Study of gas-liquid flow contactors using low-intrusive ...

Study of gas-liquid flow contactors using

low-intrusive measuring technology

Dissertation

zur

Erlangung des akademischen Grades eines

Dr.-Ing.

der

Fakultät Maschinenbau

der Ruhr-Universität Bochum

von

Dipl. -Ing. Guanghua Zheng

aus

Jilin, China

Bochum 2017

Dissertation eingereicht am: 06. Dezember 2017

Tag der mündlichen Prüfung: 04. Mai 2018

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

Zweiter Referent: Prof. Dr.-Ing. Uwe Hampel

Danksagung

Die vorliegende Arbeit entstand während meiner Tätigkeit als wissenschaftlicher

Mitarbeiter am Lehrstuhl für Fluidverfahrenstechnik der Fakultät Maschinenbau

der Ruhr-Universität Bochum.

Mein besonderer Dank gilt dem Inhaber des Lehrstuhls für Fluidverfahrens-

technik, Herrn Prof. Dr.-Ing. Marcus Grünewald, für die Überlassung des

Promotionsthemas, das Vertrauen in die Wichtigkeit messtechnischer

Fragestellungen bei der Untersuchung von Mehrphasenapparaten und vor allem

für die vielfältige Unterstützung.

Herrn Prof. Dr.-Ing. Uwe Hampel danke ich für die Erstellung des Zweitgutachtens.

Darüber hinaus bedanke ich mich bei den Kollegen am Lehrstuhl für

Fluidverfahrenstechnik für die gute Arbeitsatmosphäre und den fachlichen

Austausch. Insbesondere danke ich Melanie Bothe, Manuela Kopatschek und

Corinna Hecht für die gegenseitige Unterstützung und die angenehme gemeinsame

Zeit.

Viele wertvolle Anregungen und Diskussionen habe ich darüber hinaus aus den im

Rahmen der Forschungsarbeiten durchgeführten Studien-, Projekt- und Diplom-

arbeiten von J. Yan, S. Wu, P. Biessey, N. Abel, M. Dippel, T. Sonau, P. Zheng, C. Zhao,

K. Keshk, I. Moltup, J. Huang, J. Xin, Z. Li und W. Li erhalten.

Nicht zuletzt gilt mein Dank auch meinen lieben Eltern, meiner Frau und meiner

Tochter, die mit ihrer andauernden Geduld, ihrem Verständnis und ihrer

Unterstützung viel zum Gelingen der vorliegenden Dissertation beigetragen haben.

Content

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

2 Measuring methods for measurements of gas-liquid flow pattern ......................................... 3

2.1 Measurements of gas-liquid flow pattern using electrical tomography ................................. 4

2.1.1 Construction and working principle of the WMS ................................................................. 8

2.2 Measurement of gas-liquid flow using the WMS ..................................................................... 8

2.2.1.1 Conductive Wire Mesh Sensor ....................................................................................... 9

2.2.1.2 Capacitive Wire Mesh Sensor ....................................................................................... 11

2.2.2 Electric field simulation of capacitive WMS (own studies) ................................................ 14

2.2.2.1 Permittivity model of the capacitive WMS .................................................................. 14

2.2.2.2 Parameters of the capacitive WMS .............................................................................. 16

2.2.2.3 Finite element method ................................................................................................. 17

2.2.2.4 Two-dimensional electric field simulation .................................................................. 18

2.2.2.4.1 Influence of bubble shape on capacitance ........................................................... 20

2.2.2.4.2 Influence of bubble position on capacitance ....................................................... 20

2.2.2.4.3 Influence of bubble fraction on capacitance ....................................................... 21

2.2.2.4.4 Study of influence of medium permittivity on capacitance ................................ 24

2.2.2.5 Three-dimensional electric field simulation ................................................................ 25

2.2.2.5.1 Influence of bubble size on capacitance .............................................................. 25

2.2.2.5.2 Influence of bubble position (in contact to wires) on capacitance ..................... 26

2.2.2.5.3 Influence of bubble position (without contact to wires) on capacitance ............ 27

2.2.3 Discussion ............................................................................................................................. 28

2.3 Measurements of bubble rise velocity and bubble size using optical fiber method ............ 29

2.3.1 Single optical fiber method .................................................................................................. 29

2.3.2 Four optical fiber method .................................................................................................... 30

2.3.3 Double optical fiber method ................................................................................................ 30

2.3.4 Laser doppler anemometer ................................................................................................. 31

2.3.5 Particle image velocimetry .................................................................................................. 31

2.3.6 Optical fiber method ............................................................................................................ 32

3 Study of phase distribution in bubble columns ..................................................................... 34

3.1 Flow regime in bubble columns ............................................................................................. 34

3.2 Experimental measurements of bubble column .................................................................... 36

3.2.1 Measurements of bubble distribution using WMS ............................................................. 36

3.2.1.1 Experimental results of the capacitive WMS ............................................................... 37

3.2.1.2 Conclusion ..................................................................................................................... 44

3.2.2 Measurements of bubble rise velocity and bubble size using an optical fiber method .... 45

3.2.2.1 Experimental setup ....................................................................................................... 45

3.2.2.2 Data processing of measurements using the optical fiber method ............................ 46

3.2.2.3 Experimental measurements of bubble rise velocity using the optical fiber method 49

3.3 Conclusion ............................................................................................................................... 54

4 Study of phase distribution in packed columns ..................................................................... 56

4.1 Theoretical background of packed columns .......................................................................... 56

4.1.1 Pressure drop ....................................................................................................................... 59

4.1.2 Liquid holdup ....................................................................................................................... 61

4.1.3 Loading and flooding points ................................................................................................ 65

4.1.4 Mass transfer process ........................................................................................................... 67

4.1.4.1 Equilibrium model ........................................................................................................ 67

4.1.4.2 Rate-based model .......................................................................................................... 69

4.1.5 Study of phase distribution .................................................................................................. 73

4.2 Experimental study of packed column ................................................................................... 83

4.2.1.1 Study of hydrodynamics in structured packing .......................................................... 85

4.2.1.2 Study of hydrodynamics in random packing .............................................................. 87

4.2.1.3 Mass transfer of structured and random packing ....................................................... 90

4.2.2 Experimental investigation of phase distribution using a liquid collector ........................ 94

4.2.3 Experimental measurements using WMS ........................................................................... 98

4.2.3.1 Experimental measurements of phase distribution in random packed column ....... 98

4.2.3.2 Experimental measurements of phase distribution in structured packed column . 106

4.3 Simulation and Modeling of phase distribution .................................................................. 107

4.3.1 Cell model ........................................................................................................................... 109

4.3.2 Simulation of phase distribution using cell model ........................................................... 116

4.4 Discussion .............................................................................................................................. 119

5 Nomenclature ........................................................................................................................ 121

6 References ............................................................................................................................. 123

Introduction

1

1 Introduction

Packed columns and bubble columns are important apparatuses for gas-liquid

contacting processes.

Packed columns are widely used for gas-liquid or liquid-liquid separation

processes, e.g. absorption, desorption and rectification. In packed columns, the

liquid phase is often assumed to be homogeneously distributed over the column

cross section. So far, large scale maldistribution is not considered in many existing

theoretical models, namely volume-averaged models. The widely used models of

Mersmann [Mersmann and Deixler (1986)], Billet [Billet (1995)], Mackowiak

[Mackowiak (2010)] and Stichlmair [Stichlmair et al. (1989)]) generally constitute

simplified physical models and the parameters of the derived correlations can be

fitted with experimental results. The liquid collecting method, which is used for

measurements of liquid holdups in packed columns, strongly affects the phase

distribution, resulting in less reliable experimental measurements.

Bubble columns are commonly used for gas-liquid reactions in continuous or semi-

batch processes, due to their good heat transfer characteristics and their relatively

simple construction and operation. Since bubble columns are very successfully

applied in the chemical industry, they represent an important type of gas-liquid

contactors. Backmixing of the liquid phase through the gas phase in bubble

columns greatly influences reaction conversion rate and selectivity. Although the

design of bubble columns is simple, the determination of gas and liquid phase

interfacial area is difficult. Dispersion models studied by Deckwer [Deckwer and

Field (1992)] and Becker [Becker et al. (1994)] assumed ideal mixing in the radial

direction. The mixing of the liquid phase through the moving gas phase is also

influenced by the column wall. It is possible to calculate the rise velocity of a single

bubble. However, it is difficult to predict the rise velocity of bubble clusters.

The phase distribution in such gas-liquid contacting devices is often assumed to be

homogeneous. The phase distribution in multiphase flow can significantly

influence the performance and efficiency of mass transfer. Thus, it is essential to

study the phase distribution inside gas-liquid contacting apparatuses. In many

cases, validation of theoretical models with experimental results is still

Introduction

2

unsatisfactory, as the local flow structure and the flow regime are often not

sufficiently described by simplified models.

Many measurement techniques have already been used to measure the phase

distribution in gas-liquid contactors. Recently, new measurement methods, e.g.

electrical resistance/capacitance tomography, reviewed by Chaumat [Chaumat

et al. (2005)], allow measurements of the phase distribution inside gas-liquid

contactors with strongly reduced intrusiveness. The spatial resolution is not

satisfied.

The capacitive wire mesh sensor (WMS) developed by Da Silva [Da Silva et al.

(2007)] [Da Silva and Hampel (2010)] was used for measurements of phase

distributions in this work. The capacitive WMS is in direct contact with both, the

gas and the liquid phase. The phase distribution across the column cross-section

can be measured with high temporal resolution. The spatial resolution of the WMS

depends on the distance between neighbored wires of the WMS.

The capacitive WMS was applied for measurements of the phase distribution in

packed and bubble columns. Additionally, an optical fiber method was applied to

measure bubble size distributions and bubble rise velocity in bubble columns. The

target of this thesis is to study the influences of phase distribution on the process

parameters in packed and bubble columns based on reliable experimental

measurements.

This work attributes to experimental studies of phase distribution in gas-liquid

contactors, that are packed and bubble columns, using conventional and modern

measurement methods. The fraction of the liquid phase close to the wall of packed

columns was measured using an on-wall liquid collector. Large scale

maldistribution was observed. Depending on the packing types and operational

conditions, the phase distribution is discussed individually. The working principle,

advantages and disadvantages of the capacitive WMS are analyzed and discussed.

The capacitive WMS is applied for the measurement of the phase distribution

across the cross section of packed columns, which is the cross-sectional averaged

measuring method. The experimental results in bubble columns using the WMS

and the optical fiber method are discussed. Both methods can be classified as low-

Measuring methods for measurements of gas-liquid flow pattern

3

intrusive methods for gas-liquid contactors. The spatial and temporal resolutions

are proven to be reliable for the study of phase distribution in packed and bubble

columns. Concerning the experimental results with the WMS, a phase distribution

model for packed columns (cell model) is developed. The influence of process

parameters on the phase distribution is discussed on the basis on the cell model

simulation results.

2 Measuring methods for measurements of gas-liquid flow

pattern

Although packed columns and bubble columns are widely used in chemical

industry and separation technology, their local phase distribution is not yet well

known, limited by the measurement methods. Conventional measurement devices

have unneglectable invasiveness on the phase distribution measurements. Thus,

the results are less reliable. Measurement methods for multiphase flow remain a

challenging task in chemical engineering. Non-intrusive measurements to monitor

multiphase flow have gained more and more attention recently.

Computer tomography, electrical tomography and wire mesh sensor methods

measure phase distribution over the vessel cross section, while the optical fiber

method, which measures the local phase distribution, is considered as pointwise

method.

Computer tomography methods reviewed by Toye [Toye et al. (1997)] and

Dudukovic [Dudukovic (2002)] were have been used for measurements of the gas-

liquid distribution. These methods have satisfied the requirements on spatial

resolution. Compared to the other methods, however, the temporal resolution is

severely limited. Furthermore, tomography is not environmentally friendly due to

the radioactivity and the devices are very expensive. Electrical tomography has a

high temporal resolution, but the spatial resolution is not sufficient for the

investigation of the phase distribution. The spatial resolution of electrical

capacitance tomography was studied and is briefly discussed. In this work

measurements with the WMS and the optical fiber method are focused and

discussed.


4

2.1 Measurements of gas-liquid flow pattern using electrical

tomography

Electrical tomography methods for cross-sectional measurements have been

developed in the last decades and are of great interest for phase distribution

measurement, since these belong to the non-invasive and non-intrusive methods.

These methods enable the visualization of cross sectional phase distributions of

apparatuses. Depending on the measuring principles, e.g. resistance, capacitance,

inductance, the electrical tomography methods are categorized into electrical

resistance tomography (ERT), electrical capacitance tomography (ECT) and

electromagnetic tomography (EMT), respectively. The resistance-based methods

are suitable for electrically conductive fluids, while capacitance based methods are

suitable for electrically insulating fluids. Electrical tomography methods have been

applied to monitor two immiscible fluids inside of pipelines as industrial

application or for the observation of gas-liquid mixing in a stirred vessel by Wang

[Wang et al. (2000)]. Halow [Halow (1997)], Dyakowski [Dyakowski (1996)] and

Chaouki [Chaouki (1997)] have reviewed the non-invasive measurement methods

for multiphase flow.

The phase distribution in bubble columns can be measured with ERT. Electrical

sensors are installed in holes in the column wall, in contact with the working fluid,

as shown in Figure 2-1. As the gas bubbles flow upward, the sensors of one cross-

sectional plane are activated sequentially within a short time. The gas phase

influences the electric field depending on its position. The electrical signals (voltage

or current) are measured and analyzed with calibration signals to eliminate the

measurement noise. In theory, bubbles size and position can be reconstructed from

these signals.


5

Figure 2-1: Application of ERT in multiphase contactors

Williams [Williams and Beck (1995)] has reviewed the possible tomography

methods of multiphase flow. Electrical impedance tomography, microwave

tomography and optical tomography were explained according to the working

principles. Reconstruction algorithms and error analysis of tomography methods

were discussed by Xie [Xie (1995)]. Case studies of mixing processes using

tomography methods were widely discussed by Mewes [Mewes and Fellhölter

(1995)] and Bridgwater [Bridgwater (1995)]. In these studies, the applicability of

electrical tomography methods for two-phase distribution measurements were

verified. The accuracy of electrical tomography methods for individual

applications was not focused.

Pakzad [Pakzad et al. (2008)] studied the homogeneity of flow patterns inside a

stirred tank. The size of cavern was measured by ERT and was validated by CFD

simulation. The mixing behavior of the immiscible liquid-gas phase was studied.

Good agreement of measurements and simulation was found in this study. Bolton

[Bolton et al. (2004)] applied the ERT (8×16 electrodes) to study the flow distribution

in a packed bed. Spheres (∅ = 3 mm and ∅ = 10 mm) were used as the packed bed.

The results are questionable since the spatial resolution of the measurement was

relatively low and it was not possible to determine the liquid phase fraction. The

ECT method and its application in structured packed columns were studied by

Loser [Loser et al. (2001)] [Loser (2002)]. Although the spatial resolution could be

improved with a proposed weighting matrix, compared to the standard sensitivity

methods, the spatial resolution was not high. Matusiak [Matusiak et al. (2010)]

https://dict.leo.org/englisch-deutsch/applicability


6

measured the spatial resolution using ECT and the WMS. It was shown that the

spatial resolution of the WMS is much higher than the one of ECT.

The electric field of the electrical tomography method depends strongly on the

distribution of the immiscible fluids and the number of electrical sensors. The

spatial resolution of electrical tomography is relatively low since the number of

sensors mounted in the cross-section is limited. Better measurement accuracy can

be obtained by increasing the number of sensors and by limiting the amount of

bubbles. For a limited sensor number, electrical tomographic measurements are

not satisfied. Compared to computer tomography the evaluation algorithms of

electrical tomography are more complicated. The electric field is non-linear in

between two active electrical sensors. Many different algorithms have been

developed to reconstruct the electric field by numerical methods for better

accuracy. This is usually realized using the finite element method. Finite element

method can be used to determine a sensitivity map, which defines the sensitivity of

each measurement to changes in the contents of each pixel element. Qualitative

images can be reconstructed from the sensitivity map using a simple matrix

multiplication. Iterative approaches typically provide more accurate images, but

the process is time consuming and there may be problems with convergence as

studied by York [York (2001)]. Loser [Loser et al. (2001)] suggested to use a

reconstruction model based on finite element method. A weighting matrix, which

was derived from x-ray (along linear lines), was analogous used for ECT.

Polydorides [Polydorides and Lionheart (2002)] and Adler [Adler and Lionheart

(2006)] developed a toolkit (EIDORS) using MATLAB, that can be used to reconstruct

the electric field of electrical resistance tomography.

With the toolkit (EIDORS) the electrical tomography method was studied for bubble

columns in this thesis. In Figure 2-2 a), b) and c), there cases are shown:

a) a single bubble locates in the center of bubble column (∅ = 10 cm)

b) three smaller bubbles are in the center and two bubbles distributed near the

column wall

c) multiple bubbles distribute homogeneously

Depending on the reconstruction algorithms (Figures d, g and j are results of case


7

a, Figures e, h and k are results of case b and Figures f, i and l are results of case c),

bubbles can be reconstructed as shown in Figure 2-2.

a) b) c)

d) e) f)

g) h) i)

j) k) l)

Figure 2-2: Reconstruction of single bubble and multiple bubbles using the EIDORS

It is obvious that the position of single central bubble can be identified easily.

However, the bubble diameter is strongly dependent on the applied reconstruction

algorithms. The position reconstruction of multiple bubbles in the cross section of


8

the vessel has accuracy problems as shown in e), h) and k). Finally, results for the

reconstruction of more than 10 bubbles are not satisfied (see f), i) and l)). Bubble

positions and their number cannot be clearly resolved.

The simulation results performed using EIDORS were applied to study the accuracy

of the spatial resolution of the electrical tomography method. Although these

methods can be used to measure the phase distribution in bubble columns

qualitatively, the spatial resolution is not satisfied. With an increase of bubble

number, the accuracy decreases drastically. This method was not further applied

in this work due to the requirement of high spatial resolution necessary for the

resolution of the phase distribution in bubble columns. In the following chapter a

measurement method using a capacitive WMS, that allows measurements of the

phase distribution with higher spatial resolution, is introduced and discussed in

detail.

2.1.1 Construction and working principle of the WMS

The working principle of the WMS and measurements using WMS are reviewed in

this chapter. The electric field analysis of the WMS using the finite element method

is considered in principle. Based on the simulation results, suitable algorithms for

the conversion of capacitance to phase fraction/holdup as used in packed columns

and bubble columns were derived. The algorithm for the measured signals in

bubble columns was found different from the one for packed columns.

2.2 Measurement of gas-liquid flow using the WMS

The WMS allows to investigate the phase distribution of gas and liquid along the

column cross section. It can be categorized as an invasive, but low-intrusive

method. Advantages of the WMS are that no complicated algorithm of image

reconstruction (e.g. ERT and ECT) is required. Moreover, a high spatial and

temporal resolution of the phase distribution can be obtained since the sensor

wires are mounted within the cross section of the column, fluids having direct

contact with the wires. The diameter of the wires is relatively small. Thus, the

influence on fluid flow is relatively low.


9

As shown in Figure 2-3, the WMS comprises two planes of 32 sensor wires each.

Each plane of wires is stretched parallel (not in touch) across the cross-section.

Wires from different planes are orthogonal (not in touch), forming sets of electrode

pairs. Each crossing point acts as a local phase indicator. The WMS with

32×32 wires recieves 32 signals at one excitation. After a periodic excitation of all

wires of the transmitter plane, up to 1024 signals can be obtained. Some of the

sensing points are located outside of the circular cross section and thus they are

not considered for the measurements. The associated electronics measure the

signals (capacitance or conductivity) in the gaps of all crossing points at high

repetition rates.

Figure 2-3: Setup of capacitive WMS designed

by Helmholz-Zentrum Rossendorf-Dresden

2.2.1.1 Conductive Wire Mesh Sensor

A WMS measuring the conductivity in a two-fluid mixture flowing in a pipe was

introduced and patented by Johnson [Johnson (1987)]. The integral gas fraction in

the pipe cross section was measured. Reinecke [Reinecke et al. (1996)] presented a

device to visualize sequences of gas fraction distributions in a horizontal pipe, that

consisted of three layers of electrode grids. The distance between the layers was 3

mm and the diameter of the wires was 100 μm. Only 5% of the cross section was

occupied by the wires. Three independent projections of the gas fraction

distribution across the sensor cross section were obtained by measuring the

conductivity between two adjacent parallel wires. Phase distribution was


10

reconstructed temporally (about 100 frames per second) and spatially. Prasser

[Prasser et al. (1998)] studied the conductive WMS based on conductivity

measurements with a new circuit design. Normally, direct current (DC) was used

for the conductive WMS method.

Experimental studies using the conductive WMS in bubble columns has been

further investigated by Prasser [Prasser et al. (1998), Prasser et al. (2003), Prasser

(2008)]. The conductive WMS has been used to study the bubble flow regime.

Prasser [Prasser et al. (2002)] studied the gas fraction distributions in a cross section

of a vertical tube with a temporal resolution of 1200 frames per second and a spatial

resolution of about 2-3 mm. It should be noted that the spatial resolution not only

depends on the cross section of the pipe but also on the number of wires in the

cross section. The more wires are used, the better spatial resolutions can be

achieved. Conductive WMS developed by Prasser [Prasser et al. (2003), Prasser

et al. (2007), Prasser (2008)] can also reach increased temporal resolutions up to

10000 frames per second. An experimental comparison between a fast X-ray

method and conductive WMS was made by Prasser [Prasser et al. (2007)]. The

measurements were carried out in a vertical pipe of 42 mm inner diameter with an

air and water mixture. It was found that the agreement of the results depends on

the data processing of the X-ray method. Gas fractions of large bubbles measured

with WMS were slightly underestimated.

Dudlik [Dudlik et al. (2002)] studied the water hammer effect and cavitation shock

waves of fast closing valve using the conductive WMS. The fraction of the gas phase

was successfully measured with a conductive WMS and an acceptable temporal

resolution. The cavitation bubble behind a fast acting shut-off valve was studied in

a pipeline with a time resolution of 1000 frames per second.

The electric conductive measurement technique requires a conductive medium as

the continuous phase. Therefore, the application of the conductive WMS is limited

by the conductivity of the liquid. In packed columns the gas phase is the continuous

phase. Hence, the application of the conductive method in packed columns is

limited. Measurements of capacitance instead of electrical conductivity are

advantageous for measurements of the phase distribution in packed columns, with


11

the liquid phase fraction being relatively low.

2.2.1.2 Capacitive Wire Mesh Sensor

The capacitive WMS can be used to measure the multiphase flow of a discontinuous

conductive phase, especially in the case that the continuous phase is a non-

conductive organic phase. The sensitivity of the capacitive WMS on the electric

field, the geometry of the electrodes and excitation frequency were studied by

Da Silva [Da Silva (2008)]. The design principle of a capacitive WMS is shown in

Figure 2-4. Wires in one plane are activated sequentially, controlled by a series of

switches. Due to the excitation of one wire, all wires on the other plane are

receiving electrical signals. By repeated, successive activation of all transmitter

electrodes the displacement currents of all receiver channels can be obtained from

the measurements. The current is measured using the designed circuits. Different

as the conductive WMS which uses DC stream source, an alternative current (AC)

method is used for capacitive WMS.

Figure 2-4: Circuit diagram of a capacitive WMS by Da Silva [Da Silva et al. (2007)]

The Application of capacitive WMS in packed beds was studied by Matusiak

[Matusiak et al. (2010)]. The phase distribution measured in an electrical

capacitance tomography and capacitive WMS was compared and discussed by

Bieberle [Bieberle et al. (2010)]. In their work, some models were suggested for the

determination of the phase fraction based on the measured permittivity.

Abdulkadir [Abdulkadir et al. (2014)] applied the capacitive WMS on a mixture of


12

air and silicone oil in a 6 m long riser pipe with an internal diameter of 67 mm. The

accuracy and performance of the void fraction correlations were carried out in

terms of percentage error and Root Mean Square (RMS) error. The average

observed void fraction distribution was reported to be satisfied.

Based on the capacitive principle of the WMS, a novel multi-channel capacitive

planar sensor was investigated by Da Silva [Da Silva et al. (2009)]. The phase

distribution of a mixture of air, benzene and isopropyl alcohol can be measured

clearly. Da Silva [Da Silva and Hampel (2009)] studied the electric field of the multi-

channel capacitive planer sensor in Figure 2-5. The electrodes at the excitation

plane were sequentially connected to a sinusoidal voltage source of a fixed

frequency of 5 MHz while the non-activated electrodes were grounded.

Figure 2-5: Multi-channel capacitive planer sensor by Da Silva [Da Silva and Hampel (2009)]

Electric field within the sensors was simulated by means of three-dimensional

finite element method (FEM) using the commercial software Comsol Multiphysics

(shown in Figure 2-6 by Da Silva [Da Silva and Hampel (2009)]). Electric field

simulations were simplified as 5 × 5 sensor geometry. Since the size of the sensor

was much smaller than the wavelength of the involved electric fields, an

electrostatic model was used. It was shown that the spatial sensitivity of the

activated electrodes was better that 90 % and the perturbation between

neighbored electrodes was 30 % in the maximum on the boundary layer (shown in

Figure 2-7 by Da Silva [Da Silva and Hampel (2009)]).

Bieberle [Bieberle et al. (2010)] and Schubert [Schubert et al. (2010)][Schubert et al.


13

(2006)] studied the phase distribution in a trickle bed reactor using the capacitive

WMS for different process conditions. Good coincidence of calculated and

experimental measured results was obtained. As shown in Figure 2-8 (left), for each

excitation of the active wire, signals from the wires on the receiver plane were

measured. The generator used a harmonic excitation while current was measured

at the receiver wires.

Figure 2-6: Simulation of the electric field by Da Silva [Da Silva

and Hampel (2009)]

Figure 2-7: Spatial sensitivity of planer sensor by Da Silva [Da Silva and Hampel (2009)]

As shown in Figure 2-8 (right), the measured capacitance of the WMS is influenced

by the discontinuous phase (bubbles or droplets) passing the wires. The relative

permittivity of air and water are 1 and 80 F/m, respectively. Based on the measured

capacitance the obtained signals can be converted into phase fractions at each

crossing point.

Ultrafast X-ray tomography and WMS applied to study upward gas-liquid flow in a

vertical pipe of 50 mm diameter were studied by Zhang [Zhang et al. (2013)]. The

measurements were performed with 2500 frames per second with both

arrangements. It was reported that radial profiles of time averaged gas fraction

agree for both imaging techniques. Sharaf [Sharaf et al. (2011)] compared the WMS

to gamma densitometry for phase fraction measurements. Experimental

measurements of the capacitive and conductive WMS and with the gamma

densitometer (GD) were investigated. A vertical round pipe of approximately 1 m

in length and an internal diameter of 50 mm was used. The WMS consisting

x y


14

of 16×16 wires was used with high spatial and temporal resolution. Air and

deionized water were used as two-phase mixture. Good agreement has been

reported between WMS and the GD measured chordal void fraction near the center

of the pipe. A similar study was carried out by Rodriguez [Rodriguez et al. (2014)]

who studied the phase distribution in a 15 m long horizontal steel pipe with a

8.28 cm internal diameter, using mineral oil and brine applying a capacitive WMS.

Phase fraction was calculated with several mixture permittivity models. Two

gamma-ray densitometers were used to measure the holdup which was used to

validate the data acquired with the capacitive WMS.

Figure 2-8: Measurement principle by Schubert [Schubert et al. (2010)]

Analogous to the electric field simulation, the electric field of capacitive WMS was

studied in this work using the commercial software ANSYS. Aim of the numerical

simulation is to study the sensitivity of the capacitive WMS on multiphase flow and

the signal interpretation algorithm for bubble columns (Gas bubbles are

discontinuous) and packed columns (liquid droplets are continuous phase),

respectively.

2.2.2 Electric field simulation of capacitive WMS (own studies)

2.2.2.1 Permittivity model of the capacitive WMS

The signal implementation of the conductive WMS measurements can normally be

fitted with a linear relationship. Though, it is not yet clear which permittivity model

can be used for the measurements with the capacitive WMS. A suitable algorithm

is an important factor that strongly influences the accuracy of the measurements.


15

Thus, in the following section some conventional permittivity models for the

conversion of the electric field signal to a phase fraction were studied using the

finite element method.

The relation between voltage and fluid permittivity can be described as

proportional. Da Silva [Da Silva et al. (2007)] studied the relation between the

relative permittivity εr and the capacitance C of selected fluids (air, silicone oil, 2-

propanol, glycol and deionized water). It was shown that the relation between the

relative permittivity and capacitance can be described with a linear

function: C = 0.0095×εr. Schubert [Schubert et al. (2010)] studied permittivity

models of the capacitive WMS for trickled-bed reactors. By their work the liquid

saturation rate δL,x in an air-liquid mixture was implemented using the models

shown in Table 2-1).

Table 2-1: Permittivity models by Schubert [Schubert et al. (2010)]

Parallel model δL,x=

Kx-KxL

KxH-Kx

L

Series model δL,x=

KxHKx

L-KxKxH

KxKxL-Kx

H

Maxwell model δL,x=

(2+KxH/Kx

L)(1-Kx/KxL)

(2+Kx/KxL)(1-KX

H/Kx

L)

Log model δL,x=

log(Kx)-log(KxL)

log(KxH)-log(Kx

L)

Kx denotes for an unknown permittivity of two phase flow which was measured

with a capacitive WMS and indicates the strength of capacitance at the measuring

point. The permittivity cannot be measured directly, but can be determined using

the following equation introduced by Da Silva [Da Silva et al. (2007)]:

Vlog, x=ax⋅log(Kx)+bx (eq. 2-1)

Two unknown parameters ax and bx are shown in (eq. 2-1) and must be

determined with two boundary conditions. Therefore, the voltage Vlog, x were

measured in fluids of known permittivity. Thus, the two constants ax and bx were

determined. In case of the air-water mixture, ax and bx were determined by


16

measuring the permittivity of water KxH as the medium of higher permittivity and

air 𝐾𝑥𝐿 , which has a lower permittivity. It should be noted that the values of ax and

bx depend not only on the relative permittivity but also on the temperature.

Furthermore, the signal noise can influence both parameters significantly.

Therefore, it is recommended to perform calibration measurements (for

determination of ax and bx) before and after each measurement using the

capacitive WMS.

The results presented by Schubert [Schubert et al. (2010)] for the determination of

the permittivity model for the trickle-bed reactor were validated with a liquid

collection method for local liquid flows. However, results generated by this method

were not representative, since the collection method measured flow rates, while

the capacitive WMS measured phase fractions in across the cross section.

Literature shows that it is necessary to understand the relation between measured

permittivity and the phase fraction more accurately. However, for the application

of the capacitive WMS used in packed columns, there is no existing theoretical

model yet. In this sense, the following sections are dealing with the influence of the

electric field on the phase distribution, studied with the commercial Software

ANSYS®

2.2.2.2 Parameters of the capacitive WMS

The WMS, which was delivered by Helmholz-Zentrum Rossendorf-Dresden, with

the diameter of 288 mm comprises two planes. In each plane there are 32 stainless-

steel wires of 0.2 mm in diameter and an equidistant spacing of 9.0 mm from each

other. The distance between the two planes (transmitter and receiver plane) is 3

mm and the wires from different planes are orthogonal to each other. The sensor

measures electrical signals (capacitance), if two wires from different planes are

activated. This arrangement results in a grid of 32×32 sensing points with a total of

1024 crossings of which 840are inside the circular cross section of the column. The

remaining 184 crossings are outside of the circular column cross-section. These

outer sensing points are masked out and thus they are not considered for the

measurements. The measuring frequency is set as 400 Hz (400 frames per second).


17

Quasi-static time-harmonic electric (AC) condition is used for this electric field

simulation and the excitation frequency of the WMS is set as 10-5 Hz. For the

demodulation of the AC signals, a logarithmic detector scheme is used. Therefore,

the study of the electric field can be categorized as a low frequency electric field

problem. Dielectric changes are reflected in the measured voltage values. Due to

the fact, that many conductor wires are arranged within the cross section, the cross-

talk should be sufficiently suppressed by applying driver circuits. This leads to

limitations concerning the maximum conductivity of the liquid phase. The device

can work at liquid conductivities up to approximately 1000 μS/cm (tap water

quality). The lower limit is given by the sensitivity of the input cascades (0.1 μS/cm,

distillate water).

The permittivity of material is given by ϵ = ϵ0×ϵr, whereby ϵ0 (ϵ0 = 8.85 ×

10−12 V−1m−1) denotes the vacuum permittivity. The relative permittivity ranges of

air and water are shown in Table 2-2. Organic liquids have intermediate

permittivity values, for instance ϵr=2 for oil, ϵr=20 for 2-propanol.

Table 2-2: Dielectric constants of common materials

Material Temperature

[°C] Frequency

[Hz] Dielectric constant

air 20 3 × 106 1 water 20 low 80

Sensor wire 20 - 2000

The size and position of bubbles and droplets measured with capacitive WMS can

strongly affect the electric field. The averaged dielectric coefficient is different for

individual cases. The dielectric coefficient, depending on the medium capacitance,

can be calculated. The dependency of the capacitance measured with WMS can be

calculated by voltage (Calibration method). Finite element method (FEM)

simulation with ANSYS is used for the numerical electric field analysis.

2.2.2.3 Finite element method

Selection of finite elements using FEM is based on the freedom of element types,

e.g. element type Plane230 (quadrilateral, eight nodes, see Figure 2-9), which has


18

freedom of voltage. The element type used for the two-dimensional model are

Plane230or 𝑃𝑙𝑎𝑛𝑒121 . Both element types have the same element shapes. Element

type Plane121 is a 2-D, 8-node, charge-based electric element and PLANE230 is a 2-

D, 8-node, current-based electric element. More information about the element

types can be found in [ANSYS (2011)].

The activated plane was loaded with the harmonic load at the voltage amplitude of

10 volt and the geometry of the plane was thought of as a cylinder (0.5

mm×0.5 mm). The other plane was assumed to be grounded. The distance between

the capacitor was set to 3 mm. In this two-dimensional model, different bubble

sizes and bubble positions were simulated and discussed.

Figure 2-9: Element Type: Plane230 (see in [ANSYS (2011)])

Similar to the two-dimensional model, finite element type SOLID122 (with

Hexahedral, twenty nodes, see Figure 2-10) can be used for three-dimensional

electric field simulation. The element has one degree of freedom at each node, that

is the voltage. It can tolerate irregular shapes without much loss of accuracy.

Otherwise, the principle is the same as discussed for the two-dimensional

simulation.

2.2.2.4 Two-dimensional electric field simulation

The orthogonally crossed but non-contacting points of two activated wires of the

capacitive WMS were modeled as capacitors. The capacitance of the capacitor in

dependency of the gas phase fraction was simulated numerically to deduce suitable

permittivity models for bubble and packed columns, respectively. Using this

simplified model, the influence of phase discontinuities in the spaces of crossing


19

points can be analyzed in two dimensions. In addition, the electric field between

two wires of WMS was extended to a three-dimensional field. The three-

dimensional models were applied to study the influence of phase discontinuities in

the scenarios: the bubbles/droplets are not exactly located in the center between

two activated wires.

Figure 2-10: Element Type: Solid122 (see in [ANSYS (2011)])

The two-dimensional simulation model is shown in Figure 2-11. The range drawn

with depicted lines is concerned in the electric field simulation.

Figure 2-11: Two-dimensional geometry for electric field simulation

For this two-dimensional model, the orthogonally crossed points of activated and


20

grounded wires are assumed as capacitors. This simplification aims to study the

influence of the phase distribution on the simulated capacitance. The length of the

activated wires can influence the simulated capacitance and is studied using the

three-dimensional electric field simulation.

2.2.2.4.1 Influence of bubble shape on capacitance

As shown in Figure 2-12, both air bubbles surrounded by water have the same area,

but different shapes between the capacitor plates. The gas fraction of both bubbles

between the capacitor is 0.7 %. The capacitance of the left bubble obtained from

the simulation is 0.0437 pF while the capacitance of the right bubble is 0.0441 pF.

It is obvious that the shape of the dispersed phase has only small influence electric

field (thus small influence on capacitance). It could be the case that this bubble

shape of small bubble size does not have significant influence on the capacitance.

Figure 2-12: Study of influence of bubble shape on capacitance

2.2.2.4.2 Influence of bubble position on capacitance

The influence of the position of the dispersed phase on the electric field is shown

in Figure 2-13. The capacitance at the four positions (a, b, c and d) is relatively

constant. For the last position (e), where the bubble is near the activated capacitor,

a slight increase of capacitance is observed (1 % higher). The influence of bubble

position between the grounded and activated wires can be summarized as not

sensitive.


21

Figure 2-13: Study of influence of bubble position on capacitance

2.2.2.4.3 Influence of bubble fraction on capacitance

From the previous results, it is known that the position and shape of dispersed

phase has almost no influence on the total capacitance. Nevertheless, the gas

fraction between the capacitor plates can influence the capacitance. To study the

influence of gas phase on the capacitance, the gas fraction is varied.

Figure 2-14: Study of influence of bubble holdup on capacitance

gas phase

water phase

activated wire

grounded wire a b c d e

activated wire

grounded wire

gas phase

water phase


22

As shown in Figure 2-14, the gas fraction varies from 12 % to 93.4 %. Blue areas

denote for the liquid phase while the green area represent the gas phase. Relation

between gas fraction and capacitance was studied and results are illustrated in

Figure 2-15. It is clear that the gas fraction significantly influences the electric field

and the relation between capacitance and gas fraction in the entire range of the

capacitor for the bubble column can be fitted by a linear function.

Figure 2-15: Dependency of simulated capacitance on gas fraction

At lower gas fractions (up to 10 %), the capacitance changes relatively sensitive to

an increase of the gas fraction. With increasing gas fraction, the sensitivity of

capacitance is reduced. The relation between capacitance and phase fraction over

the entire range of gas fractions (from 0 % to 100 %) can be approximated as a

linear function.

The previously discussed procedure and analysis of gas bubbles can be extended

for the case of dispersed liquid phase and the continuous gas phase is gas, e. g.

droplets in a packed column. The influence of phase fraction on capacitance for

bubbles as dispersed phase (e.g. bubble column) and liquid as dispersed phase (e.g.


23

packed column) are summarized in Figure 2-16.

It is shown that the dependency of capacitance on gas fraction in bubble columns

is approximately linear (blue curve with rectangular symbol) and the dependency

of capacitance in packed column is strongly non-linear (black curve with circle

symbol).

Fraction of dispersed phase

Relative permittivity of liquid phase is 5 (e.g. organic solution)

Figure 2-16: Dependency of normalized capacitance on phase holdup in bubble columns and packed columns

It is observed that for a relatively low liquid holdup and the change of capacitance

is relatively insensitive to the change of liquid holdup. That means, a small change

of measured or calculated capacitance could mean a large change of liquid holdup.

At relatively high liquid holdup, the capacitance is more sensitive to liquid holdup.

These results indicate that measurements with capacitive WMS have higher

accuracy for bubble columns than for packed columns. The relations of phase

fraction and permittivity for both applications are not identical.


24

2.2.2.4.4 Study of influence of medium permittivity on capacitance

The calculated capacitance of mediums of lower and higher relative permittivity

(e. g. organic solution and tap water) for the case of a gas bubble / a liquid droplet

as the dispersed phase are shown in Figure 2-16 and Figure 2-17.

Fraction of dispersed phase

Relative permittivity of liquid phase is 80 (e.g. tape water)

Figure 2-17: Dependency of normalized capacitance on phase holdup in bubble columns and packed columns

The relative permittivities of the organic solution (relative permittivity equals 5)

and the gas phase are not very different from each other. For the case that the

capacitive WMS is immersed in the organic solution, excluding the gas phase, the

calculated capacitance is 0.0028 pF. This capacitance is much lower than the one of

deionized water. From the simulation results, it is seen that the absolute changes

in capacitance are reaching from 0.0005 pF to approximately 0.0028 pF (phase

fraction varies from 0 % to 100 %). The calculated capacitances for the system air

and organic solution is much smaller than the for the system with deionized water

(relative permittivity equals 80). These results suggest that for an air-organic

solution mixture, the relation between electrical signal and phase fraction can be

described as quasi-linear. It should be noted, that if the permittivity of both fluids


25

not significantly differs from each other, this could make measurements less

accurate.

2.2.2.5 Three-dimensional electric field simulation

As shown in Figure 2-18, gas bubbles with different radiuses which are located on

the crossing point of the WMS were studied using the three-dimensional electric

field simulation. The activated and grounded wire are marked in red. The

dispersed phase is a gas bubble which is surrounded by a liquid phase (e. g.,

deionized water). The diameter of the dispersed bubble was varied to investigate

its influence on capacitance.

2.2.2.5.1 Influence of bubble size on capacitance

Capacitance was calculated for various bubble sizes. In Figure 2-19 it is shown that

the bubble size has a strong influence on the sum of electrical flux density vectors.

Gas bubbles were assumed as spheres to focus on the influence of capacitance on

bubble size. One can certainly assume other types of dispersed bubble shapes, but

as previously discussed, the two-dimensional simulation shows that the influence

of bubble shape can be neglected with acceptable small errors. Following, the

bubble size up to 4 mm was studied. The dependency of bubble radius on

capacitance can be described by a linear function (from bubble size of 0.9 mm to

Figure 2-18: Three-dimensional geometry of the electric field simulation

activated wire

grounded wire

neighbored wires

Disperse phase (droplet or bubble)


26

4 mm) as shown in Figure 2-19.

It is observed that, although the orthogonally crossing point of the activated and

grounded wire is enclosed by a large bubble, the simulated capacitance is larger

than the capacitance of single continuous gas phase. The capacitance has merely

reached 50 % of the capacitance difference between pure water and pure gas

phase. This is since the part of wires near the crossing point still have strong

influence on capacitance. This three-dimensional simulation shows that the

capacitance also has a linear dependency on the bubble radius.

Figure 2-19: Influence of bubble size on capacitance (left Figure shows the electric field simulation; the right Figure shows the dependency of capacitance on bubble size based on

the results of electric field simulation)

2.2.2.5.2 Influence of bubble position (in contact to wires) on capacitance

As shown in Figure 2-20, the influence of decentral (from the crossing point) bubble

positions, that are still in contact with either the activated or the grounded wire by

various positions of bubbles (∅ = 2 mm), were studied.

It is shown that by the variation of bubble positions on the wire the absolute

changes of capacitance are significant. The variation of capacitance in this case

ranges from 12.65 pF to 11.9 pF. The sensitivity of a bubble can consider to be


27

(12.65 pF - 11.9 pF) / 11.9 pF =10 %. As previously discussed, the bubble size at the

cross point has a stronger influence.

2.2.2.5.3 Influence of bubble position (without contact to wires) on capacitance

In the previous case was assumed that the bubble is in contact with the wires.

However, even small bubbles could flow through the WMS without touching the

wires. Therefore, the sensitivity of small bubbles without and with contact to the

activated wires were investigated.

Figure 2-20: Influence of bubble position on capacitance (left Figure shows the electric field simulation; the right Figure shows the dependency of capacitance on bubble

position based on the results of electric field simulation)

Given the case, that the rising bubble (∅ = 2 mm) has not touched the wire yet, the

bubble towards the wire (shown in Figure 2-21) was simulated. The electrical flux

density was influenced by the bubble, even at a distance of 4.5 mm to the crossing

point (shown in the first row). Distance variations from up to 4.5 mm from the

activated wires were studied. The bubble in contact with the wire at different

position has a more significant influence on capacitance compared to the bubble

without wire contact. The bubble which is not touching the wires has still influence


28

on capacitance that depends on the distance to the wires. However, the influence

is much smaller compared to the bubble in contact with the wire.

The simulated capacitance decreases from 13.9 pF (distance of bubble to the wire

is ∅ = 2.5 mm) to 10.9 pF (bubble is in the center at the crossing point). The

sensitivity of signal of bubble position can be considered as

(13.9 pF - 10.9 pF) / 10.9 pF = 29 %. For a bubble in a distance up to 1 mm from the

wire’s crossing point, the capacitance is still influenced. If the distance is larger

than 2 mm, the change in capacitance is almost negligible.

Figure 2-21: Influence of bubble position (without contact to the wires) on capacitance (left Figure shows the electric field simulation; the right Figure shows the dependency of

capacitance on bubble position based on the results of electric field simulation)

2.2.3 Discussion

The WMS capacitance method was reviewed and studied in this chapter. By means

of the two-dimensional and the three-dimensional electric field simulation using

FEM, it was shown that the permittivity model depends on its application for

packed columns or bubble columns as well as on the fluids absolute permittivity.

In the case of the two-dimensional analysis in which the activated and grounded

wires are simplified on the crossing point of the wires as capacitor, the permittivity


29

models for both, bubble columns and packed columns, respectively, can be derived.

The relative permittivity of the medium can also strongly influence the permittivity

models.

For the three-dimensional model, analysis is more complicated due to the large

possibility of bubble positions and sizes. It is not possible to consider all scenarios

to derive a unique permittivity model for both, bubble and packed columns.

In the simulation studies it is found that the capacitance depends on the bubble

diameter quasi-linear. Moreover, it is shown that the bubble size and bubble

position have strong influence on the measured signals. The bubbles which flow

through the wires without contact are still measurable up to certain distance. In

other words, total phase fraction of very small bubbles could be underestimated

and of large bubbles will be measured more accurate according to these simulation

results.

By an increase of wire number, the spatial resolution can be certainly improved.

However, the intrusiveness will increase significantly as well. In this study, it was

shown that the application of this method is suitable for multiphase measurements

with acceptable accuracy.

2.3 Measurements of bubble rise velocity and bubble size using

optical fiber method

The optical fiber method was studied by Miller [Miller and Mitchie (1970)] to

measure bubbles in a two-phase flow. Fordham [Fordham et al. (1999)] studied the

factors that influenced the accuracy of measurements by comparison of cross-

sectional profiles across the pipe diameter and time-averaged volume fractions of

a liquid-liquid flow. It was shown that surface treatments influenced the accuracy

of measurements strongly. Fordham [Fordham et al. (1999)] studied the application

of the optical method in kerosene/air and crude oil/nitrogen flows. The bubble

profile was successfully measured using this method.

2.3.1 Single optical fiber method

Vejrazka [Vejrazka et al. (2010)] studied isolated bubbles freely rising in a still


30

liquid. The intrusiveness of the optical method was studied by comparison of the

dwell time of the probe tip within the gas phase and the expected value for a non-

perturbed bubble. It was noted that the interaction increased the dwell time and

the local void fraction was underestimated. However, the void fraction error can

be correlated with a modified Weber number. Bubble velocity and bubble diameter

were measured with a single tip optical probe in a bubble column by Mizushima

[Mizushima et al. (2013)]. The position and angle between the tip and the measured

bubble were not clearly determined. A pre-signal which was analyzed using a

three-dimensional computational ray tracing method was applied. The simulator

traced enormous ray segment trajectories in an optical fiber and rendered

complicated optical boundary conditions. Evaluation of the complex output signals

were achieved by computing the polarization and energy of every ray. On this way,

the image quality was improved.

2.3.2 Four optical fiber method

The four-point optical method studied by Guet [Guet et al. (2005)] was validated

using image analysis. A new algorithm was developed for the evaluation of the

four-point optical fiber method to estimate bubble orientation and shape. It was

also suggested to analyze bubble orientation and shape in more detail and for

multiple bubble shear flow. Xue [Xue et al. (2008)] used the four-point optical fiber

method in a cylindrical bubble column with a diameter of 16.2 cm. The bubble

velocity and size in bubbly and highly churn turbulent flow were determined.

2.3.3 Double optical fiber method

Saberi [Saberi et al. (1995)] developed a method to detect and measure bubble sizes

and velocities in a gas-liquid column. Bubble velocity was calculated using two

identical parallel fibers and the cross-correlation technique. With the velocities and

the passage time determined, it was possible to determine the bubble diameter. The

double tip fiber probe method was used by Kiambi [Kiambi et al. (2001)]. They

determined the time averaged local interfacial area in a riser of an airlift reactor

for an air/water medium. The dimensions of the riser were 0.094 m in diameter and


31

1.2 m in height. Both optical probes had a distance of 3.2 mm. Chaumat [Chaumat

et al. (2005)] also used a double tip optical probe technique in a rectangular tank.

They tested the reliability of the probe data with a high-speed camera. The shape

and velocity of even distorted and tumbling bubbles were studied. Chaumat

[Chaumat et al. (2007)] extended the double fiber probe for more complex flow in

a bubble column with a diameter of 0.2 m. Rüdisüli [Rüdisüli et al. (2012)] used the

double tip optical fiber method to measure the bubble size and bubble rise velocity

in fluidized beds. A bubble linking algorithm based on regression techniques was

proposed. Due to slugging and wall effects, the bubble rise velocity did not show a

clear trend that an increased gas velocity and an elevated probe height lead to

larger bubbles and a modified bubble size distribution.

2.3.4 Laser doppler anemometer

Laser doppler anemometer (LDA) in bubble columns were basically explained and

discussed by Gross [Gross (1990)]. Kulkarni [Kulkarni (2005)] applied the LDA

method to study the influence of flow patterns of single point sparger on the local

flow field in a bubble column. Therning [Therning and Rasmuson (2005)] measured

liquid velocities in a small-scale bubble column with an internal diameter of

50 mm, packed with glass Raschig rings of 10 and 15 mm. It was found that the axial

time-averaged liquid velocity was lower than that obtained in empty bubble

columns. Although this method was non-intrusive, the application was limited to a

relative low gas holdup, and the bubbles close to the center of the bubble column

were not accurately measurable at higher gas loads.

2.3.5 Particle image velocimetry

Particle image velocimetry (PIV) was used by Chaouki [Chaouki et al. (1997)] in gas-

liquid flow to determine either the liquid velocity or the bubble velocity and size.

This method is advantageous to clearly investigate the fluid hydrodynamics.

Images were captured using a digital camera with a charge-coupled device (CCD)

chip. Delnoij [Delnoij et al. (1999)] reviewed the basic applications of the PIV

method in bubble columns and introduced some new points considering gas and


32

liquid flow fields induced by a bubble plume rising in a rectangular bubble column.

Nevertheless, the addition of small particles which flow with the gas and liquid

influences the original process condition.

2.3.6 Optical fiber method

An experimental method using the double optical fiber method described by Ji [Ji

(2007)] was employed in this work for the measurement of the bubble rise velocity

and the bubble size in a bubble column (∅ = 288 mm). Experimental equipment

(Laser Doppler and high-speed camera) were supplied by Prof. Walzel from

University Dortmund. The method suggested by Saberi [Saberi et al. (1995)] (cross-

correlation method) for data processing using the software MATLAB® has been

applied in this work to analyze the bubble size and bubble rise velocity.

The measuring system consisted of multiple light-guide fibers with a step-index

profile, wherein the fiber core material was Polymethylmethacrylate (PMMA). An

important feature of the fibers used in this work is the relatively large fiber core

diameter of 490 μm. The large fiber core is favorable for an in-line light coupling.

The concept of the optical fiber method exploited the Fresnel-effect on the interface

between a fiber tip and the surrounding fluid, which can be either a gas phase or a

liquid phase. When light was coupled into the fiber on one side, the intensity of the

reflected light on the other end depended on the refractive index difference

between the fiber core material and the fiber environment. The intensity of the

reflected light reached its minimum when the refractive index of the fiber core

material and the surrounding fluid was almost equal. With increasing difference

in refractive index, the intensity of the reflected light increased. Applying this

principle to the multi-phase flow within a bubble column, where one fluid was air

(nA = 1) and the other was water (nW = 1.33), the maximum intensity was achieved

when the fiber tip was located within a moving bubble. For other cases, i.e. when

the fiber tip was surrounded by water, the intensity of the reflected light was

reduced. Mounting a CCD element on the opposing end of the fiber, the local phase

changes on the fiber tip within the multiphase flow were visualized as a light

intensity plot over time.


33

Since both sides of the fibers were used in the present configuration, the light

coupling had to be achieved in-line. An additional challenge was that the major

amount of the light was coupled in the direction of the sensor tip, as it otherwise

would blend the measuring signal on the receiving side of the fiber.

The procedure of light coupling was performed through laser diode. A laser diode

with a power of 1 W and a wavelength of 660 nm was used along with a CCD line

scan camera with a sampling rate of 33.7 kHz. The advantage of this set-up is the

possibility to realize a light coupling into multiple fibers with relatively low

equipment requirements. A laser line with a flat-top intensity profile was generated

using a laser-diode and a proper lens configuration. A flat-top profile was needed

to ensure that the same amount of light was coupled in each fiber, leading to a

comparable signal quality for all sensor fibers. To achieve a selective light coupling

in the preferred direction, a bending coupler was used. The bending coupler was a

massive wedge, where one or multiple fibers were bend along its sharp edge. Due

to the bending, the fibers become permeable to light. Realizing a proper

arrangement of both, the laser-diode and the wedge, most of the light can be

coupled in the measuring direction.

Study of phase distribution in bubble columns

34

3 Study of phase distribution in bubble columns

Bubble columns are widely used as gas-liquid contacting apparatuses in the

chemical, biochemical and petrochemical industry. The gaseous phase in form of

bubbles is brought in contact with the liquid phase. Compared to other chemical

reactors, bubble columns have excellent heat and mass transfer characteristics -

high heat and mass transfer coefficients. Little maintenance and low operating

costs are required. Although the construction of bubble columns is simple, the

hydrodynamics of bubble columns are complex. Therefore, it is essential to apply

reliable measurement methods for the study of hydrodynamics in bubble columns

with high temporal and spatial resolution.

3.1 Flow regime in bubble columns

The disperse phase of bubble column is the gas phase while liquid phase is

continuous. As a bubble rises upwards in bubble columns, the movement speed in

axial direction is defined as axial velocity. Fluctuations of bubbles causes an

additional radial velocity. Flow regimes of bubbles in bubble columns can be

categorized as homogeneous regime, transition regime and heterogeneous regime,

depending on the superficial gas velocity and diameter of the bubble column.

The dependency of flow regime on the superficial gas velocity and diameter of the

bubble column is illustrated in Figure 3-1. In the homogeneous flow regime, it can

be assumed that the sizes of bubbles are equal. In the heterogeneous flow regime

bubble clusters of mixed different bubble sizes are formed. The flow regimes of

bubbles in a bubble column are dependent on design parameters (e.g. distributor

design, column diameter), operating parameters (e.g. superficial gas and liquid

velocities) and physical properties (viscosity, surface tension, density and

coalescing nature of the liquid phase).

In the homogeneous flow regime, the gas holdup increases markedly with the

superficial gas velocity. The bubble size is roughly uniform and the radial profile

of gas holdup is nearly flat. This was validated by Euzen [Euzen, Jp. et al. (2000)].

The trajectory of a small bubble (1.12 mm) was experimentally studied and


35

demonstrated by Shew [SHEW et al. (2006)]. At a low gas velocity range, the

distributor design affects gas holdup as reported by Luo [Luo et al. (1999)]. The

transition flow regime can be reached by increasing the superficial gas velocity

from the homogeneous regime. In the transition flow regime, larger bubbles can

be formed. Large bubbles move more quickly than small bubbles. This flow regime

is not as homogeneous as the homogeneous flow regime. The radial profile of gas

holdup shows a maximum at the center of the bubble column, and gas distribution

is nearly zero at the wall as reported by Krishna [Krishna et al. (1996)].

Figure 3-1: Flow regimes in bubble column reported by Deckwer

[Deckwer et al. (1980)]

In the heterogeneous flow regime, bubble coalescence and breakage are

significantly present. The breakage and coalescence mechanisms are responsible

for two classes of bubbles (Large and small bubbles). Liquid recirculation and

radial gas holdup profiles were studied by Chen [Chen et al. (2004)]. An increase of

the gas superficial velocity leads to a higher gas holdup. This slug flow regime is

highly unstable. The gas passes through the liquid as intermittent plugs, while the

liquid continuously pulsates up and down near the wall. However, the slug flow

regime is generally limited to columns of small diameter. The domain of industrial


36

interest concerns in particular the heterogeneous regime, characterized by high

mass and heat transfers. Bubble columns were studied by Deckwer [Deckwer and

Field (1992)].

The capacitive WMS discussed in the previous chapter was applied for the study of

phase distribution in an air/water system. Since one WMS is not able to be used for

the determination of the bubble rise velocity, the application of two WMS is

necessary, which, however, will strongly influence the phase distribution. Large

bubbles can be cut by the wires in multiple bubbles after passing through the first

WMS. This bubble cannot be identified by the second WMS. For that reason, the

optical fiber method was applied as additional method for the study of the bubble

rise velocity.

3.2 Experimental measurements of bubble column

3.2.1 Measurements of bubble distribution using WMS

Phase distribution in a bubble column (∅ = 0.288 m) was studied with a WMS. The

working principle of the WSM was discussed previously. By the electric field

simulation of the WMS, it was seen that the electrical signals of WMS were

evaluated with a linear relation for the bubble fraction. In this chapter the

experimental measurements of bubble distribution in the bubble column with

capacitive WMS are presented and the results are discussed.

As shown in Figure 3-2, a bubble column (air/deionized water system) with a

constant diameter of 0.288 m was investigated.

The vertical distance between gas distributor and WMS was about 1 m. Gas phase

was distributed through two orthogonally crossed pipes with small holes of 2 mm

diameter. The gas phase flowed through the gas distributor from the bottom into

bubble column and left from the top of the bubble column. The liquid phase was

stationary, without further in and outlet streams. As the superficial gas velocity was

increased, the flow regime changed from the homogeneous flow regime over the

transition range to the heterogeneous flow regime (Figure 3-2). Phase distribution

at different superficial gas velocities (2 cm/s, 4.2 cm/s, 8.4 cm/s, 16.8 cm/s) was


37

measured with the capacitive WMS.

Figure 3-2: Flow regimes in studied operating points of bubble column and experimental setup for phase distribution measurements using the WMS

3.2.1.1 Experimental results of the capacitive WMS

As shown in Figure 3-3, the spatial distribution of the gas phase (colored ranges) in

the cross-section of the bubble column was measured with a WMS. The colored

regions are indicating the gas phase while the white areas are representing the

liquid phase.

It was observed that at the moment of measurement the gas phase can be clearly

distinguished from the liquid phase due to the difference in permittivity. For this

process conditions (gas superficial velocity was 2 cm/s), the flow regime was

homogeneous. Figure 3-4 illustrates the phase distribution over time in intervals of

0.025 s. Due to bubbles changing their position continuously, it is important to study

the phase distribution over an integral time interval.

uG = 16.8 cm/s

uG = 2 cm/s

uG = 8.4 cm/s


38

Figure 3-3: Gas phase distribution across the cross-section of a bubble column measured by

the WMS

At a superficial gas velocity of 8.4 cm/s a large bubble cluster was observed to pass

the WMS over a time interval of 112 ms as shown in Figure 3-4. Due to the high

temporal resolution, it can be seen, that the bubble cluster has a quite irregular

shape and within the cluster even some interfacial area was recognized between

50 and 70 ms.

Figure 3-4: Temporal distribution of bubble clusters in cross-section of bubble column


39

A bubble flow profile of the transient regime is shown in Figure 3-5. The shown

phase distribution was taken along the diameter of the bubble column with time

intervals of 0.5 s. At a low superficial gas velocity of 2 cm/s the gas flow was mainly

bubble flow. Relatively large bubbles occurred primarily at the center of the

column while close to the wall there were almost no or too small bubbles to be

detected. With an increase of the superficial gas velocity the homogeneous bubble

flow (e.g. superficial gas velocity at 8.4 cm/s) turned to a mixed size bubble flow.

Larger bubbles were also found mostly near the center of the bubble column.

Smaller bubbles were detected near the wall. With a further increase of the

superficial gas velocity to 16.8 cm/s, large bubbles in forms of bubble clusters were

observed. The reason are the larger bubbles at the center of the bubble column that

raised much faster than the surrounding small bubbles. Due to circulation of the

liquid (downwards near the column wall and upwards in the center) the small

bubbles were transferred away from the wall into the center of the bubble column.

The small and large bubbles formed bubble clusters, where the interfacial area

cannot clearly be identified.

Figure 3-5: Temporal and spatial gas phase distribution at different operating points (flow regimes)


40

To understand the temporal and spatial bubble distribution, the bubbles were

reconstructed from the measurement signals of the WMS. The mechanism of

bubble reconstruction was realized using MATLAB and it has the following working

principle: In the case, that the gas holdup value at a measurement point is found to

be larger than a defined tolerance value (e.g. 3 %), all neighbored measurement

points are checked whether their gas holdup value is larger than the defined

tolerance value. In the case that the gas holdup value is identified as gas phase, the

corresponding point is seen as part of the gas phase and further measurement

points are checked. Otherwise the measurement point is identified as the liquid

phase. This crossing can also be interpreted as containing the interfacial area

between gas and liquid phase. This relation can be applied to all measurement

points (temporally and spatially measured), and hence, the bubble interfacial area

can be determined. The volume of the detected bubbles was reconstructed using a

conventional meshing method using MATLAB code.

As shown in Figure 3-6, bubbles were reconstructed at different superficial gas

velocity of 2 cm/s, 4.2 cm/s, 8.4 cm/s and 16.8 cm/s.

3.6.1) superficial gas velocity: 2 cm/s 3.6.2) superficial gas velocity: 4.2 cm/s


41

3.6.3) superficial gas velocity: 8.4 cm/s 3.6.4) superficial gas velocity: 16.8 cm/s

Figure 3-6: Bubble distribution at different superficial gas velocity (green is for the reconstructed small bubbles and red is for the reconstructed large bubble cluster(s))

The reconstructed bubbly flow was clearly recognized as bubble flow (superficial

gas velocity of 2 cm/s), churn flow (superficial gas velocity of 4.2 cm/s), slug flow

(superficial gas velocity of 8.4 cm/s) and annular flow (superficial gas velocity of

16.8 cm/s). It was seen that for the slug and annular flow, the large bubble clusters

were mainly in the center of the bubble column. These observations match the flow

regimes, which were qualitatively shown in Figure 3-2.

As shown in Figure 3-7 (top view of Figure 3-6), the amount of small bubbles, not

held in bubble clusters, strongly decreases with an increase of the superficial gas

velocity from 2 cm/s to 16.8 cm/s. The gas holdup as well depends on the flow

regime of bubble flow.

It should be noted that the phase distribution results depend on the tolerance of the

reconstruction. It was observed that the noise of WMS due to the calibration with

pure liquid is approximately 3 %. The tolerance of 3 % was set to eliminate the

measurement noise of the WMS.


42

3.7.1) superficial gas velocity: 2 cm/s 3.7.2) superficial gas velocity: 4.2 cm/s

3.7.3) superficial gas velocity: 8.4 cm/s 3.7.4) superficial gas velocity: 16.8 cm/s

Figure 3-7: Overview of bubble distribution at different superficial gas velocities (green is for the reconstructed small bubbles and red is for the reconstructed large bubble

cluster(s))

The local gas holdup in the radial direction (time- averaged) at a low superficial gas

velocity of 2 cm/s in Figure 3-8 and a high superficial gas velocity of 16.8 cm/s are

shown in Figure 3-9. At the low superficial gas velocity of 2 cm/s the gas holdup was

between 2 % and 5 % while at the higher superficial gas velocity of 16.8 cm/s, the

gas holdup within the center of the column cross section was much higher than the

one close to the wall (shown in Figure 3-10). Although the gas holdup at a superficial

gas velocity of 16.8 cm/s was high, it mainly occurred in form of large bubble

clusters. Compared to the small bubbles, large bubble clusters with the same gas

holdup have less interfacial area and a shorter residence time.


43

Figure 3-8: Reconstructed profile for a superficial gas velocity of 2 cm/s

Figure 3-9: Reconstructed profile for a superficial gas velocity of 16.8 cm/s

Figure 3-10: Local radial gas holdup distribution

Comparison of gas holdups using the difference in height method and a WMS is

shown in Figure 3-11. It is shown that the gas holdup measured by the height

difference method is higher than the gas holdup that was measured with the WMS

for different superficial gas velocities. The reason might be small bubbles flowing

through the WMS without touching the wires. Hence, the number of small bubbles

measured with the WMS was underestimated.

Ga

s h

old

up

Column radius [m]

Tim

e [s

]

Tim

e [s

]

x coordinate [m] x coordinate

[m]

y coordinate [m]

y coordinate [m]


44

Figure 3-11: Comparison of gas holdup measured with WMS and the height difference method

3.2.1.2 Conclusion

It was shown in this chapter that the capacitive WMS was successfully used for the

measurements of phase distribution in bubble columns. The high temporal

resolution of the WMS enables the detection of bubbles in ms. The high spatial

resolution of the WMS makes possible measurements of bubble distributions over

the whole cross section of a bubble column.

The measurements of flow regimes using the capacitive WMS have been validated

as qualitatively shown in Figure 3-2. Moreover, small and large bubbles (or bubble

clusters) could be distinguished in the measurements. It has been found that large

bubbles prefer to flow in the center of the bubble columns.

Gas holdups measured with capacitive WMS at different gas superficial velocities

were qualitatively similar to the measurements which were obtained with the

volume-averaged method (height difference method). Deviations of the results

between both methods were caused by the measuring principles of the WMS, by

which too small bubbles cannot be measured.

In summary, the capacitive WMS was applied successfully for the measurements of

phase distribution. It should be noted that, although the time interval of a large

Superficial gas velocity [cm/s]

Ga

s h

old

up


45

bubble cluster can be measured, the bubble rise velocity is not measurable using

the WMS. Optical fiber methods were applied for the measurements of bubble rise

velocity in bubble columns.

3.2.2 Measurements of bubble rise velocity and bubble size using an optical

fiber method

3.2.2.1 Experimental setup

The main part of the experimental apparatus used for optical fiber method is a

cylindrical column (288 mm in diameter) that is shown in Figure 3-12. The positions

of the fibers and the corresponding distances are shown in Figure 3-13.

Figure 3-12: Bubble column equipped with the optical fiber

method

Figure 3-13: Schematic representation of the experimental setup using optical fibers in the bubble

column

Two fibers each were installed as a couple. The fibers were inserted into the bubble

column through sealed holes in the column wall. This method allows the

measurements of bubble rise velocity at 12 different positions. Each fiber couple

was inserted into a 20 cm long steel tube with 0.5 mm inner diameter to stabilize

the fibers. The length of the steel tube in the bubble column was varied over the


46

radius. Air was blown through the gas distributor (shown in Figure 3-14) from the

bottom of bubble column and its superficial velocity was measured. The vertical

distance between every fiber pair was 4 mm. There were four couples of fibers in

each measurement plane. The distance between every measurement plane was 15

cm. The measured signals were recorded as images and the images were analyzed

after the measurements.

Figure 3-14: Gas distributor used for measurements with optical fiber method

3.2.2.2 Data processing of measurements using the optical fiber method

The measurements were with same length of optical fibers in the bubble column.

The light intensity measured with 24 fibers (12 fiber pairs) is illustrated in Figure

3-15.

F1 denotes for the first fiber pair (1st and 2nd fiber) while the F2 is the 2nd fiber

pair which consists of the 3rd and 4th. fiber. The white color indicates a gas bubble

passing the fibers, while the black areas representing water during the

measurements. Since the sampling rate of the CCD camera was set to 33.7 kHz, the

pixel length could be recalculated into time scale. It is shown that many bubbles,

which were measured by the first fiber of the fiber pair was also well detected by

the second fiber of the same pair. Only such bubbles were well measured and can

be used for the data analysis.

A bubble which is detected by the fiber pair F6 is shown on the right side of Figure

3-15. It is seen that the sampled intensity signals of the detected bubble measured

by the fiber pair F6 (11st. and 12st fiber) are of similar length. This means that the


47

bubble has the same sampled frames/contact time with both fibers of fiber pair F6.

Thus, the determined bubble length was almost the same, which indicates that the

same bubble was measured by fiber pair F6. In case of different lengths, the

intensity measurements were assumed to be incorrect and results would not be

reliable. Therefore, the method is advantageous for the detection of relative large

bubbles.

Figure 3-15: Measured light intensity with optical fiber method

The vertical shifted distance of the bubbles measured by both, the 11th and 12th

fiber denotes for a shift of frames and it is used to calculate the delay Δt of the

detected bubble passing the fibers of a pair. As previously discussed, the distance


48

of the fiber pairs L is known and the time difference Δt from the first to the second

fiber can be calculated. Thus, the bubble rise velocity vb can be calculated using

(eq. 3-1).

vb=L

Δt

(eq. 3-1)

To obtain the time difference between two signals, the intensity signals of an 8-bit

monochrome image were analyzed using MATLAB®. Each intensity signal can be

represented over time. Since the noise of intensity signals influences the Δt,a

proper data processing has to be applied.

Figure 3-16: Calculation of time delay using cross-correlation used by Ji [Ji (2007)]

A well-known analysis method, namely the cross-correlation function applied by

Kipphan [Kipphan (1977)] and Ji [Ji (2007)], as shown Figure 3-16, was used for the

determination of the time difference. The correlation coefficient Ψxy(𝜏) was

determined from two signals x(t) and y(t) for each sensor pair:

ψxy

=1/T ∫ x(t-τ)⋅y(t)dt

T

0

(eq. 3-2)

In

(eq. 3-2), τ is the initial time difference and T is the considered period of time. If a

maximum of correlation coefficient ψxy(τ) is found, τ is the time difference to be

determined. It should be noted that ψxy(τ) can always be found mathematically

within a given range of τ . Therefore, it is necessary to verify whether the results

are reasonable.


49

3.2.2.3 Experimental measurements of bubble rise velocity using the optical fiber

method

Bubble size and rise velocity at various positions of the bubble column radius and

superficial velocities were studied using the optical fiber method. The measured

intensities of each experiment are shown in Figure 3-17.

r/R=0.7

r/R=0.8

r/R=0.9

Figure 3-17: Experimental results at gas superficial velocity from 1.28 to 12.8 cm/s at r/R = 0.7, 0.8 and 0.9

As shown in Figure 3-18, the intensity at the front tips of the optical fibers were

measured within 1200 ms for the superficial gas velocity of 12.8 cm/s and a

dimensionless radius of 0.9 from the sensor position to the bubble column center.

Each peak of intensity denotes the detection of a bubble at the front tip of the optical

fiber.

On the one hand, some peaks were only measured by one of the two coupled

sensors, but not by the other one. On the other hand, the form of the bubble

measured by sensor 1 and 2 differed significantly from each other. Such bubbles

cannot be applied for analysis with the methods discussed.


50

Figure 3-18: Post-processing of measured signals ((a) measured intensity; (b) filtered intensity)

The bubble shown in Figure 3-19 was detected by both sensors and the form of the

peaks from both sensors were quite similar. Thus, the captured bubble size was

7.5 mm and the bubble rise velocity was about 25 cm/s.

Figure 3-19: Signal intensity of paired sensors used for calculation of bubble size and bubble rise velocity

Measured time [ms]

(a)

(b)

Measured time [ms]

No

mil

ized

sig

na

l i

nte

nsi

ty[-

] S

mo

oth

ed s

ign

al

in

ten

sity

[-]

Sm

oo

thed

sig

na

l i

nte

nsi

ty[-

]


51

Figure 3-20: Experimental results at gas superficial velocities from 1.28 to 12.8 cm/s

Superficial gas velocity [cm/s] Superficial gas velocity [cm/s]

Bu

bb

le r

ise

vel

oci

ty [

mm

]

Bu

bb

le r

ise

vel

oci

ty [

mm

] B

ub

ble

ris

e v

elo

city

[m

m]

Bu

bb

le r

ise

vel

oci

ty [

mm

]


Bu

bb

le r

ise

vel

oci

ty [

mm

] B

ub

ble

ris

e v

elo

city

[m

m]



Bu

bb

le r

ise

vel

oci

ty [

mm

] B

ub

ble

ris

e v

elo

city

[m

m]


52

The bubble rise velocity depending on superficial gas velocity and the

dimensionless radius of the bubble column is illustrated in Figure 3-20. The bubble

rise velocity is displayed at dimensionless radiuses of r/R = 0.1, 0.2, 0.3, 0.4, 0.5, 0.6,

0.8 and 0.9. The superficial gas velocity varies from 1.28 cm/s to 12.8 cm/s.

It is observed that with an increase in superficial gas velocity, the bubble rise

velocity increases from 50 cm/s to 100 cm/s, respectively. The variation of the

measured bubble rise velocity from r/R = 0.1 to 0.5 was not considerable. From a

dimensionless radius of r/R = 0.6, a slight decrease of bubble rise velocity at low

superficial gas velocities was observed, while that at higher superficial velocities is

still approximately 90 cm/s. At a dimensionless radius of r/R = 0.8 and 0.9, the

bubble rise velocity depends on the superficial gas velocity. The bubble rise velocity

at r/R = 0.9 is considerably smaller than the one in the middle range. It was

observed that the liquid near the column wall slightly circulated downwards. This

could result in a slowdown of the rising bubble flow, so that reasonable smaller

bubble rise velocities were observed.

The bubble rise velocity shown in Figure 3-21 at r/R = 0.7 was almost independent

of the superficial gas velocity. The reason of this phenomena could be that at this

dimensionless radius the bubbles flowing upwards are affected by the liquid phase

flowing downwards (circulation of liquid phase), so that the bubble rise velocities

were similar for different superficial gas velocities.

Figure 3-21: Experimental results at gas superficial velocities from 1.28 to 12.8 cm/s

Superficial gas velocity [cm/s]

Bu

bb

le r

ise

vel

oci

ty [

cm/s

] [m

m]


53

Based on the data processing method (cross-correlation method) discussed earlier

in this chapter, the bubble diameters in dependence of superficial gas velocity and

dimensionless radius in the bubble column were also studied. The results are

shown in Figure 3-22.

Figure 3-22: Bubble size distribution in radial direction

It is seen that at a superficial gas velocity of 1.28 cm/s, the vertical bubble lengths

(assumed as bubble diameter) were approximately similar over the dimensionless

radius from 0.1 to 0.9. The measurements match the prediction that at this

superficial gas velocity the flow regime was approximately homogeneous.

Figure 3-23: Comparison of experimental results with data published

by Wallis [Wallis (1969)]

Superficial gas velocity: 12.8 [cm/s]



Dimensionless radius r/R [-]

Bu

bb

le d

iam

eter

[m

m]


54

With an increase of superficial gas velocity to 6.4 cm/s and 12.8 cm/s, larger bubbles

were detected. It was seen that the higher the superficial velocity is, the larger is

the bubble diameter. Larger bubbles were mainly detected in the center of the

bubble column. Near the column wall only small bubbles were detected for the

studied superficial gas velocities. As it was shown by the measurements with

capacitive WMS, the flow regime was heterogeneous at a superficial gas velocity of

12.8 cm/s.

The comparison of the experimental results with literature shows a generally

higher bubble rise velocity for the studied bubble sizes of 2 mm to about 30 mm.

The reason could be that the optical fibers only measure parts of the larger bubbles,

so that the bubble rise velocity of a larger bubble is underestimated. Similar results,

as shown in Figure 3-24, were reported by Chaumat [Chaumat et al. (2005)], as well.

Figure 3-24: Experimental measurements of bubble rise velocities using an optical method by Chaumat [Chaumat et al. (2005)]

3.3 Conclusion

The optical fiber method was reviewed and studied in this chapter. It was shown

that the optical fiber method can experimentally be applied for the measurement

of gas-liquid flow (air-water) in bubble columns. Bubble rise velocities and bubble

sizes in axial direction were successfully measured. However, the analysis of

measured intensity signals should be handled with care. Only well measured

bubble signals can be considered for analysis. This method can be categorized as a

Axial bubble velocity [m/s]

Eq

uiv

ale

nt

dia

met

er [

mm

]


55

pointwise method whereby the measurements depend significantly on the local

flow conditions.

Compared to other conventional experimental methods, measurements in bubble

columns with capacitive WMS and the optical fiber method, as shown in this work,

are low-intrusive. Thus, they only little affect the process hydrodynamics.

Compared to non-intrusive methods used for measurements in bubble columns,

the WMS has a higher spatial and temporal resolution while the optical fiber

method has only a high temporal resolution and can be used in the bubble column

on arbitrary positions. The limitation of both methods is the relatively complicated

data processing.

Study of phase distribution in packed columns

56

4 Study of phase distribution in packed columns

Packed columns are widely used in separation processes (e.g. distillation and

absorption) and remain the core element of diffusion separation processes. This

underlines the need for advanced design principles of packed columns to improve

design efficiency and reliability. Compared to bubble columns, packed columns are,

due to the packing structures, opaque multiphase contactors; which change the gas

and liquid flow regimes continuously and irregularly. Thus, it is difficult to observe

and measure the flow regime and phase distribution in packed columns. The

hydrodynamics of gas-liquid flow in packed columns are still not completely

understood. Normally, studies of packed columns are based on simplified physical

models and on analyzing experimentally obtained parameters, e.g. pressure drop

and liquid holdup. In packed columns it is assumed that both, gas and liquid phases

are uniformly distributed across the column cross section.

In this work, studies of packed columns were reviewed with respect to theoretical

and experimental contributions. The review is especially focused on phase

distribution in packed columns. Moreover, phase distribution in random and

structured packings was measured experimentally using the capacitive WMS

introduced in chapter 2.2. With the WMS method, the phase distribution was

measured with relatively low intrusiveness. Theoretically, the phase distribution in

packed column was studied using a cell model.

4.1 Theoretical background of packed columns

In packed columns, mass and heat transfer processes are performed with high

driving force for two-phase counter-current flow. The pressure drop of the gas

phase and the liquid holdup depends on the installed types of packing. For column

design it is necessary to study the hydrodynamics and mass transfer processes

depending on the packing types, the gas loads and the liquid flow rates. Previous

studies of packed columns have usually adopted simplified physical models. Based

on the model assumption, equations were mathematically derived. Then,

experimental results considering the process conditions are applied to determine


57

unknown characteristic parameters. The film model as suggested by Billet [Billet

and Schultes (1999), Billet (1995), Billet (1993)] is shown in Figure 4-1.

Figure 4-1: Channel model suggested by Billet [Billet (1995)]

The model was derived from the assumption that the gas and liquid phase flow in

counter-current directions as continuous phases. A small liquid volume was

differentiated and the applied forces were analyzed. The differential element was

integrated from the packing surface over the film thickness to the gas-liquid

interfacial area. On the gas-liquid boundary layer, the friction force from the gas

phase was added to the force balances. Thus, the relation between the physical

properties of the liquid-gas system and packing characteristics was derived.

Relations for hydrodynamic and mass transfer parameters were derived

mathematically and specified constants were supposed as characteristic

parameters for each packing type. This method was advantageous in generalizing

the packing characteristics using simple constant parameters. The characteristic

constants reported by Billet [Billet and Schultes (1999)] were evaluated under

assumed absence of maldistribution. Most experimental measurements were

carried out in columns with diameters smaller than 600 mm. This is contradictory,

since the maldistribution influence in small columns is more serious than in larger

columns.


58

The suspended droplet model (SDM) shown in Figure 4-2 suggested by Mackowiak

[Mackowiak (2010)] is based on experimental observations at high fractions of

liquid droplets within in the column. This mechanism of droplet formation was

experimental verified by studies carried out by Bornhütter [Bornhütter (1991)]. A

force balance analysis was established for a single droplet and droplet clusters

which were suspended inside the packed columns. It was thought that droplets

were formed before reaching the loading point and that the large amounts of liquid

droplets were the main reason for flooding effects. The model was applied for the

study of hydrodynamic parameters, e.g. pressure drop ΔP, liquid holdup hL, gas

load capacity FV. Mass transfer processes were not investigated using the

suspended droplet model.

Figure 4-2: Suspended droplet model (SDM) suggested by Mackowiak [Mackowiak

(2010)]

Stichlmair [Stichlmair et al. (1989)] applied the particle model for predicting the

pressure drop and the capacity of counter-current gas-liquid flow in random

packed columns. In this model, the random packing was conceived as a collection

of orbicular particles. The size of the orbicular particles was dependent on the beds

void fraction and the surface area of the packing. For increasing liquid flow rate,

the void fraction of the bed drops, the size of the particle increases and the pressure

drop increases as well. This model was used to predict the pressure drop in both

irrigated random and structured packings. This approach was derived on basis of

the dry pressure drop and was extended to irrigation applications by a correction

in the presence of liquid.


59

Experimental measurements of the pressure drop and the liquid holdup of

traditional random packings (e.g. Pallring) up to the loading point were predicted

more accurately with the model suggested by Billet. The reason for this is that the

traditional random packings have a relatively lower specific area and thus produce

a lower fraction of droplets. The main regime of the liquid flow is film flow.

Accordingly, above the loading point, the suspended droplet model describes the

pressure drop and liquid holdup more accurately, since liquid droplets are formed

in larger fraction.

4.1.1 Pressure drop

Based on the theoretical models, pressure drop of un-wetted and wetted packings

can be calculated. The pressure drop of packings is influenced by the ratio of the

specific surface area a of each packing to the packed volume of the column, the void

volume fraction ε, the gas load factor FV, the wall factor 𝐾 and friction coefficient ζ.

Billet [Billet and Schultes (1999)] suggested to use (eq. 4-1) for the prediction of the

dry pressure drop. The friction coefficient was calculated with the Reynolds

number 𝑅𝑒 and the packing specific pressure drop constant of an un-wetted

packing CP,0 by (eq. 4-2). A large number of CP,0 were determined experimentally.

The pressure drop of irrigated packings was calculated by (eq. 4-3). The gas flow

friction coefficient ζ was determined using the pressure drop constant of an

irrigated packing CP with (eq. 4-4). The irrigated pressure drop strongly depends

on the liquid holdup.

Similar to the model suggested by Billet, Stichlmair [Stichlmair et al. (1989)]

suggested to calculate the pressure drop using (eq. 4-5). The gas phase friction

coefficient was determined using Re of the gas phase and the constants C1, C2, C3 as

shown in (eq. 4-6).

The pressure drop equation suggested by Mackowiak [Mackowiak (2010)] is more

complicated than the methods introduced by Billet and Stichlmair. The pressure

drop of un-wetted packings was similarly computed, using (eq. 4-7). The resistance

coefficient ψ was calculated with the constants K1, K2, K3, K4, dependent on Re as

shown in (eq. 4-8) and (eq. 4-9).


60

The irrigated pressure drop was determined using (eq. 4-10). Here, the resistance

coefficient ψ was calculated using (eq. 4-11). μ in (eq. 4-11) is a packing type

dependent form factor and A as well as B were the experimentally fitted constants

for the determination the irrigated pressure drop.

The pressure drop is one of the most important parameters for packed columns.

The equations suggested by Billet [Billet and Schultes (1999)] were basically derived

on large amounts of experimental results measured at the Ruhr- University

Bochum. A large fraction of the experimental results used by Mackowiak

[Mackowiak (2010)] were also originated from Ruhr- University Bochum.

Table 4-1: Correlations for the prediction of pressure drop

Author Remarks Correlations

[Billet and Schultes (1999)]

pressure drop for unwetted packings

20 v vΔP u ρa 1

= ζH ε 2 K

20 v vΔP u ρa 1

= ζH ε 2 K

20 v vΔP u ρa 1

= ζH ε 2 K

(eq. 4-1)

pressure drop coefficient for unwetted packings 0 ,0 0.08

64 1.8( )P

V V

CRe Re

= + (eq. 4-2)

pressure drop for irrigated packings

2

3

1

2( )v V

L

uP a

H Kh

=

−

(eq. 4-3)

pressure drop coefficient for irrigated packings

1.5

0.08

1.5

64 1.8( )( )Re Re

13300exp( )

LP

v v

L

hC

Fra

−= +

(eq. 4-4)

[Stichlmair et al. (1989)]

pressure drop for irrigated packings ( )

2

3

4.652

4.65

1 10.125

1

1

/c

L

v v

hp

u ah

+

−

− − =

−

−

(eq. 4-5)

pressure drop constant of irrigated packings C1, C2 and C3 from experiments

1 230.5Re Rev v

C CC = + +

(eq. 4-6)

pressure drop for unwetted packings

20

0 3

3 1 1

4v v

P

P u

H d K

−=

(eq. 4-7)


61

[Mackowiak (2010)]

K1, K2 used for Re < 2100 2

0 1

3

4KvK Re = =

(eq. 4-8)

K3, K4 used for Re > 2100 4

0 3

3

4KvK Re = =

(eq. 4-9)

pressure drop for irrigated packings

32

3

11 1

1V L L

VL

P

F h hp

H d K

− −

= + + −

(eq.

4-10)

constants A, B used for irrigated packing

BVL LA Re = (eq.

4-11)

Generally, it can be summarized that the pressure drop by un-wetted and irrigated

packings is dependent on the specific packing area, the porosity, the packing size,

Re of gas/liquid phase, the gas load and the liquid holdup. These equations for the

determination of pressure drop were derived from the measurements of old-

fashioned packings. Thus, pressure drops of new packing types need to be

determined by experiments as well.

4.1.2 Liquid holdup

The liquid holdup ℎ𝐿 is an important parameter that strongly influences the

irrigated pressure drop, the gas loading factor and the gas-liquid-packing

interfacial area. The residence time of components in thermal separation processes

should be kept as short as possible, especially if components are not stable. The

residence time directly depends on liquid holdup (certainly other factors as well,

e.g. packing height and phase flow rates). Thus, the mass transfer process is

strongly influenced by the liquid holdup.

Similar to the pressure drop, the models for calculating liquid holdup suggested by

Billet [Billet (1995)] and Mackowiak [Mackowiak (2010)] were focused in this work,

since the experimental results in this work were measured in the same (or partly

modified) packed columns.

The liquid holdup is defined as the fraction of liquid volume which is held at a

steady-state condition by the packings in the complete packing volume of the


62

packed column. In this sense, liquid holdup is a volume-averaged parameter.

Equations for the prediction of liquid holdup are listed in Table 4-2. The

dependency of liquid holdup on the gas load factor FV can be divided into three

areas:

1) Liquid holdup remains constant and is independent of the gas load Fv, if

superficial gas velocity is below the loading point Fv,S (Fv < Fv,S). The friction force

of the gas phase on the liquid phase at the phase interface is not large enough to

slow down the liquid phase. Increasing the gas load only leads to larger pressure

drop for any constant liquid irrigation rate. The liquid holdup is not influenced.

2) If the gas load exceeds the loading point, an increase of the liquid holdup can be

observed. With a further increase of the gas load, the local velocity of the liquid

inside the packing is slowed down by the gas phase. The liquid phase strongly

accumulates with further increase of the gas load. The tendency of the liquid

holdup increase is exponential.

3) The packed column floods, if the gas load factor reaches its maximum. At the

flooding point the pressure drop is so large that a further increase of the gas load

is not possible anymore.

As shown in Table 4-2, the calculation of the liquid holdup suggested by Billet is

influenced by the gas flow velocity uv, the gas density ρv, the pressure drop

coefficient ζ, the packing porosity ε, the packing specific area 𝑎, the liquid property

(e.g. liquid density ρL) and the liquid velocity uL. Liquid holdups below loading

point were determined using (eq. 4-17), in which the wetted area was determined

using equation (eq. 4-18) and (eq. 4-19). The liquid holdup above the loading point

was calculated using (eq. 4-20). Liquid holdup below the loading point is defined

as hL and liquid holdup above loading point as hL,S. One should be aware that the

exponent 13 in (eq. 4-20) indicates that the liquid holdup above the loading points

increases very quickly. However, it has been determined experimentally, that for

kinds of structured packings with high porosity, the exponent can be much smaller

(varies from 7 to 11). This exponent strongly depends on the packing form, packing

size and packing structure.

The average liquid thickness δL on the packing can be calculated with the liquid


63

holdup and the specific area a using (eq. 4-12).

δL=hL

a

(eq. 4-12)

The liquid film thickness δL shown in (eq. 4-13) was suggested by [Buchanan

(1969)] to determine the liquid holdup using (eq. 4-21).

δL= (3⋅η

l⋅uL

ρL

⋅g⋅a)

1/3

(eq. 4-13)

Mackowiak [Mackowiak (2010)] suggested to use (eq. 4-22) for calculation of the

liquid holdup. Liquid holdup in (eq. 4-22) is dependent on the gas load. If the

loading factor is larger than 65 % of gas load factor at the flooding point, (eq. 4-23)

should be used. The liquid holdup at the flooding point can theoretically be

determined using (eq. 4-24). The parameter 𝑚 depends on other quantities, e.g the

liquid phase Reynolds number ReL or the mass flow ratio of gas-liquid phase λ0. It

is determined using (eq. 4-25).

Stichlmair [Stichlmair et al. (1989)] studied the relations between the FrL and liquid

holdup based on experimental measurements. The relation was described by (eq.

4-26). FrL was defined by (eq. 4-14) as following.

FrL = uL2

a

gε4.65 (eq. 4-14)

FrL number used in (eq. 4-18) and (eq. 4-19) was calculated using (eq. 4-15).

FrL = uL

2 ⋅a

g

(eq. 4-15)

The liquid holdup above the loading point was calculated using (eq. 4-27), where

H is the total packing height and ΔP the pressure drop.

As shown in Table 4-2, liquid holdup strongly depends on the pressure drop,

packing size, packing materials, packing porosity and process condition and vice

versa. In these models the phase distribution was not considered and assumed as

uniform in the packings.


64

Table 4-2: Correlations for prediction of liquid holdup



2 1/ 2

2( )

3 4 ( )n L

L L L v v

L L

g aa u h u

h h

= −

−

(eq. 4-16)

Liquid holdup under the loading point ( )

,

1 22 3 3

, 12v v s

hL LL L su u

L

aa uh h

g a

= =

(eq. 4-17)

ReL < 5 0.25 0.10.85 Reh

h L L

aC Fr

a

=

(eq. 4-18)

ReL > 5 0.15 0.1Reh

h L L

aC Fr

a

=

(eq. 4-19)

Liquid holdup above the loading point ( )

13

, , ,

,

vL S L L FL L S

v Fl

uh h h h

u

= + −

(eq. 4-20)

[Buchanan (1969)]

( ) ( )1/3 1/32/33 /L L Lh g a u=

(eq. 4-21)

[Mackowiak (2010)]

Calculation of constant Pi ( )

( )11

mvLi L

L L

uuP h

h h + = −

−

(eq. 4-22)

𝑢𝑣 > 65% 𝑢𝑣,𝐹𝑙 1 1( (1 ) ( 1) )mv i L L Lu P h u h + −= − − −

(eq. 4-23)

phase flow ratio λ0 at flooding point

λ0=uL/uv

( ) ( ) ( ) ( )

( )( )L Fl

m m mh

m

+ + + − − +=

+ −

20 0 0 0

,

0

2 4 1 1 2

2 1 1

(eq. 4-24)

M = f(ReL, _0)

( )

1

,

,

0 ,

1 11

L Fl

L Fl

L Fl

hm h

h

−

= + −

−

(eq. 4-25)

[Stichlmair et al. (1989)]

e.g. C=0.555 for studied Raschig rings, Pallrings,

Hiflow, Mellapak, NSW rings,

Bialeckirings and Intalox

1/3L Lh C Fr=

(eq. 4-26)

2

, 1 20L S L

L

Ph h

H g

= +

(eq. 4-27)


65

4.1.3 Loading and flooding points

As discussed in chapter 4.1.2, gas loading capacity is limited by the gas load at the

loading and flooding point. Old-fashioned packings, e.g. Pallring and Raschig ring

have comparably lower loading and flooding points due to the fact that the porosity

of the packings is relatively low resulting in higher pressure drops. Although the

mass transfer rates of such packings are acceptable, high gas and liquid load

capacities are also important properties for achieving high time to volume

conversion.

The liquid holdup near the loading point is the most studied property of interest,

since industrial packed columns are usually operated close to the loading point.

Below the loading point, the pressure drop is small and the flow rate of gas is small

as well. Moreover, the mass transfer process is less efficient than the above loading

point, because above the loading point, the liquid flow is mainly turbulent. This

improves the mass transfer rates due to an enlarged interfacial area of the gas-

liquid phases. If the gas load factor is too high, the phase distribution is negatively

affected and strong maldistributions are formed. In this state, the mass transfer

rates are significantly reduced. The suggested gas load for optimized column

operation is 75% of the gas load at the flooding point as suggested by Mackowiak

[Mackowiak (2010)] is about 75 % of the gas capacity at the flooding point. The gas

loading capacity suggested Billet [Billet and Schultes (1999)] by was about 80 %.

This difference is dependent on the experimental packing types used for loading

point determination. For some of the new type packings, the loading point can be

larger than 85 % of the flooding load.

Generally, determination of loading and flooding points are performed at constant

liquid irrigation rates. As discussed in chapter 4.1.2, the liquid holdup begins to

increase at the loading point and reaches its maximum at the flooding point.

Calculations of the gas and liquid flow velocity at the loading point uv,S and uL,S and

flooding point uv,Fl and uL,Fl are shown in Table 4-3 .

The loading point constant CS in (eq. 4-28) was experimentally determined for

many kinds of packing. If CS is known, the friction coefficient ψS is evaluated using

(eq. 4-28). The gas flow velocity uv,Fl and liquid flow velocity uL,Fl at the loading


66

point are estimated using (eq. 4-29). Since the uv,Fl and uL,Fl are unknown variables,

(eq. 4-30) it is required to evaluate them iteratively.

Table 4-3: Determination of loading and flooding points using correlations as suggested by Billet [Billet and Schultes (1999)]



0.4, 0.723Vs

L

Ln

V

= −

0.4, 0.326Vs

L

Ln

V

= −

20.4

2

sn

v LS

L vS

g L

V etaC

−

=

(eq. 4-28)

, ,( )v S L Su f u= 1/3

1/2, ,1/6

1/6

,

112

112

Lv S L S

S L

L LL S

L v

gu a u

ga

ug

= −

(eq. 4-29)

, ,( )L S v Su f u= , ,

vL S v S

L

Lu u

V

=

(eq. 4-30)

0.4, 0.708Vs

L

Ln

V

= −

0.4, 0.194Vs

L

Ln

V

= −

20.2

2

Fln

v LFl

L vFl

g L

V etaC

−

=

(eq. 4-31)

, ,( )v Fl L Flu f h= ( )3 2, , ,

63 vL

L Fl L Fl v Fl

L L

Lh h a u

g V

− =

(eq. 4-32)

, ,( )v Fl v Flh f u= 1/4 1/2

1.2,

7/2

,1

h T LV F Fl

T V

L F

d d gu C

d

h

−

=

(eq. 4-33)

, ,( )L Fl v Flu f u= , ,

vL Fl v Fl

L

Lu u

V

=

(eq. 4-34)

Similar to the determination of the gas and liquid load at the loading point, the gas

and liquid flow rates at flooding point are evaluated iteratively as well. (eq. 4-31)


67

can be used for the evaluation of CFl, if CFl is known. The parameters for many kinds

of random and structured packings were reported by Billet [Billet and Schultes

(1999)]. Both, (eq. 4-32) and (eq. 4-33) contain two unknown variables, hv, Fl and

uv, Fl, which have to be evaluated iteratively as well. Thus, the liquid load can be

calculated using (eq. 4-34).

It is shown that determination of gas and liquid velocities at loading and flooding

point can be evaluated iteratively using the equations suggested by Billet [Billet and

Schultes (1999)]. The determination of loading and flooding points suggested by

Mackowiak [Mackowiak (2010)] are iteratively as well.

4.1.4 Mass transfer process

As previously explained, the pressure drop and liquid holdup is important for the

separation efficiency. The film model derived by Billet can also be applied for the

mass transfer process. Mass transfer parameters were suggested and reported in

Billet [Billet and Schultes (1999), Billet and Schultes (1995), Billet (1995), Billet and

Schultes (1993)]. The mass transfer process strongly depends on the

hydrodynamics of the absorption/ desorption process. In general, the mass transfer

process can be described using the equilibrium model and rate-based approaches.

4.1.4.1 Equilibrium model

The equilibrium stage model assumes that the gas and liquid phase leaving a tray

or a packing segment are in thermodynamical equilibrium with each other. The

equilibrium model for the description of separation processes was studied by

Henley [Henley and Seader (1981)]. As shown in Figure 4-3 (a), physical liquid

desorption (e.g., dilutet CO2 in H2O is stripped out of liquid phase by the gas phase)

mainly occurs at the top of the desorption column and physical gas absorption in

Figure 4-3 (b) (e.g., NH3 in air is absorbed though H2O phase) occurs in the bottom

range of the absorption column. The required packed height depends on the purity

requirements of the phases, gas and liquid flow rates and packing characteristics.

The equilibrium model assumes that the soluble component in the exiting gas and

liquid phase of each stage are in equilibrium. The equilibrium constant can be


68

described with (eq. 4-35),

Kn=y

n

xn=

Yn/(1+Yn)

Xn/(1+Xn)

(eq. 4-35)

where x is the concentration of solute in liquid phase, y is the concentration of the

solute in the gas phase, X is the molar load of solute in the liquid, Y is the molar

load of solute in the gas phase and n is one of the stages between 1 and N.

(eq. 4-36) and (eq. 4-37) are derived from the mass balance. L ‘ is the molar flow

rate of solute free absorbent and G’ is molar flow rate of solute-free gas.

Yn-1=(L’/G’)(Xn-X0)+Y1 (eq. 4-36)

Yn=(L’/G’)(Xn+1-X1)+Y0 (eq. 4-37)

As shown in Figure 4-4, the number of equilibrium stages can be evaluated

graphically. This method (McCabe-Thiele method) is applicable for known

operating and equilibrium lines.

Figure 4-3: Mass balance for a) desorption column and b) absorption column

Figure 4-4: Estimation of the number of theoretical of stage using equilibrium

model

Normally, the equilibrium model is applied for the study of simple mass transfer

processes, due to a relatively simple mathematical solution. However, equilibrium

is rarely achieved in practice and the equilibrium constant is correlated based on

experimental measurements. Thus, rate-based models which describe the effective

mass transfer, considering the packing characteristics and process conditions, can

K

(a) (b) YN+1, G‘ XN, L‘

X0, L‘ Y1, G‘ YN, G‘ XN+1, L‘

Y0, G‘ X1, L‘


69

be applied for the evaluation of mass transfer efficiency with better accuracy.

4.1.4.2 Rate-based model

Figure 4-5: Mass transfer process of desorption

The efficiency of mass transfer rates can be evaluated using to the HTU-NTU model

which is applicable for a limited mass transfer rate. As shown in Figure 4-5, the

solute component is stripped from the liquid phase by the vapor phase for a

differential element. The soluble components are transferred from liquid phase

into gas phase through the gas-liquid interface. This transfer is driven by the

concentration gradient of the transferred component. The mass transfer

resistances βL and β

v shown in (eq. 4-38) are existing in both phases, the liquid and

vapor one, respectively. The mass transfer resistance of both phases determines

how many solute can be transferred from one into the other phase depending on

concentration gradient.

NA = f (βL, (xA-xA,Ph)) = f (β

v, (y

A,Ph-y

A)) (eq. 4-38)

This resistance factor should be determined experimentally. Combined with the

component mass balance, the basic equation of HTU-NTU model in either liquid

phase or gas phase can be derived as (eq. 4-39) and (eq. 4-40) for the liquid and

gas side, respectively.


70

( )A,out

L L

H xL

O xA,inL Ph L S A A,Ph

HTU NTU

L M dxH dz

a A x x

= =

−

(eq. 4-39)

( ),

,,

A out

v v

H yv

O yA inG Ph G S A A Ph

HTU NTU

V M dxH dz

a A y y

= =

−

(eq. 4-40)

Here, AS denotes for the column cross section, aPh is the interfacial area,

V and L are the gas and liquid flow rates, respectively. ML and Mv are the mole

mass of liquid and gas phase. It can be seen that in (eq. 4-39) and (eq. 4-40) the

component concentrations of gas and liquid phase at the phase interface (yA,Ph

and

xA,Ph) are required. It is not convenient to express the HTU and NTU as a function

of the component interface concentration, since they are difficult to measure.

mxy is the slope of equilibrium curve shown in Figure 4-6 and it can be calculated

using (eq. 4-41) and (eq. 4-42).

mxy=y

A,Ph-y

A

xA,Ph-xA*

(eq. 4-41)

mxy=y

A* -y

A,Ph

xA-xA,Ph

(eq. 4-42)

The overall mass transfer coefficient on the liquid side kOL and the one on the gas

side kOV can be calculated by means of (eq. 4-43) and (eq. 4-44).

1

kOL=

1

βL

+1

mxy⋅βV

(eq. 4-43)

1

kOV=

1

βV

+mxy

βL

(eq. 4-44)

Therefore, the mass transfer between the liquid and gas phase can be expressed by

the overall mass transfer coefficients kOL and kOV (yA* and xA

* are the equilibrium

concentrations):


71

Figure 4-6: Operation and equilibrium lines for mass transfer process

( ),

*,

A out

OLOL

H xL

O xA inOL Ph L S A A

HTU NTU

L M dxH dz

k a A x x

= =

−

(eq. 4-45)

( ),

*,

A out

OVOV

H yv

O yA inG Ph G S A A

HTU NTU

V M dxH dz

a A y y

= =

−

(eq. 4-46)

Mass transfer in the absorption process was generally studied by Bennett [Bennett

(1952)]. Bravo [Bravo et al. (1992)] studied the mass transfer process in a wetted-

wall column. The gas-phase transfer coefficient was suggested to be calculated by

(eq. 4-47).

𝑆ℎ𝑣 = 𝐶1𝑅𝑒𝑣𝑚𝑆𝑐𝑐

𝑛 (eq. 4-47)

The Sherwood number Shv is dependent of the Reynolds number Rev of the gas

phase and the Schmidt number Sc. Their method assumed that the phase

distribution was sufficient to guarantee complete wetting of the surface area by the

liquid phase. That means, the interfacial area is equal to the specific packing

surface. This assumption over-estimates the wetted areas, which also depends on

factors like the initial irrigation and the gas liquid flow rates.

Onda [Onda et al. (1968)] determined that the wetted surface area shown in (eq.

4-48) depends on the liquid surface tension and the surface properties of packings.

It is a function of Froude number Fr, Re and Weber number We.


72

Aph

a=1-exp(-1.45(

σc

σL)0.75

ReL0.1FrL

-0.05WeL0.2)

(eq. 4-48)

Here, σc 𝑎𝑛𝑑 σL are the packing and liquid surface tensions, respectively.

Billet [Billet (1993)] suggested to calculate the wetted area using (eq. 4-49). The

dependency of the wetted area on Re, Fr and We are significantly different than

that in (eq. 4-48). This is the reason that the influence of surface tension is not

specified in (eq. 4-49) and organic solvent was especially applied to study the

influence of the liquid surface tension on the mass transfer process. Another reason

for the different approaches is that the measurements by Onda [Onda et al. (1968)]

mainly focused on the packing type Raschig rings.

Aph

a = 1.5(adh)

-0.5ReL

-0.2FrL-0.45WeL

0.75 (eq. 4-49)

Billet [Billet and Schultes (1999)] suggested to use (eq. 4-50) for the evaluation of

HTUOV (uV and uL are the gas and liquid superficial velocity).

HTUOV = uV

βV

⋅aPh+

mxy

L/V

uL

βL

⋅aPh

(eq. 4-50)

NTUOV, HTUOL and NTUOL were evaluated using (eq. 4-51) to (eq. 4-54).

H = HTUOV⋅NTUOV (eq. 4-51)

H=HTUOL⋅NTUOL (eq. 4-52)

HTUOL=HTUOV/λ (eq. 4-53)

NTUOL=λ⋅NTUOV (eq. 4-54)

The mass transfer coefficients of both phases can be evaluated with (eq. 4-55) and

(eq. 4-56). The constants CV and CL are the packing type specific constants for the

calculation of gas and liquid side limited mass transfer (HTU and NTU). The

influence of the liquid and gas phase flow rates on these parameters was also

studied. In these equations, HL’ is the holdup under the loading point, Dv is the

diffusion coefficient and dh is the equivalent diameter of one packing element.

βLaPh = CL⋅121/6

(uL

hL’

)

0.5

(D

dH)

0.5

a (aPh

a)

(eq. 4-55)


73

βV

aPh = CV⋅1

(ε-hL’

)0.5

a1.5

dh0.5

DV (uV

a∙νV)

0.75

(νV

DV)

1/3

(aPh

a)

(eq. 4-56)

The equations of mass transfer suggested and developed by Billet are considering

data of over 3500 experimental measurements, more than 50 different test systems

and were based on measurements with over 70 packing types. The model suggested

by Billet is widely accepted and applied. Within this work, the experimental

measurements, both the hydrodynamic and mass transfer measurements, were

mainly evaluated based on this model.

4.1.5 Study of phase distribution

The previously discussed models were derived from experimental observations

and are based on a uniform phase distribution. Non-uniform phase distribution,

which is defined as maldistribution as well, is related to column diameter, column

height, packing type and packing size, to name just a few. Maldistribution of the

liquid and gas phase can severely reduce packed column efficiency. Experimental

results should be analyzed, considering the maldistribution depending on the

column dimensions.

The study of liquid spreading using Gaussian distribution was suggested by Tour

[Tour and Lerman (1939)] to analyze their experimental results. It was concluded

that liquid spreading behaves similarly to the diffusion equation. Cihla [Cihla and

Schmidt (1957)] modified their study by introducing a partial differential equation

derived from the diffusion equation. They assumed that liquid spreading in the

horizontal direction is a random process and a function of the packing size.

Experimental and theoretical investigations of phase distribution in packed

columns are summarized in Table 4-4.

Cihla [Cihla and Schmidt (1957)] suggested to use a mathematical approach

(dispersion model) for the description of the trickling liquid phase in a random

packed column. In cylindrical packed columns different types of liquid distributors

were discussed. The packed height, column radius and liquid flow rates were

considered as influencing factors which play an important role in phase

distribution. The distribution of liquid flow over a layer of packing was interpreted


74

Table 4-4: Investigations of phase distribution in packed columns

Packing/Model Condition Remarks [Cihla and Schmidt (1957)]

diffusion model, mathematical solution

Initial condition of disk, annular, ring, central point and excentric distributors

The shape of the distributors influenced the liquid phase distribution significantly.

[Bemer and Zuiderweg

(1978)]

random packing, point source, water and water butanol mixture

Experiments in = 0.2 m, single liquid phase, 177 sampling sections, Raschig rings

Radial spreading was only dependent on ring size; Local flow rates deviated strongly from the diffusion theory; Residence time distribution agreed with tracer experiments; A large proportion of the axial mixing of the liquid phase occurs.

[Hoek et al. (1986)]

dispersion model, Raschig rings, Point source

experiments in = 0.5 m, single liquid phase, 657 sampling sections

Splitting factors were defined; Liquid flow was totally reflected by the column wall; The experimental distribution coefficient agreed with the results evaluated with the dispersion model; Cell model was applied for the study of phase distribution

[Stikkelman (1989)]

Structured packing

Experiments in = 0.5 m, single liquid phase, 1289 sampling sections

Liquid wall flow rate decreased by gas velocity exceeding 1.7 m/s; Liquid phase distribution dependent on the superficial liquid velocity; Gas phase had less influence on the liquid distribution; Cell model was studied.

[Potthoff (1992)]

random and structured packing

Liquid sampling method and temperature distribution, cell model

Influencing factors were studied based on experimental measurements of random and structured packings, cell models were numerically solved.

[Higler et al.

(1999b)]

random packing Mass and energy balances, non-equilibrium cell model, maldistribution pattern

Zone/stage model in 2D was suggested. The cell models were expressed as the radial model and square grid model

[Stoter et al.

structured packing

liquid collecting device, circular and

Liquid and gas flow distribution models were


75

(1993)] MONTZ-PAK B1-250, RALU-PAK 250 YC

rectangular column studied. Wetting effect of structured packings was studied experimentally using water-ethanol, water-glycol.

[Loser (2002)]

random (Pallring) and structured packing (MELLAPAK 250Y)

Liquid collector with 50 measuring pipes under the structured packing of 0.63 m in height at uniform liquid inlet distribution

Elementary cell model was related to single phase/ two phases; impulse and mass balance equations was suggested and applied for simulation with CFD

as diffusion equation in polar coordinates (eq. 4-57):

δf

δz=D⋅(

δ2f

δr2+

1

r

δf

δr+

1

r2

δ2f

δ𝜃2)

(eq. 4-57)

D denotes for a cross-sectional area per meter packed height, z is the differential

distance between two random packings in the axial direction, f is the distribution

function, r is as the column radius and θ is the angular coordinate.

The analytical solution of (eq. 4-57) was mathematically derived by Cihla [Cihla

and Schmidt (1957)] with suitable initial and boundary conditions. With this model

the importance of the initial liquid distribution was studied. However, it did not

contain information of packing characteristics and remained only a mathematical

equation. The influence of counter current gas flow was not investigated with this

model, since any change of boundary or initial conditions made an analytical

solution of the diffusion equation almost impossible. An example for this is that the

packing layer was assumed as infinite in the radial direction. The influence of wall

effects on phase distribution was not considered.

Bemer [Bemer and Zuiderweg (1978)] employed the dispersion model suggested by

Cihla [Cihla and Schmidt (1957)] for the description of their experimental liquid

phase distributions in polar coordinates as shown in (eq. 4-58).

Δf

δz=D⋅(

1

r

δf

δr+

δ2f

δr2)

(eq. 4-58)

The analytical solution of (eq. 4-58) was derived as (eq. 4-59) (Q was the flow rate

of liquid phase).

F(r,z)=Q

4πDz⋅exp(-

r2

4Dz)

(eq. 4-59)


76

In the experimental measurements shown in Figure 4-7, performed by Bemer

[Bemer and Zuiderweg (1978)], the liquid collector was divided into 177 sampling

cells (with each cell size having 16x16 mm2).

Due to the small scale of the cells, local distribution was investigated on the scale

of a single packing element. Underneath the support plate a collection device was

installed. As irrigating liquids, both tap water and mixtures of water/ butanol were

used while the column was filled with glass and Teflon coated Raschig Rings of

different size (dP = 0.01 - 0.03 m). Superficial liquid velocity uL was varied between

2 and 30 m3/m2/h at packed heights between 5 and 30 cm. It was found that wetting

properties had no noticeable influence on the flow distribution, since typical

channeling of liquid in random packing was observed independently of the packing

wettability.

As shown in Figure 4-8, Hoek [Hoek et al. (1986)] used similar equipment as [Bemer

and Zuiderweg (1978)]. The packing height was varied up to two meters and a

distributor with 68 nozzles of 3.0 mm diameter (approximately 350 nozzles/m2,

irrigation diameter < 0.45 m) was used. It was suggested to analyze the flow

patterns measured after several splittings of the liquid flow and thus after several

packing layers, where the flow patterns were smooth and of regular shape. At the

given packed height, 12 packing layers were installed. The diffusion equation (eq.

4-58) was applied to study the flow patterns. From these flow patterns the

distribution coefficient Dr was determined as 0.0029 m for 25 mm Raschig Rings. It

was reported that the value was similar to the one in their experimental study.


77

Figure 4-7: Experimental setup used by Bemer [Bemer and Zuiderweg

(1978)]

Figure 4-8: Experimental setup used by Hoek [Hoek et al. (1986)]

For the flow pattern shown in Figure 4-9, a regular liquid flow distribution without

channeling was observed. It was found that Dr was 0.03 m for the structured

packing Mellapak at a certain packing height and liquid flow rate. Based on their

experimental results, large scale maldistribution was also studied and a correlation

for the description of liquid wall flow was suggested.

Figure 4-9: Liquid phase distribution studied by Hoek [Hoek et al. (1986)]

The effects of gas load on the liquid distribution were studied experimentally by


78

Stikkelman [Stikkelman (1989)]. His experimental results showed that the liquid

bulk flow became less uniform as the superficial liquid velocity was diminished.

However, the flow distribution was almost independent of the gas flow. The

spreading pattern of liquid flow showed a small increase up to the loading point

and a more rapid increase above it. Radial spreading mechanisms shown in Figure

4-10 were applied for the description of the phase distributions using a cell model.

The liquid flow downwards from an overlying cell is splitted: One part of the liquid

flows downward vertically, to the underlying central cell. The rest of the liquid is

symmetrically divided into the four adjacent cells of the underlying central cell.

The gas phase, which flows counter current, was described with a similar splitting

mechanism, whereby the splitting factor differed from the one of the liquid phase.

The splitting factors were experimentally determined by point source experiments.

Compared to the cell model suggested by Potthoff [Potthoff (1992)], Stikkelman

[Stikkelman (1989)] considered less cells within the splitting process. By the model

suggested Potthoff [Potthoff (1992)], it was assumed that at each cell plane both, the

gas and liquid phases are flowing in slug flow. The separation efficiency NTUOV

was evaluated using the mass transfer coefficients discussed in the previous

chapter. The cells at the column wall were considered as well. The gas and liquid

flows in the cells at the column wall were assumed as ideal counter current.

Figure 4-10: Cell model as suggested by Stikkelman [Stikkelman (1989)]

Figure 4-11: Cell model as suggested by Potthoff [Potthoff (1992)]

Billingham [Billingham et al. (1997)] suggested to define the radial spreading


79

coefficient Dr for 1st generation random packings as 0.12∙dp, the spreading

coefficient of 2nd generation random packings as 0.06∙dp and the one of structured

packing was as Dr=0.0035. The relationship between the liquid splitting factor KL

and the spreading coefficient Dr was suggested by Stikkelman [Stikkelman (1989)]

to be according to (eq. 4-60).

(1 - KL) = 4⋅Dr⋅z1

r12

(eq. 4-60)

Zuiderweg [Zuiderweg et al. (1993)] modified (eq. 4-60) and suggested that the

liquid spreading coefficient should be evaluated using (eq. 4-61). They pointed out

that the diffusion equation can only be fitted well with KL= 2/3.

(1 - KL) = 2⋅Dr⋅z1

r12

(eq. 4-61)

Higler [Higler et al. (1999b)] developed a non-equilibrium cell model (shown in

Figure 4-12) to study the flow pattern of uniform liquid spreading, considering the

maldistribution effects of the gas phase.

Figure 4-12: Cell model introduced by Higler [Higler et al. (1999a)]

Figure 4-13: Cell model of the gas phase introduced by Stoter [Stoter et al. (1993)]

The model of Higler [Higler et al. (1999b)] is based on mass and energy balances.

The mass and energy equations were solved iteratively. The zone/stage approach

was applied for the description of maldistribution. In this zone/stage model, it was

assumed that a stage was split into several annular zones. The liquid flow in zone

straight downward was calculated using the splitting factor KL. The rest of liquid

flowed to the adjacent zones. Each incoming stream in a cell from the adjacent cells


80

had to be weighted by interfacial areas of the cell. If the liquid was flowing from

the center to the column wall, the splitting factor KL was multiplied with a factor

rkao , as shown in (eq. 4-62), considering the interfacial area. In (eq. 4-62), k denotes

for the number of rings to the column center.

Rkao =

ak

ak+ak-1 =

rk

rk+rk-1 =

k

2k-1

(eq. 4-62)

For the liquid flowing from the wall towards the column center, the factor rkai ,

shown in (eq. 4-63), should be applied.

Rkao =

ak-1

ak+ak-1 =

rk-1

rk+rk-1 =

k-1

2k-1

(eq. 4-63)

Depending on the maldistribution pattern, the maldistribution factor Mf can be

used for the description of the extent of maldistribution. The maldistribution factor

is actually the standard deviation of the measured local liquid flow rates.

The influence of column diameter and packing size on the wall flow is defined as

wall factor K by Billet [Billet (1995)]. K depends on specific packing area a and the

packed column diameter dS as shown in (eq. 4-64). The wall factor defined by

Mackowiak [Mackowiak (2010)] depends on the packed column diameter ds, the

packing diameter dP and the packing porosity ϵ as shown in (eq. 4-65).

1

k=1+

4

a∙ds

(eq. 4-64)

1

k = 1+

2

3

1

1-ϵ

dP

dS

(eq. 4-65)

Stoter [Stoter et al. (1993)] used a cell model to predict gas and liquid distribution

on small and large scale. Phase distribution was measured experimentally using a

liquid collector and a gas tracer method. He observed liquid maldistribution

between two packing elements with perpendicular orientation. In the model, the

cross section was divided into 12 squares of equal size. The cell model was modified

for the simulation of gas maldistribution in small diameter columns. Gas flow left

the cell layer, flowing to the element in the next layer which was turned over by

90∘ (shown in Figure 4-13). This model assumed a uniform initial gas distribution.

It was also reported that the initial gas inlet distribution device and 𝑅𝑒 influences

the gas phase distribution.


81

For the study of liquid distribution in structured packings, Stoter [Stoter et al.

(1993)] defined four possible directions of liquid flow out of a single cell, as

illustrates in Figure 4-14.

Figure 4-14: Cell model introduced by Stoter [Stoter et al. (1993)]

Figure 4-15: Cell model introduced by Stoter [Stoter et al. (1993)]

The flow pattern for a single cell was used to simulate liquid flow paths with a

network of interconnected cells shown in Figure 4-15. In this scheme, Figure 4-15

a) represents the first type of flow direction with flow angle of 45∘. Figure 4-15 b)

shows the flow path through the perforation with the first and second type of flow

directions. If the gravity driven flow enters a gray colored cell, a change of the

packing sheet side takes place. In Figure 4-15 c) and Figure 4-15 d), liquid flows over

the corrugation ridge and changes flow channels every three cells.

Maldistribution in the gas flow was investigated by Darakchiev [Darakchiev and

Dodev (2002)]. Stikkelman [Stikkelman et al. (1989)] reported that gas phase

maldistribution in the packing was negligible compared to that of the liquid bulk

flow. However, the gas phase maldistribution at the wall is the main

maldistribution of the gas phase. Near the column wall, the packing porosity

changes strongly. Models considering the wall and the packing were studied by

Dutkai [Dutkai and Ruckenstein (1968)], Ahn [Ahn et al. (1986)] and Kouri [Kouri

and Sohlo (1996)].

Gunn [Gunn (1978)] reported that the liquid phase maldistribution agreed well

with his model in within the loading range. Farid [Farid and Gunn (1978)] suggested

to use differential equations with boundary conditions related to the permeability


82

of wall and bulk regions to study the effect of phase distribution. Gunn [Gunn and

Al-Saffar (1993)] investigated the phase distribution in a 0.3 𝑚 column. They

pointed out that the zones near the column wall had similar liquid flow

enhancement for all investigated packings. The sensitivity of structured packings

on initial maldistributions was experimentally studied by Olujic [Olujic and

de Graauw (1990)]. It was reported by Pizzo [Pizzo et al. (1998)] that the smaller the

distance was between the distributor and the packing surface, the better was the

initial distribution. Experimental measurements of the liquid phase distribution in

a 0.6 m column were performed by Sun [Sun et al. (2000)]. The investigation of Yin

[Yin et al. (2000)] determined that liquid flow distribution was strongly influenced

by the liquid distributor design, the packed bed height, the gas flow rate and the

liquid viscosity. Only a slight influence of the liquid flow rate was observed, but no

influence of the liquid surface tension. A hydrodynamical continuum model

suggested by Iliuta [Iliuta et al. (2004)] considered the real structure of the

packings. Yin [Yin et al. (2002)] used gamma ray tomography to measure the phase

distribution in packed columns. Measurements of the dynamic liquid holdup using

X-Ray computer tomography were also performed by Toye [Toye et al. (1996)]. The

gas distribution in absence of the liquid phase was studied by Petrova [Petrova

et al. (2003)] and dispersion model was suggested.

Figure 4-16: Elementary cell model used by Mahr [Mahr and Mewes (2008)]

The elementary cell model shown in Figure 4-16 was used to study single-phase

flow by Arbogast [Arbogast et al. (1990)]. It has been further developed by Loser

[Loser (2002)] and Mahr [Mahr and Mewes (2008)] for structured packings. Mahr


83

[Mahr and Mewes (2008)] studied phase distribution in MELLAPAK 250.Y (PP)

experimentally using x-Ray tomography and described the phase distribution with

the elementary cell model. The cell model shown in Figure 4-16 suggested by Loser

[Loser (2002)] and Mahr [Mahr and Mewes (2008)] is focused on the smallest

periodic elementary cell, which was used to describe the phase flow within the

whole packing. The smallest representative cell can be chosen as one or two cells.

The conservation equations of mass and momentum were applied for each

elementary cell. Due to its channel structure, corrugated structured packings

strongly feature the preference of certain flow directions. The anisotropic flow

resistance for the gas phase was modeled using a direction dependent resistance

coefficient. The liquid phase was split up into two sub-phases to separately model

the flow along each preferential flow direction. The force balance of the gas and

liquid phases were based on the liquid film flow on an inclined plate with counter-

current gas flow, that was suggested by Brauer [Brauer (1971)].

4.2 Experimental study of packed column

Pressure drop, liquid holdup and mass transfer in packed a column, which was

filled with random or structured packings, were experimentally studied at

different gas loads and without counter current gas flow. Experimental

measurements were carried out in packed column with diameter of 288 mm. A

liquid collector was applied for the measurements of the liquid fraction at the

column wall. A capacitive WMS was applied for the phase distribution

measurements in the packed column.


84

Figure 4-17: Experimental setup of

the packed column Figure 4-18: Flow sheet of the packed column (∅ =

0.288 mm)

The packed column used for experimental measurements is shown in Figure 4-17.

As shown in Figure 4-18, the gas phase is blown into the wetting column (K2) with

a fan (G) and saturated, before entering the packed column (K1). Liquid is pumped

from the depot vessel (B1) to the top of the column (K1). The liquid exiting the

packed column is pumped to another depot vessel (B2). In all experiments, the

pressure drop in the packed column was measured. Moreover, liquid holdup was

evaluated by the valve-closing method (valves V3 and V4 were closed

simultaneously). The liquid volume was measured, when no significant liquid

droplets dripped out of the packing anymore. Furthermore, efficiency of physical

mass transfer rates was determined through ammonia absorption and carbon

dioxide desorption. Ammonia and carbon dioxide concentration were measured at

the gas inlet and outlet. Ammonia/carbon dioxide concentrations in the liquid

phase were measured with an off-line method: liquid probes were taken from

liquid inlet (V3) and liquid outlet (V4) and the probes were analyzed off-line. The

concentration of desorbed carbon dioxide and ammonia in gas phase was

measured with on-line measuring devices.


85

4.2.1.1 Study of hydrodynamics in structured packing

The operating conditions for the hydrodynamic measurements of structured

packings (type A and type B) are shown in Table 4-5. Both structured packings had

the same specific area, porosity and structure. The packing types differed only in

the packing surfaces. The studied packed heights for both structured packings were

1.86 m and 1.54 m, respectively. The gas load factors Fv were varied from

0.5 Pa0.5 to 4.0 Pa0.5 , while the liquid loads 0, 10, 20, 30 to 40 m3/m2/h were

investigated.

Table 4-5: Structured packing used in packed column

Structured packing type A Structured packing type B

specific area a 240 m2/m3 240 m2/m3

porosity ε 0.945 0.945

packed height H 1.86 m 1.54 m

gas load factor FV 0.5 Pa0.5 - 4.0 Pa0.5 0.5 Pa0.5 - 4.0 Pa0.5

liquid load factor u𝐿 0, 10, 20, 30, 40 m3/m2/h 0, 10, 20, 30, 40 m3/m2/h

It is seen from Figure 4-19 that the specific pressure drops of both structured

packings are very similar. The constant parameter CP which was calculated using

(eq. 4-1) to (eq. 4-4) is shown in Table 4-6. It indicates that the roughness of the

packing surfaces does not significantly influences the pressure drop.

Typ A

Typ B

Figure 4-19: Pressure drop of different types of structured packing


86

The liquid holdup of type A and type B is shown in Figure 4-20. Unlike the pressure

drop, the liquid holdup of both structured packings significantly differs from each

other at different liquid flow rates. The liquid holdup plot of type 𝐴 is relatively

typical, as the loading and flooding condition are clearly recognized. The liquid

holdup of type 𝐵 is non-typical, since the loading and flooding points are difficult

to recognize.

Type A Type B

Figure 4-20: Liquid holdup of of different types of structured packing

Moreover, the loading point at a liquid flow rate of 10 m3/m2/h is smaller for type

B than for type A. The difference was most likely caused by the roughness of the

packing surfaces or the different packed heights resulting in in different phase

distributions (packing heights of type A and type B are 1.86 m and 1.54 m,

respectively). The holdup constant Ch was determined using (eq. 4-16) to (eq. 4-20)

for both structured packings.

The constants calculated for the Billet method for type A and type B are

summarized in Table 4-6 and Table 4-7, respectively.

It can be recognized that the constants CP and Ch of structured packings type 𝐴 and

type 𝐵 are relatively independent on the liquid flow rates, slightly on the gas load

factors below the loading point and strongly on the gas load above the loading

point. The constants CP and Ch of both packing types A and B differ significantly

from each other, since the surface roughness of both structured packings is

different.


87

Table 4-6: Characteristic constants of structured packing type A

Table 4-7: Characteristic constants of structured packing type B

𝑢𝐿 [m³/m²/h]

𝐹𝑉 [𝑃𝑎0.5]

𝐶𝑃 [-]

𝐶ℎ [-]

𝐶𝑆 [-]

𝐶𝐹𝑙 [-]

𝑢𝐿 [m³/m²/h]

𝐹𝑉 [𝑃𝑎0.5]

𝐶𝑃 [-]

𝐶ℎ [-]

𝐶𝑆 [-]

𝐶𝐹𝑙 [-]

0 0.885 0.144 - - - 0 0.877 0.148 - - - 0 1.630 0.154 - - - 0 1.630 0.159 - - - 0 2.185 0.157 - - - 0 2.184 0.158 - - - 0 2.674 0.157 - - - 0 2.674 0.161 - - - 0 3.039 0.157 - - - 0 3.052 0.162 - - - 0 3.443 0.158 - - - 0 3.454 0.160 - - - 0 3.763 0.156 - - - 0 3.800 0.160 - - -

10 0.880 0.204 0.320

3.170

2.452

10 0.877 0.222 0.351

3.194

2.474

10 1.740 0.227 0.320 10 1.590 0.229 0.336 10 2.298 0.226 0.339 10 2.261 0.223 0.425 10 2.637 0.227 0.359 10 2.601 0.223 0.517 10 2.895 0.241 0.339 10 2.894 0.216 0.586 10 3.345 0.252 0.400 10 3.341 0.226 0.704 10 3.472 0.269 0.442 10 3.511 0.243 0.828 20 0.890 0.197 0.286

3.548

2.756

20 0.934 0.196 0.428

3.713

2.910

20 1.740 0.217 0.263 20 1.694 0.199 0.506 20 2.323 0.214 0.323 20 2.286 0.198 0.545 20 2.567 0.227 0.310 20 2.578 0.202 0.556 20 2.868 0.244 0.335 20 2.879 0.208 0.567 20 3.149 0.274 0.374 20 3.157 0.242 0.622 20 3.397 0.291 0.497 20 3.635 0.308 0.659 30 0.885 0.183 0.255

3.908

3.053

30 0.826 0.196 0.362

3.940

3.083

30 1.639 0.218 0.246 30 1.599 0.205 0.386 30 2.145 0.219 0.255 30 2.099 0.201 0.481 30 2.395 0.219 0.282 30 2.323 0.200 0.462 30 2.728 0.230 0.368 30 2.743 0.212 0.574 30 2.962 0.252 0.506 30 2.914 0.243 0.591 30 3.500 0.336 0.745 30 3.543 0.331 0.833 40 0.903 0.189 0.295

3.933

3.044

40 0.852 0.184 0.387

4.055

3.157

40 1.673 0.203 0.279 40 1.608 0.193 0.450 40 2.311 0.206 0.350 40 2.191 0.190 0.521 40 2.578 0.217 0.427 40 2.561 0.190 0.590 40 2.739 0.255 0.508 40 2.743 0.224 0.643 40 3.053 0.317 0.634 40 3.052 0.316 0.802 40 3.251 0.344 0.715 40 3.402 0.405 0.854

The constants of loading (CS) and flooding (CFl) capacity factors, which are shown

in Table 4-6 and Table 4-7, were evaluated using (eq. 4-28) to (eq. 4-34). It can be

seen that the constants CS and CFl are dependent on the liquid flow rates. They are

almost constant at larger liquid flow rates (at 𝑢𝐿= 30 m3/m2/h and 𝑢𝐿= 40 m3/m2/h)

for both packing types. It should be noted that the description of pressure drop,

liquid holdup, loading and flooding points using only one constant CP, Ch, CS and

CFl can lead to relative large deviation, since the constants depend on liquid phase

flow rates or gas loading factors.

4.2.1.2 Study of hydrodynamics in random packing

Pallrings (∅ = 25 mm, a = 225 m2/m3, ϵ = 0.95) were applied with a packed height of


88

2 m. In Figure 4-21, the pressure drop at different liquid flow rates (∅ = 288 mm) is

illustrated. The comparison of the pressure drops of Palling’s, structured packing’s

type A and type B shows that the pressure drop of the Pallrings is significantly larger

at all studied liquid flow rates, although the specific area is slightly lower.

Figure 4-21: Pressure drop of Pallrings (25 𝑚𝑚, metal) in a packed column (𝜙=288 𝑚𝑚)

The liquid holdup of the Pallrings is shown in Figure 4-22. It was observed that the

liquid holdup can be well described by the discussed equations (see Billet method).

Figure 4-22: Liquid holdup of Pallring (25 𝑚𝑚) Metall in packed column (𝜙 =288 𝑚𝑚)


89

The constants evaluated with the Billet method are listed in Table 4-6 and Table 4-7.

It shows that the constants CP at low gas loads are similar. Above the loading point,

CP strongly increases. As previously emphasized, the constants CP and Ch used

within the Billet method should only be applied below the loading point. The

constants CS and CFL also show a slight dependency on liquid flow rates.

Table 4-8: Holdup characterization of Pallrings with ∅ = 25 mm

Liquid flow rates y = a + b · xc

uL=10 m³

m²∙h

a 0.0411

b 2.8635E-6

c 8.8601

uL=20 m³

m²∙h

a 0.05781

b 5.0135E-6

c 10.2831

uL=30 m³

m²∙h

a 0.05781

b 4.2037E-6

c 8.8950

uL=40 m³

m²∙h

a 0.0780

b 4.5131E-6

c 9.7734

Curves of liquid holdup (shown in Figure 4-22) were fitted with equation y = a+b⋅xc,

with 𝑥 being the gas load factor and y the liquid holdup (shown in Table 4-8). The

constant c varies from 8.8 to 10.3, which is lower compared to the exponent of 13

in (eq. 4-20). The reason is that pressure drops of old fashioned and ceramic

packings were studied in the work of Billet [Billet and Schultes (1999)]. These

contribute to higher exponents than new random and structured packings. In the

case, that the packing size is large and porosity is high, the exponents are generally

lower.

As it is seen in Figure 4-23, the exponent for the prediction of the liquid holdup

above the loading point was studied. It is seen that the exponent n strongly depends

on packing types: The liquid holdup of Pallring (25 mm, metal) at the liquid flow

rates of 10, 20, 30 and 40 m3/m2/h can be well fitted with the exponent from 10 to

13 (Exponent n = 13 is suggested by Billet in his work).

However, above the loading point of the structured packing type B, the holdup only

can be well fitted with an exponent between 3 and 4. The reason of this differences


90

in the exponent is that the structured packings, which have much lower pressure

drops and irregular liquid holdups, have different loading and flooding points.

These results indicate that for the characterization of packings, especially newer

type packings, experimental measurements are still necessary.

Figure 4-23: Liquid holdup above the loading point for Pallring and structured packing type B

4.2.1.3 Mass transfer of structured and random packing

As discussed previously in chapter 4.1.4.2, the mass transfer parameters of

structured and random packings were evaluated using the Billet model for carbon

dioxide desorption and ammonia absorption measurements. For the carbon

dioxide desorption measurements, the liquid phase (deionized water) was

previously saturated with carbon dioxide in a depot vessel. Within the packed

column, the dissolved carbon dioxide was stripped out of the liquid phase by the

counter-current gas flow (air). The gas phase inlet and outlet concentration was

measured on-line. The carbon dioxide concentration in the liquid phase at the inlet

and outlet was measured by sampling and off-line analysis (The liquid phase

sample is added to a caustic sodium hydroxide solution to bind the carbon dioxide

as carbonate. Barium chloride is added to precipitate the carbonate. The precipitate

was filtered out of the solution and the amount of carbonate was indirectly

determined by neutralization of the non-reacted sodium hydroxide within the


91

solution). Similar to the desorption of carbon dioxide, for the ammonia absorption

measurements, ammonia was mixed with air at the gas phase inlet. The

concentration of ammonia at gas in and outlet was measured on-line. The liquid

phase (pure deionized water) flowed counter-current to the gas phase and

absorbed ammonia out of the gas. The absorbed ammonia in the liquid samples

was determined off-line by neutralization (PH-value neutralization method).

As already shown in Figure 4-3 and Figure 4-4, mass transfer rates between the gas

and liquid phase can be determined by carbon dioxide desorption and ammonia

absorption. It should be noted that the mass balances of the measurements should

always be checked to guarantee satisfactory measurement accuracy. The

separation efficiency was determined by the HTU-NTU method using (eq. 4-39) to

(eq. 4-46) and (eq. 4-50). Moreover, mass transfer coefficients (calculated with (eq.

4-52) and ((eq. 4-53)) can be obtained for known interfacial areas (as suggested by

Billet using (eq. 4-49)). The necessary parameters in (eq. 4-47) can be determined

for known Reynolds numbers, Schmidt numbers and Sherwood numbers.

The mass transfer process in a random packed column with Pallrings (ϕ = 25 mm,

a = 225 m2/m3, ϵ = 0.95, metal) was studied. As seen in Figure 4-24, measurements

from Billet [Billet et al. (1987)] were validated under same conditions in the same

apparatus with the same packing type. Liquid and gas samples were taken at the

bottom and the top of the packed column. The experimentally determined

volumetric mass transfer coefficients were in agreement with the one measured by

Billet [Billet et al. (1987)].

Table 4-9: Constants of Pallrings using Billet method

uL [m³/m²/h]

𝐹𝑉

[Pa0.5]

CP [-]

Ch [-]

CS [-]

CFl [-]

0 0.433 0.712 - - - 0 0.815 0.722 - - - 0 1.387 0.727 - - - 0 2.136 0.748 - - - 0 2.389 0.763 - - - 0 2.815 0.764 - - - 0 3.128 0.780 - - -

10 0.432 0.865 0.990

10 1.055 0.901 0.935 10 1.517 0.899 0.960


92

10 2.087 0.985 0.931 2.706 2.005 10 2.384 1.003 1.230 10 2.570 1.035 1.313 10 2.807 1.047 1.877 20 0.424 0.868 0.762

2.812

2.061

20 1.048 0.874 0.844 20 1.511 0.955 0.811 20 1.856 0.980 0.843 20 2.109 0.963 1.189 20 2.387 1.092 1.415 20 2.461 1.354 2.146 30 0.432 0.906 0.747

2.862

2.080

30 1.059 0.958 0.688 30 1.346 0.948 0.761 30 1.488 1.031 0.761 30 1.842 1.123 0.965 30 2.026 1.145 0.965 30 2.258 1.430 1.730 40 0.454 0.987 0.659

2.906

2.094

40 0.861 0.996 0.641 40 1.365 0.948 0.750 40 1.608 1.132 0.760 40 1.800 1.197 0.834 40 1.972 1.409 1.121 40 2.122 1.702 1.643

Modifications of the mass transfer measurements were made using the devices

shown in Figure 4-24. Liquid and gas samples were taken from the inside of random

packings. The collection of liquid flowing at the column wall was intentionally

avoided.

The volumetric mass transfer coefficients for carbon dioxide desorption measured

within the packing were significantly higher than the one measured at the column

bottom. This indicates that the carbon dioxide concentration in liquid phase was

not homogenous over the column cross section. Especially inside the packings, the

mass transfer rate was much higher than that near the column wall.


93

Figure 4-24: Experimental measurements of volumetric mass transfer coefficients for desorption of carbon dioxide

Mass transfer measurements using Pallrings (ϕ = 25 mm, a = 225 m2/m3, ϵ = 0.95,

metal) were carried out for a packed height of 0.75 m. For the carbon dioxide

desorption, the physical mass transfer resistance is a combined liquid and gas

phase one. Mass transfer resistance in the ammonia absorption is only dependent

on the gas flow. First, the mass transfer resistance using the ammonia absorption

was calculated and the CV , obtained with the Billet method, was applied for the

carbon dioxide desorption. Thus, the mass transfer rate in the liquid phase was

determined. The results of the mass transfer measurements are listed in Table 4-10

and Table 4-11. It can be seen that the mass transfer efficiency for carbon dioxide

desorption (mass transfer coefficient βOL

⋅ ae) and ammonia absorption (mass

transfer coefficient βOV

⋅ ae) are generally higher (about 30 %) than the results

reported by Billet [Billet and Schultes (1999)].

These results indicate that the mass transfer efficiency inside the packing is higher

than the cross-sectional averaged mass transfer rates. The maldistribution of liquid

and gas phase (especially the maldistribution at the column wall) was found as the

main reason for the concentration differences along the column cross section.


94

Table 4-10: Experimental measurements of volumetric mass transfer coefficients for

carbon dioxide desorption at different gas and liquid flow rates

Table 4-11: Experimental measurements of volumetric mass transfer coefficients for ammonia absorption at different gas

and liquid flow rates

uL

[m³/m²/h]

FV

[Pa0.5]

CL [-]

HTUOL [-]

HETP [-]

βOL

∙ae

[E³∙1/s]

uL [m³/m²/h]

FV

[Pa0.5]

CL [-]

HTUOL [-]

HETP [-]

βOL

∙ae

[E³∙1/s]

10 0.456 1.740 0.245 1.251 11.338 10 0.404 0.536 0.171 0.472 2.175 10 1.021 1.747 0.244 1.441 11.349 10 1.003 0.520 0.258 0.522 3.588 10 1.450 1.799 0.239 1.489 11.586 10 1.420 0.482 0.318 0.573 4.113 10 1.860 1.957 0.222 1.432 12.512 10 1.731 0.491 0.346 0.579 4.596 10 2.575 1.966 0.223 1.510 12.450 10 2.033 0.533 0.359 0.562 5.195 20 0.713 2.301 0.223 1.087 24.894 20 0.498 0.443 0.157 0.504 2.899 20 0.981 2.175 0.235 1.219 23.609 20 0.988 0.507 0.184 0.479 4.905 20 1.336 2.306 0.223 1.221 24.914 20 1.381 0.472 0.226 0.524 5.602 20 1.677 2.257 0.228 1.299 24.341 20 1.794 0.503 0.244 0.518 6.706 20 2.372 2.391 0.216 1.304 25.664 20 2.050 0.536 0.250 0.507 7.473 30 0.458 1.833 0.310 1.264 26.946 30 0.526 0.434 0.136 0.476 3.552 30 1.015 2.039 0.278 1.345 29.959 30 0.981 0.497 0.153 0.452 5.851 30 1.506 2.063 0.275 1.460 30.271 30 1.508 0.553 0.170 0.443 8.109 30 1.777 2.037 0.279 1.499 29.887 30 1.826 0.562 0.185 0.450 8.998 30 2.008 2.882 0.196 1.076 42.474 30 2.107 0.561 0.198 0.461 9.669 40 0.488 1.965 0.320 1.222 34.852 40 0.472 0.528 0.097 0.372 4.482 40 0.856 1.984 0.317 1.376 35.226 40 0.869 0.606 0.109 0.358 7.303 40 1.356 1.901 0.331 1.584 33.725 40 1.327 0.662 0.120 0.361 10.055 40 1.605 1.967 0.319 1.582 34.891 40 1.545 0.643 0.132 0.378 10.651 40 1.699 2.272 0.268 1.350 41.612 40 1.668 0.667 0.136 0.376 11.173

4.2.2 Experimental investigation of phase distribution using a liquid

collector

Pressure drop and liquid holdup for Pallrings (ϕ = 25 mm, a = 225 m2/m3, ϵ= 0.95,

metal) were measured in packed columns with diameters of ϕ = 288 mm and ϕ =

440 mm. Figure 4-25 shows that the measured pressure drop in both packed

columns is very similar. However, the liquid holdup strongly differs at liquid flow

rates of 30 and 40 m3/m2/h.

These results indicate that the pressure drop is not dependent on the column

diameter at the measured liquid flow rates. Contrary to this, the liquid holdup is

significantly influenced by the column diameter. The reason is that the wall

fraction of a small packed column is higher than that of the larger packed column

and the liquid phase accumulates more easily on the wall of small columns than in

larger columns. Thus, the liquid holdup in small columns is lower. In other words,

maldistribution in smaller columns is much more serious than in larger columns.

It is therefore necessary to study the phase distribution, especially the wall effect,


95

in small columns. Following, the phase distribution in ϕ= 288 mm was studied.

Figure 4-25: Experimental measurements of hydrodynamic parameters

The liquid collector shown in Figure 4-26 was applied to measure the liquid flow at

the column wall. The inner diameter of the liquid collector had a smaller diameter

(∅ = 266 mm) than the column, so that the liquid at the column wall was separated

from the rest of the column. Flow rates of the wall liquid were measured at

different gas and liquid loads. The liquid fraction at the column wall in the packed

column, which was filled with Pallrings (25 mm, metal, packed height 2 m), was

measured using the liquid collector. The results are shown in Figure 4-27. It was

seen that at small gas load factors up to 1 Pa0.5 the liquid fraction was relatively

independent on the gas load for all studied liquid flow rates from 5 to 30 m3/m2/h.

Firstly, with an increase of the gas load, the liquid fraction was strongly reduced.

The reason for that was that the gas phase flowing upwards pressed the liquid away

from the inlet range of the liquid collectors. With further increase of the gas load

factor, the liquid fraction on the column wall was strongly increased.

The mass transfer rates of the liquid flowing on the wall were studied using the

liquid collector with ammonia absorption. Air phase with NH3 was blown in from

the bottom of the packed column while liquid phase was distributed by the liquid

distributor from the top of the column. Ammonia concentrations at the gas phase

inlet and outlet were measured.


96

Figure 4-26: On-wall liquid collector Figure 4-27: Liquid fraction at the column wall for Pallrings (25 mm, metal) in a packed column (𝜙 =

288 mm) measured with a liquid collector.

NH3 concentration in liquid phase was determined by titration for both, the liquid

that was collected using the liquid collector and the one at the bottom of the packed

column (bulk liquid phase). The ammonia concentration of the on-wall liquid flow

and bulk-phase liquid is illustrated in Figure 4-28.

Measurements 1 to 5 were measured at a liquid flow rate uL of 30 m3/m2/h and gas

loads ug below the flooding point. It is seen that ammonia concentration of the on-

wall liquid phase was much lower than that of the bulk liquid. The ammonia

concentration of the on-wall liquid phase was 3 mol/m3. The ammonia

concentration in the bulk liquid was about 21 mol/m3. These results indicate that

the liquid flowing on the column wall did not effectively participate in the

absorption process.


97

Figure 4-28: Study of mass transfer of on-wall liquid using NH3 Absorption

The pressure drop (with gas flow) was further studied with and without the liquid

collector to determine its influence on the accuracy of the measurements. As shown

in Figure 4-29, the depicted lines denote the measurements without liquid collector

while the solid lines denote for the measurements with liquid collector. Higher

pressure drops (about 15 % higher) were generally measured with the liquid

collector at liquid flow rates from 5 to 30 m3/m2/h. This shows that the influence of

liquid collectors on hydrodynamic measurements is considerable.

Figure 4-29: Comparison of pressure drop of Pallrings (25 mm), metal in a packed column (∅ = 288 mm) with and without liquid collector


98

The experimental results in this chapter have shown that a large amount of liquid

flow was measured on the column wall for a randomly packed column. Hence, this

area cannot sufficiently utilize the large contact area created by packings resulting

in strongly reduced mass transfer efficiencies. Although the liquid collector can be

applied for the measurements of liquid fractions which flows on the column wall

and the mass transfer rates of the effective wall and bulk liquid, it cannot supply

more information about the phase distribution inside the column bulk. Moreover,

this method is intrusive and its influence on the accuracy of the process parameter

is relatively large.

4.2.3 Experimental measurements using WMS

4.2.3.1 Experimental measurements of phase distribution in random packed

column

Depending on the position of the WMS in the packed column, the phase distribution

(with and without gas phase) was measured with the WMS at different packed

heights.

Figure 4-30: Comparison of liquid holdup measured with conventional method

and the WMS

The liquid holdup measured with the valve-closing method and the WMS was


99

studied for the Pallring (∅ = 25 mm, a = 225 m2/m3, ϵ = 0.95, metal). The results are

shown in Figure 4-30 for liquid flow rates of 10, 20 and 30 m3/m2/h with counter

current gas flow. The column cross sectional averaged liquid holdup measured by

WMS (circle symbols) was comparable with the liquid holdup (depicted lines)

measured with the valve-closing method. These results indicate that the WMS can

be well used for the determination of the holdup in packed columns.

Phase distribution without gas phase using Pallrings (25 mm, metal) was

experimentally measured and studied with the WMS. The Liquid phase was

distributed from a single point source in the middle of packed column.

The liquid phase distribution at a liquid flow rates of 20 m3/m2/h and packed

heights of 10, 20, 30, 40 and 50 cm is shown in Figure 4-31.

Figure 4-31: Liquid phase distribution in cross-section of packed column at packing height from

10 cm to 50 cm, liquid load factor is 20 m³/m²/h

Liquid phase distribution at different liquid flow rates of 5, 10, 15 and

column diameter[m]

colu

mn

hei

gh

t [c

m]

column diameter[m]


100

20 m3/m2/h and packed heights of 10, 20, 30, 40 and 50 cm is shown in Figure 4-32.

It was observed that the maldistribution factor 𝑀𝑓 varied from 0.79 to 0.98 for all

experimental conditions.

(4.32.1) uL = 5 [m³/m²/h],

H = 10 [cm], Mf = 0.98 (4.32.2) uL = 10 [m³/m²/h],

H = 10 [cm], Mf = 0.93 (4.32.3) uL = 15 [m³/m²/h],

H = 10 [cm], Mf = 0.83 (4.32.4) uL=20 [m³/m²/h],

H = 10 [cm], Mf = 0.80

(4.32.5) uL = 5 [m³/m²/h],

H = 20 [cm], Mf = 0.90 (4.32.6) uL = 10 [m³/m²/h],

H = 20 [cm], Mf = 0.89 (4.32.7) uL = 15 [m³/m²/h],

H = 20 [cm], Mf = 0.87 (4.32.8) uL =20 [m³/m²/h],

H = 20 [cm], Mf = 0.85

(4.32.9) uL = 5 [m³/m²/h],

H = 30 [cm], Mf = 0.88 (4.32.10) uL = 10 [m³/m²/h], H =

30 [cm], Mf = 0.86 (4.32.11) uL = 15 [m³/m²/h],

H = 30 [cm], Mf = 0.85 (4.32.12) uL =20 [m³/m²/h],

H = 30 [cm], Mf = 0.84

(4.32.13) uL = 5 [m³/m²/h],

H = 40 [cm], Mf = 0.87 (4.32.14) uL = 10 [m³/m²/h],

H = 40 [cm], Mf = 0.85 (4.32.15) uL = 15 [m³/m²/h],

H = 40 [cm], Mf = 0.83 (4.32.16) uL =20 [m³/m²/h],

H = 40 [cm], Mf = 0.81

(4.32.17) uL = 5 [m³/m²/h],

H = 50 [cm], Mf = 0.86 (4.32.18) uL = 10 [m³/m²/h],

H = 50 [cm], Mf = 0.85 (4.32.19) uL = 15 [m³/m²/h],

H = 50 [cm], Mf = 0.84 (4.32.20) uL =20 [m³/m²/h],

H = 50 [cm], Mf = 0.82

Figure 4-32: Liquid phase distribution in cross-section of packed column at packing height from 10 cm to 50 cm, liquid load factor varies from 5, 10, 15 to 20 m³/m²/h (Black denotes for liquid

phase in cross-section of packed column)


101

At a liquid flow rate of 5 m3/m2/h, higher maldistribution factors were determined

for each packed. This is due to the fact that the maldistribution factor was

calculated across the column cross section and the liquid phase mainly

accumulated in the center of the column. The maldistribution factors Mf at a

packed height of 10 cm (Figure 4-32 (4.32.1) to Figure 4-32 (4.32.4)) show relatively

large variances.

The reason is that liquid distribution at the entrance length of the packed column

is strongly influenced by the initial liquid distribution. It was observed that during

the measurements, most of the liquid phase was still flowing as rivulets. With an

increase of the liquid load up to 20 m3/m2/h the maldistribution was slightly

reduced for each studied packed height. These results indicate that the liquid phase

distribution can be slightly influenced by the liquid flow rates for each packed

height. The suggested equations by Cihla who used the diffusion equation to

describe the phase distribution has no dependency of the liquid load. It was

assumed that the liquid load did not influence the phase distribution. However, in

this work was experimentally confirmed that the liquid phase distribution across

the column cross section was slightly influenced by the liquid load. Furthermore, it

was observed that the maldistribution factor Mf at each studied packed height

(from 20 cm to 50 cm) slightly decreases with an increase of packed height. The

phase distribution measured by Mf was almost constant at packed heights of

40 cm and 50 cm and a further increase of the packed height has almost no

influence on the phase distribution.

The liquid holdup in the radial direction (values were averaged over 10 seconds) is

shown in Figure 4-33 for packed heights of 10 cm and 20 cm. Blue marks were

measurements at 5 m3/m2/h (fitted by the blue line), red marks were measurements

at 10 m3/m2/h (fitted by the black line) and black marks were measurements at

15 m3/m2/h (fitted by the red line). For the measurements using Pallrings (without

gas phase), it can be seen that the liquid distributed in the radial range of 6 cm for

all studied cases (different packed heights and liquid loads).

The countercurrent gas flow, can strongly influence the distribution. Therefore, the

packed height of 10 cm was used to study the gas phase influence on the liquid


102

phase distribution at the inlet section of the packing.

Figure 4-33: Liquid phase distribution in radial direction (axis of abscissae 0 is column center) with liquid load factors of 5, 10 and 15 m³/m²/h at packed heights of 10, 20 cm

(Pallring 25 mm, metal)

As shown in Figure 4-34, the phase distribution below the 10 cm Pallring (∅ =

25 mm, metal) layer was measured using the WMS for a liquid load of 10 m3/m2/h,

different gas loads and with a point-source inlet liquid distributor.

(4.34.1) FV = 0 [m³/m²/h], Mf = 0.93 (4.34.2) FV = 1.95 [m³/m²/h], Mf =

0.61

(4.34.3) FV =2.75 [m³/m²/h], Mf =

0.51

(4.34.4) FV = 3.04 [m³/m²/h], Mf =

0.65

Figure 4-34: Liquid phase distribution in cross-section of packed column at a packed height of 10 cm

https://dict.leo.org/englisch-deutsch/axis

https://dict.leo.org/englisch-deutsch/of

https://dict.leo.org/englisch-deutsch/abscissae


103

The phase distribution without countercurrent gas flow (Figure 4-34 (4.34.1)) has a

very high maldistribution factor of Mf = 0.93. In contrast, the phase distribution at

a gas load factor of Fv = 1.95 Pa0,5 was strongly influenced by the gas phase,

whereby the maldistribution factor was reduced to 0.61 (Figure 4-34 (4.34.2)).

Further increase of the gas load to Fv = 2.75 Pa0,5 leaded to better radial

distribution and the maldistribution factor was further reduced to 0.51 (Figure 4-34

(4.34.3)). The liquid phase distribution was almost distributed across whole column

cross section. A further increase of the gas load leads to strong wall flow (Figure

4-34 (4.34.4)) and Mf strongly increased from 0.51 to 0.65. It can be seen that

maldistribution was reduced by the gas flow from small to middle high gas loads.

At higher gas loads, strong maldistribution was observed: The liquid mainly flows

on the column wall instead of in the bulk of the column. This shows that the gas

phase can significantly influence the liquid phase distribution.

The phase distribution of a single point liquid inlet distributer was studied

previously. It was seen that the pecked height, the gas load and the liquid flow rates

can influence the phase distribution.

Figure 4-35 shows the measurements of the liquid phase distribution at a packed

height of 75 cm for different liquid flow rates and gas loads using a liquid

distributor. It is seen from Figure 4-35 (4.35.1) to Figure 4-35 (4.35.7) that at small

liquid loads (uL = 4 m3/m2/h) the phase distribution was only slightly influenced by

the gas phase for low gas loads (Figure 4-35 (4.35.1) to Figure 4-35 (4.35.4)).

uL = 4 m³/m²/h uL = 10 m³/m²/h uL = 20 m³/m²/h

(4.35.1) uL= 4 [m³/m²/h], FV = 0 [Pa0.5], Mf = 0.89

(4.35.8) uL= 10 [m³/m²/h], FV = 0 [Pa0.5], Mf = 0.87

(4.35.15) uL= 4 [m³/m²/h], FV = 0 [Pa0.5], Mf = 0.83

(4.35.2) uL= 4 [m³/m²/h], (4.35.9) uL= 10 [m³/m²/h], (4.35.16) uL= 4 [m³/m²/h],


104

FV = 1.11 [Pa0.5], Mf = 0.88 FV = 1.11 [Pa0.5], Mf = 0.86 FV = 1.11 [Pa0.5], Mf = 0.83

(4.35.3) uL= 4 [m³/m²/h],

FV = 1.41 [Pa0.5], Mf = 0.87 (4.35.10) uL= 10 [m³/m²/h], FV = 1.41 [Pa0.5], Mf = 0.85

(4.35.17) uL=20 [m³/m²/h], FV = 1.41 [Pa0.5], Mf = 0.83

(4.35.4) uL= 4 [m³/m²/h],


(4.35.18) uL= 20 [m³/m²/h], FV = 2.0 [Pa0.5], Mf = 0.81

(4.35.5) uL= 4 [m³/m²/h],


(4.35.19) uL= 20 [m³/m²/h], FV = 2.84 [Pa0.5], Mf = 0.77

(4.35.6) uL= 4 [m³/m²/h],


(4.35.20) uL= 20 [m³/m²/h], FV = 3.40 [Pa0.5], Mf = 0.73

(4.35.7) uL= 4 [m³/m²/h],

FV = 3.80 [Pa0.5], Mf = 0.77

(4.35.14) uL= 10 [m³/m²/h], FV = 3.80 [Pa0.5], Mf = 0.69

(4.35.21) uL= 20 [m³/m²/h], FV = 3.80 [Pa0.5], Mf = 0.71

Figure 4-35: Liquid phase distribution in cross-section of packed column with

liquid distributor at different liquid flow rates

With an increase of the gas load (Figure 4-35 (4.35.5) to Figure 4-35 (4.35.7)), the

liquid phase strongly accumulated at the column wall. Similar effects were seen for


105

the liquid load of uL = 10 m3/m2/h (see Figure 4-35 (4.35.8) to Figure 4-35 (4.35.14))

and 20 m3/m2/h (see Figure 4-35 (4.35.9) to (4.35.27)). Although at higher liquid

loads the liquid phase distributed more uniformly across the whole cross section,

the liquid flowed preferably near the column wall. Thus, it can be concluded that

the liquid phase maldistribution in the random packing is relatively high and the

gas phase can lead to strong accumulation of the liquid at the wall depending on

the gas as well as the liquid loads.

Figure 4-36 illustrates the dynamic phase distribution of Pallrings across the

column cross section measured by the WMS. The liquid flow on the column wall

was present mainly as film flow, which was stable over time. Within the column

bulk, most of the observed liquid was identified as droplets. The liquid flowing on

the column wall is not effective for mass transfer which was experimentally

determined and discussed during the mass transfer measurements.

Thus, it can be concluded that the separation efficiency in random packed columns

is strongly influenced by the liquid maldistribution on the column wall which itself

is strongly influenced by the gas load. Although in the loading range of the packed

column, the turbulence of liquid phase can facilitate the mass transfer, the fraction

of the liquid phase on the column wall is high and its influence cannot be neglected

for random packings.

Figure 4-36: Dynamic phase distribution across the column cross section (green and red denote for liquid phase)


106

4.2.3.2 Experimental measurements of phase distribution in structured packed

column

Liquid phase distribution with a liquid distributor below one piece of structured

packing type A was studied with the WMS without gas flow. As shown in Figure

4-37, the phase distribution was uniform for all studied liquid flow rates. Almost no

liquid flow on the column wall was observed. The liquid phase distribution in the

structured packing was merely influenced by the liquid flow rates.

The phase distribution in the presence of gas flow was studied as well. The results

are shown in Figure 4-38. Liquid flow rates varied from 5 over 10, 20, 30 to

40 m3/m2/h. It was observed that phase distribution was more uniform across the

column cross section for higher gas and liquid loads. The maldistribution factors

Mf which varies from 0.94 (uL = m3/m2/h) to 0.78 (uL = 40 m3/m2/h) are however

larger than that of the studied Pallrings, although the liquid phase distribution over

the cross section was more uniform. In the case random packings, the liquid phase

below the packed bed mainly exists in the form of droplets.

(4.39.1)

uL = 5 m3/m2/h Mf = 0.94

(4.39.2) uL =

10 m3/m2/h Mf = 0.91

(4.39.3) uL =

20 m3/m2/h Mf = 0.87

(4.39.4) uL =

30 m3/m2/h Mf = 0.82

(4.39.5) uL =

40 m3/m2/h Mf = 0.78

Figure 4-37: Phase distribution using one piece of structured packing without gas phase

Gas loads Fv = 0.9 Pa0.5, Fv = 1.56 Pa0.5, Fv = 2.86 Pa0.5, Fv = 3.26 Pa0.5 and Fv =

3.9 Pa0.5 were experimentally studied at the liquid flow rates uL = 5 m3/m2/h (Figure

4-38 (4.38.1) to Figure 4-38 (4.38.5)), 10 m3/m2/h (Figure 4-38 (4.38.6) to Figure 4-38

(4.38.10)), 20 m3/m2/h (Figure 4-38(4.38.11) to Figure 4-38 (4.38.15)), 30 m3/m2/h

((Figure 4-38 (4.38.16) to Figure 4-38 (4.38.20)) and 40 m3/m2/h ((Figure 4-38

(4.38.21) to Figure 4-38 (4.38.25)).

At a constant liquid flow rate, the smallest maldistribution factors were at high gas


107

loads (e.g. Fv = 3.26 Pa0.5or Fv = 3.9 Pa0.5). The liquid phase distribution at lower gas

flow rates showed better distribution patterns than that of Pallrings (25 mm,

metal). Moreover, there was measured almost no large-scale maldistribution. The

reason is that the influence of gas flow on the liquid flow is limited by the structure

of the packings. The free volume between the structured packing and the column

wall was much smaller than for the random packings. Thus, based on these

experimental results it can be concluded that large scale maldistribution mainly

occurs in randomly packed columns.

4.3 Simulation and Modeling of phase distribution

In order to predict the hydrodynamics and mass transfer processes in packed

columns more accurately, numerous attempts have been applied to model both

these processes. Among these models, two main categories can be summarized: the

volume-averaged methods (e.g. Billet method) and geometry-based methods (e.g.

CFD methods). Both methods have its drawbacks: the local phase distribution,

especially maldistribution is not considered in the volume-averaged models and

the phase distribution in random packed columns is difficult to simulate using CFD

for the whole column due to the computational effort.

uL = 5 [m3/m2/h]

uL = 10 [m3/m2/h]

uL = 20 [m3/m2/h]

uL = 30 [m3/m2/h]

uL = 40 [m3/m2/h]

Fv = 0.90 [Pa0.5],

Mf = 0.94 Fv = 0.90 [Pa0.5],

Mf = 0.85 Fv = 0.90 [Pa0.5],

Mf = 0.78 Fv = 0.90 [Pa0.5],

Mf = 0.81 Fv = 0.90 [Pa0.5],

Mf = 0.77

Fv = 1.56 [Pa0.5],

Mf = 0.94 Fv = 1.56 [Pa0.5],

Mf = 0.89 Fv = 1.56 [Pa0.5],

Mf = 0.78 Fv = 1.56 [Pa0.5],

Mf = 0.80 Fv = 1.56 [Pa0.5],

Mf = 0.68


108

Fv = 2.86 [Pa0.5],

Mf = 0.85 Fv = 2.86 [Pa0.5],

Mf = 0.75 Fv = 2.86 [Pa0.5],

Mf = 0.69 Fv = 2.86 [Pa0.5],

Mf = 0.67 Fv = 2.86 [Pa0.5],

Mf = 0.63

Fv = 3.26 [Pa0.5],

Mf = 0.83 Fv = 3.26 [Pa0.5],

Mf = 0.75 Fv = 3.26 [Pa0.5],

Mf = 0.69 Fv = 3.26 [Pa0.5],

Mf = 0.67 Fv = 3.26 [Pa0.5],

Mf = 0.64

Fv = 3.9 [Pa0.5],

Mf = 0.85 Fv = 3.90 [Pa0.5],

Mf = 0.78 Fv = 3.90 [Pa0.5],

Mf = 0.71 Fv = 3.90 [Pa0.5],

Mf = 0.65 Fv = 3.90 [Pa0.5],

Mf = 0.61 Figure 4-38: Phase distribution in structured packing type A with gas flow

Therefore, compromised methods have attracted more and more attention in

recent years. The packed column can be divided into several cells. The phase

distribution is described by different types of cells. The background of cell models

was reviewed and discussed in chapter 4.2. A two-dimensional cell model was

developed within this work. The model is focused on the description of the liquid

phase. In the model, the influence of parameters on liquid distribution was

considered, e.g. packing size and material, liquid loads, splitting factors, column

radius, packed height, liquid holdup, liquid initial distribution and cell numbers in

vertical and horizontal direction to name just a few. The packed column is divided

into several parallel layers containing interconnected cells with equal size in radial

and axial directions. Five main cell types are developed depending on the cell

position. They differ in liquid flow direction and number of inlets and outlets

streams. For cells with multiple inlets and outlets, a splitting factor is introduced to

redistribute the outlet streams to the neighbored cells. Each cell is considered as a

ideally mixed vessel. Furthermore, a weighting factor is used to describe outlet

volume streams in dependence of the splitting factor.


109

4.3.1 Cell model

The packed column was divided into parallel layers and each layer contained a

certain number of interconnected cells (see Figure 4-39).

Figure 4-39: Two-dimensional symmetric cell model

Since the phase distribution in cylindrical coordinate depends on the column

radius 𝑟 and the packed height Z, the model was simplified as a symmetrical two-

dimensional model in Cartesian coordinates.

The connections of the cells for a M×N model are illustrated in Figure 4-40.

Figure 4-40: Two-dimensional symmetric cell model with liquid inlet and outlet steams


110

For each cell, the first number represents the row and the second number

represents the column of the matrix. The cells are divided into following types:

Single inlet &single outlet, e.g. Cell(1,1)

Double inlet &single outlet, e.g. Cell(2,1)

Double inlet &triple outlet, e.g. Cell(2,2)

Single inlet &triple outlet, e.g. Cell(1,2)

Triple inlet &triple outlet, e.g. Cell(2,3)

It is assumed that the liquid phase inlet streams VL of each cell in the first row are

equal (homogeneous initial distribution). A small fraction of the liquid phase is kept

within the cells (defined as liquid holdup), while the rest of the liquid phase flows

downward into the cells of the next layer. Similar to Stikkelman’s and Higler’s

approaches, a splitting mechanism is applied to describe the distribution of the

liquid phase out of the cells. The liquid phase on the column wall is assumed not to

be reflected back into the bulk of the column. The liquid phase flows downwards

through the cells. The fraction of the liquid phase exiting a cell and flowing into the

cell of the next row but the same column is described with the splitting factor kL.

The rest of the exiting liquid phase from a cell is calculated with the splitting factor

(1-kL). As example, if the liquid phase is split into two streams flowing into two

different cells, both streams are calculated as the fraction 0.5⋅(1-kL) of the total

exiting liquid. In each cell, the liquid phase outlet streams are dependent on the

liquid phase inlet streams directions. Thus, a weighting factor β(i) is defined, which

represents the dependency of the outlet streams on the inlet stream directions.

As shown in Figure 4-41, parts of the liquid phase outlet streams of cell(i-1,j-1),

cell(i-1,j) and cell(i-1,j+1) are the inlet streams of cell(i,j). The liquid phase outlet

streams of cell(i,j) are divided to cell(i+1,j-1), cell(i+1,j) and cell(i+1,j+1). The fraction

of the liquid phase inlet streams into cell(i,j) is weighted using the weighting

factorβ(i). β(i) is further applied to describe the outlet streams out of cell(i,j), that

are the inlet streams of cell(i+1,j-1), cell(i+1,j) and cell(i+1,j+1).


111

Figure 4-41: Cell type inside packings

The weighting factor β(i) is calculated using (eq. 4-66), (eq. 4-67) and (eq. 4-68).

β1 =

V.

c(i-1,j),out1

V.

c(i,j),in

⋅kL

V.

c(i-1,j-1),out2

V.

c(i,j),in

⋅0.5(1-kL)+V.

c(i-1,j),out1

V.

c(i,j),in

⋅kL+V.

c(i-1,j+1),out3

V.

c(i,j),in

⋅0.5(1-kL)

(eq. 4-66)

β2 =

V.

c(i-1,j-1),out2

V.

c(i,j),in

⋅0.5(1-kL)

V.

c(i-1,j-1),out2

V.

c(i,j),in

⋅0.5(1-kL)+V.

c(i-1,j),out1

V.

c(i,j),in

⋅kL+V.

c(i-1,j+1),out3

V.

c(i,j),in

⋅0.5(1-kL)

(eq. 4-67)

β 3

=

V.

c(i-1,j+1),out3

V.

c(i,j),in

⋅0.5(1-kL)

V.

c(i-1,j-1),out2

V.

c(i,j),in

⋅0.5(1-kL)+V.

c(i-1,j),out1

V.

c(i,j),in

⋅kL+V.

c(i-1,j+1),out3

V.

c(i,j),in

⋅0.5(1-kL)

(eq. 4-68)

whereby β1is the weighting factor into the vertical cell of the next layer and β

2 and

β3 are the weighting factors of the left and right neighbored cells to central cell of

the next layer, respectively. The liquid phase inlet stream V.

c(i,j),in of cell(i,j) is the

sum of the liquid phase outlet streams of cell(i+1,j-1), cell(i+1,j) and cell(i+1,j+1):

V.

c(i,j),in = V.

c(i-1,j-1),out1+V.

c(i-1,j),out2+V.

c2(i-1,j+1),out3 (eq. 4-69)

The liquid phase inlets streams of cell(i+1,j-1), cell(i+1,j) and cell(i+1,j+1) depend on

the splitting factors β(i) of cell(i,j) and are described as:


112

V.

c(i,j),out1 = β1

⋅V.

c(i,j),in (eq. 4-70)

V.

c(i,j),out2=β2

⋅V.

c(i,j),in (eq. 4-71)

V.

c(i,j),out3=β3

⋅V.

c(i,j),in (eq. 4-72)

Depending on the cell position in the packed columns, various cell types are applied

in the cell model. On the first layer two types of cells are used: The first and the last

cell on the first layer are the same cell type (cells assumed as lying on the column

wall) and shown in Figure 4-42 a). The cell on the first layer, cell(1,1) and cell(1,N),

contains a single input stream and a single outlet stream. Cells between the first

and the last cell have a single inlet stream and three outlet streams (shown in

Figure 4-42 b).

a) Cells at the column wall in the first layer

b) Bulk cells in the first layer

Figure 4-42: Cell types for the initial liquid phase inlet layer

Beginning from the second layer, there are three types of cells:

1) The cells(i,1) (i ≥ 2) (cells on the column wall) receives two inlet streams from

above cells outlet flows, which are from cell(i-1,1) and cell(i-1,2), while

cell(i,N) (I ≥ 2) receives two inlet streams from above cells. Which areoutlet

flows from cell(i-1,N-1) and cell(i-1,N) (shown in Figure 4-43). The liquid

phase outlet streams of cell(i,1) and cell(i,N) are inlet streams of cell(i+1,1)

and cell(i+1,N), respectively. No splitting factors were needed for this cell

type since the liquid phase on the column wall is assumed not to be reflected

back into the packing.


113

Figure 4-43: Cell type a) since second layer

2) The cell(i,2) (i ≥ 2) (shown in Figure 4-44) receives two inlet streams from

above cells, which are outlet flows from cell(i-1,2) and cell(i-1,3), while

cell(i,N-1) (i ≥ 2) receives two inlet streams from above cells, which areoutlet

flows from cell(i-1,N-2) and cell(i-1,N-1). The liquid phase outlet streams of

cell(i,1)/cell(i,N) are inlet streams of cell(i+1,1), cell(i+1,2) and

cell(i+1,3)/cell(i+1,N-2), cell(i+1,N-1) and cell(i+1,N), respectively.

Figure 4-44: Cell type b) since second layer

The splitting factors β(i) for the outlet streams of cell(i,2) (i ≥ 2) are defined as:


114

β1=

V.

c(i-1,2),out1

V.

c(i,2),in

⋅kL

V.

c(i-1,1),out3

V.

c(i,2),in

⋅(1-kL)+V.

c(i-1,2),out1

V.

c(i,2),in

⋅kL

(eq. 4-73)

β2=

V.

c(i-1,2),out1

V.

c(i,2),in

⋅(1-γ)(1-kL)

V.

c(i-1,2),out3

V.

c(i,1),in

⋅(1-kL)+V.

c(i-1,2),out1

V.

c(i,2),in

⋅kL

(eq. 4-74)

β3=

V.

c(i-1,1),out3

V.

c(i,2),in

⋅γ(1-kL)

V.

c(i-1,1),out3

V.

c(i,2),in

⋅(1-kL)+V.

c(i-1,2),out1

V.

c(i,2),in

⋅kL

(eq. 4-75)

The factor γ is defined to describe the outlet streams of cell(i,2). Therefore, γ is

adjusted and fitted depending on the packing characteristics. The liquid phase

outlet streams of cell(i,2) are described by using the splitting factors β(i) for (eq.

4-76) to (eq. 4-79).

V.

c(i,2),in=V.

c(i-1,2),out1+V.

c(i-1,1),out3 (eq. 4-76)

V.

c(i,2),out1=β1

⋅x⋅V.

c(i,2),in (eq. 4-77)

V.

c(i,2),out2=β2

⋅x⋅V.

c(i,2),in (eq. 4-78)

V.

c(i,2),out3=β3

⋅x⋅V.

c(i,2),in (eq. 4-79)

Similar to cell(i,2) (i ≥ 2), the splitting factors β(i) for the outlet streams of cell(i,N-2)

((i ≥2) are defined as following:

β1=

V.

c(i-1,N-1),out1

V.

c(i,N-1),in

⋅kL

V.

c(i-1,N-2),out3

V.

c(i,N-1),in

⋅(1-kL)+V.

c(i-1,N-1),out1

V.

c(i,N-1),in

⋅kL

(eq. 4-80)

𝛽2 =

𝑉.

𝑐(𝑖−1,𝑁−1),𝑜𝑢𝑡1

𝑉.

𝑐(𝑖,𝑁−1),𝑖𝑛

⋅ (1 − 𝛾)(1 − 𝑘𝐿)

𝑉.


𝑉.


⋅ (1 − 𝑘𝐿) +𝑉.


𝑉.


⋅ 𝑘𝐿

(eq. 4-81)


115

β3=

V.

c(i-1,N-2),out3

V.

c(i,N-1),in

⋅γ(1-kL)

V.

c(i-1,N-2),out3

V.

c(i,N-1),in

⋅(1-kL)+V.

c(i-1,N-1),out1

V.

c(i,N-1),in

⋅kL

(eq. 4-82)

Whereby the factor γ is defined to weight the outlet streams of cell(i,N-1). The liquid

phase outlet streams of cell(i,N-1) are described using the splitting factors β(i) for

(eq. 4-83) to (eq. 4-86).

V.

c(i,N-1),in=V.

c(i-1,N-1),out1+V.

c(i-1,N-2),out3 (eq. 4-83)

V.

c(i,N-1),out1=β1

⋅x⋅V.

c(i,N-1),in (eq. 4-84)

V.

c(i,N-1),out2=β2

⋅x⋅V.

c(i,N-1),in (eq. 4-85)

V.

c(i,N-1),out3=β3

⋅x⋅V.

c(i,N-1),in (eq. 4-86)

3) The third cell type (with 3 inlet streams and 3 outlet streams) is shown in Figure

4-41 and the corresponding splitting factors β(i) were already described in (eq.

4-66) to (eq. 4-72). This cell type is used for the bulk cells which are not directly

influenced by the column wall.

Every cell illustrated in Figure 4-40 is assumed as an ideally stirred tank. Its

temporal change of the liquid holdup depends on the number of liquid inlets and

outlets streams in the consideration of the corresponding splitting factors.

Δholdup

Δtime = ∑(liquid inlet streams from upper layer) –

∑(liquid outlet streams to lower layer)

(eq. 4-87)

The outlet streams are dependent on the liquid holdup of each cell. After a short

unsteady simulation (δholdup/δt≠0), an equilibrium state is reached, whereby the

liquid cell holdups are not dependent on the simulation time anymore.

Liquid distribution is simulated with and without the weighting factors. In the case

of model without the weighting factors, the cells are assumed as well stirred tanks

and the outlet streams out of every cell are not dependent on the direction of the

inlet streams. The streams only depend on the defined splitting factors. In the

model with weighting factors the outlet streams of each cell are weighted according

to the amount and direction of the inlet streams. This means, if the amount of inlet


116

stream in one direction is much larger than the one in other directions, the outlet

streams in that direction are also larger. It should be noted that the weighting factor

should be determined based on experimental studies or fitted to experimental

measurements.

4.3.2 Simulation of phase distribution using cell model

The cell model described previously was simulated in MATLAB. The liquid

distribution was studied for a point source central inlet. Unsteady-state equations

(solved with ode45 function of MATLAB) were applied. The phase distribution is a

function of time and the temporal holdup was calculated in each cell. Steady state

was reached when the holdup was not dependent on time anymore. It was

observed that the steady-state in each cell can be obtained really quickly.

By parameter analysis of the phase distribution it was found that the cell number

in vertical and horizontal direction as well as the splitting factor most significantly

influenced the phase distribution. The packing height was not directly influencing

the phase distribution for the investigated cell numbers. Liquid flow rates and the

value of the liquid holdup did not influence the phase distribution.

As shown in Figure 4-45 and Figure 4-46, the random packed column (shown in

Figure 4-39) was divided into 10×10 and 18×18 cells, individually. The splitting

factor was varied from 0.1 to 0.4 with the same averaged liquid amount in each cell

assumed as 3 %.


117

a) splitting factor = 0.1 b) splitting factor = 0.2

c) splitting factor = 0.3 d) splitting factor = 0.4

Figure 4-45: Simulation results using cell model with 10×10 cells

Compared to the simulation with 18×18 cells, the 10×10 cell model denotes for large

packings. For the 10x10 simulation, it is seen in Figure 4-45 that for splitting factors

larger than 0.2 the liquid reaches the column wall.

For 18×18 cells, the liquid phase reaches the column wall for splitting factors larger

than 0.3. This means that larger packings lead the liquid more easily to the wall

than smaller packings.

a) splitting factor = 0.1 b) splitting factor = 0.2


118

c) splitting factor = 0.3 d) splitting factor = 0.4

Figure 4-46: Simulation results using cell model with 18×18 cells

In Figure 4-45 d) and Figure 4-46 d) it is shown that the liquid phase accumulates

on the column wall and its amount increases continuously with increasing packed

height. This assumption was realized in the cell model because it is based on the

experimental observations. The liquid phase on the column wall cannot be

redistributed back into the column bulk.

Next, the splitting factor was set as 0.3 for a 13×13 cell model. The liquid inlet was

assumed as centered and homogeneous. It is seen in Figure 4-47 that a significant

amount of the liquid fraction was observed on the column wall at homogeneous

liquid inlet conditions.

Other factors influencing the liquid phase distribution are either not significant

(e.g., local liquid amount held in the cells) or can be summarized in the liquid

splitting factor (gas phase upwards enlarged the liquid distribution, thus leading to

a larger splitting factor). The liquid flow rates is influencing the absolute liquid

holdup values but is not significantly influencing the liquid distribution.

Furthermore, the influence of cell number on liquid phase distribution was

studied. It was found that the cell number can influence the amount of liquid on

the column wall.

Splitting factors should be experimentally determined using the single point liquid


119

inlet source. The fitted splitting factor can then be used for a homogeneous liquid

inlet. It should be noted that in this model it was assumed that the splitting factor

was constant and independent of cell position. In reality, the splitting factor

strongly depends on the arrangement of the random packings.

Figure 4-47: Phase distribution for a splitting factor of 0.3 using a 13×13 cell model

4.4 Discussion

In this chapter the topic of packed columns was reviewed. Volume-averaged

models, e.g. the widely cited and used film model proposed by Billet was

experimental proved as an effective method to evaluate the hydrodynamic and

mass transfer parameters for random and structured packings. Advantages of this

method is that a large amount of experimental measurements were applied for

derivation of the equations. Especially, mass transfer processes were well

described by rate-based model. Based on the experimental measurements, some

limitations of the Billet method were found.

Moreover, the phase distribution in packed column was experimentally studied.

Phase distribution is an important factor which determines the efficiency of the

packed column. The phase distribution was experimentally studied using a

modified conventional method and the WMS method which has been discussed in

a previous chapter. The influence of the conventional method was experimentally


120

studied, and it was seen that the measuring method is very intrusive and can

strongly influence the results making the measurements less reliable. With the aid

of the capacitive WMS, the phase distribution was experimentally measured. A

large-scale liquid maldistribution, namely liquid wall flow was identified in

random packed columns.

Finally, the phase distribution, especially the liquid fraction of wall flow, was

described using the cell model. It was seen that some parameters, e.g. the splitting

factor, the cell number and the liquid exchange between cells have noticeable

influences on the phase distribution.

Nomenclature

121

5 Nomenclature

Character Unit Description g [m/s2] gravity acceleration vi [m/s] column radius a [m2/m³] specific area

aPh [m2/m³] interfacial area

ax, bx [-] constant in the permittivity model c [-] constant C1, C2, C3 [-] constants in the pressure drop model C𝐹𝑙 [-] constant of flooding point Ch [-] constant of liquid holdup C𝑆 [-] constant of loading point CP,0 [-] constants for the pressure drop calculation 𝑑𝑃 [mm] particle diameter/packing size dS [mm] packed column diameter Dv diffusion coefficient Dr [mm] distribution coefficient

f [-] function

FV [Pa0.5] gas load factor

g [m/s2] gravity hL [-] liquid holdup H [m] height HTU [m] height of a transfer unit kOL [-] overall mass transfer coefficient of the liquid side kOV [-] overall mass transfer coefficient of the gas side KL [-] splitting factor

KxH

, KxL [-] permittivity H: higher value; L: lower value

K [-] wall factor K1, K2, K3, K4 [-] Constant L [cm] length

�� [m3 h⁄ ] liquid flow rates mxy [-] slope

Mf [-] maldistribution factor

n [-] parameter NTU [-] number of transfer units r [mm] radius Pi [-] constant Δt [s] time interval T [-] time period u [m/s] velocity Vlog, x [volt] voltage

vb [cm/s] bubble rise velocity

z [mm] distance

�� [m3 h⁄ ] gas flow rates x [mol m³⁄ ] component concentration in the liquid phase X [mol mol⁄ ] mole fraction in the liquid phase y [mol m³⁄ ] component concentration in the gas phase Y [mol mol⁄ ] mole fraction in the gas phase

Nomenclature

122

Symbol

φ [mm] diameter

ψ [-] resistance coefficient

μ [-] packing type dependent factor

τ [s] residence time

𝜓𝑥𝑦 [-] function

ε [-] porosity

ρ [kg/m³] density

β1 , β

2 , β

3 [-] splitting factor in the cell model

v [m/s] velocity

σ [N/m] surface tension

ϵ [-] packing porosity

ξ [-] resistance coefficient

δ [mm] thickness

θ [°] angle

η [Pa/s] dynamic viscosity

λ0 [-] mass flow ratio of the gas-liquid phase

β [m³/m²/s] mass transfer coefficient

ML [g/mol] mole weight of the liquid phase

MV [g/mol] mole weight of the gas phase

Subscript

V gas/bubble

P pressure

L liquid

0 un-wetted

VL gas and liquid phase

S loading point

FL flooding point

Superscript

i integer

j integer

n stage number

Ph interfacial

Dimensionless number

Re [-] Reynolds number

We [-] Weber number

Fr [-] Froude number

Sc [-] Schmidt number

Sh [-] Sherwood number

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123

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