov’s law for bubble columns nor to gain

insights into such flows based on its applicability.

Zakrzewski et al. (1981) performed constant temperature film anemometer experiments

to measure liquid velocity in a 0.14 m diameter and 2.69 m high column. The liquid

phase was water and 1% Methanol. Two spargers were employed, viz., a sintered plate

(pore diameter of 5 μm) and a perforated plate (home diameter = 1 and 3 mm). They

measured the turbulent intensities and determined the energy distribution spectra.

Figure 5-19: Power spectra of liquid velocity fluctuations in a bubble column, by

Zarzewski et al. (1981).

125

Zakrzewski et al. (1981) found the slope of the log-log energy distribution plot to be –2

in the ‘inertial subrange’, as shown in Figure 5-19. They concluded that Kolomogrov’s

law for single phase turbulence with –5/3 slope was derived for grid turbulence, whereas

for the case of the bubble swarm turbulence in bubble columns, a slope of –2 is to be

expected.

Lance and Bataille (1991) performed Laser Doppler Anemometry (LDA) and hot-film

anemometry experiments in an air-water bubble column. The test section used in the

study was a 2 m long square channel (0.45 X 0.45 m) operated at ambient conditions. The

experimental conditions were such that the void fraction was varied between 0 to 3 %.

Lance and Bataille (1991) found that the classical –5/3 power law describing the behavior

of the spectra in the high wavenumber range was progressively replaced by another

power law of exponent equal to –8/3.

Recently, Groen (2004) performed LDA studies in an air-water system in three different

column diameters, i.e., 15, 23, and 40 cm. Groen (2004) found the value of the slope to

be in the range of –3/2 and –5/3. The close observation of psdf plots provided in Groen

(2004) thesis shows that the frequency range where such a power law fall-off was

observed depends on the radial location of the measurement. As one moves inwards to

the column center, the power spectra also appear to shift inwards, as shown in Figure 5-

18. The power-law fall-off seems to exist in the ‘inertial subrange’ for measurement

(a) (b)

126

(c)

Figure 5-20: LDA axial velocity signal power spectra a) D = 15 cm, Ug = 2.7 cm/s, z/D =

5.5, b) D = 23 cm, Ug = 1.2 cm/s, z/D = 6, and c) D = 40 cm, Ug = 5.5 cm/s, z/D = 5

(Groen, 2004)

locations close to the wall. However, such a slope was observed in far smaller frequency

ranges for measurement locations towards the column center. The power spectra at a few

measurement locations show a power-law fall off in the frequency range observed in the

current work.

It is worth mentioning that in earlier studies, experiments were apparently performed in

the bubbly flow regime. The power-law fall off was observed in homogeneous flow in

these studies. In the current study, no such exponent was observed in bubbly flow. Based

on this, further quantitative analysis was performed for observed power-law fall off in the

psdf plot of photon counts history at higher superficial gas velocities in the current study.

The psdf plot of photon counts history obtained in an empty column (air) and water (with

no gas flow) is shown in Figure 5-21a and b. As mentioned earlier, a Poisson distribution

was observed during scans in air and water (with no gas flow). The log-log normalized

psdf plot does not show any variation in the power. This is expected, as the photon counts

obtained in air and water indicate characteristic noise inherent to gamma-rays. This rules

out the possibility of occurrence of meaningful power spectra and its slope, due to the

contribution of, or being an artifact of, a Poisson distribution.

127

(a) (b)

Figure 5-21: Log-log plot of normalized psdf of photon counts history obtained in a)

empty column and b) water (with no gas flow).

(a) (b)

(c) (d) Figure 5-22: Log-log plot of normalized psdf with fitted slope line at superficial gas

velocities of a) 4, b) 6, c) 9, and d) 11 cm/s using an air-water system in a 0.1012 m

diameter column at ambient conditions.

128

Next, the operating conditions where the psdf plot showed a power-law fall off were

analyzed. In general, the power-law fall off was observed in the frequency range of 5 –

15 Hz, and the data points in this range were regressed to obtain the best fit. The fitted

equations are shown in Figure 5-22a, b, c, and d along with the R-squared value. The R-

squared values were found to be equal to or greater than 0.85 in all the cases. At high

superficial gas velocities, the R-squared values were close to 0.96.

The distinct slope in the psdf plot started to appear at a superficial gas velocity of 4 cm/s

where the transition regime exists (Figure 5-22a). The slope increases with an increase in

superficial gas velocity. At a superficial gas velocity of 6 cm/s, the slope is close to –1

(Figure 5-22b). Above superficial gas velocities of 6 cm/s, the slope gradually increases

and remains close to –1.7 in fully churn-turbulent flow. Figures 5-22c and d show the

log-log plot of the normalized psdf at superficial gas velocities of 9 and 11 cm/s with an

exponent close to –1.7. Table 5-3 shows the slopes of the power spectra at studied

operating conditions. It is clear that Kolomogorov’s –5/3 law appears to be applicable in

Table 5-3: Slope of power spectra at studied operating conditions

Superficial gas

velocity

(cm/s)

Slope of power spectra

1 - 2 - 3 - 4 - 0.7 5 - 0.7 6 - 1.02 7 -1.6 8 - 1.62 9 - 1.65 10 - 1.67 11 - 1.69 12 -1.7

the two phase churn-turbulent flow, as in a single phase turbulent flow, indicating that the

mechanism of energy dissipation in two-phase flow is similar to that observed in single

129

phase turbulent flows. However the power-law fall off was observed at relatively low

frequencies during these studies.

In the current study, the exponent was observed in either transition or churn-turbulent

flow regimes. The close observation of power spectra obtained in this study shows that

the values of the power in water (with no gas flow) and the values in bubbly flows are

close to each other, indicating that a Poisson distribution might be still dominant at these

conditions. The value of the coefficient of a Poisson distribution also varies up to 1.2 –

1.3. At high superficial gas velocities the appearance of large bubbles increases the

fluctuations in the system, adding significant flow dynamics information to a Poisson

distribution. This might be a possible reason for the absence of the slope in power spectra

in bubbly flow using NGD.

Apart from its analogy to a single phase turbulent flow, the observed slope can be utilized

for the main objective of this study, i.e., to demarcate the underlying flow regime. It is

worth mentioning that although the literature studies exhibit power law fall off in bubbly

flow, such behavior was not observed in the current study. The current study observed

power law fall-off in transition flow (-0.7), which gradually increased to –1.7 in churn-

turbulent flow. The previous studies were performed using either LDA or a hot film

anemometer. No experiments were performed during those studies in churn-turbulent

flow.

Based on the available information and the current study, it can be concluded that no

power law fall off in bubbly flow and power law fall off in the churn-turbulent flow can

be exclusive characteristics of photon counts time-series obtained using NGD. The main

goal of this study was not to analyze the power spectra or its utility in understanding the

flow in bubble column. However, such an observation is helpful in developing a ‘flow

regime identifier’ for NGD, which is the main objective of the current study.

In conclusion, the following ‘flow regime identifiers’ were developed for NGD using an

air-water system:

130

1) The coefficient of departure is greater than 1.4 in the churn-turbulent flow.

2) The autocorrelation curve exhibits different behavior in bubbly and churn-

turbulent flows. In bubbly flow, it exhibits a near exponential curve, while churn-

turbulent flow exhibits anti-correlation behavior superimposed on an exponential curve.

3) The normalized logarithmic psdf plot shows no slope in bubbly flow, while a

distinct slope was observed in churn-turbulent flow.

The development of NGD, along with its identifiers, presents an opportunity to identify

the prevailing flow regime without disturbing the process operation. As mentioned

earlier, NGD can be mounted externally, and analyzing the obtained time-series at

process conditions in the context of the developed identifiers can provide information

regarding the prevailing flow regime. The developed method negates the need to observe

the evolution of a secondary parameter over the range of superficial gas velocities for

flow regime identification, and hence it can be applied without changing the process

conditions.

These ‘flow regime identifiers’ were developed based on the experiments performed in

an air-water system at ambient pressure using a plexi-glass column that enables visual

observation of the flow. The next section deals with the evaluation of the developed ‘flow

regime identifiers’ at various operating and design conditions.

5.2.3 Evaluation of the ‘flow regime identifiers’ developed for NGD In this part, the ‘flow regime identifiers developed for NGD are evaluated at high

pressure and in different systems. For this purpose, the experiments were performed in a

6” diameter stainless steel column. The details of this experimental and the CT setup are

provided in Chapter 3, and will not be repeated here. During these experiments, an

existing CT was converted to densitometry by placing the central detector in front of the

radioactive source. One should recall here that the experimental setup used for these

experiments is made of stainless steel. In this way we demonstrate the applicability of the

developed technique and its ‘flow regime identifiers’ in different systems, as well as in a

131

steel column. This is important when we consider applying NGD for flow regime

monitoring in industrial columns. The overall gas holdup experiments were performed

using the column with windows (Figure B-1), while the densitometry experiments were

performed using the experimental setup shown in Figure 3-1. Table 5-4 shows the

operating conditions and the systems used. Air was used as the gas phase, while the

liquid phases were water and C9 – C11 mixture. The composition of C9 – C11 mixture was:

≤ C8 3.3 %, C9 36.3 %, C10 34.5 %, C11 23.8 %, and ≥ C12 1.9 %. The physical

properties of this mixture are different from water [density = 0.726 gm.cc-1; viscosity =

0.85 mPa s; surface tension = 23.2 mN.m-1]. The dynamic liquid height in all the

experiments was the same, i.e., L/D ~ 10. The acquisition frequency of the photon counts

history was 50 Hz. The time-series, with the number of data points, N = 15000 was

collected at superficial gas velocities of 1 to 20 cm/s with intervals of 1 cm/s and at 30

cm/s.

Table 5-4: Experimental conditions for the evaluation of ‘flow regime identifiers’

System Operating

pressure

(MPa)

Air-water 0.1

Air-water 1.0

Air-C9-C11 0.1

Air-C9-C11 1.0

First the transition velocities were determined based on the overall gas holdup and the

drift flux plot, which enable us to tag conditions based on the prevailing flow regime. The

transition velocity obtained using the traditional methods were compared with the one

obtained using the variation of Dp with superficial gas velocity. Then the photon counts

history obtained in different flow regimes were analyzed using autocorrelation analysis

and spectral analysis to evaluate the applicability of the developed ‘flow regime

identifiers’. The identifiers were found to be satisfactory.

132

5.2.3a Air-water system, P = 0.1 MPa Figures 5-23a and b show the overall gas holdup curve and the drift flux plot for an air-

water system in a 6” diameter column at ambient pressure. Based on the change in the

slope of the gas holdup curve and the drift flux plot, the transition velocity at this

condition is 5 cm/s. Hence, the developed criteria were evaluated for data collected in the

identified different flow regimes.

0

10

20

30

0 0.1 0.2 0.3 0.

Overall gas holdup (-)

Drif

t flu

x,

0

0.1

0.2

0.3

0.4

0 10 20


Ove

rall

gas

hold

up (-

4

j

30

)

(a) (b)

Figure 5-23: a) Overall gas holdup curve and b) drift flux plot in an air-water system at

ambient pressure in a 6” diameter stainless steel column

Figure 5-24: Variation of coefficient of departure, Dp with superficial gas velocity in an

air-water system at ambient pressure in a 6” diameter stainless steel column

133

-0.2

0

0.2

0.4

0.6

0.8

1

0 1 2

Time lag (sec)

Aut

ocor

rela

tion

func

tion

(-)

-0.2

0

0.2

0.4

0.6

0.8

1

0 1

Time lag (sec)

Auto

corre

latio

n co

effic

ient

(-)

2

(a) (b)

Figure 5-25: Autocorrelation curve in a) bubbly flow (Ug = 2 cm/s) and b) churn-

turbulent flow (Ug = 20 cm/s) at ambient pressure using an air-water system.

(a) `(b)

(c)

Figure 5-26: Psdf plot at superficial gas velocities of a) 2 cm/s, b) 7 cm/s, and c) 20 cm/s

and ambient pressure using an air-water system in a 6” diameter stainless steel column.

134

Figure 5-24 shows the variation of the coefficient of departure from a Poisson

distribution with superficial gas velocity. It can be observed that the value of Dp is

greater than 1.4 for superficial gas velocities above 5 cm/s. Figure 5-25a shows the

autocorrelation curve in the bubbly flow (Ug = 2 cm/s), while Figure 5-25b shows the

autocorrelation curve in the churn-turbulent flow (Ug = 20 cm/s). The autocorrelation

curve in the bubbly flow shows the exponential behavior, while the one in the churn-

turbulent flow shows characteristic anti-correlation, indicating the prevailing flow

regime. Figure 5-26 shows the psdf plot at superficial gas velocities of 2, 7, and 20 cm/s.

In the bubbly flow no power-law fall off was observed, while at the conditions above

transition velocity, i.e., 5 cm/s, a distinct power-law fall off was observed. At Ug = 7

cm/s, the slope was close to – 1, while at Ug = 20 cm/s, it was -1.7. It showed a gradual

increase in the value of the slope with an increase in superficial gas velocity. However,

the value of the slope levels off at high superficial gas velocities. At Ug =30 cm/s, the

value of slope was -1.71.

5.2.3b Air-water system, P = 1.0 MPa

0

5

10

15

20

0 0.2 0.4


Drif

t flu

x, j

0

0.2

0.4

0.6

0 10 20 3

Superficial gas velocity (cm/s)`

Ove

rall

gas

hold

up (-

0

)

(a) (b)

Figure 5-27: a) Overall gas holdup curve and b) drift flux plot in an air-water system at

an operating pressure of 1 MPa in a 6” diameter stainless steel column

Based on the overall gas holdup curve (Figure 5-27a) and drift flux plot (Figure 5-27b),

the regime transition velocity is around 8 – 9 cm/s at an operating pressure of 1 MPa in

an an air-water system. Figure 5-28 shows that for superficial gas velocities greater than

135

Figure 5-28: Variation of coefficient of departure, Dp, with superficial gas velocity in an

air-water system at an operating pressure of 1 MPa in a 6” diameter stainless steel

column

-0.2

0

0.2

0.4

0.6

0.8

1

0 0.5 1 1.5 2

Time lag (sec)

Auto

corr

elat

ion

coef

ficie

nt (-

)

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 0.5 1 1.5 2

Time lag (sec)

Aut

ocor

rela

tion

coef

ficie

nt (-

)

(a) (b) Figure 5-29: Autocorrelation curve in a) bubbly flow (Ug = 2 cm/s) and b) churn-

turbulent flow (Ug = 20 cm/s) at an operating pressure of 1 MPa using an air-water

system.

(a) (b)

136

(c ) Figure 5-30: Psdf plot at superficial gas velocities of a) 2 cm/s, b) 10 cm/s, and c) 20 cm/s

and an operating pressure of 1 MPa, using an air-water system in a 6” diameter stainless

steel column.

8 cm/s the value of Dp is higher than 1.4. In addition, the autocorrelation curves in

bubbly flow (Ug = 2 cm/s) and churn-turbulent flow (Ug = 20 cm/s) show distinctly

different behavior (Figure 5-29). The logarithmic psdf plot reveals that there is no power

law fall off in the bubbly flow (Ug = 2 cm/s), while above the transition velocities, a

distinct power law fall off was observed (Figure 5-30). The value of the slope of varies

from –1 at Ug = 10 cm/s to –1.6 at Ug = 20 cm/s, while it is –1.65 at Ug = 30 cm/s.

5.2.3c An air-C9-C11 system, P = 0.1 MPa

0

0.1

0.2

0.3

0.4

0.5

0 10 20 30


Gas

hol

dup

(-)

0

10

20

30

40

0 0.2 0.4 0.6

Gas holdup

Drif

t flu

x

(a) (b) Figure 5-31: a) Overall gas holdup curve and b) drift flux plot in an air-C9-C11 system at

an operating pressure of 0.1 MPa in a 6” diameter stainless steel column

137

Based on the overall gas holdup curve and the drift flux plot (Figure 5-31), the transition

velocity in an air-C9-C11 system at an operating pressure of 0.1 MPa was around 8 cm/s.

Figure 5-32 shows that for superficial gas velocities less than 8 cm/s the value of Dp is

less than 1.4. The autocorrelation curves in the bubbly (Ug = 2 cm/s) and the churn-

turbulent (Ug = 20 cm/s) flows show distinctly different behavior (Figure 5-33). The

logarithmic psdf plot shows power law fall off at superficial gas velocities greater than

the transition velocity (Figure 5-34).

Figure 5-32: Variation of coefficient of departure, Dp, with superficial gas velocity using

an air-C9-C11 system at operating pressure of 0.1 MPa in 6” diameter stainless steel

column

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 0.5 1 1.5 2

Time lag (sec)

Aut

ocor

rela

tion

coef

ficie

nt (-

)

-0.2

0

0.2

0.4

0.6

0.8

1

0 1

Time lag (sec)

Auto

corre

latio

n co

effic

ient

(-)

2

(a) (b) Figure 5-33: Autocorrelation curve in a) bubbly flow (Ug = 2 cm/s) and b) churn-

turbulent flow (Ug = 20 cm/s) at ambient pressure using an air-C9-C11 system.

138

log(Y) = -1 log(X) + 2 R^2 = 0 8

(a) (b)

log(Y) = -1.7 log(X) + 2 2


and an ambient pressure using an air- C9-C11 system in a 6” diameter stainless steel

column.

5.2.3d An air-C9-C11 system, P = 1.0 MPa

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 10 20


Ove

rall

gas

hold

up (-

)

30 0

5

10

15

20

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7


Drif

t flu

x, j

(a) (b)

Figure 5-35: a) Overall gas holdup curve and b) drift flux plot in an air-C9-C11 system at

an operating pressure of 1 MPa in a 6” diameter stainless steel column

139

The overall gas holdup curve and the drift flux plot (Figure 5-35) in an air-C9-C11

system at operating pressure of 1 MPa reveal that the transition velocity is around 12

cm/s. The variation of Dp with superficial gas velocity (Figure 5-36) at this condition

shows that below the transition velocity, the value of Dp is less than 1.4. Figure 5-37

shows the autocorrelation curve that exhibits different behavior in the bubbly (Ug = 2

cm/s) and the churn-turbulent (Ug = 20 cm/s) flows. The logarithmic psdf plot (Figure 5-

38) shows power law fall-off at superficial gas velocities greater than the transition

velocity while no such power law fall-off was observed for velocities less than the

transition velocity.

Figure 5-36: Variation of coefficient of departure, Dp, with superficial gas velocity using

an air-C9-C11 system at an operating pressure of 1 MPa in a 6” diameter stainless steel

column

-0.2

0

0.2

0.4

0.6

0.8

1

0 0.5 1 1.5 2

Time lag (sec)

Aut

ocor

rela

tion

coef

ficie

nt (-

)

-0.2

0

0.2

0.4

0.6

0.8

1

0 0.5 1 1.5 2

Time lag (sec)

Aut

ocor

rela

tion

coef

ficie

nt (-

)

(a) (b)

Figure 5-37: Autocorrelation curves in a) bubbly flow (Ug = 2 cm/s) and b) churn-

turbulent flow (Ug = 20 cm/s) at an operating pressure of 1 MPa using an air-C9-C11

system.

140

(a) (b)


and an operating pressure of 1 MPa using an air- C9-C11 system in a 6” diameter stainless

steel column.

In the above section, the applicability of NGD for flow regime demarcation was

evaluated in different systems and at high operating pressure. The transition velocity

obtained from the overall gas holdup curve and the drift flux plot matches the one

revealed by variation in Dp. It was also observed that the ‘flow regime identifiers’

developed for NGD [listed in Section 5.2.2c] using an air-water system in a 4” diameter

column are applicable in different systems, at high operating pressure, and more

importantly in stainless steel columns. It is evident that the developed flow regime

identifiers are functions of the nature of the obtained photon counts history rather than the

operating and design conditions. The nature of the photon counts history, in turn, is a

function of the prevailing flow behavior.

141

5.2.3e Observed effects of operating and design parameters on flow regime

transition

i) Effect of operating pressure

In the current study, two operating pressures were studied in two different systems. An

increase in operating pressure from 0.1 to 1 MPa increased the transition velocity from 5

to 8 cm/s in an air-water system, while it increased from 8 to 12 cm/s in an air- C9-C11

system. An increase in pressure increased the breakup rate, reduced the coalescence rate,

and delayed the appearance of large bubble and thereby the flow regime transition. The

effect of operating pressure observed in this study is in line with the previous findings by

Krishna et al. (1991), Wilkinson et al. (1991), Reilly et al. (1994), Lin et al., (1999), and

Lin et al. (2001).

ii) Effect of physical properties

The change in the liquid from water to C9-C11 increased the transition velocity from 5 to 8

cm/s at ambient pressure, while it increased from 8 to 12 cm/s at an operating pressure of

1 MPa. The mixture of C9-C11 has a lower viscosity and surface tension than water. The

reduction in viscosity and surface tension appear to have qualitatively similar effects on

the flow regime transition. The decrease in viscosity resulted in an unstable interface that

in turn resulted into a higher bubble break up rate and a lower coalescence rate, and

delayed the appearance of large bubble. The reduction in surface tension also shows a

similar effect. Urseanu (2000) studied the effect of surface tension by adding various

percentages of ethanol in water. Based on dynamic gas disengagement (DGD) studies,

she found that an addition of alcohol tends to suppress the coalescing tendencies of small

bubbles and thereby delays flow regime transition. Hence, the combined effect of low

viscosity and surface tension results in an increase in the transition velocity in C9-C11 at

both ambient and high pressures.

142

iii) Effect of column diameter

The reported effect of column diameter on the flow regime transition remains conflicting.

Based on their own data and the literature data in an air-water systems, Sarrafi et al.

(1999) found that transition velocity increases with an increase in column diameter,

which becomes independent of column diameter beyond 0.15 m. Earlier, Ohki and Inoue

(1970) found that transition velocity increases with an increase column diameter in the

range of 0.04 – 0.16 m. Urseanu (2000) found a general trend of an increase in transition

holdup with an increase in column diameter in an air-water and an air-Tellus oil systems.

However, Ruzicka et al. (2001) utilized their own gas holdup data from three different

column diameters (0.14, 0.29, and 0.4 m) to calculate the transition velocity. At different

liquid static heights they found that an increase in column diameter reduced the transition

velocity. Their results are in line with the observations of Zahradnik et al. (1997).

The current study provides a comparison of the transition velocity obtained in 4” (a

0.1012 m) and 6” (0.1615) diameter columns using an air-water system at ambient

pressure. In both cases, the dynamic liquid height was maintained the same (L/D ~ 10).

The transition velocity in a 4” column was 3 cm/s, while in a 6” column it was 5 cm/s.

Thus the current study observed an increase in the transition velocity with an increase in

column diameter, similar to the findings of Ohki and Inoue (1970) and Sarrafi et al.

(1999). In addition, transition gas holdup in a 4” column was 0.11, while in a 6” column

it was 0.2. Hence, an increase in column diameter increased the transition gas holdup,

similar to the findings of Urseanu (2000).

5.2.4 Evaluation of literature correlations

In this section, the transition velocities predicted using reported correlations are

compared with the ones obtained in this study. These correlations are provided in section

5.1.3.

143

Figures 5-39a and b show the comparison of the predictions of these correlations with

that of the experimental data obtained in 4 and 6 inch diameter columns. In general, both

correlations show vast differences between the prediction and experimental data. Table

5-5 shows the % relative error between predicted and experimental data. The observed

percent relative errors are higher than the permissible engineering errors. Surprisingly,

both correlations show higher percent relative errors at ambient pressure.

However, the correlation of Reilly et al. (1992) predicts the transition velocity in a 4” (a

0.1012 m) diameter column at ambient pressure using an air-water system within 2 % of

relative error. One should note here that Reilly et al. (1992) correlation was developed

based on the experimental data in a 0.15 m diameter column. Hence care should be taken

regarding such a comparison.

(a) (b)

Figure 5-39: Comparison of reported correlations with transition velocities obtained

based on variation in Dp of the photon counts history in a) an air-water system b) an air-

C9-C11 system at ambient and high pressure.

144

Table 5-5 Statistical comparisons of prediction of correlations with experimental data

% absolute relative error

System Pressure

(MPa)

Column

diameter

(m)

Experimental

Utrans

(m/s)

Reilly et al. Wilkinson et al. (1992) (1991)

Air-water 0.1 0.1012 0.03 1.7 98

Air-water 0.1 0.1615 0.05 39 96

Air-water 1.0 0.1615 0.08 29 31

Air-C9-C11 0.1 0.1615 0.08 64 95

Air-C9-C11 1.0 0.1615 0.12 58 51

5.3 Remarks

The goal set for this chapter was to develop and demonstrate non-invasive techniques

such as CT and NGD for flow regime demarcation and to explore their use as ‘flow

regime identifiers’.

In the first part, experiments were performed using a single source γ-ray CT in a high

pressure bubble column. The obtained gas holdup radial profiles were studied for flow

pattern identification. Based on the cross-sectional averaged gas holdup estimated from

the obtained radial gas holdup profiles, the regime transition velocity was calculated

using both the gas holdup curve and the drift flux plot. The evolution of the steepness

parameter with superficial gas velocity was analyzed, and the ‘break-point’ in the

steepness parameter curve was found to reveal information regarding transition velocity.

The transition velocity obtained from the steepness parameter curve was evaluated with

traditional methods and found to be in good agreement. The effect of operating pressure

on the flow regime transition was studied using the developed methodology. The

transition velocity was found to increase with an increase in operating pressure. Also, it

was observed that the change in the flow regime is noticeable at ambient conditions,

while at higher pressure, a gradual change occurs over a region of superficial gas

145

velocities. The obtained transition velocities were compared with the predicted transition

velocities of Wilkinson (1991) and Reilly et al. (1994) correlations. Both correlations

noticeably underpredict the experimental transition velocities; hence, the state of current

correlations needs to be further improved.

In the second part, the feasibility of NGD for flow regime demarcation in bubble column

reactors was explored. The well-known air-water system was utilized for such feasibility

studies, as well as to propose promising “flow regime identifiers”. Experiments were

performed in a laboratory scale column (diameter = a 0.1012 m, height = 1.2 m) at

ambient conditions. Superficial gas velocities were varied from 1 to 12 cm/s, with an

interval of 0.5 cm/s near transition region. The flow regime boundaries were determined

based on conventional methods such as the change in slope of gas holdup curve and the

drift flux plot.

The photon counts history obtained using NGD was subjected to statistical analysis,

autocorrelation analysis, and spectral analysis. Based on the comparison of such time-

series analyses with those of conventional methods, promising flow regime identifiers for

NGD were proposed. In general, the photon counts history revealed the signatures of the

underlying flow regime. Based on the inherent nature of gamma-ray emission, a new

parameter, called the coefficient of departure from Poisson distribution, was proposed

and found to be greater than 1.4 for churn-turbulent flow regimes. Autocorrelation

analysis exhibited different behavior in bubbly and churn-turbulent flow regimes.

Spectral analysis showed a distinct power-law fall off in the churn turbulent flow regime,

with its slope close to – 5/3, similar to the slope observed in a single phase turbulent

flow. The proposed “flow regime identifiers” for NGD can be helpful in demarcating

underlying flow regimes in laboratory as well as in industrial scale columns, and can be

utilized for online flow regime diagnostics. The ‘flow regime identifiers’ developed in

this work were evaluated for their applicability in different systems and at high operating

pressure, and were found to identify prevailing flow regimes satisfactorily.

146

In addition, the effects of operating and design parameters on the flow regime transition

observed during this study were discussed. The current state of correlation prediction was

also evaluated. It was found that the current state of prediction could not predict

transition velocities at the performed experimental conditions with statistical confidence.

147

Chapter 6.

Scaleup of Bubble Column Reactors

This chapter focuses on proposing and evaluating a new methodology for hydrodynamic

similarity and subsequently for scaleup of bubble column reactors. The available scaleup

procedures for bubble column reactors have summarized and critically reviewed by

Shaikh and Al-Dahhan (2007b), soon to be published. The findings were briefly

presented in Chapter 2. This part of the work develops and proposes a new hypothesis for

hydrodynamic similarity in bubble columns, based on the conclusions of the above

mentioned review and the understanding developed through abundant hydrodynamic

studies performed at the CREL over the years. The new hypothesis proposed in this work

was also evaluated using existing advanced diagnostic techniques such as CT and

CARPT.

In this chapter, the hydrodynamic similarity hypothesis is discussed in the first section,

followed by a description of the experimental conditions needed to evaluate the proposed

hypothesis. The next section presents the experimental results obtained under similarity

and mismatch conditions, followed by a discussion.

6.1 Hypothesis for hydrodynamic similarity

As mentioned in Chapter 2, the scaleup procedures reported so far utilize the similarity of

global parameters, such as overall gas holdup, for hydrodynamic similarity in two

columns. Such similarity based on global parameters is not surprising, because over the

years bubble column hydrodynamics have been quantified mostly by global parameters

such as overall gas holdup and mass transfer coefficient. However, while hydrodynamic

similarity based on overall hydrodynamics may be applicable in bubbly flow, in the

churn-turbulent flow regime, such criteria may possibly lead to a different gas holdup

distribution across the column cross-section. Figure 6-1 shows the gas holdup radial

148

profile obtained using CT in an air-water system (Ong, 2003; Kemoun et al., 2001) at

different operating conditions with the overall gas holdup of 0.41.

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

r/R

Gas

Hol

dup

D6U60P1Water

D6U12P7Water

Figure 6-1: Comparison of gas holdup radial profile in a 6” column using an air-water

system at two different operating conditions [D6U12P7Water: 7 bar, 12 cm/s, an air-

water (Kemoun et al., 2001); D6U60P1Water: 1 bar, 60 cm/s, and an air-water (Ong,

2003)] with similar overall gas holdups (~ 0.41).

Although these systems have similar overall gas holdups, the existence of different gas

holdup radial profiles possibly leads to different flow patterns and mixing intensities. The

conclusions of Macchi et al. (2001) [Section 2.3] and Figure 6-1 suggests that the two

systems can have similar overall gas holdups but different flow patterns and mixing

intensities. This indicates that two systems can be globally similar in nature, but have

different local hydrodynamics. Hence, similarity based only on overall gas holdup does

not appear sufficient.

Based on this, we propose a new methodology based on the hypothesis that

“Overall gas holdup and its radial profile or cross-sectional distribution should be the

same for two reactors to be dynamically similar.”

149

This work attempts to evaluate the proposed methodology utilizing advanced diagnostic

techniques such as CT and CARPT. Based on the combination of similarity and mismatch

experiments, we will show whether similar overall gas holdups and similar gas holdup

radial profiles indicate similar hydrodynamic performance in two reactors.

6.2 Experimental conditions

The first step in the experimental evaluation was to identify the needed operating

conditions. The experimental conditions were identified that have the same overall gas

holdup and gas holdup radial profile. These conditions are called similarity conditions.

Additionally, experimental conditions were identified such that had same overall gas

holdup, but mismatched radial profiles. These conditions are called as mismatch

conditions. The mismatch conditions were identified to further demonstrate that

similarity of gas holdup and its radial profile is essential to maintain similar

hydrodynamic performance.

The procedure for experimental evaluation of the proposed methodology is as follows,

1) Identify experimental conditions that have similar overall gas holdup. The overall gas

holdup is obtained by measuring the change in liquid height [d

SdG H

HH −=ε ] (where

Hd and HS are the dynamic and static liquid heights, respectively). In all these

experiments, the dynamic height was kept around 1.8 m (L/D ~ 11).

2) Perform CT experiments to identify similarity conditions.

3) Perform CT experiments to identify mismatch conditions.

4) Perform CARPT experiments at the identified similarity/mismatch conditions to

measure the detailed hydrodynamics (the radial profiles of liquid velocity and

turbulent parameters) in order to assess the proposed methodology for the

hydrodynamic similarity hypothesis.

150

Table 6-1 shows the similarity conditions, while Table 6-2 shows the mismatch

conditions identified during this study. The gas holdup radial profiles at the conditions of

similar overall gas holdup have been measured using CT at the desired conditions. A few

experimental conditions in this study are extracted from the CREL database (references

mentioned in Tables 6-1 and 6-2), in addition to the performed experiments. Although

CT and CARPT experiments in an air-water system were performed earlier in the CREL,

most of these experiments were repeated in this study. Unless it is otherwise referenced,

the experiments were performed as part of this study.

Table 6-1: Similarity conditions in a 6” diameter stainless steel column

Set System Pressure (MPa)


Overall gas holdup

An air-water 0.1 45 1 An air-water 0.4 30

0.35

An air-water 1.0 30 2 An air-water (Ong, 2003) 0.4 45

0.41

An air-water 0.4 30 3 Air-C9- C11 (Han, 2006) 0.1 30

0.35

Table 6-2: Experimental conditions for mismatch gas holdup radial profiles in a 6”

diameter stainless steel column

Set System Pressure (MPa)

Superficial gas velocity

(cm/s)

Overall gas holdup

An air-water 0.4 30 1 Air-C9- C11 0.4 16

0.35

An air-water 0.4 30 2 Air-C9- C11 1.0 8

0.35

The emphasis here is to show that if one maintains similar overall gas holdups and gas

holdup radial profiles, the hydrodynamic characteristics of these two systems will be the

151

same. Such a hydrodynamic similarity is the ultimate goal of any scaleup procedure to

maintain the desired conversion and process performance.

6.3 Results

The gas holdup radial profiles, axial liquid velocity profiles, and TKE radial profiles shown

in this section are time- and azimuthally averaged. The statistical difference between

hydrodynamic parameter (gas holdup and liquid axial velocity) profiles are represented in

terms of the average absolute relative difference, is defined as follows,

1

1 ( ) (( )

N )x r y rAARDN x r

−= ∑ , (6-1)

where x and y can either be gas holdup, axial liquid velocity, or TKE at the corresponding

radial location.

The strength of liquid recirculation at similarity/mismatch conditions is described in

terms of mean liquid recirculation velocity. The liquid recirculation velocity is defined as

∫

∫

−

−= *

0

*

0

)](1[

)](1[)(

η

η

ηηηε

ηηηεη

d

duu

G

Gz

rec , (6-2)

where η* is the radial position of flow inversion.

Figure 6-2a shows the gas holdup radial profiles at experimental conditions of 45 cm/s, and

4 bar (Ong, 2003), and 30 cm/s and 10 bar in an air-water system. The gas holdup radial

profiles are close to each other, with an AARD of 5.5 %. The similar gas holdup radial

profiles in these cases result in close liquid axial velocity profiles (Figure 6-2b) with an

AARD of 14 %. Figure 6-3 shows the variation of an absolute relative difference (ARD) at

these conditions. Except at the inversion point, an ARD appears to be close to 10 %. The

relatively higher AARD can be attributed to such a large difference at the inversion point.

152

(a) (b) Figure 6-2: a) Gas holdup and b) Axial liquid velocity radial profile in a 6” diameter

stainless steel column using an air-water system [D6P4U45: 6 inch diameter, 4 bar, and

45 cm/s (Ong, 2003), D6P10U30: 6 inch diameter, 10 bar and 30 cm/s] (Overall gas

holdup ~ 0.41).

Figure 6-3: Variation of AARD in liquid axial velocities between similarity conditions

[D6P4U45Water (Ong, 2003) and D6P10U30Water] along the column radius in a 6”

diameter stainless steel column using an air-water system.

153

Figure 6-4: TKE profile in a 6” diameter stainless steel column using an air-water system

[D6P4U45: 6 inch diameter column, 4 bar and 45 cm/s (Ong, 2003), D6P10U30: 6 inch

diameter column, 10 bar and 30 cm/s] (Overall gas holdup ~ 0.41).

At all the studied conditions, an ARD was found to be maximum close to the inversion

point. A possible reason is that the values of the velocities are low (i.e., -6 and -13 cm/s) in

this region (sometimes one condition has a positive value, and other has a negative value)

and the relative differences between these values gets amplified and subsequently increases

the AARD.

Additionally, mean liquid recirculation was calculated at these conditions using equation 6-

2. The mean recirculation velocity at 30 cm and 10 bar is 52 cm/s, while at 45 cm/s and 4

bar, it is 55 cm/s. The relative difference between mean recirculation velocities at these

conditions is 5.5 %. The mixing intensity at these conditions is expressed in terms of the

TKE of the system at those conditions. Figure 6-4 compares the radial distribution of TKE

at these similarity conditions. The AARD in TKE at these conditions was found to be close

to 11 %. This shows that the similar gas holdup radial profiles resulted in close axial

velocity and TKE radial profiles, and thereby the close recirculation rates and mixing

intensities.

Figure 6-5a shows gas radial profiles at operating conditions of 30 cm/s and 4 bar and 45

cm/s and 1 bar in an air-water system. The overall gas holdup in these cases is 0.35. The

154

AARD in gas holdup radial profiles was found to be 4.5 %. Such close gas radial profiles

result in close liquid axial velocity profiles (Figure 6-5b). The AARD in liquid axial

velocity profiles is 17 %. The variation of ARD along the column radius is shown in Figure


stainless steel column using an air-water system (D6P1U45Water: 6 inch diameter column,

1 bar and 45 cm/s, D6P4U30Water: 6 inch diameter column, 4 bar and 30 cm/s) [Overall

gas holdup ~ 0.35].


(D6P1U45water and D6P4U30water) along the column radius in a 6” diameter stainless

steel column using an air-water system.

155

6-6. In this case also, the ARD appears to be higher near the inversion point, as explained

above. The mean recirculation velocity at 30 cm/s and 4bar is 42 cm/s, while at 45 cm/s

and 1 bar, it is 39.5. The relative difference between mean recirculation velocities is close

to 6 %, indicating similar liquid recirculation patterns and its strength at these conditions.

Figure 6-7 shows a comparison between TKE at these conditions. The AARD in TKE was

found to be within 9 %, indicating similar mixing intensity and liquid recirculation at these

conditions.

Figure 6-7: TKE radial profile in a 6” diameter stainless steel column using an air-water

system (D6P1U45Water: 6 inch diameter column, 1 bar and 45 cm/s, D6P4U30Water: 6

inch diameter column, 4 bar and 30 cm/s) [Overall gas holdup ~ 0.35].

Figure 6-8a shows the gas holdup radial profiles at 30 cm/s and 1 bar in an air-C9C11

system (Han, 2006) and 30 cm/s and 4 bar in an air-water system. In this set of

experiments, one experimental condition uses a pure liquid (water), while the other uses a

mixture of n-paraffin liquid. The mixture of paraffinic liquid is predominantly C9 – C11

cut. The compositions of the various n-paraffins are ≤ C8 3.3 %, C9 36.3 %, C10 34.5 %,

C11 23.8 %, and ≥ C12 1.9 %. The physical properties of this mixture are also vastly

different from water [density = 0.726 gm.cc-1; viscosity = 0.85 mPa s; surface tension =

23.2 mN.m-1]. The experiments with such different liquids were motivated by the findings

of Macchi et al. (2001). Macchi et al. (2001) used one system with a pure liquid and an

other with a mixture of liquids, and found that although the overall gas holdup in these two

systems matched within allowable statistical difference (11 %), the power spectra in these

156

systems were different. Thus, even though the systems were globally similar, their local

behavior differed. The current work sought to evaluate whether maintaining the hypothesis

proposed in this work would provide similar hydrodynamic performance, even if one

system had a pure liquid and the other one had a mixture of liquids.

Figure 6-8a shows close gas holdup radial profiles in this case, except close to the center of

the column. An AARD in gas holdup radial profiles is within 4 %. Figure 6-8b shows the

(a) (b)

Figure 6-8: a) Gas holdup and b) Axial liquid velocity radial profile in a 6” diameter

stainless steel column [D6P1U30 C9-C11: 6 inch diameter column, 1 bar, 30 cm/s (Han,

2006), and air- C9-C11 fluid system, D6P4U30water: 6 inch diameter column, 4 bar, 30

cm/s, and an air-water system] [Overall gas holdup ~ 0.35].


[D6P1U30C9-C11 (Han, 2006) and D6P4U30water] along the column radius in a 6”

diameter stainless steel column.

157

Figure 6-10: TKE radial profile in a 6” diameter stainless steel column (D6P1U30 C9-C11: 6

inch diameter column, 1 bar, 30 cm/s, and air- C9-C11 fluid system, D6P4U30water: 6 inch

diameter column, 4 bar, 30 cm/s, and an air-water system) [Overall gas holdup ~ 0.35].

liquid axial velocities in these cases. An AARD in the liquid axial velocity profile was

found to be close, within 14 %. As in other cases, the maximum ARD (120 %) was found

at the inversion point. The values of the velocities at this point are 0.93 and – 3.85 cm/s.

The positive and negative values of liquid velocity led to a higher ARD at the inversion

point. The mean liquid recirculation velocity in an air-water system was 42 cm/s, while in

an air-C9C11 system it was 41 cm/s. The relative difference of mean recirculation

velocities in this set is 3 %, indicating similar liquid recirculation in these systems. Figure

6-10 shows the radial profile of TKE with an AARD of 8.5 %, reflecting similar

distributions of TKE at these conditions that indicate a similar mixing intensity in these

systems.

Based on this set of experimental conditions, we have demonstrated that maintaining the

hypothesis proposed in the current work results in similar liquid recirculation and mixing

intensity, even if one system has pure liquid and other one has a mixture of liquids. It

shows that bulk liquid physical properties are sufficient to describe the liquid phase only

when the gas holdup radial profiles are matched in two systems.

Using the identified sets of similarity experiments, we demonstrate that overall gas holdup

and gas holdup radial profiles in two systems need to be similar for similar hydrodynamic

158

performance. Additionally, to demonstrate the essence of similarity of both of these

parameters, the experiments were performed at mismatch conditions. The reason to

perform these experiments is to further buttress the proposed hypothesis.

Figure 6-11a shows a set of experimental conditions where the overall gas holdup is the

same, i.e., 0.35. Although the overall gas holdup is the same, the gas holdup radial profiles

in these cases are mismatched. AARD, of gas holdup radial profile between 30 cm/s and 4

bar in an air-water system and 16 cm/s and 4 bar in an air-C9C11 system, is 13 %. The

mismatched gas holdup radial profiles result in different liquid axial velocities (Figure 6-

11b). An AARD in liquid axial velocities is 35 %. Figure 6-12 shows that, similar to earlier

sets of experiments, the maximum ARD is near the inversion point (r/R = 0.8); moreover,

the ARD in axial velocities at the remaining radial locations was consistently above 20 %.

The mean recirculation velocity at 30 cm/s and 4 bar in an air-water system was 42 cm/s,

while at 16 cm/s and 4 bar, it was 30 cm/s. The relative difference between mean liquid


stainless steel column (D6P4U30water: 6 inch diameter column, 4 bar and 30 cm/s, an air-

water; D6P4U16C9-C11: 6 inch diameter column, 4 bar and 16 cm/s, air- C9-C11) [Overall

gas holdup ~ 0.35].

159


(D6P4U30water and D6P4U16C9-C11) along the column radius in a 6” diameter stainless

steel column.

Figure 6-13: TKE radial profile in a 6” diameter stainless steel column (D6P4U30water: 6

inch diameter column, 4 bar and 30 cm/s, an air-water; D6P4U16C9-C11: 6 inch diameter

column, 4 bar and 16 cm/s, air- C9-C11) [Overall gas holdup ~ 0.35].

recirculation velocities was 28 %. The radial profile of TKE at these conditions was

compared to evaluate how the mismatched gas holdup radial profiles affect mixing

intensity. Although the qualitative distribution of TKE appears to be similar at these

160

conditions, there exists a significant quantitative difference in their magnitudes. An

AARD in the radial profile of TKE was found to be around 27 %, as shown in Figure 6-

13.

Figure 6-14 shows one more set of mismatch experimental conditions (30 cm/s and 4 bar in

an air-water system, and 8 cm/s and 10 bar in an air-C9C11 system). The overall gas

holdup at these conditions is 0.35; however, an AARD in gas holdup radial profiles is 25

%. The mismatched radial profiles result in entirely different liquid recirculation velocities,

with an AARD in velocities close to 48 %. In this case also, the ARD of liquid axial

velocities (Figure 6-15) is consistently above 40 %. The mean recirculation velocity at 30

cm/s and 4 bar in an air-water system is 42 cm/s, while at 8 cm/s and 10 bar, it is 22 cm/s.

The relative difference between mean liquid recirculation velocities is 47 %. Figure 6-16

shows the radial distribution of


stainless steel column (D6P4U30water: 6 inch diameter column, 4 bar and 30 cm/s, an air-

water; D6P10U8C9-C11: 6 inch diameter column, 10 bar and 8 cm/s, air- C9-C11) [Overall

gas holdup ~ 0.35].

161


(D6P4U30water and D6P10U8C9-C11) along the column radius in a 6” diameter stainless

steel column.

Figure 6-16: TKE radial profile in a 6” diameter stainless steel column (D6P4U30water: 6

inch diameter column, 4 bar and 30 cm/s, an air-water; D6P10U8C9-C11: 6 inch diameter

column, 10 bar and 8 cm/s, air- C9-C11) [Overall gas holdup ~ 0.35].

TKE at these conditions. An AARD in the radial profile of TKE is around 45 %. One

should note here that in this case there exist both qualitative and quantitative differences in

TKE. The distribution of TKE at 8 cm/s and 10 bars appears to be uniform, possibly

because of the relatively uniform gas holdup radial profile.

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6.3a Discussion

Based on the sets of mismatch experiments, two points are worth mentioning:

a) The radial or cross-sectional distribution of gas holdup indicates that the second set

of mismatch experiments has one condition (30 cm/s, 4bar, an air-water) operating

in the churn-turbulent flow regime, while the other condition (8 cm/s, 10 bar, air-

C9-C11) appears close to bubbly or transition flow although they have similar overall

gas holdups. It shows that to be hydrodynamically similar it is necessary that both

the systems, apart from having similar global hydrodynamics, should operate in the

same flow regime. Operation in the same flow regime ensures that bubble

interaction and dynamics in these systems are similar.

b) It is clear from the radial or cross-sectional distribution of gas holdup in the first set

of mismatch experiments that both the systems operate in the churn-turbulent flow

regime. However due to mismatched gas holdup radial profiles, these systems show

different liquid recirculations and mixing intensities. Hence the combination of two

sets of mismatch experiments shows that the condition that two systems must

operate in the same flow regime to be hydrodynamically similar is necessary but

not sufficient. It shows the importance of matching gas holdup radial profiles or

cross-sectional distributions in two systems, even if both systems operate in the

same flow regime.

The current work combines the set of similarity and mismatch experiments and

demonstrates that to be hydrodynamically similar, it is necessary to have similarity of both

overall gas holdup and gas holdup radial profile. The similarity conditions showed that

similar overall gas holdup and gas holdup radial profiles resulted in close liquid

recirculation and mixing intensity in both systems. The mismatch experiments had similar

overall gas holdups but mismatched profiles, and resulted in varied liquid recirculation and

mixing intensity. This clearly shows that maintaining similar overall gas holdup alone can

lead to different recirculation and mixing, if gas holdup radial profiles are not matched.

Although overall gas holdup determines the magnitude of macroscopic hydrodynamics, the

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microscopic flow dynamics are controlled by gas phase motion due to the gradient of

buoyancy forces between the column center and the wall region. In churn-turbulent flow

regime, there exists an unequal distribution of gas holdup along the column cross-section,

with higher gas holdup in the center and lower holdup in the wall region. A similarity based

solely on overall gas holdup masks such distribution and lumps it into one global

parameter. This simplistic approach lead to different mixing and flow patterns, as the

momentum transferred by the gas phase motion is responsible for the liquid recirculation in

such flows.

In bubbly flow, the distribution of bubble size is narrow and uniform along the column

cross-section, resulting in relatively flat gas holdup radial profiles. Due to the absence of

nonuniform microscopic flow behavior; the determining factor in bubbly flow is the

magnitude of the macroscopic hydrodynamics. Hence, the similarity of global parameters

can be specifically applicable if both the systems operate in bubbly flow, and it may result

in similar liquid recirculation and mixing intensity. To corroborate this fact, experiments

with different operating conditions with the same overall gas holdup in bubbly flow were

identified to evaluate whether these conditions inherently have similar gas holdup radial

profiles. Two sets of such conditions extracted from the CREL database are reported here.

Figure 6-17 shows a set of experimental conditions with an overall gas holdup close to 0.1.

One condition is at 2 cm/s and 1 bar in an air-water system (Ong, 2003), while other one is

at 3 cm/s and 1 bar in an air-Therminol LT system (Shaikh and Al-Dahhan, 2005). Based

on overall gas holdup studies performed in the respective studies, it is clear that both these

conditions are in bubbly flow. The gas holdup radial profiles were close to each other, with

AARD of 6 %. Figure 6-18 shows another set of conditions operating in the bubbly flow

regime with an overall gas holdup of 0.22. In this set, one conditions is at 5 cm/s and 4 bar

in an air-Therminol LT system (Shaikh and Al-Dahhan, 2005), while other one is at 3.5

cm/s and 10 bar in an air-Therminol LT system (Shaikh and Al-Dahhan, 2005). The gas

holdup radial profiles at these conditions were found to be close, with an AARD of 4.5 %.

These results show that when both operating conditions fall in bubbly flow, the similarity

of overall gas holdup necessarily results in similar gas holdup radial profiles. As shown

164

earlier, such close gas holdup radial profiles would subsequently result in similar liquid

recirculation and mixing intensity. From the above comparisons, it is evident that similarity

based on global parameters can be generalized only when both the conditions are in bubbly

flow, because the magnitude of macroscopic hydrodynamics is the controlling

hydrodynamic parameter in the presence of uniform holdup distribution across the column

cross-section.

Figure 6-17: Gas holdup radial profile in a 6” diameter stainless steel column

(D6U2P1water: 1 bar and 2 cm/s, an air-water; D6U3P1TherminolLT: 1 bar and 3 cm/s,

air- Therminol LT) [Overall gas holdup ~ 0.1].

Figure 6-18: Gas holdup radial profile in a 6” diameter stainless steel column

(D6U5P4TherminolLT: 4 bar and 5 cm/s, air-Therminol LT; D6U3.5P10Therminol: 10 bar

and 3.5 cm/s, air- Therminol LT) [Overall gas holdup ~ 0.22].

165

The current work cautions against the generalization of similarity criteria based only on

global parameter. It was demonstrated that similarity of global parameters does not

necessarily ensure similar hydrodynamic performance, particularly in the churn-turbulent

flow regime. The similarity of gas holdup and its distribution along the cross-section are

pertinent in obtaining similar recirculation and mixing intensity in two systems.

6.4 Development of correlations for ‘a priori’ prediction of hydrodynamic parameters

In a nutshell, this work has proposed a hypothesis for hydrodynamic similarity and

successfully evaluated utilizing CT and CARPT. However to facilitate the proposed

methodology for scaleup/scaledown purposes, it needs modeling tools to ‘a priori’ predict

the needed hydrodynamic parameters. An ideal choice for such a task would be

fundamentally based Computational Fluid Dynamics (CFD) models. However, Rafique et

al. (2005) showed that interfacial closures are still an unresolved issue, and tuning the

coefficients to a known field is still a state-of-the-art practice. Additionally, available

closures do not account for the effect of turbulence. Chen (2005) implemented the

Population Balance approach where the bubble population balance equation was solved

simultaneously with solution of the flow field. In the churn-turbulent flow regime, Chen

(2005) model predicted a coalescence rate an order of magnitude higher than that of a

break-up rate. Therefore bubble diameter does not reach equilibrium, which is in contrast

with experimental observations. Hence, Chen (2005) enhanced the breakup rate to be 10

times the predicted one, in order to match experimental flow field results. He then found a

good agreement between model predictions and experimental data in different air-liquid

systems. This shows that even after incorporating detailed science, there are still unresolved

issues. Hence CFD, although certainly a promising tool, is not yet ready for use in the

design and scaleup of bubble columns.

In the absence of fully resolved CFD, the current work resorted to a state-of-the-art

modeling tool, the Artificial Neural Network (ANN). Correlations for the following

hydrodynamic parameters were developed:

i) Overall gas holdup

166

ii) Gas holdup radial profile

iii) Liquid axial velocity radial profile

iv) Center-line liquid velocity

A brief introduction to ANN and the development of the correlations using ANN for the

hydrodynamic parameters mentioned above is discussed in Appendix-F.

6.5 Remarks

Based on a comprehensive review of reported scaleup procedures in literature and industry,

the current work proposes a new hypothesis for hydrodynamic similarity and subsequently

for scale-up of bubble column reactors. The hypothesis requires the similarity of overall gas

holdup as well as of gas holdup radial profile. It was evaluated using single source γ-ray CT

and CARPT. The conditions of similarity where overall gas holdup and radial gas holdup

profiles were the same, and mismatch where overall gas holdup was the same but gas

holdup radial profiles were different, have been identified. The combination of similarity

and mismatch experiments shows the importance of maintaining the gas holdup radial

profiles the same, not just the overall gas holdup. Such similarity exhibited the similar

liquid circulation and mixing intensity in two systems.

This work also showed that the condition that two systems must operate in the same flow

regime to be hydrodynamically similar is necessary but not sufficient. It showed the

importance of matching gas holdup radial profiles or cross-sectional distributions in two

systems, even if both the systems operate in the same flow regime. Hence, the traditionally

used criterion for hydrodynamic similarity, based only on global parameters, can be fatal

and needs to be exercised with prudence.

The hypothesis proposed in this work has been evaluated in different systems and

operating conditions. However it needs to be evaluated at two different scales. Industrial

167

reactors often consist of internals such as sieve trays and heat exchangers, hence the

applicability of the proposed hypothesis needs to be checked in such systems.

168

Chapter 7 Summary and Recommendations The main objectives set for this work are to advance the state of knowledge of key

hydrodynamic parameters of bubble and slurry bubble column reactors at mimic

industrial conditions in the context of FT synthesis, using existing noninvasive techniques

such as CARPT and CT. This work was also planned to develop experimental techniques

and their flow regime identifiers for flow pattern delineation that can be useful for online

monitoring in the laboratory as well as in industrial scale reactors. With the aid of state-

of-the-art experimental and modeling tools, this work proposed and evaluated a new

hypothesis for hydrodynamic similarity and subsequently for scaleup of bubble column

reactors. 7.1 Summary and Conclusions The key findings in this work are as follows:

1. The effect of liquid phase physical properties was studied by comparing the phase

holdup profiles obtained in an air-Therminol LT-glass beads with that of an air-water-

glass beads system in bubbly and churn-turbulent flow at ambient and high pressure

(1 MPa). At ambient pressure, the comparison of the gas and solids holdup radial

profile in an air-Therminol LT-glass beads and an air-water-glass beads revealed that

in bubbly flow the magnitude of the gas holdup profile is higher in water, while in

churn turbulent flow; it is higher in Therminol LT. In transition flow, closely similar

gas holdup radial profiles were observed in water and Therminol LT. An increased

gas holdup in water in bubbly flow was due to the S-shaped behavior of the overall

gas holdup curve at the studied condition. An opposite effect of the superficial gas

velocity was observed on the solids holdup radial profile. At high operating pressure

(1 MPa), the change in the liquid phase to Therminol LT consistently increased the

169

magnitude of the gas holdup radial profile due to an increased bubble breakup rate

and decreased coalescence rate that produced more small bubbles. This effect resulted

in a relatively flatter profile in Therminol LT. The solids holdup radial profile

decreased with an increase in superficial gas velocity.

2. An addition of solids in slurry reduces the magnitude of the gas holdup radial profile

due to a higher coalescence rate that produces more large bubbles in the system. The

higher population of large bubbles concentrated at the center and resulted in a steeper

profile at increased solids loading, it thereby advanced flow regime transition. An

addition of solids linearly increased the solids holdup profile at both pressures. At

high operating pressure and high solids loading, the gas holdup radial profile showed

a consistently steeper profile. The shape of the profile at this condition is qualitatively

similar to the one observed at low solids loading and ambient pressure.

3. Within the studied experimental conditions, the effect of superficial gas velocity on

the overall gas holdup was weaker than that of operating pressure and solids loading.

The effect of the studied operating parameters on the solids holdup profile was less

significant than on the gas holdup radial profile.

4. The solids holdup profiles at all the axial locations showed the similar shapes, and fell

on each other at a given operating condition. The normalized solids holdup at low

superficial gas velocities showed similar shape and fell on each other, while the

normalized solids holdup at higher superficial gas velocities showed similar and

relatively steeper shapes and fell on each other within a band of relative error of ± 10

%. The normalized solids holdup radial profile in water and Therminol LT showed

the similar shapes and fell on each other at all the studied conditions, except in bubbly

flow at ambient pressure. This shows that the solids flow behavior in these systems

was qualitatively similar. However, the differences were to the different liquid phase


5. In general, a slurry bubble column exhibited a single circulation cell in fully

developed flow in a time-averaged sense. The solids moved upward at the center, and

moved downward near the wall. The pdf of solids axial velocity revealed that

although the net flow in the center is upward, a few negative velocities existed.

Correspondingly, the net flow near the wall is downward, a few positive velocities

170

were noted. Near the vortical region, comparable positive and negative velocities

were present, causing vigorous fluctuations. The axial solids velocity showed the

inversion point around a dimensionless radius of 0.7, while the shear stress showed a

maximum in the center of the column radius.

6. Comparison with an air-water-glass beads system shows an increased solids axial

velocity and shear stresses in an air-Therminol LT-glass beads system. However, due

to the presence of smaller bubbles in an air-Therminol LT-glass beads system, there

was less TKE and normal stresses. The qualitative flow behavior in both the systems

was similar, the quantitative differences exist due to different liquid phases.

7. An addition of solids tended to decrease the solids axial velocity, due to decrease in

the gas holdup. However, an addition of solids results in enhanced turbulence in the

system, due to an increased large bubble population.

8. The existing CT was evaluated for flow regime identification in bubble column

reactors. The evolution of the steepness of the gas holdup radial profile with

superficial gas velocity was analyzed, and the ‘break-point’ in the steepness

parameter curve was found to reveal information regarding transition velocity. The

transition velocity obtained from the steepness parameter curve was evaluated with

traditional methods such as the change in the gas holdup curve and the drift flux plot

and found to be in good agreement. The effect of operating pressure on the flow

regime transition was studied using the developed methodology. The transition

velocity was found to increase with an increase in operating pressure. Also, it was

observed that the change in the flow regime was noticeable at ambient conditions,

while at higher pressure a gradual change occurred over a region of superficial gas

velocities. The obtained transition velocities were compared with the predicted

transition velocities using the correlations of Wilkinson (1991) and Reilly et al.

(1994). Both correlations noticeably underpredict the experimental transition

velocities, hence the state of current correlations needs to be further improved.

9. The feasibility of NGD for flow regime demarcation in bubble column reactors was

explored. The well-known air-water system was utilized to propose promising “flow

regime identifiers”. The flow regime boundaries were determined based on

conventional methods such as the change in the slope of the gas holdup curve and the

171

drift flux plot. The photon counts history obtained using NGD was subjected to

statistical analysis, autocorrelation analysis, and spectral analysis. Based on the

comparison of such time-series analyses with those of conventional methods,

promising flow regime identifiers for NGD were proposed. In general, the photon

counts history revealed the signatures of the underlying flow regime. Based on the

inherent nature of gamma-ray emission, a new parameter called the coefficient of

departure from a Poisson distribution was proposed and found to be greater than 1.4

for churn-turbulent flow regimes. The autocorrelation analysis exhibited different

behavior in bubbly and churn-turbulent flow regime. Spectral analysis showed a

distinct power-law fall off in the transition and the churn turbulent flow regime, while

no such power law fall-off was observed in the bubbly flow. The proposed “flow

regime identifiers” for NGD provide a promising method for online flow regimes

monitoring in laboratory as well as industrial scale reactors. Furthermore, the

developed ‘flow regime identifiers’ were evaluated in different systems (air-water and

air-C9-C11) at different pressures (0.1 and 1 MPa) in a stainless steel column and

found to be consistent.

10. A new hypothesis was proposed for hydrodynamic similarity and subsequently for the

scale-up of bubble column reactors. It emphasizes the similarity of the overall gas

holdup as well as the gas holdup radial profile. A combination of similarity and

mismatch experiments showed the importance of maintaining the gas holdup radial

profiles the same, in addition to the overall gas holdup. Such similarity exhibited the

similar liquid circulation and mixing intensity in two systems. We showed that the

traditionally used criteria for hydrodynamic similarity based only on global parameters

can be fatal and advised that it be exercised with prudence. In addition, ANN based

correlations were developed for ‘a priori’ prediction of the needed hydrodynamic

parameters.

7.2 Recommendations The work accomplished in the last two parts of current study is, in retrospect, generic to

multiphase reactors, with bubble columns as an example. Hence, it provides promising

172

avenues to implement similar concepts in different configurations of multiphase reactors.

The few suggestions for possible extension of the work performed in different parts are

listed below:

1. Most hydrodynamic studies reported in the literature deal with systems where the

aspect ratio (L/D) was maintained equal to or above 5. The reason for performing

such studies lies in the general observation that if L/D > 5, the effect of column height

on hydrodynamics is not significant. However the demands of high throughput

necessitate industrial reactors to have a larger column diameter, often equal to or

greater than 5 m. In these cases, the column height is often restricted due to the

limitations on the weight of reactor allowable for transportation. Hence these reactors

have L/D lower than commonly studied in the literature. Very few studies have been

performed in this regard, and they are limited to overall gas holdup and mass transfer

coefficient. Detailed studies regarding low L/D and its effect on the hydrodynamics,

using CARPT and CT, will be beneficial for the design of industrial reactors.

2. This work evaluated the capability of CT for flow regime identification based on the

steepness of the gas holdup radial profiles. The systematic data obtained for the flow

regime transition studies using CT can be further analyzed using chaos analysis,

symbolic dynamic analysis, and S-statistics.

3. This work developed a new technique utilizing NGD for online flow regime

identification in bubble column reactors. The same technique can be extended for

flow monitoring in other multiphase reactors. The possibility of applying NGD for

flow regime monitoring in packed beds, fluidized beds, circulating fluidized beds, and

spouted beds should be considered. The applicability of ‘flow regime identifiers’

developed using NGD for bubble column reactors can be evaluated for other

configurations, and if needed, new ‘flow regime identifiers’ specific to those

configurations can be proposed.

173

4. Due to the requirement of using the time-series techniques that are simpler, faster,

robust, and easily used by non-experts in the plant, a basic time-series analysis was

performed on photon counts history obtained using NGD. However one can use

sophisticated time-series techniques such as chaos analysis for flow regime

delineation. In addition, one can apply symbolic dynamic analysis, χ2- analysis, and

S-statistics to evaluate their feasibility for flow regime monitoring in bubble columns.

5. There has always been considerable interest in demarcating as well as understanding

the flow regime transition. Towards this, there were attempts to describe flow regimes

and, in particular, flow during transition. However, the descriptions provided by Ohki

and Inoue (1979) and Olmos et al. (2003) are in contradiction with each other and

also with the one explained by Nedeltchev et al. (2003), which was based on the

quality of mixedness. As a preliminary evaluation of these explanations by various

authors, one can perform 4-point optical probe experiments within the flow regime

transition region at specific axial locations. High-speed camera images along with

these experiments would certainly aid in enhancing our fundamental understanding.

6. This work successfully evaluated the proposed hypothesis for hydrodynamic

similarity of bubble column reactors. Before investing efforts to extend it to different

diameter columns using CT and CARPT, as a first step the hypothesis was evaluated

in the same column at widely different operating conditions and using different

liquids. The successful evaluation of the proposed hypothesis provides an opportunity

to evaluate the proposed hypothesis at different scales.

7. The proposed hypothesis for dynamic similarity and subsequently, for scaleup needs

modeling tools for design engineers. In this work, combination of ANN based tools

for different hydrodynamic parameters were developed based on the reported

database available over wide range of operating and design conditions. However the

reactor scale models based on first principle needs to be evaluated for this purpose.

Based on CFD studies of Chen (2005), the improved breakup closures need to be

implemented during such an exercise.

174

8. The scaleup methodology developed in this work can be evaluated in other

multiphase reactors such as fluidized beds, spouted beds, and CFBs. In the literature,

there have been attempts to study the scaleup of these reactors. However, these

methods also rely on the similarity of global parameters for dynamic similarity in two

systems. The scaleup hypothesis proposed for bubble columns during this work, in

retrospect, is generic for multiphase reactors. Hence the scaleup rules proposed for

these reactors should be revisited in the light of the hypothesis developed in this

work.

175 APPENDIX A. Phase Distribution in Three Dynamic Phase Systems via Combination of Computed Tomography (CT) and Electrical Capacitance Tomography (ECT)

A-1 Background Although many tomographic techniques have been developed over the past 5-10 years

(Williams and Beck, 1995), few are readily applicable to three-phase systems. In three-

phase systems, the requisite sensed signal contains information that is a function of more

than one parameter in the object space. Most tomographic techniques are single modal

systems that can not be applied for multiple sensing in three phase flows. Approaches

adopted by the researchers to tackle this problem have been classified in the following

three categories:

I) combining two single-modal systems

II) using an inherently multi-modal system

III) modifying reconstruction techniques of single-modal system to accommodate three

dynamic phases.

The example of combination of two single modal systems in medical field is the

combination of X-ray CT (which illustrates bone structures but remains insensitive to soft

tissues) with magnetic resonance imaging (MRI) (which distinguishes between diseased

and healthy tissues but remains insensitive to bony structures). Such measurement can

provide surgeon with the position of the diseased tissue relative to the bone structure

(Beck, 1995). In multiphase reactors research there have been considerable efforts

towards developing multi-modal systems for three dynamic phase flow imaging.

A-1.1 Approach I: Combining two single-modal techniques

Table A-1 summarizes the reported investigations that use approach I.

176

Table A-1: Summary of the studies combining two single-modal systems

Author Combination Comments

Seo and Gidaspow (1987)

X-ray densitometry and γ-ray densitometry (GDT)

Measured volume fraction of particles and of the gas in fluidized bed involving particles of two sizes.

Johansen et al. (1996)

Electrical Capacitance Tomography (ECT) and GDT

Studied the gas phase distribution in three- component flows of gas, oil, and water.

Bukur et al. (1996)

γ-ray densitometry with two different sources

Failed in implementation in slurry bubble columns. Suggested using sources with widely different energy levels such as, Cs 137 and Am.

George et al. (2001)

Electrical Resistance Tomography (ERT) and GDT

Three phase system was chosen such that GDT was used to measure gas fraction while ERT to measure solids fraction.

Grassler and Wirth (2001)

Dual energy X-ray tomography

Applied in slurry bubble column. Not applicable at high pressure due to excessive attenuation.

A-1.2 Approach II: Using an inherently multi-modal system

Using the second approach, Warsito et al. (1995) implemented a dual-frequency

ultrasonic method, and Warsito et al. (1999) developed an ultrasonic tomographic (UT)

technique with two-parameter sensing, i.e., energy attenuation and sound speech to

measure simultaneously the three dynamic phase holdups. Vatankul et al. (2004)

correlated the fluctuations of sound waves, in terms of variance of transmission time and

amplitude ratio, with gas and solids holdup. Warsito et al. (1997) and Soong et al. (1995)

showed that the speed of ultrasound is independent of gas holdups, while Macchi et al.

(2001a) and Vatankul (2003) showed that gas bubbles do affect sound velocity due to the

distortion of ultrasound around bubbles. There remains a discrepancy regarding the key

177 assumption in reconstructing phase holdups using UT. In addition, due to its high signal

non-linearity the technique is limited to bubbly flow and very low solids holdup.

A-1.3 Approch III: Modifying reconstruction technique of single- modal system

Table A-2 summarizes the reported investigations that use approach III.

Table A-2: Studies that modified the reconstruction technique of single-modal techniques

Authors Technique Comments on Reconstruction Technique

Nooralahiyan and Hoyle (1997)

Electrical Capacitance Tomography (ECT)

Feedforward neural network (NN) with double sigmoid function used to image three dynamic phase flows. Reconstruction is fast once training has been done but network training is the major disadvantage for real applications.

Warsito and Fan (2001, 2003)

Electrical Capacitance Tomography (ECT)

Hopfield neural network with multicriterion optimization technique. Does not need prior training. Uniform solids loading assumption applied for three dynamic phase imaging.

Rados et al. (2004)

Single source γ-ray Tomography

Combines CT with overall gas holdup measurements, along with two sound assumptions[uniform solids loading and overall gas holdup equal to cross-sectional gas holdup]. Applied in different systems at low as well as high pressure.

Approach III is an attractive option for phase holdup measurement in three-phase systems

as it is easy to construct and implement. However, the obtained results need to be

evaluated and the validity of the improved reconstruction technique and the assumptions

used therein need to be defined. As discussed above, with the current state of imaging

techniques, while Approach III remains to be in development stage, Approach I can be

used for such evaluation. This makes it necessary to demonstrate the possibility of

coupling two single-modal tomographic techniques and evaluate the assumptions

incorporated in Approach III (Table A-2). A-2 Combination of CT/ECT

178 Based on this, the focus is to establish and implement the possibility of the combination of

two single-modal tomographic techniques, viz., single source γ-ray CT and Electrical

Capacitance Tomography (ECT). This study consists of two parts:

i) Development of the CT/ECT algorithm.

ii) Execution of the CT/ECT experiments.

A-2.1 Development of the CT/ECT algorithm

As this methodology combines two single modal systems, the development of a system of

equations to resolve three dynamic phase holdups consists of combining CT and ECT

equations. The single source γ-ray CT equation will be coupled with Two-Region Three

Phase Capacitance Model proposed by Warsito and Fan (2003), which is modified for the

current case. Such a coupling yields a system with a similar number of non-linear algebraic

equations as the unknowns, i.e., the phase holdups.

Based on the ECT data, the permittivity distribution will be estimated at Ohio State

University using Neural Network Multi Objective Iterative Reconstruction Technique

(NNMOIRT). The CT experiments were conducted under the similar experimental

conditions and the attenuation distribution was estimated using the EM algorithm

implemented by Kumar (1994). The CT/ECT algorithm developed in the current work

couples the attenuation and permittivity distribution to evaluate three dynamic phase

holdups. A user friendly compact software is developed for CT/ECT combination using

HYBRD subroutine.

This part essentially involves combining CT and ECT equations to form a system of

equations that can resolve three dynamic phase holdups. The needed ECT equation has

been derived from the three-phase two-compartment model proposed by Warsito and Fan

(2003), which has been modified to accommodate the current case.

179 According to Warsito and Fan (2003), the system is divided into two compartments, viz.,

gas and liquid-solid emulsion. The series and parallel combinations of these two

compartments can be represented, respectively, as

( )LS

G

G

G

sGLS eeeεε −

+=11

, (A-1)

( ) LSGGGpGLS eee εε −+= 1, (A-2)

where eLS is the permittivity of the solid-liquid emulsion phase.

Further, the liquid-solids emulsion has been divided into two compartments, viz., liquid

and solid. These two compartments has also been arranged in parallel and series

combinations as

( )

L

SE

S

SE

sLS eeeεε −

+=11

, (A-3)

( ) LSESSEpLS eee εε −+= 1, (A-4)

where, eS and eL are the dielectric constants of the solid and liquid phase. While SEε is

solids loading which is defined as,

G

SSE ε

εε

−=

1 (A-5)

The gas holdup in three phase system can be calculated by the possible series and parallel

combinations between liquid and solids phase within the emulsion and between the gas

and emulsion phases as follows

ppGpppspsspGspssGssG ,,, εβεβεβεβε +++= (A-6)

1=+++ pppsspss ββββ (A-7)

where, β is a constant between 0 and 1. The subscripts s and p denote series and parallel

capacitance connections between the liquid and solid in the emulsion phase for the first

180 subscript and between the gas and the emulsion phase for the second subscript. In the

present case, constant β was equally weighted.

Relative permittivity, rk for phase k can be defined as,

Gkk eer /= (A-8)

where k can be L (liquid), S (solid), LS (liquid-solid), or GLS (slurry experiment).

The resultant permittivity will be the equal contribution of above mentioned

combinations. The combination of these equations yields following ECT equation.

[ ]ppGLSpsGLSspGLSssGLSGLS rrrrr ,,,,41

+++=

( ) ( )[ ]( )

( ){ } ( )⎢⎣

⎡−+−+

−++

−+−+=

GSELSESG

SELSES

SESSELGGLS

LS

rrrr

rrrrrr

εεεεεε

εεεε 111

1141

( )( ) ( ) ( ){ ⎥

⎦

⎤−+−+

−+−

++ SELSESGSESSEL

GLSG rr

rrrr εεε

εεεε 11

112 } (A-9)

For three dynamic phase systems the resultant CT equation can be written as (Rados et

al., 2005),

ijL

ijGLSijSijLS

ijSijGS

ijG R

RRR

,

,,,0,

,

,

1 −⎟⎠⎞

⎜⎝⎛ −+

=ε

εε

ε

The above equation can be rearranged as,

( ) (⎭⎬⎫

⎩⎨⎧

−+−= SELS

SEGSGGLS RRR εεε

ε 110

)

)

(A-10)

As defined in equation (5) solids holdup can be calculated as,

( GSES εεε −= 1 (A-11)

181

The above system of equations has three non-linear algebraic equations i.e. (A-9), (A-10),

and (A-11) with three unknowns i.e. Gε , Sε , and SEε . These equations need to be solved

simultaneously to compute gas holdup, solids holdup, and solids loading in each pixel

using Newton-Raphson Method. The pixel size being used in ECT data processing will

be 32x32; hence, during the CT data processing pixel size was reduced to 32 x 32.

A-2.2 Execution of CT/ECT experiments

The experimental part of this study needs to execute the CT and ECT experiments using the

similar operating and design conditions. Therefore, the experiments were performed at

Washington University (WU) using CT and at Ohio State University (OSU) using ECT at

the similar operating and design conditions. A plexi-glass column of the same dimensions

(diameter = 10.12 cm, height = 120 cm, Figure 5-12) as OSU has been constructed at

Washington University. Air was used as the gas phase, while Norpar15 (μ = 2.53 cP, ρ =

773 kg.m-3, σ = 26.4 dyne.cm-1) was used as the liquid phase. Glass beads with an average

diameter of 200 μm and particle density of 2500 kg.m-3 constituted the solids phase. Table

A-1 shows the experimental conditions for this part of the work.

Table A-1

Experimenta

l conditions

for the

coupling of

CT/ECT

Sparger Solids loading

(% volume)

Superficial gas velocity (cm/s) Axial location

(L/D)

S1 40 5, 10,15 2, 5.5

S2 9.1, 25 5, 15 2.5, 5.5

182 S1: Single hole of size 5 mm, S2: 64 holes of 1 mm size, % OA = 1.09, triangular pitch

A-3 Results

As mentioned earlier, the main goal of this work is to combine attenuation distribution

obtained using CT with the permittivity distribution obtained using ECT. The data

processing of CT data was completed while that of ECT is still in progress. Hence in this

section the cross-sectional attenuation distribution (cm-1) obtained using CT is presented

in 32 X 32 pixel form.

z/D = 2 z/D = 5.5

(a)

z/D = 2 z/D = 5.5

183

(b)

Figure A-1: Cross-sectional attenuation distribution (cm-1) of a) 200 μm glass beads (with voids) and b) Norpar 15.

z/D = 2 z/D = 5.5

(a)

z/D = 2 z/D = 5.5

184

(b)

z/D = 2 z/D = 5.5

(c)

Figure A-2: Cross-sectional attenuation distribution (cm-1) using air-Norpar 15-(200 μm glass beads in 4” diameter column at ambient conditions, two axial locations, and solids loading of 40 % volume at Ug = a) 5, b) 10, and c) 15 cm/s with a single nozzle sparger.

185

Ug = 5 cm/s Ug = 15 cm/s

(a)

(b)

Figure A-3: Cross-sectional attenuation distribution (cm-1) using air-Norpar 15-(200 μm glass beads in 4” diameter column at ambient conditions, z/D = 5.5, two superficial gas velocities and solids loading = a) 9.1, b) 25 % volume with a uniform sparger.

186 Once ECT data processing is completed, the combination of permittivity and attenuation

distribution can provide phase holdups distribution in three dynamic phase systems

without any assumptions.

186

APPENDIX B Experimental Investigation of Hydrodynamics of Slurry Bubble Column Reactor via CT B-1: Experimental setup and employed sparger

21 1/2”

B

Figure B-1: High pressure bubble column with ports used for overall gas holdup measurement

ottom Support

12”

8 3/4”

21 1/2”

16 1/2”

4 3/4”

90”

4 1/2”

Top Cover

13”

Gas Outlet

Demister6 3/8”

View Port (6 staggered, 3 on

each radially opposite side,

1” Probe

Batch Drain

LiquidDrain

8

GasInlet

CT 1

CT 2

CT 3DP

DP

DP

187

Figure B-2: Sparger employed in the current studies in 6” diameter steel column

B-2 Reproducibility of CT scans

To address the issue of reproducibility of the experimental data, the conditions of Ug =

30 cm/s and P = 0.1 and 1 MPa at 9.1 % vol. solids loading was repeated with fresh batch

of liquid and glass beads. Figures B-3a and b show the gas holdup radial profile data at

z/D = 5.5 using superficial gas velocity of 30 cm/s, solids loading of 9.1 % vol. at

ambient pressure and high pressure, respectively.

Both figures indicate very good agreement between gas holdup radial profiles at ambient

and high pressure. At ambient pressure, the gas holdup radial profiles are within 2 %

while near the wall, it is 4 %. At operating pressure of 1 MPa, the gas holdup radial

profiles are within 3 % while near the wall, the differences are around 5 %. In conclusion,

the reproducibility of gas holdup radial profiles is very good. Also, the reproducibility of

solids holdup radial profile at both the pressures was found to be within 1.5 %.

188

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

r/R (-) 0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

r/R (-)

Gas

hol

dup

(-)

Batch1

Batch2

Batch 1 Batch 2

(-

)

dup

G

as h

ol

(a) (b) Figure B-3: Reproducibility of gas holdup radial profiles at superficial gas velocity of 30

cm/s, solids loading of 9.1 % vol., axial location of z/D = 5.5 and operating pressure of a)

0.1 MPa and b) 1 MPa using two fresh batches of air-Therminol LT-glass beads system

B-3 Effect of superficial gas velocity on gas and solids holdup radial profile

(a) (b) Figure B-4: Effect of superficial gas velocity on a) gas holdup, and b) solids holdup radial

profile in air-Therminol LT-9.1 % vol. glass beads system at ambient pressure in 6” steel

column

189


profile in air-Therminol LT-9.1 % vol. glass beads system at P = 1 MPa in 6” steel

column.


profile in air-Therminol LT-25 % vol. glass beads at ambient pressure in 6” steel column.

190

(a) (b)

Figure B-7: Effect of superficial gas velocity on a) gas holdup, and b) solids holdup radial

profile in air-Therminol LT-25 % vol. glass beads at operating pressure of 1 MPa in 6”

steel column.

B-4 Effect of operating pressure on gas and solids holdup radial profile

(a)

(b)

191

(c)

(d) Figure B-8: Effect of operating pressure on gas and solids holdup radial profile in air-

Therminol LT-9.1 % vol. glass beads system at Ug = a) 8, b) 14, c) 20, and d) 30 cm/s in

6” steel column

(a)

192

(b) Figure B-9: Effect of operating pressure on gas and solids holdup radial profile in air-

Therminol LT-25 % vol. glass beads system at Ug = a) 20 and b) 30 cm/s in 6” steel

column

B-5 Axial variation of cross-sectional averaged phases holdup

In this section, the effect of superficial gas velocity, operating pressure, and solids

loading on axial variation of cross-sectional phases holdup will be briefly discussed. As

mentioned earlier, to reconstruct three dynamic phases using single source γ-ray CT, few

assumptions were incorporated. One of the assumptions is that, cross-sectional averaged

gas holdup is equal to overall gas holdup. Hence, an axial variation of cross-sectional gas

holdup has not been discussed, as the reconstructed cross-sectional averaged gas holdup

is the same as overall gas holdup within 5 % of relative error. In this section, an axial

variation of cross-sectional solids holdup is discussed.

The cross-sectional averaged solids holdup was calculated from radial profile of solids

holdup as, 1

0

2 ( )s s dε ηε η η−

= ∫ (B-1)

where η = r/R.

Figures B-10, B-11, and B-12 illustrate the effect of operating parameters on axial

variation of cross-sectional averaged solids holdup. Solids holdup tends to decrease along

193

the column length. An increase in superficial gas velocity and operating pressure

decreases cross-sectional averaged solids holdup due to an increase in gas holdup. An

increase in solids holdup was observed with an increase in solids loading.

(a) (b)

(c) (d)

Figure B-10: Effect of superficial gas velocity on cross-sectional averaged solids holdup

in air-Therminol LT-glass beads system at a) solids loading = 9.1 % vol. and P = 0.1

MPa, b) solids loading = 9.1 % vol. and P = 1 MPa, c) solids loading = 25 % vol. and P

= 0.1 MPa, and d) solids loading = 25 % vol. and P = 1 MPa in 6” steel column

194

(a) (b)

(c) (d)

(e) (f)

Figure B-11: Effect of operating pressure on cross-sectional averaged solids holdup in

air-Therminol LT-glass beads system at a) Vs=9.1 % vol., Ug=8 cm/s, b) Vs=9.1 % vol.,

Ug=14 cm/s, c) Vs=9.1 % vol., Ug=20 cm/s, d) Vs=9.1 % vol., Ug=30 cm/s, e) Vs=25 %

vol., Ug=20 cm/s, and f) Vs=25 % vol., Ug=30 cm/s in 6” steel column

195

(a) (b)

(c) (d)

Figure B-12: Effect of solids loading on cross-sectional averaged solids holdup in air-

Therminol LT-glass beads system at a) Ug = 20 cm/s, P = 0.1 MPa, b) Ug = 30 cm/s, P =

0.1 MPa, c) Ug = 20 cm/s, P = 1 MPa, and d) Ug = 30 cm/s, P = 1 MPa in 6” steel

column

B-6 Normalized gas holdup radial profile

In this section, the normalized gas holdup radial profile at the studied operating

conditions has been analyzed. The normalized gas holdup radial profile is the ratio of gas

holdup at certain radial location and cross-sectional averaged gas holdup. The normalized

196

gas holdup radial profiles at the studied conditions were fitted to the following empirical

form proposed by Luo and Svendsen (1992),

])/(1)[22

2()/( nGG Rrc

cnn

−−++

=εε (B-2)

where n indicates steepness of holdup profile. When n is large the profile is flat, while for

small n profile is steep. The steepness of holdup profile is reflected in the intensity of

liquid circulation. Also, c is wall holdup parameter that indicates the value of gas holdup

near the wall. If c = 1 there is zero hold up close to the wall, if c = 0 hold up is constant

with changing r/R.

Table B-1 shows the values of steepness parameter at the studied experimental

conditions. It can be observed that, in general, an increase in superficial gas velocity

decreases the value of steepness parameter and thereby changing flatter gas holdup

profiles into parabolic ones. At the same superficial gas velocity and solids loading, an

increase in pressure clearly increases the value of steepness parameter that results into

relatively flatter profiles at increased pressure. As discussed earlier, such flatter profiles

are result of an increase in small bubble population in the system at higher pressure. At

the same superficial gas velocity and operating pressure, an increase in solids loading

results into decrease in the value of steepness parameter thereby resulting into steeper

profile. As mentioned above, an addition of solids increases large bubble population that

gives rise to wide bubble size distribution and steep gas holdup radial profile with lower

gas holdup.

The careful observation of the values of steepness parameters show that the effect of

operating pressure and solids loading on normalized gas holdup radial profiles is stronger

than that of superficial gas velocity.

197

Table B-1: Values of steepness parameter, n

Superficial gas velocity

(cm/s)

Pressure

(MPa) Solids loading

(% vol.) n (-)

8 0.1 9.1 3.8

14 0.1 9.1 2.9

20 0.1 9.1 2.24

30 0.1 9.1 2.4

8 1 9.1 4.2

14 1 9.1 3.13

20 1 9.1 2.94

30 1 9.1 2.8

20 0.1 25 1.64

30 0.1 25 1.53

20 1 25 2.5

30 1 25 2.22

(a) (b)

Figure B-13: Normalized gas holdup radial profile a) at different superficial gas

velocities, ambient pressure, and solids loading of 9.1 % vol. and b) at Ug = 20 cm/s and

different operating pressure and solids loading in 6” diameter steel column.

198

Figure B-13a shows the effect of superficial gas velocity on normalized gas holdup radial

profile at ambient pressure and solids loading of 9.1 % vol. in 6” diameter steel column.

An increase in superficial gas velocity, as discussed earlier, increases magnitude and

steepness of the normalized gas holdup radial profile. This clearly reflects in its steepness

parameter values. However, the effect of superficial gas velocity does not appear to have

significant effect on normalized profiles. Figure B-13b shows the normalized gas holdup

radial profiles at superficial gas velocity of 20 cm/s at low and high operating pressure as

well as solids loading in 6” diameter steel column. It can be observed that, an increase

solids loading results in steeper profile at both ambient and high pressure. An increase in

operating pressure results in flatter profile at low solids loading while the flatness of

normalized gas holdup profile due to an increased pressure is not as evident at high solids

loading. One can observe that the shapes of the normalized profiles at low solids loading

and pressure (9.1 % vol. and 0.1 MPa) and at high solids loading and pressure (25 % vol.

and 1 MPa) are close to each other.

B-7 Normalized solids holdup radial profile

In this section, the normalized solids holdup radial profile has been analyzed. The

normalized solids holdup profile is the ratio of solids holdup at any radial location and

cross-sectional averaged solids holdup.

Figures B-14a and b show the normalized solids holdup profile in air-Therminol LT-glass

beads system at Ug = 30 cm/s, P = 1 MPa, and solids loading of 9.1 % vol. and Ug = 30

cm/s, P = 1 MPa, and solids loading of 25 % vol. It can be seen that, normalized solids

holdup radial profile at all axial locations (z/D = 2.1, 5.5, 9) closely fall on each other.

Although the magnitude of solids holdup radial profile is different at various axial

locations, they follow the same qualitative behavior at a given operating condition. The

similar behavior was observed at all the performed experimental conditions.

Figures B-15a and b show the effect of studied parameters on the normalized solids

holdup radial profile at z/D = 5.5 at low and high superficial gas velocities. The

199

normalized solids holdup radial profile in Figure B-15a appears to be close and fall on

each other. Figure B-15b shows normalized solids holdup radial profile at high

superficial gas velocities where all the conditions lie in deep churn-turbulent flow regime.

The normalized solids holdup radial profiles at high superficial gas velocities are not as

close as in case of low superficial gas velocity. However, they fall on

(a) (b)

Figure B-14: Normalized solids holdup radial profile using air-Therminol LT-glass beads

system at a) Ug = 30 cm/s, P = 1 MPa, solids loading = 9.1 % vol. and b) Ug = 30 cm/s, P

= 1 MPa, solids loading = 25 % vol. in 6” stainless steel column.

(a) (b) Figure B-15: Normalized solids holdup radial profile in air-Therminol LT-glass beads

system at z/D = 5.5 in 6” stainless steel column.

each other within a range of ± 10 % from the averaged normalized solids holdup profile.

The averaged normalized solids profile is the average of normalized solids holdup

200

profiles at all these experimental conditions. The solids holdup radial profile shows

different behavior at higher and lower superficial gas velocities as evident from Figures

B-15 a and b.

Additionally, the solids holdup radial profile can be fitted to the following form for

inverse parabola,

~'' 2( )[1 '(

' 2 2 'n

s sn c

n c Rε ε +

= ++ +

) ]r (B-3)

where, ~

sε is cross-sectional averaged solids holdup, while n’ is a steepness parameter

while c’ is wall holdup parameter. Table B-2 shows the effect of operating parameters on

values of n’ and c’. An increase in superficial gas velocity and solids loading reduces the

value of n’ while operating pressure increases the value of n’. The effect of these

operating parameters on the value of c’ is not clear.

Earlier it was shown that the normalized solids holdup radial profiles fall on each other

within ± 10 % of averaged normalized solids holdup radial profile. However, based on

Table B-2, it is clear that there are significant differences in its steepness values. The

change in superficial gas velocity does not appear to have significant effect on the

steepness parameter of normalized solids holdup profile. At high superficial gas

velocities (20 and 30 cm/s), the change in operating pressure from 0.1 to 1 MPa changes

steepness parameter by 50 and 44 % at solids loading of 9.1 and 25 % vol., respectively.

An addition of solids changes steepness parameter by 8 and 11 % at 0.1 and 1 MPa,

respectively. Also, based on the significant changes in the steepness parameter, the

acceptability of ± 10 % as an allowable engineering tolerance for normalized solids

holdup profiles remain to be explored.

Figure B-16a shows the normalized solids holdup radial profile at Ug = 8 cm/s, P = 0.1

MPa, and solids loading = 9.1 % vol. while Figure B-16b shows the normalized solids

holdup radial profile at Ug = 30 cm/s, P = 1 MPa, and solids loading = 9.1 % vol. along

with two distinct slopes observed in the profile. However, the difference between these

201

two slopes at given condition is higher at higher superficial gas velocities. One distinct

slope lies in the region from 0 ≥ r/R ≤ 0.6 and other one is close to wall region. The slope

in the core of column is either uniform or less steep while the wall region is characterized

by relatively larger slope.

(a) (b) Figure B-16: Normalized solids holdup radial profile in air-Therminol LT-glass beads

system at a) Ug = 8 cm/s, P = 0.1 MPa, solids loading = 9.1 % vol., b) Ug = 30 cm/s, P =

1 MPa, solids loading = 9.1 % vol. in 6” stainless steel column with two characteristics

slope.

202

Table B-2: Steepness of solids holdup radial profile

Ug (cm/s) P (MPa) Solids loading (%

vol.)

~

sε n’ c’

8 0.1 9.1 0.074 3.58 0.15

14 0.1 9.1 0.07 3.6 0.3

20 0.1 9.1 0.067 2.28 0.74

30 0.1 9.1 0.061 2.21 0.59

8 1 9.1 0.07 6.78 0.3

14 1 9.1 0.063 5.5 0.75

20 1 9.1 0.051 4.4 0.76

30 1 9.1 0.056 4.3 0.77

20 0.1 25 0.21 2.2 0.17

30 0.1 25 0.19 2.13 0.2

20 1 25 0.18 4 0.57

30 1 25 0.17 3.92 0.85

203

APPENDIX C Experimental Investigation of Hydrodynamics of Slurry Bubble Column Reactor via CARPT C-1 Effect of superficial gas velocity on solids axial velocity and turbulent

parameters profile

(a) (b) (c) (d) Figure C-1: Effect of superficial gas velocity on radial profile of solids a) axial velocity,

b) turbulent kinetic energy, c) axial normal stress, and d) shear stress in air-Therminol

LT-glass beads system at P = 0.1 MPa, and solids loading = 9.1 % volume

204

100

0 0.2 0.4 0.6 0.8 1

(a) (b)

(c) (d) Figure C-2: Effect of superficial gas velocity on radial profile of solids a) axial velocity,


LT-glass beads system at P = 1 MPa, and solids loading = 9.1 % volume

-40

-20

0

20

40

60

0 0.2 0.4 0.6 0.8 10

500

1000

1500

2000

2500

TK

E (c

m2 /s

2 )


Ug = 20 cm/sUg = 30 cm/s

Ug = 20 cm/s80 Ug = 30 cm/s


Sol

ids

axia

l vel

ocity

(cm

/s)

0 0.2 0.4 0.6 0.8 10

1000

2000

3000


Axi

al n

orm

al s

tress

(cm2 /s

2 )


0 0.2 0.4 0.6 0.8 10

50

100

150

200

250

300

350

400

450


Trz

(cm

2 /s2 )


205

0 0.2 0.4 0.6 0.8 1-40

-20

0

20

40

60


Sol

ids

axia

l vel

ocity

(cm

/s)


0 0.2 0.4 0.6 0.8 10

500

1000

1500

2000

2500

3000

3500


TK

E (c

m2 /s

2 )


(a) (b)

0 0.2 0.4 0.6 0.8 10

50

100

150

200

250

300


Trz

(cm

2 /s2 )


0 0.2 0.4 0.6 0.8 10

1000

2000

3000

4000


Axi

al n

orm

a


l stre

ss (-

)

(c) (d) Figure C-3: Effect of superficial gas velocity on radial profile of solids a) axial velocity,


LT-glass beads system at P = 0.1 MPa, and solids loading = 25 % volume

206

(a) (b) (c) (d) Figure C-4: Effect of superficial gas velocity on radial profile of solids a) axial velocity,


LT-glass beads system at P = 1 MPa, and solids loading = 25 % volume

207

C-2 Effect of operating pressure on solids axial velocity and turbulent parameters

profile

(a) (b) (c) (d)

Figure C-5: Effect of pressure on radial profile of solids a) axial velocity, b) turbulent

kinetic energy, c) axial normal stress, and d) shear stress in air-Therminol LT-glass beads

system at Ug = 20 cm/s, and solids loading = 9.1 % volume

208

100

0 0.2 0.4 0.6 0.8 10

500

1000

1500

2000

2500

3000


TK

E (c

m2 /s

2 )

P = 0.1 MPaP = 1 MPa

0 0.2 0.4 0.6 0.8 1

(a) (b) (c) (d) Figure C-6: Effect of pressure on radial profile of solids a) axial velocity, b) turbulent


system at Ug = 30 cm/s, and solids loading = 9.1 % volume.

-40

-20

0

20

40

60


80


Sol

ids

axia

l vel

ocity

(cm

/s)

0 0.2 0.4 0.6 0.8 10

100

200

300

400


Trz

(cm

2 /s2 )


0 0.2 0.4 0.6 0.8 10

500

1000

1500

2000

2500

3000

3500


Axi

al n

orm

al s

tress

(cm2 /s

2 )


209

(a) (b)

(c) (d ) Figure C-7: Effect of pressure on radial profile of solids a) axial velocity, b) turbulent


system at Ug = 20 cm/s, and solids loading = 25 % volume

210

(a) (b)

(c) (d ) FigureC-8: Effect of pressure on radial profile of solids a) axial velocity, b) turbulent


system at Ug = 20 cm/s, and solids loading = 25 % volume

C-3 Cross-sectional averaged turbulent stresses

The cross-sectional average of the turbulent stresses, that are important in modeling of

bubble/slurry bubble column reactors, obtained from CARPT was calculated as follows,

∫=1

0

)(2 ηηηττ dijij (C-1)

211

where, , , ,i j r zθ= and η = dimensionless radius, r/R

Table C-1 shows the cross-sectionally averaged turbulent stresses at the studied

experimental conditions. An increase in superficial gas velocity increases all the turbulent

stresses. At the same superficial gas velocity and solids loading, an increase in operating

pressure decreases all the turbulent stresses except shear stress. While at the same

superficial gas velocity and operating pressure, an increase in solids loading increases all

the turbulent stresses except shear stress. The behavior of shear stress follows the

behavior of solids axial velocity while in case of normal stresses; mean bubble size

appears to be a controlling factor within the studied experimental conditions.

Table C-1: Cross-sectional averaged values of turbulent stresses at the studied operating

conditions

Ug

(cm/s)

P

(MPa)

Solids Loading (%vol.)

TKE

(dyne/cm2)

Tzz

(dyne/cm2)

Tθθ

(dyne/cm2)

τrz

(dyne/cm2)20 0.1 9.1 2904 1737 1063 153

30 0.1 9.1 3490 2149 1406 187

20 1 9.1 2317 1419 810 204

30 1 9.1 2782 1819 1170 232

20 0.1 25 3761 2144 1262 150

30 0.1 25 4243 2514 1622 160

20 1 25 2924 1670 956 176

30 1 25 3295 2023 1245 205

212

C-4 Turbulent Eddy Viscosity

In this section, turbulent eddy viscosity which signifies the turbulent transfer of

momentum by eddies giving rise to an internal fluid friction, is first evaluated from the

CARTPT experimental data. Next the turbulent eddy viscosity was predicted using the

approach proposed by Ohnuki and Akimoto (2001) in gas-liquid systems and is compared

with the experimental values.

C-4.1Experimental Evaluation of Turbulent Eddy Viscosity

The relationship between solids shear stress and the gradient of mean solids axial velocity

based on Boussinesq’s hypothesis is given as follows,

ην

ρρτddu

Ruu zeff

SzrSrzS −== '', (C-2)

where, η = dimensionless radius.

The effective turbulent eddy viscosity is estimated from the CARPT data neglecting

molecular viscosity from equation (C-2). The radial-axial shear stress and radial gradient

of solids axial velocity is obtained from the CARPT measurements. The turbulent eddy

viscosity profile of the form given in equation (C-3) was assumed,

)1()( 0αηνην ktt −= (C-3)

where, νt0, k, and α are the fitted parameters.

For each operating condition, the fitted parameters were optimized to the relationship

presented in the equation (C-2). The cross-sectional averaged turbulent eddy viscosities

are then estimated using the following equation,

)2

21(0

1

0, +

−== ∫ ανηηνν kd ttCSAt (C-4)

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213

The values of fitted parameters of eddy viscosity profiles and averaged eddy viscosity at

the performed experimental conditions is provided in Table C-2. One can observe the

effect of superficial gas velocity, operating pressure, and solids loading. An increase in

superficial gas velocity and operating pressure decreases averaged turbulent eddy

viscosity while an increase in solids loading increases turbulent eddy viscosity. However,

based on earlier discussion, the magnitude of axial velocity gradient has opposite effect

of these parameters. Since the increase in axial velocity gradient is higher than that of

turbulent eddy viscosity, the shear stress profile follows the behavior of axial velocity

gradient.

Table C-2: Optimized parameters of the eddy viscosity profile

Superficial gas

velocity (cm/s)


Solids loading

(% volume)

νt0 (cm2/s)

k (-)

α (-)

CSAt ,ν (cm2/s)

20 0.1 9.1 35.7 1.17 1.85 14 30 0.1 9.1 37.5 0.82 0.53 13 20 1 9.1 49.8 0.77 0.022 12.1 30 1 9.1 24.9 0.65 0.24 10.4 20 0.1 25 79.2 0.8 0.1 18.9 30 0.1 25 34 14.3 0.52 14.8 20 1 25 69 0.9 0.61 15.2 30 1 25 30.5 0.91 0.29 11.6

C-4.2 Prediction of Turbulent Eddy Viscosity

The effective kinematic viscosity is the sum of the contributions of shear-induced

turbulent viscosity (νSIT), and bubble-induced turbulent viscosity (νBIT) (Deen et al.,

2001; Ohnuki and Akimoto, 2001) as follows,

BITSITeff ννν += (C-5)

In the following sections, the procedure adopted to predict turbulent eddy viscosity due to

shear induced and bubble induced turbulence is discussed.

214

C-4.2a Eddy viscosity due to bubble induced turbulence

The turbulent eddy viscosity due to bubble induced turbulence is represented by the form

proposed by Sato and Sekoguchi (1975),

slipbGBITBIT udC εν μ ,= (C-6)

where, Cμ,BIT = 0.6.

The calculation of eddy viscosity using equation (C-6) needs an estimation of bubble rise

velocity and bubble size. The following correlations were utilized to predict the needed

parameters.

The slip velocity is then calculated using Richardson-Zaki correlation given as, 1

, )1( −∞ −= n

Gbslip Uu ε (C-7)

where, Ub,∞ is bubble terminal rise velocity. The bubble terminal rise velocity is obtained

from the following correlation of Fan and Tsuchiya (1990).

nnb

slb

nb

slb

slbb

dd

cdK

Mog

Uu /12/24/54/1

4/1,

' }]2'

)('

2[]')({[)( −−−−

∞Δ

++Δ

==ρρ

ρρ

σρ

(C-8)

where, the dimensionless bubble diameter is given by, 2/1)/(' σρ gdd slbb =

.

Three empirical parameters, n, c, and Kb needed to estimate terminal bubble rise velocity

reflect three specific factors governing the rate of bubble rise. They relate to the

contamination level of the liquid phase, to varying dynamic effects of the surface tension,

and to the viscous nature of the surrounding medium. The suggested values of these

parameters are,

⎩⎨⎧

=liquidspurifiedfor

liquidsatedcontaforn

6.1min8.0

(C-8a)

⎩⎨⎧

=liquidsnentmulticompoforliquidsentmonocomponfor

c4.12.1

(C-8b)

and

215

)12,max( 038.00

−= MoKK bb (C-8c)

where,

⎩⎨⎧

=mixturessolventsorganicfor

solutionsaqueousforKb /2.10

7.140 (C-8d)

These equations were developed exclusively for gas-liquid system and also at ambient

conditions. The effect of solids was accounted by using pseudo-homogeneous approach.

The effective slurry density was calculated as the linear combination of phase densities as

)1( slsssl ερερρ −+= (C-9)

To estimate the effective viscosity of slurry, the following relationship proposed by

Tsuchiya et al. (1997) was used,

])/(1

exp[scs

s

l

sl

vvKv

−=

μμ

(C-10)

with two parameters correlated by Luo et al. (1997):

φ)]1010(3.0[tanh4.11.3 2

tuK

−−= (C-11)

and 02 )]}1010(5.0tanh[1.03.1{ stsc uv ε−−= (C-12)

where ut is in m/s.

Equation (C-6) also needs an estimation of the bubble size. The number of correlations

were proposed for the estimation of bubble size in gas-liquid systems. However, none of

them were proposed for slurry bubble column reactors and weakly capture the effect of

operating pressure. In this work, the bubble size equation proposed by Wilikinson (1991)

is used as it was based on a wide range of the liquid phase properties.

02.011.045.022.034.044.03 −−−−= Ggllb Ugd ρρμσ (C-13)

where, db is in m.

216

C-4.2b Eddy viscosity due to shear-induced turbulence

The eddy viscosity due to shear-induced turbulence can be represented similar to the

single-phase isotropic turbulence (Ohnuki and Akimoto, 2001),

εν μ

2SIT

SITk

C= (C-14)

where, Cμ = 0.09.

In the equation (C-14), kSIT is the turbulent kinetic energy due to shear-induced

turbulence while ε is the energy dissipation rate per unit mass of liquid. The energy

dissipation is estimated as the product of g (gravity constant) and Ug (superficial gas

velocity) [Deckwer and Schumpe, 1987; Camacho et al., 2001].

The turbulent kinetic energy is decomposed into contributions due to shear-induced and

bubble-induced turbulence using the approach proposed by Ohnuki and Akimoto (2001).

BITSITtot kkk += (C-15)

where, 2

slipGBIT uk ε= . The slip velocity was calculated using Rischardson-Zaki

correlation mentioned above. The contribution of turbulent kinetic energy due to shear-

induced turbulence, kSIT can be calculated by subtracting kBIT from the total turbulent

kinetic energy. The estimation of turbulent kinetic energy due to shear-induced

turbulence, kSIT then enables to predict turbulent eddy viscosity due to shear-induced

turbulence using equation (C-14).

C-4.3 Comparison of Experimental and Predicted Turbulent Eddy Viscosity

Table C-3 presents the values of turbulent kinetic energy and eddy viscosity components

at the studied operating conditions using the analysis explained earlier. The predicted

turbulent eddy viscosity was compared with the one obtained from CARPT data. Based

on the available state of prediction of bubble size and slip velocity, it can be observed

that the contribution of turbulent kinetic energy due to bubble-induced turbulence is less

217

significant than that of the contribution due to shear-induced turbulence. The relative

contribution of bubble-induced turbulence to that of total turbulent kinetic energy is close

to 7-8 %. This indicates that the turbulence generation due to shearing action of slurry is

far more dominant compared to the one induced by bubbles. However, the comparison of

prediction of turbulent eddy viscosity using above procedure with that of experimental

data shows an average relative error of 63%. Such a discrepancy in the current work

might possibly due to following reasons,

- In this work, Wilkinson (1991) correlation was used for bubble size estimation.

This correlation was developed for gas-liquid flows. It was utilized, as no

correlation is available for bubble size estimation in the slurry systems and it was

developed using a wide range of liquid phase properties including highly viscous

liquid.

- The approach explained above was typically developed for gas-liquid flows. It

was extended to gas-liquid-solids system by assuming pseudo-homogeneous

properties. In the past, few studies (Krishna et al., 2001) compared the gas holdup

measured in gas-liquid-solid system to that of gas-liquid system by using a liquid

that has similar pseudo-homogeneous properties as that of slurry. The overall gas

holdup found in these two cases was close although slurry viscosities were

estimated based on Einstenian equation developed for dilute particles. However,

further studies are required to evaluate whether it is appropriate to assign a

constant resultant slurry viscosity based on pseudo-homogenous approach. A

more elaborate analysis is needed to account for the effect of bubble size on

interactions of the bubbles based either on non-Newtonian approach or

heterogeneous approach.

218



Solids loading (% volume)

Gas holdup (-)

db (cm)

Ub∞ (cm/s)

kBIT (cm2/s2)

kSIT (cm2/s2)

νSIT νBIT νtotal % Error

20 0.1 9.1 0.28 0.27 15.4 27 2877 0.45 38 38.45 64 30 0.1 9.1 0.33 0.27 15.4 26 3464 0.47 37 37.47 65 20 1 9.1 0.4 0.2 14.2 20 2297 0.35 24.3 24.65 51 30 1 9.1 0.45 0.2 14.2 19.5 2764 0.35 23.4 23.75 56 20 0.1 25 0.16 0.28 14.3 20 3740 0.3 64.3 64.6 70 30 0.1 25 0.2 0.28 14.27 22 4221 0.34 54.5 54.84 73 20 1 25 0.27 0.21 13 18.8 2905 0.28 34 34.28 56 30 1 25 0.3 0.21 13 18.4 3276 0.3 33 33.3 65

Table C-3: Eddy viscosity analysis

total

totaltCSAerrorν

νν −=%

219

C-5 Turbulent Viscosity Correlations

In this section, the cross-sectional averaged turbulent viscosity calculated using CARPT

data in Section C-4.1 is compared with the predictions of the available correlations.

These correlations are commonly utilized as closures in modeling velocity profiles in

bubble columns assuming constant turbulent viscosity. Table C-4 lists the available

correlations for turbulent viscosity while Table C-5 shows % relative error between

experimental and predicted turbulent viscosities using the last three correlations in Table

C-5. The first two correlations were not considered as they assume turbulent viscosity to

be function only of column diameter. Clearly, none of the available correlations predict

turbulent eddy viscosity with consistent statistical confidence.

Table C-4: Correlations for turbulent viscosity

Researcher Correlation Miyauchi and Shyu (1970) 8.10199.0 TD Ueyama and Miyauchi (1979) 7.10322.0 TD Miyauchi et al. (1981) 2/36/10345.0 TG DU Riquarts (1981) 3/18/1Re)9.90/( −FrUD GT

Kawase and Moo-Young (1989)

)0()43/1(

2

L

GT

VgD ε

220

Table C-5: % relative error of literature correlations for turbulent viscosity from CARPT

data

Superficial gas

velocity (cm/s)


Solids loading

(% vol )

% relative error*

Miyauchi Riquarts Kawase and Moo et al.(1981) (1981) Young (1989)

20 0.1 9.1 22.3 72.9 145 30 0.1 9.1 40.9 49.9 158 20 1 9.1 41.6 68.7 157 30 1 9.1 76.2 37.4 181 20 0.1 25 9.4 80 190 30 0.1 25 23.8 56 182 20 1 25 12.7 75.1 179 30 1 25 57.9 43.8 198

C-6 Eddy Diffusivities

Turbulent eddy diffusivities are important parameters in modeling of liquid/solids mixing

in bubble/slurry bubble column reactors. As CARPT provides lagrangian data, an

estimation of these quantities is unique to this technique. As the flow is anisotropic with

radial non-homogeneity, the radial gradient of solids axial velocity was considered in the

evaluation of axial eddy diffusivity. Degaleesan (1997) defined eddy diffusivities as

follows,

The radial eddy diffusivity is,

2

0

1( ) ( ) '( ') '( )2

t

r r rdDrr t y t u t u ddt

τ τ= = ∫ (C-16)

The axial eddy diffusivity is,

21( ) '( ) ( ) '( )2zz z z z

dD t y t y t udt

= = t

(C-17)

* CSAt

ncorrelatiotCSAterrorrelative,

,,%υυυ −

=

221

First, various correlation coefficients were calculated from CARPT experimental data

which was then used to compute these eddy diffusivities.

C-6.1 Effect of liquid phase physical properties on eddy diffusivities

Figure C-9a shows the comparison of axial and radial diffusivities in air-water-glass

beads and air-Therminol LT-glass beads system at superficial gas velocity of 30 cm/s and

solids loading of 9.1 % vol. In general, diffusivities were low in air-Therminol LT-glass

beads system. However, the effect on radial eddy diffusivity is stronger than on the axial

eddy diffusivity at ambient pressure. Figure C-9b shows the comparison of axial and

radial diffusivities in these two systems at operating pressure of 1 MPa. At higher

pressure, both axial and radial eddy diffusivities were significantly reduced in air-

Therminol LT-glass beads system. Such reduction in eddy diffusivities in Therminol LT

systems can be related to the change in physical properties that results into generation of

higher population of small bubbles/eddies. The similar effect due to change in liquid was

observed in case of TKE and normal stresses.

(a)

222

(b)

Figure C-9: Comparison of axial and radial eddy diffusivities in air-water-glass beads and

air-Therminol LT-glass beads system at and superficial gas velocity 30 cm/s, solids

loading of 9.1 % vol. and operating pressure of a) 0.1 MPa, and b) 1 MPa.

C-6.2 Effect of solids loading on eddy diffusivities Figures C-10 and C-11 show the effect of solids loading on axial and radial eddy

diffusivities in air-Therminol LT-glass beads system at ambient pressure and superficial

gas velocities of 20 and 30 cm/s. An addition of solids in the system tends to increase

bubble coalescence rate and decrease bubble breakup rate that results into higher

population of large bubbles/eddies in the system. Hence, at increased solids loading

higher values of axial and radial diffusivities were observed. The maximum in both the

diffusivities was not affected by an addition of solids. The similar qualitative effect of

solids loading was observed at higher pressure as shown in Figures C-12 and C-13.

223

Figure C-10: Effect of operating pressure on axial and radial eddy diffusivities in air-

Therminol LT-glass beads system at solids loading of 9.1 % vol. and superficial gas

velocity of 20 cm/s.

Figure C-11: Effect of solids loading on axial and radial eddy diffusivities in air-

Therminol LT-glass beads system at ambient pressure and superficial gas velocity of 30

cm/s.

224


Therminol LT-glass beads system at operating pressure of 1 MPa and superficial gas



Therminol LT-glass beads system at operating pressure of 1 MPa and superficial gas

velocity of a) 20 cm/s, and b) 30 cm/s.

C-6.3 Effect of superficial gas velocity on eddy diffusivities

Figures C-14 and C-15 show the effect of superficial gas velocity on axial and radial

eddy diffusivities in air-Therminol LT-glass beads system at Ug = 30 cm/s, solids loading

225

of 9.1 % vol and operating pressure of 0.1 MPa. An increase in superficial gas velocity

increases axial and radial eddy diffusivities. The maximum values of axial diffusivities

are observed at dimensionless radius of about 0.7, while maximum radial eddy

(a) (b) Figure C-14: Effect of superficial gas velocity on a) axial and b) radial eddy diffusivities

in air-Therminol LT-glass beads system at ambient pressure and solids loading of 9.1 %

vol.


in air-Therminol LT-glass beads system at operating pressure of 1 MPa and solids

loading of 9.1 % vol.

diffusivities are observed at dimensionless radius of about 0.5. The locations of these

maximum values can be explained on the basis of inversion point in axial solids velocity

226

and the maximum values of solids shear stresses. The similar effect of eddy diffusivities

was observed at high solids loading (Figures C-16 and C-17).

(a) (b)

Figure C-16: Effect of superficial gas velocity on a) axial and b) radial eddy diffusivities

in air-Therminol LT-glass beads system at ambient pressure and solids loading of 25 %

vol.


in air-Therminol LT-glass beads system at operating pressure of 1 MPa and solids

loading of 25 % vol.

227

C-6.4 Effect of operating pressure on eddy diffusivities

Figures C-18 and C-19 show the effect of operating pressure on axial and radial eddy

diffusivities in air-Therminol LT-glass beads system using solids loading of 9.1 % vol.

and superficial gas velocity of 20 and 30 cm/s, respectively. Similar to the effect of

pressure on turbulent kinetic energy and other normal stresses, axial and radial eddy

diffusivities were found to decrease with an increase in pressure. As mentioned earlier,

an increase in pressure increases bubble breakup rate while decreases coalescence rate.

This results into relatively higher population of small bubbles/eddies at increased

pressure and thereby reduced diffusivities.

Figures C-20 and C-21 show the effect of operating pressure at solids loading of 25 %

vol. and superficial gas velocity of20 and 30 cm/s. The similar qualitative effect of

operating pressure was observed at high solids loading.




228





Therminol LT-glass beads system at solids loading of 25 % vol. and superficial gas


229


Therminol LT-glass beads system at solids loading of 25 % vol. and superficial gas


C-6.5 Cross-sectional averaged eddy diffusivities

The cross-sectional average of the eddy diffusivities obtained from CARPT was

calculated as follows,

1

0

2 ( )ii iiD D dη η η= ∫(C-18)

where, and η = dimensionless radius, r/R. ,i r z=

Table C-6 shows the cross-sectionally averaged axial and radial eddy diffusivities at the

studied experimental conditions.

230

Table C-6: Cross-sectional averaged values of axial and radial diffusivities at the studied

operating conditions in air-Therminol LT-glass beads system

Ug

(cm/s)

P

(MPa)

Solids Loading (%vol.)

Dzz

(cm2/s)

Drr

(cm2/s) 20 0.1 9.1 535 31

30 0.1 9.1 570 35

20 1 9.1 450 22

30 1 9.1 482 25

20 0.1 25 644 42

30 0.1 25 721 46

20 1 25 548 29

30 1 25 585 32

In general, an increase in superficial gas velocity increases eddy diffusivities. At the same

superficial gas velocity and solids loading, an increase in operating pressure reduces eddy

diffusivities. While at the same superficial gas velocity and operating pressure, an

increase in solids loading increases eddy diffusivities.

An increase in operating pressure from 0.1 to 1 MPa decreases axial eddy diffusivity by

15 and 20 % at solids loading of 9.1 and 25 % vol., respectively. While an increase in

solids loading from 9.1 to 25 % vol. increases axial diffusivity by 20 and 23 % at

operating pressures of 0.1 and 1 MPa, respectively. The radial eddy diffusivities exhibit

the same qualitative but slightly different quantitative behavior.

231

APPENDIX D Sedimentation-Dispersion Model An axial distribution of solid/catalyst particles is an important parameter for design and

scaleup of slurry bubble column reactors. The axial solids distribution influences

residence time distribution of solid particles that in turn affects the conversion rates and

the heat and mass transfer inside the reactor. Catalyst concentration in the reactor is a

function of catalyst concentration in feed, direction and magnitude of the liquid/slurry

velocity, mixing characteristics of the system, axial location in the reactor, and physical

properties of slurry (Cova, 1966). The solids axial distribution is quantitatively described

using Sedimentation-Dispersion Model (SDM). It is the popular and only predictive

model available. SDM was originally proposed by Cova (1966) and Suganuma and

Yamanishi (1966). In this model, the solids flux is obtained by the superposition of a

Fickian type solids dispersion flux and a solids settling (sedimentation) flux on the

convective slurry flux.

The following assumptions were used in formulating the model:

i) All the solids particles have identical terminal velocity.

ii) Solids phase dispersion coefficient is constant along the column axis.

iii) The gas holdup is constant along the column axis.

iv) The settling velocity of solids particles is constant along the column axis.

v) All solids particles are completely suspended in liquid.

vi) No radial gradients in the concentration of solids particles.

If one considers a horizontal cross-sectional element of slurry bubble column reactor with

thickness Δz. A mass balance in the vertical z-direction with respect to solid particle can

be written as

Rate of accumulation within volume element = rate of mass (in-out) due to dispersion +

rate of mass (in-out) due to convective

232

slurry flow + rate of mass (in-out) due to

settling of solids …………….. (D-1)

Equation (D-1) can be written as,

])()([])1

()1

([][ 2222zzStzStT

zz

SG

sl

z

SG

slTzzdzdT

sT CuCuDC

uC

uDnnD

tc

zDΔ+

Δ+

−−

Δ++−+

−−

−+−=

∂∂

Δ πεε

πππ

…………….(D-2)

Dividing equation (D-2) by and taking limit as zDTΔ2π zΔ tends to zero yields

StSG

slds Cuz

Cu

zzn

tc

∂∂

+−∂

∂−

∂∂

=∂∂

−

)1

(ε

…………….(D-3)

The dispersion flux, nd of solid particles is given as,

zc

En sSd ∂∂

−= …………….(D-4)

The substitution of equation (D-4) into (D-3) along with steady state assumption gives

following simplified general form,

0)1

(2

2

=−−

−

−

dzdC

uu

dzcd

E St

G

slsS ε

……………(D-5)

To obtain the solids axial distribution, the equation (D-5) needs to be integrated twice and

needs two boundary conditions.

For semi-batch operation (as employed in the current work), equation (D-5) can be

written as

02

2

=+dz

dCu

dzcd

E St

sS ……………….(D-6)

The general solution of this differential equation is

233

][exp21 zEu

CCCS

tS −+= …………………..(D-7)

The first boundary condition is

00 1 =⇒∞→= CzasCS

Therefore equation (D-7) becomes

][exp2 zEu

CCS

tS −= ………………….(D-8)

The second constant can be obtained from the knowledge of nominal solids mass in the

column. Let m be the initial mass of particles, V be the total slurry volume while S and L

are cross-sectional column area and slurry height. Hence

∫=V

S dVCm0

………………(D-9)

Substitution of equation (D-9) into equation (D-8) yields

∫ −=L

S

t dzSzEu

Cm0

2 )(exp ………………(D-10)

Integration of equation (D-10) will give the value of second constant. The substitution of

second constant in equation (D-8) will result into the following equation

][exp1

][exp

LEu

zEu

SEmu

C

S

t

S

t

S

tS

−−

−= ………………(D-11)

The nominal solids concentration is

VCm S

−

= ……………….(D-12)

Hence the final form for semi-batch operation is

][exp1

][exp

S

S

SSS BoLzBo

BoCC−−

−=

−

…………….(D-13a)

where, StS ELuBo /=

234

The final form of SDM can be written in terms of solids loading (equation D-13b) and

solids holdup (equation D-13c) as follows

][exp1

][exp

S

S

SSS BoLzBo

Bovv−−

−=

−

…………….(D-13b)

][exp1

][exp

S

S

SSS BoLzBo

Bo−−

−=

−

εε …………….(D-13c)

To predict solids axial profile using SDM, one need to predict two parameters, i.e.,

terminal velocity and solids axial dispersion coefficient. Various correlations are

available to predict these parameters. In this work, the most commonly used correlations

in literature were utilized.

Solids axial dispersion coefficient

The solid phase Peclet number is calculated in terms of Froude number as follows

DH

Fr81Fr13Pe D

85.0S += (D-14)

C

G

gDU

Fr = (D-15)

where, S

GS E

LUPe = .

Particle terminal velocity

The terminal velocity of particles, ut calculated from the single particle settling velocity in

a quiescent liquid (uts) using a following set of correlations (Kato et al., 1972).

2/5

*0

4/1

11

2.1 ⎟⎟⎠

⎞⎜⎜⎝

⎛−−

⎟⎟⎠

⎞⎜⎜⎝

⎛=

S

S

ts

GTSt v

vuU

uu (D-16)

235

PL

LPts d

Reu

ρμ

= (D-17)

⎪⎩

⎪⎨⎧

>≤

=5.0Refor )9.13/Ar(5.0Refor 18/Ar

ReP

7.0P

P (D-18)

2L

3PLLS gd)(

Arμ

ρρρ −= (D-19)

S

*S

1.0vρ

= (D-20)

236

APPENDIX E Material Safety Data Sheet for Therminol LT 1. PRODUCT AND COMPANY IDENTIFICATION Product name: THERMINOL® LT Heat transfer fluid Reference Number: 000000000208 Date: 12/03/2004 Company Information: United States: Canada: Solutia Inc. Solutia Canada Inc. 575 Maryville Center Drive, P.O. Box 66760 6800 St. Patrick Street St. Louis, MO 63166-6760 LaSalle, PQ H8N 2H3 Emergency :1-800-424-9300 Emergency: 1-613-996-6666 Non-Emergency: 1-314-674-6661 Non-Emergency: 1-314-674-6661 Mexico: Brazil: Solutia MEXICO, S. DE R.L. DE C.V. Solutia Brazil Ltd. Paseo de la Reforma No. 2654 Piso 3-A Avenue Carlos Marcondes, 1200 Col. Lomas Altas, CP 11950 Mexico DF CEP: 12241-420-São José dos Campos/SP-

Brazil Emergency: 01-800-002-1400 Emergency: 55 12 3932 7100 (PABX) Non-Emergency: 01-55-5259-6800 Non-Emergency: 55 11 3365 1800 (PABX) 2. HAZARDS IDENTIFICATION EMERGENCY OVERVIEW Form: liquid Colour: clear to colourless Odour: strong odour, aromatic, hydrocarbon WARNING STATEMENTS WARNING! Flammable liquid and vapour Contains material which can cause nervous system damage May cause skin irritation May cause respiratory tract irritation POTENTIAL HEALTH EFFECTS Likely routes of exposure:

237

eye and skin contact, inhalation Eye contact: Slightly irritating to eyes. Skin contact: Moderately irritating to skin.

Prolonged or repeated skin contact may result in irritant dermatitis. Can be absorbed rapidly through the skin. No more than slightly toxic if absorbed.

Inhalation: Moderately irritating if inhaled. No more than slightly toxic if inhaled. Significant adverse health effects are not expected to develop under normal conditions of exposure.

Ingestion: No more than slightly toxic if swallowed. Significant adverse health effects are not expected to develop if only small amounts (less than a mouthful) are swallowed.

Signs and symptoms of overexposure: headache dizziness/incoordination nausea/vomiting loss of consciousness vertigo confusion anxiety laboured breathing drowsiness Target organs/systems: May cause nerve damage

Based on animal data excessive exposure may cause bluish discoloration of tissue and urine.

Refer to Section 11 for toxicological information. 3. COMPOSITION/INFORMATION ON INGREDIENTS Components CAS No. Average conc. Concentration range Units diethylbenzene 25340-17-4 100.0 % 4. FIRST AID MEASURES If in eyes: Immediate first aid is not likely to be required.

This material can be removed with water. If on skin: Immediately flush the area with plenty of water.

Remove contaminated clothing. Get medical attention if irritation persists. Wash clothing before reuse.

238

If inhaled: Remove patient to fresh air. If not breathing, give artificial respiration. If breathing is difficult give oxygen. Remove material from eyes, skin and clothing.

If swallowed: Immediate first aid is not likely to be required.

A physician or Poison Control Center can be contacted for advice. Wash heavily contaminated clothing before reuse.

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239

7. HANDLING AND STORAGE Handling: Keep away from heat, sparks, and flame. Avoid contact with eyes, skin and clothing. Avoid breathing vapour or mist. Keep container closed. Use with adequate ventilation. Wash thoroughly after handling. Heat transfer fluids are intended for INDIRECT heating purposes ONLY. This product has not been approved for food grade use. Container hazardous when empty: Emptied containers retain vapour and product residue. Follow labeled warnings even after container is emptied. Residual vapours may explode on ignition. Do not cut, drill, grind or weld on or near this container. Improper disposal or reuse of this container may be dangerous and/or illegal. The reuse of this material's container for non industrial purposes is prohibited and any reuse must be in consideration of the data provided in this material safety data sheet. Storage General: Stable under normal conditions of handling and storage. 8. EXPOSURE CONTROLS/PERSONAL PROTECTION Airborne exposure limits: (ml/m3 = ppm) THERMINOL® LT No specific occupational exposure limit has been established. Eye protection: Does not cause significant eye irritation or eye toxicity requiring special

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240

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Components referred to herein may be regulated by specific Canadian provincial legislation. Please refer to exposure limits legislated for the province in which the substance will be used. 9. PHYSICAL AND CHEMICAL PROPERTIES Flash point: 57 0C Pensky-Martens closed tester Autoignition temperature: 429 0C ASTM D-2155 Specific gravity: 0.864 @ 25 0C Density: 8.62 g/cm3 @ 25 0C Boiling point : 181 0C @ 1,013 hPa Freezing point -75 0C Vapour pressure: 1 hPa @ 20 0C Water solubility: 14 mg/l @ 25 0C Kinematic viscosity: 0.81 mm2/s @ 40 0C VOC Content: 100 % ; NOTE: These physical data are typical values based on material tested but may vary from sample to sample. Typical values should not be construed as a guaranteed analysis of any specific lot or as specifications for the product. 10. STABILITY AND REACTIVITY Conditions to avoid: All sources of ignition. Materials to avoid: Contact with oxidizing agents. Hazardous reactions: Hazardous polymerization does not occur. Hazardous decomposition products: None known 11. TOXICOLOGICAL INFORMATION Human experience: Prolonged or repeated skin contact may result in irritant dermatitis. Accidental inhalation during ingestion or vomiting may cause lung injury leading to

241

death. This product has been tested for toxicity. Results from Solutia sponsored studies or from the available public literature are described below. Acute animal toxicity data Oral: LD50 , rat, 2,050 mg/kg , Slightly toxic following oral administration. Dermal: LD50 , rabbit, > 5,000 mg/kg , Practically nontoxic after skin application

in animal studies. Inhalation: LC50 , mouse, > 27.4 mg/l , , No mortality or signs of toxicity at the

highest level achievable. Eye irritation: rabbit , Slightly irritating to eyes (rabbit)., 24 h Skin irritation: rabbit , Moderately irritating to skin., 24 h Repeat dose toxicity: rat, subchronic, Repeated administration produced discoloration of fur, organs and urine. Target organs affected liver, kidneys Neurotoxicity: rat, Exposure produced weakness in hind limbs and gait disturbances which progressed to complete paralysis in some cases. Developmental toxicity: rat, gavage, , No birth defects were noted in rats given the active ingredient orally during pregnancy. Carcinogenicity: mouse, dermal, chronic, Produced tumours at the site of application. Mutagenicity: No genetic effects were observed in standard tests using bacterial and animal cells. 12. ECOLOGICAL INFORMATION Environmental Toxicity: Invertebrates 48 h, EC50 Water flea (Daphnia magna) 9.42 mg/l Fish: 96 h, LC50 Fathead minnow (Pimephales promelas) > 1.0 mg/l Algae: 96 h, EC50 Algae (Selenastrum capricornutum) > 20 mg/l EC50/LC50 greater than water solubility. Environmental fate Biodegradation theoretical CO2 evolution 8 % 28 d Not readily biodegradable. 13. DISPOSAL CONSIDERATIONS US EPA RCRA Status: This material when discarded is a hazardous waste as that term is

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242

EPA disposal requirements. Consult regulatory officials for performance standards.

US EPA RCRA hazardous waste number: D001 Compound/Characteristic: Ignitability Disposal considerations: Incineration Recycle Miscellaneous advice: This product meets the criteria for a synthetic used oil under the U.S. EPA Standards for the Management of Used Oil (40 CFR 279). Those standards govern recycling and disposal in lieu of 40 CFR 260 -272 of the Federal hazardous waste program in states that have adopted these used oil regulations. Consult your attorney or appropriate regulatory official to be sure these standards have been adopted in your state. Recycle or burn in accordance with the applicable standards. Solutia operates a used fluid return program for certain fluids under these used oil standards. Contact your Sales Representative for details. This product should not be dumped, spilled, rinsed or washed into sewers or public waterways. 14. TRANSPORT INFORMATION The data provided in this section is for information only. Please apply the appropriate regulations to properly classify your shipment for transportation. US DOT Proper shipping name: DIETHYLBENZENE Hazard Class: 3 Hazard Identification number: UN2049 Packing Group: Packing Group III Transport label: Flammable liquid. Canadian TDG Proper shipping name: DIETHYLBENZENE Other: See DOT Information Hazard Class: 3 Hazard Identification number: UN2049 Packing Group: Packing Group III Transport label: Flammable liquid. ICAO/IATA Class Other: See DOT Information

243

15. REGULATORY INFORMATION All components are in compliance with the following inventories: U.S. TSCA, EU EINECS, Canadian DSL, Australian AICS, Korean, Japanese ENCS, Phillipine PICCS, Chinese Canadian WHMIS classification: B3 - Combustible Liquids D2(B) - Materials Causing Other Toxic Effects SARA Hazard Notification: Hazard Categories Under Title III Rules (40 CFR 370): Immediate Delayed Fire Section 302 Extremely Hazardous Substances: Not applicable Section 313 Toxic Chemical(s): Not applicable CERCLA Reportable Quantity: Not applicable This product has been classified in accordance with the hazard criteria of the Canadian Controlled Products Regulation and the MSDS contains all the information required by the Canadian Controlled Products Regulation. Refer to Section 11 for OSHA/HPA Hazardous Chemical(s) and Section 13 for RCRA classification. Safety data sheet also created in accordance with Brazilian law NBR 14725 16. OTHER INFORMATION Product use: Heat transferring agents Reason for revision: New ANSI Standard

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244

Appendix F

Development of Artificial Neural Network (ANN)

Correlations for Hydrodynamic Parameters

As discussed in Chapter 6, the objective of this chapter of Appendix is to develop state-

of-the-art correlations for ‘a priori’ prediction of hydrodynamic parameters that will aid

the proposed methodology for hydrodynamic similarity. The specific focus is to develop

unified correlations for overall gas holdup, radial profile of gas holdup and liquid axial

velocity in bubble columns that can be useful for design engineers. To develop such

correlations, an approach that combines both an Artificial Neural Network (ANN) and

Dimensional Analysis has been used. These correlations were derived from a broad

experimental data bank collected from the open literature.

In the first part, a brief introduction to ANN is provided. The detailed information can be

referred to Shaikh and Al-Dahhan (2003). The next section deals with the general

procedure for the development of these correlations in the context of overall gas holdup.

The similar procedure is being adopted to develop the correlations for radial profile of

gas holdup and liquid axial velocity. The general structure of ANN correlations for radial

profile of gas holdup and liquid axial velocity and centerline velocity is presented.

F-1 Artificial Neural Networks

Neural Networks are computer algorithms inspired by the way information is processed

in the nervous system. An Artificial Neural Network is a massively parallel distributed

processor that has a natural propensity for storing experimental knowledge and making it

available (Ripley, 1996).

245

In this work, a multilayer neural network has been used, as it is effective in finding

complex non-linear relationships. It has been reported that multilayer ANN models with

only one hidden layer are universal approximators (Hornik et al., 1989). Hence, a three-

layer feedforward neural network is chosen as a regression model. The weighting

coefficients of the neural network are calculated using the special-purpose software

NNFit (Cloutier et al.,1996). NNFit is a non-linear regression software that discloses

relationships between a set of normalized input variables, Ui, and a set of normalized

output variable, Sk. Figure F-1 shows the transformation S = f (U) using a neural network

with a single hidden layer. The transformation of actual variables (X, Y) to normalized

variables (U, S) is given by (Cloutier et al., 1996),

(F-1)

(F-2)

where, Xi and Yk are raw input and output variables. The basic structure of this type of

neural network is described by the following set of equations. The various layers are

interconnected to each other by a sigmoid function through the fitted parameters wij, wjk

in the following manner,

(F-3)

and

(F-4)

where I,J,K indicate the input, hidden and output nodes of the ANN structure,

respectively. HJ+1 and UI+1 (Figure 7-1) are the bias constants which are set equal to one.

)/log( X)/log(

minmax

min

XX XU i

i =

)/log()/log(

minmax

min

YYYYS k

k =

∑−+= +

=

1

1]exp[1

1J

jjjk

kHw

S

∑−+= +

=

1

1]exp[1

1I

iiij

jUw

H

246

wij and wjk are weighting parameters which are fitted by the NNFit regression model,

using a quadratic criterion as a minimization algorithm, a quasi-Newton method of the

BGFS type (Broyden-Fletcher-Goldfrab-Shanno) (Cloutier et al., 1996).

Figure F-1: Architecture of the three-layered feedforward neural network with a single hidden layer

F-2 Development of the ANN based correlation for Overall Gas Holdup

Over the years, overall gas holdup has been studied extensively with various

measurement techniques, ranging from measuring the change in dynamic height or

measuring conventional pressure drop to CT. In the literature, numerous correlations

have been proposed for overall gas holdup. Some of the important correlations can be

referred to Shaikh and Al-Dahhan (2003). Kemoun et al. (2001) compared gas holdup

predicted by various correlations with the cross-sectional averaged gas holdup measured

using CT in the fully developed region at atmospheric to high pressure and at low to high

superficial gas velocities. The comparison between their experimental data and predicted

gas holdups from various correlations at atmospheric and high pressure (0.7 MPa) can be

summarized as follows,

At atmospheric pressure, the correlation of Idogawa et al. (1985) gives the best

agreement with the CT experimental data, except at UG = 5 cm/s.

247

At higher pressures and over the entire superficial gas velocity range studied, the

correlation of Hammer et al. (1984) gives better prediction, followed by Wilkinson et

al. (1992) and Idogawa et al. (1987).

At higher pressures and higher superficial gas velocity (UG = 10 cm/s), the correlation

of Krishna et al. (1996) and Luo et al. (1999) also provides reasonable prediction of

gas holdup.

While several correlations give reasonable predictions at different conditions, Kemoun et

al. (2001) did not find any correlation that consistently predicted their experimental data

at the studied operating conditions. To facilitate the scale-up of bubble columns, there is a

need for a correlation that can predict overall gas holdup over a range of operating

conditions, physical properties, and column dimensions.

The development of the ANN-based correlation began with the collection of a large

databank. The physical parameters were then subjected to force analysis in order to

maintain dimensional homogeneity. The last step was to perform a neural regression, and

to validate it statistically.

F-2.1 Collection of data

As mentioned earlier, over the years researchers have amply quantified the

hydrodynamics of bubble column reactors based on the overall gas holdup. In this work,

about 3500 experimental points have been collected from 60 sources spanning the years

1965 to 2000. This wide range of database includes experimental information from

different physical systems to provide a unified correlation for overall gas holdup. Table

F-1 suggests the wide range of the collected databank for gas holdup. Most of the

hydrodynamic studies on bubble columns were performed using air-water systems.

Hence, the majority of the current database (around 45%) comprises overall gas holdup

data from air-water studies.

248

Table F-1: Range of column dimensions, physical properties, operating pressures and type of spargers included in the collected databank

Column Diameter 0.045 - 5.5 m Liquid Density 681 - 2965 kg.m-3

Liquid Viscosity 0.41 - 2.95 cP

Surface Tension 20 - 72 mN.m-1

Gas Density 0.083 - 1.2 kg.m-3

Pressure 0.1 - 2 MPa Superficial Gas Velocity 0.005 – 0.75 m/s Superficial Liquid Velocity 0 (batch liquid)

Overall gas holdup 0.05 – 0.685

Gases: air, N2, CO2 , He, Ar, mixture of N2 and H2 Liquids: water, tetradecane, paraffin oil (A, B), soltrol-130, isopropanol, monoethylene glycol, n-heptane, isopar-G etc. Sparger types: perforated plates with different no. of holes, geometry and hole sizes, single nozzle sparger, cross-sparger, sintered plate etc. Number of Sources: 60 (1965 – 2000) Number of data points: 3500

Most of the hydrodynamic studies on bubble columns were performed using air-water

systems. Hence, the majority of the current database (around 45%) comprises overall gas

holdup data from air-water studies. To assess the impact of physical properties such as

density, surface tension, and viscosity, several other gas-liquid systems were included in

the database. However, in this work we have included only pure liquids systems

(approximately 30 different liquids). Bubble columns are generally operated with low

liquid velocities, which have been reported to have little or no effect on overall gas

holdup (Kelkar et al., 1983, Shetty et al., 1992). Hence, in this work we have considered

data only for columns with liquid in batch mode and gas in continuous mode. As

industrial conditions of interest are at high pressure, we have added experimental studies

at high pressures up to 2 MPa. Since reactor scale-up extends small diameter behavior to

large diameters, and in order to make the developed correlation industrially useful, we

249

have included data obtained up to 5.5 m column diameter, the largest diameter described

in the open literature. All the data was collected for cylindrical columns, as they are the

favored geometry in a majority of industrial applications. There are different spargers

used in various studies. We have mentioned only the most commonly used spargers in

Table F-1. However, in the most literature studies the mentioned spargers have been used

with some modifications in geometry or by changing number of holes or hole sizes. Since

the data was collected from wide range of sources, there is no uniformity in the

measurement techniques of gas holdup. The techniques range from measurement by level

change, or pressure drop up to densitometry and computed tomography.

F-2.2 Force Analysis

The force analysis checked whether the physical parameters in the database can be

formulated in a dimensionally homogeneous manner or not. It consists of two steps

i) All physical parameters that influence overall gas holdup are put in a so called

“wish-list”.

ii) The dimensional homogeneity of the physical parameters was checked by

transforming them into various forces.

Based on the extensive literature review, the input variables that have been found to affect

gas holdup are superficial gas velocity, column diameter, operating pressure, liquid phase

physical properties, and sparger design. However, the effect of sparger is significant only

in bubbly flow.

Once the crucial identification of raw variables has been performed, the input variables

were then converted into various physical forces. Some of the important forces are

a) gas inertial force: 2GGuρ

b) gas viscous force: duGG /μ

250

c) liquid gravitational force: gdLρ

d) gas gravitational force: gdGρ

e) capillary force: dL /σ

Dimensionless numbers were then formed by taking ratios of various physical forces

which are determined from the input variables. In addition to this, the various

dimensionless groups used in the gas holdup correlations reported in literature were

considered. Then, on the basis of the observed effect of some parameters on the overall

gas holdup, some of the dimensionless groups such as ratios of densities, etc., were

added.

The main advantage of performing dimensional analysis is to reduce the number of input

parameters, i.e., there are fewer dimensionless input groups than the raw parameters. The

other advantage of dimensional analysis lies in the “scale-invariant” property of a

dimensionless frame. The “scale-invariance” makes dimensional analysis a primary step

in scale-up of reactors (Zlokarnik, 1998).

F-2.3 Neural Regression

Force analysis is used to produce dimensionless groups in this case, but it alone cannot

determine which groups are relevant and should be used as input. Therefore, we used the

following methodology to select the most pertinent inputs (Bensetiti et al., 1997).

Out of the number of dimensionless groups derived, we used ANN regression to establish

the best set of chosen dimensionless groups, which describes overall gas holdup

(Bensetiti et al., 1997, Larachi et al., 1998). The following criteria guide the choice of the

set of input dimensionless groups:

- The dimensionless groups should be as few as possible,

- Each group should be highly cross-correlated to the output parameter,

- These input groups should be weakly cross-correlated to each other,

251

- The selected input set should give the best output prediction, which is checked by

using statistical analysis [e.g., average absolute relative error (AARE), standard

deviation, cross-correlation coefficient].

- There should be minimum complexity in neural network architecture, i.e., a

minimum number of hidden layers J.

While choosing the most expressive dimensionless groups, there is a compromise

between the number of dimensionless groups and prediction. The main concern with the

number of dimensionless groups is due to two reasons: first, there should be fewer

expressive groups than raw parameters, and second for feasible scale-up we may need a

minimum number of dimensionless groups.

The cross-correlation analysis which signifies the strength of the linear relation between

input and output is then used to find the dependence between input and output groups. A

number of inputs can be highly cross-correlated to output, but there should not be any

dependency between these groups; otherwise, it just adds to the complexity of the

structure rather than contributing significantly to improve the quality of the network. One

should be careful here: although the cross-correlation analysis reveals the dependence

between inputs and outputs, it also hides non-monotonic relationships. This can result

into losing an important dimensionless group. Therefore in this study, several sets of

input groups were made and tested via rigorous trial-and-error on the Artificial Neural

Network. The above mentioned criteria were then used to identify the most pertinent set

of input groups.

The statistical analysis of prediction is based on the following criteria:

The average absolute relative error (AARE) should be minimum.

∑−

=N

erimental

erimentalpredicted

yyy

NAARE

1 exp

exp1

The standard deviation should be minimum.

252

∑= −

−−

=N

i

ierimental

ierimentalipredictedl

N

AAREy

yy

1

2

)(exp

)(exp)(

1

)(

σ

The cross-correlation coefficient, R between input and output should be around

unity

∑∑

∑

==

=

−−

−−=

N

imeanpredictedipredicted

N

imeanerimentalierimental

meanpredictedipredicted

N

imeanerimentalierimental

yyyy

yyyyR

1

2)()(

1

2)(exp)(exp

)()(1

)(exp)(exp

)()(

))((

Neural networks often encounter the well known ‘overfitting’ problem, which can make

use of the ANN unreliable. To avoid ‘overfitting’ and make the ANN more useful, the

following approach was used. The whole database was split into two parts, learning and

generalization. The first part, called the ‘learning file’, was used to perform minimization

using the ANN. The remaining part, called the ‘generalization file’, was used to validate

the model. Following the common practice, the learning file was made by randomly

selecting about 70% of the database to train the network. The remaining 30% of data was

then used to check the generalization capability of the model. The hidden layers, J, and

fitting parameters wij and wjk are a priori unknown. The number of hidden layers was

varied and chosen empirically according to the above criteria. The weighting parameters

were then determined by non-linear least-square regression over known random

inputs/outputs (70% of the data, which was picked randomly). The remaining 30% of the

database was utilized for validation of predicted weighting parameters. The chosen set of

inputs must show the best prediction during training and generalization, i.e., show the

least error on both learning and generalization files.

F-2.4 Results

After collecting the large databank, we subjected it to dimensional analysis, which

resulted into hundreds of dimensionless groups. As a matter of fact, using all these groups

253

is not feasible. Hence, to make the use of the developed model feasible, after forming a

number of sets of dimensionless groups, cross-correlation analysis was performed. As the

cross-correlation analysis can hide non-monotonic relationships, rigorous trial-and-error

testing with the aid of ANN was also performed. The criteria mentioned above led to four

pertinent input dimensionless groups: Reg, Frg, Eo/Mo, and Lg ρρ / . The ratio of the

densities of the gas and liquid was added to account for the effect of high pressure. This

particular set of dimensionless groups showed consistent performance on both the

learning and generalization file. The sets of dimensionless groups which did not show

consistent performance were omitted, despite their remarkable performance on the

learning file.

Figure F-2 shows the parity plot of the experimental and predicted overall gas holdup

using the ANN correlation on the whole database. The ANN predicts the overall gas

holdup with an AARE of 15%. For comparison, Figure F-3 is the parity plot of the

experimental and predicted overall gas holdup, based on the whole database and using

selected literature correlations along with the ANN correlation. In this case, the

correlations were selected based on the conclusions of Kemoun et al., (2001). From the

figure, it is clear that the ANN correlation predicts overall gas holdup better than these

two correlations. Moreover, the comparison of additional important correlations in

literature on the basis of statistical analysis is shown in Table F-3, and confirms that the

ANN performs better than they do.

254

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Experimental gasholdup

Pre

dict

ed g

asho

ldu

Figure F-2: Parity plot for ANN correlation using the whole databank (AARE = 15 %)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.2 0.4 0.6

Experimental gasholdup

Pre

dict

ed g

asho

ldu

Luo et al. (1999)

Hammer et al. (1984)

ANN (current w ork)

Figure F-3: Parity plot for ANN and selected literature correlations

256

ε )

Table F-2: Set of equations and fitting parameters for the neural network correlation (I = 4, J = 10)

Overall Gas holdup ( G

4

222

/L

LLOO

dME

μσρ

=L

gLgg

duμ

ρρ )(Re

−=

gdu

Fr gg

2

=L

gRD

ρρ

=

8.35E-5 – 2.40E-2 ρg/ ρL

2.3E-7 – 7.35E-1 Frg

5.7 – 7.1E5 Reg

7.5E5 – 1.14E16 EO/MO

Range Dimensional Group 64.2

)002.0/log(1

GS ε=

2.10)797.1/)/log((

1EME

U oo=

1.5)71.5/log(Re

3gU =

5.6)73.2/)log(

2

−=

EFrU g

Wij 1 2 3 4 5 6 7 8 9 10 111 3.44E+01 -9.81E+00 -5.78E+01 1.36E+02 +00 -2.64E+01 6.07E+01 1.74E-012 -3.18E+01 -4.26E+01 -3.35E+01 -1.03E+02 +00 6.71E+01 5.32E+01 -8.98E-023 2.25E+01 -3.18E+01 2.56E+01 7.55E+01 3.54E+01 4.58E+01 9.27E-01 -1.19E+02 -3.81E+01 1.79E+004 -1.37E+01 -6.86E+00 -4.88E+01 -8.64E+01 1.52E+01 3.23E+01 -9.38E-01 1.03E+02 5.00E+01 2.08E+005 5.01E+00 -1.65E+01 6.48E+01 -1.33E+01 1.46E+01 -2.07E+01 1.82E+00 -1.62E+00 -7.11E+01 -4.72E+00

Wjk 1 2 3 4 5 6 7 8 9 10 111 1.37E+01 -1.05E+00 3.35E+00 2.49E-01 -2.89E+01 -2.40E+00 1.32E+01 1.99E-01 3.19E+00 1.44E+01 1.56E+00

1.46E+01 -4.25E+01 -2.00E1.77E+01 8.36E+01 3.57E

64.2)002.0/log(

]exp[1

11

1

1G

J

jjjk Hw

Sε

=−+

=

∑+

=

46.2)53.8/)/log((

4

−=

EU Lg ρρ

∑−= +

=

1

1]

1I

iiijUw

H+ exp[1

j

257

Table F-3: Comparison of ANN and previous literature correlations Correlation AARE

(%) Standard Deviation (%)

Akita and Yoshida (1973) 27 32 Hikita et al. (1981) 25 20 Hammer et al. (1984) 37 26 Idogawa et al. (1985) 24 24 Reilly et al. (1986) 28 47 Dharwadkar et al. (1987) 47 45 Idogawa et al. (1987) 54 10 Wilkinson et al. (1992) 25 20 Krishna et al. (1996) 29 23 Kojima et al. (1997) 48 49 Joshi et al. (1998) 30 24 Luo et al. (1999) 25 25 Jordan et al. (2001) 24 19 ANN (This Work) 15 14

The developed ANN correlation showed an improved prediction of overall gas holdup

over the wide range of database. However, to evaluate the consistency of the developed

correlation, the predictions of ANN correlation in different liquids, at different pressures,

in different column diameters were checked and found to be satisfactory. In addition, the

trends of the effect of various operating and design parameters were checked. It was

observed that, the developed correlation captures the trend reported in the literature. The

details of this part can be found in Shaikh and Al-Dahhan (2003).

F-3 ANN correlations for gas holdup and liquid axial velocity radial profile The correlations were developed for prediction of gas holdup and liquid axial velocity

radial profiles using ANN as described above. The database for gas holdup radial profile

consists of 110 data points while for liquid axial velocity profile consists of 55 data

points.

258

F-3.1 Gas holdup radial profile

As discussed in Chapter 6, the radial profile of gas holdup is an important hydrodynamic

parameter. The similarity of gas holdup profile is pertinent for hydrodynamic similarity

criteria. In absence of reliable first principle models, we have resorted to ANN

correlation for prediction of gas holdup radial profile.

The number of empirical forms has been proposed over the years to fit the experimental

gas holdup radial profile. Nassos and Bankoff (1967) were the first one suggest following

empirical form,

])/(1)[2(~

nGG Rr

nn

−+

= εε (F-5a)

where, Gε~ is the radial chordal averaged gas holdup, the exponent n is steepness

parameter, and r/R is dimensionless radius. As mentioned in Chapter 2 and Chapter 5, the

value of n is large for flat profiles while it is small for steep profiles.

Ueyama and Miyauchi (1979) modified the above equation to accommodate the

possibility of finite gas holdup at the wall. They presented the following empirical form,

])/(1)[2(~

nGG Rrc

nn

−+

= εε ` (F-5b)

where, c is the wall holdup parameter. If c = 1, wall hold up is zero while c = 0 for

constant holdup with changing r/R.

Later, Luo and Svendsen (1991) was modified this form as,

])/(1)[22

2( nGG Rrc

cnn

−−++

= εε (F-5c)

where, is the cross-sectional averaged gas holdup. _

Gε

It is clear from above empirical forms that steepness parameter, n and wall holdup

parameter, c are necessary to predict radial profile of gas holdup. Hence, it was decided

259

to correlate these parameters with operating and design conditions. The procedure to

develop overall gas holdup correlation was also employed in this case. The operating and

design conditions were represented in terms of dimensionless numbers as per the force

analysis described in F-2.2. Table F-4 provides the range of operating and design

parameters in the collected data bank. One should note here that, gas holdup radial

profiles in air-water system constituted close to 60 % of databank. In addition, the data

was collected using different experimental techniques ranging from optical probe to

various tomographic techniques. Amongst this databank, few experimental datasets were

not used for training and validation of neural network. These datasets were utilized to

compare the predictions the developed ANN correlation.

Table F-4: Range of operating and design parameters in the collected databank for gas holdup radial profile

Column Diameter 0.05 – 0.8 m Liquid Density 866 - 1000 kg.m-3

Liquid Viscosity 0.88 - 1 cP Surface Tension 17 - 72 mN.m-1

Gas Density 1.2 - 24 kg.m-3

Superficial Gas Velocity 0.01 – 0.6 m/s Superficial Liquid Velocity 0 (batch liquid)

Number of data points: 550

After rigorous trial-and-error, dimensional analysis, and cross-correlation analysis, n and

c were correlated in terms of the following dimensionless numbers that were found to

have profound effect on these parameters,

)}/(,Re,,{ GGFrMofn ρρ= (F-6)

{ ,Re,( / )G Gc f Mo }ρ ρ= (F-7)

The table of normalized inputs and weighting parameters is provided in Table F-5a and b.

260

Table F-5a: Set of equations for ANN correlation of steepness parameter, n

2

log( / 3.5 5)3.81

gFr EU

−=1

lo g (R e / 2 5 0 )2 .6 5

gU =3

log( / 0.001)1.14

RDU =

4log( / 2 11)

7.47oM EU −

=

1 1

1

1 log( /1.2)1.241 exp[ ]

J

jk jj

nSw H

+

=

= =+ −∑∑−+

= +

=

1

1]exp[1

1I

iiij

jUw

H

Steepness parameter (n) Table F-5b: Set of equations for ANN correlation of wall holdup parameter, c

2

log( / 3.5 5)3.81

gFr EU

−=1

lo g (R e / 2 5 0 )2 .6 5

gU =3

log( / 0.001)1.14

RDU =

5log( / 250)

2.54oEU =

4log( / 2 11)

7.47oM EU −

=

1 1

1

1 log( / 0.005)2.31 exp[ ]

J

jk jj

cSw H

+

=

= =+ −∑∑−+

= +

=

1

1]exp[1

1I

iiij

jUw

H

Wall holdup parameter (c) The parity plot for n and c with the final ANN model is shown in Figures F-4a and b,

respectively. In case of steepness parameter, n, AARE, standard deviation, and cross-

correlation coefficient (between experimental and predicted output) were 9.5 %, 12.5 %,

and 0.98, respectively. In the case of wall holdup parameter, c, AARE, standard

261

deviation, and cross-correlation coefficient were 12.5 %, 13 %, and 0.85, respectively.

The trends of the effect of operating and design parameters on gas holdup radial profile

predicted using ANN correlation were found to be consistent with the literature findings.

0

5

10

15

20

0 5 10 15 20

Experimental 'n'

Pre

dict

ed 'n

'

(a)

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

Experimental 'c'

Pre

dict

ed 'c

'

(b)

Figure F-4: Parity plot of a) steepness parameter, n and b) wall holdup parameter, c.

262

F-3.2 Axial velocity radial profile

This part deals with the development of a correlation to predict liquid axial velocity

profile. We have adopted the procedure similar to the one utilized in above mentioned

correlations. In literature, various empirical forms have been proposed to fit observed

axial velocity profile. However, the following empirical form proposed by Kawase and

Moo-Young (1986) and Tobajas and Garcia-Calvo (1996) is commonly used in the

literature.

])/(21[ 2/0

NNLL RrVV −= (F-8)

where, N is parameter that defines the strength of the circulation.

Kawase and Moo-Young (1986) proposed to use the value of N to be 2 while Tobajas and

Garcia-Calvo (1996) proposed it to be 2.3. We have shown in Chapter 6 that, the

magnitude of gas holdup and its radial profile are responsible for liquid recirculation in

bubble columns. Hence, we have decided to relate the axial velocity profile with gas

holdup radial profile. For this purpose, the value of exponent N was correlated as

),( cnfN = (F-9)

Table F-6 shows the range of operating and design parameters in the databank collected

for liquid axial velocity profile. The collected database was fitted to the above mentioned

empirical form to obtain the values of N. The values of n and c were calculated using the

correlations developed in F-3.1. ANN was used to correlate the values of n and c as

inputs with the corresponding values of N as output. The table of normalized inputs and

weighting parameters is provided in Table F-7.

263

Table F-6: Range of operating and design parameters in the collected databank for liquid

axial velocity profile

Column Diameter 0.1 – 0.6 m Liquid Density 724 - 1000 kg.m-3

Liquid Viscosity 1 - 30 cP Surface Tension 24 - 72 mN.m-1

Gas Density 1.2 - 12 kg.m-3

Superficial Gas Velocity 0.006 – 0.45 m/s Superficial Liquid Velocity 0 (batch liquid)

Number of data points: 250

Table F-7: Set of equations and fitting parameters for ANN correlation of circulation strength, N

1log( /1.2)

1.24nU =

2log( / 0.005)

2.3cU =

1 1

1

1 log( / 0.02)21 exp[ ]

J

jk jj

NSw H

+

=

= =+ −∑∑−+

= +

=

1

1]exp[1

1I

iiij

jUw

H

Recirculation strength parameter (N)

Figure F-5 shows the parity plot of the exponent, N using the final ANN model. AARE,

standard deviation, and cross-correlation coefficient (between experimental and predicted

output) were found to be 9 % %, 7 %, and 0.92, respectively. The trends of the effect of

operating and design parameters on liquid axial velocity profile predicted using ANN

correlation were found to be consistent with the literature findings.

264

0

1

2

3

0 1 2 3

Experimental 'N'

Pre

dict

ed 'N

'

Figure F-5: Parity plot of exponent of velocity profile, N.

F-3.3 Center-line axial velocity

The prediction of center-line velocity is crucial in design and scaleup of bubble column

reactors as it determines the magnitude of liquid axial velocity profile. Hence, the

database collected for liquid axial velocity profile was utilized to develop a correlation

for center-line velocity. First, we have evaluated the reported center-line velocity

correlations with collected experimental center-line velocities. Table F-8 shows the

reported correlations along with the authors. Figure F-6 compares the predictions of these

correlations with experimental data while Table F-9 shows the statistical analysis of these

correlations. It is clear that, none of the reported correlations predict center-line velocity

with statistical confidence. Hence, a correlation was developed for center-line velocity

with the using ANN. Based on the ANN, dimensional analysis, and cross-correlation

analysis, the center-line axial velocity was correlated in terms of the following

dimensionless numbers,

)}/(,Re,,,{)0( GGL FrMoEofV ρρ= (7-10)

The table of structure of model and weighting parameters is provided in Table F-10.

265

Table F-8: Literature correlations for center-line velocity

Author Center-line velocity correlation Ohki and Inoue (1970)

6.09.1 GU

Riquarts (1981)

8/1)(21.0g

UgD

L

LG

μρ

Zehner (1982) 3/1)(73.0 DUg G

Nottenkamper (1983)

GL UDU 11.166.0 69.0 ++ Ulbrecht et al.

(1985) 08.015.046.023.0 )/(34.3 LLG DUg ρμ

0

0.5

1

1.5

2

2.5

0 0.2 0.4 0.6 0.8 1

Experimental center-line velocity (m/s)

Pre

dict

ed c

ente

r-lin

e ve

loci

ty (m

/s)

Ohki and Inoue (1970)Riquarts (1982)Zehner (1983)Nottenkamper (1983)Ulbrecht et al. (1985)Experimental

Figure F-6: Parity plot for literature correlations using the whole database.

266

velocity (VL0)

Table F-9: Comparison of prediction of literature correlations with the

experimental databank.

Author AARE

(%)

Standard Deviation

(%)

Cross-correlation coefficient

Ohki and Inoue (1970)

49

45 0.48

Riquarts (1981) 27 25 0.82 Zehner (1982) 19 20 0.89 Nottenkamper (1983)

22 10 0.71

Ulbrecht et al. (1985)

43 30 0.65

This work 11 10 0.96

Table F-10: Set of equations for ANN correlation of center-line axial velocity, VL0

2

log( /1 5)4.36

gFr EU

−=1

lo g (R e / 2 5 0 )5 .4 8

gU =3

log( / 0.001)1.22

RDU =

Center-line

4log( / 2 11)

7.47oM E −

=U

∑−+= +

=

1

1]exp[1

1I

iiij

jUw

H0

1 1

1

log( / 0.02)121 exp[ ]

LJ

jk jj

VSw H

+

=

= =+ −∑

5log( /1000)

3.65oEU =

267

Figure F-7 shows the parity plot of center-line liquid velocity using the developed ANN

correlation. AARE, standard deviation, and cross-correlation coefficient was found to be

11 %, 10 %, 0.96, respectively. The trends of the effect of operating and design

parameters on center-line liquid velocity predicted using ANN correlation was found to

be consistent with the literature findings.

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

Experimental center-line velocity (m/s)

Pre

dict

ed c

ente

r-lin

e ve

loci

ty (m

/s)

Figure F-7: Parity plot for ANN correlation using whole database.

F-4 Remarks

This chapter deals with the development of ANN based correlations for ‘a priori’

prediction of needed hydrodynamic parameters. As an example, the correlation to predict

overall gas holdup is demonstrated. The correlation is developed by collecting

experimental results from open literature (3500 measurements) with the aid of Artificial

Neural Network and Dimensional Analysis. Neural Network correlation shows noticeable

improvement in the prediction of overall gas holdup compared to selected literature

correlations. The neural network correlation yields AARE of 15 % with standard

deviation of 14 %, which is better than those obtained for the selected literature

correlations. This work identified Re Lg ρρ /g, Fr Eo/Mo,g, as expressive dimensional

groups to overall gas holdup. Also, there is improved prediction for variety of liquids,

wide range of operating pressures and column diameters, which can be useful in the

268

scale-up of bubble column reactors. The simulations have been performed using

developed ANN correlation and found to give the trends reported in literature.

The ANN correlations were developed for additional hydrodynamic parameters such as

radial profile gas holdup and liquid axial velocity and center-line liquid velocity. The

developed correlations were found to be statistically consistent with the databank.

However, it is worth mentioning that databank available for radial profile gas holdup and

liquid axial velocity and center-line liquid velocity is limited and mostly comprises the

databank in air-water system. Hence, the performance of these developed correlations

outside its range cannot be guaranteed. However, in absence of reliable predictions of

models based on first principles, it presents a preliminary predictive platform that may

provide an initial guideline towards scaleup and design of these reactors.

269

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Vita Date of Birth July 5, 1975 Place of Birth Mangalvedha (Maharashtra), India Degrees

Bachelor of Technology in Petrochemical Engineering, 1992- 1996 Dr. B. A. Technological University, Lonere (MS), India Master of Technology in Chemical Engineering, 1998- 2000 Indian Institute of Technology (IIT), Madras, India Doctor of Science in Chemical Engineering, 2001-2007 Washington University, St. Louis, MO Industrial Experience Summer Intern at Amar Dyechem Ltd., Mahad, India, (1993) Summer Intern at Vinati Organics Ltd., Mahad, India, (1994) Summer Intern at Hikal Chemicals Ltd., Mahad, India (1995)

Process Engineer, Kesar PetroProducts Ltd. Lote Parashuram, India, (1996-1998)

Professional Societies American Institute of Chemical Engineering (AIChE)

International Association for Energy Economics (IAEE) Publications Shaikh A. and Al-Dahhan, M. H.; A New Methodology for Online Flow Regime Monitoring in Bubble Column Reactors to be submitted. Shaikh, A.; and Al-Dahhan, M. H., A New Methodology for Scaleup of Bubble Column Reactors to be submitted. Shaikh, A.; and Al-Dahhan, M. H.; Scaleup of Bubble Column Reactors: A Review of Current-State-of-the-Art, submitted.

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Nedeltechev, S.; Shaikh, A.; and Al-Dahhan, M. H.; (2007). Prediction of the Kolmogorov Entropy Derived from CT Data in an Atmospheric Bubble Column Operated in Transition Regime accepted Chemical Engineering and Technology. Shaikh, A.; and Al-Dahhan, M. H.; (2007). A Review on Flow Regime Transition in Bubble Columns, accepted International Journal of Chemical Reactor Engineering Nedeltechev, S.; Shaikh, A.; and Al-Dahhan, M. H.; (2006). Identification of Flow Regimes in a Bubble Column Based on Chaos Analysis of γ-ray Computed Tomography Data. Chemical Engineering and Technology, 29 (9), 1 (Special Issue dedicated to 65th Anniversary of Prof. W. D. Deckwer). Rados, N.; Shaikh, A.; and Al-Dahhan, M. H.; (2005). Solids Flow Visualization in High Pressure Slurry Bubble Column, Chem. Eng. Sci., 60 (22), 6067 (Special Issue on Gas-Liquid and Gas-Liquid-Solid Reactor Engineering). Shaikh, A.; and Al-Dahhan, M. H.; (2005). Characterization of Hydrodynamic Flow Regime in Bubble Columns via Computed Tomography, Flow Measurement and Instrumentation, 16(2-3), 91 (Special Issue on Tomographic Techniques for Multiphase Flow Measurements). Rados, N.; Shaikh, A.; Al-Dahhan, M. H.; (2004). Phase Distribution in a High Pressure Slurry Bubble Column via Single Source Computed Tomography, Can. J. Chem. Eng., 83 (1), 104 (Special Issue on Industrial Process Tomography). Shaikh, A.: and Al-Dahhan, M. H.; (2003). Development of an Artificial Neural Network Correlation for Prediction of Overall Gas Holdup in Bubble Column Reactors, Chem. Eng. Proc., 42, 599 (Special Issue on Application of Neural Networks to Multiphase Reactors). Presentations Shaikh A. and Al-Dahhan, M. H.; (2007). A New Methodology for Online Flow Regime Monitoring in Bubble Column Reactors. accepted Oral Presentation 5th world Congress on Industrial Tomography, Bergen, Norway. Al-Dahhan, M. H. and Shaikh A.; (2006). Advances in Reactor Technology for Fischer-Tropsch Synthesis with Biomass as a Feedstock: A New Methodology for Scale-up of Bubble Column Reactors. Plenary Lecture at BTLtec06, Munich, Germany. Shaikh A. and Al-Dahhan, M. H.; (2005). A New Methodology for Scale-up of Bubble Column Reactors. North American Mixing Forum, AIChE Annual Meeting, Cincinati, OH, USA.

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Shaikh A. and Al-Dahhan, M. H.; (2005). A New Methodology for Scale-up of Bubble Column Reactors. Plenary Talk at 5th International Chemical Engineering Conference, Amman, Jordan. Shaikh, A.and Al-Dahhan, M. H.; (2004). Characterization of Hydrodynamic Flow Regime in Bubble Columns via Computed Tomography, Oral Presentation, North American Mixing Forum, AIChE Annual Meeting, Austin, USA. Rados, N.; Shaikh, A.; Al-Dahhan, M. H.; (2003). Phase Distribution in a High Pressure Slurry Bubble Column via Single Source Computed Tomography, Keynote Presentation at 3rd world Congress on Industrial Tomography, Banff, Canada. Rados, N.; Kemoun, A.; Shaikh, A.; Al-Dahhan, M. H.; Dudukovic, M. P.; (2002). Implementation of Radioactive Particle Tracking and Tomography in Flow Visualization of High Pressure Slurry Bubble Column Reactors, Oral Presentation, 4th Symposium on High Pressure Technology and Chemical Engineering, Venice, Italy. Shaikh, A.; Al-Dahhan, M. H.; (2001). Development of Neural Network based Correlation for Overall Gas Holdup in Bubble Column, Poster Presentation, AIChE Annual Meeting, Reno, USA. August 2007.

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