Gas holdup in two phase bubble columns at industrial processing conditions – effect of

operating parameters, liquid properties and column scale

Dissertation

zur

Erlangung des Grades

Doktor-Ingenieur

der

Fakultät für Maschinenbau

der Ruhr-Universität Bochum

von

Philipp Rollbusch

Aus Magdeburg

Bochum 2016

Dissertation eingereicht am : 19.10.2015

Tag der mündlichen Prüfung : 22.01.2016

Erster Referent : Prof. Dr.-Ing. Marcus Grünewald

Zweiter Referent : Prof. Dr.-Ing. Michael Schlüter

IV

Acknowledgements

I would like to express my gratitude to Prof. Dr.-Ing. Marcus Grünewald for supervising this

dissertation and thus enabling me to work on this project.

I also want to thank Prof. Dr.-Ing. Michael Schlüter who readily agreed to be the second

surveyor of this thesis.

Very special thanks to Dr.-Ing. Marc Becker who, besides of his other tasks, always found time

to discuss organizational and subject specific matters and for assigning me responsibilities

beyond scientific topics.

Furthermore I would like to thank the laboratory staff of the Process Technology & Engineering

department of Evonik Industries AG for helping me with technical issues and giving me advices

where needed.

I wish to acknowledge Dr. Martin Tuinier who was of great help during the first year of my work

at Evonik Industries AG. I would also like to thank Martina Ludwig, who took over after Martin

Tuinier, for her help during the design phase of the pressurized column.

Additionally I would like to recognize Linda Schlusemann and Nils Abel, my co-workers at the

Ruhr-University Bochum.

Above all I want to express my greatest gratitude to my parents for their support in educational

matters. Special acknowledgements to my brother Carsten for the ongoing political

discussions.

At last I wish to thank all of the interns who assisted me with the experimental work and the

construction of our facilities. Without them there would not be a single measurement. A special

gratitude is expressed to Christian Meyer and Christian Tomala.

V

Abstract

In this thesis the effects of various influencing parameters on gas holdup in two phase bubble

columns are examined on various scales. The effect of gas density due to elevated pressure,

liquid properties, liquid velocity, temperature, column diameter and height to diameter ratio

were experimentally analyzed and compared to literature data. For this purpose three bubble

columns were setup. Two of them were glass columns of 0.16 and 0.30 m diameter. Another

steel column of 0.33 m diameter was capable of operation at elevated pressures of up to 3.6

MPa. Deionized water, aqueous alcohol solutions, acetone and cumene were employed as the

liquid phase while nitrogen served as the gas phase. All columns operated at concurrent flow

of both phases.

An extensive literature survey was conducted to gather available information about

hydrodynamic parameters, which are gas holdup, liquid backmixing and heat and mass

transfer, at elevated pressures. It is pointed out that statements are contradictory and nearly

no reliable data is available.

An axial dispersion model to simulate the effect of uncertainties in hydrodynamic parameter

estimation on reactor performance was built. The autooxidation of cyclohexane was chosen

as a model reaction. With the help of this model it is shown that the exact estimation of gas

holdup is crucial for the correct prediction of reactor performance.

The experimental results show that literature data is barely comparable to the measurements

obtained in this study. An effect of increasing column diameter, liquid properties and gas

density on gas holdup was observed while temperature and superficial liquid velocity do not

seem to influence gas holdup at the parameter range studied. Additionally it is shown that gas

holdup slightly increases with column height.

A correlation which is not based on empirical fitting factors was identified and modified to

predict the experimental gas holdups of this study within reasonable accuracy.

VI

Kurzreferat

Die vorliegende Arbeit beschäftigt sich mit dem Einfluss diverser Parameter auf den Gasgehalt

in zweiphasigen Blasensäulen verschiedener Größenordnungen. Der Einfluss der Gasdichte

durch erhöhten Betriebsdruck, der Stoffeigenschaften, der Leerrohr-geschwindigkeit der

flüssigen Phase, der Betriebstemperatur, des Säulendurchmessers und des Durchmesser zu

Höhe Verhältnisses wurde experimentell untersucht und mit Literaturdaten abgeglichen. Zu

diesem Zweck wurden drei Versuchsanlagen aufgebaut, zwei Glassäulen mit jeweils 0.16 und

0.3 m Durchmesser und eine Stahlsäule mit 0.33 m Durchmesser. Letztere war für

Experimente unter erhöhtem Betriebsdruck bis 3.6 MPa geeignet. Als flüssige Phase wurden

entionisiertes Wasser, wässrige Alkohollösungen, Aceton und Cumol eingesetzt, während

Stickstoff als Gasphase Verwendung fand.

Eine ausgiebige Literaturstudie zu vorhandenen Studien zur Ermittlung hydrodynamischer

Parameter wie Gasgehalt, Rückvermischung der flüssigen Phase und des Wärme- und

Stofftransports unter erhöhtem Betriebsdruck wurde durchgeführt. Es existieren nahezu keine

verlässlichen Informationen bezüglich dieser Parameter und die experimentellen Ergebnisse

sind oft widersprüchlich.

Ein axiales Dispersionsmodell zur Abschätzung des Einflusses von Unsicherheiten bei der

Parameterbestimmung wurde unter Verwendung der Autooxidation von Cyclohexan als

Modellreaktion aufgestellt. Mit Hilfe dieses Modells konnte gezeigt werden, dass der genauen

Bestimmung des Gasgehalts bei der Reaktorauslegung besondere Bedeutung zukommt.

Die experimentellen Ergebnisse zeigen einen Einfluss des Säulendurchmessers und des Höhe

zu Durchmesser Verhältnisses, der Stoffeigenschaften und der Gasdichte auf den Gasgehalt.

Eine Korrelation zur Bestimmung des Gasgehalts, die nicht auf empirisch angepassten

Parametern basiert, wurde identifiziert und modifiziert um die Versuchsergebnisse mit

hinreichender Genauigkeit wiederzugeben.

VII

Table of contents

Acknowledgements .............................................................................................................. IV 

Abstract .................................................................................................................................. V 

Kurzreferat ............................................................................................................................ VI 

Table of contents ................................................................................................................. VII 

List of figures ......................................................................................................................... X 

List of tables ....................................................................................................................... XIV 

1  Introduction .................................................................................................................. 1 

1.1  Integration in Project “Multi-Phase“ ................................................................... 2 

1.2  Objectives ......................................................................................................... 4 

1.3  Thesis structure ................................................................................................. 5 

1.4  References ........................................................................................................ 6 

2  Literature survey ......................................................................................................... 7 

2.1  Introduction ....................................................................................................... 7 

2.2  Industrial applications of bubble columns ....................................................... 11 

2.3  Single bubble behavior .................................................................................... 13 

2.3.1  Correlations validated under elevated pressure .............................................. 15 

2.3.2  Comparison of correlations and experimental data under elevated pressure . 19 

2.4  Gas holdup at higher pressures ...................................................................... 24 

2.4.1  Studies involving two phases .......................................................................... 26 

2.4.2  Studies involving a third phase ....................................................................... 39 

2.5  Liquid backmixing ............................................................................................ 41 

2.6  Mass transfer studies ...................................................................................... 48 

2.7  Heat transfer ................................................................................................... 52 

2.8  Conclusions ..................................................................................................... 56 

2.9  Notation ........................................................................................................... 59 

VIII

2.10  References ...................................................................................................... 60 

3  Sensitivity of a complex reaction to hydrodynamic parameters .......................... 68 

3.1  Introduction ..................................................................................................... 68 

3.2  Cyclohexane oxidation .................................................................................... 70 

3.2.1  General information ......................................................................................... 70 

3.2.2  Reaction network ............................................................................................ 70 

3.3  Model development ......................................................................................... 73 

3.3.1  Balance equations ........................................................................................... 75 

3.3.2  Parameter estimation ...................................................................................... 76 

3.3.3  Reaction rate constants and physical properties ............................................ 78 

3.4  Results ............................................................................................................ 79 

3.4.1  Hydrodynamic parameter estimation .............................................................. 80 

3.4.2  Effect on selectivity and yield .......................................................................... 82 

3.4.3  Possible economic consequences .................................................................. 85 

3.5  Conclusions ..................................................................................................... 87 

3.6  Notation ........................................................................................................... 88 

3.7  References ...................................................................................................... 89 

4  Experimental investigation of gas holdup .............................................................. 92 

4.1  Introduction ..................................................................................................... 92 

4.2  Experimental facilities and procedures ........................................................... 94 

4.2.1  Experimental facilities ..................................................................................... 94 

4.2.2  Procedures and data evaluation ................................................................... 102 

4.3  Results .......................................................................................................... 104 

4.3.1  Influence of liquid properties ......................................................................... 104 

4.3.2  Influence of scale and liquid velocity ............................................................. 114 

4.3.3  Influence of temperature ............................................................................... 123 

4.3.4  Influence of pressure ..................................................................................... 125 

4.3.5  Axial evolution and radial distribution of gas holdup ..................................... 130 

4.3.6  Prediction of gas holdups .............................................................................. 136 

IX

4.4  Conclusions ................................................................................................... 145 

4.5  Notation ......................................................................................................... 147 

4.6  References .................................................................................................... 148 

5  Summary .................................................................................................................. 152 

5.1  Conclusions ................................................................................................... 153 

5.2  Recommendations ........................................................................................ 155 

X

List of figures

Figure 1.1 Structure of project „Multi-phase“ ............................................................................ 3 

Figure 2.1 left: examples of bubble column designs A) empty, B) cascaded, C) packed, D)

multishaft, E) equipped with static mixers, right: examples of gas spargers A) simple tube, B)

perforated plate, C) perforated ring, D) porous plate, figure taken from [11] ........................... 8 

Figure 2.2 The most common flow regimes encountered in bubble columns [29] ................... 9 

Figure 2.3 Scheme of a distorted oblate spheroid .................................................................. 18 

Figure 2.4 Influence of pressure on single bubble velocity in Paratherm NF at 27°C [62] ..... 20 

Figure 2.5 Influence of pressure on single bubble velocity in Paratherm NF at 78°C [62] ..... 21 

Figure 2.6 Comparison of measured and calculated Re of single bubble velocity in Paratherm

NF under variation of pressure and temperature [62]. ........................................................... 23 

Figure 2.7 Effect of higher liquid viscosity compared to higher gas density due to elevated

pressure ................................................................................................................................. 28 

Figure 2.8 Gas holdup as a function of pressure (data from Letzel et al. [85]) ...................... 29 

Figure 2.9 Influence of scale on gas holdup at varying pressures, adapted from Wilkinson et

al. [80] ..................................................................................................................................... 31 

Figure 2.10 Radial gas holdup profiles at different system pressures [89] ............................. 32 

Figure 2.11 Regime transition favored with increasing pressure [93] .................................... 34 

Figure 2.12 : Independence of gas holdup on pressure according to Pohorecki et al. [75] ... 37 

Figure 2.13 Gas holdups measured by Therning and Rasmuson [71] ................................... 38 

Figure 2.14 Measured dispersion coefficients, Wilkinson et al . [118] .................................... 43 

Figure 2.15 Experimentally obtained dispersion coefficients at ug = 0.135 m/s, Therning and

Rasmuson [71] ....................................................................................................................... 44 

Figure 2.16 Effect of pressure and column dimensions on liquid dispersion according to Yang

and Fan [120] ......................................................................................................................... 46 

Figure 2.17 Increase in kla due to pressure (data from Lau et al. [116], d = 0.1016 m) ......... 50 

XI

Figure 2.18 Effect of temperature on kla (data from Lau et al. [116] , d = 0.1016 m, p = 0.1

MPa) ....................................................................................................................................... 51 

Figure 2.19 Increase of heat transfer coefficients with pressure (data from Lin and Fan [91])

............................................................................................................................................... 53 

Figure 2.20 Decrease of heat transfer coefficients with pressure (data from Yang et al. [131])

............................................................................................................................................... 54 

Figure 3.1 Illustration of the reaction scheme, taken from Schäfer [11], RH – cyclohexane,

ROOH – cyclohexyl-hydroperoxide, ROH – cyclohexanol, R’O – cyclohexanone, P – reactive

organic secondary product, P’ – non-reactive organic secondary product, HO2 – hydroperoxide

radical, OH – hydroxyl radical, R – cyclohexyl radical, RO – cyclohexyl-oxo radical, RO2 –

cyclohexyl-peroxy radical ....................................................................................................... 72 

Figure 3.2 predicted gas holdups, correlations of Reilly et al. [23], Idogawa et al. [22] and

Wilkinson et al. [21] ................................................................................................................ 80 

Figure 3.3 Dispersion coefficients calculated with equation (3-19), same correlations as in

Figure 3.2 were used to estimate gas holdups ....................................................................... 81 

Figure 3.4 Mass transfer coefficients estimated with equation (3-20), same correlations as in

Figure 3.2 were used to estimate gas holdups ....................................................................... 82 

Figure 3.5 yield of KA oil depending on gas holdup ............................................................... 83 

Figure 3.6 gas holdup influencing selectivity to KA oil ........................................................... 83 

Figure 3.7 influence of confidence interval of a specific correlation on yield to KA oil ........... 84 

Figure 3.8 influence of confidence interval of a specific correlation on selectivity to KA oil ... 85 

Figure 3.9 resulting difference in produced amount of KA oil ................................................. 86 

Figure 3.10 corresponding monetary uncertainty ................................................................... 86 

Figure 4.1 simplified schematic of 0.16 m diameter glass column ......................................... 96 

Figure 4.2 simplified schematic of 0.3 m diameter glass column ........................................... 97 

Figure 4.3 simplified schematic of 0.33 m diameter stainless steel column ........................... 99 

Figure 4.5 Expected flow regimes in this study .................................................................... 102 

Figure 4.5 Measured gas holdups for N2/H2O, acetone and cumene................................... 105 

XII

Figure 4.6 calculated bubble swarm velocities for H2O, acetone and cumene .................... 106 

Figure 4.7 Photographs of nitrogen bubbles in (a) water, (b) acetone and (c) cumene ....... 107 

Figure 4.8 Clift diagram [17] with values of Table 4-5 (blue: H2O, black: acetone, purple:

cumene) ............................................................................................................................... 108 

Figure 4.9 Estimation of regime transition holdup for N2/H2O, acetone and cumene ........... 109 

Figure 4.10 Overall gas holdups of this study compared with data from Krishna et al. [23],

Letzel et al. [20], Grund et al. [21] and Ohki and Inoue [22] ................................................. 110 

Figure 4.11 Effect of solvent addition to deionized water on gas holdup ............................. 112 

Figure 4.12 Comparison of aqueous acetone solutions with pure acetone .......................... 113 

Figure 4.13 Influence of diameter on gas holdup according to Wilkinson et al. [8] .............. 115 

Figure 4.14 Diameter influence on gas holdup according to Krishna et al. [6] ..................... 116 

Figure 4.15 influence of column diameter on gas holdup ..................................................... 117 

Figure 4.16 Influence of column diameter on nitrogen holdup in acetone ............................ 119 

Figure 4.17 Influence of column diameter on nitrogen holdup in cumene ............................ 120 

Figure 4.18 Variation of superficial liquid velocity, 0.16 m diameter glass column .............. 121 

Figure 4.19 Variation of superficial liquid velocity, 0.30 m diameter glass column .............. 122 

Figure 4.20 Variation of superficial liquid velocity, 0.33 m diameter steel column ............... 122 

Figure 4.21 Influence of temperature on gas holdup ............................................................ 124 

Figure 4.22 Pressure effect on gas holdup, N2/H2O ............................................................. 126 

Figure 4.23 Pressure effect on gas holdup, N2/cumene ....................................................... 127 

Figure 4.24 Comparison of own measurements with industrial plant data published by Weber

[46] ....................................................................................................................................... 128 

Figure 4.25 Gas holdups along the column height, N2/H2O, p = 0.1 MPa ............................ 131 

Figure 4.26 Gas holdups along the column height, N2/H2O, p = 3.6 MPa ............................ 132 

Figure 4.27 Gas holdups along the column height, N2/cumene, p = 0.1 MPa ...................... 133 

Figure 4.28 Gas holdups along the column height, N2/cumene, p = 3.6 MPa ...................... 134 

Figure 4.29 Validation of gas holdups obtained by pressure difference measurements with

wire-mesh sensor and gamma-CT measurements .............................................................. 135 

XIII

Figure 4.30 Gamma-CT measurements in deionized water and cumene compared to pressure

difference measurements ..................................................................................................... 135 

Figure 4.31 Comparison of gas holdup correlations by Akita and Yoshida [38], Hikita et al. [58],

Hughmark [59], Joshi et al. [60], Mersmann [61], Reilly et al. [62], Sharma [63], Wilkinson et

al. [8], Idogawa et al. [49] ..................................................................................................... 137 

Figure 4.32 Prediction of column diameter influence by correlations of Zehner [64] and Akita

and Yoshida [38] .................................................................................................................. 138 

Figure 4.33 Comparison of predicted holdups with measured values .................................. 141 

Figure 4.34 parity plot measured and predicted holdups N2/H2O ......................................... 142 

Figure 4.35 parity plot measured and predicted holdups N2/acetone ................................... 142 

Figure 4.36 parity plot measured and predicted holdups N2/cumene ................................... 143 

Figure 4.37 parity plot for various pressures, measured and predicted holdups N2/H2O ..... 144 

Figure 4.38 parity plot for various pressures, measured and predicted holdups N2/cumene

............................................................................................................................................. 144 

XIV

List of tables

Table 2-1: Correlations for terminal velocity of singles bubble validated under pressure by [62]

............................................................................................................................................... 23 

Table 2-2: Summary of gas holdup studies at elevated pressures ........................................ 24 

Table 2-3: Summary of liquid backmixing studies .................................................................. 42 

Table 2-4: Summary of mass transfer studies at elevated pressures .................................... 48 

Table 2-5: Summary of heat transfer studies at elevated pressures ...................................... 52 

Table 3-1 Modelling approaches according to Deckwer [6] ................................................... 73 

Table 3-2 Correlations for gas holdup estimation ................................................................... 77 

Table 3-3 Reactions and corresponding reaction kinetic constants, taken from Schäfer [11],

notation according to Figure 3.1 ............................................................................................. 79 

Table 4-1 column dimensions and H/D ratio .......................................................................... 94 

Table 4-2 density of nitrogen at various pressures ................................................................ 95 

Table 4-3 liquid properties at different temperatures .............................................................. 95 

Table 4-4 sparger geometries ................................................................................................ 95 

Table 4-5 Eötvös and Morton numbers for N2 bubbles (dB = 0.001…0.01 m, p = 0.1 MPa) 107 

Table 4-6 Experimental setups of publications depicted in Figure 4.10 .............................. 110 

Table 4-7 Experimental conditions of literature studies on diameter influence on gas holdup

............................................................................................................................................. 114 

Table 4-8 relative change of liquid properties with temperature, reference 20 °C ............... 123 

Table 4-9 measured surface tensions of cumene and water at various pressures and 35 °C,

data provided by Eurotechnica GmbH ................................................................................. 129 

Table 4-10 Measured and calculated bubble velocities, pressure as indicated in brackets . 140 

1

1 Introduction

During the last two decades the discussion on energy efficient and environmental friendly

production processes reached new heights in Germany and the whole of Europe as well. It is

demanded by the European Union to lower CO2 emissions by 40 % below the level of 1990

until the year 2030. A reduction by 80 to 95 % until 2050 is stipulated on the longer term [1].

This is of course not only restricted to industrial production. Furthermore public transportation,

construction of buildings, energy efficient electric devices, construction of automotive vehicles

and the generation and distribution of energy in general is questioned.

The production of chemicals is a key factor to succeed on the named examples. Producers of

chemicals are providing solutions for thermal insulations of buildings, lightweight design

materials for automotive and aircraft constructors, additives for exhaust treatment and fuel

quality enhancements, materials for the production of electric and energy storage devices and

many other fields of interest.

In Germany the monetary value of produced chemicals amounted to 114.1 billion Euros in

2012 [2]. The energy consumption of chemical plants already slightly decreases and reached

a value of 654741.8 TJ in 2011. On the other hand the energy costs are steadily increasing to

7.731 billion Euros in 2011. This amasses to 3.8 % of the net production value of chemicals.

Another 34.2 % of production costs are related to resources needed for the production of

chemicals. The CO2 emissions of Germany’s chemical producers reached a value of 44.487

million tons per year. These numbers point out that the chemical industry is on the one hand

necessary to provide solutions for greenhouse gas and energy reduction but on the other hand

one of the biggest producers of greenhouse gases and consumers of energy and resources.

Especially the demand for energy and resource efficient production is of vital importance for

the German and European industries because of increasing energy prices as they are not able

to benefit from shale gas exploration like North American companies do.

To ensure a sustainable production of chemicals in Europe the use improved or even new

reactor concepts is of significant importance. Up to now reactors like stirred tanks are often

2

used within chemical production sites, especially for reactions with multiple phases [3]. Stirred

tanks are well understood and a lot of experience with them exists in engineering departments

and production staff. However they may not be the best choice for the reaction and therefore

might not be the most efficient reactor concept. It is desired to produce chemicals with less

byproducts to minimize energy intensive downstream processing and few resources as

possible. To commence multiphase reactions a number of alternatives like trickle bed, fluidized

bed and bubble column reactors are well known but not so well understood [4]. Often it is not

the reaction itself which hampers implementation or scale-up of such reactors. It is merely the

missing understanding of the hydrodynamics of e.g. bubble column reactors which makes it

difficult to efficiently design this reactor type [5]. Especially for bubble column reactors it is still

not possible to avoid experimentation on laboratory, technical and pilot scale during scale-up

and no validated comprehensive model for the design process exists which predicts the reactor

performance with the needed accuracy [6].

To resolve the limitations in modelling and scaling-up bubble column reactors a multiscale

approach covering aspects of single bubble to bubble swarm phenomena and ultimately the

whole flow field of an industrial scale bubble column reactor is appropriate to improve the

understanding of the hydrodynamics of this reactor class. Moreover the combination of

experimental work and the development of models on these scales is of importance to advance

the reactor design process.

1.1 Integration in Project “Multi-Phase“

This thesis is part of a public funded project called “Low carbon dioxide emitting chemical

processes for future industries: Multiscale Modelling of Multi-Phase Reactors” as described by

Becker et al. [7]. The structure of the whole project is shown in Figure 1.1. It consists of a

network of ten industrial and academic partners. The work packages are divided into three

divisions.

3

Figure 1.1 Structure of project „Multi-phase“ with numbering of work packages and participating universities and companies

One division (work package 1) is responsible for the development of measurement techniques

which are suited for the task of examining multiphase reactor hydrodynamics at pilot scale and

processing conditions, which means high pressure and temperature under presence of organic

solvents. An endoscopic measurement technique was developed by Intelligent Laser

Applications GmbH to measure single bubble phenomena. A wire mesh sensor [8] and a

gamma computer tomographic device [9] was provided by the Helmholtz-Center Dresden

Rossendorf (HZDR) for the measurement of radial gas holdup profiles. Other techniques to be

developed include an attenuated total refection probe to observe the course of a reaction [10],

gas concentration sensors and devices capable of measuring liquid properties at severe

operating conditions.

Another division (work packages 2, 3 and 7) is focused on generating experimental results with

respect to single bubble sizes and velocities, axial and radial gas holdup profiles and the

characterization of liquid backmixing at various scales ranging from laboratory apparatuses to

technical and pilot scale plants. Other parameters of interest are mass transfer coefficients and

4

liquid velocity profiles. In addition it is necessary to test the developed measurement

techniques at pilot scale and processing conditions which is part of sub-package 7.

The third division (work packages 4, 5 and 6) is using the experimental data for the validation

and development of models on small and large scale. Within these groups direct numerical

simulations and computational fluid dynamic simulations are used to access hydrodynamic

parameters while short-cut models like dispersion [11] and compartment models [12] are

developed to provide tools for general and early reactor design purposes.

The thesis presented here is part of package 6 and 7 and is associated with experimental work

on technical and pilot scale and modelling activities regarding the development of short-cut

dispersion models.

1.2 Objectives

Despite of decades of research on bubble column hydrodynamics and especially gas holdup

in bubble columns nearly no reliable data exists at pilot scale, industrial relevant operating

conditions or for liquids other than water. This leads to severe uncertainties during the design

process of this reactor type. In addition the proposed design equations have mostly been

proven to be unable to extrapolate beyond the experimental borders from which they are

derived from.

The primary objectives of this thesis are on the one hand the compilation of available data with

respect to hydrodynamic design parameters at industrial relevant processing conditions.

Furthermore the utilization of an axial dispersion model with a model reaction in order to assess

the importance of hydrodynamic parameter estimation for reactor design and performance

prediction. At last several experimental facilities are to be built to measure the parameters of

interest. For this purpose three bubble columns of varying dimensions are setup. Two of them

can be operated at atmospheric pressure with organic liquids and are used to study the effect

of different liquid properties and column scale on gas holdup. The third column will be used to

identify the effect of pressure and temperature on gas holdup and to test the developed

measurement devices. The generated results will then be used by other workgroups to validate

5

modelling approaches and to advance the capability of bubble column simulations with suitable

tools. In addition the measured gas holdups are used to identify reliable correlations for the

prediction of holdups as this is of primary concern for modelling bubble columns with short-cut

approaches.

1.3 Thesis structure

The structure of this thesis is straightforward to provide solutions for the objectives formulated

above. The first chapter sums up and discusses the available publications concerned with gas

holdup, liquid backmixing and heat and mass transfer at elevated pressure in bubble columns.

Based on this literature survey a sensitivity analysis using an axial dispersion model is

presented to emphasize the importance of gas holdup for bubble column design. In the

following chapter the experimental work necessary to contribute to the solution of the problem

of gas holdup estimation is presented. The design of the experimental setups is explained and

the methods of data evaluation are presented. The results are discussed and analyzed with

available literature data. Finally a design equation for gas holdup prediction at various scales

and operating conditions is proposed.

6

1.4 References

[1] European Commission, A 2030 framework for climate and energy policies, 2013, Brussels.

[2] Verband der chemischen Industrie, Chemiewirtschaft in Zahlen 2013, 2013. [3] Stitt, E.H., Alternative multiphase reactors for fine chemicals: A world beyond stirred

tanks? Chemical Engineering Journal, 2002. 90(1-2): p. 47-60. [4] Mills, P.L. and R.V. Chaudhari, Multiphase catalytic reactor engineering and design for

pharmaceuticals and fine chemicals. Catalysis Today, 1997. 37(4): p. 367-404. [5] Deen, N.G., et al., Bubble Columns, in Ullmann's Encyclopedia of Industrial

Chemistry2000, Wiley-VCH Verlag GmbH & Co. KGaA. [6] Jakobsen, H.A., H. Lindborg, and C.A. Dorao, Modeling of Bubble Column Reactors:࣯

Progress and Limitations. Industrial & Engineering Chemistry Research, 2005. 44(14): p. 5107-5151.

[7] Becker, M., et al., BMBF Project ”Multi-Phase”. Chemie Ingenieur Technik, 2013. 85(7): p. 989-991.

[8] Schlusemann, L., G. Zheng, and M. Grünewald, Messung der Phasenverteilung in

Blasensäulen. Chemie Ingenieur Technik, 2013. 85(7): p. 997-1001. [9] Bieberle, A., et al., Gamma-Ray Computed Tomography for Imaging of Multiphase

Flows. Chemie Ingenieur Technik, 2013. 85(7): p. 1002-1011. [10] Lüttjohann, S., Infrarotspektroskopie mit ATR-Sonden-Messtechnik. Chemie Ingenieur

Technik, 2013. 85(7): p. 1012-1015. [11] Rollbusch, P., et al., Shortcut-Modellierung von Blasensäulenreaktoren. Chemie

Ingenieur Technik, 2013. 85(9): p. 1425-1425. [12] Abel, N.H., L. Schlusemann, and M. Grünewald, Beschreibung von Blasensäulen

mithilfe von Kompartment-Modellansätzen. Chemie Ingenieur Technik, 2013. 85(7): p. 1112-1117.

7

2 Literature survey

Despite the fact that bubble columns are widely established within the process industry as

multiphase reactors and gas-liquid contactors, common research has been focused on the

description of bubble column hydrodynamics under atmospheric conditions. Industrial

production is usually conducted at pressures above atmospheric and temperatures above

ambient in processes primarily involving the use of organic solvents. Because hydrodynamic

parameters such as gas holdup and backmixing determine the necessary reactor design and

impact reactor performance, detailed knowledge of these variables is crucial for optimal design

and operation of bubble column reactors. The purpose of this chapter is to give an overview of

research studies that deal with bubble column hydrodynamics at elevated pressures. A

recommendation for further research concerning this topic is provided as well.

2.1 Introduction

Bubble columns are widely employed within the chemical industry as gas-liquid contactors and

multiphase reactors [1-3]. Examples of applications of this reactor type include oxidations [3-

6], hydrogenations [7], fermentations [8, 9] and the production of synthetic fuels [10].

One of the main features of bubble column operation is that gas and liquid or suspended solid

phases are brought in contact without the need for additional mechanical stirring equipment,

making bubble column design and operation appear easier than that of other gas-liquid

reactors [11-14]. The gas distributor is usually located at the bottom of the column, while the

liquid phase can either be distributed co-currently or counter-currently with respect to the flow

direction of the gas phase. Semi-batch operation without any liquid flow is also possible. Gas

distribution itself takes place via perforated plate spargers, ring type distributors, perforated

pipes, porous plates and jet nozzles in various geometrical configurations suited to the needs

of a specific process [15, 16]. Some examples of bubble column and sparger designs

* Published as Rollbusch, P., et al., Bubble columns operated under industrially relevant conditions – Current understanding of design parameters. Chemical Engineering Science, 2015. 126(0): p. 660-678.

8

according to [11] can be seen in Figure 2.1. To make things more complicated bubble columns

are often equipped with internal heat exchangers (vertical or horizontal) to control the reactor

temperature, which in addition to other internals influence the hydrodynamics of the reactor.

Figure 2.1 left: examples of bubble column designs A) empty, B) cascaded, C) packed, D) multishaft, E) equipped with static mixers, right: examples of gas spargers A) simple tube, B) perforated plate, C) perforated ring, D) porous plate, figure taken from [11]

As hydrodynamic parameters such as gas holdup and liquid backmixing affect not only the

overall design of a bubble column reactor but also important variables such as yield and

selectivity of a given chemical reaction [17-19], a brief overview of some important definitions

encountered when dealing with bubble columns would seem appropriate. A more detailed

introduction to the characteristics of bubble columns may be found in Kantarci et al. [20].

According to Deckwer [12], the hydrodynamic flow regimes of a bubble column are divided into

four main groups (Figure 2.2): the homogeneous regime (equal bubble sizes), the

heterogeneous regime preceded by a transition regime (wide bubble size distribution) and the

slug-flow regime (bubbles and slugs up to the column diameter in size).

9

Figure 2.2 The most common flow regimes in bubble columns [29]

The prevailing flow regime is dependent on superficial gas velocity, column diameter, the

physical properties of the components, the type of gas distribution, integrated internals, and

the pressure and temperature at which the reactor is operated [21-23]. Homogeneous flow

regime, however, is characterized by relatively small, uniformly sized bubbles, and occurs at

low superficial gas velocities. Heterogeneous flow can be described by the existence of a wider

bubble size distribution due to the coalescence and breakup of bubbles. Heterogeneous flow

appears at higher superficial gas velocities after passing the transition regime, which is merely

a mixture of homogeneous and heterogeneous flow. According to several authors, the

transition point of an air/water system at ambient conditions can be found at superficial gas

velocities of approximately 0.05 m/s [24]. While the radial gas holdup distribution in

homogeneous flow is rather uniformly distributed, it is highly developed in heterogeneous or

churn-turbulent flow due to large liquid circulations. This in turn is caused by large, rapidly

ascending bubbles in the column center, and smaller, descending bubbles near the column

walls [25]. A more detailed overview of regime transition and an estimation of the transition

point is given by Shaikh and Al-Dahhan [26].

Overall gas holdup behavior is directly affected by a change of flow regimes. Gas holdup rises

with rising superficial gas velocity, while the slope of a typical gas holdup curve is steeper

during homogenous bubble flow than in heterogeneous flow. The gas holdup of bubble

columns of different sizes has already been studied extensively under atmospheric conditions

10

by various authors, such as Hikita et al. [27], Akita and Yoshida [28], Reilly et al. [29] and

Krishna and Ellenberger [30]. An extensive review of gas holdup behavior in general is given

by Joshi et al. [31].

The same is true for investigations concerning liquid mixing inside bubble columns of various

scales. Tracer studies are usually carried out in order to ascertain the degree of liquid

backmixing [32-34]. Often the results are described by an axial dispersion coefficient, which in

turn is used in mathematical models [35]. Ohki and Inoue [36], Hikita and Kikukawa [37] and

Kantak et al. [38] are among a few well-known authors who developed correlations for

predicting axial dispersion coefficients under atmospheric conditions. A review by Lefebvre et

al. [39] considers phase mixing models for gas-liquid systems in multiphase reactors. Another

extensive literature review on heat transfer in two- and three-phase bubble columns has also

been published by Hulet et al. [40].

Despite of the fact that most industrially relevant operations involving bubble columns are

carried out at pressures above atmospheric, the studies mentioned above are based on

ambient pressure.

Designing and scaling up bubble columns requires information about the hydrodynamic

behavior of the column at operating conditions. Because of increasing gas density, gas holdup

is directly influenced by pressure, which affects all other important fluid dynamic parameters

as well. Often a combination of the dimensionless Reynolds, Morton and Eötvös numbers are

used to describe the deviation of real fluids from ideal fluids in terms of bubble shape [41]. The

shape of a bubble affects for example its drag coefficient, which is in turn among others a vital

parameter for fluid dynamic modelling. Therefore the use of correlations derived at ambient

conditions can lead to severe design failures during the scale-up process of bubble column

reactors. As pointed out earlier by Becker et al. [42] and Rollbusch et al. [43], this is especially

the case as the estimated value for one hydrodynamic parameter might be used directly to

calculate another. The purpose of this article is therefore to discuss the available literature

dealing with the above phenomena at pressures higher than atmospheric. This can be used

11

as a basis for drawing conclusions with respect to future research aimed at improving

understanding of pressurized multiphase systems.

2.2 Industrial applications of bubble columns

To visualize the gap between academic research and industrial needs, some important

chemical processes involving bubble columns will be outlined briefly, i.e., their process

parameters and, if available, column designs will be presented. One oxidation process of major

importance is the production of phenol via cumene oxidation within the Hock process [44].

Cumene is oxidized in a series of bubble column reactors operating at temperatures between

80 and 120°C and pressures of up to 0.7 MPa. According to Weber [3], column dimensions

can be as large as 4.6 m in diameter and 22 m in height, with internal or external heat

exchangers to eliminate reaction heat. The formation of the desired oxidation product cumene

hydroperoxide is accompanied by two byproducts, which may lead to product losses if the

process is not operated or designed properly.

An example for the use of a three-phase bubble column is the coal liquefaction process used

for synthetic fuel production. Bakopoulos [45] reported the existence of bubble column reactors

for this purpose with diameters larger than 4 m and lengths greater than 50 m. Coal liquefaction

conditions are found to be at pressures of 30 MPa and temperatures of 470°C. The reactors

mentioned by Bakopoulos are either cascaded or fitted with internal circulation tubes.

Montan wax bleaching represents another example for the use of cascaded bubble columns.

The bleaching process comprises several reaction steps in series, the last of which leads to

wax degradation and is thus undesirable. To avoid the degradation reaction, residence times

need to be adjusted carefully and maintained by avoiding liquid backflow inside the reactor

segments through the installation of suitable partition plates. According to Steiner [46], typical

reaction conditions involve temperatures of about 100 - 125°C and pressures of 0.1 to 0.5

MPa, with residence times around 1 to 3 hours.

12

Steiner [46] also mentions an application for a bubble column designed with a draft tube used

for the biological purification of wastewater. The dimensions of this specific reactor vary

between 10 and 45 m in diameter and 15 to 25 m in length. Other examples indicated by

Steiner include downflow bubble columns and bubble reactors with external heat exchangers

for processes such as chlorination reactions.

Several patents also state the usability of bubble column reactors for important commercial

processes. For example Zimmermann [47] describes a slurry bubble column used as a

hydrocracking unit operated at temperatures ranging up to 600°C and pressures of up to 27.6

MPa. A German patent by the former Degussa-Hüls AG [48] (now Evonik Industries AG) claims

the applicability of a cascaded bubble column operated at slight overpressures of about 0.5

MPa for the production of hydrogen peroxide. Another patent by Zou and Gupta [49] refers to

the production of silanes in a bubble column. The proposed operating conditions are

temperatures of up to 100°C and pressures of up to 0.3 MPa.

It can be seen from the listed processes and their corresponding production rates that bubble

columns are employed within world-scale production units, making it vital that these reactors

be designed and operated for optimum efficiency in order to save resources and energy

consumed by downstream processing units. The following overviews of publications dealing

with the estimation of hydrodynamic parameters are thought to be helpful for practicing

engineers and researchers who are confronted with choosing design equations or identifying

topics for their own scientific programs. Compared to the amount of published data dealing

with bubble columns and their characteristics under ambient conditions (atmospheric pressure

and temperature) and air/water systems, the quantity of available studies regarding high

pressure and temperature conditions with organic liquids is relatively scarce. The following

chapters are divided into sections addressing individual design parameters, beginning with an

introduction to single bubble behavior.

13

2.3 Single bubble behavior

In order to characterize the single bubble rising behavior, the terminal bubble velocity is mostly

utilized. This is, indeed, an important parameter due to the fact that the models/ correlations

to describe the bubble rising velocity in swarm are usually based on single (terminal) bubble

velocity and gas hold-up (Marucci [50], Lockett and Kirkpatrick [51], Ishii and Zuber [52],

Krishna et al. [53], Joshi [31], Simmonnet et al. [54]). All these models/ correlations going back

to the pioneer correlation

拳長鎚┸追勅鎮 噺 拳長盤な 伐 綱直匪怠┻戴苔 (2-1)

developed by Richardson and Zaki [55], actually for the sinking of rigid particles in a swarm.

Further information about the swarm velocity can be obtained by Bothe [135].

After being ejected on the disperser, the bubble is accelerated until the force equilibrium

between drag force FD

繋帖 噺 耕穴長態 講ね 貢鎮憲長態に

(2-2)

and buoyancy force FB

繋喋 噺 穴長戴 講は 訣盤貢鎮 伐 貢直匪

(2-3)

is reached. At that point the relative velocity of a single bubble

憲長態 噺 ねぬ 磐な 伐 貢弔貢挑 卑 訣穴長耕 (2-4)

14

can be determined. However, the rising velocity is influenced by the surrounded liquid velocity

induced by previous rising bubbles. Therefore it is required to distinguish between relative

velocity w嘆奪狸┸沢醍and absolute velocity w叩但坦┸沢醍of the bubble. The relative bubble velocity

憲長 噺 憲銚長鎚┸鎮 伐 憲銚長鎚┸長

(2-5)

represents the difference of the liquid velocity uabs,l and the absolute velocity of the bubble

uabs,b w叩但坦┸沢醍. For bubble movement in a stagnant media, it can be assumed that

憲長 噺 憲銚長鎚┸長

(2-6)

the absolute velocity is equal to the relative velocity [56].

Eq. (2-2) shows that in addition to the physical properties, the bubble velocity also depends on

the drag coefficient, representing the shape and deformability. As can be obtained from Eq.

(2-4), bubble velocity and drag coefficient are inversely proportional and be converted through

the force equilibrium. Various equations are derived for the determination of the terminal rise

velocity of a single bubble including the drag coefficient. Peebles and Garber divided the

bubble shapes in four categories with specific equation to determine the velocity. For each

category the validity of range is determined by physical properties represented by the liquid

number

計庁 噺 貢鎮購戴訣考鎮替 噺 な警剣

(2-7)

and flow condition

15

迎結 噺 憲長穴長貢鎮航鎮

(2-8)

corresponding to the Reynolds number. Schlüter and Räbiger [57] give a detailed overview of

the four categories and their correlations.

2.3.1 Correlations validated under elevated pressure

In the case of elevated pressure the correlations of Fan und Tsuchiya [58], Tomiyama [59] and

Mendelson [60] are validated. Mendelson [60] derived his correlation in analogy to the

dispersion of water waves

潔 噺 俵に講購貢挑 膏 髪 訣膏に講

(2-9)

where he displaced the wave length そ by the bubble contour ヾd台態

憲長 噺 俵 に購貢挑穴長 髪 訣穴長に ┻

(2-10)

However, there is no validated physical relation between bubble and wave movements.

The equation of Fan und Tsuchiya

憲長 噺 盤憲岫ひ岻貸賃鉄 髪 憲岫怠怠岻貸賃鉄匪貸 怠賃鉄

(2-11)

is based on the Mendelson equation (eq. (2-9)) and on the Levich equation

16

憲長 噺 貢挑 訣 穴長態倦戴考挑 ┻

(2-12)

For small bubbles the ratio of eq. (2-9) dominates, whereas it is eq. (2-11) for bigger bubbles.

According to Fan and Tsuchiya [58] the Levich equation refers to spherical bubbles with higher

Re-numbers, e.g. 50 – 500 for air bubbles in water. Whereas for ellipsoid and spherical cap

bubbles (also Taylor-Davis-Cup bubbles called) the Mendelson equation is applicable. The

bubble rise velocity according to Fan und Tsuchiya [58] can be calculated by

憲長 噺 琴欽欽欽欣嵜警貸怠替倦戴 蕃穴長 岾貢挑訣購 峇怠態否態崟貸賃鉄

髪 均僅 に倦怠穴長 岾貢挑訣購 峇怠態 髪 穴長に 岾貢挑訣購 峇怠態斤巾貸賃鉄態

筋禽禽禽禁貸 怠賃鉄 磐訣購貢挑 卑怠替

(2-13)

and is valid for 10-5<KF< 1012.

Fan und Tsuchiya [58] fitted the parameters ki for 20 different newtonic liquids and mixtures

and found out constant values k1 und k2 for defined systems. The constant k1 refers to the

differences of surface tension of pure liquid and multi component systems

倦怠 噺 犯な┸に血剣堅嫌件券訣健結潔剣兼喧剣券結券建嫌検嫌建結兼な┸ね血剣堅兼憲健建件潔剣兼喧剣券結券建嫌検嫌建結兼

whereas k2 takes into account any contaminants in the system

17

倦態 噺 犯 ど┸ぱ 血剣堅 喧憲堅結 健件圏憲件穴嫌な┸は 血剣堅 潔剣券建欠兼件券欠建結穴 健件圏憲件穴

Further values of the fitted constants are given in [58]. The movement of the interface is

included in k3

倦戴 噺 倦長待警剣貸待┸待戴腿 噺 倦長待計庁待┸待戴腿岫倦戴 伴 なに岻

(2-14)

where

倦長待 噺 犯 など┸に血剣堅剣堅訣欠券件潔嫌剣健懸結券建嫌なね┸ば血剣堅拳欠建結堅欠券穴欠圏憲剣憲嫌嫌剣健憲建件剣券

the constants distinguish between organic and aqueous liquid phase. According to Schlüter

and Räbiger [57] this equation is inadequate to describe the radical change of the bubble shape

for increasing bubble diameters. However, this empirical equation is sophisticated to describe

material systems which deviate from the pure system.

In order to investigate deformation of the bubble shape in detail, the correlation of Tomiyama

et al. [61] can be applied. For the bubble shape a distorted oblate spheroid rotation body is

assumed. The equation according to Tomiyama et al. [61]

憲長 噺 嫌件券貸怠ヂな 伐 継態 伐 継 ヂな 伐 継態な 伐 継態ゲ 俵 ぱ購貢挑 穴長 紘継替戴 髪 ッ貢訣穴長に貢挑 ゲ 紘継態戴な 伐 紘態継態

(2-15)

consists of an aspect ratio E

18

継 噺 決 髪 紅決に欠

(2-16)

for consideration of the bubble shape and the deformation factor け

紘 噺 にな 髪 紅┻

(2-17)

For ellipsoid bubbles, b 噺 くb and thus け 噺 な the equation can be simplified to

憲長 噺 嫌件券貸怠ヂな 伐 継態 伐 継ヂな 伐 継態な 伐 継態 ゲ 俵 ぱ購貢挑 穴長 継替戴 髪 ッ貢訣穴長に貢挑 ゲ 継態戴な 伐 継態

(2-18)

Figure 2.3 Scheme of a distorted oblate spheroid

Tomiyama et al. [59] also developed a correlation for bubble rising in liquid in the form

耕 噺 ね訣ッ貢穴長ぬ貢鎮憲長

(2-19)

19

of a drag coefficient. They separated the range of validity in dependence on the system purity.

For purified systems

耕 噺 兼欠捲 犯兼件券 釆なは迎結 岫な 髪 ど┸なの 迎結待┸滞腿胎岻┸ ねぱ迎結挽 ┸ ぱぬ 継剣継剣 髪 ね般

(2-20)

whereas for partially contaminated systems

耕 噺 兼欠捲 犯兼件券 釆にね迎結 岫な 髪 ど┸なの迎結待┸滞腿胎岻┸ ばに迎結挽 ┸ ぱぬ 継剣継剣 髪 ね般

(2-21)

and for contaminated systems

耕 噺 兼欠捲 犯にね迎結 岫な 髪 ど┸なの迎結待┸滞腿胎岻┸ ぱぬ 継剣継剣 髪 ね般

(2-22)

the rising velocity has to be determined implicitly.

2.3.2 Comparison of correlations and experimental data under elevated

pressure

Lin et al. [62] conducted experiments of single bubbles under pressure in the range from 0.1

to 19.4 MPa and for three different temperature levels (27°C, 47°C and 78°C). Using

Paratherm NF for the liquid phase and nitrogen as gas phase, they compare their results with

three empirical equations by Fan and Tsuchiya [63], Tomiyama et al. [61] as well as with

憲長 噺 俵 に購貢挑穴長 髪 磐ッ貢貢挑 卑 訣穴長に

(2-23)

the modified Mendelson equation.

20

In Figure 2.4 and Figure 2.5 these results for two different temperatures (27 and 78 °C) in

dependence on the pressure (0.1-19.4 MPa) are shown. Fan et.al. [64] explains the decreasing

bubble rising velocity with an increasing pressure due to significant change (200-fold) in gas

density. In the case of a higher gas density, the density difference between liquid and gas

phase is smaller, and thus the buoyancy force (compare Eq. 2-3) is decreased.

Figure 2.4 Influence of pressure on single bubble velocity in Paratherm NF at 27°C [62]

 

0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,1 1 10 100

bubble

 velocity

 [m/s]

bubble diameter [mm]

T = 27°C 

p = 0.1 MPa

p = 19.4 MPa

p = 10.4 MPa

p = 3.5 MPa

ModifiedMendelsonFan-Tsuchiya

Tomiyama

p = 0.1 MPa

p = 19.4 MPa

21

Figure 2.5 Influence of pressure on single bubble velocity in Paratherm NF at 78°C [62]

The correlation by Fan and Tsuchiya [58] sufficiently approximates the measurement, except

for the higher temperature at the velocity peak. Whereas the equation of Tomiyama et al. [61]

is applicable at the velocity peak. However, the equation underestimates the remaining bubble

diameter range. For the modified Mendelson equation there is a limited agreement between

measured and predicted values due to the invsicid condition. This also explains the better

agreement for measurements for higher temperature and db> 2mm, because the condition is

almost inviscid [64]. This also confirms the statement that the bubble rise velocity for larger

bubbles is insensitive to the properties of the liquid phase [65].

According to Clift et al. [41] the shape and motion of bubbles can be described with the help

of the three dimensionless numbers the Eötvös number

継剣 噺 訣 弘貢 穴長態購 噺 激結繋堅 ┸

(2-24)

the Morton number

0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,1 1 10 100

bu

bb

le v

elo

cit

y [

m/s

]

bubble diameter [mm]

T = 78°C

p = 0.1 MPa

p = 19.4 MPa

p = 10.4 MPa

p = 3.5 MPa

Modified Mendelson

Fan-Tsuchiya

Tomiyama

p = 0.1 MPa

p = 19.4 MPa

22

警剣 噺 訣考挑替弘貢貢挑態購戴 噺 激結戴迎結戴繋堅┸

(2-25)

and the Reynolds number eq. (2-8). The diagram of Clift [41], shown in Figure 2.6, describes

the general rise behavior with the help of these three numbers.

An increase of pressure and/ or temperature also changes physical properties and, therefore,

the Eötvös and Morton number is shifted. From Figure 2.6it can be obtained that the shape of

the bubble and thus, the drag coefficient is different. Consequently the bubble rise velocity

must change, too.

Coming back to the experiments by Lin et al. [62] for both temperatures (27°C and 78°C) there

is a change for the density of Paratherm NF within the pressure range of just 5 to 6 %. Whereas

viscosity and surface tension have a major dependence on pressure and temperature.

Viscosity is increasing in dependence on the pressure about 65 % at 20°C and about 10% at

100°C. Surface tension is influenced more by temperature than by pressure. For both

pressures there is an increase of about 4 % per 10°C. [62]

The experimental data are implemented in the Clift diagram [41] in Figure 2.6 and show that

they are in good agreement with the correlation by using the exact physical properties.

23

Figure 2.6 Comparison of measured and calculated Re of single bubble velocity in Paratherm NF under variation of pressure and temperature [62].

Table 2-1: Correlations for terminal velocity of singles bubble validated under pressure by [62]

Author Physical system Experimental

conditions

Fan [58] Different liquids Ambient

Mendelson [60] Water/Air

Ambient

Tomiyama et al. [61] Water/Air

Siliconeoil/Air

Ambient

0,01

0,1

1

10

100

1000

10000

0,01 1 100

Re

[-]

Eo [-]

T = 27°C; p = 0.1 MPa;M = 3.53 x 10^-4

T = 27°C; p = 19.4 MPa;M = 3.85 x 10^-3

T = 78°C; p = 0.1 MPa;M = 3.39 x 10^-7

T = 78°C; p = 0.1 MPa;M = 9.87 x 10^-7

-6

-8

-4

-202

4

6

8

10- log M = 12

24

2.4 Gas holdup at higher pressures

As previously mentioned, gas holdup determines residence times, interfacial area and the

overall reactor size. Furthermore, gas holdup is linked to all other hydrodynamic parameters

in bubble column reactors, making correct gas holdup estimates vital for avoiding design

failures and overestimations of investment costs with respect to the reactor itself and

downstream processing units. Rollbusch et al. [66] offers a brief survey of how uncertainties in

gas holdup calculations may effect economic aspects of a complex oxidation reaction.

Because non-invasive gas holdup detection can be performed relatively easy via pressure

difference measurements or by using more advanced methods like tomographic [67, 68] or

ultrasonic [69] devices, a number of experimental studies of gas holdup in pressurized bubble

columns have already been performed. An extensive overview about non-invasive and

invasive measurement techniques suitable for investigating multiphase systems is given by

Tayebi et al. [70].

Table 2-2: Summary of gas holdup studies at elevated pressures

Author Physical system

(gas/liquid/solid)

Experimental conditions

(Pmax [MPa]/T [°C]/DC [m])

Idogawa et al. [73] Air/H2O 15/ambient/0.05

Therning and

Rasmuson [71]

Air/H2O

0.66/20/0.15

Pohorecki et al. [75] N2/H2O 1.1/30-160/0.3

correlation derived

Letzel et al. [85] N2/H2O 1.3/ambient/0.15

correlation derived

Kemoun et al. [89] Air/H2O 0.7/ambient/0.162

Ishiyama et al. [102] N2,CO2/H2O 1.1/20 – 35/0.045

25

Krishna et al. [95] He,Ar,N2,CO2, SF6/H2O 2/ambient/0.16

correlation derived

Wilkinson and

Dierendonck [83]

He,Ar,N2,CO2, SF6/H2O 2/ambient/0.16

Idogawa et al. [74] Air,H2,He/H2O,

methanol,ethanol, acetone,

aqueous alcohol solutions

5/ambient/0.05

correlation derived

Wilkinson et al. [80] N2/n-Heptane, mono-

ethylene glycol,H2O

2/20/0.15 – 0.23

correlation derived

Reilly et al. [96] Air,N2,He,Ar, CO2/Isopar G,

Isopar M, TCE,Varsol DX

3139, H2O

1.1/ambient/0.15

correlation derived

Clark [97] N2,H2/H2O,methanol 10/20 – 180/0.075

Jordan et al. [114] N2/H2O,ethanol, toluene,1-

butanol

1/20/0.115

correlation derived

Kojima et al. [88] N2-O2 mixture/H2O, aqueous

enzyme and citric acid

solutions

1.1/17 – 27/0.045

correlation derived

Urseanu et al. [82] N2/Tellus oil, aqueous

glucose solutions

1/ambient/0.15 – 0.23

correlation derived

Oyevaar [101] CO2,N2/aqueous DEA

solutions

8/25/0.081 0.0855

Kang et al. [115] Air/aqueous CMC solutions 0.6/ambient/0.152

correlation derived

Pohorecki et al. [76] N2/Cyclohexane 1.1/30 – 160/0.3

Nedeltchev and

Schumpe [100]

Air,He,N2,H2, CO2/various

organic liquids

4/ambient/0.095 – 0.102

correlation derived

Luo et al. [108] N2/Paratherm NF 5.6/28, 78/0.102

correlation derived

26

Lin et al. [62] N2/Paratherm NF 20/27 – 78/0.0508 – 0.1016

Lin et al. [92] N2/Paratherm NF 15/ambient/0.0508

Lau et al. [116] Air,N2/Paratherm NF 4.24/ambient – 92/0.0508 –

0.1016

Jiang et al. [72] N2/Paratherm NF 21/ambient/0.0508

Shaikh and Al-

Dahhan [93]

Air/Therminol-LT 1/25/0.162

De Bruijn et al. [99] H2/vacuum residue 14/300/0.0508

Deckwer et al. [113] N2/Paraffin/Al2O3 powder 1.1/143 – 270/0.041 – 0.1

correlation derived

Tarmy et al. [87] N2/Heptane/raw coal 0.52/25/0.024 – 0.61

Behkish et al. [112] N2,He/Isopar-M/alumina

powder

3/27 – 100/0.29

Kölbel et al. [105] H2,Ethylene/C13-C18

mixture/suspended catalyst

particles

0.588/ambient/0.0418

Chilekar [106] Air,N2/H2O,Isopar

M/carbon,silica

1.3/ambient/0.15

correlation derived

Sangnimnuan et al.

[110]

Air/Tetralin/coal 15/ambient – 384/0.019

correlation derived

Soong et al. [111] N2/Drakeol-10 1.36/20 – 265/0.1

Behkish et al. [117] - correlation derived

2.4.1 Studies involving two phases

These studies differ with respect to their experimental conditions (pressure and temperature

range applied, superficial gas and liquid velocities established), column dimensions and the

physical properties of the gas and liquid phase studied. Table 2-2 summarizes publications

27

dedicated to gas holdup studies at elevated pressures. These publications show that pressure

ranges from slightly above atmospheric at 0.6 MPa (Therning and Rasmuson [71]) to high

pressure conditions of 21 MPa (Jiang et al. [72]). There are also considerable differences

regarding the column diameters used. Idogawa et al. [73, 74] used a 0.05 m diameter column

while Pohorecki et al. [75, 76] used columns of 0.3 m in diameter. This is an important question

because, as Krishna et al. [77] have indicated, gas holdup is dependent on column diameter

until a certain limit is reached. Shah et al. [78] propose that a column diameter of at least 0.15

m should be used in order to guarantee independence of gas holdup from column dimensions.

This has been confirmed by the investigations of Forret et al. [79], who used three columns

with diameters of 0.15, 0.4 and 1 m, and found gas holdup to be independent of column

diameter. In addition, Wilkinson et al. [80] stated that a height to diameter ratio of HC/DC > 5

should be maintained during experiments to prevent liquid height from influencing dispersed

phase holdup. As indicated above, sparger design also influences gas holdup. Wilkinson et al.

[80] advise to use orifice diameters of 1 – 2 mm. Smaller distributor openings would mask the

effect of applying high pressures by producing smaller bubbles at the orifice. Another important

point is the influence of liquid properties on gas holdup in bubble columns. As can be seen in

Table 2-2, the most studied system so far is the air/water combination. As previously stated,

however, most industrial processes are based on organic solvents, and the properties of these

differ from water at least with respect to density, surface tension and viscosity. These

properties in turn affect bubble break up, coalescence and rise velocity. Kulkarni and Joshi

[81] provided a detailed review of bubble growth and rise, and discussed these parameters in

detail. A rise in liquid viscosity usually hinders bubble breakage and thus promotes the

formation of larger bubbles. This has also been studied by Urseanu et al. [82] and compared

to the effect of higher gas density due to high pressure conditions. The effect of higher

pressures vanishes gradually with increasing liquid viscosity, which is shown in Figure 2.7 as

a comparison between glucose B/N2 and H2O/N2 (Wilkinson et al. [83]) .

28

Figure 2.7 Effect of higher liquid viscosity compared to higher gas density due to elevated pressure

The pressure range studied was 0.1 to 1 MPa in 0.15 and 0.23 m diameter columns. The

physical system was either N2/glucose A/B or N2/ Tellus oil. As a result of their work, they

propose a new correlation for predicting the gas holdup of media with a dynamic viscosity in

the range of 0.05 to 0.55 Pas (eq. 2-26).

綱直 噺 ど┻にな憲直待┻泰腿経頂貸待┻怠腿考鎮貸待┻怠態貢直岷待┻戴奪淡丹岫貸苔挺如岻峅 (2-26)

Because the findings of one research group are based on their specific experimental setup

(column diameter, sparger used, superficial gas and liquid velocities studied) and the physical

system investigated, it remains to be seen whether these results can be extrapolated to other

column geometries operated with different gases and liquids. This is an important question for

every engineer tasked with designing a production-scale bubble column reactor with stringent

restrictions on investment costs and production efficiency. From a publication by Weber [3],

one can imagine that choosing the right correlations for describing the hydrodynamics of a 4.6

m diameter reactor is a daunting task if all of the available correlations are based on laboratory-

scale columns.

It is generally agreed that gas holdup increases with increasing pressure. This is due to a

higher gas density at elevated pressure, which results in lower bubble rise velocities (caused

29

by a reduction in buoyancy force) and therefore larger residence times of the gas bubbles.

Idogawa et al. [73] also claimed that the initial bubble size formed at the distributor openings

also decreases with increasing pressure due to an increase in momentum, thus making the

entire bubble size distribution narrower than is the case under atmospheric conditions. Smaller

bubble sizes ultimately lead to an increase in gas holdup. This was also found by Kang et al.

[84], who utilized pressure fluctuation measurements taken in a 0.058 m diameter column

(height = 1.5 m) in order to investigate bubble properties by applying the deterministic chaos

theory. The highest pressure utilized for their investigations was 0.6 MPa. In conclusion, Kang

et al. determined that, while higher pressure leads to a narrower bubble size distribution than

is the case at atmospheric pressure, it also contributes to higher bubble frequencies.

Figure 2.8 illustrates the differences in gas holdup at elevated pressures versus atmospheric

pressure. The data shown in Figure 2.8 are taken from Letzel et al. [85], who used a 0.15 m

diameter column with a height of 1.22 m. The column was equipped with a perforated plate

sparger, with nitrogen and water as the gas and liquid phases, respectively.

Figure 2.8 Gas holdup as a function of pressure (data from Letzel et al. [85])

The system pressure was varied up to 1.3 MPa. The main observations are a shift of regime

transition to higher values of iG and a decrease in bubble size and bubble rise velocity due to

an increase in pressure. Letzel et al. used the Kelvin-Helmholtz theory to explain the difference

30

in gas holdups (especially prevalent at higher superficial gas velocities) and derived a

correlation (Eq. (2-27)): 綱直 噺 綱鎮長 髪 岫な 伐 綱鎮長岻綱直┸鎚長 (2-27)

綱鎮長 噺 ど┻にはぱ 怠帖頓轍┻迭添 怠盤通虹貸通虹┸濡弐匪轍┻鉄鉄 盤憲直 伐 憲直┸鎚長匪替 泰斑 磐 諦虹諦虹┸尼禰尿卑待┻泰 (2-28)

Equation (2-27) is mainly based on a correlation suggested by Krishna and Ellenberger [30]

for estimating holdups at atmospheric pressure in the heterogeneous regime, and has been

expanded to include a term accounting for the influence of gas density on gas holdup. Total

gas holdup is then the sum of large and small bubble holdup, while small bubble holdup is

assumed to be equal to transition holdup.

According to Letzel et al. [86], rising gas density favors the propagation of instabilities and

therefore leads to an increase in large bubble breakup, decreasing the bubble size distribution

until a new state of equilibrium between bubble coalescence and breakup occurs. This

explanation has also been used by Wilkinson and van Dierendonck [83]. Wilkinson and van

Dierendonck themselves used a column with a diameter of 0.16 m and studied the influence

of the density of different gases sparged into water (see Table 2-2 for details) at pressures of

up to 2 MPa. Visual examination of photographs taken at different pressures revealed a

complete absence of large bubbles. In a later study, Wilkinson et al. [80] proposed a correlation

for estimating gas holdups that also accounts for the occurrence of regime transition. Gas

holdup measurements taken at high pressure while varying column diameters (0.15 and 0.23

m) represent another interesting aspect of their study (see Figure 2.9). For future studies it

might be interesting to see if it is a feasible extension of their proposed holdup model to

correlate gas density together with bubble sizes and column diameter to predict the point of

regime transition at various operating conditions and column configurations.

31

Figure 2.9 Influence of scale on gas holdup at varying pressures, adapted from Wilkinson et al. [80]

A comparison with experimental data obtained by Idogawa et al. [74] and Tarmy et al. [87]

revealed that the previous statement regarding the independence of column diameter for

columns larger than 0.15 m is also valid for pressures above atmospheric. Idogawa et al.’s gas

holdup results [74] were higher than those of Wilkinson et al., because Idogawa et al. used a

very small diameter column (d = 0.05 m). As such, wall effects and slugging could have

influenced their holdup measurements. The differences in gas holdups between Wilkinson et

al. and Tarmy et al. are rather negligible.

Kojima et al. [88] also studied bubble column hydrodynamics with respect to elevated

pressures and different liquids. The investigators used a 0.045 m diameter column (liquid

height = 0.9 to 1.2 m) and O2/N2 gas mixtures combined with tap water, citric acid solution and

aqueous solutions of glucose oxidase. A single nozzle sparger with different orifice diameters

was used for phase contact. The pressure was varied between 0.1 and 1.1 MPa, and the

superficial gas velocity was adjusted between 0.005 and 0.15 m/s. The liquid height was

measured by level indicators in order to obtain the gas holdup as a function of pressure und

ug. As a result, Kojima et al. pointed out that gas holdup increases with increasing pressures

due to reduced bubble coalescence and earlier bubble break-up, resulting in the formation of

more small bubbles.

32

Kemoun et al. [89] used computed tomography to gain insights into the behavior of bubble

characteristics and mean and radial gas holdup in a bubble column with a diameter of 0.162

m and a height of 2.5 m. The column was operated in batch mode within a pressure range of

0.1 to 0.7 MPa at superficial gas velocities of 0.02 to 0.18 m/s in an air/H2O system. The gas

was distributed by a plate distributor with 61 holes (0.0004 m in diameter), which were arranged

in a circular pattern. The authors were able to verify that bubble size decreases and gas holdup

increases with rising pressure. The study also confirmed that at higher superficial gas velocities

more gas is in the center of the column than near the wall region, a phenomenon caused by

an increase in liquid circulation due to higher gas velocities. The radial gas holdup profile

flattens at higher system pressures, which is related to a delay in regime transition at higher

pressures (Figure 2.10).

Figure 2.10 Radial gas holdup profiles at different system pressures [89]

A study conducted by Schäfer et al. [90] confirms the conclusion that decreasing bubble sizes

are due to elevated pressures. Schäfer et al. investigated the bubble size distribution in a

bubble column with a diameter of 0.2 m and a length of 1 m. They installed a glass tube with

a diameter of 0.054 m as the measurement section in order to obtain bubble sizes via PIV and

LDA. The authors varied pressure up to 4.6 MPa and temperatures as high as 175°C. Nitrogen

was used as the gas phase and water, cyclohexane, cyclohexanone, cyclohexanol and ethanol

33

as the liquid phase. As a result, Schäfer et al. determined that bubble size decreases with

increasing pressure and temperature, primarily due to a delay in bubble break-up and

coalescence induced by high pressures. A rise in temperature usually results in higher liquid

viscosities and lower surface tension and gas density. This hinders bubble coalescence and

promotes the formation of small bubbles. This effect was confirmed by comparing bubble

behavior when water was used as the liquid phase to organic liquids. Schäfer et al. also used

different gas spargers of varying orifice diameters and geometries (single nozzle, ring sparger,

porous plates). They concluded that a decrease in hole diameter leads to a decrease in bubble

size.

Lin and Fan [91] used PIV measurements and a heat transfer probe to study the effect of high

pressure on the heat transfer coefficient (which will be discussed later) and on bubble

properties in a column with a height of 0.8 m and a diameter of 0.0508 m. They also used the

N2/Paratherm NF system at pressures of up to 15.2 MPa and a temperature of 27°C. The

authors found that bubble diameter decreased and bubble frequency increased with increasing

pressure, up to a pressure of 4 MPa. The transition point from a homogenous to a

heterogeneous bubbling regime is proportional to the superficial gas velocity taken to the

power of -0.38 at a fixed temperature. A more fundamental study examining the effect of

elevated pressure and temperature on bubble breakup, coalescence and gas holdup was

conducted by Lin et al. [62]. Inside columns with diameters of 0.058 and 0.1016 m, the authors

varied the pressure up to 20 MPa and the temperature between 27 and 78°C. The effects of

pressure and temperature were measured online by measuring the physical properties

(viscosity, surface tension, density) of the liquid phase. The flow behavior was visualized using

a CCD Camera. The physical system used was N2/Paratherm NF. The authors concluded that

an increase in temperature yields a smaller maximum stable bubble size due to a decrease in

surface tension. An increase in pressure at lower temperatures also decreases the stable

bubble size, but to a lesser extent. Increased temperature and pressure both lead to an

increase in gas holdup, which is again explained by a reduced stable bubble size and thus a

retarding effect on bubble coalescence.

34

Lin et al. [92] also used pressure fluctuation analysis to examine the effect of elevated

pressures on the regime transition velocity. The established range of pressure was between

0.1 and 15 MPa. The authors of this study came to the general conclusion that the point of

regime transition shifts with increasing pressure to higher superficial gas velocities. Another

publication dedicated to identifying regime transition at elevated pressures was commenced

by Shaikh and Al-Dahhan [93], who evaluated the usability of a CT measurement technique

inside a 0.162 m diameter column filled with Therminol LT as the liquid phase. They likewise

concluded that, within the applied pressure range of 0.4 to 1.1 MPa, the point of regime

transition switches to higher values of superficial gas velocities. A drift flux analysis, as

described in [26], was used to estimate the point of regime transition (Figure 2.11).

Figure 2.11 Regime transition favored with increasing pressure [93]

Krishna et al. [94] performed a study based on the findings by Letzel et al. [85] in which they

compared the effect that adding alcohol to water has on gas holdup versus the effect of high

system pressures measured by Letzel et al. [85]. The authors found that even adding small

amounts of alcohol causes gas holdup to increase. Thi0s result is attributed to a delay in

regime transition due to coalescence suppression. According to the authors, increasing

pressure does not suppress coalescence, but prevents the spread of instabilities that may

favor the transition to heterogeneous flow. Nine years earlier, Krishna et al [95] commenced a

35

study in which they sought to explain the effect that gas density due to high pressures has on

gas holdup by sparging different gases into de-ionized water in a 0.16 m diameter column at

pressures of up to 2 MPa. The authors concluded that the main effect of higher gas densities

is to stabilize the homogeneous flow regime. Krishna et al. also found that the use of gases

with a higher molar mass had the same effect on gas holdup as the use of elevated pressures.

On the basis of their observations, the authors proposed a model for calculating gas holdup

versus gas density that incorporated the difference between homogeneous and

heterogeneous flow regime. A possible setback of this model is that it is based on

measurements taken with water as the liquid phase, calling into question the use of the

proposed equations for describing systems involving organic solvents. Three years later, Reilly

et al. [96] used a column of comparable size (0.15 m diameter), and sparged various gases

into water and organic liquids. Thus Reilly et al. were also able to investigate how the effect of

gas density on dispersed phase holdup plays out over a broad range of physical properties of

the gas and liquid phase. Regarding the effect of gases with different molar masses and

operating pressures on gas holdup, they also concluded that the differences are negligible.

Furthermore, the authors found that gas density has a more pronounced effect on gas holdup

in the heterogeneous flow regime than it does in the homogeneous regime, citing stabilization

of the homogeneous flow regime as a reason for the gas density dependent variations in gas

holdup. Finally, Reilly et al. also reported a model for calculating gas holdup as a function of

gas phase momentum, which incorporates liquid phase density. Calculations using their model

were also able to reproduce Tarmy et al.’s [87] experimental gas holdup values with sufficient

accuracy.

Another researcher, Clark [97], likewise referred to Tarmy et al.’s [87, 98] measured holdup

values. Clark used a 0.075 m diameter column equipped with a sinter plate sparger (pore

diameters = 60 µm) operated at pressures between 2.5 and 10 MPa. While he found a

pressure-dependent increase in gas holdup and a delay in regime transition, Clark also noted

that this gas holdup increase cannot be attributed to the effects of pressure effect but rather to

a change in gas surface tension. He also admits that the use of a sinter plate as gas distributor

36

masks any gas density effects, as the bubbles created by the sparger are already small. De

Bruijn et al. [99] also measured hydrogen holdup. Their studies were performed using a

differential pressure transmitter and a slim column (diameter = 0.0508 m), with a vacuum

distillation residue as the liquid phase at a temperature of 300°C and pressures ranging

between 5 and 14 MPa. Although the range of superficial gas and liquid velocity was limited

(the maximum superficial gas velocity studied was 0.02 m/s), De Bruijn et al. noted an increase

in gas holdup at higher operating pressures. Gas holdup was twice as much at 13.89 MPa

than at 5.57 MPa when the maximum superficial gas velocity was applied. The same quantity

of gas holdup increase was also observed by Jiang et al. [72] in column of identical diameter.

In addition to their focus on examining how bubble shape evolves while elevating the operating

pressure, Jiang et al. also measured the holdup of nitrogen in Paratherm NF liquid. Bubble

shapes and local holdups were recorded and identified via a PIV system. The authors observed

a shift from ellipsoidal bubbles to more spherical bubbles at higher pressures. An analysis of

Eo, Re and Mo numbers under different experimental conditions revealed that this result is in

conformity with the bubble shape diagram proposed by Clift [41], which indicates that bubbles

tend to be smaller when pressures above atmospheric are applied. During their

measurements, Jiang et al. also noticed that the gas density effect on gas holdup is more

distinct at higher superficial gas velocities up to a pressure of 10 MPa. Above this limit, the

authors did not observe any further influence of pressure on gas holdup. They also found that,

within the range of operating parameters under examination, the Sauter mean diameter seems

to be unaffected by pressures above 1.5 MPa.

Nedeltchev [100] proposed a new correlation for predicting gas holdups in the homogeneous

flow regime. He examined the gas holdups of 21 organic liquids, 17 liquid mixtures, and tap

water at pressures of up to 4 MPa in a column with a height of 1.3 m and diameter of 0.102 m.

The resulting correlation is heavily dependent upon the geometric characteristics of an

ellipsoidal bubble. A correction factor has been introduced in order to account for the interfacial

area of rigid spheres and oblate ellipsoidal bubbles.

37

Although working in the general field of gas-liquid reactors, Oyevaar [101] also investigated

the gas holdup and interfacial area of two bubble columns with diameters of 0.0855 and 0.081

m at pressures of up to 8 MPa, and found that interfacial area and gas holdup both increase

with increasing pressure. The author concludes that the regime transition is shifted to higher

superficial gas velocities and thus gas holdups as pressure increases. He also attributes those

effects to the buildup of smaller bubbles with lower rise velocities due to higher pressure.

Up to this point, the publications described above have concluded that gas holdup rises with

increasing pressure. Pohorecki et al. conducted two studies in a 0.3 m diameter column (height

= 4 m) at temperatures between 30 and 160°C and pressures of up to 1.1 MPa under co- and

counter-current operation. The authors measured bubble sizes and gas holdups of N2/H2O [75]

and of N2/cyclohexane. Using the values measured for dB and ig, Pohorecki et al. were able to

calculate the interfacial area a. To study the effect of different sparger designs, Pohorecki used

spargers with between 1 and 27 holes ranging in diameter between 1 and 5 mm, and came to

the conclusion that pressure, temperature and sparger design do not interfere with gas holdup

(Figure 2.12).

Figure 2.12 : Independence of gas holdup on pressure according to Pohorecki et al. [75]

The researchers felt that the main influence on gas holdup is superficial gas velocity ug, which

was varied in the range of 0.002 to 0.02 m/s. One might argue that the reason for this result

38

may be found in the pressure conditions applied by Pohorecki et al., but Therning and

Rasmuson [71], Tarmy et al. [87, 98] and Ishiyama et al. [102] also applied pressures in the

range of 0.1 to 1.1 MPa and noticed increasing gas holdups. The data obtained by Therning

and Rasmuson (Figure 2.13) clearly show that pressure has a significant influence on

dispersed phase holdup. It should be noted that Therning and Rasmuson operated a packed

bubble column, but the data shown in Figure 2.13 also clearly show that pressure influences

gas holdup.

Figure 2.13 Gas holdups measured by Therning and Rasmuson [71]

Neubauer [103] contributed to the design of sieve plate spargers at elevated pressures by

experimentally investigating the design principles of perforated plates as gas distributors for

bubble columns under high pressure conditions (pressure ranged up to 30 MPa) in a 36 mm

diameter reactor. Neubauer also used another column with a diameter of 0.24 m operating at

pressures of up to 10 MPa. His work is based on the bubble size measurements above, varying

orifice diameters between 0.5 and 5 mm (height above the orifices = 1.2 m). The physical

systems involved were H2O/air, n-Octanol/air and n-Propanol/N2. The distributor plates

investigated had a relative free surface area of 0.15 and 0.34%. The author concluded that

higher pressure decreases bubble size, especially at pressures of up to 1 MPa. Possibly

Neubauer’s most important conclusion is that the design criteria to prevent weeping in sieve

39

plates with constant We or Fr numbers (introduced by Ruff et al. [104]) also hold with increasing

system pressure.

2.4.2 Studies involving a third phase

A number of investigators, including Kölbel et al. [105], Tarmy [87, 98], Chilekar et al. [106,

107], Luo et al. [108], Cui [109], Sangnimnuan et al. [110], Soong et al. [111], Behkish et al.

[112] and Deckwer et al. [113], focused their work on the hydrodynamics of three-phase slurry

bubble columns. According to Deckwer et al. [113] the addition of a third phase slightly

decreases gas holdup above superficial gas velocities of 0.04 m/s. Clark [97] found that

additional solids promote bubble coalescence and therefore significantly decrease gas holdup.

This leads to the conclusion that solids tend to decrease overall gas holdups but that a clearly

defined statement about the influence of a third phase is again not possible because of different

experimental setups and conditions.

Kölbel et al. [105] and Sangnimnuan et al. [110] used very small column diameters of 0.0418

and 0.019 m respectively. One of Kölbel et al.’s [105] results is that gas holdup does not

change with increasing pressure, a conclusion that might be related to the gas sparger applied,

which was a frit with a mean pore diameter of 10 µm. Sangnimnuan et al. [110] also came to

this conclusion as a result of their experiments under coal liquefaction conditions and further

stated that liquid superficial velocity does not interfere with gas holdup. Both authors noted

that gas holdup depends on temperature (liquid viscosity) and gas superficial velocity. The

results obtained by Sangnimnuan et al., Soong et al. and Kölbel et al. contradict those of Tarmy

et al., who also investigated gas holdups under coal liquefaction conditions. Tarmy et al.

describe a remarkable increase in gas holdup as pressure is increased from ambient to 0.52

MPa. Unfortunately, the small diameter column (d = 0.024 m) was not a pressurized vessel,

which prevented the authors from evaluating scale effects at higher pressure conditions.

Deckwer et al. conducted experiments in two slurry bubble columns with diameters of 0.041

and 0.1 m, at pressures of up to 1.1 MPa, and sparged with nitrogen through sintered metal

plates (mean pore diameter = 75 µm). Like Kölbel et al. and Sangnimnuan et al., the

40

researchers state that pressure does not influence gas holdup in either column. Not even

temperature rise seems to affect gas holdup. The gas sparging method used was identified as

a reason for this. Sintered plates or frits produce very small initial bubble sizes, producing

higher gas holdups—even at ambient conditions. It follows that this could mask the effect of

elevated pressure on bubble size and thus on gas holdup. Regrettably, there is no information

available on the sparger used by Sangnimnuan et al. The experimental setups of Chilekar and

Behkish et al. included columns with even larger diameters of 0.15 and 0.29 m, which is above

the 0.15 m limit indicated previously for avoiding wall effects when measuring hydrodynamic

parameters. Both authors found an increase in gas holdup with pressure. This again

contradicts the authors above except for Tarmy et al. An explanation might be found by

considering the gas spargers used by Behkish et al. and Chilekar. Each used spider spargers:

in the case of Behkish et al., the hole diameters were 0.005 m, and Chilekar’s experimental

setup describes a perforated plate distributor with hole diameters of 0.0005 m. It may be

assumed that the pressure effect on bubble sizes is not masked by other parameters. Behkish

et al., Chilekar and Kölbel et al. all, however, consistently observed a decrease in gas holdup

as solids loading increased. As indicated above, it had been assumed that the smaller column

diameter used by authors such as Deckwer et al. might be the reason why gas holdup was

found to be independent of increasing pressure. This assumption could be disproved by the

findings of Luo et al., whose setup consisted of a column with a diameter of 0.102 m operated

at pressures of up to 5.6 MPa. Gas holdup at the maximum applied pressure of 5.6 MPa is

approximately double that at atmospheric pressure. By contrast, Soong et al. also used a slurry

bubble column with a diameter of 0.1 m and measured gas holdups at atmospheric pressure

and 1.36 MPa. Soong et al. did not find that elevated pressure had an effect on gas holdup,

despite the fact that they were able to measure smaller bubble sizes and a concomitant

decrease in bubble rise velocities at 1.36 MPa than is the case under atmospheric conditions.

The argument that spargers with small pore diameters are responsible for the contradictory

results likewise does not apply to Soong et al.’s measurements, because the sparger that they

41

used was a perforated plate with 5 holes with diameters of 1 mm, i.e., the sparger was in

accordance with Wilkinson et al.’s design recommendations.

2.5 Liquid backmixing

Reliable understanding of liquid phase backmixing is as crucial as accurate prediction of gas

holdup. The deviation from ideal fluid dynamic states like complete backmixing and plug flow

hampers reactor performance. This is dependent on the structure of the chemical reaction

network, the corresponding reaction rate parameters and the desired degree of chemical

conversion. The next point is that the amount of backmixing is mainly expressed in terms of

an axial dispersion coefficient which is very difficult to scale. Dispersion coefficients are

obtained by evaluating residence time measurements with an axial dispersion model or cell

models. One should keep in mind that small deviations from plug flow are better described by

an axial dispersion and small deviations from perfect backmixing with a tanks-in-series model.

This is of special concern as empty bubble columns are most likely to be expected as perfectly

backmixed. The hydrodynamic state also influences the mass and heat transfer efficiency

which emphasizes the importance of correct reactor design.

Of course, liquid dispersion and gas holdup are two coupled phenomena because bubble

movement induces mixing of the continuous liquid phase. If a bubble moves upward inside a

liquid, a wake forms behind the bubble, which entrains liquid. The dimensions of the wake are

heavily dependent on bubble shape and size, which in turn is a function of operating

parameters and liquid phase properties. In other words, a large, quickly rising bubble causes

more turbulence due to its bubble wake, accelerating liquid upward. Small, slow moving or

even temporarily stagnant bubbles, by contrast, might not induce any serious turbulence.

Interactions between fast and slow rising bubbles occur in technical reactors due to high bubble

density and non-uniform bubble size distributions, and this complicates the explanation of

backmixing phenomena encountered in bubble columns. Consequently, the impact of pressure

on liquid backmixing - unlike the relationship between gas holdup and pressure—is subject to

42

differing opinions. As in most studies, there exist three main views, and the following review is

divided accordingly.

Table 2-3: Summary of liquid backmixing studies

Author Physical system

(gas/liquid/solid)

Experimental conditions

(Pmax [MPa]/T [°C]/DC [m])

Holcombe et al. [123] N2/H2O 7.1/-/0.1

derived correlation

Therning and Rasmuson

[71]

Air/H2O 0.66/20/0.15

Wilkinson et al. [118] N2/H2O 1.5/-/0.158

derived correlation

Houzelot et al. [122] Air,He/H2O, H2O

sucrose solutions

0.3/-/0.05

derived correlation

Lorenz et al. [119] N2/H2O,ethanol,1-

butanol

0.5/25 – 50/0.1

Yang and Fan [120] Air,N2/H2O, Paratherm 10.3/ambient/0.0508, 0.1016

Onozaki et al. [121] H2 rich gas/mixture of

recycle oil and coal

16.8/387 – 417/1

Sangnimnuan et al. [110] Air/tetralin/coal 15/ambient–384/0.019

derived correlation

Tarmy et al. [87] N2/heptane/raw coal 0.52/25/0.024 – 0.61

The first group describes enhanced liquid backmixing as a result of pressurized conditions.

This group includes Wilkinson et al. [118], Lorenz et al. [119] and Therning and Rasmuson

[71]. Lorenz et al. studied H2O, ethanol and 1-butanol/N2 systems in a 0.1 m column with a

height of 2.1 m. The operating pressure was varied between 0.1 and 0.5 MPa. Column

temperature was also varied between 25 and 60°C, while ug was adjusted to be between 0.01

and 0.21 m/s. The authors’ aim was to study the extent of axial liquid mixing and to develop a

CFD model for calculating the residence time distribution of the liquid phase. Lorenz et al.

43

explained that the increase in backmixing at elevated pressure is caused by reduced eddy

diffusivity and lower liquid circulation velocities. This in turn is related to a narrower bubble size

distribution that favors bubble sizes at high pressure that are smaller than those under

atmospheric conditions. The same opinion is shared by Wilkinson et al., who conducted their

experiments in a 0.158 m diameter column filled with water as the liquid phase and sparged

with nitrogen as the dispersed phase. The pressure itself was varied between 0.1 and 1.5 MPa.

Their results are shown in Figure 2.14.

Figure 2.14 Measured dispersion coefficients, Wilkinson et al. [118]

The investigators argued that small bubbles occur more often at elevated system pressures,

which in turn leads to a flatter liquid radial velocity profile. As a consequence, having fewer

large bubbles in the reactor reduces interaction between liquid flowing up and liquid flowing

down, which in turn reduces radial dispersion. Figure 2.14 shows that the effect of pressure on

liquid dispersion is only present at higher superficial gas velocities, i.e., more than 0.05 m/s,

which marks the point of transition between homogeneous and heterogeneous flow. It can be

assumed that beyond this point more large bubbles are present at atmospheric pressure and

therefore, according to the authors, the amount of axial mixing decreases. In addition holdup

rises with increasing superficial gas velocity which in turn increase the extent of liquid mixing.

On this basis, Wilkinson et al. were able to describe the extent of liquid mixing at high pressures

using data obtained under atmospheric conditions. They did so by assuming the dispersion

44

coefficient to be based on the liquid volume fraction and developing a calculation method

capable of predicting the amount of backmixing at pressurized conditions if the gas holdup at

this operating point is known (Eq. 2-29).

経銚掴岫喧 伴 欠建兼岻 噺 経銚掴岫欠建兼岻 岫怠貸悌虹岫銚痛陳岻岻岫怠貸悌虹岫椎苧銚痛陳岻岻 (2-29)

Therning and Rasmuson also found a relationship between liquid dispersion and pressure.

They investigated a 0.15 m diameter column packed with plastic ball rings (ring diameters =

0.015 mm) at pressures ranging from 0.1 to 0.56 MPa. Their studies were conducted at a

single superficial gas velocity of 0.135 m/s (see Figure 2.15), which can be seen as a main

limitation both of their experiments and of the conclusions drawn. Nevertheless Therning and

Rasmuson explained their results by using Wilkinson et al.’s argument (given above) and

further stated that the packing serves as a coalescence suppressor. The magnitude of the

results for atmospheric pressure, 0.5 and 0.43 MPa (obtained by Therning and Rasmuson and

Wilkinson et al., respectively) are the same, which is rather surprising as liquid backmixing

should be lower when using packings than is the case with empty bubble columns.

Figure 2.15 Experimentally obtained dispersion coefficients at ug = 0.135 m/s, Therning and Rasmuson [71]

An indirect proportionality between pressure and liquid dispersion was found by Yang and Fan

[120], Onozaki et al. [121] and Tarmy et al. [87]. Yang and Fan found enhanced liquid

dispersion to be highly dependent on superficial gas velocity, while the influence of superficial

45

liquid velocity was weaker. The authors also found that the reduction in liquid mixing in the

presence of elevated pressure is explained by the occurrence of smaller bubbles, which

produce less developed bubble wakes and thus induce a lesser amount of liquid turbulence.

This explanation is in turn completely contrary to Wilkinson et al., whose attitude has been

cited above. It is worth remarking that Yang and Fan’s study was carried out in two bubble

columns with diameters of 0.0508 and 0.1016 m. The range of pressure and superficial liquid

and gas velocities applied is also worth noting. The pressure ranged up to 10.3 MPa while the

superficial gas and liquid velocities were varied up to 0.4 and 0.01 m/s, respectively. As

mentioned above, the aim of this investigation was to study the effect of column dimensions,

superficial gas velocities, sparger design and pressure on the axial liquid dispersion coefficient

and gas holdup. To measure the axial liquid dispersion, the authors used a thermal tracer

technique that involved obtaining the axial temperature profile after a thermal pulse was

applied to the system. The dispersion coefficient was then calculated by fitting experimental

data on a one-dimensional axial dispersion model. The physical system studied used nitrogen

as the gas phase and Paratherm NF as the liquid phase. One of the main results of their studies

was that increasing pressure decreases the axial dispersion dramatically, especially for larger

column diameters and higher superficial gas velocities. Another point mentioned is that for

column diameters greater than 0.1 m, higher pressures due to weaker wall effects were found

to have practically no observable influence on gas holdup. Nevertheless, the larger column

diameter is still below the limit cited above (0.15 m), and because mixing is accompanied by

gas holdup, wall effects could have affected the measurements. Figure 2.16 depicts some of

their results in order to visualize the above discussion. Results are presented for ul = 0.0017

(d = 0.1016 m) and 0.0018 m/s (d = 0.0506 m). An increase in liquid mixing of about 100% can

be observed. This can be the result of larger scale of liquid circulation in larger columns.

Comparing Figure 2.16 to the results of Wilkinson et al. [118], which are depicted in Figure

2.14, shows that the amount of liquid dispersion in Paratherm NF, as used by Yang and Fan

[120], is significantly lower than in water. With respect to the discussion above, this can be

attributed to the presence of smaller bubbles in organic liquids.

46

Figure 2.16 Effect of pressure and column dimensions on liquid dispersion according to Yang and Fan [120]

Tarmy et al. compared their measured dispersion coefficients, which were obtained in slurry

bubble columns at pressures of up to 0.56 MPa, to predictions of correlations valid for

atmospheric conditions. The measured values of axial dispersion are, according to Tarmy et

al., 2.5 times lower than the model predictions. One conclusion of Tarmy et al.’s study is that

correlations valid for atmospheric conditions should not be used for estimating liquid dispersion

coefficients at higher pressures.

A third group of contributors found that pressure had no influence on liquid mixing in either

direction. This particular group includes Houzelot et al. [122], Holcombe et al. [123] and

Sangnimnuan et al. [110]. Houzelot et al.’s results are based on quite limited operating

parameters. The maximum pressure applied was 0.3 MPa, which cannot be treated as high

pressure. The column diameter was also very small (0.05 m). Liquid axial dispersion

coefficients had been obtained by adding salt as a tracer, and using a conductivity probe to

detect its concentration. As indicated previously, the investigators found that pressure did not

have any influence, nor did liquid velocity or viscosity. Consequently, the proposed correlation

for predicting axial dispersion is only dependent on gas superficial velocity (Equation 2-30).

Because of the limited range of parameter variation, the applicability of this correlation for

describing liquid mixing in industrial scale bubble columns should be tested carefully.

47

経銚掴 噺 ど┻どね憲直待┻替胎 (2-30)

Holcombe et al. used a larger column with a diameter of 0.1 m, applied pressures of 0.3, 5.1

and 7.1 MPa, and measured thermal dispersion coefficients, which can be correlated to mass

dispersion coefficients. Holcombe et al. likewise found that liquid velocity had no influence on

axial dispersion. Because Holcombe et al. came to the conclusion that gas superficial velocity

is the main influencing factor for liquid dispersion, the correlation they developed (Equation 2-

31) uses gas velocity and, like Houzelot et al., column diameter as input variables.

経銚掴 噺 な┻には経頂替 戴斑 憲直待┻替滞 (2-31)

Sangnimnuan et al. examined a small diameter slurry column (d = 0.019 m) at pressures of

up to 15 MPa and temperatures as high as 384°C. The range of liquid and gas superficial

velocities investigated was limited to 0.001 – 0.003 m/s and 0.02 – 0.012 m/s, respectively. As

the method of measurement, the authors used gas chromatography for analyzing the pulse

response of the system. The result obtained was that liquid axial dispersion is proportional to

gas superficial velocity taken to the power of 1.53, which is shown in Equation (2-32). 経銚掴 噺 なの┻ね憲直怠┻泰戴 (2-32)

Equation (2-32) obviously does not account for the influence of diameter or other column-

specific details. Because its diameter was also very small, the column used bore no relation to

technical reactors. Possibly because of the small diameter, Sangnimnuan et al. applied very

low gas and liquid flows, which is not necessarily a drawback.

To conclude this section on liquid backmixing, it must be stated that each of the suggested

correlations should be used within their boundaries. Usually this is logical, but as the available

data on backmixing are scarce and sometimes contradictory, engineers need to use the

existing design equations and might add their own experience to the results obtained. From

an industrial point of view, more studies need to be carried out under pressurized conditions

in pilot-scale columns and using organic solvents or mixtures of organic solvents, as long as

the physical properties are still known. These experiments should also cover a wide range of

superficial liquid and gas velocities. These studies are necessary due to the wealth of industrial

48

applications for bubble column reactors and their unique operating parameters (such as

specific requirements for phase residence times).

2.6 Mass transfer studies

The available mass transfer studies at pressures above atmospheric are listed in Table 2-4.

Table 2-5: Summary of mass transfer studies at elevated pressures

Author Physical system

(gas/liquid/solid)

Experimental conditions

(Pmax [MPa]/T [°C]/DC [m])

Han, Al-Dahhan [127] N2/H2O 1.0/-/0.162

Letzel et al. [85] N2/H2O 1.3/ambient/0.15

derived correlation

Chilekar et al. [107] Air,N2/H2O,Isopar

M/carbon,silica

1.3/ambient/0.15

Jordan et al. [114] O2,N2/

H2O,ethanol,tolouene,1-

butanol

1.0/20/0.115

derived correlation

Kojima et al. [88] N2-O2 mixture/H2O,

aqueous enzyme and

citric acid solutions

1.1/17 – 27/0.1016

derived correlation

Maalej et al. [126] N2,CO2/aqeous

solutions of NaOH and

Na2CO3-NaHCO3

2.0/20/0.046

Wilkinson et al. [124] Air/aqueous solution of

sodium sulfite

0.4/20/0.158

derived correlation

Kang et al. [115] air/viscous medium 0.6/-/0.152

Lau et al. [116] Air,N2/Paratherm NF 4.24/ambient – 92/0.0508 –

0.1016

derived correlation

Nedeltchev et al.

[128]

- -

derived correlation

49

Han and Al-Dahhan [127] measured the gas-liquid mass transfer coefficient in a 0.162

diameter column. Three different pressure stages were utilized: 0.1 MPa, 0.4 MPa and 1.0

MPa. The values of mass transfer were obtained using an optical oxygen probe and then fitted

to three models: axial dispersion, continuous stirred tank, and recycle with cross flow. Of these

models the axial dispersion model was found to best represent the measured values. A

significant increase in the measured kla values was noted, which can be attributed to the

smaller bubble sizes and higher gas holdups that occur at elevated pressures, ultimately

leading to increased interfacial areas. A decrease in the liquid-side mass transfer coefficient kl

itself was found, mostly notable at pressures of up to 0.4 MPa. The authors explain this

behavior with the penetration theory: smaller bubbles rise more slowly, increasing the

residence time of each bubble at the interfacial area and thus reducing mass transfer

efficiency. Letzel et al. [85] and Wilkinson et al. [124] conducted mass transfer experiments

with similar column dimensions and physical properties. Besides coming to the same

conclusion with respect to the relationship between pressure and mass transfer, Letzel et al.

also defined a ratio of mass transfer coefficients to gas holdup (kla/eps) that seems to be

constant at a value of 0.5 up to a pressure of 1.0 MPa. The authors conclude that estimating

mass transfer coefficients at pressures above atmospheric should be sufficiently accurate

provided the gas holdup is known at these operating points. Wilkinson et al., by contrast,

reported that the kla/eps ratio increased with increasing pressure and superficial gas velocity.

Both are primarily attributable to decreased bubble sizes. While increased gas throughputs

enhance turbulence, and rising turbulence induces bubble breakup, increasing pressure

promotes the formation of smaller bubbles (see previous discussion). As a result, the pressure

effect is more pronounced at superficial gas velocities below 0.03 m/s. In addition, Kang et al.

[115] also used a similar bubble column and investigated the effect of gas distribution and

liquid viscosity on mass transfer. They concluded that a near-wall gas distribution is preferable

to a centered mode of distribution, and, contrary to the findings of Letzel et al., pressure-

enhanced mass transfer is more developed at higher superficial gas velocities. According to

50

Kang et al., increased liquid viscosity will lead to decreased mass transfer rates by improving

bubble coalescence, which is in agreement with observations on single bubble behavior.

Studies incorporating liquids other than water were conducted by Jordan et al. [114], Kojima

et al. [88] and Lau et al. [116] in bubble columns that were comparable in terms of diameter.

Among these researchers, Lau et al. investigated mass transfer in two columns of different

diameters (see Table 2-5 for details). In the authors’ opinion, mass transfer coefficients are

larger in the smaller column because wall effects cause higher gas holdups, thus enlarging

interfacial areas and causing kla to rise. In other words, an increase in pressure also increases

the values of kla (Figure 2.17).

Figure 2.17 Increase in kla due to pressure (data from Lau et al. [116], d = 0.1016 m)

Their ability to study the effect of temperature on mass transfer is also worth mentioning.

Because temperature significantly changes liquid properties such as surface tension and

viscosity, which are directly linked to single bubble behavior, a rise in temperature could be

observed to increase mass transfer as well (Figure 2.18). Moreover, liquid properties are also

linked to bubble shape and size as was mentioned in the introductory chapters. This results in

different contact angles at the gas-liquid interface and also affects the Schmidt number. From

the Schmidt number one can see that increased liquid viscosity reduces mass transfer

efficiency.

51

Figure 2.18 Effect of temperature on kla (data from Lau et al. [116] , d = 0.1016 m, p = 0.1 MPa)

This is due to a reduction in liquid viscosity and surface tension, which promotes bubble

breakup. By considering the penetration theory, Lau et al. concluded that the lower rise velocity

of a smaller bubble yields lower values of kl. This is in agreement with the findings from Han

and al-Dahhan, and demonstrates two competing effects of temperature: reducing surface

tension and viscosity to provide higher interfacial areas while increasing contact times between

a bubble and the liquid interface. As kla rises with temperature, the effect of temperature on

the interfacial area must be dominant over its other effect. Jordan et al., Kang et al. and Kojima

et al. found that mass transfer rates increased with pressure, especially at higher superficial

gas velocities. A comparison with literature data obtained by Öztürk et al. [125], who used

different gases at ambient pressure to study the effect of gas density on mass transfer,

revealed that the weak dependency on gas density found by Öztürk et al. is much higher under

pressurized conditions and is proportional to the power of 0.24 instead of 0.04.

Another publication, namely Maalej et al. [126], deals with mass transfer inside a column with

a smaller diameter (0.046 m) and equipped with a sintered plate gas distributor. It follows that

wall and sparger effects on gas holdup need to be considered when discussing mass transfer

results. Despite these experimental complications, pressure conditions of up to 2 MPa were

generated for the mass transfer studies, which showed that interfacial area and the gas- and

liquid-side mass transfer coefficients decrease with pressure. Maalej et al. explain this

52

behavior as a reduction in superficial gas velocity due to an increase in gas density caused by

elevated pressures. If the superficial gas velocity decreases, less gas (and thus bubbles) are

present in the system, which ultimately has to decrease interfacial areas and mass transfer

rates. To avoid this, Maalej et al. adapted the gas flow to each pressure condition, thus

maintaining a constant superficial gas velocity, which was then comparable to results from

other experiments. After this adjustment, the interfacial area was found to increase with

pressure. Further evidence of this contribution is that the values of the mass transfer

coefficients do not change with pressure. Therefore the volumetric mass transfer coefficient

rises with pressure, as interfacial areas tend to become larger.

2.7 Heat transfer

Heat transfer studies in bubble columns at elevated pressures are even more of a rarity than

studies of any other parameter discussed within this article. Correctly determining heat transfer

is a prerequisite for correctly calculating heat exchanger areas in order to dissipate reaction

heat and to ensure that the reactor remains thermally stable. Hence the design of specific

internals, such as heat exchanger tubes or other cooling or heating devices, is linked to heat

transfer coefficient estimation. Only five studies are available to date that investigate heat

transfer at pressures higher than atmospheric. These are listed in Table 2-6.

Table 2-6: Summary of heat transfer studies at elevated pressures

Author Physical system

(gas/liquid/solid)

Experimental conditions

(Pmax [MPa]/T [°C]/DC [m])

Holcombe et al. [123] N2/H2O 7.1/-/0.1

derived correlation

Wu et al. [130] air/H2O 1/-/0.16

Cho et al. [129] Air/viscous medium 0.6/-/0.152

Lin and Fan [91] N2/ Paratherm NF 15.2/27/0.0508

Yang et al. [131] N2/Paratherm

NF/glass beads

4.2/up to 81/0.1016

derived correlation

53

Despite of the small number of publications, the results from the different research groups are

contradictory. All of the researchers indicated here do, at least, claim that heat transfer in

bubble columns is dependent on superficial gas velocity, which is in accordance with studies

at atmospheric pressure (summarized by Hulet et al. [40], among others). Regarding the effect

of pressure, Cho et al. [129] and Lin and Fan [91] found that heat transfer coefficients increase

with pressure (Figure 2.19), while Wu et al. [130] and Yang et al. [131] claim that heat transfer

coefficients decrease with pressure (Figure 2.20). Holcombe et al. [123] actually found that

heat transfer was not dependent on system pressure and argued that changes in heat transfer

coefficients are mainly caused by varying the superficial gas velocity.

Figure 2.19 Increase of heat transfer coefficients with pressure (data from Lin and Fan [91])

54

Figure 2.20 Decrease of heat transfer coefficients with pressure (data from Yang et al. [131])

Liquid phase velocity makes only a weak contribution to heat transfer, especially at low liquid

velocities of less than 0.005 m/s. Above this threshold, Holcombe et al. did not observe liquid

velocity to have any significant influence on heat transfer. To account for the effect of liquid

velocities of up to 0.05 m/s on heat transfer, Holcombe et al. proposed the following correlation

in terms of a Stanton number (Eq. 2-33). This correlation is an altered version of the one

previously reported by Steiff et al. [132]. 鯨建 噺 ど┻な岫迎結直繋堅直鶏堅鎮態岻貸待┻態滞exp岫に┻ね 茅 など貸替迎結鎮岻 (2-33)

Equation (2-33) is valid for air/water systems only, so caution should be exercised if using it to

estimate heat transfer in the liquid mixtures encountered in industrial reactors.

Cho et al. carried out their experiments in a 0.152 m diameter column at pressures between

atmospheric and 0.6 MPa, focusing primarily on the influence of liquid viscosity on heat

transfer. Unfortunately, no detailed information about the liquid phase was given, except that

the viscosity varied between 1 and 38 mPas. The results obtained, indicate that heat transfer

coefficients tend to rise due to increasing pressure and gas superficial velocity, and in response

to decreasing liquid viscosity. The authors attribute this behavior to the higher gas holdups and

smaller bubble sizes observed at elevated pressures and lower viscosities, as this correlates

55

to a higher degree of turbulence within the gas-liquid dispersion. As indicated above, the heat

transfer trend that these investigators reported is similar to the one published by Lin and Fan.

The heat transfer coefficients measured by Lin and Fan, however, are lower than those

reported by Cho et al., who applied a lower maximum pressure (0.6 MPa) in a 0.152 m

diameter column. One explanation for the differences in the measured heat transfer values

might also be that the physical system examined was different, resulting in different dispersed

phase holdups and bubble behavior. Another issue is that the column diameter (0.0508 m) is

very small, which might also influence gas holdup values, and these in turn are directly linked

to the measured heat transfer values. Wu et al. and Yang et al. both reported that heat transfer

coefficients shrink with increasing operating pressure. Wu et al. considered an air/water

system in a 0.16 m diameter column at pressures of up to 1 MPa, while Yang et al. examined

nitrogen/Paratherm NF in a slurry bubble column filled with glass beads (d = 0.1016 m) at

temperatures of up to 81°C and pressures varying between atmospheric and 4.2 MPa. Both

authors concluded that pressure directly influences the physical properties of the examined

system—especially liquid viscosity, which decreases when pressure is applied. Furthermore,

they propose that smaller bubbles produce less turbulence in the liquid phase due to smaller

bubble wakes. As such, decreasing bubble sizes due to increasing pressure is given as the

explanation for the decrease in heat transfer coefficients under pressurized conditions. In

addition, Yang et al. also proposed a correlation for predicting heat transfer coefficients in

slurry bubble columns based on the slurry properties (Equation 2-34).

鯨建陳 噺 ど┻どぬば 釆岫迎結陳繋堅鶏堅陳怠┻腿胎岻岫 悌虹怠貸悌虹岻挽貸待┻態態 (2-34)

As the superficial gas velocity was varied up to 0.2 m/s and pressure up to 4.2 MPa, this

correlation should be applicable to a broad range of industrially relevant operating conditions.

Another positive aspect of this study is that it investigated an organic liquid medium, Paratherm

NF heat transfer oil, making this equation useful for predicting heat transfer coefficients in

systems other than water. Unfortunately, the column diameter established is smaller than 0.15

56

m, and wall effects could therefore have affected the gas holdup measurements and, by

extension, heat transfer results, especially at large superficial gas velocities.

A few points are worth emphasizing in summary: First of all, the number of available

publications is relatively small, which limits the amount of available data on heat transfer at

elevated pressure in bubble column reactors. Uncertainties also arise because the available

data were obtained from either small-scale bubble columns with organic liquids or from larger

diameter columns operated with water as the liquid phase. As has been stated previously in

this article, experiments carried out with water yield different results than measurements with

organic solvents because the physical properties differ significantly. Furthermore, with the

exception of Cho et al. [129], all studies were performed in empty bubble columns. Heat

transfer in processing units is provided by internal heat exchangers of various geometrical

configurations (tube bundles, spiral tubes, horizontal heat exchangers to name a few). These

internals alter the hydrodynamics of the column and therefore the heat transfer intensity. The

arising question is how to extrapolate data obtained in empty columns to columns with

internals. A promising tool might be CFD simulations [133] , but these simulations do also

depend on submodels which need to be validated.

2.8 Conclusions

The publications introduced above demonstrate that there exists a gap between research

conducted so far and the industrial needs for designing and engineering production-scale

bubble columns. Fortunately, there are several publications that are dedicated to the main

fields of interest—gas holdup, backmixing, and mass and heat transfer. Unfortunately, the

results are partly controversial or derived from small-scale columns operated with water as the

liquid phase. It has been demonstrated that the results obtained in aqueous systems cannot

be fully extrapolated to the liquids used in industrial applications. Problems arise not only in

preliminary engineering tasks, in which mostly short-cut models are used for estimating reactor

performance and size. More serious difficulties occur if detailed calculations are needed for

determining the flow field in bubble columns with and without internals. Similarly, there are few

57

published experimental results available on hydrodynamic parameters for industrial relevant

systems and dimensions that could validate existing models for phenomena such as

turbulence. More measurements in systems such as these should therefore be done to further

improve our understanding of the complex fluid dynamics encountered in bubble columns and

in other multiphase contactors. As the experimental conditions of each publication differ, these

experiments need to be clearly defined with respect to gas sparging, liquid flow, physical

properties of the liquid (and gas), dimensions of the experimental plant and operating

variables. On the other hand, the evaluation of the experimental data in terms of correlations

to predict the mentioned hydrodynamic parameters should ideally contain no fitting parameters

and need to be derived from physical phenomena. In practice, this might not be possible at

this point but the number of fitting parameters need to be reduced to a minimum. Even

correlations derived with the help of generally accepted methods like dimensional analysis fail

to predict bubble column hydrodynamics if used beyond their experimental boundaries. To

identify such a correlation a more fundamental approach which focusses on general

parameters like gas holdup on various scales from laboratory to pilot scale columns at

industrial operating conditions should be pursued as in this thesis. The generated experimental

data will then be used to identify models which can be implemented in short-cut approximation

methods and on the other hand the data is useful to validate more physically correct calculation

methods like CFD simulations.

When compared to the full body of literature on bubble columns, the articles described above

clearly reveal that publications on bubble column hydrodynamics under pressurized conditions

comprise only a small percentage of the whole. The reasons behind this are worth

investigating.

To begin with, one should keep in mind that operating pressurized vessels of industrially

relevant dimensions and filled with organic solvents requires a certain degree of laboratory

infrastructure and safety considerations. As these two requirements are usually directly linked

to the financial situation of a specific research project, it should come as no surprise that very

few publications meet the criterion of large columns used under industrial operating conditions.

58

Another issue is the accessibility of the desired parameters to be investigated. Pressurized

columns are not made of glass or plastics, and, if operated at high pressures and filled with

flammable and environmentally hazardous organic substances, they must be properly sealed

to prevent accidents. This reduces the number of available measurement techniques to a

limited number of options and leads to the conclusion that basic research alone is not enough.

Reliable measurement techniques also need to be developed in order to examine bubble

column hydrodynamics, preferably in a non-invasive way. The next concern is likewise readily

apparent, as it concerns the organic materials necessary for conducting experimental runs: a

pilot-scale bubble column might require at least one metric ton of liquid if more than a few

experiments are desired. If the vessel is to be operated under pressure, a huge amount of gas

will be needed as well. More extensive automation and control of the experimental facility is

desirable for safety reasons, which again raises the costs of the whole apparatus. Finally, the

time frame needed for modifying the facility—which may be necessary during the

measurement period—will become longer as the scale of the column increases. This would

require additional technical staff, which is often not available at universities. A possible solution

to these problems is to have universities, scientific institutes and industrial corporations work

together more closely, provided a suitable platform exists to ensure that such joint projects

serve the needs of each project member. One of these projects is described in more detail by

Becker et al. [134]. Although this specific project is limited to Germany, it demonstrates that

close collaboration between academia and industry is possible and encompasses scientific

fields ranging from single bubble behavior to hydrodynamics of large-scale pilot facilities.

Additionally it would be helpful if the demands of industrial production are clearly

communicated to find organic model fluids to substitute the processed fluids. In a following

step the influence of internals needs to be more properly investigated as there are practically

no empty bubble columns in production plants. However, this is also a very difficult task as this

involves the protection of corporate intellectual property due to intense economic competition.

59

2.9 Notation

List of symbols

Symbol Meaning Unit

a major axis m

b, くb

cp

minor axes

heat capacity

m

J/(kgK)

d diameter m

Dax axial dispersion coefficient m²/s

Db Bubble diameter m

E aspect ratio -

Eo Eötvös-number [-]

FB buoyancy force N

FD drag force N

Fr Froude-number [-]

H

h

height

heat transfer coefficient

m

W/(m²K)

kla mass transfer coefficient 1/s

Mo Morton-number [-]

p pressure MPa

Re Reynolds-number [-]

St = h/(cp,lugとl)

Stm = h/(cp,mugとm)

Stanton-number, based on

liquid properties

Stanton-number, based on

slurry properties

[-]

[-]

T temperature K

u superficial velocity m/s

Uabs,b absolute bubble velocity m/s

ub relative bubble velocity m/s

け deformation factor -

60

i holdup [-]

こ Drag coefficient -

そ Wave length m

た dynamic viscosity Pas

と density kg/m³

Subscripts

Subscript Meaning

g gas

l liquid

lb large bubble

sb small bubble

atm atmospheric pressure

m slurry

2.10 References

[1] Schumpe, A., Y. Serpemen, and W.D. Deckwer, Effective Application of Bubble

Columns. German Chemical Engineering, 1979. 2(4): p. 234-241. [2] Dudukovic, M.P., F. Larachi, and P.L. Mills, Multiphase reactors – revisited. Chemical

Engineering Science, 1999. 54(13–14): p. 1975-1995. [3] Weber, M., Large bubble columns for the oxidation of cumene in phenol processes.

Chemical Engineering and Technology, 2002. 25(5): p. 553-558. [4] Sifniades, S., A.B. Levy, and H. Bahl, Acetone, in Ullmann's Encyclopedia of Industrial

Chemistry2000, Wiley-VCH Verlag GmbH & Co. KGaA. [5] J. Sheehan, R., Terephthalic Acid, Dimethyl Terephthalate, and Isophthalic Acid, in

Ullmann's Encyclopedia of Industrial Chemistry2000, Wiley-VCH Verlag GmbH & Co. KGaA.

[6] Oppenheim, J.P. and G.L. Dickerson, Adipic Acid, in Kirk-Othmer Encyclopedia of

Chemical Technology2000, John Wiley & Sons, Inc. [7] Dadyburjor, D.B., Z. Liu, and B.H. Davis, Coal Liquefaction, in Kirk-Othmer

Encyclopedia of Chemical Technology2000, John Wiley & Sons, Inc. [8] Junker, B., Fermentation, in Kirk-Othmer Encyclopedia of Chemical Technology2000,

John Wiley & Sons, Inc. [9] Merchuk, J., S. Ben-Zvi, and K. Niranjan, Why use bubble-column bioreactors? Trends

in Biotechnology, 1994. 12(12): p. 501-511. [10] Han, S. and C.D. Chang, Fuels, Synthetic, Liquid Fuels, in Kirk-Othmer Encyclopedia

of Chemical Technology2000, John Wiley & Sons, Inc. [11] Deen, N.G., et al., Bubble Columns, in Ullmann's Encyclopedia of Industrial

Chemistry2000, Wiley-VCH Verlag GmbH & Co. KGaA.

61

[12] Deckwer, W.D., Reaktionstechnik in Blasensäulen. 1 ed1985, Frankfurt am Main: Salle+Sauerländer.

[13] Gerstenberg, H., Blasensäulen-Reaktoren. Chemie Ingenieur Technik, 1979. 51(3): p. 208-216.

[14] Mersmann, A., Gas/Flüssig-Reaktoren. Chemie Ingenieur Technik, 1989. 61(2): p. 97-104.

[15] Kulkarni, A.V. and J.B. Joshi, Design and selection of sparger for bubble column

reactor. Part II: Optimum sparger type and design. Chemical Engineering Research and Design, 2011. 89(10): p. 1986-1995.

[16] Kulkarni, A.V. and J.B. Joshi, Design and selection of sparger for bubble column

reactor. Part I: Performance of different spargers. Chemical Engineering Research and Design, 2011. 89(10): p. 1972-1985.

[17] Shah, Y.T., G.J. Stiegel, and M.M. Sharma, Backmixing in Gas-Liquid Reactors. AIChE Journal, 1978. 24(3): p. 369-400.

[18] Bałdyga, J., J.R. Bourne, and S.J. Hearn, Interaction between chemical reactions and

mixing on various scales. Chemical Engineering Science, 1997. 52(4): p. 457-466. [19] Levenspiel, O. and K.B. Bischoff, Backmixing in the Design of Chemical Reactors.

Industrial & Engineering Chemistry, 1959. 51(12): p. 1431-1434. [20] Kantarci, N., F. Borak, and K.O. Ulgen, Bubble column reactors. Process Biochemistry,

2005. 40(7): p. 2263-2283. [21] Ruzicka, M.C., et al., Effect of bubble column dimensions on flow regime transition.

Chemical Engineering Science, 2001. 56(21–22): p. 6117-6124. [22] Vial, C., et al., Influence of gas distribution and regime transitions on liquid velocity and

turbulence in a 3-D bubble column. Chemical Engineering Science, 2001. 56(3): p. 1085-1093.

[23] Ruzicka, M.C., et al., Homogeneous–heterogeneous regime transition in bubble

columns. Chemical Engineering Science, 2001. 56(15): p. 4609-4626. [24] Thorat, B.N. and J.B. Joshi, Regime transition in bubble columns: experimental and

predictions. Experimental Thermal and Fluid Science, 2004. 28(5): p. 423-430. [25] Jin, H., et al., Measurement of gas holdup profiles in a gas liquid cocurrent bubble

column using electrical resistance tomography. Flow Measurement and Instrumentation, 2007. 18(5–6): p. 191-196.

[26] Shaikh, A. and H. Al-Dahhan Muthanna, A Review on Flow Regime Transition in

Bubble Columns. International Journal of Chemical Reactor Engineering, 2007. 5(1). [27] Hikita, H., et al., Gas hold-up in bubble columns. The Chemical Engineering Journal,

1980. 20(1): p. 59-67. [28] Akita, K. and F. Yoshida, Gas Holdup and Volumetric Mass Transfer Coefficient in

Bubble Columns. Effects of Liquid Properties. Industrial & Engineering Chemistry Process Design and Development, 1973. 12(1): p. 76-80.

[29] Reilly, I.G., et al., A correlation for gas holdup in turbulent coalescing bubble columns. The Canadian Journal of Chemical Engineering, 1986. 64(5): p. 705-717.

[30] Krishna, R. and J. Ellenberger, Gas holdup in bubble column reactors operating in the

churn-turbulent flow regime. AIChE Journal, 1996. 42(9): p. 2627-2634. [31] Joshi, J.B.P., U. V. ; Prasad, C. V. S. ; Phanikumar, D. V. ; Deshpande, N. S. ; Thorat,

B. N., Gas hold - up structures in bubble column reactors. Proceedings of the Indian National Science Academy, 1998. 64A(4): p. 441-567.

62

[32] Duduković, M.P., Tracer Methods in Chemical Reactors. Techniques and Applications, in Chemical Reactor Design and Technology, H. Lasa, Editor 1986, Springer Netherlands. p. 107-189.

[33] Geike, R., et al., Investigation of Residence Time Distribution in Two-Phase Bubble

Columns - Analysis and Problems. Verweilzeituntersuchungen in Zweiphasenblasensaeulen - Auswertung und Probleme., 1987. 39(3): p. 98-101.

[34] Mills, P.L., W.P. Wu, and M.P. Duduković, Tracer analysis in systems with two-phase

flow. AIChE Journal, 1979. 25(5): p. 885-890. [35] Jung, S., et al., One-Dimensional Modeling and Simulation of Bubble Column Reactors.

Chemical Engineering & Technology, 2010. 33(12): p. 2037-2043. [36] Ohki, Y. and H. Inoue, Longitudinal mixing of the liquid phase in bubble columns.

Chemical Engineering Science, 1970. 25(1): p. 1-16. [37] Hikita, H. and H. Kikukawa, Liquid-phase mixing in bubble columns: Effect of liquid

properties. The Chemical Engineering Journal, 1974. 8(3): p. 191-197. [38] Kantak, M.V., S.A. Shetty, and B.G. Kelkar, Liquid Phase Backmixing in Bubble

Column Reactors - a New Correlation. Chemical Engineering Communications, 1994. 127(1): p. 23-34.

[39] Lefebvre, S., J. Chaouki, and C. Guy, Phase mixing modeling in multiphase reactors

containing gas bubble: A review. International Journal of Chemical Reactor Engineering, 2004. 2.

[40] Hulet, C., et al., Literature review on heat transfer in two and three-phase bubble

columns. International Journal of Chemical Reactor Engineering, 2009. 7. [41] Clift, R., J.R. Grace, and M.E. Weber, Bubbles, drops, and particles1978: Academic

Press. [42] Becker, M., et al., Mehrphasenreaktoren: Zusammenspiel von Prozessentwicklung und

Hydrodynamik. Chemie Ingenieur Technik, 2012. 84(8): p. 1223-1223. [43] Rollbusch, P., et al., Hydrodynamics of High-Pressure Bubble Columns. Chemical

Engineering & Technology, 2013. 36(9): p. 1603-1607. [44] Weber, M., M. Weber, and M. Kleine-Boymann, Phenol, in Ullmann's Encyclopedia of

Industrial Chemistry2000, Wiley-VCH Verlag GmbH & Co. KGaA. [45] Bakopoulos, A., Fluid dynamics and mixing in three-phase coal and oil residue

hydrogenation sieve cascade reactors. Chemical Engineering Science, 2001. 56(17): p. 5131-5145.

[46] Steiner, R., Operating characteristics of special bubble column reactors. Chemical Engineering and Processing, 1987. 21(1): p. 1-8.

[47] Zimmermann, P.R., System and Process for Reacting a Petroleum Fraction, Honeywell/UOP, Editor 2009: USA.

[48] Eickhoff, H.R., Dr., D.-H. AG, Editor 1998: Germany. [49] Zou, B.G., P., Processes for Producing Silane in a Bubble Column, 2013, MEMC

Electronic Materials, Inc.: USA. [50] Marrucci, G., Rising velocity of a swarm of spherical bubbles. Industrial and

Engineering Chemistry Fundamentals, 1965. 4(2): p. 224-225. [51] Locket, M.J. and R.D. Kirkpatrick, Ideal bubbly flow and actual flow in bubble columns.

Trans. Inst. Chem. Eng., 1975. 53(4). [52] Ishii, M. and N. Zuber, Drag coefficient and relative velocity in bubbly, droplet or

particulate flows. AICHE. J., 1979. 25(5 , Sep. 1979, p.843-855.). [53] Krishna, R., et al., Influence of increased gas density on hydrodynamics of bubble-

column reactors. AIChE Journal, 1994. 40(1): p. 112-119.

63

[54] Simonnet, M., et al., Experimental determination of the drag coefficient in a swarm of

bubbles. Chemical Engineering Science, 2007. 62(3): p. 858-866. [55] Richardson, J.F. and W.N. Zaki, The sedimentation of a suspension of uniform spheres

under conditions of viscous flow. Chemical Engineering Science, 1954. 3(2): p. 65-73. [56] Schlüter, M., Blasenbewegung in praxisrelevanten Zweiphasenströmungen2002: VDI-

Verlag. [57] Chemieingenieurwesen, V.-G.V.u. and V. Gesellschaft, VDI Heat Atlas2010: Springer. [58] Fan, L.S. and K. Tsuchiya, Bubble wake dynamics in liquids and liquid-solid

suspensions1990: Butterworth-Heinemann. [59] Tomiyama, A., I. Kataoka, and T. Sakaguchi, Drag Coefficients of Bubbles : 1st Report,

Drag Coefficients of a Single Bubble in a Stagnant Liquid. Transactions of the Japan Society of Mechanical Engineers Series B, 1995. 61(587): p. 2357-2364.

[60] Mendelson, H.D., The prediction of bubble terminal velocities from wave theory. AIChE Journal, 1967. 13(2): p. 250-253.

[61] Tomiyama, A., et al., Terminal velocity of single bubbles in surface tension force

dominant regime. International Journal of Multiphase Flow, 2002. 28(9): p. 1497-1519. [62] Lin, T.J., K. Tsuchiya, and L.S. Fan, Bubble flow characteristics in bubble columns at

elevated pressure and temperature. AIChE Journal, 1998. 44(3): p. 545-560. [63] Fan L.; Tsuchiya, K., Bubble Wake Dynamics in Liquids and Liquid-Solid

Suspensions1990, Boston: Butterworth-Heinemann. [64] Fan, L.S., et al., Some aspects of high-pressure phenomena of bubbles in liquids and

liquid–solid suspensions. Chemical Engineering Science, 1999. 54(21): p. 4681-4709. [65] Fan, L.S., Gas-liquid-solid fluidization engineering1989: Butterworths. [66] Rollbusch, P., et al., Shortcut-Modellierung von Blasensäulenreaktoren. Chemie

Ingenieur Technik, 2013. 85(9): p. 1425-1425. [67] Parasu Veera, U. and J.B. Joshi, Measurement of Gas Hold-up Profiles in Bubble

Column by Gamma Ray Tomography: Effect of Liquid Phase Properties. Chemical Engineering Research and Design, 2000. 78(3): p. 425-434.

[68] Jin, H., M. Wang, and R.A. Williams, Analysis of bubble behaviors in bubble columns

using electrical resistance tomography. Chemical Engineering Journal, 2007. 130(2–3): p. 179-185.

[69] Widyanto, M.R., et al., Local gas holdup measurement of a bubble column using

SONIA-ultrasonic non-invasive method. Sensors and Actuators A: Physical, 2006. 126(2): p. 447-454.

[70] Tayebi, D., et al., Measurement techniques and data interpretations for validating CFD

multi phase reactor models. Chemical Engineering Communications, 2001. 186: p. 57-159.

[71] Therning, P. and A. Rasmuson, Liquid dispersion, gas holdup and frictional pressure

drop in a packed bubble column at elevated pressures. Chemical Engineering Journal, 2001. 81(1): p. 331-335.

[72] Jiang, P., et al., Flow visualization of high pressure (21 MPa) bubble column: bubble

characteristics. Chemical Engineering Research and Design, 1995. 73(A3): p. 269-274. [73] Idogawa, K., et al., Behavior of Bubbles of the Air-Water System in a Column under

high Pressure. International chemical engineering, 1986. 26(3): p. 468-474. [74] Idogawa, K., et al., Effect of gas and liquid properties on the behavior of bubbles in a

column under high pressure. International chemical engineering, 1987. 27(1): p. 93-99. [75] Pohorecki, R., W. Moniuk, and A. Zdrójkowski, Hydrodynamics of a bubble column

under elevated pressure. Chemical Engineering Science, 1999. 54(21): p. 5187-5193.

64

[76] Pohorecki, R., et al., Hydrodynamics of a pilot plant bubble column under elevated

temperature and pressure. Chemical Engineering Science, 2001. 56(3): p. 1167-1174. [77] Krishna, R., J.M.v. Baten, and M.I. Urseanu, Scale Effects on the Hydrodynamics of

Bubble Columns Operating in the Homogeneous Flow Regime. Chemical Engineering & Technology, 2001. 24(5): p. 451-458.

[78] Shah, Y.T., et al., Design Parameters Estimations for Bubble Column Reactors. AIChE Journal, 1982. 28(3): p. 353-379.

[79] Forret, A., et al., Influence of scale on the hydrodynamics of bubble column reactors:

an experimental study in columns of 0.1, 0.4 and 1.0 m diameters. Chemical Engineering Science, 2003. 58(3–6): p. 719-724.

[80] Wilkinson, P., A. Spek, and L. van Dierendonck, Design parameters estimation for

scale-up of high-pressure bubble columns. AIChE Journal, 1992. 38(4): p. 544-554. [81] Kulkarni, A.A. and J.B. Joshi, Bubble formation and bubble rise velocity in gas-liquid

systems: A review. Industrial and Engineering Chemistry Research, 2005. 44(16): p. 5873-5931.

[82] Urseanu, M.I., et al., Influence of operating pressure on the gas hold-up in bubble

columns for high viscous media. Chemical Engineering Science, 2003. 58(3–6): p. 697-704.

[83] Wilkinson, P.M. and L.L. v. Dierendonck, Pressure and gas density effects on bubble

break-up and gas hold-up in bubble columns. Chemical Engineering Science, 1990. 45(8): p. 2309-2315.

[84] Kang, Y., et al., Bubble properties and pressure fluctuations in pressurized bubble

columns. Chemical Engineering Science, 2000. 55(2): p. 411-419. [85] Letzel, H.M., et al., Gas holdup and mass transfer in bubble column reactors operated

at elevated pressure. Chemical Engineering Science, 1999. 54(13–14): p. 2237-2246. [86] Letzel, H.M., et al., Influence of elevated pressure on the stability of bubbly flows.

Chemical Engineering Science, 1997. 52(21-22): p. 3733-3739. [87] Tarmy, B.L., et al. Three phase hydrodynamic characteristics of the eds coal

liquefaction reactors: their development and use in reactor scaleup. 1984. Edinburgh, Scotl: Inst of Chemical Engineers (EFCE Event n 299).

[88] Kojima, H., J. Sawai, and H. Suzuki, Effect of pressure on volumetric mass transfer

coefficient and gas holdup in bubble column. Chemical Engineering Science, 1997. 52(21–22): p. 4111-4116.

[89] Kemoun, A., et al., Gas holdup in bubble columns at elevated pressure via computed

tomography. International Journal of Multiphase Flow, 2001. 27(5): p. 929-946. [90] Schäfer, R., C. Merten, and G. Eigenberger, Bubble size distributions in a bubble

column reactor under industrial conditions. Experimental Thermal and Fluid Science, 2002. 26(6–7): p. 595-604.

[91] Lin, T.-J. and L.-S. Fan, Heat transfer and bubble characteristics from a nozzle in high-

pressure bubble columns. Chemical Engineering Science, 1999. 54(21): p. 4853-4859. [92] Lin, T.J., R.C. Juang, and C.C. Chen, Characterizations of flow regime transitions in a

high-pressure bubble column by chaotic time series analysis of pressure fluctuation

signals. Chemical Engineering Science, 2001. 56(21–22): p. 6241-6247. [93] Shaikh, A. and M. Al-Dahhan, Characterization of the hydrodynamic flow regime in

bubble columns via computed tomography. Flow Measurement and Instrumentation, 2005. 16(2–3): p. 91-98.

65

[94] Krishna, R., M.I. Urseanu, and A.J. Dreher, Gas hold-up in bubble columns: influence

of alcohol addition versus operation at elevated pressures. Chemical Engineering and Processing: Process Intensification, 2000. 39(4): p. 371-378.

[95] Krishna, R., P.M. Wilkinson, and L.L. Van Dierendonck, A model for gas holdup in

bubble columns incorporating the influence of gas density on flow regime transitions. Chemical Engineering Science, 1991. 46(10): p. 2491-2496.

[96] Reilly, I.G., et al., Role of gas phase momentum is determining gas holdup and

hydrodynamic flow regimes in bubble column operations. Canadian Journal of Chemical Engineering, 1994. 72(1): p. 3-12.

[97] Clark, K.N., The effect of high pressure and temperature on phase distributions in a

bubble column. Chemical Engineering Science, 1990. 45(8): p. 2301-2307. [98] Tarmy, B., et al., Hydrodynamic characteristics of three phase reactors. Chemical

Engineer (London), 1984(407): p. 18-23. [99] de Bruijn, T.J.W., J.D. Chase, and W.H. Dawson, Gas Holdup in a Two-Phase Vertical

Tubular Reactor at High Pressure. Canadian Journal of Chemical Engineering, 1988. 66(2): p. 330-333.

[100] Nedeltchev, S. and A. Schumpe, A New Approach for the Prediction of Gas Holdup in

Bubble Columns Operated under Various Pressures in the Homogeneous Regime. Journal of Chemical Engineering of Japan, 2008. 41(8): p. 744-755.

[101] Oyevaar, M.H., Gas-liquid contacting at elevated pressures, 1989, University of Twente: Twente.

[102] Ishiyama, H., et al., Hydrodynamics in a small size pressurized bubble column. Chemical Engineering Science, 2001. 56(21): p. 6273-6278.

[103] Neubauer, G., Beitrag zur Auslegung von lochböden für die Flüssigkeitsbegasung

unter Hochdruck, in Lehrstuhl A für Verfahrenstechnik der TU München1977, TU Munich: Munich.

[104] Ruff, K., T. Pilhofer, and A. Mersmann, Vollständige Durchströmung von Lochböden

bei der Fluid-Dispergierung. Chemie Ingenieur Technik, 1976. 48(9): p. 759-764. [105] Kölbel, H., D. Klötzer, and H. Hammer, Zur Reaktionstechnik von Blasensäulen-

Reaktoren mit suspendiertem Katalysator bei erhöhtem Druck. Chemie Ingenieur Technik, 1971. 43(3): p. 103-111.

[106] Chilekar, P.V., Hydrodynamics and Mass Transfer in Slurry Bubble Columns: Scale

and Pressure Effects, 2007, Eindhoven University of Technology: Eindhoven. [107] Chilekar, V.P., et al., Influence of elevated pressure and particle lyophobicity on

hydrodynamics and gas–liquid mass transfer in slurry bubble columns. AIChE Journal, 2010. 56(3): p. 584-596.

[108] Luo, X., et al., Maximum stable bubble size and gas holdup in high-pressure slurry

bubble columns. AIChE Journal, 1999. 45(4): p. 665-680. [109] Z., C., Hydrodynamics in a Bubble Column at Elevated Pressures and Turbulence

Energy Distribution in Bubbling Gas-Liquid and Gas-Liquid-Solid Flow Systems, 2005, Ohio State University: Columbus.

[110] Sangnimnuan, A., G.N. Prasad, and J.B. Agnew, Gas Hold-Up and Backmixing in a

Bubble-Column Reactor Uder Coal-Hydroliquefaction Conditions. Chemical Engineering Communications, 1984. 25(1-6): p. 193-212.

[111] Soong, Y., et al., Hydrodynamic study in a slurry-bubble-column reactor. Catalysis Today, 1997. 35(4): p. 427-434.

66

[112] Behkish, A., et al., Gas holdup and bubble size behavior in a large-scale slurry bubble

column reactor operating with an organic liquid under elevated pressures and

temperatures. Chemical Engineering Journal, 2007. 128(2–3): p. 69-84. [113] Deckwer, W.D., et al., Hydrodynamic properties of the Fischer-Tropsch slurry process.

Industrial & Engineering Chemistry Process Design and Development, 1980. 19(4): p. 699-708.

[114] Jordan, U., et al., Stoffübergang in Druckblasensäulen mit organischen Flüssigkeiten. Chemie Ingenieur Technik, 2001. 73(8): p. 982-985.

[115] Kang, Y., et al., Diagnosis of bubble distribution and mass transfer in pressurized

bubble columns with viscous liquid medium. Chemical Engineering Science, 1999. 54(21): p. 4887-4893.

[116] Lau, R., et al., Gas-Liquid Mass Transfer in High-Pressure Bubble Columns. Industrial and Engineering Chemistry Research, 2004. 43(5): p. 1302-1311.

[117] Behkish, A., et al., Novel correlations for gas holdup in large-scale slurry bubble column

reactors operating under elevated pressures and temperatures. Chemical Engineering Journal, 2006. 115(3): p. 157-171.

[118] Wilkinson, P.M., et al., Liquid mixing in a bubble column under pressure. Chemical Engineering Science, 1993. 48(10): p. 1785-1791.

[119] Lorenz, O., et al., Liquid phase axial mixing in bubble columns operated at high

pressures. Chemical Engineering Science, 2005. 60(13): p. 3573-3586. [120] Yang, G.Q. and L.S. Fan, Axial liquid mixing in high-pressure bubble columns. AIChE

Journal, 2003. 49(8): p. 1995-2008. [121] Onozaki, M., et al., Dynamic simulation of gas–liquid dispersion behavior in coal

liquefaction reactors. Chemical Engineering Science, 2000. 55(21): p. 5099-5113. [122] Houzelot, J.L., et al., Contribution to the hydrodynamic study of bubble columns.

International chemical engineering, 1985. 25(4): p. 645-650. [123] Holcombe, N.T., et al., Thermal dispersion and heat transfer in nonisothermal bubble

columns. Chemical Engineering Communications, 1983. 21(1-3): p. 135-150. [124] Wilkinson, P.M., H. Haringa, and L.L. Van Dierendonck, Mass transfer and bubble size

in a bubble column under pressure. Chemical Engineering Science, 1994. 49(9): p. 1417-1427.

[125] Öztürk, S.S., A. Schumpe, and W.D. Deckwer, Organic liquids in a bubble column:

Holdups and mass transfer coefficients. AIChE Journal, 1987. 33(9): p. 1473-1480. [126] Maalej, S., B. Benadda, and M. Otterbein, Interfacial area and volumetric mass transfer

coefficient in a bubble reactor at elevated pressures. Chemical Engineering Science, 2003. 58(11): p. 2365-2376.

[127] Han, L. and M.H. Al-Dahhan, Gas–liquid mass transfer in a high pressure bubble

column reactor with different sparger designs. Chemical Engineering Science, 2007. 62(1–2): p. 131-139.

[128] Nedeltchev, S., U. Jordan, and A. Schumpe, Correction of the penetration theory based

on mass-transfer data from bubble columns operated in the homogeneous regime

under high pressure. Chemical Engineering Science, 2007. 62(22): p. 6263-6273. [129] Cho, Y.J., et al., Dynamic characteristics of heat transfer coefficient in pressurized

bubble columns with viscous liquid medium. Chemical Engineering and Processing: Process Intensification, 2002. 41(8): p. 699-706.

[130] Wu, C., M.H. Al-Dahhan, and A. Prakash, Heat transfer coefficients in a high-pressure

bubble column. Chemical Engineering Science, 2007. 62(1–2): p. 140-147.

67

[131] Yang, G.Q., et al., Heat-Transfer Characteristics in Slurry Bubble Columns at Elevated

Pressures and Temperatures. Industrial & Engineering Chemistry Research, 2000. 39(7): p. 2568-2577.

[132] Steiff, A. and P.-M. Weinspach, Heat Transfer in Stirred and non-Stirred Gas-Liquid

Reactors. Ger Chem Eng, 1978. 1(3): p. 150-161. [133] Laborde-Boutet, C., et al., CFD simulations of hydrodynamic/thermal coupling

phenomena in a bubble column with internals. AIChE Journal, 2010. 56(9): p. 2397-2411.

[134] Becker, M., et al., BMBF Project ” Multi-Phase”. Chemie Ingenieur Technik, 2013. 85(7): p. 989-991.

[135] Bothe, M., Experimental Analysis and Modeling of Industrial Two-Phase Flows in Bubble Column Reactors, Ph.D Thesis, Technical University of Hamburg-Harburg, Institute of Multiphase Flows, Hamburg-Harburg, to be published

68

3 Sensitivity of a complex reaction to hydrodynamic parameters

Multiphase reactor design still requires the use of relatively simple models like axial dispersion

models. Sensitivity studies regarding economic aspects are carried out using these models

before more advanced models are used for detailed studies. Despite of their simplicity, axial

dispersion models rely on several hydrodynamic parameters (e.g. axial dispersion coefficients,

gas holdup, mass and heat transfer) to be estimated. These calculations are usually done with

empirical and semi-empirical correlations that are restricted to a narrow parameter range of

operating conditions and reactor dimensions. Uncertainties in the parameter estimation directly

influence the modelling results with respect to yield and selectivity of a specific reaction. To

assess these uncertainties, an axial dispersion model is used to describe a cyclohexane

oxidation reactor. It is shown that the calculation of gas holdup is vital for the prediction of

reactor performance and that false estimations may cause severe economic miscalculations.

Furthermore it is discussed that available design equations are most often not suited for

reliable reactor design and that experimental work at processing conditions is necessary to

validate available correlations.

3.1 Introduction

Multiphase reactors are of utmost importance for the production of fine and bulk chemicals. In

a series of articles Dudukovic [1, 2] and Dudukovic et al. [3, 4] pointed out the importance of

multiphase reactor engineering for the producers of chemicals. According to Dudukovic et al.

[3] the value of produced material with multiphase reactors involved summed up to 637 billion

$ in 1999. This number makes clear that there is a defined economic perspective in optimized

reactor designs and efficient reactor operation. In addition the demand for resource and energy

efficiency (at least in Europe) is directly coupled with reactor performance as inefficient

operation requires complicated purification steps after the reaction unit. To ensure optimal

reactor designs it is necessary to understand and to calculate the hydrodynamics of such units.

It would be desirable to be able to calculate the whole flow field of multiphase reactors with the

help of CFD tools. This is especially difficult if bubble column reactors are considered. CFD

69

calculations of bubble column flow are on one hand time consuming and therefore very costly

and on the other hand not possible without certain limitations as was pointed out by Jakobsen

et al. [5]. To overcome time consuming CFD calculations simpler reactor models like ideal

reactor (plug flow, ideal mixed), dispersion [6] or compartment models [7] are used. But even

those models depend on the estimation of hydrodynamic parameters which are namely gas

holdup, liquid backmixing and mass and heat transfer. Correlations are available to estimate

the mentioned parameters but are mostly derived from lab scale columns which were operated

at conditions far away from processing conditions and liquids other than organic material which

is usually encountered in production plants [8]. As can be seen from [8] gas holdup seems to

be of vital importance because it creates the interfacial area at which reaction and mass

transfer takes place. Besides that the gas introduced to the column also defines the degree of

mixing in the reactor and is therefore coupled to liquid residence times. From this

argumentation it seems clear that gas holdup influences bubble column reactor performance.

This is the reason why research with respect to bubble column reactor hydrodynamics is still

ongoing besides catalyst development in order to optimize chemical processes [9].

To confirm the statements above an axial dispersion model is setup. Cyclohexane oxidation

was chosen as model reaction because all necessary parameters, including reaction kinetics

and reactor dimension, were published by Schäfer [10, 11] who examined this reaction in a lab

scale bubble column reactor. Different correlations which should theoretically be suited for the

hydrodynamic description of the reactor are evaluated with respect to yield and selectivity of

the reaction. The possible ecological impact is then analyzed and discussed. The situation

encountered can be seen as typical during early project stages and demonstrates the

difficulties incorporated with bubble column design.

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3.2 Cyclohexane oxidation

3.2.1 General information

Cyclohexane is oxidized to yield cyclohexanone and cyclohexanol which is referred to as “KA

oil” as it is a mixture of a ketone and an alcohol. In 2011 KA oil world production capacity was

about 6.8 million tons. It is mainly used for the production of adipic acid (34 %) and caprolactam

(62 %) on site, only about 4 % is sold via merchant markets. Commercially the oxidation of

cyclohexane can take place in presence of a catalyst or without a catalyst [12]. The catalyst

does not improve conversion of cyclohexane but influences the yield of either cyclohexanone

or cyclohexanol. Conversions are limited to 1 to 4 % in order to achieve selectivities of 65 to

90 % and yields of 83 to 86 %. Selectivities of 90 % are usually reached if conversion is as low

as 1 %. Typical reaction conditions encountered are 145 to 175 °C temperature, 1.1 to 1.8

MPa pressure and residence times ranging between 15 and 60 minutes [13]. Plant sizes vary

between 155 and 330 kt/a production capacity [12].

According to a patent by DSM [14] the reaction may be carried out in several reactors and a

number of purification steps is needed after the reaction unit. A first step separates the product

mixture in the presence of a cobalt catalyst and a hydroxide containing phase. The so-called

decomposed reaction mixture is then handled in a distillation unit and purified in further stages

to yield the desired KA oil mixture. Unreacted cyclohexane is recycled to the reaction units

after separation. Like other reactions, the reactor performance is crucial for the optimal

economic performance of the whole process. Unfortunately the KA oil mixture is very reactive

and therefore it must be handled at an optimal parameter range to avoid further reactions to

unwanted byproducts and to keep purification steps to a necessary minimum.

3.2.2 Reaction network

The autooxidation of cyclohexane with air to cyclohexanone and cyclohexanol is a complex

multistage reaction involving radicals and undesired side-products. A variety of proposed

kinetic schemes ranging from 3 [15] to 19 [16] reactions exist in the literature. To model an

oxidation reactor the proposed reaction scheme and kinetics by Schäfer [11] are used. After

71

comparing his own experimental results obtained in a bubble column reactor with available

kinetic models, Schäfer [11] adapted the model of Khar`kova et al. [16] and reduced the

number of reaction steps to 14, which according to Schäfer [11], accounts for all significant

reactions and contains no redundant steps. In addition he recalculated Arrhenius constants

because Schäfer [11] found a slower rate of degradation of intermediates. The reason for this

is according to Schäfer [11] that the steel reactor used by Khar`kova et al. [16] to determine

the reaction rate parameters catalyzed the reaction.

Cyclohexane oxidation is induced by the formation of cyclohexyl radicals, which is a relatively

slow process and is therefore determining the induction period until the chain reaction starts.

A second step involves the reaction of radicals with oxygen to cyclohexylperoxy radicals.

These radicals react subsequently with cyclohexane to cyclohexanehydroperoxid and

cyclohexyl radicals. Cyclohexanehydroperoxid is relatively unstable and decomposes into

cyclohexyl-oxo and hydroxyl radicals. The desired cyclohexanol is built as a result of the

reaction of cyclohexyl-oxo radicals with cyclohexane. Cyclohexanone forms during another

consecutive reaction of cyclohexanol with cyclohexyl-peroxy radicals. The desired

components cyclohexane and cyclohexanone are more reactive than the initial cyclohexane

and are actually intermediates of the oxidation reaction. Both intermediates would react to

undesired side products like esters, acids and water. That is why reaction residence times

must be stringently controlled and conversions are limited to low percentages to gain

economically feasible selectivities and yields of KA oil. The reaction scheme presented here

serves for the basic understanding of the reaction pathway. A very detailed description of the

reaction scheme including the formation of side products can be found in [11].

72

Figure 3.1 Illustration of the reaction scheme, taken from Schäfer [11], RH – cyclohexane, ROOH – cyclohexyl-hydroperoxide, ROH – cyclohexanol, R’O – cyclohexanone, P – reactive organic secondary product, P’ – non-reactive organic secondary product, HO2 – hydroperoxide radical, OH – hydroxyl radical, R – cyclohexyl radical, RO – cyclohexyl-oxo radical, RO2 – cyclohexyl-peroxy radical

73

3.3 Model development

To predict the performance of the cyclohexane oxidation reactor described in [11] and to test

the influence of hydrodynamic parameter estimation on output variables as conversion, yield

and selectivity a short-cut reactor model is built. Depending on the case considered bubble

columns may not be treated as ideal reactors. Consequently a model which regards non-ideal

flow behavior is needed. Deckwer [6] proposes a matrix of short-cut approaches to

mathematically describe the mixing of both gas and liquid phase (presented in Table 3-1).

Table 3ど1 Modelling approaches according and arranged to a suggestion by Deckwer [6] 

phase gas

liquid CSTR ADM PFTR

CSTR 11 12 13

ADM (21) 22 23

PFTR (31) (32) 33

As stated by Deckwer [6] models which describe the gas phase as more mixed than the liquid

phase are rather unrealistic. Consequently they are set in brackets in Table 3-1. All other

approaches are suited for modelling bubble column reactors and should be chosen according

to the specific reactor in question. For the problem statement examined here plug flow is

chosen for the gas phase and an axial dispersion model for the liquid phase. Plug flow is

assumed for the gas phase because the gas throughput is very low. The liquid phase is

considered to be partially backmixed which can be described with an axial dispersion model

as it inherits an axial dispersion coefficient, a lumped parameter which describes backmixing.

It is often questioned if dispersion coefficients can project physical backmixing phenomena

and if these coefficients are scalable. Of course, a dispersion coefficient is merely a fitting

parameter which mostly results out of residence time measurements done in lab or pilot scale

facilities. A different approach to account for partial backmixing is the use of cell models.

However the correct number of mixing cells is still a result of measurements in test facilities

74

and therefore a fitting parameter to match an output signal, too. A detailed discussion of these

considerations may be found in [17-19]. The approach used for this study is similar to the one

presented by Jung et al. [20]. Jung et al. [20] used a dispersion model to describe the

hydrogenation of 2-ethylhexanal in order to design a pilot scale facility. The dispersion model

established here is not used for design purposes but for showing trends of parameter

uncertainties with respect to reactor performance.

The following assumptions are made for the reactor model:

liquid phase is considered to be partially backmixed

gas phase is in plug flow

only one direction (column axis z) will be considered, no internals present

isothermal operation (operating temperature according to Schäfer [11])

thermodynamic equilibrium ( T = Tg = Tl)

no mass transfer limitations (reaction completely in liquid phase)

stationary operation.

The assumptions of isothermal operation and absence of reactor internals were necessary as

no detailed information were available. The laboratory reactor operating parameters extracted

from Schäfer [11] are as follows:

reactor diameter: 0.054 m

reactor length: 1.746 m

operating temperature: 148 °C

operating pressure: 1.48 MPa

cocurrent flow of gas and liquid phase.

In the following two chapters the balance equations and necessary correlations to predict

hydrodynamic and other relevant parameters are presented.

75

3.3.1 Balance equations

The material balance for a component i of phase j reads as follows.

盤な 伐 綱珍匪 擢頂日┸乳擢痛 噺 伐憲珍 擢頂日┸乳擢佃 髪 盤な 伐 綱珍匪継銚掴 擢鉄頂日┸乳擢佃鉄 罰 倦沈┸珍欠盤潔沈茅 伐 潔沈┸珍匪 罰 盤な 伐 綱珍匪 デ 荒沈┸賃堅賃津賃退怠 (3-1)

Where u is the superficial velocity of a phase, k the mass transfer coefficient, ち the

stoichiometric coefficient of a reactant, r the rate of a reaction, E the dispersion coefficient

, i the holdup of a phase and c the concentration of a component in a phase. With the above

mentioned assumptions, the balance equation for a component i in the liquid phase results into

equation (3-2).

ど 噺 伐憲鎮 擢頂日┸如擢佃 髪 盤な 伐 綱直匪継銚掴 擢鉄頂日┸如擢佃鉄 髪 倦沈┸鎮欠盤潔沈茅 伐 潔沈┸鎮匪 髪 盤な 伐 綱直匪 デ 荒沈┸賃堅賃津賃退怠 (3-2)

The resulting component material balance for the gas phase simplifies to equation (3-3)

because the gas mass changes only due to mass transfer.

擢頂日┸虹擢佃 噺 伐倦沈┸鎮欠盤潔沈茅 伐 潔沈┸鎮匪 (3-3)

A momentum balance is also included to account for changes in static head (equation 3-4).

擢椎擢佃 噺 伐盤な 伐 綱直匪貢鎮訣 (3-4)

Although isothermal operation is assumed due to a lack of available information, a heat

balance (equation 3-5) is included for the case that detailed information about temperature

profiles become available.

ど 噺 伐盤貢鎮潔椎┸鎮憲鎮 髪 貢直潔椎┸直憲直匪 擢脹擢佃 髪 盤な 伐 綱直匪膏銚掴 擢鉄脹擢佃鉄 伐 月畦頂墜墜鎮岫劇 伐 劇頂墜墜鎮岻 伐 盤な 伐 綱直匪ッ茎追堅 (3-5)

Both component material balances and the heat balance need boundary conditions.

Danckwert`s boundary conditions were chosen, meaning that backmixing is taken into account

at the reactor inlet (bottom, z = 0) and no backmixing takes place at the reactor outlet (top, z =

L). This might be unrealistic because liquid backmixing possibly also occurs at the reactor

outlet. But the available correlations for estimation of the axial dispersion coefficient were

derived on the basis of the below suggested boundary conditions and because of this they had

to be used for this model to maintain consistency with the derivation of the correlation.

76

潔沈┸鎮岫権 噺 ど岻 噺 潔沈┸鎮岫件券岻 髪 盤な 伐 綱直匪 帳尼猫通如 擢頂日┸如擢佃 (3-6)

擢頂日┸如岫佃退挑岻擢佃 噺 ど (3-7)

擢津日┸虹岫佃退挑岻擢佃 噺 ど (3-8)

劇岫権 噺 ど岻 噺 劇岫件券岻 髪 盤な 伐 綱直匪 碇尼猫盤諦如頂妊┸如通如袋諦虹頂妊┸虹通虹匪 擢脹擢佃 (3-9)

擢脹岫佃退挑岻擢佃 噺 ど (3-10)

3.3.2 Parameter estimation

The above presented balance equations need parameters to be calculated. This can either be

done per definition or with the help of correlations. The superficial velocity of a phase j is

defined as the quotient of volumetric flux of the phase j and cross sectional column area.

憲珍 噺 蝶剥岌凋迩 (3-11)

Gas holdup has to be estimated via correlations which are mostly of empirical nature. In the

case considered several problems arise. First of all, cyclohexane oxidation takes place at

elevated pressure, temperature and of course physical properties other than water are

encountered. There are nearly no available correlations suited for estimating gas holdup at

these conditions. Fortunately a laboratory scale reactor is studied. If the reactor size would be

of production scale dimensions, absolutely no correlations would be available. Rollbusch et al.

[8] give a brief survey of studies which accounted for organic solvents and higher pressures.

Besides many available correlations for the system air/water only a few exist for predicting

holdups in organic solvents. Three suited correlations are chosen for this study. These are the

correlations by Wilkinson et al. [21], Idogawa et al. [22] and Reilly et al. [23] which are

summarized in Table 3-2.

77

Table 3-2 Correlations for gas holdup estimation

Author equation

Reilly et al. [23] 綱直 噺 にひは憲直待┻替替貢直待┻怠苔貢鎮貸待┻苔腿購鎮貸待┻怠滞 髪 ど┻どどひ (3-12)

Idogawa et al.[22] 悌虹岫怠貸悌虹岻 噺 ど┻どのひ 岾憲直待┻腿貢直待┻怠胎 蹄如貼轍┻鉄鉄胎態 exp岫伐喧岻峇 (3-13)

Wilkinson et al. [21] homogeneous flow regime:

綱直 噺 通虹通濡弐 (3-14)

heterogeneous flow regime:

綱直 噺 通禰認尼韮濡通濡弐 髪 通虹貸通禰認尼韮濡通如弐 (3-15)

transition velocity utrans:

通禰認尼韮濡通濡弐 噺 ど┻のexp盤伐なひぬ貢直貸待┻滞怠考鎮待┻泰購鎮待┻怠怠匪 (3-16)

small bubble velocity usb:

通濡弐挺如蹄如 噺 に┻にの峭購鎮戴 磐 諦如直挺如填卑貸待┻態胎戴 磐諦如諦虹卑待┻待戴嶌 (3-17)

large bubble velocity ulb:

通如弐挺如蹄如 噺 通濡弐挺如蹄如 髪 に┻ね峭磐挺如盤通虹貸通禰認尼韮濡匪蹄如 卑待┻胎泰胎 磐蹄如典諦如直挺如填 卑貸待┻待胎胎 磐諦如諦虹卑待┻待胎胎嶌 (3-18)

Dispersion coefficients are most often expressed as functions of superficial gas velocity and

column diameter. Surprisingly gas holdup is seldom part of dispersion coefficient correlations

despite of the fact that gas itself is the main cause for liquid mixing in bubble columns. The

superficial gas velocity alone is not sufficient to describe the extent of gas holdup. Furthermore

liquid properties and pressure are of vital importance to sufficiently calculate gas holdup.

Consequently it seems necessary to use an equation to estimate the value of axial dispersion

which relies not only on superficial as velocity and column diameter alone but also on gas

holdup itself. Kantak et al. [24] derived such a correlation on a broad basis of literature data.

78

継銚掴 噺 ど┻に経怠┻態泰 通虹悌虹 (3-19)

The same considerations apply for the estimation of mass and heat transfer coefficients. Mass

transfer coefficients can be predicted with Akita and Yoshida`s [25] equation.

倦鎮欠 帖鉄帖如 噺 ど┻は 岾 挺如諦如帖如峇待┻泰 岾帖鉄直諦如蹄如 峇待┻滞態 磐帖典直諦如鉄挺如卑待┻戴怠 綱直怠┻怠 (3-20)

For heat transfer coefficients no correlation was found which is directly linked to gas holdup

except the one developed by Yang et al. [26] which is applicable for three phase slurry bubble

columns. As this study is related to a two phase bubble column at assumed isothermal

operation the estimation of this parameter is not necessary at this point. This pertains also for

the heat conductivity which can be estimated with the Lewis analogy. 膏銚掴 噺 貢鎮潔椎┸鎮継銚掴 (3-21)

The saturation concentration can be obtained using Henry`s law. 潔沈茅 噺 桁沈喧茎沈 (3-22)

Missing Henry constants for oxygen and nitrogen are calculated with correlations suggested

by Tekie [27].

茎潮鉄 噺 怠岫泰怠┻苔替勅掴椎岫迭添添轍馴畷 岻岻 (3-23)

茎朝鉄 噺 怠岫戴待┻胎滞勅掴椎岫填展店轍馴畷 岻岻 (3-24)

3.3.3 Reaction rate constants and physical properties

The parameters to calculate the rates for each reaction k are listed in Table 3-3.

79

Table 3-3 Reactions and corresponding reaction kinetic constants, taken from Schäfer [11], notation according to Figure 3.1

reaction kk (T = 150 °C) 圭著 Eact 三殺 髪 鮫匝 蝦 三 髪 殺鮫匝 な┻ひに 茅 など貸腿 ば┻ひね 茅 など怠態 167 三 髪 鮫匝 蝦 三鮫匝 など苔 など苔 - 三殺 髪 三鮫匝 蝦 三 髪 三鮫鮫殺 4.65 に┻になば 茅 など腿 62.2 三鮫鮫殺 髪 三 蝦 三鮫匝 髪 三殺 な┻はな 茅 など滞 は┻ぬな 茅 など腿 21.0 三鮫鮫殺 蝦 三鮫 髪 鮫殺 に┻なは 茅 など貸泰 ひ┻なぱに 茅 など怠怠 134.7 三鮫鮫殺 髪 三鮫殺 蝦 匝三鮫 髪 殺匝鮫 は┻ひな 茅 など貸替 ね┻の 茅 など腿 95.7 三殺 髪 鮫殺 蝦 三 髪 殺匝鮫 ば┻はの 茅 など腿 に┻ひどひ 茅 など怠待 12.8 三殺 髪 三鮫 蝦 三 髪 三鮫殺 ば┻はの 茅 など胎 に┻ひどひ 茅 など苔 12.8 三鮫鮫殺 髪 三 蝦 三鮫 髪 三鮫殺 な┻ひね 茅 など替 に┻ど 茅 など滞 16.3 三鮫鮫殺 髪 三鮫匝 蝦 三鮫 髪 鮫殺 髪 三鮫鮫殺 7.44 は┻ぱには 茅 など泰 40.2 匝三鮫匝 蝦 三┸鮫 髪 三鮫殺 髪 鮫匝 な┻のの 茅 など滞 に┻ななね 茅 など怠苔 106.4 三鮫殺 髪 三鮫匝 蝦 三┸鮫 髪 三鮫匝 4.56 な┻なひぱ 茅 など滞 43.9 三┸鮫 髪 三鮫匝 蝦 三鮫匝 髪 皿 37.53 ね┻ばどは 茅 など胎 49.4 皿 髪 三鮫殺 蝦 皿┸ ば┻ぬに 茅 など貸戴 な┻ぱはぱ 茅 など泰 60.0

The model was implemented in ASPEN Custom Modeler and therefore all physical properties

are obtained using ASPEN Plus databanks.

3.4 Results

The modelling results are presented in three steps. At first, the estimates of hydrodynamic

parameters for the model are analyzed and the role of gas holdup is examined. Based on this,

effects of parameter uncertainties are presented with respect to selectivity and yield of KA oil

in cyclohexane autooxidation. At last simplified economic consequences are presented.

80

3.4.1 Hydrodynamic parameter estimation

Looking at the structure of the listed equations in 3.2 a direct influence of gas holdup on

dispersion and mass transfer is expected. If the gas holdup correlations listed in Table 3-2 are

compared with each other, divergent results are obtained. Figure 3.2 shows the holdup

estimates at reaction conditions (although there is no reaction present yet) in cyclohexane. Not

only the magnitude of the results differs, also the shapes of the curves are not identical. Results

predicted with the correlation suggested by Wilkinson et al. [21] yield a straight line. The

reason for this might be that at the superficial gas velocities the so called homogeneous flow

regime is expected and usually a direct proportionality of holdup and superficial gas velocity is

found at this flow condition. However, correlations by Reilly et al. [23] and Idogawa et al. [22]

predict a change of slope at about 0.003 m/s and their results are remarkably higher than those

obtained with Wilkinson et al.`s [21] equation. Another look at Table 3-2 reveals that the

mentioned correlations inherit a number of fitted parameters. Consequently these correlations

are likely to fail if they are used to predict gas holdups in reactors of different geometry and

other physical systems than they are derived from. Furthermore if other parameters of interest

are calculated with the results of these correlations more uncertainties arise as is shown in

Figure 3.3 and Figure 3.4 for the example of liquid dispersion and mass transfer coefficients.

Figure 3.2 predicted gas holdups, correlations of Reilly et al. [23], Idogawa et al. [22] and Wilkinson et al. [21]

81

The ratio of superficial gas velocity and gas holdup determines the amount of liquid backmixing

estimated with Kantak et al.`s [24] proposed equation. Therefore a constant degree of

backmixing is obtained if gas holdup is calculated with the method developed by Wilkinson et

al. [21]. Gas holdup rises over proportional if it is estimated with equations given by Reilly et

al. [23] and Idogawa et al. [22]. Because of that variable gradient, estimated axial dispersion

coefficients also change with superficial gas velocity. Interestingly lower gas holdup seems to

provoke higher predicted dispersion coefficients at first sight. This rather unexpected behavior

is the result of the previously discussed disproportional rise of gas holdup with superficial gas

velocity.

Figure 3.3 Dispersion coefficients calculated with equation (3-19), same correlations as in Figure 3.2 were used to estimate gas holdups

The estimations of volumetric mass transfer coefficients by the correlation of Akita and Yoshida

on the basis of the three different gas holdup correlations discussed are depicted in Figure 3.4.

As expected, with rising gas holdup volumetric mass transfer coefficients are clearly higher.

Gas holdup determines interfacial area and therefore higher holdup estimates cause higher

values of volumetric mass transfer coefficients. There are however significant differences of

the magnitude of estimated mass transfer coefficients and it is definitely not clear, without

proper model validation, which estimate is correct. The same is true for the estimated axial

dispersion coefficients. To quantify the effect of such uncertainties on reactor performance the

82

developed axial dispersion model is used to predict yield and selectivity of cyclohexane

autooxidation.

Figure 3.4 Mass transfer coefficients estimated with equation (3-20), same correlations as in Figure 3.2 were used to estimate gas holdups

3.4.2 Effect on selectivity and yield

As the cyclohexane autooxidation comprises a reaction network with competing side reactions

and a reactive desired intermediate, significant influence of hydrodynamic parameter

estimation on reactor performance is expected.

The model results with respect to yield and selectivity are presented in the figures below. It is

possible to predict the expected magnitudes of conversions and selectivity of 1 to 3 % and 60

to 90 % respectively. The estimation of yields of KA oil is limited to a single reactor and not to

the whole process of cyclohexane oxidation. Therefore values of yields are significantly lower

than those given in economic reports. From Figure 3.5 and Figure 3.6 one can see that with

rising gas holdup yield of KA oil and selectivity of the reaction to KA oil decreases. The main

reason for this is an enhanced rate of mass transfer due to higher gas holdup (as was

discussed in Figure 3.4). Because of the high reactivity of the desired intermediate product KA

oil more unwanted side products are formed if more oxygen is available for the oxidation

reaction.

83

Figure 3.5 yield of KA oil depending on gas holdup

Figure 3.6 gas holdup influencing selectivity to KA oil

Immense different gas holdups were obtained at reaction conditions. The correlations by

Wilkinson et al. [21] predicts a holdup of 4.42 %, Idogawa et al. [22] a holdup of 9.69 % and

Reilly et al. [23] predicts even higher holdups of 21.22 %. There is a span of a fivefold

magnitude in gas holdups predicted by the above presented correlations. With respect to yield

of KA oil this means that yields vary between 0.95 and 3.3 % as can be seen in Figure 3.5.

Selectivity to KA oil significantly reduces with gas holdup from 89.9 % to 56.5 %. As the

magnitudes of estimated gas holdups are significantly different these results might be

84

somewhat expected. Another example which takes the error margin of only one correlation

into account is shown in Figure 3.8 and Figure 3.7. A confidence interval for gas holdups of ±

20 % is assumed as sufficiently adequate for basic reactor calculations and applied to the

correlation given by Wilkinson et al. [21]. Gas holdups of around ± 0.8 % to the original value

of 4.42 % are estimated. The impact of these lower changes of magnitude with respect to KA

oil yield is shown in Figure 3.7. Yield of KA oil varies between 2.73 and 3.24 % which is about

± 0.2 % difference to the original value of 2.97 %. If the original value of overall selectivity is

compared to the ones estimated within the confidence interval a difference of around ± 2 % is

observed. Despite the relatively low change in gas holdup this is still a huge impact on reaction

selectivity.

Figure 3.7 influence of confidence interval of a specific correlation on yield to KA oil

85

Figure 3.8 influence of confidence interval of a specific correlation on selectivity to KA oil

 

3.4.3 Possible economic consequences

The previous model calculations demonstrated that gas holdup and its direct connection to

other hydrodynamic parameters massively influences estimations with respect to reactor

performance. To further visualize the demand for precise calculation methods for gas holdup

a simplified economic scenario is setup. A 330 kt/a production plant is considered. As the

information about purification steps and reactor configurations from literature and patents is

not evaluable for a whole process model, a single reactor is assumed and no purification after

the reaction is examined. Based on calculations of KA oil yield trends for possible uncertainties

with respect to money and product quantities are estimated. A price for KA oil of 1.82 $/kg [28]

is assumed for this purpose. It is further assumed that the correlation given by Wilkinson et al.

[21] predicts the correct holdups and thus correct yield of KA oil. This is necessary in order to

be able to calculate financial and product uncertainties because absolutely no reliable

information is available.

The results are depicted in Figure 3.9 and Figure 3.10. Differences of up to 7 kt/a KA oil

production and 12.08 million $/a monetary value are obtained. Because of the high differences

of predictions between the three presented holdup correlations, this result might be expected.

But even if the confidence interval of one correlation is examined non negligible uncertainties

86

of 1 kt/a KA oil amount and 2 million $ sales value are encountered. If the produced KA oil is

not sold on merchant markets (which is the case for the largest portion) the uncertainties with

respect to KA oil yield are still of interest for the design and operation of downstream

purification steps.

Figure 3.9 resulting difference in produced amount of KA oil

Figure 3.10 corresponding monetary uncertainty

87

3.5 Conclusions

The example of applying a shortcut model to a complex chemical reaction to estimate reactor

performance shows the complications which arise if basic hydrodynamic parameters need to

be estimated. The main parameter of interest was identified as gas holdup. Gas holdup directly

influences other hydrodynamic parameters and determines interfacial area. Without precise

estimation of gas holdup all other parameter calculations are prone to errors. This in turn

affects the model accuracy with respect to performance parameters like yield and selectivity.

Although more detailed models are available and state of the art, dispersion models and ideal

reactor models are still used for estimations at least

during early project stages. On the other hand even advanced models rely on parameter

estimations. Available correlations to predict these parameters are mostly of empirical nature

and are not suited for extrapolation beyond the experimental limits on which they were derived

from. Published data with respect to gas holdup and other hydrodynamic parameters at

industrial relevant conditions is also very scarce. Ultimately no information exists which

correlation is the most accurate one. It is often necessary to conduct costly and time consuming

experiments from laboratory to pilot scale in order to validate existing correlations and to design

bubble column reactors. Because of that such parameter studies give information on worst

case approximations of the reactor performance.

It is thought helpful to develop design equations which are not based on fitting parameters to

ensure better reliability for scale-up purposes and the applicability of these equations for

systems other than air/water at operating conditions which reflect processing requirements.

The inclusion of single bubble and bubble swarm phenomena might be advantageous in the

development process of more fundamental calculation methods. Finally this could eventually

reduce the amount of necessary experimental work. Furthermore a better understanding of the

governing hydrodynamics of bubble columns might contribute to more efficient reactor designs.

88

3.6 Notation

List of symbols

Symbol Meaning Unit k著 preexponential factor m³/(mole*s)

A area m²

c concentration mole/m³

cp heat capacity kJ/(kg*K)

D column diameter m

Dl diffusion coefficient m²/s

Eact activation energy kJ/mole

Eax axial dispersion coefficient m²/s

g acceleration m/s2

H Henry constant mole/(m³*bar)

h heat transfer coefficient W/(m²*K)

kk rate constant m³/(mole*s)

kla volumetric mass transfer

coefficient

1/s

n molar flow rate mole/s

p pressure MPa

R gas constant kJ/(mol*K)

r reaction rate mole/(m³*s)

T temperature °C

u superficial velocity m/s

V volumetric flow rate m³/s

Y gas fraction [-]

〉Hr reaction enthalpy kJ/mole

i holdup [-]

さ viscosity Pas

そ heat conductivity W/(m*K)

89

ち stoichiometric coefficient [-]

と density kg/m³

j surface tension N/m

Subscripts

Subscript Meaning

* saturation

c column

cool coolant/cooling

g gas

i refers to a component

in inlet

j refers to a phase

l liquid

lb large bubbles

sb small bubbles

trans transition

3.7 References

[1] Dudukovic, M.P., Relevance of multiphase reaction engineering to modern

technological challenges. Industrial and Engineering Chemistry Research, 2007. 46(25): p. 8674-8686.

[2] Dudukovic, M.P., Frontiers in reactor engineering. Science, 2009. 325(5941): p. 698-701.

[3] Dudukovic, M.P., F. Larachi, and P.L. Mills, Multiphase reactors – revisited. Chemical Engineering Science, 1999. 54(13–14): p. 1975-1995.

[4] Duduković, M.P., F. Larachi, and P.L. Mills, Multiphase catalytic reactors: A perspective

on current knowledge and future trends. Catalysis Reviews - Science and Engineering, 2002. 44(1): p. 123-246.

[5] Jakobsen, H.A., H. Lindborg, and C.A. Dorao, Modeling of Bubble Column Reactors:࣯ Progress and Limitations. Industrial & Engineering Chemistry Research, 2005. 44(14): p. 5107-5151.

[6] Deckwer, W.D., Reactor models for gas/liquid reactions. Reaktormodelle fuer Gas-Fluessig-Reaktionen, 1988. 114: p. 247-263.

[7] Abel, N.H., L. Schlusemann, and M. Grünewald, Beschreibung von Blasensäulen

mithilfe von Kompartment-Modellansätzen. Chemie Ingenieur Technik, 2013. 85(7): p. 1112-1117.

90

[8] Rollbusch, P., et al., Hydrodynamics of High-Pressure Bubble Columns. Chemical Engineering & Technology, 2013. 36(9): p. 1603-1607.

[9] Becker, M., et al., Mehrphasenreaktoren: Zusammenspiel von Prozessentwicklung und

Hydrodynamik. Chemie Ingenieur Technik, 2012. 84(8): p. 1223-1223. [10] Schäfer, R., C. Merten, and G. Eigenberger, Autocatalytic cyclohexane oxidation in a

bubble column reactor. Canadian Journal of Chemical Engineering, 2003. 81(3-4): p. 741-748.

[11] Schäfer, R., Bubble Interactions, Bubble Size Distributions, and Reaction Kinetics for

the Autocatalytic Oxidation of Cyclohexane in a Bubble Column Reactor2005: VDI-Verlag.

[12] Fisher, W.B. and J.F. VanPeppen, Cyclohexanol and Cyclohexanone, in Kirk-Othmer

Encyclopedia of Chemical Technology2000, John Wiley & Sons, Inc. [13] Oppenheim, J.P. and G.L. Dickerson, Adipic Acid, in Kirk-Othmer Encyclopedia of

Chemical Technology2000, John Wiley & Sons, Inc. [14] Tinge, J.T.D., C.; Verschuren, I., Process for the production of a mixture comprising

cyclohexanol and cyclohexanone, DSM, Editor 2003: Netherlands. [15] Suresh, A.K., T. Sridhar, and O.E. Potter, Autocatalytic oxidation of cyclohexane -

modeling reaction kinetics. AIChE Journal, 1988. 34(1): p. 69-80. [16] Kharkova, T.V., Arest-Yakubovich, I. L., & Lipes, V. V., Kinetic model of the liquid-phase

oxidation of cyclohexane. I. Homogeneous proceeding of the process. Kinetika i Kataliz, 1989. 30: p. 954-958.

[17] Millies, M. and D. Mewes, Back-mixing of the continuous phase in bubble columns. Chemical Engineering Science, 1995. 50(13): p. 2107-2115.

[18] Schlüter, S., A. Steiff, and P.M. Weinspach, Modeling and simulation of bubble column

reactors. Chemical Engineering and Processing: Process Intensification, 1992. 31(2): p. 97-117.

[19] Shah, Y.T., G.J. Stiegel, and M.M. Sharma, Backmixing in Gas-Liquid Reactors. AIChE Journal, 1978. 24(3): p. 369-400.

[20] Jung, S., et al., One-Dimensional Modeling and Simulation of Bubble Column Reactors. Chemical Engineering & Technology, 2010. 33(12): p. 2037-2043.

[21] Wilkinson, P., A. Spek, and L. van Dierendonck, Design parameters estimation for

scale-up of high-pressure bubble columns. AIChE Journal, 1992. 38(4): p. 544-554. [22] Idogawa, K., et al., Effect of gas and liquid properties on the behavior of bubbles in a

column under high pressure. International chemical engineering, 1987. 27(1): p. 93-99. [23] Reilly, I.G., et al., A correlation for gas holdup in turbulent coalescing bubble columns.

The Canadian Journal of Chemical Engineering, 1986. 64(5): p. 705-717. [24] Kantak, M.V., S.A. Shetty, and B.G. Kelkar, Liquid Phase Backmixing in Bubble

Column Reactors - a New Correlation. Chemical Engineering Communications, 1994. 127(1): p. 23-34.

[25] Akita, K. and F. Yoshida, Gas Holdup and Volumetric Mass Transfer Coefficient in

Bubble Columns. Effects of Liquid Properties. Industrial & Engineering Chemistry Process Design and Development, 1973. 12(1): p. 76-80.

[26] Yang, G.Q., et al., Heat-Transfer Characteristics in Slurry Bubble Columns at Elevated

Pressures and Temperatures. Industrial & Engineering Chemistry Research, 2000. 39(7): p. 2568-2577.

[27] Tekie, Z., et al., Gas-liquid mass transfer in cyclohexane oxidation process using gas-

inducing and surface-aeration agitated reactors. Chemical Engineering Science, 1997. 52(9): p. 1541-1551.

91

[28] Davis, S., CEH Marketing Research Report Cyclohexanol and Cyclohexanone. IHS, 2012.

92

4 Experimental studies on gas holdup

Measurements of gas holdups in bubble columns of 0.16, 0.30 and 0.33 m diameter were

carried out. These columns were operated in concurrent flow of gas and liquid phases and in

semibatch mode. The column of 0.33 m diameter was operated at elevated pressures of up to

3.6 MPa. Nitrogen was employed as the gas phase and deionized water, aqueous solutions of

ethanol and acetone and pure acetone and cumene as the liquid phase. The effects of differing

liquid properties, gas density (due to elevated pressure), temperature, column diameter and

superficial liquid velocity on gas holdup were studied. The gas holdup measurements were

utilized by differential pressure measurements at different positions along the height of the

bubble columns which allowed for the identification of axial gas holdup profiles. A decrease of

gas holdup with increasing column diameter and an increase of gas holdup with increasing

pressure was observed. The effect of a slightly decreasing gas holdup with increasing liquid

velocity was found to exist at smaller column diameters. The use of organic solvents as the

liquid phase resulted in a significant increase in gas holdup compared to deionized water. It is

found that published gas holdup models are mostly unable to predict the results obtained in

this study.

4.1 Introduction

Within the chemical and petrochemical industry bubble columns are present as multiphase

reactors and contactors in a variety of processes. Bubble columns are thereby utilized in

various modes of operation, ranging from semibatch to co- and countercurrent operation with

two or three phases involved. The basic construction of bubble columns is relatively simple,

unless no internals are present, as they are mainly cylinders in which gas and liquid are brought

in contact. The main features of bubble columns have been summarized by e.g. Deckwer [1]

and Kantarci et al. [2].

* Published as Rollbusch et al. - Experimental investigation of the influence of column scale, gas density and liquid properties on

gas holdup in bubble columns, International Journal of Multiphase Flow, 2015. 75: p. 88-106.

93

Precise prediction of the governing hydrodynamic parameters and the overall flow field is still

not possible which has been pointed out by Jakobsen et al. [3] recently. As pointed out in the

introductory chapter of this thesis the predictions of available models tend to fail if they are

used for scale-up purposes or to predict holdups for systems with physical properties other

than they are derived from. The reasons for this can be found in several factors.

A first point to be stated is that the experimental facilities differ in terms of column diameter,

height to diameter H/D ratio and mode of gas distribution. There are several recommendations

summarized by e.g. Shah et al. [4] concerning the minimum diameter (at least 0.15 m) and

H/D ratio (greater than 5) which should be used in order to measure gas holdups independently

from undesired side effects.

A second point concerns the qualities of the liquids used. Even if deionized water or tap water

is used as the liquid phase different water qualities and accidental impurities cause differences

in the experimental data. This is due to a bubble coalescence inhibiting or promoting effect of

the specific impurity.

A third point accounts for the availability of experimental data especially for scale-up and gas

density studies. Only a few studies, e.g. by Forret et al. [5] ,Krishna et al. [6, 7] and Wilkinson

et al. [8], with varying column diameters are present up to this date and their results are

contradictory. Therefore even fewer gas holdup models exist which account for the influence

of column diameter.

It is the purpose of this chapter to present and discuss gas holdup results obtained in three

gas-liquid bubble columns of different sizes but comparable gas distributors and liquids

employed. In addition the influence of impurities is simulated by adding small amounts of

ethanol and acetone to the liquid phase. To discuss the effect of gas density due to elevated

pressure on gas holdup experimental studies at pressures of up to 3.6 MPa were carried out.

Some other influencing parameters which are important for production scale bubble columns

like temperature and liquid superficial velocity are also examined within the studies presented.

94

4.2 Experimental facilities and procedures

4.2.1 Experimental facilities

To perform the experimental studies three bubble columns of different diameters and heights

were set up. Table 4-1 summarizes the column dimensions together with their H/D ratio based

on liquid height.

Table 4-1 column dimensions and H/D ratio

column diameter D [m] liquid height H [m] H/D ratio [-]

0.16 1.8 11.25

0.30 2.63 8.75

0.33 3.88 11.75

As can be seen from Table 4-1 all columns are above the minimum H/D ratio of 5 and the

minimum diameter of 0.15 m mentioned by Shah et al. [4] to avoid any wall effects on gas

holdup during the measurements. The columns of 0.16 and 0.3 m diameter are used to study

the effect of column dimensions, superficial liquid velocity and liquid properties on gas holdup.

A third column of 0.33 m diameter is primarily used to examine the effect of a higher gas density

due to elevated pressures and the effect of temperature on gas holdup. As the difference in

diameter to the 0.30 m diameter column is small, no remarkable effects of scale are expected.

Nitrogen was always used as the gas phase (see Table 4-2 for nitrogen densities at

investigated pressure levels) and deionized water, acetone, cumene and aqueous solutions of

organic solvents as liquid phase (properties related to investigated temperature levels listed in

Table 4-3).

95

Table 4-2 pressure dependent density of nitrogen

p [MPa] 0.1 1 1.85 3.6

nitrogen

density [kg/m³] 1.15 11.50 21.28 41.38

Table 4-3 temperature dependent liquid properties

T [°C] 20 50 75

deionized H2O

density [kg/m³] 998 988 975

viscosity [mPas] 1 0.55 0.38

surface tension [N/m] 0.074 0.068 0.063

acetone

density [kg/m³] 767 - -

viscosity [mPas] 0.32 - -

surface tension [N/m] 0.024 - -

cumene

density [kg/m³] 867 844 823

viscosity [mPas] 0.79 0.54 0.42

surface tension [N/m] 0.028 0.025 0.022

All columns were operated in concurrent flow of gas and liquid phase. The gas was distributed

by a perforated plate sparger with holes of 1 mm diameter. The spargers were designed

according to the methods proposed by Ruff et al. [9] and its dimensions are listed in Table 4-4.

All spargers match flow characteristics in each column which results in a different number of

openings due to the varying column diameters and the associated flow rates.

Table 4-4 sparger geometries

column diameter D [m] number of holes [-] free area [%]

0.16 92 0.36

0.30 352 0.85

0.33 352 0.65

Simplified schematics of all three facilities are given in Figure 4.1 to Figure 4.3. Note that nearly

all security devices, valves and outlets are not shown here to enhance the clarity of the

96

depicted experimental setups. Security devices include for example pressure relief valves,

concentration sensors, groundings, buffer vessel level indication and automatic shut-down

mechanisms. Figure 4.1 shows the 0.16 m diameter column which is made of glass.

Figure 4.1 simplified sketch of 0.16 m diameter glass column

Liquid is circulated via a pump from bottom to top of the column. At the top the liquid leaves

the column through an overflow and flows into a buffer vessel. The liquid flow rate is measured

by a Coriolis flow meter (Endress+Hauser, promass63a, 0.1 % measurement error). Liquids

employed were deionized water, aqueous solutions of ethanol, acetone and cumene. Nitrogen

as the gas phase also enters the column at the bottom and is distributed by a perforated plate

sparger. It leaves the column at the top from where it enters the buffer vessel to separate

entrained liquid from the gas. Afterwards nitrogen passes through a condenser, again to

separate liquid and gas, before it enters the exhaust system. The amount of gas flowing

through the column is measured by two gas flow meters (Krohne, H250, 1.6 % measurement

error), one for low and one for higher gas throughputs, to ensure a better accuracy of the

97

measurement. Gas and liquid superficial velocities were varied up to 0.1 m/s and 0.01 m/s

respectively. Gas holdups are measured by glass capillaries which are connected with the

column by PTFE hoses. The glass capillaries measure the pressure difference caused by the

gas flowing through the column by liquid level indication. To avoid inaccuracies by dynamic

pressure losses caused by the passing gas bubbles PTFE plugs with 1 mm openings are

installed at the bottom of each glass capillary. The level indicators allow for the determination

of gas holdups along the column axis in three 0.6 m sections which are denominated as

sections S1 to S3. The calculation method is provided in the later section of this chapter.

The second glass column 0f 0.3 m diameter is sketched in Figure 4.2.

Figure 4.2 simplified sketch of 0.3 m diameter glass column

98

Basically the operation of this column is identical with the former one. Gas and liquid enter the

column at the bottom and flow concurrently to the top of the column. Liquid leaves the column

via an overflow and flows into a buffer vessel to be recirculated by a pump. The gas passes

through a series of condensers (due to reasons of simplification only one is shown) to get rid

of entrained liquid and leaves through the exhaust. The liquid and gas flow rates are identical

with the ones of the 0.16 m diameter column. Nitrogen was used as gas phase and deionized

water, aqueous solutions of ethanol and acetone as liquid phase. Again, gas holdups are

measured by level indication in glass capillaries which are damped by PTFE plugs to ensure

higher accuracies as described before. Similar to the smaller column the positions of the

holdup measurements are distributed along the column axis to allow for the measurement of

the axial gas holdup distribution.

The third column used in this study is pictured in Figure 4.3.

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Figure 4.3 simplified sketch of 0.33 m diameter stainless steel column

As this column is operable at elevated pressures the functionality of this stainless steel column

is somewhat different compared to the above described two glass columns. First of all liquid

and gas are in concurrent flow and enter the column at the bottom. Nitrogen, which was used

as the gas phase, is provided by a compressor and introduced to the column by a perforated

plate sparger (see Table 4-4 for details). The gas flow is measured by a gas flow meter

(Krohne, H250, 1.6 % measurement error). After the gas leaves the column at the top it enters

a buffer vessel for phase separation. Afterwards it is cooled by a condenser and leaves through

the exhaust. Liquid is circulated by a pump and its flow rate is measured by a flow meter

(Krohne H250, 1.6 % measurement error). It is possible to heat the liquid up to 75 °C before

entering the column by the use of a heat exchanger. Deionized water and cumene were

100

employed as liquid phase. Gas holdups were measured by six differential pressure transmitters

(Endress+Hauser, Deltabar S FMD78) distributed along the column height (see Figure 4.3 for

details and distances) to measure the axial evolution of dispersed phase holdup. The

evaluation procedure is presented in section 2.2. If the column is to be operated under pressure

a backpressure regulator at the gas outlet was used to adjust the pressure. The pressure itself

is raised by the use of a nitrogen gas bundle and varied between 0.1 and 3.6 MPa.

Radial gas holdups were measured by a gamma ray CT and a wire-mesh-sensor (WMS) which

were developed by the Helmholtz-Center Dresden-Rossendorf (see Bieberle et al. [10] and

Schlusemann et al. [11] for details). As the gamma ray CT measurements are based on

radiation transmission, the section of measurement is constructed with a lower wall thickness

of 30 mm which is sketched in Figure 4.3.

For radiation based CT a radiation source is directed to an object of interest and a detector

measures the radiation attenuation by the object of investigation. For full CT scans such

radiographic projections must be obtained from various angular positions. The data sets are

then used as input for CT reconstruction algorithms to calculate the material distribution within

a measuring slice or volume section. In contrast to medical CT, isotopic sources with high

photon energy can be used for industrial CT. This enables penetration of dense walls of a few

centimeters. However, the higher the photon energy of the isotopic source the worse is the

phase contrast between, e.g. gas and liquid. HireCT is a transportable CT system and consists

mainly of three parts: an isotopic source, a radiation detector arc and a rotational unit. As

isotopic source 137Cs with an activity of 180 GBq is used emitting gamma photons with an

energy of approximately 662 keV. The radiation is limited to a 40° wide and 8 mm height fan

beam and is automatically moved-back into a shielding container in case of a power loss. The

radiation detector arc consists of 320 temperature stabilized scintillation detector elements

operated in pulse mode and each with an active area of 2 mm in width and 4 mm in height.

Projection data read-out is automatically triggered by an optical positioning system installed

below a rotational ring on which source and detector arc are placed on. The spatial resolution

101

of HireCT is about 2 mm. Note, CT scans take several minutes, thus, only averaged phase

fraction distributions can be measured. (Bieberle et al. [10], Hampel et al. [12])

The wire-mesh sensor consists of two planes of 64 parallel, equally distributed, stretched wires

positioned orthogonally but offset by a small axial distance of approximately 2 mm. It was

especially developed for the high pressure column. Thus, spatial resolution of about 5 mm is

achieved. One wire plane is operated as a transmitter plane, while the second acts as a

receiver plane. The working principle is to measure the local instantaneous gas holdup at the

virtual crossing point of transmitter and receiver wires. By activating each transmitter wire

successively, the electrical currents at each virtual crossing point, flowing towards the receiver

wires, are measured. Data sampling rates of up to 10,000 Hz are possible.

To visualize the expected flow regimes in this study, the above introduced columns and their

operating conditions with respect to superficial gas velocity are marked in Figure 4.4. This

classification is taken from Shah et al. [4] and is only valid for air/water and air/dilute alcohol

systems at atmospheric pressures. It can be seen from Figure 4.4 that the studied flow regime

in this work is mainly the homogeneous flow regime.

102

4.2.2 Procedures and data evaluation

It has been stated that gas holdups in all three columns were measured by the manometric

method. The difference between the two glass columns and the pressurized stainless steel

column is that level measurements in glass capillaries are used to obtain gas holdups. As both

methods are based on pressure differences the holdup calculations are similar and presented

below.

Gas holdup is usually defined as the ratio of gas volume to total two or three phase volume.

綱弔 噺 撃弔撃弔 髪 撃鎮 (4-1)

Equation (4-2) yields the easiest way of estimating holdups by measuring the clear liquid height

H0 and the gassed liquid height HG.

綱弔 噺 茎弔 伐 茎待茎弔 (4-2)

Figure 4.4 Expected flow regimes in this study, modified from Shah et al. [4]

103

As this method of measurement is prone to uncertainties because HG might be difficult to

measure accurately due to disengaging gas bubbles at the surface a manometric method was

chosen for holdup measurements. If one-dimensional steady-state flow, isothermal behavior,

constant properties and negligible cross-sectional mass transfer are assumed, equation (4-3)

represents a flow model to calculate gas holdups.

綱弔 噺 磐な 髪 ッ喧貢鎮訣ッ月卑 髪 ね酵栂貢鎮訣経 髪 憲鎮態ッ綱弔岫な 伐 綱弔岻訣ッ月 (4-3)

According to Hills [13] and Tang and Heindel [14] the neglection of inertia and shear forces is

justified at low superficial liquid velocities (ul < 0.1 m/s) in concurrent two-phase flow. If shear

stress and inertia forces are neglected, equation (4-3) simplifies to equation (4-4). Rearranging

yields equation (4-5), which can be used to calculate gas holdups at the experimental

conditions of this study. ッ喧 噺 貢鎮訣ッ捲盤な 伐 綱弔岫捲岻匪(4-4岻

綱弔岫捲岻 噺 な 伐 ッ喧貢鎮訣ッ捲 (4-5)

As level indication in capillaries is used for both glass columns, equation (4-6) is used to

calculate holdups for these columns.

綱弔岫捲岻 噺 な 伐 ッ月ッ捲 (4-6)

It should be noted that it is vital to clean the capillaries after each experimental run because

equation (4-5) is only valid if exactly the same fluid is present in the column and all capillaries.

Gas holdups in the pressurized stainless steel column of 0.33 m diameter could be calculated

with equation (4-4). A study by Tang and Heindel [14] offers another calculation method, which

104

takes wall shear stresses into account. Equation (4-7) represents the proposed method of

estimation.

綱弔岫捲岻 噺 な 伐 ッ喧ッ喧待 (4-7)

As can be seen from equation (4-7) the proposed method requires the measurement of

differential pressures 〉p0 for each operating condition without sparging gas into the column.

As this can be comfortably realized and equation (4-7) yields more accurate holdup values

according to Tang and Heindel [14], this method is chosen to obtain the experimental holdups

of this study.

To ensure a high accuracy of measurement all pressure difference readings of the stainless

steel column are recorded for a period of 10 minutes with a frequency of 1/s after steady state

conditions are met. These values are then averaged and the holdup is calculated with equation

(4-7). In addition, all flow and other related measurements are also recorded and averaged

over the same period of time. As no signal processing is possible for the glass column setups,

all experiments are repeated to validate the measurement principle. The total holdup in all

three columns is calculated by averaging the holdups of each axial section.

4.3 Results

4.3.1 Influence of liquid properties

In this section the results obtained in the 0.16 m diameter column at atmospheric pressure are

presented. Dispersed phase measurements were carried out with deionized water, aqueous

solutions of organic solvents, acetone and cumene as the liquid phase and nitrogen as the gas

phase. The superficial gas velocity did not exceed 0.10 m/s and it can be expected that the

bubble column was mainly operated in the homogeneous flow regime and at the beginning of

the transition to heterogeneous flow. Figure 4.5 shows the obtained overall gas holdup values

of nitrogen in deionized water, acetone and cumene. In all three systems the gas holdup rises

with increasing superficial gas velocity.

105

Figure 4.5 Measured gas holdups for N2/H2O, acetone and cumene

It is obvious that the increase in holdup is significantly higher in both organic solvents. The

reason for this is a lower viscosity, lower liquid density and an about three times lower surface

tension of acetone and cumene compared to water. A lower liquid density decreases the

buoyancy force acting on a bubble as the density difference between both phases lowers. This

reduces the bubble rise velocity which in turn increases the gas holdup. Bubble swarm

velocities can be obtained by equation (4-8) [1] directly from the experimental data.

憲長鎚 噺 憲直綱直 (4-8)

With equation (4-8) calculated swarm velocities are plotted in Figure 4.6 and a significantly

lower swarm velocity is obtained for bubbles in acetone and cumene which proves the previous

statements.

106

Figure 4.6 calculated bubble swarm velocities for H2O, acetone and cumene

Decreasing the liquid surface tension enhances bubble breakage and therefore promotes the

existence of smaller bubbles if the breakage rate exceeds the coalescence rate of the bubbles.

The bubble frequency at the sparger also increases with decreasing surface tension because

less momentum is needed to detach a bubble from a sparger orifice and the time for bubble

growth before detachment is reduced [15]. As a result smaller primary bubbles are formed at

the sparger. The same is true for the effect of a lower liquid viscosity on gas holdup. A higher

viscosity favors bubble growth and coalescence and consequently reduces gas holdups [16].

Another interesting point is an observable shift of bubble shapes from larger wobbling nitrogen

bubbles in water to smaller spherical bubbles in acetone and cumene as shown in Figure 4.7.

107

(a) (b) (c)

Figure 4.7 Photographs of nitrogen bubbles in (a) water, (b) acetone and (c) cumene, p = 0.1 MPa, ug =

0.05 m/s

This trend can also be theoretically derived from a diagram proposed by Clift [17] if the

dimensionless Morton and Eötvös numbers for a specific gas/liquid system are calculated. Eo

and Mo numbers are listed in Table 4-5 for assumed bubble diameters of 0.001 to 0.01 m. In

addition these values are charted in Figure 4.8. It can be seen from Figure 4.8 that bubble

shapes for acetone shift to spherical cap bubbles and for cumene to spherical and ellipsoidal

bubbles dependent on the Reynolds number. A different bubble shape affects the drag force

acting on a bubble and therefore also influences the bubble movement within the liquid which

in turn interacts directly with gas holdup.

Table 4-5 Eötvös and Morton numbers for N2 bubbles (dB = 0.001…0.01 m, p = 0.1 MPa)

liquid Eö [-] log(Mo) [-]

H2O 0.13…13.41 -10.6

acetone 0.31…30.69 -11.02

cumene 0.30…30.13 -9.72

108

Figure 4.8 Clift diagram [17] with values of Table 4-5 (blue: H2O, black: acetone, purple: cumene)

As acetone and cumene have comparable physical properties no significant differences in

holdup might be expected. Nevertheless at about 0.03 m/s an observable mismatch between

gas holdups in acetone and cumene can be noted. This difference can be attributed either to

the formation of froth at the top of the column if the superficial gas velocity exceeds 0.03 m/s

in cumene or to a change in flow regimes. As it is inaccurate and often impossible to distinguish

between homogeneous and heterogeneous flow by optical observation, a method to determine

the point of regime transition based on measured parameters will be used. The regime

transition point can either be obtained directly from a holdup vs. superficial gas velocity

diagram if a clear change of the holdup curve gradient occurs or it can be estimated with a

Wallis plot as shown in Figure 4.9 [18]. The approximated point of regime transition is the point

where the measured holdup values level off from the fitted drift flux curve. The fitting parameter

is the bubble rise velocity which was estimated to be 0.47 m/s in deionized water and 0.254

m/s in acetone and cumene. It is noteworthy that the fitted parameters agree with the

calculated bubble swarm velocities in Figure 4.6. With this method a transition holdup of 0.068

in water, 0.12 in acetone and 0.16 in cumene were obtained. Translated into transition

109

velocities this means that the flow regime starts to shift to heterogeneous flow at about 0.03

m/s in water, 0.034 m/s in acetone and 0.038 m/s in cumene.

Figure 4.9 Estimation of regime transition holdup for N2/H2O, acetone and cumene

These values also agree with the points where the bubble swarm velocities begin to increase

in Figure 4.6. The rising swarm velocities at the point of regime transition can be attributed to

the formation of larger bubbles. At this point it can be stated that the starting point of regime

transition shifts to higher gas velocities if surface tension and viscosity of the liquids are lower

than in water because of less bubble coalescence. The experimentally determined regime

transition velocity for water agrees well with data from Krishna et al. [19] and Letzel et al. [20],

who experimentally determined the point of transition of an air/water system in a 0.15 m

diameter column to be at a superficial gas velocity slightly above 0.02 m/s and 0.03 m/s

respectively. An interesting point is that the transition holdups measured by Krishna et al. [19]

and Letzel et al. [20] are around 10 % higher than those obtained in this study. Figure 4.10

compares the measured overall gas holdups of these authors with the ones obtained in this

work and data from Grund et al. [21] and Ohki and Inoue [22].

110

Figure 4.10 Overall gas holdups of this study compared with data from Krishna et al. [23], Letzel et al. [20],

Grund et al. [21] and Ohki and Inoue [22]

The criteria for selecting these authors were a comparable experimental setup with respect to

column diameter and investigated gas/liquid system. More details are summarized in Table

4-6 and it can be concluded that the facilities mainly differ in terms of H/D ratio and sparger

type used. For completeness it should be mentioned that Ohki and Inoue [22] used three

columns (0.04, 0.08 and 0.16 m in diameter) and different types of spargers. The setup listed

in Table 4-6 is the closest to our own.

Table 4-6 Experimental setups of publications depicted in Figure 4.10

Author D [m] H/D [-] gas/liquid sparger type

Krishna et al. [23] 0.16 7.5 N2/H2O ring sparger, 37 x 2 mm

Letzel et al. [20] 0.15 8.13 N2/H2O perforated plate, 200 x 0.5 mm

Grund et al. [21] 0.15 28.66 air/H2O perforated plate, 7 x 2.3 mm

Ohki/Inoue [22] 0.16 18.75 air/H2O perforated plate, 37 x 2 mm

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It is obvious that the results measured in this study are the lowest in Figure 4.10. To explain

this behavior the following reasons can be identified. First of all it is possible that too small

sparger orifices produce very small bubbles which generate higher holdup values. A proposal

of minimum diameter openings of 1 mm was given by Wilkinson et al. [8] in order to measure

gas holdups independently from sparger design and not to mask other effects occurring during

the experiments. As only Letzel et al. [20], who measured the highest holdups of the studies

presented here, used openings with a diameter of less than 1 mm this alone cannot be the

explanation for the deviations. It should be stated that the sparger used in this study is not

completely uniformly distributing the gas until a superficial gas velocity of 0.04 m/s is reached,

which might account for lower holdups obtained in the distributor region at lower gas

throughputs. As can be seen from Figure 4.10, the measured holdups begin to differentiate

from literature data at gas velocities above 0.02 m/s and it can be concluded that the effect of

non-uniform gas distribution on overall holdup is not too large. A second factor listed in Table

4-6 is the aspect ratio of the column. A study by Ruzicka et al. [24] revealed that at constant

column diameter, overall gas holdups decrease with increasing column height. If this would be

the explanation than Krishna et al. [23] should have obtained higher results than Ohki and

Inoue [22] or Grund et al. [21].

One parameter which seems to be underestimated is the quality of the water used for the

measurements. This has recently been stated in a publication by Kemoun et al. [25] as well. If

tap water is used the liquid qualities usually differ from location to location. But even if

deionized water is used the qualities may differ from day to day since the ion exchangers used

to deionize the water become less effective with time and need to be renewed. In addition it is

often not possible or at least very difficult to clean pilot scale facilities. Consequently remnants

of used liquids and dirt may be present and affect each experiment. This seems to be plausible

as small amounts of surfactants already decisively influence the gas holdup which was proven

by a number of publications [19, 26-34]. The effect of addition of small amounts of solvents to

deionized water on gas holdup is shown in Figure 4.11.

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An increase in gas holdup can already be observed for low solvent concentrations of 0.1 vol.-

% in deionized water. The reason for this is a coalescence inhibiting effect of polar solvents in

water. After absorbing at the phase interface the hydrophilic polar part of a solvent will orient

towards the water while the hydrophobic part will arrange itself towards the bubble. This

orientation results in a repelling effect of approaching bubbles and thus hinders bubble

coalescence [33]. Another statement associated with coalescence hindrance due to addition

of solvents implies that a local surface tension gradient occurs at the interphase of dispersed

and continuous phase which prevents bubble coalescence [29]. If less coalescence takes

place, the bubble size distribution is expected to shift to smaller bubbles and as a consequence

a higher gas holdup is found in coalescence hindered systems. This surface tension gradient

also increases the drag acting on the bubble and thus slowing down its rise velocity.

Figure 4.11 Effect of solvent addition to deionized water on gas holdup

Figure 4.11 shows that gas holdup in a 1 vol.-% aqueous ethanol solution is 2.2 times higher

than in pure deionized water. The addition of 0.1 vol.-% ethanol and same amounts of acetone

to water also causes a remarkable increase of the measured holdups. No significant difference

of measured holdups is observable for 0.1 vol.-% ethanol and acetone. The large discrepancy

between ethanol and acetone concentrations of 1 vol.-% above 0.03 m/s superficial gas

113

velocity might be related to evaporation and entrainment of volatile acetone during the

measurement. As the quantities of added solvents are very low the downstream condensers

were not expected to condense entrained acetone or ethanol.

There are certain security requirements to be met if large quantities of organic liquids are used

for experimentation. That is why it might be desirable to substitute these pure liquids with less

dangerous media like aqueous mixtures with low organic content as discussed above. Figure

4.12 proves that this approach is inappropriate. Gas holdups measured in acetone are lower

than in aqueous solutions of 0.1 and 1.0 vol.-% acetone. This can be referred to the complex

interaction of liquid properties as discussed above. The mechanism of inhibiting bubble

coalescence due to addition of small amounts of organic solvents can primarily be related to

bubble-liquid interphase phenomena while the overall mechanism of bubble generation,

movement, coalescence and breakup in pure liquids because of a more complex interaction

of liquid properties in general.

Figure 4.12 Comparison of aqueous acetone solutions with pure acetone

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4.3.2 Influence of scale and liquid velocity

After discussing the influences of pure liquid properties and binary liquid mixtures on gas

holdup two other parameters are of primary concern when designing bubbling multiphase

contactors. It has been stated that bubble column reactors are often used for slow gas-liquid

reactions and that these reactors are operated continuously. Therefore the influence of liquid

velocity on dispersed phase holdup needs to be examined. Furthermore the influence of

column diameter on gas holdup will be discussed in this chapter in order to be able to gain

insights into holdup behavior at larger reactor scales. The analysis of both parameters is

necessary as the few available publications state different opinions about their influence on

gas holdup.

As an example Wilkinson et al. [8] and Forret et al. [5] state no significant influence of column

diameter on gas holdup. A constraint for the validity of the statement above given by Wilkinson

et al. [8] is that the column diameter needs to be larger than 0.15 m. On the other hand, Krishna

et al. [6, 7] and Botton et al. [35] found a decrease in gas holdup with increasing column

diameter in both homogeneous and heterogeneous flow regime. Botton et al. [35] state

additionally that this is true for their experimental results if column diameters of less than 0.25

m are used. Table 4-7 summarizes the experimental conditions of each group.

Table 4-7 Experimental conditions of literature studies on diameter influence on gas holdup

author D [m] ug [m/s] gas/liquid

H/D [-] ul [m/s]

Wilkinson et al. [8] 0.15, 0.23 0 – 0.3 N2/H2O, n-Heptane, mono-

ethylene glycol 8, 5.22 -

Forret et al. [5] 0.15, 0.40, 1.0 0.05 – 0.2 air/H2O

> 4 -

Krishna et al. [6, 7] 0.1, 0.174, 0.19,

0.38, 0.63

0 – 0.866 air, He, Ar, SF6/H2O, tetradecane,

paraffin oil, polyacrylamide

solutions 0.8 - 13 -

115

Botton et al. [35] 0.02, 0.075, 0.25,

0.48

0 – 14 air/H2O, aqueous glycol solutions,

H2O + surface active agent

16, 57.33, 8.8,

4.16

0 – 0.025

As the flow conditions of this study are limited to maximum superficial gas velocities of about

0.12 m/s, the comparison of the present results will be restricted to that point. It is noteworthy

that Wilkinson et al. [8] examined gas holdups at elevated pressures, too. This will be

discussed in a later section. Forret et al. [5] disclosed only one holdup value for each column

diameter. Thus a comparison of their results with other authors seems not expedient. From the

above mentioned authors only Botton et al. [35] operated two of their columns with non-

stagnant fluids but concentrated on very high gas throughputs. The data of Wilkinson et al. [8]

for gas holdups in water and mono-ethylene glycol and Krishna et al. [6] in water are depicted

in Figure 4.13 and Figure 4.14 respectively.

Figure 4.13 Influence of diameter on gas holdup according to Wilkinson et al. [8]

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There are nearly no deviations of gas holdups observable in both columns used by Wilkinson

et al. [8]. The lower holdups of nitrogen in mono-ethylene glycol can be referred to the 20 fold

higher liquid viscosity of mono-ethylene glycol compared to water. The data of Krishna et al.

[6] show a significant decrease of gas holdup if the column diameter is enlarged from 0.1 to

0.15 m. An increase of lower magnitude of gas holdup can be noted if the column diameter is

further enlarged from 0.15 to 0.38 m. The larger increase in the first case might be referred to

occurring wall effects which affect gas holdups in columns of diameters less than 0.15 m.

Dropping holdups in larger diameter columns occur according to Krishna et al. [6] due to larger

liquid circulations in columns of greater diameters.

Figure 4.14 Diameter influence on gas holdup according to Krishna et al. [6]

The measurements of this study show a similar trend of gas holdup with respect to column

diameter like the data presented by Krishna et al. [6]. Holdups tend to decrease by about 1.5

– 2 % if the column diameter is increased from 0.16 to 0.30 m diameter. Surprisingly it is found

that holdup continuingly decreases if the diameter of the column is further increased to a value

of 0.33 m (Figure 4.15).

117

Figure 4.15 influence of column diameter on gas holdup

This behavior can be explained as the aspect ratio of the 0.33 m diameter column is of the

same magnitude as the 0.16 m diameter column, while the 0.3 m diameter column is of lower

H/D ratio. According to Ruzicka et al. [24], columns of increased height at a fixed diameter

have lower gas holdups as their shorter relatives. This means that the column height is the

main cause for the differences between gas holdups measured in the 0.3 and 0.33 m bubble

column. While the holdups of the 0.16 and 0.30 m diameter column have a difference of 1.5 to

2 % at superficial gas velocities below 0.04 m/s, the comparison between the 0.30 and 0.33 m

diameter column reveals that gas holdups start to differ at superficial gas velocities above 0.02

m/s. If both glass columns are compared one can also see that the difference between holdups

above superficial gas velocities of 0.04 m/s, which is in the region of flow regime transition,

seems to be constant if measurement errors are considered. The fluctuation of holdups occurs

because the bubble size distribution developed at these conditions becomes more non-uniform

than in the homogeneous flow regime which in turn intensifies bubble coalescence resulting in

a non-linear relationship of gas holdup and superficial gas velocity. Despite of the same trends

the magnitudes of the results of the present study differ widely from the ones presented by

Krishna et al. [6]. This can be attributed to the initial liquid height of 1 m which was maintained

118

by Krishna et al. [6] and resulted in significant lower column aspect ratios than in this

publication. Another experimental condition contributing to higher holdups is a sparger with

smaller orifice openings (0.5 mm) used by Krishna et al. [6]. The difference in gas holdups of

both studies is about the same magnitude as the difference of H/D ratios. As the column

dimensions with respect to diameter and spargers do not exactly match, this of course remains

to be a speculative relationship. Anyhow, gas holdup is defined as the fraction of gas in total

column volume which comprises liquid and gas. When aspect ratios are decreased by lowering

the liquid level, the total volume also decreases. If the same amounts of gas are introduced to

achieve the same superficial gas velocity the fraction of gas in the column will be higher

because of the same volume of gas in a smaller volume of liquid.

A clear influence of column diameter on gas holdup can also be seen if acetone or cumene is

employed as the liquid phase. Because of safety reasons cumene could not be used in the 0.3

m diameter glass column. Acetone was not used in the steel column because the seals of

some equipment devices were not acetone resistant. Therefore column diameter effects on

gas holdups in acetone are examined in both glass columns, while cumene was examined in

the 0.16 m diameter glass column and the larger steel column. A larger decrease in gas

holdups in both acetone (Figure 4.16) and cumene (Figure 4.17) especially at higher superficial

gas velocities of up to 4 % is noted as column diameter increases. Additionally measurements

of holdups in acetone done by Öztürk et al. [36] in a 0.095 m diameter column are plotted in

Figure 4.16. Despite of the smaller column diameter used for their measurements the results

obtained are within the range of the presented holdups of this study obtained in a 0.16 m

diameter column. Öztürk et al. [36] used a single orifice sparger of 3 mm diameter and

measured gas holdups by comparing the ungassed liquid height (which was 0.85 m, resulting

in an aspect ratio of 8.95) to the gassed liquid level. Keeping the discussion above about

column diameter and aspect ratio in mind one would expect higher holdups in the 0.095 m

diameter column used by Öztürk et al. [36] compared to the present results. A possible

explanation could be the less effective single orifice sparger used by the authors which

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contingently distributes bubbles non-uniformly over the column cross section resulting in a

longer sparger inlet zone and thus a lower overall gas holdup.

Figure 4.16 Influence of column diameter on nitrogen holdup in acetone

Almost an identical behavior is observed when nitrogen holdups in cumene are compared with

measurements by Matsubara et al. [37], who examined gas holdups in cumene in a column of

0.3 m diameter (Figure 4.17). Matsubara et al.`s [37] results are about 2 % higher relative to

the results obtained in this investigation. This difference might be attributed to a lower H/D

aspect ratio of their column compared to the 0.33 m diameter steel column. According to the

authors their column had an aspect ratio of 5, related to aerated liquid height. Consequently

the unaerated aspect ratio is even lower. As stated and shown above lower aspect ratios cause

higher holdups. Anyhow Matsubara et al.`s [37] results show a similar trend like the results

obtained in the 0.16 and 0.33 m diameter column with a change in slope at about 0.04 m/s

superficial gas velocity. This change indicates the beginning of flow regime transition as

pointed out earlier (Figure 4.9). A change in column diameter from 0.16 to 0.33 m seems not

to influence the point of regime transition.

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Figure 4.17 Influence of column diameter on nitrogen holdup in cumene

A parameter not yet discussed while comparing the present results with literature data is the

superficial liquid velocity. Semibatch operation is often encountered in publications, but is

almost never applied as the mode of operation of industrial production units. Nevertheless, the

number of publications dealing with this topic is limited as well as publications which examined

organic solvents. Usually low liquid velocities are found in bubble columns because their main

purpose is to carry out slow multiphase reactions. It is generally imaginable that concurrent

flow of liquid and gas tends to reduce and countercurrent flow increases gas holdup as bubbles

are either accelerated by liquid motion (concurrent) or decelerated (countercurrent). As liquid

velocities are low to achieve residence times in the magnitude of hours, its influence on holdup

is often thought to be negligible. Akita and Yoshida [38] examined the influence of liquid

velocity on gas holdup in a 0.152 m diameter column and found no relationship between these

parameters as gas holdup did not change with superficial liquid velocity. On the other hand,

Shah et al. [39] noted a slight decrease of gas holdup in an empty and packed bubble column

of both 0.29 m diameter with an aspect ratio of 6.9. Liquid velocities were varied up to 0.002

m/s in countercurrent operation of gas and liquid. The decrease in gas holdup was attributed

121

to an increase in friction force between liquid and gas which, according to the authors,

enhances bubble coalescence.

Measurements of gas holdup with variation of superficial liquid velocities in this study seem to

confirm that there is no influence of liquid velocity on gas holdup within the range of parameters

studied and the corresponding accuracy of measurement. Figure 4.18 shows the results with

consideration of liquid velocity in the 0.16 m diameter glass column. Figure 4.19 shows results

of the greater 0.3 m diameter glass column and Figure 4.20 the effect of superficial liquid

velocity on gas holdup in the steel column.

Figure 4.18 Variation of superficial liquid velocity, 0.16 m diameter glass column

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Figure 4.19 Variation of superficial liquid velocity, 0.30 m diameter glass column

 

Figure 4.20 Variation of superficial liquid velocity, 0.33 m diameter steel column

It is evident that there is no distinct relationship between gas holdup and superficial liquid

velocity observable at all column dimensions and liquids studied. Variations of holdups with

liquid velocity are within the measurement errors. Hills [13] mentioned that if the applied

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superficial liquid velocity is low compared to the bubble rise velocities, no impact of liquid

velocity on gas holdup is expected as the acceleration of the bubbles in concurrent operation

of both phases will be negligible. A comparison between the bubble swarm velocities in Figure

4.6 with the applied liquid velocities shows that bubble swarm velocities are up to 280 times

higher than the liquid velocities. Therefore it is not surprising that a potential dependence of

both parameters will not be found at these operating conditions, although they are realistic with

respect to liquid circulation rates in production plants.

4.3.3 Influence of temperature

The influence of temperature mainly affects liquid viscosity, density and surface tension. As all

three properties change with temperature, however with different magnitudes as shown in

Table 4-8, it is thought to be difficult to isolate the effect of one property on gas holdup due to

a temperature increase. The property most affected by temperature is liquid viscosity (Table

4-8).

Table 4-8 relative change of liquid properties with temperature, reference 20 °C

ǻT [°C] 30 55

H2O

〉と [%] -1.0 -2.3

〉た [%] -45 -62

〉j [%] -8.10 -14.86

cumene

〉と [%] -2.7 -5.0

〉た [%] -31.64 -46.83

〉j [%] 10.7 21.4

Expected are smaller bubbles and slightly reduced bubble coalescence at lower viscosity.

Surface tension and liquid density changes only a little with rising temperature in the parameter

range examined here. Figure 4.21 shows results obtained in the steel column for liquid phase

temperatures of 20, 50 and 75 °C of water and 20 and 75 °C of cumene.

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Figure 4.21 Influence of temperature on gas holdup

No clear relationship between temperature or rather liquid viscosity and gas holdup is

observable. If cumene was used the measured holdups did not deviate from each other at both

temperature levels. As water becomes less viscous with rising temperature an increase of

holdup from 20 to 50 and 75 °C would be expected. Figure 4.21 shows a more diffuse behavior

because holdups measured at 50 °C are lower than the ones at 20 °C while the results at 75

°C are higher than at 20 °C. These differences can be related to impurities present in the liquid

phase and the accuracy of measurement. Kulkarni and Joshi [15] stated that the results with

respect to viscosity obtained so far are contradictory, ranging from no-influence to slight

influence on bubble size with rising viscosity. The observation of smaller holdups with rising

viscosity was already mentioned in Figure 4.13 where gas holdup measurements of Wilkinson

et al. [8] in mono-ethylene glycol are compared with water. In addition, Urseanu et al. [16]

found a significant increase in gas holdups with lower liquid viscosities for high viscous media

(0.07 – 0.55 Pas). Obviously the cited authors used liquids far more viscous than the ones

employed in this study. Although a notable decrease in viscosity occurs at the conditions

examined, compared to the viscosity range studied by Urseanu et al. [16] or reviewed by

Kulkarni and Joshi [15] these differences appear to be negligible.

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However this finding is of importance for the experiments reported here because no possibility

to cool the liquid was installed in all three experimental facilities. As the pump always

introduces some heat into the column it was not possible to keep the liquid temperature exactly

constant at the desired level. The temperature increased at a rate of about 1 K/10 min which

was exactly the time needed to acquire one measurement point. Approximately 6 – 8 K

temperature difference should be considered to complete one experimental run. As discussed

above this complication does not influence the results of this study as the changes in gas

holdup with rising temperature are small.

4.3.4 Influence of pressure

Often production of chemicals in multiphase reactors takes place at elevated pressure.

However, the effect of gas density on gas holdup at higher pressure has not been studied as

extensive as one would expect it considering the importance of this parameter for bubble

column design. It is most generally agreed that gas holdup rises if pressure is increased. This

has been experimentally verified by Wilkinson et al. [40], Letzel et al. [20] and Clark [41] to

name a few. A brief survey of other studies can be found in Rollbusch et al. [42]. The reasons

for increased holdups at elevated pressure can be found in the formation of smaller bubbles

[43] because of enhanced bubble breakup and less buoyancy force as a result of a lower

difference in phase densities. Also for operation at higher gas throughputs the point of regime

transition is shifted to higher superficial gas velocities [8] because less large bubbles form at

these conditions.

In this study 4 different pressure levels (0.1, 1.0, 1.85 and 3.6 MPa) were investigated for the

system nitrogen/deionized water and 3 levels (0.1, 1.85 and 3.6 MPa) for nitrogen/cumene in

the 0.33 m diameter bubble column. Superficial gas velocities were limited to a maximum of

0.05 m/s because low gas holdups were of interest for this study. Generation of lower holdups

was also necessary to test some of the developed measurement techniques in this specific

project. A laser endoscopic measurement technique developed by ILA (Intelligent Laser

Applications GmbH, Jülich) was used to characterize bubble size and velocity. High holdups

or high bubble loads would have permitted the use of this measurement technique as it is

126

based on evaluation of photographs. On the other hand it is quite difficult to establish higher

superficial gas velocities at this scale and operating condition. The use of gas bundles was not

feasible because the necessary operating time of the tested tomographic measurement device

was about 10 minutes for one operating point and the needed amount of gas for one complete

experimental run cannot be provided by gas bundles.

The effect of pressure on gas holdup is shown in Figure 4.22 for nitrogen holdups in deionized

water and in Figure 4.23 for holdups of nitrogen in cumene. First of all it can be seen from both

figures that gas holdup rises with increasing superficial gas velocity even at the applied low

superficial gas velocities.

Figure 4.22 Pressure effect on gas holdup, N2/H2O

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Figure 4.23 Pressure effect on gas holdup, N2/cumene

Gas holdup also seems to be a function of pressure at these conditions which is contrary to

the findings published by Pohorecki et al. [44, 45] who conducted studies in a similar column

(height: 4 m, diameter: 0.3 m) and comparable operating conditions to study the effect of

pressure on holdup in water and cyclohexane. They found no dependence between holdup

and pressure at all and mentioned that besides liquid properties the superficial gas velocity is

mainly affecting holdup values. Letzel et al. [20] also measured gas holdups at similar

experimental conditions, except the smaller column diameter, and found no influence of

pressure on holdup below 0.05 m/s superficial gas velocity. Further comparison with literature

data is difficult as most results are focused on higher superficial gas velocities or were

measured in columns of very different geometry. Fortunately Weber [46] published two gas

holdup data points of a commercial cumene oxidizer bubble column (diameter: 4.6 m, p : 0.7

MPa) which can be extracted and compared with the results of this study (Figure 4.24). If the

1.85 MPa points are linearly extrapolated, which is justified as the column was operated in the

homogeneous regime and the extrapolation does not exceed the limits of expected

homogeneous flow, one observes that both holdup values of the industrial plant lie above the

measurements at 0.1 MPa and slightly beneath those obtained at 1.85 MPa. Keeping the

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earlier discussion about the data presented in Figure 4.23 in mind mainly three aspects can

be identified for the observed variation in holdups. Obviously the pressure is 1.05 MPa lower

as during the experiments presented here which should result in lower holdups. Another point

is that the industrial column is much larger in diameter than the facility used here and that the

cumene used in the production plant should be considered as a reaction mixture mainly

consisting of cumene. As pointed out earlier the cumene used in this study had a purity of 99

% according to the product data sheet. As all three contributions to the deviations interact with

each other the lower pressure of the oxidizer might be considered as the main reason.

Furthermore the gas sparger of the cumene oxidizer is oriented downwards [47] which may

affect the initial bubble movement. Anyway, Figure 4.24 proves that the conditions examined

during the present experiments are realistic with respect to industrial production units.

Figure 4.24 Comparison of own measurements with industrial plant data at 0.7 MPa published by Weber [46]

Despite the lack of available experimental data some conclusions can be drawn from the

figures above and compared with argumentations derived from other studies. It has already

been stated that the measured holdups increase with rising pressure in water and cumene as

well. This is the result of increased bubble breakage which leads to the existence of smaller

bubbles at elevated pressure than compared to atmospheric conditions [48-52]. Bubble

129

breakup at pressures above atmospheric might be enhanced because of a more pronounced

propagation of instabilities at the phase interface [52]. Of course buoyancy force reduces

significantly as gas density increases with pressure (Table 4-2 lists nitrogen densities for

conditions established here) which results in slower bubble rise velocities and therefore higher

bubble residence times. Liquid surface tension also lowers slightly with increasing pressure

(Table 4-9) and promotes bubble breakup. Of course one should not forget that during the

experiments presented liquid impurities might play a special role. The bubble column was

cleaned and dried as good as possible after switching liquids (water or cumene) but it is always

possible that remnants of the used liquids remained inside the facility as it is quite difficult to

completely clean experimental setups of this dimension. As noted earlier, the cumene used

during this experiments had a purity of 99 % by delivery.

Table 4-9 measured surface tensions of cumene and water at various pressures and 35 °C, data provided by Eurotechnica GmbH

p [MPa] deionized water [N/m] cumene [N/m]

0.10 0.0715 0.026

1.10 0.0698 -

1.85 0.0687 0.0255

3.60 0.0671 0.0252

Comparing the data in Figure 4.22 with the ones of Figure 4.23 a larger relative increase of

holdups with pressure in water than in cumene is noted. The relative holdup increase in water

from 0.1 to 3.6 MPa is about 500 % while the relative increase in cumene is about 125 %. As

reasons for this mainly two arguments can be identified. First, the primary bubble size at

atmospheric conditions in cumene or any other organic liquid is smaller than in water because

of the different liquid properties which influence bubble formation, coalescence and breakup

(see the above discussion on liquid properties for details). The effect of increased gas density

on bubble size is therefore less pronounced in organic liquids than in water. On the other hand

the decrease in surface tension if pressure is increased from 0.1 MPa to 3.6 MPa listed in

Table 4-9 is more distinct in water, about 6.2%, than in cumene, which is about 3.1 %. As

130

surface tension is directly influencing bubble breakup and coalescence its relative change with

pressure might also account for different rates of holdup increase due to pressure.

4.3.5 Axial evolution and radial distribution of gas holdup

Most publications focus on integral or radial holdup measurements. Only a few describe the

axial distribution of gas holdup along the column height. Information about axial holdup

distribution can be vital to characterize sparger inlet zones or the effect of internals on gas

holdup. Pressure decreases along the column height because the liquid height reduces.

Deckwer [53] already pointed out to correct the superficial gas velocity according to the liquid

height because of this circumstance. Of course reduced pressure interacts with bubble

properties which are known to affect gas holdup. Consequently at least a minor increase in

gas holdup with column height is expected. Brauer [54] defined three zones of varying holdup

magnitudes. According to Brauer [54] a sparger inlet zone near the bottom of the column with

lowest holdups is followed by a zone in which bubble breakup and coalescence are in

equilibrium in the middle of the column. Holdups increase in the first zone until the second

zone is reached. From that point gas holdup is constant until the third one begins. This zone

is near the top of the column where gas disengages and highest holdups are to be found.

Experimental evidence for this behavior is given by Jin et al. [55] who measured axial holdup

profiles with pressure difference and gamma-ray devices in a 6.6 m high bubble column of 0.3

m diameter. Water or acetic acid was employed as the liquid phase and the pressure was as

high as 1.0 MPa. Jin et al. [55] observed a sharp ascent of holdups with column height and the

forming of a foam layer at the top of the column. However the authors established very high

superficial gas velocities between 0.1 and 0.4 m/s. Kumar et al. [56] examined axial holdups

with a gamma-CT device and noted increasing holdups along the column height. They

attributed this result to the formation of larger primary bubbles at the sparger which breakup

as they travel to the top of the column. Consequently more bubbles with smaller diameter will

be found at higher elevations than at the sparger causing higher holdups.

131

The results presented here show a similar trend. The lowest holdups are found near the bottom

e.g. sparger of the column. At 0.1 MPa (Figure 4.25) a zone with slightly increasing gas holdup

can be observed until 2.83 m of column height are reached. This increase is within the error of

measurement and should therefore be treated carefully. Beyond 2.83 m liquid level a sudden

decrease of holdup occurs. The reason for this might be a significant reduction of pressure at

atmospheric conditions due to less liquid head which causes increased bubble coalescence.

At the top of the column (3.88 m) a sharp increase of gas holdup is noted which is due to gas

bubble disengagement and the forming of a foam like layer.

Figure 4.25 Axial gas holdup profiles along the column height, N2/H2O, p = 0.1 MPa

Comparing the results at atmospheric conditions with results obtained at 3.6 MPa (Figure 4.26)

it is observable that the zone between 1.63 and 2.83 m inherits constant holdups and that the

coalescing partition above 2.83 m is missing as gas holdups steadily increase beyond 2.83 m

liquid level. Because system pressure influences bubble breakup, as discussed in the previous

chapter, the breakup rate is faster than the coalescence rate and therefore more small bubbles

are present in the column which enhances gas holdup. The foam like layer at the top of the

column might also be increased because a larger number of bubbles disengage. A missing

coalescence zone between 2.83 m and 3.3 m liquid height might be explained by a reduction

132

of liquid head in conjunction with the effects of elevated pressure. At atmospheric conditions

bubbles tend to grow and coalesce as they travel upward the column because of a lower liquid

head. At pressurized conditions the change in pressure due to less liquid head is low compared

to the overall pressure of 3.6 MPa. Despite of that bubbles moving upward in the column might

slightly grow but do not coalesce. This means that a larger number of bubbles is present in the

column at pressurized than at atmospheric conditions which causes the observed increase of

gas holdup along the column axis.

Figure 4.26 Axial gas holdup profiles along the column height, N2/H2O, p = 3.6 MPa

The same result is obtained in cumene at atmospheric pressure (Figure 4.27). Gas holdup

increases continuously towards the column. Additionally this effect seems to be more

pronounced at higher superficial gas velocities. Nitrogen bubbles do not coalesce that much

in cumene compared to bubbles in water. Nevertheless they tend to grow because of the

reduced liquid head and therefore occupy more volume at a constant number of bubbles. A

foam layer is expected to exist at the top of the column because this was observed during the

measurements in the glass column of 0.16 m diameter.

133

Figure 4.27 Axial gas holdup profiles along the column height, N2/cumene, p = 0.1 MPa

Surprisingly a different result is obtained at pressurized conditions (Figure 4.28). The expected

increase of gas holdup above 1.16 m seems to stay constant within the accuracy of

measurement until 2.83 m are reached. At this point a sharp increase occurs before the

measured holdups tend to decrease at the gas disengagement zone. A possible explanation

might be the earlier observation of a strong tendency of foaming in cumene at the top of the

column. At atmospheric conditions this foam might contribute to higher measured gas holdups

at the disengagement zone while the foam layer might collapse at pressurized conditions

resulting in an abrupt decrease of holdup.

134

Figure 4.28 Axial gas holdup profiles along the column height, N2/cumene, p = 3.6 MPa

Some interesting remarks about radial holdup profiles obtained during this study seem

appropriate. During this study a cooperation with the Helmholtz-Center Dresden-Rossendorf

made it possible to compare gas holdups measured by pressure difference sensors with the

ones measured with a wire-mesh sensor and a gamma-CT (see section 4.2.1 for details) in

the 0.33 m diameter column. The results are shown in Figure 4.29. One can see that all three

methods of measurement deliver comparable results. Deviations occur mainly due to the fact

that both WMS and Gamma-CT deliver local holdups while the pressure difference

measurements shown here are overall holdups. The general difference between WMS and

Gamma-CT is again caused by differing water qualities. Obviously gas bubbles in water seem

to concentrate in the middle of the column which causes a radial difference in gas holdup. This

is quite the opposite behavior if compared to Gamma-CT measurements done in cumene

(Figure 4.30). In cumene nearly no radial holdup profile exists. This is explained by the

existence of smaller bubbles which are evenly distributed along the radial coordinate than the

bubbles formed in water (which are of broader size distribution).

135

Figure 4.29 Validation of gas holdups obtained by pressure difference measurements with wire-mesh sensor and gamma-CT measurements

Figure 4.30 Gamma-CT measurements in deionized water and cumene compared to pressure difference measurements

136

4.3.6 Prediction of gas holdups

Precise prediction of gas holdup is essential for the design of bubble column reactors and

contactors. Gas holdup directly determines reactor size and interfacial area and is furthermore

connected to liquid backmixing and heat and mass transfer rates. Thus gas holdup is one of

the most important design parameters and should be estimated as accurately as possible in

order to avoid designs which might lead to ineffective reactor operation [57].

A vast number of empirical correlations exist to calculate the amount of gas holdup. In addition

some semi-theoretical equations based on idealized model assumptions have also been

published. Figure 4.31 shows an example calculation of gas holdup in the 0.33 m diameter

column at atmospheric pressure and water as liquid phase with various correlations. Obviously

large deviations of up to 400 % occur within the presented correlations. Even at low superficial

gas velocities in the homogeneous flow regime, where a linear dependency of holdup and gas

throughput is expected, very large differences prevail. Because bubble column hydrodynamics

react very sensitive on column geometry, sparger design, gas and liquid properties it is very

difficult to identify suitable equations for predicting gas holdups (and other hydrodynamic

parameters as well). Some of the depicted correlations are based on the principles of

dimensional analysis (Akita [38], Hikita [58], Idogawa [49]). Wilkinson et al. [8] considered

changing flow regimes and consequently large and small bubble holdups. However whether

the design equation is based on engineering fundamentals like dimensional analysis or

theoretical considerations it most commonly fails if it is used for setups other than it is derived

from and matching experimental and calculated results are to be considered as flukes. With

the points mentioned of the result discussion above it is obviously difficult enough to establish

comparable experimental conditions as even water is not comparable without being extra

cautious with respect to impurities and general water qualities. On the other hand, correlations

suited for the prediction of holdups in organic material are very scarce.

137

Figure 4.31 Comparison of gas holdup correlations by Akita and Yoshida [38], Hikita et al. [58], Hughmark [59], Joshi et al. [60], Mersmann [61], Reilly et al. [62], Sharma [63], Wilkinson et al. [8], Idogawa et al. [49]

From an industrial point of view an equation to predict gas holdup must not only be reliable

with respect to accuracy of holdups in water. Furthermore this correlation needs to be able to

predict gas holdup under consideration of column diameter, different liquid properties (as water

is most often not of interest for industrial production plants) and of course gas density. Almost

no correlations exist which fulfill these requirements. Krishna et al. [6] screened available

correlations with the same scope as this study and identified two possible equations, namely

Akita and Yoshida [38] and Zehner [64, 65]. Both correlations are plotted in Figure 4.32 for the

three column dimensions used in this study.

138

Figure 4.32 Prediction of column diameter influence by correlations of Zehner [64] and Akita and Yoshida [38]

Only the Zehner [65] correlation is able to predict the trends observed in the results presented

here and by Krishna et al. [6]. Despite of having the column diameter as an input parameter

the equation derived by Akita and Yoshida [38] does not predict any influence of column

diameter. Interestingly, Zehner`s [65] correlation predicted a decrease of holdups with column

diameter which is about the same magnitude as observed in the present experiments and even

Krishna et al.`s [6] results. Because of that the correlation proposed by Zehner [65] will be

examined more closely. Zehner`s [65] correlation is based on an improved circulation cell

model originally suggested by Joshi and Sharma [63]. The original model describes bubble

column hydrodynamics as circulating cells of vertical alignment. Zehner [64] adapted this

model and substituted the circulation cells with crosswise aligned roller cells. According to

Zehner [64], this has the advantage that the centerline velocity of the liquid phase is always

directed upwards and the liquid velocity near the wall is directed downwards which has been

experimentally confirmed by several authors (e.g. Wu and Al-Dahhan [66]). The downwards

moving liquid decelerates and entrains some bubbles while the upwards moving liquid contains

bubbles moving in the opposite direction. As a result a difference in gas holdups occurs which

causes a pressure difference which is relieved by pressure losses due to liquid movement.

139

The resulting correlation to predict gas holdups (equation (4-9)) is then based on the liquid

centerline velocity, which can be calculated with equation (4-10), and the velocity of the largest

stable bubble which should according to Zehner [65] be calculated with equation (4-11).

綱弔 噺 通虹 通弐濡斑俵怠袋替磐 祢虹祢弐濡卑鉄 典斑 磐祢如轍祢弐濡卑 (4-9)

憲鎮待 噺 謬岾 怠態┻泰 諦如貸諦虹諦如 憲直訣経峇典 (4-10)

憲長鎚 噺 な┻のの 磐蹄直盤諦如貸諦虹匪諦如鉄 卑待┻態泰 (4-11)

The above presented equations inherit all parameters which were identified as important with

respect to gas holdup during the experimental runs. Included are superficial gas velocity, liquid

density and surface tension, reactor diameter and gas density to account for the pressure

influence on gas holdup. Unfortunately the calculated do not match the measured holdups.

This is shown in Figure 4.33. A general overestimation of the predicted holdups can be

observed. The possible reason for this is the calculated bubble velocity ubs. For bubbles in

water at atmospheric conditions a value 0f 0.25 m/s is predicted by the given equation (4-11).

Zehner [65] stated that this equation is taken from Mersmann [61]. Actually a slightly different

equation for the bubble velocity is found in [61] with a prefactor of 2 instead of 1.55 (equation

(4-12)).

憲長 噺 に 磐蹄直盤諦如貸諦虹匪諦如鉄 卑待┻態泰 (4-12)

Measurements of bubble velocities were carried out at the Technical University of Hamburg-

Harburg [67] and are listed and compared with the ones calculated with equation (4-12) in

Table 4-10. As one can see equation (4-12) predicts bubble velocities of nitrogen in cumene

with outstanding accuracy. About 10 % deviation between calculation and measurement of

bubble velocities in water are obtained. As discussed earlier, water seems to be more difficult

to characterize than organic material with respect to coalescence behavior and possible

140

impurities or slightly different water qualities are regarded as the reason for the larger

deviations.

If equation (4-12) is used to predict the bubble velocity and consequently subsets of the

measured gas holdups within a given accuracy the Zehner [65] correlation and the

measurements are in satisfactory agreement, which is shown and discussed below.

Table 4-10 Measured [67] and calculated bubble velocities, pressure as indicated in brackets

deionized H2O

ub [m/s] measured 0.3681 [0.1 MPa] 0.3605 [5 MPa] -

ub [m/s] calculated 0.328 [0.1 MPa] 0.327 [1.85 MPa] 0.325 [3.6 MPa]

deviation [%] 10.89 9.29 -

cumene

ub [m/s] measured 0.2664 [0.1 MPa] 0.2601 [2 MPa] 0.2567 [4 MPa]

ub [m/s] calculated 0.2667 [0.1 MPa] 0.265 [1.85 MPa] 0.263 [3.6 MPa]

deviation [%] 0.11 1.85 2.39

It is possible to predict gas holdups with equation (4-9) within a given accuracy for subsets of

the experimental results presented here. It was not possible to reproduce all experimental

results with equation (4-9). A possible reason might be the presence of tracer substances and

therefore impurities which affect the coalescence behavior of bubbles during the experiments.

141

Figure 4.33 Comparison of predicted holdups with measured values

Figure 4.34 and Figure 4.35 show that equation (4-9) is able to predict the decrease in holdup

with column diameter in deionized water and acetone. In addition the gas holdup at

atmospheric conditions in cumene of the 0.33 m diameter column (Figure 4.36) is also

accurately predicted by the proposed correlation. However it fails to predict holdups in cumene

for the 0.16 m diameter column. The reason for this is the formation of a large foam layer

during the experiments in the 0.16 m column. This effect is not considered by the equations

used to predict gas holdups and consequently the correlation underestimates nitrogen holdups

in cumene. Larger deviations occur when holdups are predicted in water because of possible

impurities present in the experimental facility during the measurements. On the other hand it

is more difficult to measure holdups at gas fluxes of low magnitude which is the reason for

larger deviations between experiment and prediction at very low superficial gas velocity.

142

Figure 4.34 parity plot measured and predicted holdups N2/H2O

Figure 4.35 parity plot measured and predicted holdups N2/acetone

143

Figure 4.36 parity plot measured and predicted holdups N2/cumene

The modified Zehner correlation is also able to predict subsets of holdups at higher pressures

than atmospheric in organic liquids and in deionized water. Figure 4.37 and Figure 4.38 show

the corresponding comparisons between prediction and experimental results. The results at

3.6 MPa depicted in Figure 4.37 are completely underestimated. As previously discussed the

addition of small tracer substances was necessary and additionally water qualities might have

changed due to the presence of surfactants. Consequently it is hard to evaluate measurements

done in deionized water and to compare them with predictions. More important is the

applicability of the proposed equation for holdups in organic liquids at elevated pressures. As

can be seen from Figure 4.38 the experimental holdups in cumene at elevated pressure can

be predicted within reasonable accuracy by the modified Zehner correlation.

144

Figure 4.37 parity plot for various pressures, measured and predicted holdups N2/H2O

Figure 4.38 parity plot for various pressures, measured and predicted holdups N2/cumene

145

4.4 Conclusions

The effect of various operating and design parameters on gas holdup in two phase bubble

columns was experimentally verified and a correlation was proposed to calculate holdups at

the examined conditions. Studies were carried out in three columns of varying diameter and

height to diameter ratios with deionized water, acetone, cumene and aqueous ethanol and

acetone solutions. It was found that gas holdups decrease with increasing column diameter

and height to diameter ratio. Low superficial liquid velocities do not affect gas holdup whereas

increased gas density drastically increases holdup. The increase of holdups in deionized water

is higher than in cumene because of a larger initial bubble size and a more pronounced

reduction of surface tension due to elevated pressure. The use of organic solvents as liquid

phase material has shown that decreased surface tension and liquid density results in higher

holdups than in deionized water. The addition of small amounts of aqueous ethanol and

acetone solutions increased holdups dramatically due to coalescence inhibition. A comparison

between the measured holdups of the aqueous solutions and pure organic liquids revealed

that aqueous solutions are not suitable as substitutes for organic substances. Regarding the

effect of temperature no dependency was found. This is mainly because liquids of low

viscosities were examined and no effect of decreasing viscosity due to higher temperatures

was observed. It was found that holdups slightly increase with column height and that three

zones along the column axis can be defined. A sparger inlet zone, a zone of near constant gas

holdup where equilibrium between breakup and coalescence exists and a gas disengagement

zone were identified. To predict gas holdups a modified form of the Zehner [65] correlation is

proposed. It was shown that this equation is able to predict the effect of column diameter, liquid

properties and pressure on gas holdup at conditions studied here.

To further validate the ability to reliably predict gas holdups results at higher superficial gas

velocity will be necessary. The parameter range of this study was suited to chemical processes

operating at low superficial gas velocities in the homogeneous flow regime. If the proposed

correlation is used to predict holdups in the heterogeneous regime one should be cautious.

Nevertheless the proposed correlation here relies on a simplified flow model, bubble and liquid

146

centerline velocities and does not inherit any fitting parameters. Therefore it seems promising

to predict holdups using the suggested correlation.

Besides validating correlations the generated experimental results, especially the axial

distribution of gas holdups, might be useful to validate CFD models. This is of special interest

as data measured at processing conditions and technical scales to validate models are hard

to find.

It was pointed out additionally that bubble column hydrodynamics are only comparable if

identical experimental setups are used. Therefore it is extremely difficult to compare own

results with literature data. Even if the column dimension and the liquid phase are identical,

deviations in the sparger design hamper comparability. It seems not promising to compare

holdups in water because water qualities differ too much and are sensitive to surfactants.

Another point is that water as liquid phase is mostly not of interest for industrial needs. Organic

liquids are processed at pressurized conditions and therefore future experiments should

concentrate on this subject. However the use of organic material requires elaborate security

measures and the operation of pressurized vessels makes things not easier as a certain

infrastructure is required to run them.

147

4.5 Notation

Symbols

Symbol Meaning Unit

D column diameter m

Eo Eötvös-number [-]

g acceleration m/s2

H height m

Mo Morton-number [-]

p pressure MPa

T temperature °C

u superficial velocity m/s

V volume m³

i holdup [-]

と density kg/m³

j surface tension N/m

k stress N/m2

Subscripts

Subscript Meaning

b bubble

bs bubble swarm

C column

g gas

l liquid

l0 liquid centerline

w wall

148

4.6 References

[1] Deckwer, W.D., Reaktionstechnik in Blasensäulen. 1 ed1985, Frankfurt am Main: Salle+Sauerländer.

[2] Kantarci, N., F. Borak, and K.O. Ulgen, Bubble column reactors. Process Biochemistry, 2005. 40(7): p. 2263-2283.

[3] Jakobsen, H.A., H. Lindborg, and C.A. Dorao, Modeling of Bubble Column Reactors:鳥 Progress and Limitations. Industrial & Engineering Chemistry Research, 2005. 44(14): p. 5107-5151.

[4] Shah, Y.T., et al., Design Parameters Estimations for Bubble Column Reactors. AIChE Journal, 1982. 28(3): p. 353-379.

[5] Forret, A., et al., Influence of scale on the hydrodynamics of bubble column reactors: an experimental study in columns of 0.1, 0.4 and 1.0 m diameters. Chemical Engineering Science, 2003. 58(3–6): p. 719-724.

[6] Krishna, R., J.M.v. Baten, and M.I. Urseanu, Scale Effects on the Hydrodynamics of Bubble Columns Operating in the Homogeneous Flow Regime. Chemical Engineering & Technology, 2001. 24(5): p. 451-458.

[7] Krishna, R. and J. Ellenberger, Gas holdup in bubble column reactors operating in the churn-turbulent flow regime. AIChE Journal, 1996. 42(9): p. 2627-2634.

[8] Wilkinson, P., A. Spek, and L. van Dierendonck, Design parameters estimation for scale-up of high-pressure bubble columns. AIChE Journal, 1992. 38(4): p. 544-554.

[9] Ruff, K., T. Pilhofer, and A. Mersmann, Vollständige Durchströmung von Lochböden bei der Fluid-Dispergierung. Chemie Ingenieur Technik, 1976. 48(9): p. 759-764.

[10] Bieberle, A., et al., Gamma-Ray Computed Tomography for Imaging of Multiphase Flows. Chemie Ingenieur Technik, 2013. 85(7): p. 1002-1011.

[11] Schlusemann, L., G. Zheng, and M. Grünewald, Messung der Phasenverteilung in Blasensäulen. Chemie Ingenieur Technik, 2013. 85(7): p. 997-1001.

[12] Hampel, U., et al., High resolution gamma ray tomography scanner for flow measurement and non-destructive testing applications. Review of Scientific Instruments, 2007. 78(10): p. -.

[13] Hills, J.H., The operation of a bubble column at high throughputs: I. Gas holdup measurements. The Chemical Engineering Journal, 1976. 12(2): p. 89-99.

[14] Tang, C. and T.J. Heindel, Estimating gas holdup via pressure difference measurements in a cocurrent bubble column. International Journal of Multiphase Flow, 2006. 32(7): p. 850-863.

[15] Kulkarni, A.A. and J.B. Joshi, Bubble formation and bubble rise velocity in gas-liquid systems: A review. Industrial and Engineering Chemistry Research, 2005. 44(16): p. 5873-5931.

[16] Urseanu, M.I., et al., Influence of operating pressure on the gas hold-up in bubble columns for high viscous media. Chemical Engineering Science, 2003. 58(3–6): p. 697-704.

[17] Clift, R., J.R. Grace, and M.E. Weber, Bubbles, drops, and particles1978: Academic Press.

[18] Shaikh, A. and H. Al-Dahhan Muthanna, A Review on Flow Regime Transition in Bubble Columns. International Journal of Chemical Reactor Engineering, 2007. 5(1).

[19] Krishna, R., A.J. Dreher, and M.I. Urseanu, Influence of alcohol addition on gas hold-up in bubble columns: Development of a scale up model. International Communications in Heat and Mass Transfer, 2000. 27(4): p. 465-472.

[20] Letzel, H.M., et al., Gas holdup and mass transfer in bubble column reactors operated at elevated pressure. Chemical Engineering Science, 1999. 54(13–14): p. 2237-2246.

[21] Grund, G., A. Schumpe, and W.D. Deckwer, Gas-liquid mass transfer in a bubble column with organic liquids. Chem. Eng. Sci., 1992. 47(Copyright (C) 2014 American Chemical Society (ACS). All Rights Reserved.): p. 3509-16.

[22] Ohki, Y. and H. Inoue, Longitudinal mixing of the liquid phase in bubble columns. Chemical Engineering Science, 1970. 25(1): p. 1-16.

149

[23] Krishna, R., P.M. Wilkinson, and L.L. Van Dierendonck, A model for gas holdup in bubble columns incorporating the influence of gas density on flow regime transitions. Chemical Engineering Science, 1991. 46(10): p. 2491-2496.

[24] Ruzicka, M.C., et al., Effect of bubble column dimensions on flow regime transition. Chemical Engineering Science, 2001. 56(21–22): p. 6117-6124.

[25] Kemoun, A., et al., Gas holdup in bubble columns at elevated pressure via computed tomography. International Journal of Multiphase Flow, 2001. 27(5): p. 929-946.

[26] McLaughlin, J.B., The hydrodynamics of two-phase flows with surfactants. Multiphase Science and Technology, 2003. 15(1-4): p. 365-371.

[27] Nguyen, P.T., et al., The influence of gas velocity, salt type and concentration on transition concentration for bubble coalescence inhibition and gas holdup. Chemical Engineering Research and Design, 2012. 90(1): p. 33-39.

[28] Posarac, D. and M.N. Tekic, Gas holdup and volumetric mass transfer coefficient in bubble columns with dilute alcohol solutions. AIChE Journal, 1987. 33(3): p. 497-499.

[29] Syeda, S.R. and M.J. Reza, Effect of surface tension gradient on gas hold-up enhancement in aqueous solutions of electrolytes. Chemical Engineering Research and Design, 2011. 89(12): p. 2552-2559.

[30] Zahradnik, J., et al., Effect of electrolytes on bubble coalescence and gas holdup in bubble column reactors. Chemical Engineering Research and Design, 1995. 73(A3): p. 341-346.

[31] Krishna, R., M.I. Urseanu, and A.J. Dreher, Gas hold-up in bubble columns: influence of alcohol addition versus operation at elevated pressures. Chemical Engineering and Processing: Process Intensification, 2000. 39(4): p. 371-378.

[32] Camarasa, E., et al., Influence of coalescence behaviour of the liquid and of gas sparging on hydrodynamics and bubble characteristics in a bubble column. Chemical Engineering and Processing: Process Intensification, 1999. 38(4–6): p. 329-344.

[33] Keitel, G. and U. Onken, Inhibition of bubble coalescence by solutes in air/water dispersions. Chemical Engineering Science, 1982. 37(11): p. 1635-1638.

[34] Prince, M.J. and H.W. Blanch, Bubble coalescence and break-up in air-sparged bubble columns. AIChE Journal, 1990. 36(10): p. 1485-1499.

[35] Botton, R., D. Cosserat, and J.C. Charpentier, Influence of column diameter and high gas throughputs on the operation of a bubble column. Chem. Eng. J. (Lausanne), 1978. 16(Copyright (C) 2014 American Chemical Society (ACS). All Rights Reserved.): p. 107-15.

[36] Öztürk, S.S., A. Schumpe, and W.D. Deckwer, Organic liquids in a bubble column: Holdups and mass transfer coefficients. AIChE Journal, 1987. 33(9): p. 1473-1480.

[37] Matsubara, H., et al., Influence of operating pressure on gas holdup and flow regime transition in a bubble column. J. Chem. Eng. Jpn., 2010. 43(Copyright (C) 2014 American Chemical Society (ACS). All Rights Reserved.): p. 829-832.

[38] Akita, K. and F. Yoshida, Gas Holdup and Volumetric Mass Transfer Coefficient in Bubble Columns. Effects of Liquid Properties. Industrial & Engineering Chemistry Process Design and Development, 1973. 12(1): p. 76-80.

[39] Shah, M., et al., Gas holdup, axial dispersion, and mass transfer studies in bubble columns. Industrial and Engineering Chemistry Research, 2012. 51(43): p. 14268-14278.

[40] Wilkinson, P.M. and L.L. v. Dierendonck, Pressure and gas density effects on bubble break-up and gas hold-up in bubble columns. Chemical Engineering Science, 1990. 45(8): p. 2309-2315.

[41] Clark, K.N., The effect of high pressure and temperature on phase distributions in a bubble column. Chemical Engineering Science, 1990. 45(8): p. 2301-2307.

[42] Rollbusch, P., et al., Hydrodynamics of High-Pressure Bubble Columns. Chemical Engineering & Technology, 2013. 36(9): p. 1603-1607.

[43] Schäfer, R., C. Merten, and G. Eigenberger, Bubble size distributions in a bubble column reactor under industrial conditions. Experimental Thermal and Fluid Science, 2002. 26(6–7): p. 595-604.

150

[44] Pohorecki, R., W. Moniuk, and A. Zdrójkowski, Hydrodynamics of a bubble column under elevated pressure. Chemical Engineering Science, 1999. 54(21): p. 5187-5193.

[45] Pohorecki, R., et al., Hydrodynamics of a pilot plant bubble column under elevated temperature and pressure. Chemical Engineering Science, 2001. 56(3): p. 1167-1174.

[46] Weber, M., Large bubble columns for the oxidation of cumene in phenol processes. Chemical Engineering and Technology, 2002. 25(5): p. 553-558.

[47] Weber, M., Some safety aspects on the design of sparger systems for the oxidation of organic liquids. Process Safety Progress, 2006. 25(4): p. 326-330.

[48] Idogawa, K., et al., Behavior of Bubbles of the Air-Water System in a Column under high Pressure. International chemical engineering, 1986. 26(3): p. 468-474.

[49] Idogawa, K., et al., Effect of gas and liquid properties on the behavior of bubbles in a column under high pressure. International chemical engineering, 1987. 27(1): p. 93-99.

[50] Jekat, H., Messung von Blasengrößenverteilungen in Druckblasensäulen im Bereich von 1 bis 100 bar, in Fachbereich für Maschinenwesen1975, Technical University of Munich: Munich.

[51] Jiang, P., et al., Flow visualization of high pressure (21 MPa) bubble column: bubble characteristics. Chemical Engineering Research and Design, 1995. 73(A3): p. 269-274.

[52] Letzel, H.M., et al., Influence of elevated pressure on the stability of bubbly flows. Chemical Engineering Science, 1997. 52(21-22): p. 3733-3739.

[53] Deckwer, W.D., Non-isobaric bubble columns with variable gas velocity. Chemical Engineering Science, 1976. 31(4): p. 309-317.

[54] Brauer, H., Grundlagen der Einphasen- und Mehrphasenströmungen1971, Aarau und Frankfurt am Main: Verlag Sauerländer.

[55] Jin, H., et al., The axial distribution of holdups in an industrial-scale bubble column with evaluated pressure using け-ray attenuation approach. Chemical Engineering Journal, 2005. 115(1–2): p. 45-50.

[56] Kumar, S.B., D. Moslemian, and M.P. Duduković, Gas-holdup measurements in bubble columns using computed tomography. AIChE Journal, 1997. 43(6): p. 1414-1425.

[57] Rollbusch, P., et al., Shortcut-Modellierung von Blasensäulenreaktoren. Chemie Ingenieur Technik, 2013. 85(9): p. 1425-1425.

[58] Hikita, H., et al., Gas hold-up in bubble columns. The Chemical Engineering Journal, 1980. 20(1): p. 59-67.

[59] Hughmark, G.A., Holdup and mass transfer in bubble columns. Ind. Eng. Chem. Process Des. Dev., 1967. 6(Copyright (C) 2014 American Chemical Society (ACS). All Rights Reserved.): p. 218-20.

[60] Joshi, J.B.P., U. V. ; Prasad, C. V. S. ; Phanikumar, D. V. ; Deshpande, N. S. ; Thorat, B. N., Gas hold - up structures in bubble column reactors. Proceedings of the Indian National Science Academy, 1998. 64A(4): p. 441-567.

[61] Mersmann, A., Auslegung und Maßstabsvergrößerung von Blasen- und Tropfensäulen. Chemie Ingenieur Technik, 1977. 49(9): p. 679-691.

[62] Reilly, I.G., et al., A correlation for gas holdup in turbulent coalescing bubble columns. The Canadian Journal of Chemical Engineering, 1986. 64(5): p. 705-717.

[63] Joshi, J.B. and M.M. Sharma, A circulation cell model for bubble columns. Trans. Inst. Chem. Eng., 1979. 57(Copyright (C) 2014 American Chemical Society (ACS). All Rights Reserved.): p. 244-51.

[64] Zehner, P., Momentum, mass, and heat transfer in bubble columns. 1. Flow model of bubble columns and liquid velocity. VT, Verfahrenstech., 1982. 16(Copyright (C) 2014 American Chemical Society (ACS). All Rights Reserved.): p. 347-51.

[65] Zehner, P., Multiphase flows in gas-liquid reactors. DECHEMA-Monogr., 1989. 114(Copyright (C) 2014 American Chemical Society (ACS). All Rights Reserved.): p. 215-32.

[66] Wu, Y. and M.H. Al-Dahhan, Prediction of axial liquid velocity profile in bubble columns. Chemical Engineering Science, 2001. 56(3): p. 1127-1130.

151

[67] Bothe, M., Experimental Analysis and Modeling of Industrial Two-Phase Flows in Bubble Column Reactors, Ph.D Thesis, Technical University of Hamburg-Harburg, Institute of Multiphase Flows, Hamburg-Harburg, to be published

152

5 Summary

The presented thesis is part of a larger research project which dealt with the investigation of

two phase bubble column hydrodynamics and the development of measurement devices

suitable for this task. Consequently this study represents only a part of the entire project and

should be treated in the context of the whole project “Multi-phase”.

It was the purpose of this thesis to investigate two phase bubble column hydrodynamics with

respect to gas holdup at various scales and experimental conditions which are of relevance

for industrial processing units. The fundament of the experimental studies was an extensive

literature survey which covered existing publications dealing with design parameters at

elevated pressure. To identify gas holdup as vital for bubble column design a sensitivity study

was carried out with the help of an axial dispersion model. The uncatalyzed cyclohexane

autooxidation served as an example reaction to study the influence of uncertainties in

parameter estimation on yield of a desired product and the resulting monetary value. In an

attempt to contribute to a better understanding of bubble column hydrodynamics and existing

design and scale-up routes three experimental facilities of different scale and operating ranges

were set up. The effect of different liquid properties, liquid superficial velocity, impurities, gas

density due to elevated pressure, temperature and column scale were examined and

compared to available literature data and statements. In addition, it was possible to measure

axial gas holdup distributions. Radial holdup distributions were also measured by means of a

wire-mesh sensor and a gamma computer tomographic device. These results are evaluated

and presented by the Helmholtz-Center Dresden-Rossendorf and the Ruhr-University

Bochum. Based on the experimental results available correlations for holdup estimation were

examined and a correlation originally proposed by Peter Zehner in 1982 was slightly modified

and used to estimate the experimental results of this thesis within reasonable accuracy.

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5.1 Conclusions

The detailed examination of publications dedicated to bubble column hydrodynamics at

elevated pressure showed that a huge gap exists between academic research and industrial

demands. Besides some general statements regarding gas holdup and the effect of pressure

nearly no reliable data exists to validate existing models and design equations. This is mainly

because the facilities from which the data were derived from are too small in scale. In addition,

water was most often used as the model liquid. Usually water is not processed in chemical

production plants and as a consequence liquid properties other than that of water are of

interest. Additionally water seems to be prone to impurities and changing qualities which affect

the coalescence behavior of gas bubbles in the liquid and therefore the overall gas holdup

measurement. Consequently it is very difficult to validate own measurements with literature

data. Moreover the experimental setups differ not only in scale and operating conditions but

also with respect to the gas sparger used and general method of measurement. This applies

also for publications concerned with experimental studies at atmospheric pressure. As a result

confusing and contradictory statements are to be found within the literature. Furthermore

correlations to predict gas holdup were developed using parameter fittings, whether a

dimensional analysis was done or not. This results in correlations incapable to estimate the

parameter of interest beyond its experimental limitations.

To visualize the difficulties of estimating gas holdup and other hydrodynamic parameters an

axial dispersion model was used in chapter 3 of this thesis. The main goal of this short-cut

model was to calculate yield and selectivity of the uncatalyzed cyclohexane oxidation. Such a

scenario is often seen during early process or reactor design stages to estimate worst case

scenarios. The purpose of short-cut approaches is to estimate reactor performance at a point

where no detailed information about processing conditions and reactor geometry is available

and to conduct parametric studies to assess the influence of varying parameters on reactor

performance. It was shown that gas holdup, as it is responsible for creating the interfacial area,

clearly influences all other hydrodynamic parameters which appear in short-cut model

approaches and which are necessary to estimate. As the calculated rate of mass-transfer is of

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course directly affected by gas holdup the predicted yield of KA oil and selectivity of the

reaction to KA oil is consequently a function of the gas holdup estimate. It is demonstrated that

not only the choice of a correlation but also the confidence interval tremendously impacts

selectivity and therefore yield of the desired product KA oil and that this uncertainty leads to a

possible non-negligible miscalculation of product amount and monetary value.

As gas holdup was identified in chapter 3 as the crucial parameter for bubble column design

this parameter was experimentally examined in chapter 4. The effect of column dimension with

respect to column diameter and height to diameter ratio was examined at atmospheric

pressure and with water and organic solvents as the liquid phase. The experiments were

conducted at flow conditions which can be referred to as the homogeneous flow regime. It was

shown that gas holdup reduces with increasing column diameter and height to diameter ratio.

Physical properties like liquid surface tension have a significant influence on gas holdup. The

effect of higher pressure (or gas density) on gas holdup was studied at pressures of up to 3.6

MPa with nitrogen sparged into water and cumene. The found statement of increasing gas

holdup with increasing gas density was confirmed at the conditions applied. No influence of

superficial liquid velocity on gas holdup was found at the parameter range studied. The same

is true for changes in liquid viscosity because of raised temperatures. The viscosity span during

the experiments of this thesis did not influence gas holdup. In addition axial gas holdup profiles

were measured and evaluated. Gas holdup slightly increase with column height, which is

related to the existence of a sparger inlet zone at the bottom, a zone of equilibrium between

bubble coalescence and breakup and a gas disengagement zone at the top of the column.

The measured holdups were used for the validation of computational fluid dynamics models.

Moreover a promising correlation to estimate holdups was identified. The above considerations

made clear that a design equation is needed which takes liquid and gas properties and column

scale into account. One such correlation was proposed by Peter Zehner and was modified

during the course of this thesis. The suggested approach is based on information about single

bubble velocities and centerline liquid velocities which were measured at the Technical

University of Hamburg-Harburg and the Ruhr-University Bochum respectively. Both measures

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validated the calculation method for the estimation of single bubble velocity and liquid

centerline velocity. The gas holdup estimates were in reasonable accordance with the

measured values. However not all experimental subsets were reproduced by the proposed

equation. As reasons for this impurities in the liquid phase and the influence of other liquid

material (the addition of which was necessary in order to test developed measurement devices

within project “Multi-phase”) were identified. Further the sparger used during the presented

studies might have caused fluctuations in bubble formation and therefore have additionally

influenced some of the experimental results.

5.2 Recommendations

Based on the experience and findings of this thesis, recommendations for future research

activities are derived and proposed.

First of all a structured approach like in “Multi-phase” seems to be necessary to investigate

influencing factors on bubble column hydrodynamics. It is crucial to use comparable

experimental facilities with respect to column dimension, sparger design, liquids and gases

used and operating conditions. Moreover the use of water as the liquid phase should be

avoided as long as it is not necessary for the specific aim of the study. This is necessary as

water qualities are hard to quantify and even very low impurities massively influence the

coalescence behavior of gas bubbles. Organic solvents are generally of more interest than

water for the chemical industries and organics seem to be less prone to small amounts of

impurities, at least regarding their hydrodynamic behavior.

Unlike other disciplines, experimental examination of bubble column hydrodynamics seems to

be less standardized. The development of standardized routines would be desirable because

the generated results will most likely be used to validate CFD models or to adapt existing model

equations. This is easier and more reliable if specified guidelines are used.

The results of this thesis are restricted to the homogeneous flow regime and to two phase

bubble columns without internals. This can be considered to be a first structured approach to

a better understanding of bubble columns in general. However for a complete description

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measurements in the heterogeneous flow regime at pressurized conditions and with organic

solvents are desirable.

This study was also restricted to the use of one specific sparger. A more detailed study on the

influence of sparger design seems to be necessary. As industrial bubble columns are usually

equipped with internals additional measurements of hydrodynamics under consideration of

internals are of utmost importance for the validation of CFD models. The addition of a third

solid phase, as it is the case for heterogeneously catalyzed reactions, would broaden the areas

of interest and is definitely necessary as a third phase affects hydrodynamics, too. Another

parameter of interest, especially for biological processes, is the liquid viscosity. Liquids of low

viscosity have been used during this study and no statement with respect to high viscous

liquids and bubble column hydrodynamics could be made.

The use of correlations for the estimation of hydrodynamic parameters in ideal reactor models,

dispersion models or more advanced compartment models should still be accompanied with

caution. One correlation for gas holdup prediction was identified which is able to reproduce the

observed phenomena of this study. However, the above discussed parameters should be

examined more closely in conjunction with this correlation in order to validate its applicability.

Despite of the obvious lack of accuracy, short-cut models deliver worst case approximations

and are therefore not suited for very detailed reactor studies but for engineering studies in early

phases of a project.

Lebenslauf

Philipp Rollbusch

geboren am 03. Dezember 1985 in Magdeburg

Beruf

07/15 – heute Evonik Technology & Infrastructure GmbH, Marl

Projektingenieur, Engineering

02/15 – 06/2015 Evonik Industries AG – Process Technology & Engineering, Marl

Projektingenieur, Engineering

12/11 – 01/2015 Evonik Industries AG – Process Technology & Engineering, Marl

Doktorand, Abteilung Verfahrenstechnik – Reaktionstechnik

Studium

10/06 – 10/11 Otto-von-Guericke-Universität Magdeburg

Studium zum Dipl.-Ing. Verfahrenstechnik

Schulbildung

08/96 – 07/05 Albert-Einstein-Gymnasium Magdeburg, Magdeburg

Allgemeine Hochschulreife

Zivildienst

08/05 – 04/06 Universitätsklinikum Magdeburg, Magdeburg

Philipp Rollbusch Dortmund, 02.02.2016