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
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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
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
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
[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
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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.
70
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.
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
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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.
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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]
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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)
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).
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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
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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
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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.
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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
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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.
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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
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
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[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.
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[50] Jekat, H., Messung von Blasengrößenverteilungen in Druckblasensäulen im Bereich von 1 bis 100 bar, in Fachbereich für Maschinenwesen1975, Technical University of Munich: Munich.
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[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.
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[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.
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[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.
153
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
154
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