Gas-liquid solid foam reactors : hydrodynamics and mass transfer

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Gas-liquid solid foam reactors : hydrodynamics and mass

transfer

Citation for published version (APA):

Stemmet, C. P. (2008). Gas-liquid solid foam reactors : hydrodynamics and mass transfer. Technische Universiteit Eindhoven. https://doi.org/10.6100/IR635735

DOI:

10.6100/IR635735

Document status and date: Published: 01/01/2008

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Gas-liquid Solid Foam Reactors:

Hydrodynamics and Mass Transfer

PROEFSCHRIFT

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

commissie aangewezen door het College voor Promoties in het openbaar te verdedigen op

donderdag 4 september 2008 om 16.00 uur

door

Charl Philip Stemmet

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Copromotoren: dr.ir. B.F.M. Kuster en

dr.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., BASF Nederland B.V. (formally Engelhard De Meern B.V.), and Shell Global Solutions International 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. Stemmet Proefschrift.– ISBN 978-90-386-1326-0

Trefwoorden: chemische reactoren, gepakt bed, gestructuteerde pakking, fysische transport verschijnselen, stoftransport, meerfase stroming, hydrodynamica, vloeistof fractie

Subject headings: Chemical reactors; packed beds; structured packing / physical

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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 bed with the gas and liquid flowing either counter-currently, (a), or co-currently up, (b), or co-currently down, (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 packpack-ings to solid foam

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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 kLaGLin the order of 6 s−1have 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, k}

L, 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 kLwas 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−1L ) 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 kLwas 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: kLaGLεLDL−1 = 311u0.44G (uLρLµL−1)

0.92

(ScL) 0.5

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Summary vii

Downflow: kLaGLεLDL−1 = 3.7 (uLρLµL−1)

1.16

(ScL)0.5 [SI units, mLm−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: kLaGLεL(ScL/ScW ater)0.69= 2.05 × 10−4(Pf)0.8 [SI units, m

3 Lm

−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 supsup-port 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.

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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 m

2 Lm

−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−3G

CL concentration in the liquid phase mol m−3L

de strut length m

DL diffusivity in the liquid, typically 1· 10−9 m2Ls−1

dm strut diameter mm De effective diffusivity m 3 Lm −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 m

2 P s−1

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

Eo∗

modified E ¨otv ¨os number, ρLgd 2 eε/σ (1 − ε) 2 -Fα interfacial force kg m−1 s−1 fα relative permeability -F r Froude number, (εαvα) 2 /(deg)

-g acceleration due to gravity m2

s−1 Gaα Galileo number, ρ 2 αgd 3 eε 3 /(µ2 α(1 − ε) 3 -GaG Galileo number of the gas, ρ2Ggd

3 eε 3 /(µ2 L(1 − ε) 3 )

-GaL Galileo number of the liquid, ρ 2 Lgd 3 eε 3 /(µ2 L(1 − ε) 3 )

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-H Henry coefficient m3

LPa mol−1

h1,2 constants in Equation 2.7 and Equation 5.2

kL liquid-side mass transfer coefficient mLs−1

ki

r intrinsic reaction rate coefficient in Equation 6.3 m

3 Ls

−1 _mol−1 Cat

Lt loading of catalyst on the solid molCatkg−1S

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−1P

R universal gas constant, 8.314 m3

Pa K−1 _mol−1

r reaction rate mol m−3P 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 m3αm

−2 P s−1

uG superficial gas phase velocity m3Gm

−2 P s−1

uL superficial liquid phase velocity m3Lm

−2 P s−1

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

W eL Weber number of the liquid, ρLu 2

Lde/(σL(1 − ε))

-Z total length of packing mP

Greek Symbols

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-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 m

3 void m

−3 P

εα holdup of the liquid or gas phase m3α m

−3 P εG gas holdup m 3 G m −3 P εL liquid holdup m 3 Lm −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−3G ρL liquid density kg m−3L

σL liquid surface tension N m−1

τ tortuosity factor m2

Lm −2 S

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

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

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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,

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maintain-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) reactor packings.

1.1.2 Structured packings

(a) Monolith (b) Internally finned 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

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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 commercial name 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

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(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 packpack-ings 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

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Gas-liquid flow through packings 5

Figure 1.5: Specific geometric surface area for solid foam packings of various ppi numbers and a

comparison with common random and structured packings of different voidages, ε ( = 1_{− ε}S).

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.

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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 bed with the gas and liquid flowing either counter-currently, (a), or co-currently up, (b), or co-currently down, (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 wettbypass-ing 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;

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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

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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.

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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 = 41.5dmN 2 − 0.91d2 mN 3 (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

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

tortuosity, and deis 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 are

increased (dmincreases, εSincreases), and (c) where the ppi number of the solid foam has increased

(N and dmdecreases, εSremains constant).

0 0.1 0.2 0.3 0.4 0.5 0 1 2 3 4 5 6 7 8

Solid volume fraction, ε S [−] Strut length, d e , [mm] 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, Fourie

and Plessis (2002), for different values of the solid holdup, εSand 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

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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 0.3 0 2000 4000 6000 8000 10000

Solid volume fraction, ε

S [mS 3 m P −3 ]

Specific surface area, a

P [m S 2 m P −3 ] ppi number [−] 5 10 20 40 45

(a) Surface area, aP

0 0.1 0.2 0.3 0.4 0.5 0 0.5 1 1.5 2

Solid volume fraction, ε

S [−] Strut diamter d m , [mm] 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

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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}

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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. 12-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 distillaconstruc-tions columns. However, for fast reacconstruc-tions the mass

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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 coefficoeffi-cient, 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 = C1Rem_GScn_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

r DL

πte

(2.2) where DLis the diffusivity in the liquid phase, and teis 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 − 1.203F r 0.111

L (2.3)

where aP is the specific surface area of the packing, and F rLis 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.

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(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 Fαis 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 + BRe 2 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

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Experimental 17 respectively. The voidage of the solid packings is represented by ε, (ε = 1_{− ε}S):

Sα = εα ε (2.6) fG= SGh1, fL = SL− SL0 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 E ¨otv ¨os 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

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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. Gas mass flow controller, 4. Liquid holdup measurement tank placed on a balance, 5. Main liquid supply tank, 6. Liquid pump, 7. Hose pump, 8. Liquid overflow (for high liquid holdup), 9. Liquid drainage 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

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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 Reynolds numbers. 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 E ¨otv ¨os 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.

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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 E ¨otv ¨os 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.

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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, ε0

L[-] 0.067 0.094 0.111 0.115 0 50 100 150 200 250 0 0.05 0.1 0.15 0.2 Eo* [−]

Static Liquid Holdup,

ε L

0 [−]

Experimental data points Model: ε L 0 = 1/ ( 9 + 0.025 Eo*), this work Model: ε L 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 against the E¨otv¨os number.

SL0 = ε0 L ε = [ε (9 + 0.025Eo ∗ )]−1, Eo∗ = ρLgd 2 eε 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

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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. The size 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 high liquid holdup case (pulsing flow regime). From image (a) to (c), time is increasing. The size of each image is 30 x 30 cm, and shows a 5 ppi foam, 1 cm thick, 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.The white line represents the front of the slug of gas moving upwards. A video of this slugging behaviour may be viewed at: http://www.chem.tue.nl/scr/

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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 1 0 0.2 0.4 0.6 0.8 1 Gas Flux [kg m−2 s−1] Liquid Holdup [−] 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 foam}

packings for the different flow regimes. Results for the low liquid holdup regime (εL< 0.4) and the

high 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

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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 foam packings; also given is the 95% confidence interval of the fitted parameters.

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

de[x 103m] 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 funcassump-tions of the respective single phase Ergun equaassump-tions, 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

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Results 25 0 1000 2000 3000 4000 5000 0 0.2 0.4 0.6 0.8 1 Re G [−] Liquid Holdup, ε L [−] Experimental points Re_L = 1185 [−] Re_L = 889 [−] Re L = 593 [−] Re_L = 296 [−] Model (a) 5 ppi 0 200 400 600 800 1000 0 0.2 0.4 0.6 0.8 1 Re G [−] Liquid Holdup, ε L [−] Experimental points Re_L = 296 [−] Re_L = 222 [−] Re L = 148 [−] Re_L = 74 [−] Model (b) 20 ppi 0 100 200 300 400 500 0 0.2 0.4 0.6 0.8 1 Re G [−] Liquid Holdup, ε L [−] Experimental points Re L = 148 [−] Re_L = 111 [−] Re_L = 74 [−] Re_L = 37 [−] Model (c) 40 ppi 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 −10% +10% Liquid Holdup, ε L [−], experimental Liquid Holdup, ε L [−], calculated 5 ppi 20 ppi 40 ppi (d) Parity plot

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

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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 1.5 0 10 20 30 40 50 Gas Flux [kg m−2 s−1] Liquid Flux [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 1.5 0 10 20 30 40 50 Gas Flux [kg m−2 s−1] Liquid Flux [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 40 ppi 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

Gas-liquid solid foam reactors : hydrodynamics and mass transfer

Gas-liquid solid foam reactors : hydrodynamics and mass

transfer

Gas-liquid Solid Foam Reactors:

Hydrodynamics and Mass Transfer

PROEFSCHRIFT

Charl Philip Stemmet

Summary

Gas-liquid Solid Foam Reactors:

Hydrodynamics and Mass Transfer

List of Symbols

Table of Contents

Chapter 1

Introduction

1.1

Conventional packings

1.1.1 Random packings

1.1.2 Structured packings

1.2

Solid foam packings

1.3

Geometric surface area

1.4

Gas-liquid flow through packings

1.5

Scope and outline of the thesis

Appendix: Unit cell model

Chapter 2

Hydrodynamics and modeling of mass

transfer for counter-current flow

Abstract

2.1

Introduction

2.1.1 Mass transfer

2.1.2 Liquid holdup models

2.2

Experimental

2.2.1 Static liquid holdup

2.2.2 Low liquid holdup - trickle flow

2.2.3 High liquid holdup

2.3

Results

2.3.1 Static liquid holdup

2.3.2 Liquid flow regimes

2.3.3 Liquid holdup

2.3.4 Liquid holdup modeling

2.3.5 Flooding

2.3.6 Pressure drop