Gas-liquid solid foam reactors : hydrodynamics and mass ... · PDF fileGas-liquid Solid Foam Reactors: Hydrodynamics and Mass ... (trickle bed) and two high liquid holdup ... the gas-liquid

Gas-liquid solid foam reactors : hydrodynamics and masstransferStemmet, C.P.

DOI:10.6100/IR635735

Published: 01/01/2008

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Citation for published version (APA):Stemmet, C. P. (2008). Gas-liquid solid foam reactors : hydrodynamics and mass transfer Eindhoven:Technische Universiteit Eindhoven DOI: 10.6100/IR635735

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https://doi.org/10.6100/IR635735

https://research.tue.nl/en/publications/gasliquid-solid-foam-reactors--hydrodynamics-and-mass-transfer(07bb8a6a-0355-4e51-9d0d-fc94166a13e6).html

Gas-liquid Solid Foam Reactors:Hydrodynamics and Mass Transfer

PROEFSCHRIFT

ter verkrijging van de graad van doctor aan deTechnische Universiteit Eindhoven, op gezag van deRector Magnificus, prof.dr.ir. C.J. van Duijn, voor een

commissie aangewezen door het College voorPromoties in het openbaar te verdedigen opdonderdag 4 september 2008 om 16.00 uur

door

Charl Philip Stemmet

geboren te Durban, Zuid-Afrika

Dit proefschrift is goedgekeurd door de promotor:

prof.dr.ir. J.C. Schouten

Copromotoren:dr.ir. B.F.M. Kusterendr.ir. J. van der Schaaf

The work described in this thesis was financed by the Dutch Technology Foundation(STW). Financial support from ABB Lummus Global Inc., DSM Research B.V., BASFNederland B.V. (formally Engelhard De Meern B.V.), and Shell Global SolutionsInternational B.V. is gratefully acknowledged.

A catalogue record is available from the Library Eindhoven University of Technology

Gas-liquid Solid Foam Reactors: Hydrodynamics and Mass Transfer / by C.P. StemmetProefschrift.– ISBN 978-90-386-1326-0

Trefwoorden: chemische reactoren, gepakt bed, gestructuteerde pakking, fysischetransport verschijnselen, stoftransport, meerfase stroming, hydrodynamica, vloeistoffractie

Subject headings: Chemical reactors; packed beds; structured packing / physicaltransport phenomena; mass transfer / multiphase flow / hydrodynamics; liquid holdup

dedicated to my mother, my family, and my friends

Summary

Gas-liquid Solid Foam Reactors:

Hydrodynamics and Mass Transfer

In the field of reactor engineering the chemical industry continually strives for more ef-

ficient reactors and in doing so considers the use of more advanced packing materials to

optimize and intensify packed bed reactors to desired process conditions. Reactor pack-

ings which act as a support for the catalyst are either randomly placed in the reactor such

as the conventional dumped packings (spherical particles, Raschig rings, Berl saddels,

etc.) or structured to fill up the complete reactor volume such as structured packings

(Katapak-S, monoliths, etc.). In the advancement of these reactor packings the goal is to-

wards reducing the volume fraction of the reactor filled with solid thereby reducing the

frictional pressure drop, while maintaining high packing surface area to volume ratio’s

(specific area) to accommodate high rates of mass transfer towards the catalytic surface.

L

G

Packed

Bed

L G

Packed

Bed

L G

Packed

Bed

(a) (b) (c)

Figure 1: Schematic representation of the direction of the gas (G) and liquid (L) in a packed bedwith the gas and liquid flowing either counter-currently, (a), or co-currently up, (b), or co-currentlydown, (c).

This thesis deals with the hydrodynamics and gas-liquid mass transfer when the pack-

ing is changed from the conventional packed bed or structured packings to solid foam

vi Summary

packings which is an new structured packing considered for multiphase flow. These solid

foams have the advantage of a high surface area (for catalyst deposition and generation of

gas-liquid mass transfer area) and of a high voidage, which decreases the frictional pres-

sure drop and hence enhances the reactor efficiency. These foams are characterized by a

uniform cell size, and may be viewed as the inverse of a packed bed.

In the counter-current flow configuration a low liquid holdup regime (trickle bed) and

two high liquid holdup regimes (bubble and pulse) have been studied (Chapter 2) for 5,

20 and 40 ppi solid foam packings. The liquid holdup has been studied experimentally

and been modeled using the relative permeability model (Saez and Carbonell, 1985). This

model was originally used to describe the liquid holdup for different gas and liquid ve-

locities in conventional packings but also describes the liquid holdup in all three regimes

for solid foam packings. The total pressure drop has been obtained experimentally and

found to be much lower than packed beds of spherical particles. The flooding points have

been determined for counter-current flow and found to be similar to Katapak-S packings.

An estimate has been made for the gas-liquid mass transfer coefficient using penetration

theory and values of kLaGL in the order of 6 s−1 have been found.

The co-current flow configuration has been studied for 10 and 40 ppi solid foam pack-

ings (Chapter 3) and experimentally a bubble regime and a pulse regime (at gas velocities

higher than 0.3 m s−1) was observed. A high degree of axial dispersion was found to affect

the gas-liquid mass transfer, but in solid foams packings the axial dispersion is quite low,

and plug flow can be assumed. The gas-liquid mass transfer coefficient was found exper-

imentally to increase with increasing liquid and gas velocities, up to a maximum value of

1.3 s−1. An estimate of the intrinsic liquid-side mass transfer coefficient, kL, showed it to be

increasing only with increasing liquid velocity. Increasing the gas velocity increasing the

available gas-liquid area for mass transfer (by the decrease in liquid holdup). The value

of kL was found to decrease with increasing ppi number (smaller pores) of the solid foam

packing but the value of kLaGL remains constant (higher aGL for smaller pores). The gas-

liquid mass transfer coefficient is compared to monoliths and packed bed micro-reactors

in terms of a parameter known as the frictional energy dissipation, EL (= PfuLε−1

L ) and all

are found to correlate according to: kLaGLεL = 0.0134(EL)0.44.

The co-current downflow of gas-liquid flow was studied (Chapter 4) and the trickle

regime investigated. The gas-liquid mass transfer coefficient increased with increasing

liquid velocity and decreased with increasing ppi number (smaller pores) of the solid foam

packing. The value of the gas-liquid mass transfer coefficient for 10 ppi solid foam was

described by a correlation similar to Sherwood and Holloway (1940) for packed beds and

Raschig rings. The value of kL was estimated to be a factor 10 smaller than in the upflow

regime.

The liquid properties (the liquid viscosity, µL, and the liquid surface tension, σL) have

a large influence on the resulting hydrodynamics and gas-liquid mass transfer and are

studied in the co-current flow configurations (upflow and downflow) for gas-liquid flow

(Chapter 5). The gas-liquid mass transfer coefficient is correlated in the co-current flow

configuration to the gas and liquid velocities and liquid properties according to:

Upflow: kLaGL εLDL−1 = 311u0.44

G (uLρLµL−1)

0.92(ScL)0.5 [SI units, mL m−3

P ], and

Summary vii

Downflow: kLaGL εLDL−1 = 3.7 (uLρLµL

−1)1.16

(ScL)0.5 [SI units, mL m−3

P ],

where increases in the liquid viscosity, µL, are accounted for by the dimensionless Schmidt

number, ScL. In the co-current upflow configuration the gas-liquid mass transfer coeffi-

cient is correlated to a parameter describing the energy dissipation (the frictional pressure

drop) with increases in the liquid viscosity accounted for by the Schmidt number:

Upflow: kLaGL εL(ScL/ScWater)0.69 = 2.05 × 10−4 (Pf)

0.8 [SI units, m3L m−3

P s−1]

The decrease in the liquid surface tension (from 72 N m−1 to 56 N m−1 ) increases the

gas-liquid mass transfer coefficient by a factor of 6 studied in the co-current downflow

configuration.

Aluminum foam packings (93 % voidage) were used to study the hydrodynamics and

gas-liquid mass transfer but are not as chemically inert as carbon foam packings (97%

voidage). A comparison was made in the co-current upflow configuration to test the in-

fluence of the type of material (and the voidage of solid foam packings), Chapter 6. This

showed that there was no influence of the type of the material (nor the voidage) on the in-

trinsic mass transfer coefficient, kL. A difference however was found in the liquid holdup

and frictional pressure drop for the two different solid foam materials, resulting in slightly

lower mass transfer coefficients for the carbon foam packings. This difference could not be

described by differences in the hydrophobicity of the materials as the three phase contact

angle of the materials, a measure of a liquid to form droplets or spread evenly over the

solid, was found to be similar. The 10 ppi solid foam packing can be used as catalyst sup-

port for catalyst support for glucose oxidation over a palladium catalyst. The conversions

in a reactor packed with solid foam packing and with conventional spherical particles

have been compared. The reactors are all kinetically limited due to the low surface area

for catalyst deposition considering a non-porous support. The addition of a washcoat

layer (in the order of 1 µm thickness) increases the surface area for catalyst deposition and

hence mass transfer limited reactors may be obtained. In the co-current downflow (trickle

flow) the solid foam packings can achieve similar reaction rates than in a conventional

packed bed. This conversion is achieved at a factor ten lower frictional pressure drop and

hence factor ten lower energy dissipation. In the co-current upflow configuration the solid

foam packings can achieve half the rate of reaction as in a conventional packed bed oper-

ated in upflow, however, at a factor ten lower frictional pressure drop. This indicates that

solid foam packed beds operate more energy efficient than the conventional packed bed

of spherical particles. This is due to the high voidage of the solid foam packings.

List of Symbols

Roman Symbols

A constant in the viscous term of the Ergun equation -

aGL interfacial gas-liquid area per unit volume of liquid m2L m−3

L

aP packing surface area per unit volume m2P m−3

P

B constant in the inertial term of the Ergun equation -

BoL Liquid Bodenstein number, uLZ/(Dax,LεL) -

CG concentration in the gas phase mol m−3

G

CL concentration in the liquid phase mol m−3

L

de strut length m

DL diffusivity in the liquid, typically 1 · 10−9 m2L s−1

dm strut diameter mm

De effective diffusivity m3L m−1

S s−1

Dax,G axial dispersion coefficient in the gas phase m2P s−1

Dax,L axial dispersion coefficient in the liquid phase m2P s−1

EL energy dissipation per unit volume of reactor W m −3

P

Eo∗ modified Eotvos number, ρLgd2eε/σ (1 − ε)2 -

Fα interfacial force kg m−1 s−1

fα relative permeability -

Fr Froude number, (εαvα)2/(deg) -

g acceleration due to gravity m2 s−1

Gaα Galileo number, ρ2αgd3

eε3/(µ2

α(1 − ε)3 -

GaG Galileo number of the gas, ρ2

Ggd3eε

3/(µ2

L(1 − ε)3) -

GaL Galileo number of the liquid, ρ2

Lgd3eε

3/(µ2

L(1 − ε)3) -

x List of Symbols

H Henry coefficient m3L Pa mol−1

h1,2 constants in Equation 2.7 and Equation 5.2

kL liquid-side mass transfer coefficient mL s−1

kir intrinsic reaction rate coefficient in Equation 6.3 m3

L s−1 mol−1

Cat

Lt loading of catalyst on the solid molCat kg−1

S

M molar mass kg mol−1

m1,2 constants in Equation 5.15 -

N number of pores per inch (ppi) of the solid foam packing inch−1

n constant in Equation 4.1 -

n1,2 constants in Equation 5.7 -

Pf frictional pressure drop per unit height of packing Pa m−1

P

R universal gas constant, 8.314 m3 Pa K−1 mol−1

r reaction rate mol m−3

P s−1

Reα Reynolds number, ραεαvαde/(µα (1 − ε)) -

ReG Reynolds number of the gas, ρGuGde/(µG (1 − ε)) -

ReL Reynolds number of the liquid, ρLuLde/(µL (1 − ε)) -

Sα saturation -

Scα Schmidt number, µα/(Dαρα) -

Shα Sherwood number, kαde/Dα -

ShL Sherwood number of the liquid, kLde/DL -

te exposure time s

uα superficial velocity m3α m−2

P s−1

uG superficial gas phase velocity m3

G m−2

P s−1

uL superficial liquid phase velocity m3L m−2

P s−1

vα intersticial velocity, vα = uα/εα mP s−1

WeL Weber number of the liquid, ρLu2

Lde/(σL (1 − ε)) -

Z total length of packing mP

Greek Symbols

β constant in Equation 5.15 -

List of Symbols xi

γ constant in Equation 5.8 -

δ layer thickness m

ε voidage of the solid foam material, ε = εL + εG = 1 − εS m3

void m−3

P

εα holdup of the liquid or gas phase m3α m−3

P

εG gas holdup m3

G m−3

P

εL liquid holdup m3L m−3

P

η effectiveness factor -

λ constant in Equation 5.7 -

µG gas viscosity Pa s

µL liquid viscosity Pa s

ρG gas density kg m−3

G

ρL liquid density kg m−3

L

σL liquid surface tension N m−1

τ tortuosity factor m2L m−2

S

τi shear stress at the gas-liquid interface N m−2

GL

φ Thiele modulus -

χ tortuosity of the strands -

Superscripts

0 at static conditions

α gas or liquid phase as given in Chapter 2

I inlet

O outlet

Subscripts

G gas phase

L liquid phase

P packing

S solid phase

W washcoat

Table of Contents

Summary v

List of Symbols ix

1 Introduction 1

1.1 Conventional packings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1.1 Random packings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1.2 Structured packings . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Solid foam packings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.3 Geometric surface area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.4 Gas-liquid flow through packings . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.5 Scope and outline of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Appendix: Unit cell model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2 Hydrodynamics and modeling of mass transfer for counter-current flow 13

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.1.1 Mass transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.1.2 Liquid holdup models . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.2 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.2.1 Static liquid holdup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.2.2 Low liquid holdup - trickle flow . . . . . . . . . . . . . . . . . . . . . 20

2.2.3 High liquid holdup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.3.1 Static liquid holdup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.3.2 Liquid flow regimes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.3.3 Liquid holdup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.3.4 Liquid holdup modeling . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.3.5 Flooding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.3.6 Pressure drop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.3.7 Mass transfer modeling results . . . . . . . . . . . . . . . . . . . . . . 27

2.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3 Hydrodynamics and mass transfer for co-current upflow 31

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.1.1 Overall volumetric mass transfer . . . . . . . . . . . . . . . . . . . . . 32

3.2 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

xiv Table of Contents

3.2.1 Liquid holdup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.2.2 Liquid axial dispersion coefficient . . . . . . . . . . . . . . . . . . . . 35

3.2.3 Mass transfer coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.2.4 Frictional pressure drop . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.3 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.3.1 Liquid holdup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36


3.3.3 Overall mass transfer coefficient . . . . . . . . . . . . . . . . . . . . . 37

Effect of liquid phase axial dispersion coefficient . . . . . . . . . . . . 37

Entrance and exit effects . . . . . . . . . . . . . . . . . . . . . . . . . . 38

Effect of liquid velocity . . . . . . . . . . . . . . . . . . . . . . . . . . 39

Effect of ppi number . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.3.4 Comparison with other packings . . . . . . . . . . . . . . . . . . . . . 41

3.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

4 Hydrodynamics and mass transfer for co-current downflow 45

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

4.1.1 Gas-liquid mass transfer coefficient . . . . . . . . . . . . . . . . . . . 46

4.2 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47


4.3.1 Liquid holdup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49


4.3.3 Intrinsic liquid-side mass transfer coefficient . . . . . . . . . . . . . . 51

4.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

5 Influence of liquid viscosity and surface tension on the hydrodynamics and masstransfer in co-current flow configurations 55

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56



Sherwood correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

Energy dissipation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

Effect of liquid surface tension . . . . . . . . . . . . . . . . . . . . . . 61

5.2 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62


5.3.1 Co-current upflow - Effect of liquid viscosity . . . . . . . . . . . . . . 64

Liquid Holdup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

Pressure Drop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

Gas-liquid mass transfer coefficient . . . . . . . . . . . . . . . . . . . 67

Energy dissipation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

5.3.2 Co-current downflow - Effect of liquid viscosity . . . . . . . . . . . . 70

Liquid Holdup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70


5.3.3 Co-current downflow - Effect of liquid surface tension . . . . . . . . 72

Liquid holdup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

Table of Contents xv


5.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

6 Hydrodynamics and mass transfer for a gas-liquid-solid foam reactor 75

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

6.2 Overview of hydrodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

6.2.1 Flow regimes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

6.2.2 Liquid holdup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

6.3 Intrinsic mass transfer coefficient . . . . . . . . . . . . . . . . . . . . . . . . . 79

6.4 Effect of material type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

6.5 Reactor comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

6.5.1 Overall reaction rate of multi-phase reactors . . . . . . . . . . . . . . 84

6.5.2 Mass transfer coefficients . . . . . . . . . . . . . . . . . . . . . . . . . 86

Spherical particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

Solid foam packing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

6.5.3 Non-porous support . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

6.5.4 Washcoat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

6.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

7 Perspectives 93

7.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

7.2 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

7.3 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

Bibliography 97

List of Publications 105

Acknowledgements 107

About the author 109

Chapter 1

Introduction

The chemical industry continually strives for more cost efficient processes and in doing

so considers the use of more advanced materials to optimize and intensify processes to

desired process conditions. Reactor packings such as monoliths, cloths, foams, and other

structured packings are investigated and used for two- and three-phase flow operation

due to their improved hydrodynamic performance compared with more conventional

packings, e.g. spherical particles, Raschig rings, etc. The main advantages of these struc-

tured reactor packings are reduced pressure drop per packing height, improved hydrody-

namic properties, and a greater window of stable operating conditions. The relatively high

surface area ensures that adequate catalyst loadings may be applied. Improved gas-liquid

contacting is advantageous to avoid mass-transfer limitations under reaction conditions.

In counter-current operation, flooding, the point at which flow reversal of the liquid oc-

curs with increasing gas flow, is regarded as the limiting factor for using these packings in

real industrial processes.

1.1 Conventional packings

1.1.1 Random packings

In Figure 1.1 some of the commonly used packings are given for use as a catalyst support

in a reactor. These packings are randomly packed (dumped) in the column and not or-

dered as their structured counterparts. Liquid mal-distribution over these packings and

channeling (which may lead to hot-spot formation) are a common problem when these

types of packings are used. To increase the surface area of the packing material, aP , the

size of the packing material may be reduced, at the expense of an increased pressure drop.

However, recently packings have been introduced that have a low pressure drop (due to

the high voidage) and an increase in the specific surface area of the packing; examples of

these is the Q-pac given in Figure 1.1d (Lantec Products Inc., www.lantecp.com). This ran-

dom packing controls the pathways of the fluids in a three-dimensional structure to maxi-

mize the contact between the gas, the liquid and the solid. In the development of random

packings the trend has been towards increasing the voidage of the material, maintain-

2 Chapter 1

ing high surface areas, and towards control of the fluid movement in three-dimensional

pathways.

(a) Spherical particles (b) Raschig rings (c) Berl saddles (d) Q-pac

Figure 1.1: Schematic representation of commonly available randomly packed (dumped) reactorpackings.

1.1.2 Structured packings

(a) Monolith (b) Internallyfinned monolith

(c) Mellapak (Sulzer) (d)Katapak-S(Sulzer)

Figure 1.2: Schematic representation of commonly available structured reactor packings.

Structured packings have the advantage that they are made to fit the dimensions of

the column in which they are placed and thus avoid the mal-distribution of liquid and

formation of channeling or bypassing of the solids. Examples of these structured packing

materials are given in Figure 1.2. In monoliths and internally finned monoliths the liq-

uid and gas flows in channels created within the structured packings, while in Mellapak

the liquid and gas flow down corrugated sheets of gauze stacked to form open channels

between these sheets, and in Katapak some of the open channels are filled with spherical

particles. These packing materials however have commonly a two-dimensional structure

that redirect the liquid and gas flow to planar directions. In the development of these

packings the aim is for increasing the rather low geometrical surface area, while main-

taining a low pressure drop (high voidage) and adequate contact between the flowing

phases. However, as with conventional dumped packing, the geometric surface area of

these packings is difficult to increase without increasing the solids holdup. Solid foams

Solid foam packings 3

can be viewed as the Q-Pac equivalent to structured packings as it maintains a high ge-

ometric area with low solids holdup (and hence low pressure drop) due to its cell-like

structure.

1.2 Solid foam packings

Solid foam packings represent a generation of materials combining relatively high specific

surface area with low pressure drop per unit height. This is due largely to the open-celled

structure with relatively high voidages (up to 97%). Solid foams may be produced in a

variety of materials (metal, ceramics, carbon, SiC, polymers, etc.). The review article by

Banhart (2001) outlines the methods and procedures for producing these and many other

solid foams. The focus here, however, is only on the open-celled foams, more specifically

in the range of 5 to 40 ppi (pores per linear inch), see Figure 1.3.

(a) 5 ppi (b) 20 ppi (c) 40 ppi

Figure 1.3: Images of foam structure supplied by ERG Aerospace Corp., under the commercialname of Duocel. The white bar indicates a characteristic length scale of 5 mm.

Thus far the applications considered for these solid foam materials in the chemical

industry have been minimal. Only single phase studies have been reported on chemi-

cal reaction by Richardson et al. (2003), pressure drop by Fourie and Plessis (2002), and

axial dispersion by Montillet et al. (1993). Figure 1.11a gives the specific surface area as

a function of the voidage of the foam for the 5, 20, and 40 ppi foams from geometrical

considerations as described in the study of Fourie and Plessis (2002). Due to the high

voidage of the solid foam, the pressure drop per unit length over the packing material is

low as described in previous studies on these materials by Fourie and Plessis (2002), Smit

and Plessis (1999), and Richardson et al. (2000). Single phase axial dispersion coefficients

and laminar flow limits for solid foams were compared with conventional packings in the

studies of Montillet et al. (1993) and Seguin et al. (1998), respectively, and reduced axial

dispersion and increased laminar flow were observed.

Modeling of the viscous flow through solid foam packings has been performed in the

study by Smit and Plessis (1999). Boomsma and Poulikakos (2001), Lu et al. (1998), Bhat-

tacharya et al. (2002), and Phanikumar and Mahajan (2002) have investigated the heat

4 Chapter 1

(a) 10 ppi aluminium (b) 40 ppi aluminium (c) 45 ppi carbon

Figure 1.4: Images of solid foam packings supplied by ERG Aerospace Corp. The graduated mark-ings are in mm.

transfer properties of metal foams to be used as heat sinks or highly compact heat ex-

changers. Seijger et al. (2001) and Richardson et al. (2003) have investigated solid foams

as potential catalytic surfaces for gas phase reactions. Friedrich et al. (2004), Armalis and

Kubiliene (2000), and Deab and Saleh (2003) have considered the use of carbon solid foams

as the working electrode for an electrochemical cell, see Figure 1.4c. These studies all in-

dicate the potential for the use of these foams, also for the field of multiphase processing.

Improved gas-liquid mass transfer with solid foam packings has been outlined in the ex-

amples given in some patents concerning polyurethane foams (Ernest and Ravault, 1974;

Pretorius and Hahn, 1980).

1.3 Geometric surface area

In Figure 1.5 the geometric surface area of some common random and structured pack-

ings is presented. The geometric surface area of solid foam packings have been calculated

using the model of Fourie and Plessis (2002) using a tetrakaidecahedra to represent the

interconnected cell structure (further details given in the Appendix). Here the geomet-

ric surface area of solid foam packings can be seen to increase much higher than any of

the other packing materials with increasing ppi number of the solid foam packing. Also

the high voidage (thus low pressure drop) is maintained, ranging from 97% to 80%, de-

pending on the thickness of the struts making up the solid foam packings. The geometric

surface area of the solid foam packings also increases as the voidage is decreased (solids

holdup increasing) due to the struts making up the unit cells increasing in diameter. The

ppi number of the solid foam packings is an independent parameter to describe the aver-

age cell size and increases the geometric surface area as the cell size decreases (ppi number

increases).

The geometric surface area should however not be confused with the surface area for

the deposition of catalytically active components as this surface area (often measured with

BET physisorption and referred to as BET surface area) includes also contributions from

Gas-liquid flow through packings 5

Figure 1.5: Specific geometric surface area for solid foam packings of various ppi numbers and acomparison with common random and structured packings of different voidages, ε ( = 1 − εS).

internal pores or surface roughness. The BET surface area for solid foam packings may be

as much as 200 times larger (Richardson et al., 2000). Richardson et al. (2003) also indicate

that with established techniques a wash-coat may be added giving a specific surface area

as high as 40 m2 g−1. In common random and structured packings this specific BET area

may also be of the same order or even larger, but due to most of the area being internal

(up to 98% of BET surface area inside pores created within the solid material) the area

is not hydrodynamically accessible and diffusion limitations within the pores may still

affect the transfer of components to the active catalyst. This transfer of components from

the gas into the liquid and to the active catalyst located on the solid support is essential

for the operation of multiphase heterogenous reactions and a clear understanding of the

resistances that play a role in the mass transfer process is vital.

1.4 Gas-liquid flow through packings

Multiphase flow of gas and liquid through packing materials is commonplace and can

occur in three configurations, co-current upflow and downflow and counter-current flow.

These configurations have been presented schematically in Figure 1.6.

Each configuration has many advantages, but also disadvantages, when evaluating

6 Chapter 1

L

G

Packed

Bed

L G

Packed

Bed

L G

Packed

Bed

(a) (b) (c)

Figure 1.6: Schematic representation of the direction of the gas (G) and liquid (L) in a packed bedwith the gas and liquid flowing either counter-currently, (a), or co-currently up, (b), or co-currentlydown, (c).

the hydrodynamics, mass transfer and general operation of such reactors. Some of these

are listed below:

Counter-current flow

• Close to plug flow behavior of the reactor, allowing for high conversions and satu-

ration issues of the fluid phases is avoided;

• Uniform distribution of the gas and liquid can be achieved;

• Flooding may limit the reactor as higher gas and liquid flow rates cannot be achieved;

• The reactor may suffer from flow mal-distributions such as channeling, and bypass-

ing and incomplete wetting of the catalyst can occur at low liquid flow rates.

Co-current upflow

• Better distribution in an upflow reactor which gives better heat transfer and in many

cases better performance than in a co-current downflow configuration;

• Higher gas-liquid mass transfer coefficients are obtained in an upflow reactor when

compared to a downflow operated column under similar flow conditions;

• Large pressure drop in an upflow reactor compared to trickle bed reactors. This may

cause a large partial pressure gradient of components over the length of the reactor.

Co-current downflow

• The low liquid holdup provides lower liquid phase resistance to mass transfer of the

gaseous reactants to the catalyst surface;

Scope and outline of the thesis 7

• Lower pressure drop will allow essentially uniform partial pressure of the reactant

across the length of the reactor;

• Catalyst pores do not fill up completely with liquid, providing a higher effectiveness

factor when compared to a reactor operated in the upflow configuration;

• Since the catalyst is held in place by the fluid flow, undesired cementation of the soft

catalyst particles can occur.

• Liquid mal-distribution and dry zones are encountered in co-current downflow, and

avoided in the co-current upflow.

1.5 Scope and outline of the thesis

In single phase flow (e.g. liquid) through a solid support material the reactor performance

is governed by the (liquid-solid) mass transfer of reactants from the flowing phase to the

solid surface and into the pores of the support to reach the catalyst. Here the high velocity

difference between the flowing phase and the stationary support gives a high rate of mass

transfer and the reactor performance is controlled by the quantity and distribution of the

catalyst on the support and referred to as kinetically limited. In multiphase reactors with

a gas and a liquid flowing through a support material the transfer of gaseous components

through the gas-liquid interface is an additional resistance to the transfer of reactants to-

wards the catalyst. Here this mass transfer from the gas to the solid is commonly the

slowest giving a limitation to the overall performance of the reactor as the reaction is lim-

ited to the availability of both components (shown schematically in Figure 1.7).

Gas Liquid Solid

X(g) X(aq) + Y(aq) Products (aq)

Figure 1.7: Schematic representation of the transfer of a gaseous component, X, through the liquid,Y to the active catalyst supported on the solid.

In these types of reactors increasing the concentration of catalyst has no effect on the

overall rate of reaction of reactants (X and Y) into products and the reactor is said to be

mass transfer limited. The overall reactor performance is determined by the mass transfer

8 Chapter 1

over the gas-liquid interface which is characterized by a gas-liquid mass transfer coeffi-

cient, kLaGL. This coefficient is constituted of two parts, the intrinsic mass transfer coeffi-

cient, kL, and the area for mass transfer aGL. This area for mass transfer is related to the

geometric surface area of the packings, and since solid foam packings have an increased

geometric area, the expectation is that the area for mass transfer is also increased.

The main scope of the PhD project is to determine the rate of mass transfer of gaseous

components through the gas-liquid interface that is achieved when the gas and liquid are

flowing through a solid foam packing material. This coefficient can be used to relate the

rate of mass transfer to the rate of reaction. If the transfer of the gaseous components

is high enough, adding more catalyst results in higher reaction rates and the reactor is

said to be kinetically limited. The other important factors relating to the quantification of

the mass transfer and reaction are the hydrodynamic parameters such as liquid holdup

and the frictional pressure drop. These parameters are quantified for the gas and liquid

moving either counter-currently or co-currently (upflow and downflow) through the solid

foam packings at varying gas and liquid velocities. The ppi number of the solid foam

packings is also investigated to quantify the effects that particular length scales, such as

reactor dimensions (in the order of meters) to the size of the cells constituting the solid

foam packings (in the order of millimeters) have on the design of these types of multiphase

reactors.

In the next chapters the gas-liquid mass transfer performance is the main parameter

of interest for packed bed reactors fitted with solid foam packings previously described

(Section 1.2). The hydrodynamic parameters such as the frictional pressure drop, total

pressure drop, and the liquid holdup are studied experimentally in all three of the flow

configurations. In Chapter 2 the counter-current flow configuration is studied experimen-

tally and the relative permeability model, which describes the liquid holdup and pressure

drop, is presented. In Chapters 3 and 4 the co-current downflow and upflow configura-

tions are studied, respectively. In Chapter 5 the effect of changes in the liquid viscosity

and the liquid surface tension are investigated for the co-current flow configurations. In

Chapter 6 the liquid holdup model (relative permeability model, described in Chapter 2) is

used to give an overview of the results obtained and a reactor design based on chemically

inert carbon foam packings is made. This reactor performance is compared to a packed

bed of spherical particles.

Appendix 9

Appendix: Unit cell model

Figure 1.8: Unit cell in the shape of a tetrakaidecahedron, as described by Fourie and Plessis (2002).

In Figure 1.8 a diagram of the unit cell, described by Fourie and Plessis (2002) as-

suming that solid foam packings are made up of interconnecting tetrakaidecahedra (or

truncated octahedra), is given, and was used to describe single phase pressure drop mea-

surements for solid foam packings in the range 10 to 30 ppi. Earlier work by Plessis et al.

(1994) assuming a cubic cell model, where the strands are orthogonal to each other, could

not described the geometric specific surface area adequately. This geometric surface area,

however, is an important parameter in the evaluation of the hydrodynamics and thus the

later unit cell model of Fourie and Plessis (2002) using tetrakaidecahedron as the char-

acteristic shape is applied. The specific surface area of the solid foam packings can be

calculated from the voidage of the solid foam and the number of pores per linear inch

(usually characterized by the supplier). The following implicit set of equations needs to

be solved:

εS = 6.0 · 10−3 (dmN)2 + 1.1 · 10−3 (dmN)3 (1.1)

aP = 41.5dmN2 − 0.91d2

mN3 (1.2)

χ = 2 + 2 cos

[4π

3+

1

3arccos (1 − 2εS)

]

(1.3)

de =3 (3 − χ) (χ − 1)

aP

(1.4)

where εS , is the solids volume fraction, 1− ε, obtained from the bulk density, or given

by the supplier, dm is the average thickness of the strands making up the solid foam, N is

10 Chapter 1

the number of pores per linear inch, aP is the specific surface area, χ is the pore structure

tortuosity, and de is the effective length of the strands, see Figure 1.8.

(a) Unit cell (b) Thicker struts (c) Larger ppi number

Figure 1.9: Diagrams of (a) the unit cell of the solid foam, (b) the size of the struts of the unit cell areincreased (dm increases, εS increases), and (c) where the ppi number of the solid foam has increased(N and dm decreases, εS remains constant).

0 0.1 0.2 0.3 0.4 0.50

1

2

3

4

5

6

7

8

Solid volume fraction, εS [−]

Str

ut

length

, d

e, [m

m]

ppi number [−]

5

10

20

40

45

Figure 1.10: Strut length, de, for the solid foam packings as described by the unit cell model, Fourieand Plessis (2002), for different values of the solid holdup, εS and ppi number, N .

Figures 1.9a to 1.9c depict some of the general changes that occur in the unit cell di-

mensions when the strut thickness is increased and when the ppi number is increased.

This model is used to find the geometric surface area, the average strut length and the

average strut diameter for a range of ppi numbers (5 to 45 ppi) and solid holdups (0.01

to 0.5) and results are given in Figures 1.10 and 1.11. The length of a strut decreases with

increasing ppi number, but remains constant for varying solids volume fraction, as seen in

Figure 1.10. Figure 1.11a gives the specific geometric surface area as a function of the solid

Appendix 11

volume fraction in the range of 5 to 45 ppi (pores per linear inch) and increases as the ppi

number and the solids volume fraction increase. The diameter of a strut decreases with

increasing ppi number and increases as the solids holdup is increased. This is expected

and can be clearly seen by comparing the unit cells given in Figures 1.9a to 1.9c.

0 0.05 0.1 0.15 0.2 0.25 0.30

2000

4000

6000

8000

10000

Solid volume fraction, εS [m

S

3 m

P

−3]

Sp

ecif

ic s

urf

ace

area

, a P

[m

S2 m

P−3]

ppi number [−]

5

10

20

40

45

(a) Surface area, aP

0 0.1 0.2 0.3 0.4 0.50

0.5

1

1.5

2

Solid volume fraction, εS [−]

Str

ut

dia

mte

r d

m, [m

m]

ppi number [−]

5

10

20

40

(b) Strut diameter, dm

Figure 1.11: Characteristics for the solid foam as described by the unit cell model, Fourie and Plessis(2002), for different values of the solid holdup, εS and ppi number, N .

Chapter 2

Hydrodynamics and modeling of mass

transfer for counter-current flow

Parts of this chapter are excerpts from:

• C.P. Stemmet, J.N. Jongmans, J. van der Schaaf, B.F.M. Kuster, J.C. Schouten, Hydro-

dynamics of gas-liquid counter-current flow in solid foam packings, Chem. Eng. Sci.,

60, p 6422, (2005).

• C.P Stemmet, J. Van der Schaaf, B.F.M. Kuster, J.C. Schouten, Solid foam packings

for multiphase reactors: Modelling of liquid holdup and mass transfer, Chem. Eng.

Res. Des., 84 (A12), p 1134, (2006).

Abstract

Experimental and modeling results are presented of the liquid holdup and gas-liquid mass

transfer characteristics of solid foam packings. Experiments were done in a semi-2D trans-

parent bubble column with solid foam packings of aluminum in the range of 5 to 40 pores

per inch (ppi). The relative permeability model described by Saez and Carbonell (1985) is

used to describe the liquid holdup data. The regimes studied are two high liquid holdup

regimes and a low liquid holdup regime (trickle flow regime). Also the flooding points

for counter-current flow have been determined. The investigated system variables are

the superficial gas and liquid velocities, using counter-current flow with maximum gas

velocities and liquid velocities of 0.8 m s−1 and 0.02 m s−1, respectively. The relative per-

meability model is able to describe the liquid holdup in the low liquid holdup or trickle

flow regime as well as in the high liquid holdup regime, which resembles flow in a packed

bubble column. Gas-to-liquid mass transfer is modeled using the penetration theory. Mass

transfer coefficients up to 6 s−1 are predicted; these high values are largely due to the high

specific surface area of the solid foam packings.

14 Chapter 2

2.1 Introduction

In the design of chemical engineering processes, reaction and separation are regarded as

the most important steps. For reactions in multiphase systems, a more active catalyst does

not necessarily lead to an increased rate of conversion; the mass transport rate may be the

limiting factor that determines reactor efficiency. Reactor packings aim to increase the rate

of mass transfer by increasing the gas-liquid contact area and by increasing the turbulence

within the fluid phases. Additionally, in counter-current two-phase flow, mass transfer is

increased by maintaining high concentration gradients, the driving force for mass trans-

fer. For two-phase and three-phase flow, reactor packings such as monoliths, cloths, open-

cell foams, and other structured packings have been demonstrated to improve hydrody-

namic performance compared to the more conventional packings, e.g. spherical particles,

Raschig rings. With ever-increasing catalyst activity being developed and demanded by

the chemical industry, the mass transfer in conventional packings becomes the limiting

factor in the reactor. Structured packings can solve this problem; within the same reactor

volume a significantly higher rate of mass transfer can be achieved (Frank, 1996). Alterna-

tively, for an existing mass transfer limited process the same conversion can be achieved

in a much smaller reactor volume. Other advantages of structured reactor packings are

a reduced pressure drop per packing height, improved hydrodynamic properties, and a

larger window of stable operating conditions. In terms of mass transfer, structured pack-

ings may also be operated at higher contact efficiency, viz. the ratio of gas-liquid contact

area and the geometrical surface area of the packing.

The open-cell structures in the range of 5 to 40 ppi have a higher specific surface area

than conventional packings, e.g. 1

2-inch Raschig rings and 1

2-inch Intalox saddles 400 and

650 m2 m−3, respectively (Treybal, 1980). The solid foam packings also have comparable

or higher surface area than other structured packings e.g. internally finned monoliths, de

= 2.85 mm, and Katapak-S filled with 1.5 mm spheres, approximately 1000 and 800 m2

m−3, respectively (Lebens et al., 1999). Improved gas-liquid mass transfer with solid foam

packings has been reported for polyurethane and ceramic foam packings by Ernest and

Ravault (1974) and Pretorius and Hahn (1980). This higher mass transfer rate is ascribed

to an increase in the degree of turbulence in the liquid flow, which is induced by the many

junctions encountered by the down-flowing liquid.

This chapter investigates the liquid hold-up and the mass transfer rate of solid foam

packings. These parameters are most important for the design of multiphase reactors that

use these (catalytic) solid foam packings, and are evaluated for the two-phase, counter-

current air-water system.

2.1.1 Mass transfer

The mass transfer in packed columns is especially important in the design and construc-

tion of absorbers, strippers, and distillations columns. However, for fast reactions the mass

Introduction 15

transfer between the respective phases may be the limiting factor, and thus is also impor-

tant in the design of multiphase reactors. In literature, many correlations are available that

predict the rate of mass transfer for packed columns, for the gas-side mass transfer coeffi-

cient and the liquid-side mass transfer coefficient, which will be discussed consecutively.

The gas-side mass transfer coefficient for packed beds and structured packings is cor-

related in the following form:

ShG = C1RemGScn

G (2.1)

where C1 is a constant and depends on the type and properties of the packing, m and n

are parameters depending on the flow type and the packing. Sh, Re, and Sc are the di-

mensionless Sherwood, Reynolds and Schmidt numbers, respectively. Rocha et al. (1996)

found Equation 2.1 with C1 = 0.054, m = 0.8 and n = 0.333, for various structured pack-

ings (e.g. Flexpac 2, Gempak 2A Sulzer B, Mellapak, Intalox 2T). The broad applicability

of Equation 2.1, also for conventional packings (Treybal, 1980), suggests that it may also

be used to correlate the gas-side mass transfer coefficients in structured foam packings.

However, for most systems especially for poorly soluble gases the overall rate of mass

transfer is not limited by the transport through the gas film (Treybal, 1980) and thus the

focus in this work will be to predict the liquid-side mass transfer coefficient.

Rocha et al. (1996) described the liquid-side mass transfer coefficient for various struc-

tured packings with the well-known penetration model:

kL = 2

√

DL

πte(2.2)

where DL is the diffusivity in the liquid phase, and te is an assumed exposure time for the

pockets of liquid flowing down the solid foam material. Rocha et al. (1996) have assumed

that the exposure time is proportional to the ratio of a characteristic length of the packing

to the interstitial liquid velocity. A proportionality factor of 1.1 was found, which corrects

for parts of the packing that do not encourage rapid surface renewal. In the present study,

the length of the strands of the solid foam packing is taken as the characteristic length.

This length, de, is calculated from the ppi number, N , and the solid volume fraction, εS,

according to Equations 1.1 to 1.4.

The gas-liquid specific surface area, aP , is another important parameter in obtaining

the overall mass transfer coefficient. The gas-liquid surface area for gauze type packings

is correlated by Rocha et al. (1996) as a function of the Froude number:

aGL

aP

= 1 − 1.203Fr0.111L (2.3)

where aP is the specific surface area of the packing, and FrL is the liquid Froude number.

The correlation in Equation 2.3 predicts that the effective gas-liquid surface area decreases

as the liquid flow rate is increased. This decrease in area is not described by Rocha et al.

16 Chapter 2

(1996), but is possibly due to liquid films occupying more volume at higher liquid flow

rates and coalescence of these liquid films. If we assume that the solid material is wettable

and that no coalescence of liquid films occur, and thus liquid flows as a film over the

strands of the solid foam packing, an estimate of the gas-liquid interfacial area can be

obtained. The specific surface area for the solid foams in the study of Fourie and Plessis

(2002) was used. Here, for the trickle flow regime, the solid volume fraction is replaced

by the sum of the solid volume fraction of the foam (εS) and the liquid holdup, εL. The

specific gas-liquid interfacial area is then given by Equations 1.1 to 1.4 with εS replaced

by εL + εS . This shows that the gas-liquid interfacial area would increases as the liquid

velocity increases due to liquid holdup increasing.

2.1.2 Liquid holdup models

Liquid holdup and pressure drop in counter-current flow for packed columns can be de-

scribed and correlated by many models available in literature. An overview of the ap-

proaches thus far are outlined and reviewed by Carbonell (2000). The relative perme-

ability model, the slit model, and the fluid-fluid interactions model are used to predict

liquid holdup and pressure drop for a wide range of packings. All these models solve the

one dimensional average momentum balance assuming incompressible flow for the fluid

phases:

εαραvα

dvα

dz= −εα

dPα

dz+ εαραg − Fα, α = G, L (2.4)

where εα is the holdup of the fluid phase, ρα is the density, να is the interstitial velocity,

dPα/dz is the pressure gradient along the distance z, and Fα is the drag force on the fluid

phase per unit volume of the bed. The models differ in the calculation of the drag force.

Carbonell (2000) concludes that the relative permeability model is the most accurate in de-

scribing experimental holdup and pressure drop data for two-phase flow. This approach

is used here for modeling the liquid holdup.

The relative permeability model assumes that the drag force per unit volume for each

fluid is a function of the relative permeability, fα, of each phase:

Fα

εα

=1

fα(Sα)

(

AReα

Gaα

+ BRe2

α

Gaα

)

ραg, α = G, L (2.5)

The factors A and B in Equation 2.5 are, respectively, the viscous and inertial coeffi-

cients in the Ergun equation for single phase flow in a packed bed of the packings stud-

ied. The relative permeability, fα, is assumed to be a function of the saturation, Sα, of

each phase. The relative permeabilities for the gas and liquid are given in Equation 2.7,

according to Saez and Carbonell (1985). The values of h1 and h2 found by the authors for

the packings studied (spheres, Raschig rings, cylinders and Berl saddles) are 4.8 and 2.43,

Experimental 17

respectively. The voidage of the solid packings is represented by ε, (ε = 1 − εS):

Sα =εα

ε(2.6)

fG = Sh1

G , fL =

(SL − S0

L

1 − S0

L

)h2

(2.7)

S0

L is the saturation of liquid at the static holdup condition and is correlated by Saez and

Carbonell (1985) for the packings studied to a modified Eotvos number, Eo∗:

S0

L =ε0

L

ε= [ε (20 + 0.9Eo∗)]−1, Eo∗ =

ρLgd2eε

σL (1 − ε)2(2.8)

The relative permeability model as it is described in Saez and Carbonell (1985) for

co-current flow has been used by Dankworth and Sundaresan (1989) as a macroscopic

model for counter-current flow. The velocity and pressure gradients in Equation 2.4 are

zero under the assumption of having a uniform velocity throughout the column and the

holdup of the respective gas phase and liquid phase being uniformly distributed. Thus,

Equation 2.4 for the liquid phase is subtracted from that for the gas phase and reduces to:

FG

εG

− FL

εL

+ (ρG − ρL) g = 0 (2.9)

At different gas and liquid Reynolds numbers (varying superficial velocities), the liq-

uid holdup, εL, can be calculated by solving Equations 2.5 to 2.9 for each phase with

εG = ε − εL.

2.2 Experimental

The solid foams used in this study are commercially available under the brand name of

Duocel from ERG Aerospace Corp. (flat rectangular blocks of size 30 x 30 x 1 cm). Figure

1.3 shows the detail of the solid aluminium foam in the range of 5 to 40 ppi. All of these

foams have a voidage of 92 to 94%. The foams were placed to a height of 80 cm in a 2D per-

spex column with cross section 30 x 1 cm and height of two meters, shown schematically

in Figure 2.1. This flat geometry allows visual observation of the gas-liquid flow through

the solid foam packings. The pressure drop per unit height was measured using a Druck

DP610 pressure sensor with an accuracy of 1 Pa. Air-water is used as the gas-liquid two-

phase system in this study. The air and water are flowing counter-currently. The liquid

is distributed on top over the solid foam packing through five rectangular nozzles (8 x 12

x 50 mm) with sixteen 0.5 mm diameter holes to avoid liquid mal-distribution. A liquid

rotameter is used to measure the liquid flow rate. The gas flow is supplied through five

holes at the bottom of the column and controlled at the desired flow rate with mass flow

18 Chapter 2

controllers. A Dalsa CA-D6 high speed camera was used to capture images if the packing

was sufficiently transparent.

T2

T1

1

2

4

5

6

7

3 P3

8

9

80 cm

1 cm 30 cm

Gas

Supply

P1

P2

Figure 2.1: Counter-current flow setup: 1. Solid foam packed bed, 2. Liquid rotameter, 3. Gasmass flow controller, 4. Liquid holdup measurement tank placed on a balance, 5. Main liquidsupply tank, 6. Liquid pump, 7. Hose pump, 8. Liquid overflow (for high liquid holdup), 9. Liquiddrainage point (for low liquid holdup).

The flooding point can be described in a number of ways, but the clearest definition

is the point where at a certain gas flow, flow reversal of the liquid occurs and the liquid

is unable to flow through the packing and collects on the top of the bed. The pressure

drop per unit height increases rapidly due to this liquid accumulation. This point is the

operating limit for counter-current flow of gas and liquid through packings. The regime

usually described for counter-current flow at low liquid holdup is called the trickle flow

regime. However, also a high liquid holdup regime similar to gas-liquid flow in packed

beds was studied.

The liquid holdup for both the high and low liquid holdup regimes was measured ex-

ternally by the weighing method and using the liquid holdup measurement tank depicted

in Figure 2.1. This vessel was placed on a balance for accurate measurement of the liquid

volume. The main liquid circulating through the solid foam packing is supplied from a

Experimental 19

10 liter vessel, also depicted in Figure 2.1. A liquid loop from this tank to the 2D column

and back to this vessel, ensures that the main liquid supply tank remains completely filled

with liquid.

Figure 2.2: Schematic representation of the liquid holdup for different gas and liquid Reynoldsnumbers. The three regimes are the trickle, bubble and pulse regime.

2.2.1 Static liquid holdup

The static liquid holdup is described in Saez and Carbonell (1985) as the specific amount

of liquid that remains in the bed after the bed has been drained with no liquid nor gas

flow. This amount of liquid that remains is due to the balance of surface tension and

gravitational forces. The static holdup is described by Saez and Carbonell (1985) as a

function of the Eotvos number, the contact angle at the gas-liquid-solid contact line, and

the geometry of the packing.

The static liquid holdup was measured using foam pieces of 10 x 30 x 1 cm for the

aluminium foams in the pore sizes of 5, 10, 20, and 40 ppi. These were weighed, placed in

water and allowed to drain for 10 minutes, and then weighed again.

20 Chapter 2

2.2.2 Low liquid holdup - trickle flow

The trickle of liquid over a packing material is the operating regime for many types of

packings. Correlations to predict the pressure drop and operating limits for counter-

current gas-liquid flow for a variety of packings is given by Stichlmair et al. (1989).

This trickle flow regime is attained with the experimental setup given in Figure 2.1 by

starting with the void spaces in the foam filled with gas and with the liquid supply tank

completely filled. A constant liquid flow is circulated through the column and is collected

and returned to the supply tank. An additional liquid stream is circulated through the

column from the liquid holdup measurement tank and is returned via the liquid drainage

point at the bottom of the column. The liquid holdup in the trickle flow regime is de-

termined at this liquid flow rate and with zero gas flow. As the gas flow is increased, it

opposes the flow of the liquid in the column giving rise to a higher holdup of liquid, thus

the volume in the liquid holdup measurement vessel decreases. At the flooding point, the

liquid is unable to flow down the packing due to the high gas flow and collects at the top

of the column and gas is entrained with the liquid into the main liquid supply tank.

2.2.3 High liquid holdup

A high liquid holdup regime is also possible using the experimental setup as shown in Fig-

ure 2.2. This regime resembles a packed bubble column in co-current gas-liquid up-flow,

but operated under counter-current flow conditions. This regime is described as unsta-

ble in Dankworth and Sundaresan (1989) and is considered to arise only by a restrictive

support plate at the bottom of the column. This high liquid holdup regime has not been

studied in the literature before for other types of packings.

In the high liquid holdup case the main liquid supply tank, the packed column, and

the associated piping are completely filled with liquid, with no gas flow. A liquid flow

is set to flow counter-currently from the top to the bottom of the solid foam packing and

is returned to the main liquid supply tank. As the gas flow rate is steadily increased, the

liquid holdup in the column decreases, the additional liquid is expelled at the top and is

collected in the liquid holdup measurement vessel, giving a measure of the liquid holdup

within the column. A small liquid flow from this tank ensures stabilization of the liquid

volume collected at a particular gas and liquid flow through the column.

2.3 Results

2.3.1 Static liquid holdup

The measured static liquid holdup for the solid foam packings is given in Figure 2.3 as a

function of the Eotvos number. The static liquid holdup is higher in the structured foam

packings; Equation 2.8 underestimates this static liquid holdup. The liquid holdup is best

described by Equation 2.10, also shown in Figure 2.3.

Results 21

Table 2.1: Static liquid holdup for the aluminium solid foam packings of different ppi number.

5 ppi 10 ppi 20 ppi 40 ppi

Static liquid holdup, ε0L [-] 0.067 0.094 0.111 0.115

0 50 100 150 200 2500

0.05

0.1

0.15

0.2

Eo* [−]

Sta

tic

Liq

uid

Hold

up, ε

L0 [

−]

Experimental data points

Model: εL

0 = 1/ ( 9 + 0.025 Eo

*), this work

Model: εL

0 = 1 / ( 20 + 0.09 Eo

*),

Saez and Carbonell (1985).

Figure 2.3: Static liquid holdup for the solid foam packings in the range 5 to 40 ppi, plotted againstthe Eotvos number.

S0

L =ε0

L

ε= [ε (9 + 0.025Eo∗)]−1, Eo∗ =

ρLgd2eε

σ (1 − ε)2(2.10)

Increasing the ppi number increases the number of junctions where the liquid remains

due to capillary forces, and possibly increases the static liquid holdup. The thickness of the

liquid film remaining on the surface of the solid foam packing was calculated, assuming

that the static liquid holdup spreads evenly over the entire surface and using Equations

1.1 to 1.4. The film thickness is 17, 34, 60 and 91 µm for the 40, 20, 10 and 5 ppi solid foam,

respectively.

2.3.2 Liquid flow regimes

In the low liquid holdup trickle regime, the liquid introduced at the top of the column

flows in a thin film of liquid over the solid foam packing. In the high liquid holdup

regime, two visually different regimes can be discerned: a bubbly flow similar to packed

bubble columns at low gas velocities and a high gas-liquid interaction regime similar to

pulsed flow in trickle beds, but operated in a counter-current flow configuration. In the

high interaction regime, waves of gas appear to move through the bed, although a stable

distribution of liquid is still capable of flowing down the column as a film on the strands

of the solid foam packing. This is largely due to the high voidage and high surface area

of the solid foam packing. The gas rate is increased until the flooding point is reached.

At this point liquid collects at the top of the column and a steady liquid flow through the

22 Chapter 2

foam cannot be maintained. As in the low liquid holdup trickle flow case, gas is entrained

with the liquid flow to the main liquid supply tank.

(a) (b) (c)

Figure 2.4: Different flow regimes possible in solid foams: a. Image of liquid filled solid foam, b.Image of low liquid holdup, trickle flow regime, c. Image of high liquid holdup bubble regime. Thesize of each image is 30 x 30 cm, and shows a 5 ppi foam, thickness 1 cm, placed in the 2D column.The black strip through the image is a seal to cover pressure sensor holes at the back of the column.

Figure 2.4c shows the high liquid holdup bubble flow regime. Bubbles of gas (darker

regions) are moving upwards through the solid foam packing (black). In the series of

images in Figure 2.5, the high liquid holdup pulsing regime is depicted. The images show

a slug of gas, the front of the slug depicted by the white line, traveling through a distance

of 30 cm of the column; these slugs appear to travel at determined time intervals through

the column. However, within these gas slugs the liquid still trickles down the solid foam

packing. In the high liquid holdup bubble regime, bubbles become larger with increasing

gas flow rate and start spanning the whole column width. Thus, a gradual transition to

the pulsing regime is observed. In this regime only gas slugs are moving upwards.

(a) (b) (c)

Figure 2.5: Images showing a gas slug moving upwards through the solid foam packing in the highliquid holdup case (pulsing flow regime). From image (a) to (c), time is increasing. The size of eachimage is 30 x 30 cm, and shows a 5 ppi foam, 1 cm thick, placed in the 2D column. The black stripthrough the image is a seal to cover pressure sensor holes at the back of the column.The white linerepresents the front of the slug of gas moving upwards. A video of this slugging behaviour may beviewed at: http://www.chem.tue.nl/scr/

Results 23

2.3.3 Liquid holdup

The measurement of the liquid holdup for counter-current flow of gas and liquid is given

in Figure 2.6 for the 5 and 40 ppi metal foams packings. As the gas flow rate is increased

in some instances, gas bubbles are entrained in the liquid flow back to the liquid supply

tank and it is not possible to obtain an accurate measurement of the liquid holdup. Exper-

imentally however, flooding, as described in Section 2.2, may occur only at a later stage.

In the trickle flow regime, the liquid holdup increases with increasing liquid and gas flow

rates. In the high liquid holdup regimes, the highest liquid holdup that can be obtained is

equal to the voidage of the solid foam material (approximately 93%). The liquid holdup

decreases with increasing gas and liquid flow rates. Here, the liquid is not confined to

move along the solid foam surface; the gas bubbles move through the open pore space of

the foam, thus resembling a (packed) bubble column. As the gas flow rate is increased,

the gas finally moves through the open foam space as a slug. Liquid drains through the

gas slug and appears to flow along the solid foam surface. Even at relatively high liquid

and gas fluxes, the solid foam packing allows counter-current flow of both gas and liquid

through the internal volume. This is largely due to the open structure of the foam mate-

rial. These trends can be seen for the foams of 5 to 40 ppi. It should be mentioned that for

this experimental setup the maximum gas flow rate possible within the column is 0.88 kg

m−2 s−1.

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

Gas Flux [kg m−2

s−1

]

Liq

uid

Hold

up [

−]

Liquid Flux [kg m−2

s−1

]

27.8 (5 ppi)

6.8 (5 ppi)

27.8 (40 ppi)

6.8 (40 ppi)

Figure 2.6: Liquid holdup at different liquid fluxes for 5 ppi (◦,⊳) and 40 ppi (•,◭) solid foampackings for the different flow regimes. Results for the low liquid holdup regime (εL < 0.4) and thehigh liquid holdup regimes (εL > 0.4) are given.

In Figure 2.6 the liquid holdup for the 5 and 40 ppi foams is given on the same axis.

In the trickle flow regime, the tendency is to a higher liquid holdup for the 40 ppi solid

foam compared to the 5 ppi foam. This is to be expected because the 40 ppi foam has

a higher specific surface area that gives a higher restriction to the liquid flow through

24 Chapter 2

the foam. Also the static liquid holdup for the 40 ppi foam is higher. The same trend is

observed in the high liquid holdup regime. The result is a combination of contributing

factors: the tortuous path of the flow of liquid and gas is increased as the ppi number

increases, the restriction of the gas and liquid flows is increased due to the increase of the

specific surface area, but also the drainage of the liquid downwards is eased by this larger

surface as well. All these factors affect the liquid holdup. It is clear, however, that as the

ppi number of the solid foam packing decreases, the solid foam packing may have larger

operating capabilities.

2.3.4 Liquid holdup modeling

The liquid holdup in the solid foam was predicted using the models as described previ-

ously. The model developed by Saez and Carbonell (1985) was fitted to the experimental

data, using A, B, h1, and h2 as fitting parameters. The experimental data and the fitted

model results for the solid foams are presented in Figure 2.7a to Figure 2.7c. The results

for the fitting parameters are given in Table 2.2.

Table 2.2: Parameters in the relative permeability model of Saez and Carbonell (1985) for solid foampackings; also given is the 95% confidence interval of the fitted parameters.

5 ppi 20 ppi 40 ppi Average Saez et al. (1985)

de [x 103 m] 3.0 0.75 0.38

A [x 105] 8.31 42.1 0.088 180 x 105

B 25.09±7.04 14.03±1.86 5.04±1.34 1.8

h1 5.17±0.37 3.88±0.16 4.25±0.26 4.43 4.8

h2 2.33±0.2 1.55±0.09 1.73±0.16 1.88 2.43

In the high liquid holdup situation the data is well represented by the model. How-

ever, the low liquid holdup is not predicted well, because here it is highly dependent on

the static liquid holdup, and the model is unable to describe the increase in holdup with

increasing gas velocity near the flooding point. The model is also based on the assump-

tion that the drag forces are functions of the respective single phase Ergun equations, and

thus the interaction between the respective phases is not taken into account. This is most

prominent for the 5 ppi solid foam packing. Here the foam struts are least densely packed,

which makes the interaction between gas and liquid most significant and the deviation be-

tween the experimental results and the liquid holdup model the largest. The values of A

and B are very different compared to other packings (A = 180 and B = 1.8, respectively).

The value of A, the viscous contribution to the pressure drop, does not have significant

influence on the liquid holdup modeling at the flow velocities studied and may be disre-

garded. The value of B in the single phase Ergun equation is modeled with the relative

Results 25

0 1000 2000 3000 4000 50000

0.2

0.4

0.6

0.8

1

ReG

[−]

Liq

uid

Hold

up, ε

L [

−]

Experimental points

ReL = 1185 [−]

ReL = 889 [−]

ReL = 593 [−]

ReL = 296 [−]

Model

(a) 5 ppi

0 200 400 600 800 10000

0.2

0.4

0.6

0.8

1

ReG

[−]

Liq

uid

Hold

up, ε

L [

−]

Experimental points

ReL = 296 [−]

ReL = 222 [−]

ReL = 148 [−]

ReL = 74 [−]

Model

(b) 20 ppi

0 100 200 300 400 5000

0.2

0.4

0.6

0.8

1

ReG

[−]

Liq

uid

Hold

up, ε

L [

−]

Experimental points

ReL = 148 [−]

ReL = 111 [−]

ReL = 74 [−]

ReL = 37 [−]

Model

(c) 40 ppi

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

−10%

+10%

Liquid Holdup, εL [−], experimental

Liq

uid

Hold

up, ε

L [

−],

cal

cula

ted

5 ppi

20 ppi

40 ppi

(d) Parity plot

Figure 2.7: Experimental data and modeling results of the liquid holdup versus Reynolds numberof the gas using the relative permeability model (Saez and Carbonell, 1985) for (a) 5 ppi, (b) 20ppi and (c) 40 ppi solid foam packings, respectively. A parity plot of all of the liquid holdup datacompared to the predictions of the relative permeability model is given in (d).

permeability model and is not constant for the foams, but decreases with increasing ppi

number.

In Richardson et al. (2000) the single phase pressure drop was studied and the value of

B also varied with ppi number. This value is usually quoted as being a constant (B = 1.8)

for all types of packings, but should be seen as an averaged value, e.g. ranging from 1.18

to 4.4 for the packings listed in Iliuta et al. (2003). However, for solid foam packings the

value of B is significantly higher. The values of h1 and h2 given in Table 2.2 are in the

same range but not comparable to the values found by Saez and Carbonell (1985). The

results of the model vs. the experimental data are summarized in the parity plot given

in Figure 2.7d. It is clear that in the low liquid holdup regime for all the packings the

26 Chapter 2

model describes the experimental liquid holdup data less accurately, possibly due to the

interaction between the relative phases not taken into account by the model.

2.3.5 Flooding

0 0.5 1 1.50

10

20

30

40

50

Gas Flux [kg m−2

s−1

]

Liq

uid

Flu

x [

kg

m−

2 s

−1]

Katapak−S

Monoliths 25 cpsi

Solid foam 40 ppi

Solid foam 20 ppi

Solid foam 5 ppi

(a) Low liquid holdup

0 0.5 1 1.50

10

20

30

40

50

Gas Flux [kg m−2

s−1

]

Liq

uid

Flu

x [

kg

m−

2 s

−1]

Katapak−S

IFM 25 cpsi

Solid foam 40 ppi

Solid foam 20 ppi

Solid foam 5 ppi

(b) High liquid holdup

Figure 2.8: Gas and liquid fluxes at the flooding point for Katapak-S (Ellenberger and Krishna(1999)), internally finned monoliths (Lebens et al. (1999)), and solid foam packings of 5, 20 and 40ppi as reached from the low liquid holdup and high liquid holdup regimes, respectively.

The results for the flooding point are given in Figure 2.8. These are combinations

of gas and liquid fluxes where the flooding condition as described in Section 2.2 is ob-

served. Flooding is encountered at lower gas and liquid flow rates as the ppi number is

increased. Here the flow path is more tortuous and the restriction to flow is increased. The

flooding point is considered as an unstable operating point and a number of factors may

induce a premature flooding condition within the column. Inadequate contact between

two adjacent solid foam sections may induce flooding and is viewed as the largest con-

tributing factor. The flooding data obtained for the solid foam packings is compared with

two structured packed systems: Sulzer Katapak-S (Ellenberger and Krishna, 1999) and

monoliths (Lebens et al., 1999) for an air-water system. The results indicate that flooding

for the solid foam closely resembles that found for the Katapak-S packing, with inter-

nally finned monoliths (IFM) having higher flow rates of gas and liquid before flooding is

reached. Comparison between the packings should be done cautiously, as the distribution

of the gas and liquid into the volume of the packing material is but one factor affecting the

flooding point. This distribution may differ between the different experimental setups.

2.3.6 Pressure drop

The pressure drop per unit height of packing is presented in Figure 2.9 for the 5 and 40 ppi

foams. In the low liquid holdup regime, the pressure drop increases as the liquid and gas

Results 27

0 0.2 0.4 0.6 0.8 10

200

400

600

800

1000

Gas Flux [kg m−2

s−1

]

PT

ota

l [P

a m

−1]


s−1

]

17.2 (40 ppi)

10.3 (40 ppi)

Dry (40 ppi)

17.2 (5 ppi)

10.3 (5 ppi)

Dry (5 ppi)

(a)

0 0.2 0.4 0.6 0.8 10

2000

4000

6000

8000

10000

Gas Flux [kg m−2

s−1

]

PT

ota

l [P

a m

−1]


s−1

]

17.2 (40 ppi) with error bars

10.3 (40 ppi)

17.2 (5 ppi)

10.3 (5 ppi)

(b)

Figure 2.9: Pressure drop per unit length of reactor in (a) low liquid holdup, and (b) high liquidholdup regimes. Dry pressure drop given in (a). In the slugging regime the pressure drop per unitlength has a large variation from the mean, as indicated by the error bars.

fluxes are increased. The 40 ppi foam exhibits consistently higher pressure drop than the 5

ppi foam as expected. For the 5 and 40 ppi foams, the dry packing displays similar trends

due to an increase in the number of restrictions in the path of the flow. The pressure drop

per unit height of solid foam packing is lower in comparison to packed beds of spherical

particles, which is due to the high voidage of the solid foam packing. In the high liquid

holdup regime, the same result is found. The pressure drop, however, is mainly due to

the liquid holdup in the bed. In the high liquid holdup slug regime, a high variation in

the pressure drop over the bed is observed, as indicated by the error bars. As the flooding

point is approached, the average pressure drop behaves erratically due to the presence of

gas and liquid filled slugs.

2.3.7 Mass transfer modeling results

The gas-liquid mass transfer coefficients were estimated by the penetration theory, pre-

sented in Section 2.1.1, for the 5, 20, and 40 ppi solid foams, and are given in Figure 2.10

for the trickle flow regime. Liquid-side mass transfer coefficients found for the solid foam

are quite high, largely due to the high geometric surface area for the solid foam packings,

which is estimated to generate high gas-liquid area. The 40 ppi foam has a specific surface

area, aP , of approximately 4500 m2m−3 for a solids volume fraction of 7%. Unlike other

packings, the gas-liquid surface area increases as the liquid holdup is increased. This in-

crease in surface area assumes that the liquid spreads evenly over the surface of the solid

foam packing, which may not always be the case. Droplet formation or coalescence of the

liquid films may occur, which would ultimately decrease the area for mass transfer.

In Figure 2.10 it can be seen that the value of kLaGL increases with liquid velocity

28 Chapter 2

0 200 400 600 800 1000 12000

1

2

3

4

5

6

ReL

kL a

GL [

m s

−1]

5 ppi

20 ppi

40 ppi

Figure 2.10: Liquid side mass transfer coefficient for 5 to 40 ppi solid foam packings, according toEquation 2.2, with DL = 10−9 m2 s−1 and ReG < 100.

(higher values of ReL). The interstitial velocity of the liquid is higher, giving lower expo-

sure times. This increases the value of kL and subsequently the value of kLaGL for higher

liquid flow rates. Additionally, it can be seen in Figure 2.10 that as the ppi number of the

solid foam increases, the value of kLaGL increases. This is mainly due to an increase of

the specific surface area of the dry packing, which increases with the ppi number. The

highest value of kLaGL estimated for the solid foams is approximately 6 s−1 for the 40 ppi

foam at the highest superficial liquid velocity. These are not experimentally obtained gas-

liquid mass transfer coefficients, but estimates using penetration theory for the trickle flow

regime. In the setup used the gas-liquid mass transfer coefficient could be determined ex-

perimentally, possibly by the method of oxygen desorption. However, this was not done

in the present study.

2.4 Conclusions

Solid foam packings can be used excellently for gas-liquid counter-current flow combin-

ing the properties of relatively high specific surface areas with high voidage. In counter-

current operating, three flow regimes are found:

• Low liquid holdup: trickle flow regime;

• High liquid holdup: bubble flow regime;

• High liquid holdup: pulsing regime.

In the low liquid holdup regime, the liquid holdup increases as the liquid and gas flow

rates are increased, and increases with an increase in the foam ppi number. In the two high

liquid holdup regimes, the liquid holdup decreases with increase in gas and liquid flow

Conclusions 29

rates, and increases with increasing foam ppi number. Each of the regimes mentioned

above are stable operating regimes for gas-liquid counter-current flow, and especially the

high liquid holdup regimes may be useful for highly exothermic processes.

The gas and liquid flow rates where flooding is observed are similar to those found in

Katapak-S packing and increase with decreasing ppi number. The pressure drop per unit

height of packing is low compared to other packing materials due to the open structure of

the foam material. In the pulsing regime, the pressure drop over the solid foam packing

fluctuates due to the formation of gas and liquid slugs.

The relative permeability model by Saez and Carbonell (1985) can be applied to de-

scribe the liquid holdup in structured solid foam packings. It describes the liquid holdup

for the high liquid holdup regimes, but underestimates the liquid holdup in the the low

liquid holdup regime (trickle flow), possibly a result of the interaction between the respec-

tive phases not taken into account. The static liquid holdup in the structured solid foam

packings at zero gas and liquid flows is described as a function of the Eotvos number,

Equation 2.10.

The mass transfer predicted for the solid foam packing material in the low liquid

holdup case increases with increasing ppi number of the solid foam and liquid Reynolds

number. The liquid-side mass transfer coefficients predicted for the foams using pene-

tration theory is quite high compared to other structured packings, the highest value of

kLaGL is approximately 6 s−1, for the available data set of liquid and gas flows and liquid

holdups. This high value of kLaGL is largely due to the high specific surface area of the

solid foam packing materials, aP which is assumed to be fully wetted.

Chapter 3

Hydrodynamics and mass transfer for

co-current upflow

This chapter has been published as:

C.P. Stemmet, M. Meeuwse, J. van der Schaaf, B.F.M. Kuster, J.C. Schouten, Gas-liquid

mass transfer and axial dispersion in solid foam packings, Chem. Eng. Sci., 62, p 5444,

(2007).

Abstract

The mass transfer coefficient and other hydrodynamic parameters are presented for a gas

and liquid (air-water) system moving in a co-current upflow configuration through solid

foam packings in the range of 10 to 40 pores per linear inch (ppi). Axial dispersion in the

liquid has been excluded by observing that the liquid was in plug flow in the range of

superficial liquid and gas velocities studied (0.02 < uL < 0.1 m s−1 and 0.1 < uG < 0.8 m

s−1). Also entrance and exit effects have been taken into account by evaluating the gas-

liquid mass transfer for two different lengths of solid foam packing. The average pore size

of the solid foam (ppi number) does not influence the overall volumetric mass transfer

coefficient. Increasing the gas and liquid velocities increases the gas-liquid mass transfer

and the maximum mass transfer coefficient was found to be approximately 1.3 s −1. The

results are correlated with the energy dissipation rate and compared with a packed bed of

spherical particles.

32 Chapter 3

3.1 Introduction

The chemical industry is continuously developing more active catalysts for multiphase

processes thereby shifting the limitation for the design of a gas-liquid reactor towards the

mass transfer of reactants or products between the gas and the liquid phases rather than

the subsequent mass transfer and reaction in the solid phase. Industrial applications of

multiphase reactors include Fischer-Tropsch synthesis, hydrogenations, oxidations, epox-

idations, and alkylations. The solid catalyst is either in the form of pellets or powders,

hence, either slurry or fixed bed operations are commonly employed. Structured reactor

packings such as monoliths, wire gauze packings, Sulzer Katapak-S, or cloths have the ad-

vantage that they show improved hydrodynamic properties when compared with more

conventional reactor packings, e.g. telleretts and spherical particles, in terms of pressure

drop, flow distribution, and gas-liquid contact. However, these packings have rarely been

employed due to the relatively low surface area to deposit catalysts.

Solid foam packings are available in a variety of materials (metal, carbon, ceramics)

and pore sizes. These foams combine both the properties of high surface area and low

solid holdup especially suited for low pressure drop applications.

This chapter aims at quantifying the mass transfer coefficient for gas-liquid flow through

these solid foam packings when operated in the co-current upflow condition. Hydrody-

namic parameters such as frictional pressure drop per unit height of packing and liquid

holdup are also quantified.

3.1.1 Overall volumetric mass transfer

The overall mass transfer coefficient for sparingly soluble gases is commonly controlled

by the liquid-side film resistance. Thus the overall mass transfer coefficient is equal to the

liquid-side mass transfer coefficient.

The gas-liquid mass transfer coefficient (kLaGL) is mainly determined by the interfacial

area (aGL), which for packings is usually a function of the specific geometric surface area

of the packing and of the liquid holdup. The liquid side mass transfer coefficient (kL) is

determined largely by the slip velocity between the gas and liquid phases. The value of

kLaGL is also affected by the physical properties of the gas-liquid system, the velocities of

the gas and the liquid, the lyophobicity of the solid and the solids holdup.

The axial dispersion coefficient in either the gas or liquid phase characterizes the

amount of mixing with a single parameter, Dax,G or Dax,L. The axial dispersion within a

column may be quantified by performing tracer experiments. A pulse of non-transferring

tracer is introduced at the phase inlet and the residence time distribution of this pulse is

obtained at the reactor outlet. The outlet concentrations are modeled with an axial disper-

sion model as given in Equations 3.1 and 3.2 with the value of kLaGL set to zero; and for

Experimental 33

co-current upflow of gas and liquid:

∂CG

∂t= Dax,G

∂2CG

∂z2− uG

εG

∂CG

∂z− kLaGL

(CGRT

H− CL

)(εL

εG

)

(3.1)

∂CL

∂t= Dax,L

∂2CL

∂z2− uL

εL

∂CL

∂z+ kLaGL

(CGRT

H− CL

)

(3.2)

Compared with the liquid phase, the gas bubbles move with relatively high interstitial ve-

locities and low axial mixing, and thus plug flow for the gas phase is assumed (Dax,G ≈ 0).

Two extreme conditions can be considered to determine the influence of the axial disper-

sion in the liquid phase on the gas-to-liquid mass transfer:

I. Gas and liquid phases both in plug flow;

II. Gas phase in plug flow and liquid phase ideally mixed.

These two conditions give Equations 3.3 and 3.4, respectively, for determining the value of

kLaGL, given a concentration difference between the inlet, CIL, and outlet, CO

L , liquid phase

concentrations:

I.

kLaGL = ln

(CI

GRT

H− CI

L

COGRT

H− CO

L

)(RT

uGH+

1

uL

)−1(1

εLZ

)

(3.3)

II.

kLaGL = ln

(CI

GRT

H− CO

L

COGRT

H− CO

L

)(RT

uGH

)−1(1

εLZ

)

(3.4)

The value for the outlet gas phase concentration, COG , can be obtained from the overall

mass balance, where CIG is the known concentration in the gas phase at the reactor inlet:

COG = CI

G +uL

uG

(CI

L − COL

)(3.5)

3.2 Experimental

The solid foams used in this study are commercially available under the brand name of

Duocel from ERG Aerospace Corp. (flat rectangular blocks of size 30 x 30 x 1 cm). All of

these foams have a voidage of 92 to 94%. The foams were placed in a specially designed

semi 2-dimensional column with varying height; either 30, 60, or 90 cm high with cross

section 30 x 1 cm, shown schematically in Figure 3.1.

Air-water is used as the gas-liquid two-phase system in this study. The air and water

are flowing co-currently. The liquid enters the bottom of the column through five distri-

bution holes placed along the complete width of the column and the flowrate is measured

34 Chapter 3

O2

1

2

4

7

5

8

9

1 cm

30 cm

Air N2

6

30-90 cm

O2

8

L

10

DP

3

Figure 3.1: Co-current upflow setup: 1. Solid foam packed bed, 2. Main liquid supply vessel, 3.Liquid mass flow controller, 4. Liquid control valve, 5. Gas flow control to each of five distributors,6. Air/Nitrogen flow controller, 7. Gas-liquid separator, 8. Dissolved oxygen sensors, 9. Liquidlevel measurement, 10. Differential pressure measurement.

and controlled by a coriolis mass flow meter (Rheonik) and Badger control valve. The gas

enters through five distributor blocks each with 20 holes of 0.5 mm in diameter and in-

dependently controlled by a Brooks thermal mass flow controller. The maximum gas and

liquid flows within the column are 1.4 and 0.1 m s−1, respectively. The liquid is recycled

via a gas-liquid separator back to the supply vessel feeding the pump. In the gas-liquid

separator the liquid level is measured to determine the liquid holdup in the column with

the solid foam. The liquid temperature is maintained at approximately 30◦ Celsius. To

ensure complete wetting of the packing, the column is completely filled with liquid and

thereafter the experiments are conducted at various gas and liquid velocities.

3.2.1 Liquid holdup

The liquid holdup is an important parameter especially for determining the values of

kLaGL and the frictional pressure drop, Pf . The typical flow regimes in an upflow co-

current column are the spray-, bubble- and pulse regimes. The values for the liquid

Experimental 35

holdup were determined in the experimental setup comparing the amount of liquid in

the gas-liquid separator for a 0.3 and a 0.6 m column. The difference in the measured liq-

uid volumes being the additional liquid holdup in the column at specific gas and liquid

flow rates.

3.2.2 Liquid axial dispersion coefficient

The liquid phase axial dispersion coefficient was determined by injecting a pulse of non-

transferring tracer (KCl) at the inlet of the column and by measuring the conductivity

of the liquid with conductivity sensors at the inlet and the outlet (Buerkert, K = 0.1, 0.5-

200 µS cm−1). Examples of the inlet and outlet normalized response curves are given in

Figures 3.2a and 3.2b. The liquid Bodenstein number (BoL) was determined from these

response curves using the linearized transfer function method described by Fahim and

Wakao (1982). The liquid Bodenstein number, BoL, affects the calculation of the gas-liquid

mass transfer coefficient, assuming the liquid as plug flow (Equation 3.3) or well mixed

(Equation 3.4), and thus needs to be determined. Values of the Bodenstein number, BoL,

greater than 10 indicate that plug flow may be assumed for the liquid at the lowest liquid

velocity (uL = 0.02 m s−1). It is expected that at higher liquid velocities the value of BoL

increases and thus plug flow in the liquid phase is assumed for all estimations of kLaGL.

0 50 100 150 200−0.5

0

0.5

1

1.5

2

2.5

3

3.5

4x 10

−3

Time [s]

No

rmal

ized

ou

tpu

t

Inlet

Outlet

(a) uG = 0.1 m s−1 (BoL = 19).

0 50 100 150 200−0.5

0

0.5

1

1.5

2

2.5

3

3.5

4x 10

−3

Time [s]

No

rmal

ized

ou

tpu

t

Inlet

Outlet

(b) uG = 1 m s−1 (BoL = 50).

Figure 3.2: Response of KCl tracer injected into the liquid phase flowing at 0.02 m s−1 through 10ppi solid foam packing.

3.2.3 Mass transfer coefficient

The method of oxygen desorption with nitrogen was used to measure the mass transfer

coefficients within the solid foam packings (CIG = 0). The dissolved oxygen concentrations

were measured at the liquid inlet and outlet using InPro 6800 oxygen sensors (Mettler

36 Chapter 3

Toledo). The liquid from the exit of the column was recycled to the inlet via the gas-liquid

separator, thus during an experiment the liquid phase oxygen concentration gradually

dropped. The value of kLaGL thus obtained is from the pseudo-steady state liquid phase

concentration difference between the inlet and outlet of the column.

3.2.4 Frictional pressure drop

The frictional pressure drop per unit height was measured using a differential pressure

sensor (Druck, LPX9831) connected to the column with the measurement positions spaced

7 cm apart (∆Z = 0.07 m). The measured value is corrected for the liquid holdup as

follows:

Pf =∆Pmeasured

∆Z− ρL

(εL

εL + εG

)

g (3.6)

3.3 Results and discussion

3.3.1 Liquid holdup

The liquid holdup results are shown in Figures 3.3a and 3.3b for different velocities and

ppi numbers respectively. Also indicated are the bubble and pulsing regimes observed.

The spray regime, which occurs at relatively high gas velocities, was not observed in the

current study.

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

Gas velocity, uG

[m s−1

]

Liq

uid

hold

up, ε

L [

mL3 m

P−3]

→ PulseBubble ←→

Liquid velocity

uL = 0.02 m s

−1

uL = 0.04 m s

−1

uL = 0.10 m s

−1

(a)

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

Gas velocity, uG

[m s−1

]

Liq

uid

hold

up, ε

L [

mL3 m

P−3]


10 ppi, uL = 0.02 m s

−1

10 ppi, uL = 0.04 m s

−1

40 ppi, uL = 0.02 m s

−1

40 ppi, uL = 0.04 m s

−1

(b)

Figure 3.3: Liquid holdup for (a) 10 ppi solid foam packing at different liquid velocities, and (b)comparing the liquid holdup for 10 and 40 ppi solid foam packings in the co-current upflow config-uration.

The liquid holdup increases with increasing liquid velocity and decreasing gas veloc-

ity, up to the maximum voidage of the solid foam packings (93%). The liquid is moving

upward with a certain velocity, and as the residence time of the gas phase in the column

decreases, the gas holdup decreases, effectively increasing the liquid holdup. The liquid

Results and discussion 37

holdup increases as the ppi number of the solid foam increases. As the ppi number in-

creases the average pore cell size decreases resulting in higher capillary pressures and

higher static liquid holdup.


The frictional pressure drop per unit height is calculated with Equation 3.6 and presented

in Figure 3.4. Increasing the liquid and gas velocities increases the frictional pressure drop.

Also, the pressure drop increases by increasing the ppi number. At the highest liquid ve-

locity investigated (uL = 0.1 m s−1) the 40 ppi solid foam packing has a significant increase

in frictional pressure drop over the 10 ppi solid foam packing, when the gas is introduced.

The high liquid velocity possibly causes the gas-liquid flow to homogenize giving higher

interaction with the solid struts. The 40 ppi solid foam packing has more struts restricting

the flow and the frictional pressure drop increases. At lower liquid velocities this interac-

tion is lower because the gas phase is moving through as bubbles or pulses and the liquid

as the continuous phase the interaction with the solid is less pronounced. The pressure

drop per unit height is relatively low due to the open structure of the solid foam packing

(voidage approximately 93%).

0 0.5 1 1.5 20

50

100

150

200

250

300

Gas velocity, uG

[m s−1

]

Fri

ctio

nal

pre

ssu

re d

rop

, P

f [1

02 P

a m

−1]

uL = 0.02 m s

−1, 10 ppi

uL = 0.04 m s

−1, 10 ppi

uL = 0.10 m s

−1, 10 ppi

uL = 0.02 m s

−1, 40 ppi

uL = 0.04 m s

−1, 40 ppi

uL = 0.10 m s

−1, 40 ppi

Figure 3.4: Frictional pressure drop, Pf , for 10 and 40 ppi solid foam packings at different liquidvelocities in the co-current upflow configuration.

3.3.3 Overall mass transfer coefficient

Effect of liquid phase axial dispersion coefficient

The liquid phase axial dispersion has a large effect on the calculation of the mass transfer

coefficient as can be seen in Figure 3.5 , using Equations 3.3 and 3.4. Results from the tracer

38 Chapter 3

studies indicated that the values of BoL were greater than 10 for the range of the liquid

and gas velocities studied (0.02 < uL < 0.1 m s−1 and 0.1 < uG < 0.8 m s−1).

0 0.2 0.4 0.6 0.8 10

0.5

1

1.5

2

2.5

3

3.5

4

Gas velocity, uG

[m s−1

]

kLa G

L [

s−1]

k

La

GL for plug flow (Bo

L → ∞)

Range of kLa

GL (10 < Bo

L < ∞)

kLa

GL for well mixed liquid

Figure 3.5: Mass transfer coefficient for 10 ppi foam for different liquid Bodenstein numbers (BoL),uL = 0.02 m s−1.

Figure 3.5 shows the values of kLaGL determined by solving the PDE’s given in Equa-

tions 3.1 and 3.2 in Matlab R© assuming Dankwerts’ closed boundary conditions with BoL =

10, and the gas phase in plug flow, Dax,G = 0. Figure 3.5 shows that the influence of this

value of BoL on kLaGL is quite small, which suggests that plug flow of the liquid phase,

i.e. Equation 3.3, is a fair assumption for all results; further results are evaluated using this

assumption.

Entrance and exit effects

The so-called entrance effect is caused by the gas and liquid distribution. The column

entrance is the region where the bubble size distribution and flow velocities have not

stabilized yet. Here a higher value of kLaGL is expected due to the small bubbles exiting

the distributor, moving at quite high velocities. The exit effect accounts for additional mass

transfer occurring between the gas and liquid phases from the column outlet to where the

exit oxygen concentration is measured. At given gas and liquid velocities the entrance

and exit effects are assumed to be constant. Luo and Ghiaasiaan (1997) have accounted

for these effects by evaluating kLaGL using Equation 3.7, where Z ′ and Z ′′ are two different

lengths of packing; in our case 0.3 and 0.6 m:

kLaGL =(kLaGL)Z′Z ′ − (kLaGL)Z′′Z ′′

Z ′ − Z ′′(3.7)

In Figure 3.6 the values of kLaGL are shown for lengths of 10 and 40 ppi solid foam pack-

ings of 0.6 m and 0.3 m. If the entrance and exit effects are not considered, the mass


transfer coefficient is up to 20% higher, and increases to 150% at low liquid velocities. The

entrance and exit effects for the 10 ppi solid foam packing at the lower liquid velocity, see

Figure 3.6a (especially in the pulse regime), contribute significantly to the gas-liquid mass

transfer coefficients measured, resulting in low values of kLaGL. This is not observed in

the 40 ppi solid foam packing. Possibly the more densely packed struts of the 40 ppi solid

foam packing reduce the entrance effect. The mass transfer coefficients obtained for the

different lengths of packings can be reproduced to within 5%.

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

Gas velocity, uG

[m s−1

]

kLa G

L [

s−1]

(k

La

GL)Z = 30 cm

(kLa

GL)Z = 60 cm

kLa

GL by Equation 3.7

(a) uL = 0.02 m s−1, 10 ppi

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

Gas velocity, uG

[m s−1

]

kLa G

L [

s−1]

(k

La

GL)Z = 30 cm

(kLa

GL)Z = 60 cm

kLa

GL by Equation 3.7

(b) uL = 0.04 m s−1, 10 ppi

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

Gas velocity, uG

[m s−1

]

kLa G

L [

s−1]

(k

La

GL)Z = 30 cm

(kLa

GL)Z = 60 cm

kLa

GL by Equation 3.7

(c) uL = 0.02 m s−1, 40 ppi

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

Gas velocity, uG

[m s−1

]

kLa G

L [

s−1]

(k

La

GL)Z = 30 cm

(kLa

GL)Z = 60 cm

kLa

GL by Equation 3.7

(d) uL = 0.04 m s−1, 40 ppi

Figure 3.6: Mass transfer coefficient for 10 ppi solid foam packing, (a) and (b), and 40 ppi solidfoam packing, (c) and (d), for 0.6 m and 0.3 m packing height, and after accounting for the entranceand exit effects by Equation 3.7.

Effect of liquid velocity

Figure 3.7a gives the results of the mass transfer coefficient for different gas and liquid

velocities. The results indicate a smooth transition when going from the bubble to the

40 Chapter 3

pulse regime (at approximately 0.3 m s−1) and in general the higher the liquid velocity the

higher the overall mass transfer coefficient. Surface renewal theory describes gas-liquid

mass transfer according to the following proportionality:

kL ∝ 1√te

(3.8)

where te is an assumed exposure time. Mass transfer between the gas and liquid phases

is thought to occur mainly with liquid remaining on the solid foam packing structure

when a gas bubble passes. As the liquid velocity increases, the bubble moves through

the solid foam at a higher velocity and the contact time of the bubble with the liquid on

the packing decreases. Thus, according to surface renewal theory, the value of the mass

transfer coefficient increases with increasing liquid velocity, as observed.

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

1.2

1.4

Gas velocity, uG

[m s−1

]

kLa G

L [

s−1]


10 ppi, uL = 0.02 m s

−1

10 ppi, uL = 0.04 m s

−1

10 ppi, uL = 0.10 m s

−1

40 ppi, uL = 0.02 m s

−1

40 ppi, uL = 0.04 m s

−1

(a)

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8


Gas velocity, uG

[m s−1

]

kLa G

L ⋅ ε

L [

m3 L m

−3

P s

−1]

10 ppi, uL = 0.02 m s

−1

10 ppi, uL = 0.04 m s

−1

10 ppi, uL = 0.10 m s

−1

40 ppi, uL = 0.02 m s

−1

40 ppi, uL = 0.04 m s

−1

(b)

Figure 3.7: Mass transfer coefficient (a) per unit of liquid volume and (b) per unit of reactor vol-ume for 10 and 40 ppi solid foam packings for different liquid velocities in the co-current upflowconfiguration.

Effect of ppi number

In Figure 3.7b the mass transfer coefficient per unit of reactor volume, kLaGL εL, is given.

The main contribution to the gas-liquid mass transfer coefficient is thought to occur be-

tween liquid films remaining on the solid foam packing as the gas passes by in the form of

bubbles or slugs. These liquid films are refreshed by the continuous liquid phase. At the

low liquid velocity (uL = 0.02 m s−1) the gas-liquid mass transfer for the 10 ppi solid foam

packing decreases for increasing gas velocity and is lower than measured for the 40 ppi

solid foam packing. Entrance and exit effects contributing to the mass transfer possibly

cause local depletion of the oxygen in the liquid film and low refreshment by mixing with

the continuous liquid phase. This is not observed for the 40 ppi solid foam packing. At the


highest liquid velocity the measurement of kLaGL was not performed for the 40 ppi solid

foam packing because liquid holdup measurements could not be done, and thus a com-

parison between 10 and 40 ppi solid foam packings is only possible for the intermediate

liquid velocity. At the intermediate liquid velocity (uL = 0.04 m s−1), the liquid holdup is

similar at the same flow conditions for 10 and 40 ppi solid foam packings. A higher solid

geometric surface is available which does not generate a higher mass transfer coefficient

(1080 and 4300 m2 m−3 respectively, using the unit cell approach, Fourie and Plessis, 2002).

This can be due to a lower value of the liquid-side mass transfer coefficient, kL. If the as-

sumption is made that the area for the gas-liquid mass transfer is equal to the surface area

of the solid foam, aP , covered with a liquid film exposed to the gas, εG, i.e. aGL ≈ aP · εG,

an approximate value for kL may be obtained, given in Figure 3.8.

The value of kL remains constant over the entire range of gas velocities for most of the

solid foam packings and velocities, with only the 10 ppi solid foam for the lowest velocity

case giving lower values of kL. This decrease in the values of kL are not expected and

are possibly due to entrance and exit effects affecting these results. Also observed is that

as the ppi number of the solid foam increases, the value of kL decreases. The distance

between the struts making up the solid foam decreases as the ppi number increases, and

as the liquid flows through the foam it encounters more of these restrictions to the flow,

observed also by an increase in the pressure drop. These small restrictions to the flow

decrease the local velocity of the liquid flowing over the solid foam packing which results

in a lower turbulence and hence a lower kL. It may also be argued that the lower kL for the

higher ppi solid foam packing is a result of the strut thicknesses being smaller, incapable

of inducing large eddies in the liquid phases, leading to a reduced level of turbulence in

the flowing liquid.

3.3.4 Comparison with other packings

The solid foam packings give high rates of mass transfer, in the order of 0.1-1.3 s−1 for

the range of gas and liquid velocities studied. The mass transfer coefficient per unit of

reactor volume (kLaGL εL) is plotted against the level of energy dissipation for the solid

foam packings and other (spherical) packings in Figure 3.9. Losey et al. (2001) report

mass transfer coefficients for packed micro-reactors in the range of 5 to 15 s−1. However,

when the intersticial velocity (assuming εL ≈ 0.2) is used for the energy dissipation term,

the results may be compared with that of Specchia et al. (1974), where 6 mm spherical

particles were studied. The high voidage in the solid foam packings (93% compared to

40% for spherical particles) results in lower intersticial liquid velocities and hence the

associated mass transfer coefficients are lower. This can also be associated with a lower

rate of energy dissipation (lower pressure drop per unit height of packing) as seen in

the correlation. This correlation takes the liquid holdup into account when calculating the

energy dissipation term and is able to compare reactors packed with structures of different

42 Chapter 3

0 0.2 0.4 0.6 0.8 10

0.5

1

1.5

Gas velocity, uG

[m s−1

]

kL [

10

3 m

L s

−1]

10 ppi, u

L = 0.02 m s

−1

10 ppi, uL = 0.04 m s

−1

10 ppi, uL = 0.10 m s

−1

40 ppi, uL = 0.02 m s

−1

40 ppi, uL = 0.04 m s

−1

Figure 3.8: Intrinsic liquid-side mass transfer coefficient, kL, for 10 and 40 ppi solid foam packingsfor different liquid velocities in the co-current upflow configuration. At the lowest liquid velocity,uL = 0.02 m s−1 the decrease in kL for the 10 ppi solid foam packing is ascribed to local depletionof the liquid film remaining on the solid surface.

100

101

102

103

104

105

10−1

100

101

102

Energy dissipation, EL ( = P

f u

L ε

L

−1) [W m

P

−3]

kLa G

L ε

L [

m3 L m

−3

P s

−1]

u

L = 0.02 m s

−1, 10 ppi foam

uL = 0.04 m s

−1, 10 ppi foam

uL = 0.10 m s

−1, 10 ppi foam

uL = 0.02 m s

−1, 40 ppi foam

uL = 0.04 m s

−1, 40 ppi foam

uL = 0.02 m s

−1, 6 mm spheres

uL = 0.04 m s

−1, 6 mm spheres

400 µm packed micro−reactor, 75 µm spheres

kLa

GL ε

L = 0.0134 ⋅ E

L

0.44

Figure 3.9: Mass transfer coefficient for 10 and 40 ppi solid foam packings at different levels ofspecific energy dissipation, EL. A comparison is made with spherical particles (Specchia et al.(1974)) and packed micro-reactors (Losey et al. (2001)).

Conclusions 43

voidages. A similar equation was found by Hirose et al. (1974) for co-current downflow.

3.4 Conclusions

Volumetric mass transfer coefficients are presented for solid foam packings in the range of

10 to 40 ppi. The following conclusions can be drawn:

• The liquid axial dispersion is low, with BoL greater than 10 for the solid foam pack-

ings in the range of the liquid and gas velocities studied (0.02 < uL < 0.1 m s−1 and

0.1 < uG < 0.8 m s−1).

• Exit and entrance effects tend to increase kLaGL and can be accounted for by using

Equation 3.7 for two different lengths of packing. For 10 ppi solid foam packing at a

low liquid velocity uL = 0.02 m s−1 the measurement of the gas-liquid mass transfer

coefficient is low due to high contributions of entrance and exit effects.

• Volumetric mass transfer coefficients, kLaGL, are not a function of the ppi number

of the solid foam packing, but increase with increasing gas and liquid velocities.

Experimentally found values of the volumetric mass transfer coefficients are high

and in the range of 0.1 to 1.3 s−1.

• The mass transfer coefficient per unit of reactor volume, kLaGLεL, were correlated

against the rate of energy dissipation, and this equation, kLaGL εL = 0.014 E0.44L , is

also valid for packings with different voidages.

Chapter 4

Hydrodynamics and mass transfer for

co-current downflow

This chapter will be submitted for publication as:

C.P. Stemmet, F. Bartelds, J. van der Schaaf, B.F.M. Kuster, J.C. Schouten, Hydrodynamics

and mass transfer for gas-liquid co-current downflow through solid foam packings, Ind.

& Eng. Chem. Res., in preparation, (2008).

Abstract

The gas-liquid mass transfer coefficient and the liquid holdup are presented for a gas and

liquid (air-water) system moving in a co-current downflow configuration through solid

foam packings of 10 and 40 pores per linear inch (ppi). The superficial liquid and gas

velocities studied are 0.02 < uL < 0.05 m s−1 and 0.1 < uG < 0.8 m s−1, respectively.

In the trickle flow regime the gas-liquid mass transfer coefficient increases as the average

pore size of the solid foam packing increases. This is possibly due to the increase in the

average strut diameter which creates more turbulence in the liquid phase. The gas-liquid

mass transfer coefficient is not influenced by the gas velocity in the trickle flow regime,

whereas increasing the liquid velocity increases the gas-liquid mass transfer coefficient.

The intrinsic mass transfer coefficient, kL, was estimated to be an order of magnitude

smaller than in the co-current upflow configuration under similar gas and liquid flow

rates. Slug flow was observed at high gas flow rates and the gas-liquid mass transfer

coefficient is significantly higher than in the trickle flow regime.

The gas-liquid mass transfer coefficient per unit of reactor volume, kLaGLεL, for co-

current downflow through 10 ppi solid foam packings is correlated by the following equa-

tion:

kLaGL εLDL−1 = 3.7 (uLρLµL

−1)1.16


P ]

46 Chapter 4

4.1 Introduction

In the chemical industry large quantities of gas streams are processed and purified by the

stripping of gas components into suitable liquids using trickle beds, either by physical

or chemical absorption. These beds are commonly packed with catalytically active par-

ticles and act as the reactors for many processes such as hydro-desulphurization, hydro-

cracking, hydro-treating, or sorbitol production. These reaction processes occurring on

the solid surface are often limited by the rate of gas-liquid mass transfer and by the liquid

capacity before slug flow (pulse downflow) is observed. Structured reactor packings such

as monoliths, wire gauze packings, Sulzer Katapak-S, or cloths have the advantage that

they show improved hydrodynamic properties when compared with more conventional

reactor packings, e.g. telleretts and spherical particles, in terms of pressure drop, flow dis-

tribution, and gas-liquid contact. Also higher production rates can be achieved due to the

higher voidage of these structured packings. However, these packings have rarely been

employed for catalytic reactions due to the relatively low surface area to deposit catalysts.

Solid foam packings are another type of structured packing and combine high specific

surface area and low solid holdup and are especially suited for low pressure drop applica-

tions. This is due to the high voidage of the open-celled structure (up to 97%). These solid

foam packings are available in a variety of materials (metal, carbon, ceramics) and pore

sizes. In Figure 1.4 (page 4) images of the reticulated structure described by the pores per

linear inch (ppi) is given, both at the same voidage. As the cell-size increases (ppi number

decreasing) the struts making up the cell also increases in diameter.

This chapter aims at quantifying the gas-liquid mass transfer coefficient for gas-liquid

flow through these solid foam packings (10 ppi and 40 ppi) when operated in the co-

current downflow condition. The liquid holdup is also quantified over a range of gas and

liquid velocities.

4.1.1 Gas-liquid mass transfer coefficient

The gas-liquid mass transfer coefficient (kLaGL) is mainly determined by the gas-liquid

interfacial area (aGL). This area is usually a function of the specific geometric surface

area of the packing, in the order of 103 to 104 m2S m−3

P for solid foams, and of the liquid

holdup, εL. The liquid-side mass transfer coefficient (kL) is determined largely by the

liquid velocity in the co-current downflow condition. The values of kL and aGL are also

affected by the physical properties of the gas-liquid system, the velocities of the gas and

the liquid (uG and uL, respectively), the lyophobicity of the solid, and the solids holdup.

The flow through the solid foam in the co-current upflow configuration may be regarded

to be in plug flow, Section 3.3.3 (page 37), and it can also be assumed also for the co-current

downflow configuration as the axial dispersion in this configuration is considered to be

lower, Alper (1983).

Experimental 47

Sherwood and Holloway (1940) have presented their results for the gas-liquid mass

transfer coefficient for 0.5 to 1.5-inch Raschig rings, Berl saddles, and 3-inch spiral tiles

operating in the co-current downflow configuration in the following form:

kLaGL εL

DL

= λ

(uLρL

µL

)n

(ScL)0.5 (4.1)

where λ and n are constants that characterize the packing, DL is the diffusivity of the gas in

the liquid, and ScL is the Schmidt number of the liquid, µL/(ρLDL). Here for the packings

investigated, a constant value of n was found (in the range of 0.78 to 0.72) for all sizes of the

packings. Spherical particles (4.1 mm to 0.54 mm) were also investigated, Goto and Smith

(1975), and the value of n was found to be 0.40. In both studies the value of λ increases

with decreasing particle size. This dependency of λ on the size of the packing is possibly

due to the difficulty in defining the characteristic length for gas-liquid mass transfer. This

characteristic length gives an average contact time, te, for mass transfer between pockets

of gas and liquids to occur given by the penetration theory for mass transfer:

kL = 2

√

DL

πte(4.2)

The contact time is an averaged value describing the intrinsic gas liquid mass transfer

coefficient and is dependent on the liquid velocity as it flows over the surface. At the

gas-liquid surface a pocket of liquid stays and interacts with the gas for this contact time

and reducing this contact time increases the mass transfer. This is because the pocket of

liquid is refreshed by mixing with the bulk liquid. This micromixing can be increased

by turbulence within the bulk liquid and for single phase flowing through solid foam

packings has been found to increase, Ferrouillat et al. (2006), with decreasing ppi number

(larger pore diameters). This counterintuitive result is explained by considering the flow

as external flow around a tube and that larger struts making up the solid foam packings

generate higher levels of turbulence within the liquid. In the gas-liquid trickle flow the

liquid flows as a film over the surface of the solid foam packing, similar to the single

phase. Increased gas-liquid mass transfer due to higher micromixing for decreased ppi

lumber (larger pore diameters) is evaluated experimentally.

4.2 Experimental

The solid foam packings used in this study are made of aluminum and have a voidage of

93%. Solid foam packings of 10 and 40 ppi, commercially available from ERG Aerospace

Corp., have been used for this study. These foams were placed in a semi 2-dimensional

column with varying height; either 30, 60, or 90 cm high with a cross section of 30 cm by 1

cm, shown schematically in Figure 4.1. All measurements are obtained at a temperature of

48 Chapter 4

O2

1

2

4

7

5

8

9

1 cm

30 cm

Air N2

6

30-90 cm

O2

8

L

10

DP

3

Figure 4.1: Co-current downflow setup: 1. Solid foam packed bed, 2. Main liquid supply vessel, 3.Liquid mass flow controller, 4. Liquid control valve, 5. Gas flow control to each of five distributors,6. Air/Nitrogen flow controller, 7. Gas-liquid separator, 8. Dissolved oxygen sensors, 9. Liquidlevel measurement, 10. Differential pressure measurement.

30◦C. The volumetric mass transfer coefficient was measured using the method of oxygen

desorption (DL = 2.75 × 10−9 m2L s−1 for oxygen in water, at 30◦C) by measuring the

dissolved oxygen concentration at the liquid inlet and outlet (InPro 6800 oxygen sensors

Mettler Toledo). The following equations (assuming plug flow) are used to determine

the gas-liquid mass transfer coefficient as in the co-current upflow configuration (Section

3.1.1, page 32):

kLaGL = ln

(CI

GRT

H− CI

L

COGRT

H− CO

L

)(RT

uGH+

1

uL

)−1(1

εLZ

)

(4.3)

COG = CI

G +uL

uG

(CI

L − COL

)(4.4)

where CIG and CO

G are the inlet and outlet gas phase concentrations, respectively, CIL and

COL are the inlet and outlet liquid phase concentrations, respectively, R is the universal

gas constant, T is the temperature, H is the Henry coefficient, and Z is the height of the

packing. In the co-current upflow configuration (Section 3.3.3, page 3.3.3) it was shown


that the entrance and exit effects affect the gas-liquid mass transfer coefficient and thus

also here the gas-liquid mass transfer coefficient for two different heights of packings (Z ′′

= 30 cm and Z ′ = 60 cm) were used to evaluate the contribution of the solid foam packing

by the following equation:

kLaGL =(kLaGL)Z′Z ′ − (kLaGL)Z′′Z ′′

Z ′ − Z ′′(4.5)

The liquid holdup was measured in the co-current downflow regime as for the co-

current upflow configuration, Section 3.2.1, page 34. Mainly the trickle flow regime was

observed, but slug flow was observed for superficial gas velocities higher than 0.7 m s−1.


4.3.1 Liquid holdup

Figure 4.2 gives the results for the liquid holdup for the 10 and 40 ppi solid foam packings.

The liquid holdup is mainly dependent on the liquid velocity, uL, and gradually decreases

as the gas velocity is increased. The intersticial liquid velocity for the different superficial

liquid velocities remains virtually constant (uL/εL ≈ 0.1 mL s−1), but increases slightly

with increasing gas velocity. The relatively constant nature of the intersticial velocity is

mainly due to gravity being the main force acting on the liquid volume as it flows down

the solid foam packing. As the gas velocity is increased, the friction between the gas

and liquid increases and the liquid film has a slightly higher intersticial velocity and thus

slightly thinner liquid films result.

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

Gas velocity, uG

[m s−1

]

Liq

uid

ho

ldu

p, ε

L [

mL3 m

P−3]

u

L = 0.02 m s

−1, 10 ppi

uL = 0.04 m s

−1, 10 ppi

uL = 0.02 m s

−1, 40 ppi

uL = 0.04 m s

−1, 40 ppi

Figure 4.2: Liquid holdup, εL, for solid foam packings in the co-current downflow configuration.

50 Chapter 4


0 0.2 0.4 0.6 0.8 10

0.02

0.04

0.06

0.08

0.1

0.12

Gas velocity, uG

[m s−1

]

kLa G

L ε

L [

m3 L m

P−3 s

−1]

uL = 0.02 m s

−1, 10 ppi

uL = 0.04 m s

−1, 10 ppi

uL = 0.02 m s

−1, 40 ppi

uL = 0.04 m s

−1, 40 ppi

(a) kLaGLεL

0 0.005 0.01 0.015 0.02 0.025 0.030

0.005

0.01

0.015

0.02

0.025

0.03

−20%

+20%

kLa

GL ε

L D

L

−1 Model [10

9 m

L m

P

−3]

kLa G

L ε

L D

L−1 E

xper

imen

tal

[10

9 m

L m

P−3]

10 ppi :kLaGL εL

DL= 3.7

(uLρL

µL

)1.16

Sc0.5L

uL = 0.02 m s

−1

uL = 0.03 m s

−1

uL = 0.04 m s

−1

uL = 0.05 m s

−1

(b) Parity plot

Figure 4.3: (a) Mass transfer coefficient per unit of reactor volume, kLaGLεL, for solid foam pack-ings in the co-current downflow configuration at different liquid viscosities, µL. The circle (©)indicates experiments where slug flow was observed. In (b) the parity plot of the correlation ofkLaGLεL with superficial liquid velocity as described in Equation 4.1 is given for the 10 ppi solidfoam packing.

Figure 4.3a shows the mass transfer coefficient in the co-current downflow configura-

tion. For the 10 ppi solid foam packing, the mass transfer coefficient decreases as the liquid

velocity decreases. The mass transfer is constant in the trickle flow regime with increas-

ing gas velocity, while it decreases with increasing ppi number (decreasing cell size). This

can be explained by the increase in the strut size of the solid foam packing decreasing ppi

number. These struts serve as flow obstructions for the liquid phase when the liquid film

flows down the solid foam packing. The larger the obstruction, the higher the degree of

turbulence (in the form of liquid circulation eddies or wakes), and hence an increase in the

refreshment of the liquid at the gas-liquid interface and enhanced gas-liquid mass transfer

result. In Figure 4.3b a parity plot of the mass transfer coefficient per unit of reactor vol-

ume, described by Equation 4.1, is given and is largely affected by the liquid velocity. The

values of the correlating parameters λ and n were found to be 3.68 ± 0.79 and 1.16 ± 0.30,

respectively, giving the following correlation for the 10 ppi solid foam packing:

kLaGL εL

DL

= 3.68

(uLρL

µL

)1.16

(ScL)0.5 (4.6)

The value of n is higher than the values found for spherical particles, Berl saddles and

Raschig rings (0.4, 0.72 and 0.78, respectively), but a general trend emerges that increasing

the voidage of the packing (0.44, 0.65-0.7 and 0.72-0.77, respectively), increases the value

of n. Thus the higher value of n for solid foams is expected (n = 1.16 for εS = 0.93).


However, in contrast to other packings investigated (where the value of λ increases with

decreasing packing size), decreasing the cell size (10 ppi to 40 ppi) clearly gives lower

values of kLaGLεL, see Figure 4.3a, and hence a lower value of λ. In the case of spherical

particles, smaller particles generate higher levels of turbulence and, in the case of solid

foams, a smaller unit cell (smaller struts) delivers less gas-liquid mass transfer. This is

also reflected in the value of n being greater that one. In general a correlation such as for

liquid-solid mass transfer, as for single phase flow through solid foam packings, Pletcher

and Whyte (1991), should also be observed for gas-liquid mass transfer, i.e.:

(kLl

DL

)

∝(

uLρLl

µL

)n

Sc0.5L (4.7)

where the Sherwood number (kLl/DL) and the Reynolds number (uLρLl/µL) are corre-

lated for a characteristic length scale, l. For multiphase systems the value of l is difficult

to define (boundary layer analogies with heat transfer done for single phase studies are

not applicable). However, Equation 4.7 indicates that a lower value of kL is expected for

smaller value of l for values of n greater than one, which is what we find for solid foam

packings. This indicates that the value of l (and the associated Reynolds number) for 40

ppi is smaller than that of the 10 ppi solid foam packing. In the pulsing regime the mass

transfer coefficient increases due to the refreshment of the liquid on the solid surface with

passing liquid pulses and possibly as a result of a higher degree of wetting of the solid

surface.

4.3.3 Intrinsic liquid-side mass transfer coefficient

0 0.2 0.4 0.6 0.8 10

0.01

0.02

0.03

0.04

0.05

Gas velocity, uG

[m s−1

]

kL [

10

3 m

L s

−1]

10 ppi, uL = 0.02 m s

−1

10 ppi, uL = 0.04 m s

−1

40 ppi, uL = 0.02 m s

−1

40 ppi, uL = 0.04 m s

−1

Figure 4.4: Intrinsic liquid-side mass transfer coefficient, kL, for solid foam packings in the trickleflow regime for the co-current downflow configuration.

In Figure 4.4 the value for the intrinsic mass transfer coefficient is given for 10 and 40

52 Chapter 4

ppi solid foam packings in the downflow configuration. If we assume that the liquid flows

over the solid foam packing in the form of a thin film, an estimate of the film area, aGL, can

be made from Figure 1.11a (page 11) by replacing the solid holdup, εS, by (εS + εL). This

assumption may not always apply as pore filling or coalescence of liquid films (resulting

in channeling) would result in lower gas-liquid interfacial areas. However, using this as-

sumption, the results indicate that the value of kL is dependant on both the liquid velocity

and the ppi number of the solid foam packings, but independent of the gas velocity. In

the co-current downflow configuration, the liquid film is continuously exposed to the gas

phase and refreshment of the liquid film at the gas-liquid interface is mainly caused by dis-

turbances in the liquid film as the liquid flows down the struts making up the solid foam.

This results in the formation of liquid eddies when liquid flows past the struts making up

the solid foam packing. The results indicate that the intrinsic mass transfer coefficient for

the co-current downflow configuration is higher for the 10 ppi solid foam packing than

for 40 ppi, approximately a factor 4. This higher rate of mass transfer is a result of higher

local mixing within the film flowing over the 10 ppi solid foam packing due to the larger

strut thickness (0.55 mm compared to 0.07 mm for the 40 ppi solid foam packing, accord-

ing to the unit cell model, Fourie and Plessis (2002)). This resulting local mixing occurring

within the film is similar to the single phase study, Ferrouillat et al. (2006), where larger

struts were found to generate higher turbulence in the liquid and shorter micromixing

times. Therefore the strut thickness, and hence the ppi number of the solid foam packing,

has a large influence on the resulting value of kL.

The value of kL for the co-current downflow configuration is an order of magnitude

lower than that for the co-current upflow configuration, see Figure 3.8, page 42. In the

co-current upflow configuration the liquid film on the solid foam packing is continuously

being refreshed by the bulk liquid after the passing of a gas bubble, and hence the contact

time decreases giving an increase in the value of kL. This indicates a higher level of turbu-

lence and shorter micromixing times for solid foam packings operating in the co-current

upflow configuration when compared to the downflow configuration.

4.4 Conclusions

• The gas-liquid mass transfer coefficient per unit of reactor volume, kLaGLεL, for co-

current downflow through the 10 ppi solid foam packing is correlated by the follow-

ing equation:

kLaGL εL

DL

= 3.68

(uLρL

µL

)1.16


P ]

• The gas-liquid mass transfer for 40 ppi solid foam packings is lower than for 10 ppi

solid foam packings due to the lower characteristic length for mass transfer. This

Conclusions 53

characteristic length is difficult to define for gas-liquid mass transfer and is related

to the level of turbulence in the liquid phase.

• The intrinsic mass transfer coefficient, kL, for the 10 ppi solid foam packing is about

4 times higher than for the 40 ppi solid foam packing due to the higher turbulence

created in the liquid film as it flows over the surface. This higher turbulence is caused

by the larger strut size of the 10 ppi solid foam packing. In the co-current downflow

regime the intrinsic mass transfer coefficient is a factor 10 times smaller than in the

upflow configuration.

Chapter 5

Influence of liquid viscosity and surface

tension on the hydrodynamics and mass

transfer in co-current flow configurations

This chapter is accepted for publication as:

C.P. Stemmet, F. Bartelds, J. van der Schaaf, B.F.M. Kuster, J.C. Schouten, Gas-liquid mass

transfer coefficient for solid foam packings in co-current flow configurations: Influence of

liquid viscosity and surface tension, Chem. Eng. Res. Des., accepted (2008).

Abstract

The gas-liquid mass transfer coefficient and other hydrodynamic parameters such as liq-

uid holdup and frictional pressure drop are presented for gas and liquid moving in co-

current flow configurations (upflow and downflow) through solid foam packings of 10

and of 40 pores per linear inch (ppi). The effect of increasing the liquid viscosity on the

mass transfer coefficient in the co-current upflow configuration is quantified and corre-

lated to the frictional pressure drop, a measure of the frictional energy dissipation:

kLaGL εL(ScL/ScWater)0.69 = 2.05 × 10−4 P 0.8

f [SI units, m3L m−3

P s−1]

The gas-liquid mass transfer coefficient in the co-current downflow configuration is cor-

related to the liquid velocity and the Schmidt number using the correlation proposed by

Sherwood and Holloway (1940):


−1)1.16


P ]

The results for the gas-liquid mass transfer coefficient in the co-current upflow configu-

ration were correlated with a similar equation, where the influence of the gas velocity is

included, similar to the correlations for packed beds of spherical particles proposed in

Fukushima and Kusaka (1979):

kLaGL εLDL−1 = 311u0.44

G (uLρLµL−1)


P ]

In this study the liquid Schmidt number dependency of the gas-liquid mass transfer coef-

ficient points to the penetration theory describing the rate of mass transfer for gas-liquid

flow through solid foam packings.

56 Chapter 5

5.1 Introduction

The chemical industry uses multiphase reactors operating under a variety of physical

conditions (e.g., total pressure, aqueous or organic liquids) for reactions which include

Fischer-Tropsch synthesis, hydrogenation, oxidation, epoxidation, alkylation, etc. Hydro-

dynamic parameters and gas-liquid mass transfer under process conditions are important

for the design and operation of these reactors. Scaling rules for the design of these indus-

trial reactors are common but have to be evaluated especially when a different structure

is used as the catalyst support. The solid catalyst is usually in the form of pellets or pow-

ders. Hence, either slurry or fixed bed operations are commonly employed. The fixed bed

operation of catalytic reactors has received a lot of attention over the last few decades and

different packing structures have been proposed as a catalyst support. In Dudukovic et al.

(2002) a review of the correlations thus far developed to describe the hydrodynamics and

mass transfer for co-current upflow (flooded bed reactor) and downflow (trickle bed re-

actor) has been given. Bensetiti et al. (1997) use artificial neural networks to correlate the

liquid holdup with dimensionless numbers for packings with a voidage in the range of

0.37 to 0.47 for co-current upflow. Iliuta et al. (1999) correlate the gas-liquid mass transfer

coefficient for co-current downflow to dimensionless numbers also using artificial neural

networks. These correlations do not allow physical interpretation and because these cor-

relations are developed for dumped packing structures (spherical particles, Raschig rings,

Berl saddles, etc.) with a high solids holdup (0.3 to 0.6), large errors are possibly incurred

if applied to structured packings with low solids holdup (0.05 to 0.2). Structured pack-

ings commonly have a high voidage and are made to fit the dimensions of the reactor

(Mellapak, Katapak-S, monoliths, etc.). The main advantage of structured packings are

reduced pressure drop, better flow distribution and better gas-liquid contact. Solid foam

packing is a new type of structured packing considered for multiphase applications and is

available in a variety of materials (metal, carbon, ceramics) and pore sizes usually charac-

terized by pores per linear inch (or ppi). These solid foam packings, shown in Figure 1.4,

combine both the properties of high surface area and low solid holdup and are especially

suited for low pressure drop applications. In Chapter 3 and Chapter 4 the gas-liquid mass

transfer coefficient for solid foam packings of 10 and 40 ppi has been determined in the

co-current upflow and downflow configuration, respectively. This study investigated the

air-water gas-liquid system at low liquid viscosity. Two flow regimes (bubble and pulse)

were investigated in co-current upflow and in the co-current downflow configuration ex-

periments were performed in the trickle flow regime. Extrapolation of these results to

liquids with a different liquid viscosity or liquid surface tension may lead to large errors.

The wettability of the packing material also has an effect on the gas-liquid mass transfer

performance (Onda et al., 1968).

This study quantifies hydrodynamic parameters (frictional pressure drop and liquid

holdup) and the gas-liquid mass transfer coefficient for co-current two-phase flow through

Introduction 57

these solid foam packings for conditions when the viscosity of the liquid has been in-

creased. These parameters are quantified in the co-current upflow as well as in the co-

current downflow condition. The gas-liquid mass transfer coefficient is correlated to the

liquid and gas velocities, and to the frictional pressure drop. In the co-current downflow

configuration (trickle flow), the gas-liquid mass transfer is investigated for the case when

the liquid surface tension has been decreased.


The frictional pressure contribution in the co-current upflow configuration is obtained

from the total pressure drop by the following equation (Molga and Westerterp (1997)):

(

−dP

dz

)

Total

=(

ρG

εG

ε+ ρL

εL

ε

)

g︸︷︷︸

Static pressure drop

+Pf (5.1)

where Pf is the frictional pressure drop. The frictional pressure drop is described accord-

ing to the relative permeability model (Section 2.1.2, page 16) by the following equation:

Pf =εG

ε

(ε

εG

)h1(

AReG

GaG

+ BRe2

G

GaG

)

ρGg +εL

ε

(ε − ε0

L

εL − ε0L

)h2(

AReL

GaL

+ BRe2

L

GaL

)

ρLg (5.2)

where the factors A and B in Equation 5.2 are the viscous and inertial coefficients in the

Ergun equation for single phase flow, respectively. The values of h1 and h2 found in Sec-

tion 2.3.4 (page 24) were 4.43 and 1.88 for the solid foams. Using the definitions of the

Reynolds and Galileo numbers for the gas and liquid phases, and collecting the viscous

and inertial terms, yields the following equation for the frictional pressure drop:

Pf =

(

A (1 − ε)2

ε4d2e

)(

εG

(ε

εG

)h1

(uGµG) + εL

(ε − ε0

L

εL − ε0L

)h2

(uLµL)

)

· · ·

· · ·+(

B(1 − ε)

ε4de

)(

εG

(ε

εG

)h1 (u2

GρG

)+ εL

(ε − ε0

L

εL − ε0L

)h2 (u2

LρL

)

)

(5.3)

In the equation above the characteristic length, de, used to describe the solid foam

packing is the length of a strut, determined using the unit cell model of Fourie and Plessis

(2002). Here it is assumed that the unit cell making up the solid foam packing is described

by a tetrakaidecahedron, given in Figure 1.8. In Section 2.3.4 (page 24) the analysis of

holdup data showed that viscous effects are small, leading only to the inertial term being

important for the frictional pressure drop. This second term on the right hand side of

Equation 5.3 is used to calculate the experimental frictional pressure drop data using this

model.

58 Chapter 5


The gas-liquid mass transfer coefficient (kLaGL) is determined by the intrinsic mass trans-

fer coefficient, kL, and the gas-liquid interfacial area (aGL). This area is usually a function

of the specific geometric surface area of the packing (given in Figure 1.11a for the solid

foam packings using the model of Fourie and Plessis (2002)) and of the liquid holdup. The

values of kL and aGL are also affected by the physical properties of the gas-liquid system

that affect the diffusion coefficient of the gas component in the liquid, and the velocities

of the gas and the liquid affecting the gas and liquid holdup, and the solids holdup. In

general the gas-liquid mass transfer coefficient is described by the penetration model:

kL = 2

√DL

πte(5.4)

where te is an assumed exposure time. In Kasturi and Stepanek (1974) the analogy be-

tween momentum and mass transfer is used to describe the rate of momentum transfer at

the gas-liquid interface, given by the following equation:

τi = 2ρLuL

√µL

ρLπte(5.5)

Equations 5.4 and 5.5 combine to give the following relationship between intrinsic mass

and momentum transfer:

kL =τi

uL

√

DL

ρLµL

(5.6)

According to Tomida et al. (1975) the shear stress at the gas-liquid interface, τi, is a

measure of the frictional pressure drop and hence also depends on the holdup and veloc-

ities of the gas and liquid phases, see Equation 5.2. The correlations thus far developed

for co-current flow can be divided into two categories where the gas-liquid mass transfer

is related either to the gas and liquid velocities and the liquid properties, see Sherwood

and Holloway (1940), or to the frictional pressure drop, commonly referred to as the en-

ergy dissipation rate. A summary for Raschig rings, Berl saddles, and spherical particles

can be found in Morsi (1989) and Midoux et al. (1984) for co-current downflow. The co-

current upflow regime in general has received less attention in literature. Specchia et al.

(1974) studied spherical particles, Berl saddles, and ceramic rings, and Molga and Westert-

erp (1997) studied glass spheres as the packing structures. In general the gas-liquid mass

transfer coefficient for co-current flow is correlated using the rate of energy dissipation

(Fukushima and Kusaka (1979) being the exception, where 1

2and 1-inch ceramic spheres

were studied).

Introduction 59

Sherwood correlation

Sherwood and Holloway (1940) have presented their results for the mass transfer coeffi-

cient in the following form:

Co-current downflow:

(kLaGL εL

DL

)

= α

(uLρL

µL

)n

(ScL)0.5 (5.7)

where α and n are constants that characterize the packing. This correlation was developed

for co-current downflow where the gas velocity has little influence on the mass transfer.

The exponent on the liquid Schmidt number as given in Sherwood and Holloway (1940) is

found experimentally to be approximately the value described by the penetration theory,

a value of 0.5. However, to check the assumption, the liquid Schmidt number is varied by

increasing the liquid viscosity.

The mass transfer coefficient for co-current upflow also increases with gas velocity, and

the following correlation is proposed (similar to the approach of Fukushima and Kusaka

(1979)):

Co-current upflow:

(kLaGL εL

DL

)

= γ

(uLρL

µL

)n1

(uG)n2 (ScL)0.5 (5.8)

Also here the exponent on the Schmidt number is assumed to be 0.5, but this will be

checked using liquids with different Schmidt numbers by increasing the liquid viscosity.

Energy dissipation

The energy dissipation in single phase systems is obtained from the following mechanical

energy balance:

1

ρ

(dP

dz

)

+ vdv

dz+ g +

dF

dz= 0 (5.9)

where v is the intersticial velocity, and F is the frictional energy loss per unit mass. For

gas-liquid flow this is extended for each phase and the equations describing the frictional

energy loss is recognized as including changes in internal energy, U , work done between

phases, w, and heat transferred between phases, q, and are given by the following equa-

tions:

dFG

dz=

dUG

dz+

1

WG

dw

dz+

1

WG

dq

dz(5.10)

dFL

dz=

dUL

dz− 1

WL

dw

dz− 1

WL

dq

dz(5.11)

where WL and WG are the weighting factors of the gas and liquid phase contributions to

the overall energy balance. These weighting factors are described in Isbin and Su (1961) as

60 Chapter 5

the mass of phase in the differential volume, dz, given by WG = ρGεGdz and WL = ρLεLdz,

respectively. This analysis results in the following overall energy balance:

ε

(dP

dz

)

+ ρGεGvG

dvG

dz+ ρLεLvL

dvL

dz+ g (ρGεG + ρLεL) + · · ·

· · · + εGρG

(dUG

dz

)

+ εLρL

(dUL

dz

)

︸︷︷︸

Frictional energy dissipation

= 0 (5.12)

For assumptions of uniform intersticial velocity throughout the column and using the

definition of the frictional pressure drop (Equation 5.1), the frictional energy dissipation,

EGL, is given by:

EGL = g(

ρG

εG

ε+ ρL

εL

ε

)

+

(dP

dz

)

= −Pf (5.13)

However, Vohr (1962) and Lamb and White (1962) combine Equations 5.9 to 5.11 by

weighting each equation by the mass flow rate (WG = uGρG and WL = uLρL, with veloci-

ties based on the void volume), resulting in the frictional energy dissipation described by

the following equation:

EGL = (ρGuG + ρLuL) g + uG

(dP

dz

)

+ uL

(dP

dz

)

(5.14)

The equation above has widely been used (see Midoux et al. (1984) and Charpen-

tier (1976) for co-current downflow, and Specchia et al. (1974) and Molga and Westerterp

(1997) for co-current upflow) as the rate of energy dissipation to correlate this to the gas-

liquid mass transfer coefficient. It is conveniently independent from the holdup of the gas

and liquid phases which are quantities difficult to measure, and can be evaluated from

two-phase pressure drop measurements. However, Equation 5.14 is only valid for a no-

slip condition (i.e. vG = vL or uG/εG = uL/εL), which is rarely the case for two-phase flow,

and thus in general can not be used, see Isbin and Su (1961).

Charpentier (1976) gives an overview of the correlations developed for co-current

downflow through spheres, Raschig rings, Berl saddles, pall rings and pellets, correlat-

ing the gas-liquid mass transfer coefficient, kLaGLεL, to the gas and liquid velocities or

a group of parameters described as the rate of energy dissipation. In these correlations,

however, the correlating group to describe the energy dissipation is not consistent and

usually a combination of the two-phase pressure drop and superficial velocity, PTotaluL,

and in many cases the gravity terms in Equation 5.14 are ignored. Hirose et al. (1974) use

PTotaluLε−1

L as the energy delivered to the liquid to correlate the mass transfer coefficient

Introduction 61

for co-current downflow by the following equation:

Co-current downflow:

kLaGL εL

ε= β

(uG

ε

)m1

(

PTotal

uL

εL

)m2

(5.15)

with β, m1 and m2 constants that characterize the packing. In co-current downflow the

liquid holdup is low giving PTotal ≈ Pf . However, in co-current upflow the liquid holdup

is high and the static pressure drop provides a large contribution to the total pressure

drop. In Section 3.3.4 a similar correlation is developed for the gas-liquid mass transfer

per unit of reactor volume, kLaGLεL, correlated to PfuLε−1

L , as described by the following

equation:

Co-current upflow:

kLaGL εL = 0.0134

(

Pf

uL

εL

)0.44

(5.16)

In the case of co-current upflow of the gas and the liquid, the dependency on the gas

velocity was found to be negligible with changes in the frictional pressure drop and the

liquid holdup accounting for changes in the mass transfer coefficient, m1 = 0. However,

in view of Equation 5.13, the group to correlate the gas-liquid mass transfer should be the

frictional pressure drop, Pf , as this is the energy dissipated per unit volume of reactor and

thus the following correlation is proposed to compare different packing materials:

Co-current upflow:

kLaGLεL = c1 (Pf )c2 (5.17)

Tomida et al. (1975) find that (µwater/µL)1.7 corrects the mass transfer coefficient depen-

dency on the energy dissipated in the liquid when the liquid viscosity has been increased.

However, in this study a Schmidt number proportionality, (ScL/Scwater), similar to Equa-

tion 5.7, is used to account for changes in the liquid viscosity.

Effect of liquid surface tension

The number of studies that deal with the influence of the liquid surface tension on the

gas-liquid mass transfer coefficient are relatively low in comparison to the effects of the

surface tension has on the overall mass transfer coefficient. In co-current flow the gas

moves through the column either in the form of bubbles or pulses (up-flow) or in the form

of the continuous phase, the liquid film flowing over the packing surface due to gravity

(trickle flow) and hence different mechanisms are expected to affect the gas-liquid mass

transfer when the liquid surface tension is decreased.

In an upflow bubble column the lower liquid surface tension enhances the formation

62 Chapter 5

of small bubbles and hence increases the surface area for mass transfer. In a trickle system

two factors, see Francis and Berg (1967), are to be considered:

• the liquid forms a stable film around the solid surface;

• a mechanism of film rupture which depends on the mass transfer of a low surface

tension component into the liquid phase from the gas (a mechanism typically found

in distillation).

The first factor is satisfied if the difference in the surface energies of the gas-solid and

liquid-solid interfaces exceeds that of the gas-liquid interface (surface tension of the liq-

uid), which for most packing materials (with high surface energies) is the case, especially

when dealing with organic liquids (typically low surface tension liquids). The second

mechanism relates to the mass transfer of low surface tension components which may

cause rupture of the film surface, observed by Zuiderweg and Harmens (1958), which re-

sults in higher rates of refreshment due to formation of rivulets or droplets and hence a

higher intrinsic mass transfer. For trickle beds, Onda et al. (1968) found an increase in the

wetted surface area and thus an increase in the gas-liquid mass transfer coefficient with

decreasing liquid surface tension. No influence on the value of the intrinsic mass transfer

coefficient, kL, is described. The influence of the liquid surface tension on the wetted area

is described by Onda et al. (1968) by the following equation:

aGL

aP

= 1 − exp(−1.45 (σc/σL)0.75 Re0.1

L Fr−0.05L We0.2

L

)(5.18)

where aP is the surface area of the packing, σc (33-75 mN m−1, Sinnot (1999)) is a parame-

ter relating to the surface energy of the packing material, σL is the liquid surface tension,

and ReL, FrL and WeL are the Reynolds, Froude and Weber numbers of the liquid, re-

spectively. The equation above gives a maximum value of the gas-liquid area equal to the

surface area of the packing, which for solid foam packings is not necessarily the case. The

gas-liquid area increases as the liquid holdup increases, see Figure 1.11a with εS replaced

by (εL + εS). This estimate of the gas-liquid area, aGL, is used to describe the difference in

the gas-liquid mass transfer coefficient when the liquid surface tension is reduced. As in

Onda et al. (1968) the assumption of no influence on the intrinsic mass transfer coefficient,

kL, is made.

5.2 Experimental

The solid foam packings used in this study are commercially available from ERG Aerospace

Corp and made of aluminum with a voidage of 93%. These foams were placed in a semi

2-dimensional column with varying height; either 30, 60, or 90 cm high with cross sec-

tion 30 cm by 1 cm, shown schematically in Figure 3.1 (page 34) for the co-current upflow

Experimental 63

configuration. The co-current downflow experiments were performed in the same setup

with the inlet and outlet positions exchanged (Figure 4.1, page 48). The gas-liquid mass

transfer coefficient was measured using the method of oxygen desorption by measuring

dissolved oxygen concentrations at the liquid inlet and outlet (InPro 6800 oxygen sensors

Mettler Toledo). The liquid holdup and the frictional pressure drop were measured in the

co-current upflow regimes as in Section 3.2, page 33, and a similar procedure was followed

to determine the liquid holdup for the co-current downflow regime (Section 4.2, page 47).

Mainly the trickle flow regime was observed, but pulse flow was observed for superficial

gas velocities higher than 0.7 m s−1. The static liquid holdup was measured using the

drainage method (Section 2.2, page 17) and results are summarized in Table 5.1.

Table 5.1: Static liquid holdup and static film area for the solid foam packings (aluminum) and forthe low and high viscosity liquids.

Static liquid Static film

µL σL holdup, ε0L areaa

ppi [mPa s] [10−3 N m−1] [m3L m−3

P ] [m2GL m−3

P ]

10 0.80 72.8 0.094 1502

10 2.0 72.0 0.074 1430

10 0.80 56.2 0.057 1364

40 0.80 72.8 0.115 6282

40 2.0 72.0 0.098 6061

40 0.80 56.2 0.098 6061

a Determined using the unit cell model of Fourie and Plessis (2002) with thesolid holdup, εS, as given in Figure 1.11a, replaced by (εS + ε0

L).

The physical properties of the liquid solutions were measured from samples taken

from the column. The liquid viscosity, µL, was increased by the addition of glycerol

(99.5% pure from Merck, Germany) and measured using a Ubbelohde viscometer (Schott

Gerate AVS310) at 30◦C; all solutions (water, 30v% glycerol and 5v% isopropanol) used

were Newtonian fluids. The liquid surface tension was determined using a bubble ten-

siometer (Sensadyne). The physical constants of the liquid determined are summarized in

Table 5.2.

Co-current upflow was used to evaluate the influence of increasing the liquid viscosity

and co-current downflow was used to evaluate the effect of changes in the liquid viscosity

and the liquid surface tension. In co-current upflow the experiments for changes in the

liquid surface tension resulted in depletion of the liquid for a 30 cm column because of the

high rate of gas-liquid mass transfer. Consequently the mass transfer coefficient could not

be calculated from a comparison between 30 cm and 60 cm of packing material.

64 Chapter 5

Table 5.2: Overview of the experiments performed for determining the gas-liquid mass transfercoefficient, kLaGL, the liquid holdup, εL, and the frictional pressure drop, Pf , in the range of gasvelocities (uG = 0.1 - 0.8 m s−1) for 10 and 40 ppi solid foam packings.

Air Air Air

Water 30v% Glycerol 5v% Propanol

σL [10−3 N m−1] 72.8 72.0 56.2

µL [mPa s] 0.80 2.0 0.83

DLa [10−9m2 s−1] 2.75 1.14 2.64

ρL [kg m−3] 996 1068 992

Hb [m3L Pa mol−1] 85628 82203 85628

a Determined using a correlation (Wilke and Chang, 1955).b H = kH

101.325, where kH = kθ

H · exp(−∆solnH

R

(1

T− 1

T θ

))with the constants kθ

H and−∆solnH

Rfrom http://webbook/nist/gov/chemistry.


5.3.1 Co-current upflow - Effect of liquid viscosity

Liquid Holdup

In Figure 5.1 the liquid holdup is given for 10 and 40 ppi solid foam packings for the

experiments where the liquid viscosity has been increased from 0.8 to 2.0 mPa s−1. An

increase in the gas velocity increases the gas holdup and decreases the liquid holdup. At

a gas velocity of 0.3 m s−1 a transition from the bubble to the pulse regime is observed;

liquid and gas slugs alternately move through the solid foam packing. The velocity of

the gas bubbles increases with increasing liquid velocity. This results in an increase in the

liquid holdup. Due to the open structure of the solid foam packings the liquid holdup for

the 10 and 40 ppi solid foam packings are similar, increasing slightly as the ppi number of

the solid foam packing increases due to higher static liquid holdup for 40 ppi solid foam

packing, see Table 5.1. Increasing the liquid viscosity from 0.8 to 2 mPa s results in a slight

increase in the liquid holdup. This increase in liquid holdup is more pronounced in the

10 ppi solid foam packing. This is not a result of an increased static liquid holdup which

decreases with increasing liquid viscosity, see Table 5.1. This is possibly a result of the

higher wetting of the packing material, resulting in more effective drainage of the solid

foam packing.

In Section 2.3.4, page 24 the relative permeability model (Saez and Carbonell (1985))

is used to describe the liquid holdup, εL (= ε − εG), in the counter-current operation as an

implicit function of gas and liquid velocities and four parameters, A, B, h1, and h2, also

used to describe the frictional pressure in Equation 5.3. It was found that the effect of the

viscous term associated with A in the description of the drag forces of the gas and liquid

phases is negligible. Extending this to the co-current flow gives Equation 5.19 with uG and


0 0.2 0.4 0.6 0.8 10.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


Gas velocity, uG

[m s−1

]

Liq

uid

hold

up, ε

L [

mL3 m

P−3]

(a) 10 ppi

0.02 m s -1

0.04 m s -1

u L

L = 0.8

mPa s -1

L = 2.0

mPa s -1

µ µ

0 0.2 0.4 0.6 0.8 10.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


Gas velocity, uG

[m s−1

]

Liq

uid

hold

up, ε

L [

mL3 m

P−3]

(b) 40 ppi

0.02 m s -1

0.04 m s -1

u L

L = 0.8

mPa s -1

L = 2.0

mPa s -1

µ µ

Figure 5.1: Liquid holdup, εL, for (a) 10 ppi and (b) 40 ppi solid foam packings in the co-currentupflow configuration at different liquid viscosities, µL.

uL giving the flow direction (upflow is in the positive direction).

(B(1 − ε)

ε3de

)((ε

εG

)h1 (u2

GρG

)(

uG

|uG|

)

−(

ε − ε0

L

εL − ε0L

)h2 (u2

LρL

)(

uL

|uL|

))

+ · · ·

· · ·+ ρGg − ρLg = 0 (5.19)

In Figure 5.2 the experimental liquid holdup for 40 ppi solid foam packing and for

the air-water system are compared to the predictions of this model. The liquid holdup is

slightly overestimated by the model. The effect of liquid viscosity on liquid holdup from

this model is minor (viscous term in the description of the drag force has minor influence)

and the increase in the liquid holdup associated with an increase in liquid viscosity is

likely due to an increase in the liquid density from 996 to 1068 kg m−3, see Equation 5.19.

Pressure Drop

The results for the frictional pressure drop per unit height of packing are shown in Figure

5.3. The frictional pressure drop increases with increasing liquid viscosity in both the 10

and 40 ppi solid foam packings. The increase in frictional pressure drop with higher liquid

viscosity is higher in the 40 ppi solid foam, especially at higher liquid velocities. This is

possibly due to the larger wetted surface area and the higher number of struts restricting

the flow path of the liquid and gas when compared to the 10 ppi solid foam packing. In

Section 2.3.4 (page 24) it was determined that the contributions to the frictional pressure

66 Chapter 5

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

uG

[m s−1

]

uL = 0.02 m s

−1

uL = 0.04 m s

−1

Figure 5.2: Experimental liquid holdup for the 40 ppi solid foam packing in co-current upflowcompared to the relative permeability model, Saez and Carbonell (1985), using the parameters (A,B, h1 and h2) found for countercurrent flow. The model predictions are given by the continuouslines for the case of uL = 0.02 m s−1 (· · · ) and uL = 0.04 m s−1 (− · −).

0 0.2 0.4 0.6 0.8 10

50

100

150

200


Gas velocity, uG

[m s−1

]

Fri

ctio

nal

pre

ssure

dro

p, P

f [10

2 P

a m

−1]

(a) 10 ppi

0.02 m s -1

0.04 m s -1

u L

L = 0.8

mPa s -1

L = 2.0

mPa s -1

µ µ

0 0.2 0.4 0.6 0.8 10

50

100

150

200


Gas velocity, uG

[m s−1

]

Fri

ctio

nal

pre

ssure

dro

p,P

f [10

2 P

a m

−1]

(b) 40 ppi

0.02 m s -1

0.04 m s -1

u L

L = 0.8

mPa s -1

L = 2.0

mPa s -1

µ µ

Figure 5.3: Frictional pressure drop, Pf , for (a) 10 ppi and (b) 40 ppi solid foam packings in theco-current upflow configuration at different liquid viscosities, µL.


drop are largely from the inertial terms, (BRe2/Ga), thus:

Pf =

(B(1 − ε)

ε4de

)

F inertialf

︷︸︸︷(

εG

(ε

εG

)h1 (u2

GρG

)+ εL

(ε − ε0

L

εL − ε0

L

)h2 (u2

LρL

)

)

(5.20)

The results have been presented in Figure 5.4 according to Equation 5.20. The results

indicate that, as in Section 2.3.4, the frictional pressure drop is largely determined by the

inertial forces. The difference in the liquid density (1068 kg m−3 compared to 996 kg m−3)

is the cause of the increase in the frictional pressure drop measured. The values of B (16.0

for 10 ppi and 4.27 for 40 ppi solid foam packings) are in the range of expected values

determined in Section 2.3.4, page 24.

0 2 4 6 8 100

50

100

150

200

Ff

inertial

Fri

ctio

nal

pre

ssure

dro

p, P

f [10

2 P

a m

−1]

(a) 10 ppi, de = 1.5 mm , B ≈ 16.0

0.02 m s -1

0.04 m s -1

u L

L = 0.8

mPa s -1

L = 2.0

mPa s -1

µ µ

0 2 4 6 8 100

50

100

150

200

Ff

inertial

Fri

ctio

nal

pre

ssure

dro

p, P

f [10

2 P

a m

−1]

(b) 40 ppi, de = 0.38 mm , B ≈ 4.27

0.02 m s -1

0.04 m s -1

u L

L = 0.8

mPa s -1

L = 2.0

mPa s -1

µ µ

Figure 5.4: Experimental pressure drop, Pf , for aluminium foam packings in the co-current upflowconfiguration according to Equation 5.20. The slope of the line is the value of B(1 − ε)/(ε4de).

Gas-liquid mass transfer coefficient

Figure 5.5a gives the gas-liquid mass transfer coefficient for an increase in the liquid vis-

cosity with the change in the diffusion coefficient of oxygen taken into account. It is clear

in Figure 5.5a that the mass transfer coefficient per unit of reactor volume increases with

increasing gas and liquid velocity and decreases with increasing liquid viscosity, as de-

scribed by Equation 5.8. The results were correlated using this equation and the parity

plot is given in Figure 5.5b. The correlating parameter values of γ, n1 and n2 were found

to be 311 ± 35, 0.92 ± 0.10 and 0.44 ± 0.06, respectively.

(kLaGL εL

DL

)

= 311(uG)0.44

(uLρL

µL

)0.92

(ScL)0.5 (5.21)

68 Chapter 5

The 10 and 40 ppi solid foam packings have similar kLaGLεL and mass transfer coefficients

are both described by Equation 5.21. This similarity in the obtained mass transfer coeffi-

cients, even though the geometric surface area of the solid foam packing increases fourfold

(1080 m2 m−3 for 10 ppi and 4300 m2 m−3 for 40 ppi solid foam packing), is ascribed to

a decrease in the local velocity of the liquid with more tightly packed struts (smaller ppi

number of solid foam packings). The main contribution to the decrease in mass transfer is

the decrease in diffusion coefficient. The changes in the liquid viscosity and liquid diffu-

sion coefficient were best described by the liquid Schmidt number, (ScL)0.5. This indicates

that penetration theory describes the rate of mass transfer in co-current upflow.

0 5 10 15 200

0.05

0.1

0.15

0.2

uG

ScL

0.5 [m s

−1]

kLa G

L ε

L D

L−1 [

10

9 m

L m

−3

P]

(a) kLaGLεL

0.02 m s -1


0.04 m s -1

u L

L = 0.8

mPa s -1

L = 2.0

mPa s -1

µ µ

0 0.02 0.04 0.06 0.08 0.1 0.12 0.140

0.02

0.04

0.06

0.08

0.1

0.12

0.14

−20%

+20%

kLaGLεL

DL= 311 u

0.44G

(uLρL

µL

)0.92

Sc0.5L

kLa

GL ε

L D

L

−1 Model [10

9 m

L m

−3

P]

kLa G

L ε

L D

L−1 E

xper

imen

tal

[10

9 m

L m

−3

P]

(b) Parity plot

0.02 m s -1


0.04 m s -1

u L

L = 0.8

mPa s -1

L = 2.0

mPa s -1

µ µ

Figure 5.5: (a) Mass transfer coefficient per unit of reactor volume, kLaGL εL, for solid foam pack-ings in the co-current upflow configuration at different liquid viscosities, µL. (b) Parity plot wherekLaGLεL is modeled using the correlation proposed by Sherwood and Holloway (1940) as given inEquation 5.8.

Energy dissipation

Figure 5.6b shows the gas-liquid mass transfer coefficient per unit reactor volume plotted

against the frictional energy dissipation term (PfuLε−1

L ) as described by Equation 5.15. The

values found for the correlating parameters were the same as the air-water system (Section

3.3.4): β = 0.0134 ± 0.0073, m1 = 0, and m2 = 0.44 ± 0.077. In Figure 5.6b the frictional

pressure drop, Pf , is used to correlate the mass transfer coefficient according to Equation

5.13. The coefficients c1 and c2 are 2.05 x 10−4 and 0.8, respectively.

kLaGL εL

(ScL

ScWater

)0.69

= 2.05 × 10−4 (Pf)0.8 (5.22)


This shows that both these parameters, PfuLε−1

L and Pf , may be used to correlate the

gas-liquid mass transfer coefficient and a term of the form (ScL/ScWater)0.5−0.7 corrects for

the lower gas-liquid mass transfer with an increase in the liquid viscosity. The frictional

pressure drop, Pf , which is shown to be related to the energy dissipated in the gas-liquid

system, correlates to the gas-liquid mass transfer, kLaGLεL, with a factor of 0.8. This fac-

tor indicates the energy efficiency achieved within the co-current gas-liquid system and

upholds the analogy between momentum and mass transfer. The parameter, PfuLε−1

L (or

other forms of this parameter, see Equation 5.14), described as the rate of energy dissi-

pation should no longer be used as it assumes a no-slip condition, which for gas-liquid

systems is rarely the case.

101

102

103

104

105

10−2

10−1

100

101

kLaGL εL

(ScL

ScW ater

)0.54

= 0.0134 · (Pf uL

εL)0.44

kLa G

L ε

L (

Sc L

/ S

c Wat

er)0

.54 [

m3 L m

−3

P s

−1]

Pf u

L ε

L

−1 [W m

P

−3]

0.02 m s -1


0.04 m s -1

u L

L = 0.8

mPa s -1

L = 2.0

mPa s -1

µ µ

(a) PfuLε−1

L

102

103

104

105

106

10−2

10−1

100

101

kLaGL εL

(ScL

ScWater

)0.69

= 0.000205 · (Pf )0.8

kLa G

L ε

L (

Sc L

/ S

c Wat

er)0

.69 [

m3 L m

−3

P s

−1]

Pf [J m

P

−4]

0.02 m s -1


0.04 m s -1

u L

L = 0.8

mPa s -1

L = 2.0

mPa s -1

µ µ

(b) Pf

Figure 5.6: Correlation of the mass transfer coefficient for 10 and 40 ppi solid foam packings. In(a) the correlating parameter PfuLε−1

L , as given in Equation 5.16 is used and in (b) the frictionalpressure drop, Pf , as given by Equation 5.13, is used. These are compared to packed micro-reactors(⋆), a packed bed of 6mm spherical particles (+), and monoliths (⊕).

In Figures 5.6a and 5.6b a comparison is made with a packed bed micro-reactor, a

packed bed of spherical particles (6 mm) operated in co-current upflow, and a monolith

(from Losey et al. (2001), Specchia et al. (1974), and Kreutzer et al. (2005), respectively). In

Kreutzer et al. (2005) and Losey et al. (2001) no solids holdup was given and an estimate

of 0.6 was made for packed beds and 0.15 for monoliths (1.5 mm diameter channels with

0.1 mm walls) was used. This comparison shows that the correlation as developed also

correlates the gas-liquid mass transfer coefficient for these other packing materials. This

indicates the general applicability of the correlations proposed as the energy dissipated is

related per unit volume of the packing material and not only the volume of the liquid.

70 Chapter 5

5.3.2 Co-current downflow - Effect of liquid viscosity

Liquid Holdup

Figure 5.7 gives the results for the liquid holdup for the 10 and 40 ppi solid foam packings.

The liquid holdup increases with increasing liquid velocity and decreases with increasing

gas velocity due to acceleration of the liquid film flowing down the solid foam packing.

The liquid holdup increases as the ppi number of the solid foam packing increases due

to the larger number of struts that restrict the flow of the liquid and because of higher

static liquid holdup, see Table 5.1. Increasing the liquid viscosity decreases the liquid

holdup compared at similar gas and liquid velocities. In the air-water system channeling

of the packing was observed in the solid foam packings at the higher air-water velocities.

Channeling is when the liquid film flowing down the packing coalesces to form a liquid

channel thereby decreasing the contact between the gas and liquid phases. The degree of

wetting of the packing was increased with an increase in the liquid viscosity (as observed

by Mangers and Ponter (1980)), which avoided channeling. Also the lower static liquid

holdup for an increase in the liquid viscosity and more interaction between the gas and

liquid gives rise to the lower liquid holdup measured.

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

Gas velocity, uG

[m s−1

]

Liq

uid

hold

up, ε

L [

mL3 m

P−3]

(a) 10 ppi

0.02 m s -1

0.04 m s -1

u L

L = 0.8

mPa s -1

L = 2.0

mPa s -1

µ µ

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

Gas velocity, uG

[m s−1

]

Liq

uid

hold

up, ε

L [

mL3 m

P−3]

(b) 40 ppi

0.02 m s -1

0.04 m s -1

u L

L = 0.8

mPa s -1

L = 2.0

mPa s -1

µ µ

Figure 5.7: Liquid holdup, εL, for (a) 10 ppi and (b) 40 ppi solid foam packings in the co-currentdownflow configuration at different liquid viscosities, µL.


Figure 5.8 shows the results for the gas-liquid mass transfer coefficient per unit of reac-

tor volume in co-current downflow. The gas-liquid mass transfer coefficient for the 10

ppi solid foam packings increases as the liquid velocity increases and remains relatively

constant in the trickle flow regime with increasing gas velocity. In the pulsing regime

(uG larger than 0.7 m s −1) the mass transfer coefficient significantly increases due to the


refreshment of the liquid on the solid foam surface with passing liquid pulses. Increas-

ing the liquid viscosity for the 10 ppi solid foam packing decreases the gas-liquid mass

transfer coefficient due to a decrease in the diffusivity of the gas species. Results for the

gas-liquid mass transfer coefficient for the 40 ppi solid foam packing are more difficult

to interpret as the gas-liquid mass transfer increases with increasing viscosity. A similar

effect was observed by Mangers and Ponter (1980) and is ascribed to the increase in the

wetting of the packing with an increase in the liquid viscosity using glycerol, possibly

with the added effect of less channeling. At the lower liquid viscosity the gas-liquid mass

transfer coefficient for 40 ppi solid foam packing is constant for increasing gas velocity

and lower than 10 ppi solid foam packing, possibly a result of a lower level of turbulence

caused in the liquid film by the smaller strut thickness, dm, of the solid foam, given in

Figure 1.8 (0.55 mm for 10 ppi compared to 0.07 mm for 40 ppi solid foam packing). In-

creasing the liquid viscosity increases the wetting of the packing and thus the geometric

area of the packing used for gas-liquid mass transfer and higher gas-liquid mass transfer

coefficients are observed.

0 0.2 0.4 0.6 0.8 10

0.05

0.1

0.15

Gas velocity, uG

[m s−1

]

kLa G

L ε

L [

m3 L m

P−3 s

−1]

(a) 10 ppi

0.02 m s -1

0.04 m s -1

u L

L = 0.8

mPa s -1

L = 2.0

mPa s -1

µ µ

0 0.2 0.4 0.6 0.8 10

0.05

0.1

0.15

Gas velocity, uG

[m s−1

]

kLa G

L ε

L [

m3 L m

P−3 s

−1]

(b) 40 ppi

0.02 m s -1

0.04 m s -1

u L

L = 0.8

mPa s -1

L = 2.0

mPa s -1

µ µ

Figure 5.8: Mass transfer coefficient per unit of reactor volume, kLaGLεL, for (a) 10 ppi and (b) 40ppi solid foam packings in the co-current downflow configuration at different liquid viscosities, µL.The circles (©) indicate experiments where slug flow was observed.

In Figure 5.9 the gas-liquid mass transfer coefficient per unit of reactor volume is cor-

related to the liquid velocity described by Equation 5.7 for the 10 ppi solid foam packing.

The values of the correlating parameters α and n were found to be 3.7 and 1.16, respec-

tively.

kLaGL εL

DL

= 3.7

(uLρL

µL

)1.16

(ScL)0.5 (5.23)

72 Chapter 5

0 0.005 0.01 0.015 0.02 0.025 0.03 0.0350

0.005

0.01

0.015

0.02

0.025

0.03

0.035

−20%

+20%

10 ppi :kLaGL εL

DL= 3.7

(uLρL

µL

)1.16

Sc0.5L

kLa

GL ε

L D

L

−1 Model [10

9 m

L m

P

−3]

kLa G

L ε

L D

L−1 E

xper

imen

tal

[10

9 m

L m

P−3]

0.05 m s -1

0.04 m s -1

0.02 m s -1

0.03 m s -1

u L

L = 0.8

mPa s -1

L = 2.0

mPa s -1

µµ

Figure 5.9: Parity plot of the correlation of kLaGLεL with superficial liquid velocity, as describedin Equation 5.7, is given for 10 ppi solid foam packings.

As in co-current upflow the value of (ScL)0.5 corrects the decrease in the mass transfer

coefficient due to the increase in the liquid viscosity and decrease in the diffusion coef-

ficient of the gas species in the liquid. This indicates that also in co-current downflow

penetration theory describes the rate of gas-liquid mass transfer.

5.3.3 Co-current downflow - Effect of liquid surface tension

Liquid holdup

The liquid holdup found experimentally for co-current downflow when decreasing the

liquid surface tension using isopropanol is given in Figure 5.10a for the trickle flow regime.

The liquid is spread more evenly over the packing by the lower surface tension and the

formation of tiny bubbles in the liquid film cause the liquid holdup for zero gas velocity

to be higher. Increasing the gas velocity decreases the liquid holdup, as observed for the

air-water system, Section 4.3.1 (page 49). This is expected because the forces between the

gas and liquid are not dependent on the surface tension of the liquid, see Equation 5.19.


In Figure 5.10b the gas-liquid mass transfer coefficient is plotted against the gas veloc-

ity for different liquid velocities. It is independent of the gas velocity (as found for the

air-water and air-water-glycerol cases) and increases with increasing liquid velocity. The

influence of the decrease in the surface tension of the liquid is that the gas-liquid mass

transfer coefficient increases by a factor 6. This increase is assumed due to an increase

in the available gas-liquid interfacial area for mass transfer and not as a result of an in-

crease in the intrinsic mass transfer coefficient, kL (Onda et al., 1968). However, the liquid

holdup has remained relatively the same for the air-water and air-water-isopropanol sys-


0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

Gas velocity, uG

[m s−1

]

Liq

uid

hold

up, ε

L [

mL3 m

P−3]

(a) Liquid holdup, εL

0.04 m s -1

0.02 m s -1

u L

L = 72

mN m -1

L = 56

mN m -1

µµ

0 0.2 0.4 0.6 0.8 10

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Gas velocity, uG

[m s−1

]

kLa G

L ε

L [

m3 L m

P−3 s

−1]

(b) kLaGLεL

0.04 m s -1

0.02 m s -1

u L

L = 72

mN m -1

L = 56

mN m -1

µµ

Figure 5.10: (a) Liquid holdup, εL, and (b) Mass transfer coefficient per unit of reactor volume,kLaGLεL, for 10 ppi solid foam packings in the co-current downflow configuration at differentliquid surface tensions, σL. The circles (©) indicate experiments where slug flow was observed,here only for the uL = 0.04 m s−1 case.

tems, see Figure 5.10a, the increase is unlikely to be due to an increase in the surface

area due to liquid holdup effects. Adding isopropanol to water in small concentrations (5

v/v%) decreases the liquid surface tension but also induces the formation of tiny bubbles

(observed visually) in the liquid flowing down the solid foam surface giving the liquid

film an opaque appearance. A similar observation of drastic reduction in bubble size was

made by Hu et al. (2006) for a stirred tank reactor. These tiny bubbles (estimated in the

range of 0.05 - 0.15 mm in diameter) increase the gas-liquid area for mass transfer. An

estimate of the contribution to the gas-liquid mass transfer area and the volume of these

tiny bubbles is made for the 10 ppi solid foam packings (uL = 0.04 m s−1). If it is assumed

for the air-water case that the area for mass transfer is the geometric surface area for a

solid foam packing with increased solids holdup, εS + εL ≈ 0.3, see Figure 1.11a, the gas-

liquid area is approximately 1900 m2GL m−3

P . The difference in the gas-liquid mass transfer

area between the air-water and air-water-propanol system is thus about 9000 m2

GL m−3

P .

This area can be achieved assuming an average bubble diameter of 0.1 mm (dbubble) at a

gas holdup half of the liquid holdup, a value of 0.15 m3

G m−3

P (aGLεL = 6εG/dbubble). This

estimate indicates that the liquid film flowing over the solid surface consist for about 30%

by volume of these tiny bubbles. The use of isopropanol to decrease the surface tension of

the liquid in the trickle flow regime does not give a clear indication of the effect of liquid

surface tension on the gas-liquid mass transfer. The effects observed are a combination of

the reduction of surface tension and the formation of tiny bubbles flowing with the liq-

uid film down the packing which enhances the gas-liquid mass transfer by creating larger

gas-liquid mass transfer area. In Larachi et al. (1998) trickle flow at elevated pressure was

74 Chapter 5

studied and a similar flow of small bubbles in a film of liquid flowing down the surface

of the packing was described to account for the increase in the gas-liquid mass transfer

through the increase in the gas-liquid mass transfer area.

5.4 Conclusions

The following conclusions can be made regarding the effects of increasing the liquid vis-

cosity and decreasing the liquid surface tension:

Co-current upflow

Increasing the liquid viscosity (from 0.8 to 2 mPa s) increases the liquid holdup slightly

in the co-current upflow regime. Frictional pressure drop is increased which is due to the

increase in the density of the liquid by the glycerol used to increase the liquid viscosity.

The increase in liquid viscosity adversely affects the gas-liquid mass transfer coefficient by

decreasing the liquid diffusion coefficient. The results for co-current upflow can be cor-

related by Equation 5.21, based on the correlation proposed by Sherwood and Holloway

(1940) developed for downflow, with an effect of the gas velocity on the mass transfer in-

cluded by u0.44G . The gas-liquid mass transfer coefficient was also correlated to the energy

dissipation, Equation 5.22, which is shown to be equal to the frictional pressure drop. The

factor (ScL/ScWater)0.69 describes the decrease in the gas-liquid mass transfer coefficient

by an increase in liquid viscosity and the associated decrease in the diffusion coefficient of

the gas species in the liquid.

Co-current downflow

The observed rates of gas-liquid mass transfer in co-current downflow are largely de-

termined by the liquid velocity. For the 10 ppi solid foam packing, the gas-liquid mass

transfer decreases when the liquid viscosity increases with the factor (ScL)0.5 correcting

for the increase in liquid viscosity, see Equation 5.23. However, for the 40 ppi solid foam

the mass transfer increases with an increase in the liquid viscosity. This is possibly due

to less channeling caused by higher wetting of the surface of the solid foam packing. De-

creasing the liquid surface tension affects the liquid holdup slightly but has a very large

influence on the gas-liquid mass transfer coefficient, increasing it by a factor of 6. Since

the value of kL is assumed independent of liquid surface tension, this increase is due to

an increase in the gas-liquid area for mass transfer. This increase may be ascribed to tiny

bubbles flowing with the liquid film down the solid foam packings.

Chapter 6

Hydrodynamics and mass transfer for a

gas-liquid-solid foam reactor

Abstract

Hydrodynamic parameters such as liquid holdup obtained for co-current gas-liquid flow

are discussed and further evaluated using the relative permeability model by Saez and

Carbonell (1985). This model describes the complete flow map for the counter-current and

co-current (upflow and downflow) configurations with the parameters found in Chapter

2. Also the flow regimes found experimentally are indicated on this map. In the co-current

downflow configuration the model describes the liquid holdup less accurately. This is due

to the model not taking the interaction between the gas and liquid phases into account.

The effect of the type of material (aluminum and carbon) and solid holdup (93% com-

pared to 97%, respectively) on the hydrodynamic parameters is small and it is found that

the intrinsic mass transfer coefficient is unaffected by the material and voidage of the solid

foam packings. This is possibly due to the materials exhibiting similar hydrophobicities.

As carbon is a suitable inert material in chemical reactions it is preferred as catalyst sup-

port.

A chemical reactor using solid foam packings as the catalyst support is compared with

a packed bed of spheres for the oxidation of glucose over palladium catalyst in upflow and

downflow configurations. The low surface area for depositing the catalyst results in the

reactors being kinetically limited. A reactor operating under mass transfer limitations is

obtained by applying washcoats in the order of 1 µm. In the co-current downflow config-

uration the same reactor performance is obtained for a reactor packed with spherical par-

ticles or solid foam packing. In the co-current upflow configuration the spherical particles

achieve twice the overall reaction rate than a reactor using solid foam packing, however,

at an order of magnitude higher pressure drop. This indicates that solid foam packings

operate at higher energy efficiencies and can achieve production rates comparable to con-

ventional reactors.

76 Chapter 6

6.1 Introduction

The chemical industry uses multiphase reactors operating under a variety of physical

conditions (e.g., total pressure, aqueous or organic liquids) for reactions which include

Fischer-Tropsch synthesis, hydrogenation, oxidation, epoxidation, hydroformulation, and

alkylation. Hydrodynamic parameters and gas-liquid mass transfer under process condi-

tions are important for the design and operation of these reactors. Scaling rules for the

design of these industrial reactors are common but have to be evaluated especially when

a different structure is used as catalyst support. The solid catalyst is usually in the form

of pellets or powders. Hence, either slurry or fixed bed operations are commonly em-

ployed. The particles’ hydrophobicity (also commonly referred to as the lyophobicity)

influences the gas-liquid mass transfer and subsequently affects the overall reactor per-

formance (Ruthiya et al., 2004). In Rangwala et al. (1990), a mixture of hydrophobic and

hydrophilic spherical particles was studied in the co-current downflow configuration for

an water-air system. Here the area for mass transfer was found to decrease with an in-

crease in the fraction of hydrophobic packing introduced, possibly a result of a decrease

in the wetted area of the packing which leads to decreased mass transfer.

This chapter gives an overview of the main hydrodynamic and gas-liquid mass trans-

fer parameters quantified in the preceding chapters. Additionally the effects the type of

packing material (aluminium or carbon) have on these parameters are quantified in the

co-current upflow configuration. The solid foam packings are compared to spherical par-

ticles, where the solid is used as the support for depositing palladium used as a catalyst for

the oxidation of glucose. A fair comparison is made between the different reactor config-

urations whether co-current upflow or downflow, and a reactor design is used to evaluate

the key differences in the two operating configurations.

6.2 Overview of hydrodynamics

The liquid holdup and the two-phase frictional pressure drop is described in the counter-

current flow configuration by the relative permeability model of Saez and Carbonell (1985),

given in Equation 2.4 to Equation 2.9 in Section 2.1.2 (page 16). This model may be ex-

tended to the co-current configurations with appropriate changes in the sign of the liquid

and the gas velocities. The counter-current configuration described in Section 2.1.2 takes

flow upward as the positive direction. In the following sections this model is used to

quantify the liquid holdup in all configurations (counter-current and co-current upflow

and downflow) using the parameters (A, B, h1 and h2) in Table 2.2 (page 24). The pa-

rameters for the 40 ppi solid foam packings are used to give an overview of these model

predictions. The model predictions are compared to the experimental results obtained in

Chapters 2, 3 and 4.

Overview of hydrodynamics 77

6.2.1 Flow regimes

The flow regimes observed in the counter-current flow are described qualitatively in Fig-

ure 2.2 on page 19. This regime map is extended to the co-current flow configurations, see

Figure 6.1.

−2 −1 0 1 20

0.2

0.4

0.6

0.8

1

1.2

Bubble

up

Bubble

down

Pulse

up

Pulse

down

Trickle

Gas upflowGas downflow

uL = −0.01 m s

−1u

L = −0.02 m s

−1

uL = −0.04 m s

−1

uL = −0.10 m s

−1

uL = 0.00 m s

−1

uL = +0.02 m s

−1

uL = +0.04 m s

−1

uL = +0.10 m s

−1

← ε

← εL

0

Liq

uid

Ho

ldu

p, ε

L [

m3 L m

−3

P]

uG

[m s−1

]

Co−current downflow

Counter−current flow (trickle)

Flooding points

Counter−current flow (bubble and pulse)

Co−current upflow

Figure 6.1: The complete regime map for the co-current and counter-current flow configurations,with the associated liquid holdup, the lines indicating different liquid velocities.

The flow regimes for the co-current flow configurations overlap with those of the

counter-current flow configuration producing a complete regime map for two-phase (air-

water) flow. In the co-current downflow configuration the liquid holdup increases as the

liquid velocity increases and decreases slightly with increasing gas velocity. The trickle

regime is predominant at low gas and liquid velocities and is characterized by a liquid

film flowing down the packing surface and a continuous gas phase flowing up or down.

At higher liquid flow rates, a downflow bubble regime can be observed. At high gas ve-

locity, a downflow pulsing regime is observed where gas and liquid pulses alternate in

moving down the packing structure. In the co-current upflow configuration the bubble

and pulse regimes are observed. At low gas velocities the gas travels through the contin-

uous liquid phase in the form of bubbles. As the gas velocity is increased these bubbles

grow bigger up to the width of the column, the start of the pulsing upflow regime. In the

co-current upflow configuration, the liquid holdup decreases with increasing gas velocity

and increases with increasing liquid velocity. In the counter-current flow configuration

the same results as found in Section 2.3.4 are observed, with both a high liquid holdup

regime (bubble and pulse flow) and a low liquid holdup regime (trickle flow) observed

for identical gas and liquid velocities. The difference in the regimes is attained through

78 Chapter 6

a different operation of the column, see Sections 2.2.2 and Section 2.2.3 on page 20 for

details. The flooding point separates these two regimes into distinct regions.

6.2.2 Liquid holdup

The relative permeability model described in Section 2.1.2 (page 16), may be reduced to

the following intrinsic equation for describing the liquid holdup, εL (= ε − εG).

(B(1 − ε)

ε3de

)((ε

εG

)h1 (u2

GρG

)(

uG

|uG|

)

−(

ε − ε0

L

εL − ε0L

)h2 (u2

LρL

)(

uL

|uL|

))

+ · · ·

· · ·+ ρGg − ρLg = 0 (6.1)

where B, h1, and h2 are parameters previously determined, see Section 2.3.4, page 24. The

relative permeability model is used to describe the liquid holdup for 40 ppi solid foam

packing at different gas and liquid velocities (upflow taken in the positive direction) and

compared to the liquid holdup obtained experimentally for two-phase flow in the counter-

current and co-current flow configuration, see Figure 6.2.

0 0.5 1 1.50

0.2

0.4

0.6

0.8

1

uG

[m s−1

]

Counter−current flow

uL = −0.028 m s

−1

uL = −0.021 m s

−1

uL = −0.014 m s

−1

uL = −0.007 m s

−1

−1.5 −1 −0.5 00

0.2

0.4

0.6

0.8

1

uG

[m s−1

]

Liq

uid

Ho

ldu

p, ε

L [

m3 L m

−3

P]

Co−current downflow

uL = −0.02 m s

−1

uL = −0.04 m s

−1

0 0.5 1 1.50

0.2

0.4

0.6

0.8

1

uG

[m s−1

]

Co−current upflow

uL = 0.02 m s

−1

uL = 0.04 m s

−1

Figure 6.2: Liquid holdup, εL, for 40 ppi aluminium foam packings in the co-current downflow, thecounter-current and the co-current upflow configurations.

In the counter-current and the co-current upflow configurations the model is able

to describe the observed liquid holdup for the high liquid holdup regimes. In the co-

current downflow configuration the model overestimates the liquid holdup. This model

does not describe phenomena such as the wetting of the packing or channeling. In the

counter-current low liquid holdup regime (trickle flow) the model underestimates the

Intrinsic mass transfer coefficient 79

liquid holdup. This deviation in the liquid holdup predicted is possibly a result of the

interaction between the gas and liquid phases not taken into account in the relative per-

meability model.

6.3 Intrinsic mass transfer coefficient

The intrinsic mass transfer coefficient, kL, is estimated for the co-current upflow and

downflow configuration from the values of the gas-liquid mass transfer coefficient, kLaGL,

and estimates of the surface area for mass transfer, aGL. The gas-liquid mass transfer co-

efficients for solid foam packings in the co-current upflow and downflow configurations

are given in Section 3.1.1 and Section 4.3.2, respectively.

The surface area for gas-liquid mass transfer per unit of reactor volume, aGLεL, can be

estimated in the co-current upflow configuration as the product of the geometric surface

area of the packing, assuming a static liquid film on the surface described by the static

liquid holdup, ε0L (see Table 5.2, page 64), and the bubble fraction, εb. The bubble fraction

is the fraction of the reactor that can be used for gas-liquid mass transfer and is estimated

in the co-current upflow configuration according to the following equation, see Figure 6.3:

εb =εG

1 − εS − ε0

L

(6.2)

Figure 6.3: Image of the experimental setup with the solid foam packing operating in the co-currentupflow bubbling regime, uL = 0.02 m s−1 and uG = 0.2 m s−1. The bubbles appear as the darkerareas and the liquid phase as the the lighter areas. A schematic drawing representing a bubble andthe liquid film on the surface of the solid foam is given at the right, with VG representing the volumeof the gas inside the bubble volume, Vb.

80 Chapter 6

In the co-current downflow configuration, the assumption is made that the liquid

flows over the packing material in the form of a thin film. An estimate of the film area,

aGLεL, can be made from Figure 1.11a by replacing the solid holdup, εS, by (εS + εL).

0 0.2 0.4 0.6 0.8 10

0.01

0.02

0.03

0.04

0.05

Gas velocity, uG

[m s−1

]

kL [

10

3 m

L s

−1]

10 ppi, uL = 0.02 m s

−1

10 ppi, uL = 0.04 m s

−1

40 ppi, uL = 0.02 m s

−1

40 ppi, uL = 0.04 m s

−1

(a) Co-current downflow

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

Gas velocity, uG

[m s−1

]

kL [

10

3 m

L s

−1]

10 ppi, uL = 0.04 m s

−1

40 ppi, uL = 0.02 m s

−1

40 ppi, uL = 0.04 m s

−1

(b) Co-current upflow

Figure 6.4: Intrinsic liquid side mass transfer coefficient, kL, for different metal foam packings forthe co-current upflow and downflow configurations.

In the co-current downflow and upflow configurations shown in Figure 6.4, the intrin-

sic mass transfer coefficient, kL, is not a function of the gas velocity and depends solely

on the properties of the solid foam packing and the liquid velocity. The intrinsic mass

transfer coefficient, kL, in the upflow configuration is an order of magnitude larger than in

the co-current downflow configuration. The value of kL for the 10 ppi solid foam packing

is larger than that for the 40 ppi solid foam packing. This increase is possibly due to the

larger struts generating more turbulence within the liquid film on the surface of the solid

foam packing which enhances gas-liquid mass transfer.

6.4 Effect of material type

In using a solid support for a catalyst, one of the main criteria is that the material is inert

and is not affected by the reaction conditions (pH, temperature, pressure, etc.) and that

suitable active catalysts can be deposited over the surface area of the support with high

dispersion. The aluminum foam packings thus far may be treated to form aluminum oxide

which is chemically resistant. However, a better alternative would be to use a carbon

support and to deposit active catalyst (usually Pt or Pd) with standard methods used also

for slurry and trickle bed catalysts. The carbon foams (shown in Figures 6.5c and 6.5d)

however have a smooth graphitic layer on the surface. The surface area of untreated 65

ppi carbon (3v%) foam was measured using krypton physisorption (evacuated to vacuum

for 24 hours at 300◦C, and measured at boiling liquid nitrogen using an ASAP 2020) and

Effect of material type 81

found to be 0.11 m2 g−1. This corresponds to a geometric surface area of 5260 m2S m−3

P per

unit volume of packing. The unit cell model of Fourie and Plessis (2002) predicts a value

of 4959 m2S m−3

P .

(a) 10 ppi aluminium (b) 40 ppi aluminium

(c) 10 ppi carbon (d) 45 ppi carbon

Figure 6.5: Images of solid foam packings supplied by ERG Aerospace Corp. The graduated mark-ings are in mm.

Table 6.1: Static liquid holdup for the aluminium and carbon foam packings.

Contact angle Solid Static liquid Static film

θ holdup (εS) holdup,ε0

L areaa

Material ppi [◦] [m3S m−3

P ] [m3L m−3

P ] [m2GL m−3

P ]

Aluminium 10 45 0.07 0.094 1502

Aluminium 40 - 0.07 0.115 6282

Carbon 10 37 0.03 0.070 1244

Carbon 45 - 0.03 0.191 7503

a Determined using the unit cell model of Fourie and Plessis (2002) with thesolid holdup, εS, as given in Figure 1.11a, replaced by (εS + ε0

L).

The hydrodynamics and mass transfer of the carbon foam packings, without any pre-

treatment and impregnation was experimentally determined in the co-current upflow con-

figuration using the methods and techniques as given in Chapter 3 for the air-water sys-

tem. These results were compared to the results thus far obtained for aluminum foam

packings (Chapter 3). The determination of the three phase contact angle (a measure of

82 Chapter 6

the hydrophobicity of the material) was performed using droplets on the surface of a flat

part of a strut. The curvature of the strut will have an influence on the measurement, and

only serves as a rough estimate of this parameter is obtained this way. The struts of the

solid foam packing are assumed to be non-porous for these measurements.

0 0.2 0.4 0.6 0.8 10.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


Gas velocity, uG

[m s−1

]

Liq

uid

hold

up, ε

L [

mL3 m

P−3]

0.02 m s -1


0.04 m s -1

u L

Aluminum Carbon

(a) Liquid holdup

0 0.2 0.4 0.6 0.8 10

20

40

60

80

100


Gas velocity, uG

[m s−1

]

Pre

ssure

dro

p, P

f [10

2 P

a m

−1]

0.02 m s -1

0.04 m s -1

u L

Aluminum Carbon

(b) Frictional pressure drop, Pf

Figure 6.6: (a) Liquid holdup and (b) frictional pressure drop mass transfer coefficient per unit ofreactor volume, for 10 ppi aluminium and carbon foam packings in the co-current upflow configu-ration.

In Figure 6.6a the liquid holdup results for the carbon and aluminum solid foam pack-

ings are given for the co-current upflow configuration for two-phase gas-liquid flow for

the air-water system. The results show that the liquid holdup for the 45 ppi carbon foam

is significantly higher than for the 10 ppi foams and 40 ppi aluminium foam at the same

gas and liquid velocities. The static liquid holdup, as given in Table 6.1, is higher in the 45

ppi case and may explain these results. Here the unit cells are possibly filled with liquid

droplets and drainage from the solid foam packing is more difficult. At liquid and gas

flows conditions through the solid foam packings, possibly unit cells are filled with liquid

droplets giving rise to higher liquid holdup.

The frictional pressure drop per unit length of packing is given in Figure 6.6b for 10

ppi solid foam packings (aluminum and carbon). The frictional pressure drop of the car-

bon foam packing is lower than that of the aluminum foam packing in the pulse regime.

Equation 5.20 describes the frictional pressure drop in terms of the voidage of the pack-

ing, the static liquid holdup, and the gas and liquid velocities and decreases as the voidage

increases. These packings have similar pore sizes but carbon foam packing has a higher

voidage and hence a lower frictional pressure drop.

The results for the gas-liquid mass transfer coefficient per unit of reactor volume,

kLaGLεL, shown in Figure 6.7a, indicate that the influence of the material type is negligible.

The intrinsic mass transfer coefficient, kL, is given in Figure 6.7b using Equation 6.2 and

Reactor comparison 83

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5


Gas velocity, uG

[m s−1

]

kLa G

L ε

L [

m3 L m

−3

P s

−1] 0.02 m s -1


0.04 m s -1

u L

Aluminum Carbon

(a) Mass transfer coefficient, kLaGLεL

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5


Gas velocity, uG

[m s−1

]

kL [

10

3 m

L s

−1]


0.04 m s -1

u L

Aluminium Carbon

(b) Intrinsic mass transfer coefficient, kL

Figure 6.7: (a) mass transfer coefficient per unit of reactor volume and (b) , for aluminium andcarbon foam packings in the co-current upflow configuration.

the values of the static liquid holdup given in Table 6.1. The results show that although the

solid surface area and the voidage of the packings change (97% for carbon as opposed to

93% for aluminum), the value of kL remains the same for similar ppi number solid foam

packings. This indicates that the type of the packing material influences the gas-liquid

mass transfer coefficient by influencing the gas-liquid contact area. No influence on the

resulting intrinsic mass transfer coefficient is observed. However, the measurements per-

formed on aluminium foam packings may be used to determine the performance of the

more chemically inert carbon foam packings. The measurement of the hydrophobicity

of the two materials remains somewhat inconclusive but for the two materials investi-

gated the influence is found to be negligible in terms of the gas-liquid mass transfer for

aluminium and carbon foam packings.

6.5 Reactor comparison

In the design of a commercial reactor, the most important factors determining the eventual

reactor design are the intrinsic rate constant of the active catalyst, the production rate, and

the heat of reaction. In selecting a reactor packing to support the active catalyst for a gas-

liquid reaction, an additional aspect of the mass transfer of reactants from the gas phase

and liquid phase to the catalytically active sites needs to be considered. These reactor

packings are available in a large number of geometric shapes (see Figure 1.5, page 5) in an

attempt to increase the mass transfer to the catalytically active sites and provide enough

area for deposition of large quantities of active catalyst.

In this section a comparison is made between a packed bed of spherical particles of

nominal diameter 5.6 mm and a 10 ppi solid foam packing (see Figure 6.8) for the oxidation

84 Chapter 6

of glucose over a palladium catalyst. These packings have approximately the same specific

surface area, and spherical particles of 5.6 mm at high gas and liquid velocities have been

studied extensively in the co-current upflow and downflow configurations (see Lakota

and Levec (1990); Specchia et al. (1978, 1974); Hirose et al. (1974)). The differences in

terms of the liquid holdup, the frictional pressure drop, the mass transfer of reactants, and

ultimately the overall reaction rate for this comparison is made for two-phase co-current

flow (upflow and downflow). This comparison is based on equal gas and liquid flow rates

through the two different packings which have similar geometric surface areas.

(a) Spherical particle, aP = 642 m2

S m−3

P (b) Solid foam packing, aP = 763 m2

S m−3

P

Figure 6.8: In (a) a schematic representation of a spherical particle is shown and in (b) an image ofthe solid foam packing is given, with the graduated markings in mm.

6.5.1 Overall reaction rate of multi-phase reactors

In Figure 6.9 the phenomenological model of a multiphase heterogeneously catalyzed re-

actor, where a gas and liquid component is reacting on a supported catalyst, is given

schematically. Here the gas component has to undergo absorption in the liquid, trans-

fer through the liquid to the catalyzed surface, and adsorption on the active catalyst for

reaction to occur.

The overall reaction rate describing this phenomena for a (pseudo) first order reaction

is given by the following, (taken from Levenspiel (1999)) :

−r =

1

kGaGLεLH︸︷︷︸

Gas

+1

kLaGLεL︸︷︷︸

Liquid

+1

kSaLSεL︸︷︷︸

Liquid−Solid

+1

η (kir) LtρSεS

−1

pG

H(6.3)


Gas Liquid Solid

X(g) X(aq) + Y(aq) Products (aq)

Figure 6.9: Schematic representation of the transfer of a gaseous component, X, through the liquid,Y to the active catalyst supported on the solid.

where −r is the overall reaction rate, and the first three terms represent the resistance to

mass transfer of the gas reactant with partial pressure, pG, either in the gas, the liquid film

at the gas-liquid interface, or the liquid film surrounding the solid support of the cata-

lyst, respectively. The intrinsic reaction rate coefficient is given by kir, and Lt represents

the amount of catalyst per unit weight support. The concentration profile of the gas com-

ponents as it travels from the gas phase to the solid surface is depicted schematically in

Figure 6.10.

Solid Liquid

G/L interface

Gas

C i p

G p i = C i H

C L

C S

k G

k L

k S

C S

L/S interface

Figure 6.10: Sketch showing the resistances to mass transfer in a gas-liquid system with reactionon the surface of the catalyst.

In describing the transfer of the gaseous component, most often either the resistances

to mass transfer (gas-liquid and liquid-solid) or the kinetics of the reaction occurring at

the catalytic surface is dominating and subsequently limits the reactor performance. The

following criteria are used to describe whether a reactor is mass transfer limited or kineti-

cally limited:

Mass transfer limited :

1

η (kir) LtρSεS

≤ 1

10

(1

kGaGLεLH+

1

kLaGLεL

+1

kSaLSεL

)

(6.4)

86 Chapter 6

Kinetically limited :

1

η (kir) LtρSεS

≥ 10

(1

kGaGLεLH+

1

kLaGLεL

+1

kSaLSεL

)

(6.5)

In general, heterogeneously catalyzed multiphase reactors are mass transfer limited, where

the kinetic term contributes less than 10% to the overall performance of the reactor, given

in Equation 6.4. The contributions of the mass transfer and kinetics may be evaluated once

the mass transfer resistances are known.

6.5.2 Mass transfer coefficients

In determining the mass transfer coefficients for spherical particles and solid foam pack-

ings a few assumptions had to be made. The diffusion coefficient in the gas is typically of

the order of 1 × 10−5 m2 s−1 and in the liquid phase 1 × 10−9 m2 s−1. Since the intrinsic

mass transfer coefficients, kL and kG, are related to the diffusion coefficient kG ∝ D0.5−1

G ,

it can be assumed that the mass transfer resistance in the liquid phase at the gas-liquid

interface and the liquid-solid interface is much higher than that in the gas phase, and thus

gas-phase resistance to mass transfer, kGaGL, is neglected. The correlations and assump-

tions for determining the liquid-side mass transfer coefficient and the liquid-solid mass

transfer for oxygen in the air-water system are described in the following sections.

Spherical particles

Spherical particles were studied by Hirose et al. (1974) and Specchia et al. (1974) in terms of

the gas-liquid mass transfer coefficient in co-current downflow and upflow, respectively.

Values of kLaGLεL are given in Table 6.2 at the gas and liquid velocities used in the de-

sign (uL = 0.04 m s−1 and uG = 0.4 m s−1). The liquid-solid mass transfer coefficient is

studied by Lakota and Levec (1990) and Specchia et al. (1978) for co-current downflow

and upflow, respectively. In co-current upflow, the liquid-solid mass transfer coefficient

for single phase flow is described by:

(

ksingle phaseS de

DL

)

=

(

0.99 + 2.14

(uLdeρL

µL

))0.5(µL

ρLDL

)0.33

(6.6)

The gas bubbles or pulses increase the intersticial velocity of the liquid flowing over the

packing and thus increase the liquid-solid mass transfer coefficient. Specchia et al. (1978)

describe this increase by the following expression:

ln

(

kS

ksingle phaseS

)

= 0.480 ln

(ReL

ReG

102

)

− 0.030

[

ln

(ReL

ReG

102

)]2

− 0.30 (6.7)

which for the comparison in Table 6.2 gives a value of kS/ksingle phaseS ≈ 4.


Solid foam packing

The gas-liquid mass transfer coefficient for 10 ppi solid foam packing is described in Chap-

ter 3 for co-current upflow and Chapter 4 for co-current downflow. Tentorio and Casolo-

Ginelli (1978) studied solid foam packings as the electrode in an electrochemical cell and

report the liquid-solid mass transfer coefficient for single phase flow. They describe the

liquid solid mass transfer coefficient for 10 ppi solid foam packing by the following equa-

tion:kS

DL

= 1.03 × 10−4

(µL

ρLDL

)0.33(uLρL

µL

)0.53

(6.8)

The liquid-solid mass transfer coefficient for the solid foams operating in co-current up-

flow is calculated using Equation 6.8 for single phase flow and assuming that a similar

enhancement is achieved for gas-liquid flow, kS/ksingle phaseS ≈ 4.

In Table 6.2 the gas-liquid and liquid-solid mass transfer coefficients for the trickle bed

reactor, the flooded bed reactor, and the solid foam packing (co-current downflow and

upflow) are given. The values of kLaGLεL and kSaLSεL for the solid foam packing are in the

same order of magnitude while for the reactors using spherical particles (trickle bed and

flooded bed reactors) the liquid-solid mass transfer coefficient is much lower than the gas-

liquid mass transfer coefficient. This indicates that reactors packed with spherical particles

are operated with significant mass transfer limitations in the liquid film surrounding the

solid surface.

6.5.3 Non-porous support

In designing a catalyst, the catalyst can either be deposited on the outer surface of particles

or inside porous structures within the particles. The kinetic limitation for a non-porous

support (spherical particles and solid foam packing) where the catalyst is only deposited

on the outer layer, and thus hydrodynamically accessible (η = 1), is given here. The

contribution of kinetic limitations to the overall reaction rate is calculated assuming non-

porous particles and catalyst deposition only to occur on the outer surface of the catalyst

support.

The intrinsic reaction rate coefficient for glucose oxidation, kir, is 125 m3

L mol−1

Cat s−1 at

50◦C, Ruthiya (2005). The catalyst loading, Lt, which may be deposited on the outer sur-

face of the solids considered (spherical particles and solid foam packings), is determined

using the following equation:

Lt =

(aS,non−porous

aCat

)

(6.9)

where aS,non−porous is the specific surface area of the solid support (here the specific geomet-

ric surface area), and aCat is the specific surface area of support per unit mol of catalyst,

using the characterization of a reference catalyst (5 wt% Pd/C catalyst, see Wenmakers

88 Chapter 6

Table 6.2: Hydrodynamic parameters and mass transfer characteristics for 5.6 mm spherical parti-cles and 10 ppi solid foam packing.

Trickle Flooded

bed bed Solid Solid

reactor reactor foam foam

(downflow) (upflow) downflow upflow

Catalyst Packing : spheres spheres foam foam

de [103 m] 5.6 5.6 10 ppi 10 ppi

ap [m2S m−3

P ] 642 642 763 763

εS [m2

S mP−3] 0.6 0.6 0.03 0.03

ρS [kgS m−3

S ] 1560 1560 1560 1560

Hydrodynamics :

uL [m3L m−2

P s−1] 0.04 0.04 0.04 0.04

uG [m3G m−2

P s−1] 0.4 0.4 0.4 0.4

Regime [-] Pulse down Pulse up Trickle Pulse up

εL [ m3L m−3

P ] 0.16 0.21 0.30 0.55

PTotal [102 Pa m−1 ] 400 490 19.5 105.0

Pf [102 Pa m−1 ] 439 439 50 50

Mass transfer :

kLaGLεL [m3L m−3

P s−1 ] 0.50 0.95 0.05 0.25

kSaLSεL [m3L m−3

P s−1 ] 0.047 0.28 0.035 0.27(

1

kLaGLεL+ 1

kSaLSεL

)−1

[m3L m−3

P s−1 ] 0.0428 0.218 0.035 0.129

Non-porous particles :

kir [m3

L molCat−1 s−1] 125 125 125 125

aS,non−porous [m2S kgS

−1] 0.656 0.656 16.3 16.3

Lt [10−6molCatkg−1

S ] 0.378 0.378 8.97 8.97

−rH/pG [ m3L m−3

P s−1] 0.021 0.037 0.021 0.037

Kinetic contribution [%] 49 83 41 71

Washcoat :

Lt,required [10−6molCatkg−1

S ] 3.66 18.7 61.5 221.1

aS,required [m2

S kgS−1] 6.65 33.9 111.8 401.9

(aS,required)/(aS,non−porous) [-] 9.7 49.4 6.9 24.7

δW [10−6m] 0.40 2.06 0.29 1.03

φ [-] 0.49 2.51 0.35 1.26

η [-] 0.92 0.39 0.96 0.67

−rH/pG [ m3L m−3

P s−1] 0.039 0.17 0.033 0.11


et al. (2008)). The value of aCat is given by the following:

aCat =

(SBET

SSchem

)

MCatSmchem = 1.818 × 106 [m2

Smol−1

Cat] (6.10)

where SBET is the specific area per unit mass of the reference support (850 m2

ref,S g−1

ref,S),

SSChem is the metallic surface area per unit mass of reference support (4.3 m2

Cat g−1

ref,S), MCat

is the molar mass of the catalyst metal (palladium = 106.42 gCat mol−1

Cat), and SmChem is the

metallic surface area per unit mass of catalyst metal (86.4 m2Cat g−1

Cat), given by Wenmakers

et al. (2008).

In Table 6.2 the overall reaction rate coefficient, −rH/pG (= koverall), is given for the

spherical particles and the solid foam packing. Due to the low surface area of the non-

porous solid used as a support for the catalyst, the reaction rates for all four the reactors

(spherical particles or solid foam packings either operating in co-current upflow or down-

flow), is similar. Here it is clear that kinetic limitations are restricting the reactor as in all

cases the kinetic contribution to the overall reactor performance is greater than 10%. The

kinetic limitation may be decreased by increasing the catalyst loading of the solid support,

which usually entails creating pores within the solid support which increases the surface

area for catalyst deposition. In an experiment with graphitic carbon foam of 65 ppi the

surface area could be increased by a factor of approximately 2000 (to 200 m2

S g−1

S ) by oxi-

dation in boiling HNO3, for one hour. However, the resulting solid foam packing is brittle

and the application of a washcoat is rather considered for increasing the surface area for

catalyst deposition. The minimum thickness of such a layer is calculated assuming mass

transfer limitation to dominate.

6.5.4 Washcoat

The outer surface of the solids considered (spherical particles or solid foam packing) is

too low for deposition of enough catalyst to obtain a mass transfer limited reactor. Higher

amounts of catalyst may be deposited on a washcoat layer which serves to increase the

surface area for catalyst deposition. The thickness of this washcoat layer is determined

once the required catalyst loading, Lt,required, for a mass transfer limited reactor has been

calculated according to Equation 6.4. The required loading gives the surface area required

for catalyst deposition, obtained from the following equation:

aS,required = (Lt,required · aCat) (6.11)

The required increase in the surface area of the solid needed for catalyst deposition,

aS,required, for each of the packing materials is given in Table 6.2. The ratio of the mini-

mum surface area required for deposition of the catalyst to the non-porous surface area

of the packing material is in the range of 10 to 50. The minimum layer thickness may be

90 Chapter 6

calculated for typical washcoats:

δW =

(aS,required

aW ρW

)1

aS,non−porous

(6.12)

where aW is the specific surface area of the washcoat (typically 20 m2 g−1

W ) and ρW the bulk

density of the washocat (1200 kgW m−3

W ). The layer thickness is obtained assuming the

washcoat is spread evenly over the non-porous surface of the support material.

In Table 6.2 the layer thickness for the spherical particles and the solid foam pack-

ing is given. The supports (spherical particles and solid foam packings) operating in co-

current upflow and downflow require a washcoat layer thickness in the order of 1 µm. The

layer thickness required for the co-current upflow configurations is the highest due to the

fact that in this flow configuration predominantly higher gas-liquid and liquid-solid mass

transfer coefficients are encountered. The layer thicknesses of the washcoats to be applied

to the solid surfaces is low compared to the washcoat layer thicknesses commonly found

in industrial reactors, where larger loadings of catalyst are applied to account for catalyst

deactivation or leaching. In Giani et al. (2006) a washcoat of Al2O3 is applied to metal

foams and thicknesses of 28 µm were obtained. Wenmakers et al. (2008) applied carbon

nanofiber coatings on carbon foams and thicknesses up to 25 µm were formed. Diffusion

limitations, however, within the pores of the washcoat may cause concentration gradients

within the solid, reducing the efficiency of the catalyst. The effectiveness factor for a flat

plate geometry can easily be calculated (the choice of geometry not affecting the value of

η significantly, Levenspiel (1999)) by :

η =tanh (φ)

φ(6.13)

where φ is the Thiele modulus indicating if the reaction is diffusion limited or not. If the

value of φ is less than 0.4, no diffusion limitation is encountered within the washcoat. The

reaction is pore diffusion limited for φ greater than 4. The value of φ for a (pseudo) first

order reaction is given by:

φ =δW

2

√

kirLt

δW aS,non−porousDe

(6.14)

where δW is the thickness of the washcoat layer, and De is the effective diffusivity, given

by:

De =DLεW

τW

(6.15)

where DL is the molecular diffusivity, εW is the porosity of the washcoat and τ is the tortu-

osity factor, which is defined as the square of the tortuosity. The tortuosity of the washcoat

is a parameter which is difficult to measure, and in general the effective diffusivity, De, is

taken as an order of magnitude lower than the molecular diffusivity, for calculation of φ.

Conclusions 91

In Table 6.2 the Thiele modulus for the layer thicknesses required for increasing the

surface area of the solid supports (spherical particles and solid foam packing) is given.

The Thiele modulus for the solid foam packing operating in the co-current downflow con-

figuration is lower than 0.4 indicating that no diffusion limitation is encountered within

the washcoat. In the reactors with spherical particles and the solid foam packing operating

in the co-current upflow configuration, the Thiele modulus is between 0.4 and 4 indicating

that intermediate pore diffusion limitation is encountered. This, however, does not limit

the overall reaction rate as enough catalyst is deposited on the washcoat to ensure that

the reactors are operated with external mass transfer limitations (gas-liquid and liquid-

solid). The effectiveness factors are the lowest in the co-current upflow configuration for

the spherical particles and the solid foam packing, due to the larger thickness of the wash-

coat layer to be applied. Increasing the thickness of the washcoat layer would result in the

deposition of more catalyst, increasing Lt, but also introduce further diffusion limitations,

which affects the effectiveness factor, η.

The comparison between the two different solid supports (spherical particles and solid

foam packing) using a washcoat gives a general description of the overall reactor. In Table

6.2 the overall reaction rate coefficient, −rH/pG (= koverall), is given for such reactors. The

overall reaction rate for a co-current downflow reactor using spherical particles and solid

foam packing, is similar. This indicates that using a solid foam packing operating at a

reduced pressure gives comparable overall reactor performance. In co-current upflow

the flooded bed reactor using spherical particles as the catalyst support gives twice the

overall reaction rate as the same reactor operating with solid foam packing. However, the

solid foam packing operates at significantly lower pressure drop and hence lower energy

dissipation. In general solid foams operate more energy efficiently than their packed bed

counterparts.

6.6 Conclusions

The liquid holdup for gas-liquid flow through solid foam packings can be described in the

counter-current and co-current (upflow and downflow) configurations by the relative per-

meability model (Saez and Carbonell (1985)). In the co-current downflow configuration

(trickle flow), the model describes the general trends observed, but due to the interaction

between the gas and liquid phases not taken into account, the model over-predicts the

liquid holdup found experimentally.

The voidage of the solid foam material, whether 97% (carbon) or 93% (aluminium),

has little influence on the overall mass transfer coefficient, kLaGL εL and the intrinsic mass

transfer coefficient, kL. Carbon foams have higher voidages but less specific geometric

surface area and have a higher static liquid holdup for 40 ppi foam, when compared to

aluminum foam. Frictional pressure drops for carbon foam are slightly lower than for

aluminum foam. However, carbon foam packing serves as a better support material for

92 Chapter 6

catalysts, especially for fine-chemistry applications, due to its chemical inertness.

A comparison of solid foam packings with a packed bed of spherical particles for co-

current gas-liquid flow shows that for a reactor packed with spherical particles or with the

solid foam packing, both would suffer kinetic limitation for the reaction of glucose oxida-

tion. This is due to the low surface area of the packing materials for catalyst deposition.

This surface area may be increased using a washcoat for the two different packings with

layer thicknesses in the order of 1 µm. Overall reaction rate for solid foam packing with

co-current downflow is similar to that of trickle bed reactors, however at a much lower

frictional pressure drop. In the co-current upflow configuration the flooded bed reactor

packed with spherical particles has twice the overall reaction rate than the same reactor

using solid foam packing. However, the lower overall rate of reaction is achieved at an

order of magnitude lower frictional pressure drop and hence much higher energy effi-

ciency. This indicates that solid foam packings operate at higher energy efficiencies and

can achieve production rates comparable to conventional reactors.

Chapter 7

Perspectives

7.1 Conclusions

The research work presented in this thesis deals with the hydrodynamics and gas-liquid

mass transfer when the packing structure is changed from the conventional packed bed

or structured packings to solid foam packings. These solid foams have the advantage of a

high surface area (for catalyst deposition and generation of gas-liquid mass transfer area)

and high voidage, which decreases the frictional pressure drop and hence enhances the

reactor efficiency.

The solid foam packings have been studied in the counter-current and co-current (up-

flow and downflow) configurations and five different regimes have been found depending

on the gas and liquid superficial velocities. These regimes are summarized in Figure 6.1,

page 77. This map shows the five different regimes observed for co-current and counter-

current flow, trickle flow, bubble upflow, pulse flow upwards, bubble downflow and pulse

downflow. The trickle, bubble upflow and pulse upflow have been studied in more de-

tail. In the counter-current operating condition all these three flow regimes have been

observed. In the co-current upflow configuration the bubble and pulse flow regimes are

studied and in the co-current downflow configuration the trickle flow regime is studied.

For all these configurations the relative permeability model (Saez and Carbonell, 1985)

was used to describe the liquid holdup for different gas and liquid velocities. The values

for the parameters A, B, h1 and h2 for the relative permeability model have been obtained

either by liquid holdup or frictional pressure drop measurements for the different solid

foam packings studied (5, 10, 20, and 40 ppi).

The gas-liquid mass transfer coefficient per unit volume of reactor in the co-current

configurations have been found experimentally and the following correlations (similar to

Sherwood and Holloway (1940)) can be used to describe the results:

Co-current upflow:

kLaGL εLDL−1 = 311u0.44

G (uLρLµL−1)


P ]

Co-current downflow (10 ppi):


−1)1.16


P ]

94 Perspectives

In the co-current downflow configuration the gas-liquid mass transfer coefficient was

found to be dependent on the superficial liquid velocity and in the co-current upflow con-

figuration dependent on both the gas and liquid superficial velocities. The intrinsic mass

transfer coefficient, kL was found in both configurations to be independent of the gas ve-

locity and a strong function of the liquid velocity. In the co-current upflow configuration

values were a factor ten higher than for the co-current downflow configuration. The value

of the Schmidt number of the liquid to the exponent 0.5 was able to describe the decrease

in the gas-liquid mass transfer with increasing liquid viscosity (and decrease in the dif-

fusion coefficient, DL). The gas-liquid mass transfer may also be correlated to the energy

dissipated per unit volume of reactor (found equal to the frictional pressure drop) and

was correlated in the co-current upflow configuration as follows:

Co-current upflow:

kLaGL εL(ScL/ScWater)0.69 = 2.05 × 10−4 P 0.8

f [SI units, m3L m−3

P s−1]

Chemically inert carbon foam packings can be used as catalyst support for catalyst and

results from the aluminum foam packings obtained in this study are valid also for such

solid foam packings. A reactor packed with solid foam packings or spherical particles has

been compared in terms of the overall reaction rate. Due to the low surface area for cat-

alyst deposition the the overall rate of reaction is kinetically limited for the oxidation of

glucose over a palladium catalyst. A washcoat applied to the surface of the support, with

a thickness in the order of 1 µm, increases the surface area for catalyst deposition and reac-

tors operating under mass transfer limitation can be obtained. In the co-current downflow

(trickle flow), the solid foam packings can achieve the same reaction rate than a conven-

tional packed bed. This reaction rate is achieved at a factor ten lower frictional pressure

drop and hence factor ten lower energy dissipation. In the co-current downflow config-

uration the solid foam operate at a factor ten lower frictional pressure drop, and achieve

half the reaction rate of a packed bed of spherical particles operating. This indicates that

solid foam packings operate more energy efficiently than the conventional packed bed of

spherical particles. This is due to the high voidage of the solid foam packings.

7.2 Recommendations

In the work presented in this thesis a relatively small comparison between solid foam

packings and other packing materials is made in terms of the liquid holdup, the pressure

drop and the gas-liquid mass transfer coefficient. The information presented however

should provide a clear understanding of the flow conditions (gas and liquid velocities),

the liquid holdup (a parameter reported as difficult to measure accurately), and the fric-

tional pressure drop of multiphase flow through solid foam packings. In studies regarding

reactor packing to be used for multiphase flow this is not always the case and the follow-

ing recommendations are made:

The hydrodynamic parameters, such as liquid holdup and pressure drop, and the solid

Recommendations 95

surface (its structure and the solid holdup) for the solid packing material under investiga-

tion give a reactor its characteristics in terms of mass transfer (gas-to-liquid, liquid-to-solid

and under non-wetting conditions also gas-to-solid) and heat transfer capabilities. If the

liquid holdup has not been measured for different gas and liquid velocities then a clear

physical understanding of the gas-liquid flow is lacking and the use of such a support

structure is difficult. Comparing these to other reactors using different packings also be-

comes problematic. The superficial velocity is based on the available area for flow, and

using an example for liquid flow through a monolith the two methods are described, see

Figure 7.1.

Open area

of channels

Total area

for fluid flow

Voidage =

Fluid Flow

Figure 7.1: Schematic drawing of a monolith reactor indicating both the open area of channels andthe total area for fluid flow. The ratio of these is known as the voidage.

The liquid superficial velocity is defined as a volumetric flow (m3L s−1) per unit of

”reactor area”. This area can be defined as the open area (thus ignoring the effects of

solids and effective increase in the frictional pressure, and underestimation of the actual

size of the reactor) or the total area for fluid flow, including the walls of the monolithic

structures (which may amount to approximately 20% of the reactor volume, depending

on the wall thickness of the channels). This seemingly subtle difference may be used

to explain increases in the frictional pressure drop and makes comparison with different

reactor packings (e.g. packed beds of spherical particles) possible. Thus to account for

the effect of the solids in the reactor, the superficial velocities should be defined per total

unit area of the reactor; and the voidage, and the phase holdups should be defined per

unit volume of the reactor, e.g. solids holdup is the volume of solids per unit volume

of the total reactor. The liquid holdup and gas holdup are defined similarly. The use of

relative liquid holdup (the volume of liquid per unit open volume) should not be used as

confusion over the actual size of the reactor and the pressure drop over the reactor may

arise. This distinct difference in the superficial velocity and holdup of the phases is not

always clearly indicated in the available literature. Increase in the pressure drop due to

96 Perspectives

the presence of the solid which acts as a constriction in the total flow path and phenomena

such as increased mass transfer due to an increase in the intersticial velocities may easily

be explained. It is thus recommended to base all further studies on reactor packings on

the total area for fluid flow and the total volume of all the phases constituting the reactor.

A further study on the work presented in this thesis may focus the attention on the

gas-liquid mass transfer coefficients in the counter-current flow configuration. An esti-

mate using the penetration theory was made which resulted in values of kLaGL of up to

6 s−1. In the context of the results for co-current flow these estimations are high and a

value similar to co-current upflow, with kLaGL up to 1.3 s−1, should be realistic for the

high holdup counter-current configurations and values similar to the co-current down-

flow configuration where the values of kLaGL have a maximum of 0.18 s−1 should hold

for the low liquid holdup counter-current configuration (trickle flow). This is yet to be

experimentally verified. Also the effects of the reactor wall on the resulting liquid holdup

and mass transfer should be determined. This may be done by increasing the width of the

packing material and measuring all hydrodynamic and mass transfer parameters. If the

difference between the two packing thicknesses is insignificant the wall effects are small.

If this is not the case, further investigation of the effect of the reactor wall should be made

to obtain the true contribution of the solid foam packings to the liquid holdup and the

gas-liquid mass transfer coefficient. The effect of entrance and exit effects in the case of

10 ppi solid foam packings in the co-current upflow configuration (Section 3.1.1, page 40)

should be further investigated. These entrance and exit effects possibly cause local de-

pletion which gives a low mass transfer coefficient contributed by the solid foam packing

of oxygen from the liquid film remaining on the solid foam as pulses pass by. This effect

may be studied using a suitable reactive system such as formate oxidation over a plat-

inum catalyst fixed on the solid foam packing which is used as the catalyst support. In

this instance the gas-liquid mass transfer, usually the limiting factor in gas-liquid-solid

reactions, can be measured following the reaction by changes in the pH of the liquid, and

a depletion of the oxygen in the liquid film would not result in a lower gas-liquid mass

transfer coefficient being measured. The gas-liquid mass transfer coefficient for the exper-

iments with lowered liquid surface tension (Section 5.3.3 page 72) in the co-current upflow

configuration lead to a de-saturation of the liquid within the 30 cm of packing length. This

de-saturation of the liquid film was not observed for co-current downflow experiments as

kLaGL is lower. As a comparison between 30 cm and 60 cm of packing is not possible in

this case, the gas-liquid mass transfer coefficient was not measured. Suitable probes using

spectroscopic analysis of the liquid flowing within the column may be used to measure

the concentration of dissolved oxygen and hence the gas-liquid mass transfer coefficient.

These probes are not sensitive to bubbles passing as the probe containing a fluorescing

Rh film is continually wetted, and measurement may be done in-situ (probes being quite

small, 1 mm diameter) to compare two different packing lengths smaller than 30 cm.

Outlook 97

7.3 Outlook

In this section some ideas are presented for further research based on the work presented

in the thesis.

The solid foam packing is a promising material also for the chemical industry due to

its high surface area for catalyst deposition at high voidage (reduces pressure drop). This

gives many opportunities to exploit this material for chemical reactions such at hydro-

genations, oxidations, epoxidations, alkylations etc. where a change in the partial pressure

of the reactants may lead to a reduced conversion or selectivity. However, in this study

only a basis for the development of these reactors have been laid, and further research to

the deposition of catalyst is required to further the advancement towards a chemical reac-

tive system using solid foam packings. The realization of the gas-liquid solid foam reactor

can be achieved by studying the deposition mechanisms of the catalyst components on

the solid support surface (such as carbon) and the effect of pre-treatments of the surface,

such as oxidation in nitric acid. This would lead to a catalyst system that exploits both the

hydrodynamic and mass transfer advantages of solid foam packings and the open struc-

ture would provide a catalyst which is hydrodynamically accessible and hence efficiently

used, giving higher selectivity towards the desired components. The deposition of chemi-

cally selective layers such as zeolites on the solid surface and subsequent deposition of the

active catalyst may even improve these selectivities. This brings about the possibilities of

designing a catalyst at every length scale (reactor to pore size) to exploit a specific reaction,

or reaction mechanism.

In this thesis the gas-liquid mass transfer coefficient was found to correlate to the en-

ergy dissipated per unit volume of reactor (frictional pressure drop) and was found to

also apply to conventional packing materials (spherical particles of 6 mm) with voidages

of 40% or packed micro-reactors. The generality of this equation should be evaluated as

it gives a maximum to the resulting mass transfer for a certain amount of energy input,

indicating some maximum energy efficiency. A higher energy input may result in more

energy dissipation through the formation of liquid circulations which do not necessar-

ily contribute to the overall mass transfer. This energy efficiency may also extend to the

heat transfer (an important parameter for highly exothermic reactions) through heat-mass

analogies commonly found in single phase studies between a solid and a fluid. This un-

derstanding of three phase systems would provide substantial increase in commertial ap-

plication of available reactor designs found in the field of chemical reaction engineering.

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List of Publications

Patent application

• C.P. Stemmet, B.F.M. Kuster, J. van der Schaaf, J.C. Schouten, Multiphase reactions

using solid foams, WO2006065127-A1 (2004).

Journal publications

• C.P. Stemmet, J.N. Jongmans, J. van der Schaaf, B.F.M. Kuster, J.C. Schouten, Hydro-

dynamics of gas-liquid counter-current flow in solid foam packings, Chem. Eng. Sci.,

60, p 6422, (2005).

• C.P Stemmet, J. Van der Schaaf, B.F.M. Kuster, J.C. Schouten, Solid foam packings

for multiphase reactors: Modelling of liquid holdup and mass transfer, Chem. Eng.

Res. Des., 84 (A12), p 1134, (2006).

• C.P. Stemmet, M. Meeuwse, J. van der Schaaf, B.F.M. Kuster, J.C. Schouten, Gas-

liquid mass transfer and axial dispersion in solid foam packings, Chem. Eng. Sci., 62,

p 5444, (2007).

• C.P. Stemmet, F. Bartelds, J. van der Schaaf, B.F.M. Kuster, J.C. Schouten, Influence

of the liquid viscosity and surface tension on the hydrodynamics and mass transfer

in co-current gas-liquid flow through solid foam packings, Chem. Eng. Res. Des.,

accepted, (2008).

• C.P. Stemmet, F. Bartelds, J. van der Schaaf, B.F.M. Kuster, J.C. Schouten, Hydrody-

namics and mass transfer for gas-liquid co-current downflow through solid foam

packings, in preparation, (2008).

Refereed conference proceedings

• C.P. Stemmet, J.N. Jongmans, J. van der Schaaf, B.F.M. Kuster, J.C. Schouten, Hy-

drodynamics of gas-liquid counter-current flow in solid foam packings, Proc. 7th

International Conference on Gas-Liquid and Gas-Liquid-Solid Reactor Engineering (GLS7),

August 21-25, 2005; Editors: -, Strasbourg, France, CD Rom paper 5.1, (2005).

106

• C.P. Stemmet, J. van der Schaaf, B.F.M. Kuster, J.C. Schouten, Axial dispersion and

mass transfer for solid foam packings, Proc. International Symposia on Chemical Re-

action Engineering, (ISCRE-19), September 3-6, 2006; Editors: -, Potsdam, Germany,

Poster number: 157 p 498 (2006).

Non-refereed conference proceedings

• J.C. Schouten, C.P. Stemmet, P.W.A.M. Wenmakers, R. Tschentscher, T.A. Nijhuis,

J. van der Schaaf, B.F.M. Kuster, Novel structured reactor packings - The potential

of solid foam materials for multiphase applications, Proc. Int. Symp. on Catalysis

Engineering; Delft, Netherlands, 23-24, (2007).

Oral presentations

• C.P. Stemmet, J. van der Schaaf, B.F.M. Kuster, J.C. Schouten, Structured foam pack-

ings for multiphase reactors: mass transfer characteristics for counter-current gas-

liquid flow, Proc. 7th World Congress of Chemical Engineering (WCCE 2005), July 10-14,

2005; Editors: -, Glasgow, United Kingdom, 84774/1-84774/30 (2005).

• C.P. Stemmet, J. van der Schaaf, B.F.M. Kuster, J.C. Schouten, Multiphase solid foam

reactors, 6th Netherlands’ Process Technology Symposium (NPS6), Veldhoven, October,

2006.

Acknowledgements

The last four years have been truly memorable with colleagues, friends, and family giving

their support every step of the way and I would like to acknowledge them in this section.

The first person I would like to thank is Prof.dr.ir. J.C. Schouten. Jaap, during the last

four years you have given me the support and inspiration needed in completing this novel

project. At difficult times you were always there with a guiding hand. Your guidance in

completing this project has inspired me and I wish to sincerely thank you for the time

you have spent, albeit your tight schedule. The critical remarks and eye for detail on

articles and other material to be submitted (as with this thesis) have always been greatly

appreciated. I have learnt so much from you and know that I will use these skills further

in my career. I am indebted to Dr.ir. John van der Schaaf and Dr.ir. Ben Kuster for their

insight into what needs to be done, investigated, and further investigated, and for the

fruitful discussions we have had. John, thank you for your lively discussions and critical

comments on the procedures for the experimental work and the interpretations of the

results. Ben, thank you for the discussions and comments during the progress meetings

and feedback when looking at results, and for proposing this novel study. I hope I have

fulfilled some of your expectations.

I would like to thank STW (Dutch Technology Foundation) for their financial support

and the industrial partners DSM, BASF (formally Engelhard B.V.), ABB, and Shell for their

co-operation in the project, and Recemat and Ecoceramics for their input during our half-

yearly meetings.

My appreciation goes out to the people who help build (and adjust) the setup so

that the data contained in this thesis could be measured. Roland Haghuis (Zeton), Karel

Janssen (Janssen Engineering) and Anton Bombeeck (TU/e) have input a great deal of

time and effort into the design and construction of the experimental setup and I would

like to acknowledge them. In doing such a novel project the experimental setup needs

some adjustments and I would like to thank Frank Grootveld, Madan Binderaban, and

Chris Luyk for their efforts and technical help to get the setup up and running after these

adjustments have been made.

I am greatly indebted to my colleagues during my time at the TU/e and appreciate

your support and kind words when obstacles seemed too great. I would like to say a

special thank you to Denise for all her effort in arranging all the administrative matters.

108

We sometimes forget how much effort it takes to keep such a large group going, and I

would like to say thanks for all the nice excursions and New Years parties organized. I

have always appreciated the company of my office mates, Keshav, Vinit, Patrick, Roman.

Thanks you for keeping the office lively and for the great discussions.

The quality of this thesis is a reflection of the people I have had the opportunity to

coach during my time here at SCR. I would like to thank all my students, Jurgen, Monique,

Alida, Otto, Leidy, Marco, and Frank for all the experimental work you have performed

in the lab, and the time and effort you have made in understanding the concepts. Your

efforts have not gone unnoticed and I greatly appreciate your help in the completion in

this project.

In deciding to do a PhD in a foreign country some obstacles pose themselves and I

have been blessed in having many dear friends to help in overcoming these obstacles and

lending me their support during some difficult times. I would like to thank my extended

family and friends here in Europe for their support. The difficulty in maintaining a friend-

ship is forgotten when we meet and it seems like just yesterday we spoke. I will not try

to mention all of you but would like to let you know that you are all dear to me and have

made me feel at home here in Europe. I would like to say a special thank you to the family

Christophersen for the times spent at their home during Christmas. The warmth of your

family made me forget the cold winters. To the family Hohmann-Van Kempen I would

like to say a special thank you for including me into your family.

I would like to thank my mother, my siblings, nieces, and nephew for their support

during this time. Mom, Juan, Iloma, Lolene, Deidre, Amy, Tayla, and Matthew whom I

have yet to meet, you have not veered far from my thoughts or heart during the entire

time I have spent here in the Netherlands.

Many thanks to you all,

Charl, 2008

About the author

Charl Philip Stemmet was born on April 19, 1978, in Durban, South Africa. In December

1999 he graduated in Chemical Engineering (Cum Laude) from the School of Chemical

Engineering at the University of Natal in Durban (currently known as the University of

Kwa-Zulu Natal). His dissertation was to design a plant for the ”Production of Maleic

Anhydride from n-Butane using a VPO catalyst”. In March 2001 he joined the Process

Development School at the University of Twente, The Netherlands. In March 2003 he

completed his Masters in Technological Design (PDEng, formerly known as MTD) and

acquired his Ingenieur (Ir.) title from the University of Twente, The Netherlands. His

masters’ dissertation was titled ”Sasol slurry phase reactor with the use of a novel fractal

distributor” and was prepared under the supervision of Prof.dr.ir. M.-O. Coppens (TU

Delft). In April 2003 he started his PhD project in the area of multiphase reactors at the

Eindhoven University of Technology, TU/e, The Netherlands, under the supervision of

Prof. dr. ir. J.C. Schouten. The PhD research covered ”Gas-liquid solid foam reactors:

Hydrodynamics and Mass transfer” and was carried out with the financial support from

the Dutch Technology Foundation, STW, and several industrial partners. Currently, the

author is working as a Postgraduate Researcher at the same group at the TU/e on an STW

project entitled ”In-situ spectroscopy engineering”.

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