Application of air in membrane filtration

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APPLICATION OF AIR

IN MEMBRANE FILTRATION

J.Q.J.C. Verberk

ltration

J.Q.J.C. V

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ISBN 90-9019344-8 NUR 950

Published and distributed by: Jasper Verberk

Work: T: +31 15 2781585, F: +31 15 2784918, E: j.q.j.c.verberk@citg.tudelft.nl website: www.sanitaryengineering.tudelft.nl or www.library.tudelft.nl/dissertations

Keywords: membrane ﬁ ltration, drinking water treatment, two-phase ﬂ ow, fouling, concentration polariza-tion, maldistribution

All rights reserved. No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any infor-mation storage and retrieval system, without written permission from the publisher.

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Proefschrift

ter verkrijging van de graad van doctor aan de Technische Universiteit Delft,

op gezag van de Rector Magniﬁ cus prof. dr. ir. J.T. Fokkema, voorzitter van het College van Promoties,

in het openbaar te verdedigen op dinsdag 26 april 2005 om 15.30 uur door Jasper Quirinus Jozef Cornelis VERBERK

civiel technisch ingenieur geboren te ‘s-Hertogenbosch

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Prof. ir. J.C. van Dijk

Samenstelling promotiecommissie: Rector Magniﬁ cus, voorzitter

Prof. ir. J.C. van Dijk, Technische Universiteit Delft, promotor Prof. dr. ir. W.G.J. van der Meer, Universiteit Twente

Prof. dr.-ing. R. Gimbel, Universität Duisburg-Essen

Prof. dr. G. Amy, IHE-UNESCO, Technische Universiteit Delft Prof. dr. F. Kapteijn, Technische Universiteit Delft

Prof. dr. ir. B. van der Bruggen, Katholieke Universiteit Leuven Prof. dr. J. Haarhoff, Johannesburg University

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(Aristoteles, Metaphysica, A 3, 983 b)

Aan Iris en Maurits

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1. INTRODUCTION

1.1 Application of membrane ﬁ ltration 1.2 Transport phenomena in membranes 1.3 Membrane and module geometry 1.4 Operation mode

1.5 Two-phase ﬂ ow

1.6 Two-phase ﬂ ow in membrane ﬁ ltration 1.7 Outline and scope of thesis

2. MASS TRANSFER IN MEMBRANE FILTRATION AND IN TWO- PHASE FLOW

2.1 Introduction

2.2 Hydrodynamics in membrane fi ltration 2.3 Two-phase fl ow in large diameter tubes 2.4 Two-phase fl ow in industrial processes

2.5 Air sparging in cross-ﬂ ow operated ultraﬁ ltration

2.6 Application of air in membrane ﬁ ltration in water treatment processes

2.7 Conclusions

3. TWO-PHASE FLOW IN SMALL DIAMETER TUBES 3.1 Introduction

3.2 Material and methods 3.3 Results

3.4 Discussion 3.5 Conclusions

4. COMBINED WATER AND AIR FLOW IN TUBULAR DEAD-END ULTRAFILTRATION

4.1 Introduction

4.2 Experimental set-up 4.3 Results and discussion 4.4 Industrial relevance 4.5 Conclusions

5. COMBINED WATER AND AIR FLOW IN CROSS-FLOW CAPILLARY NANOFILTRATION 5.1 Introduction 5.2 Experimental set-up 1 2 2 3 6 7 8 10 13 14 15 25 33 39 48 50 57 58 60 63 66 70 73 74 75 79 84 85 89 90 92

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5.4 Industrial relevance 5.5 Conclusions

6. DISTRIBUTION OF WATER AND AIR OVER THE CROSS SECTIONAL AREA OF MEMBRANE MODULES

6.1 Introduction

6.2 Material and methods

6.3 Results water distribution during forward ﬂ ush 6.4 Results water distribution during water and air ﬂ ow 6.5 Discussion

6.6 Conclusions

7. CONCLUSIONS AND EPILOGUE 7.1 Introduction

7.2 Two-phase ﬂ ow in small diameter tubes

7.3 Application of two-phase ﬂ ow in membrane ﬁ ltration 7.4 Maldistribution in large diameter modules

7.5 Practical applications, open questions and recommendation for further research

SAMENVATTING

PUBLICATIONS AND PRESENTATIONS DANKWOORD CURRICULUM VITAE 106 108 113 114 116 123 125 131 134 139 140 141 141 142 143 145 151 157 159

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1.1 Application of membrane ﬁ ltration

Membrane fi ltration is used in many chemical and industrial processes. In the biochemical, food and beverage industries membranes have been applied for many years. Since the last decade membranes are also introduced in drinking water and waste water treatment. Membrane fi ltration, compared to other liquid-solid separation processes, like fi ltration or sedimentation, is an attractive separation process at economical rates with additional fl exibility and improved effi ciency.

Applications of membrane fi ltration in water treatment can be divided into two groups : (1) micro- and ultrafi ltration for the removal of particulate material and micro organisms and (2) nanofi ltration and reverse osmosis for the removal of dissolved material and micro pollut-ants. Although the type and the geometry of the membranes and modules are different the principle of membrane fi ltration is the same. The permeation rate (fl ux) ranges from roughly 40 - 300 l·m-2_·h-1_·bar-1_{for microfi ltration to 0,08 - 40 l·m}-2_·h-1_·bar-1_{for reverse osmosis. At}

capacities up to several hundreds of thousands cubic meters of drinking water per day large membrane areas are needed. Although careful selection of suitable membrane material (hydrophilic/hydrophobic) is a necessity for successful application, other phenomena, like mass transfer, back transport, diffusion and maldistribution are also important. All these phenomena have a clear relation to the hydrodynamics in the installation. In the design of membrane installations these hydrodynamics play an important role in the membrane (module design) and module arrangement (plant design) to provide successful applications and limit energy consumption and investment costs.

1.2 Transport phenomena in membranes

The driving force for membrane fi ltration in water treatment is the pressure gradient across the membrane. As a result of this driving force a convective transport of material from the bulk to the membrane surface is obtained. Solvent (water) permeates through the mem-brane and solutes (dissolved and particulate material) are partly or completely retained by the membrane. The retained dissolved solutes and particulate material accumulate in a boundary layer at the membrane surface and a concentration build-up (in time), the so-called concentration polarisation, is observed (fi gure 1.1). As a result of the build-up of retained solutes at the membrane surface the permeation rate will decrease. The convective transport to the membrane surface is balanced by the back transport from the membrane surface to the bulk. This back transport is governed by diffusion or turbulence. When the convective transport is equal to the back transport a steady state situation is reached and the permeate fl ux is constant in time. The back transport is infl uenced by the fl ow condi-tions inside the membrane. Increase in back transport of rejected solutes and particles by more turbulent fl ow conditions results in improvements in permeation and selectivity. Concentration polarization can result in fouling. Fouling is defi ned as “the process result-ing in loss of performance of a membrane due to deposition of suspended or dissolved

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substances on its external surfaces, at its pore openings, or within its pores” (Koros et al., 1996). Fouling will always occur when particulate material is present in water. Especially in micro- and ultraﬁ ltration the particulate fouling is a major point of attention because rapid undesired ﬂ ux decreases occur.

1.3 Membrane and module geometry

The application of membrane fi ltration in water treatment started about forty years ago when it became clear that membrane fi ltration could be used to desalinate sea water. In arid countries many desalination installations are nowadays in use to produce drinking water from sea water. To obtain a small footprint of the installation, membranes are housed in so-called modules. Besides economic considerations, engineering aspects are of prime importance for the design of membrane modules and systems (Rautenbach and Albrecht, 1989). Membrane fi ltration processes differ signifi cantly in operational concept and appli-cation. Therefore different membrane module confi gurations have been developed based on two types of module confi guration: (1) fl at membranes and (2) tubular membranes. The most common type of fl at membranes is the spiral wound membrane. Two or more leaves (permeate envelopes) are attached to and wound around a central tube. Each leaf is made up of two fl at membranes supported and separated by a highly porous support material (permeate-side spacer) in between: these three components are glued together along three edges. The fourth edge of the “pocket” is attached to the permeate collect-ing tube. Several of these pockets are spirally wound around a permeate collectcollect-ing tube

D

CONVECTIVE TRANSPORT

FEED BOUNDARY MEMBRANE PERMEATE

BACK TRANSPORT

CONCENTRATION

Figure 1.1 - Concentration proﬁ le of dissolved or particulate material and the main transport mechanisms in a membrane ﬁ ltration process.

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with a feed spacer placed between two adjacent leaves to provide fl ow channels for the feed on the outside of the permeate envelop. The feed-side spacer generates turbulence and back mixing. The feed stream fl ows axially through the channels between the spiral windings. The length of the described membrane element is generally one meter. High feed pressures are needed in desalination to overcome the osmotic pressure of the feed water. To withstand these high feed pressures, a stainless steal pressure vessel is used, generally housing six membrane elements in series. To obtain a high overall production (recovery) several modules are placed in a so-called christmas tree confi guration. As a result of the introduction of low pressure membranes in recent years hydraulically optimal module confi gurations have been developed (Meer van der, 2003).

The mass transfer in spiral wound membranes is controlled by the cross-ﬂ ow velocity in the feed-side spacers. Because of turbulence created in these feed-side spacers a spiral wound membrane installation can be operated at relatively low cross-ﬂ ow velocities. Due to the small hydraulic diameter of the feed channels, the packing density of spiral wound membranes is high (in the order of 1.000 m2_·m-3_{). However it is not possible to hydraulically}

clean spiral wound membranes. Therefore spiral wound membranes are only used to treat water with a low fouling potential and thus most commonly spiral wound membranes are only used in nanoﬁ ltration and reverse osmosis applications.

The other often used membrane conﬁ guration is the tubular membrane. The membranes belonging to this group all have a tubular shape (high ratio of length to diameter). The length is ranging from one to three meter and the diameter of the membranes is ranging from half a millimeter to two centimeter. Tubular membranes with a diameter ranging from

Figure 1.2 - Spiral wound reverse osmosis element. ! " # $ % % # $ " ! _$ "

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0,5 to 5 mm are called capillary membranes, while membranes with a diameter larger than 5 mm are called tubular membranes. Tubular membranes are made by casting a membrane onto porous supporting tubes. These supporting tubes are manufactured from ﬁ ber glass, ceramics, carbon, porous plastics, stainless steel or paper and must be strong enough to withstand the feed pressures.

In a tubular and capillary membrane module several to a few thousand membranes are placed in parallel and moulded at each end into tube sheets. The bundle of membranes is surrounded by a low pressure jacket to collect the permeate. The pressurized feed solution fl ows down the tube bore and the product solution permeates the membrane and is collected in the outer shell. Sometimes a central permeate collection tube is used to facilitate permeate discharge. Depending on the module design tubular and capillary membranes can be cleaned hydraulically by means of forward and back fl ush. In tubular membranes turbulent fl ow conditions are obtained at already low fl ow velocities and low hydraulic pressure losses, while the blocking potential is low as result of the large inner diameter of the membranes. However the packing density is low (in order of 200 m2_·m-3_).

The packing density of capillary membranes is high (in order of 1.000 m2_·m-3_{) and blocking}

of capillaries is sometimes observed (Gimbel et al., 1997; Heijman et al., 2004). In capil-lary membranes turbulent fl ow conditions are more diffi cult to obtain, especially because these conditions occur only at high hydraulic pressure losses. Therefore the options to clean capillary membranes hydraulically are more limited. To facilitate hydraulic cleaning ingenious fl ow structures (fi gure 1.3 right) have been designed. Until recently only tubular membranes were used in nanofi ltration. However also capillary nanofi ltration membranes have been developed (Frank et al., 2001). In this thesis the effect of air in the tubular and capillary membranes will be investigated

Figure 1.3 - Schematic drawing of capillary membranes in a membrane module (left picture) and photo of capillary membranes housed in a special designed module (right picture).

&EED 0ERMEATE

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1.4 Operation mode

Membrane systems can be operated in cross-fl ow mode, semi dead-end mode and combinations of these two modes. In cross-fl ow mode the feed fl ow is pumped along the surface of the membrane. In this way turbulence and shear forces are created limiting concentration polarization and fouling. Only a small fraction of the feed water is produced as permeate. The ratio between the fl ow of permeate and the feed fl ow at the inlet of the module is called conversion. The conversion is depending on the module confi guration. According to Aptel and Buckley (1996) the conversion for RO/NF in spiral wound modules (10-25% per element) is in general higher than in tubular modules (0,2-2% per tube). Nanofi ltration and reverse osmosis installations are always operated in cross-fl ow mode to limit the concentration polarization. Several membrane modules are housed in a pres-sure vessel and the concentrate of the fi rst module is fl owing to the second module in the pressure vessel. In order to reduce the energy consumption and to obtain proper fl ow conditions pressure vessels are placed in a so-called christmas tree confi guration or recirculation of the concentrate is used. Micro- and ultrafi ltration system are sometimes operated in cross-fl ow mode. The feed fl ows along the membrane surface at velocities creating turbulent fl ow conditions. The shearing effect of the fl uid as it passes over the surface of the membrane acts to remove particles which have been accumulated at the membrane surface. This shearing effect helps to maintain a relatively steady fl ux across the membrane. In industrial applications cross-fl ow fi ltration at turbulent fl ow conditions is used to limit fouling. However the energy consumption of cross-fl ow operated systems is high and therefore semi-dead end mode is also used (Blume et al., 1995), especially when the solid content of the feed water is low.

In a semi dead-end operated system all water supplied to the membrane passes the membrane as permeate. Because there is no back transport of material to the bulk ﬂ ow

Figure 1.4 - Operation of membrane ﬁ ltration systems and accompanying transport mecha-nisms. #2/33 &,/7 FILTRATION CLEANING $%!$ %.$ CONVECTION BACK CONVECTION BACK

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retained particulate material accumulates at the membrane surface and in the membrane pores. Their size prevents them from passing through the membrane. The trapped particles start to build up a resistance against fi ltration resulting in a rapid permeate fl ux decrease. To obtain a suffi cient overall system performance the membrane has to be cleaned on a regular basis. During a cleaning the back transport is maximized while there is no convec-tive transport of material to the membrane.

In cross-fl ow operated membrane systems the back transport (see fi gure 1.1) can be en-hanced by infl uencing the hydraulic conditions inside the membrane. The simplest method is increasing the cross-fl ow velocity. However this cross-fl ow velocity increase results in an increased head-loss and energy consumption. In nanofi ltration and reverse osmosis systems the increase in cross-fl ow velocity can be quite effective to limit the concentra-tion polarizaconcentra-tion layer. In ultrafi ltraconcentra-tion systems this method is often not very effective to prevent fouling. To prevent fouling, a number of other hydrodynamic enhancement techniques have been used. Most of these techniques are based on the creation of fl ow instabilities. An extensive overview of these fl ow instabilities is given by Al-Bastaki and Abbas (2001). Cleaning of the membrane can be done by different methods. Some are based on hydrodynamics effects to remove fouling, other make use of chemicals to break done fouling material.

Recently, the capillary nanofi ltration membrane has been developed (Frank et al., 2001). This system combines the advantages of ultrafi ltration (good hydraulic cleaning possibility) with the advantages of nanofi ltration (good water quality). The operation of the system is a combination of a cross-fl ow and a dead-end operated system. During fi ltration convec-tive transport to the membrane surface takes place and also a back transport due to the cross-fl ow velocity, while periodically a hydraulic cleaning is performed.

1.5 Two-phase ﬂ ow

Two-phase fl ow is the area of fl uid mechanics that describes the fl ow of mixtures consist-ing of two or more immiscible phases. Two-phase fl ow is the simplest case of multi-phase fl ow. The different phases of multi-phase fl ow are liquid, gas and solid. Two-phase fl ow is constantly met in our daily practice. For example sandstorm, fog, snow and rain are natu-ral examples of two-phase fl ow. Other well known examples are cooking of eggs, carbon dioxide bubbles in beer and baking of cake. In industrial processes many examples of two-phase fl ow are found. Over half of all chemical engineering is concerned with multi-phase fl ow (Wallis, 1969). Water and air two-multi-phase fl ow is already used in water treatment processes. Well known examples are the water-air backwashing of rapid sand fi lters and the water-air scouring of pipelines in the distribution network.

From literature on heat and mass transfer it is known that Taylor fl ow, a specifi c two-phase fl ow pattern, results in an increased liquid-to-solid mass transfer rate from bulk to wall

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compared to single phase liquid fl ow. This increased mass transfer is caused by second-ary rotating fl ows in the liquid slugs. The increased mass transfer takes place at even lower pressure drops compared to single phase fl ow (Kreutzer, 2003). In the automotive exhaust gas cleaning Taylor fl ow is used to enhance mass transfer in monolith reactors. Monolith reactors are ceramic structures of many parallel straight channels with a diam-eter in order of one millimdiam-eter. Based on structural confi guration membrane modules can be well compared with monoliths and the question arises whether water-air two phase fl ow is also applicable in membrane fi ltration processes to enhance the mass transfer. A major difference between monoliths and membrane processes is the operational mode. In monoliths the superfi cial velocities are low compared to the velocities in membranes so extrapolation of existing pressure loss equations, mass transfer relations and scale-up guide lines is not directly possible.

1.6 Two-phase ﬂ ow in membrane ﬁ ltration

The limited back transport in especially (dead-end) membrane fi ltration and the positive experience with two-phase fl ow to increase mass transfer in other industrial applications have raised the question whether water-air two-phase fl ow can be used in membrane fi ltration.

Disturbing the mass transfer boundary layer near the membrane wall is the key factor for enhancing the performance of membrane processes. An increase in cross-fl ow velocity is a simple and commonly used method to enhance mass transfer. However, increasing the cross-fl ow velocity to obtain a more turbulent fl ow is not always effi cient and also has drawbacks like increased energy consumption. In literature different other methods are reported to disturb the mass transfer boundary layer. These methods range from intro-duction of turbulence promoting spacers, intermittent and frequent back washing, vortex generators to injection of fl uidised particles (glass, steel). However all these techniques result in extra hydraulic resistance and costs. An alternative is injection of gas bubbles into the feed fl ow.

Pilot scale experiments with injection of air in the feed fl ow during a forward fl ush cleaning in a dead-end operated ultrafi ltration installation have been performed (van der Meer et al., 1999). This combined water and air fl ow cleaning is called AirFlush®_{. Also experiments} with only a forward fl ush cleaning were performed. The results of the pilot plant experi-ments are presented in fi gure 1.5 and table 1.1. In the experiexperi-ments with only a periodically forward fl ush cleaning the membranes had to be cleaned with chemicals very regularly. When a water-air two-phase fl ow was performed the chemical consumption was reduced signifi cantly while a much more stable process was obtained (van der Meer et al., 2000). Based on these pilot plant experiments it was concluded that the periodic cleaning using a combined water and air fl ow results in a higher and stable fl ux, decreased chemical consumption and an increase of overall system recovery. These experimental results show that a combined water-air two-phase fl ow can improve operation of membrane fi ltration.

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0 24 48 72 96 120 144 168 192 216 240 0 20 40 60 80 100 120 140 160 Time (hour) Flux (l·m -2 ·h -1 ) 0 24 48 72 96 120 144 168 192 216 2400 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6 TMP (bar) flux horizontal UF

flux vertical UF with AirFlush TMP horizontal UF

TMP vertical UF with AirFlush

Figure 1.5 - Results of pilot installation experiments with and without AirFlush®_.

Table 1.1 - Experimental pilot plant results with periodic cleaning with forward ﬂ ush and Air-Flush®_.

Periodic cleaning with forward ﬂ ush

Periodic cleaning with AirFlush® Duration of pilot test

Stable ﬂ ux production Net ﬂ ux

Trans membrane pressure AirFlush® - frequency - discharge air - discharge water - air/water ratio Regular cleaning - frequency - applied chemicals - soak time Expanded cleaning - frequency - applied chemicals - soak time ± 5 weeks ± 135 l·m-2_·h-1 ± 95 l·m-2_·h-1 ± 0,7 bar not applied not applied not applied not applied ± 12 times a day HCl and H₂O₂ 5 - 15 minutes ± 2 times a week Stork Memclean and NaOCl

2 hours ± 10 weeks ± 145 l·m-2_·h-1 ± 130 l·m-2_·h-1 ± 0,6 bar ± 8 times a day ± 20 Nm3_·h-1 ± 5 m3_·h-1 ± 4

± 1 time per 3 days HCl and H₂O₂ 5 - 15 minutes

not applied not applied not applied

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1.7 Outline and scope of thesis

The overall hypothesis for this thesis is

a combined water-air two phase fl ow will have benefi cial effects on mass transfer in membrane fi ltration

This hypothesis will be discussed by answering several sub questions originating from operational points of view.

These sub questions are:

- which two-phase ﬂ ow patterns occur in tubular and capillary membranes at opera-tional conditions?

- does the orientation of the membranes inﬂ uence the performance of air sparged membrane system?

- is the mass transfer improved by air during cleaning in dead-end operated ultraﬁ ltra-tion? And what are optimal operational parameters?

- is the mass transfer improved by air during operation of capillary nanoﬁ ltration? And what are optimal operational parameters?

- is it possible to use studies on small scale and translate these to larger scale applica-tions?

- what are other promising application areas for air in membrane ﬁ ltration?

In chapter 2 a literature review of the principles of capillary and tubular membrane fi ltration systems and two-phase fl ow will be made fi rst. The hydrodynamical parameters neces-sary to discuss mass transfer and their values as found in fi eld installations will be given. Also the basic principles of two-phase fl ow with emphasis on small diameter tubes and literature of two-phase fl ow in relation to mass transfer will be discussed.

In chapter 3 the two-phase fl ow patterns as occurring in capillary and tubular membranes at operational conditions are investigated by visualization experiments in glass tubes. Flow patterns in tubes with diameters corresponding to commercially available membranes have been recorded by taking pictures of fl ow patterns at different values of the superfi cial water and air velocities. From these pictures fl ow pattern maps have been constructed which are compared with available literature data. Also the effect of the orientation of the membranes and modules and the infl uence of this orientation on the possibilities to use two-phase fl ow in membrane fi ltration installations will be discussed.

Chapter 4 deals with the application of water-air two-phase fl ow to remove fouling in dead-end operated ultrafi ltration system treating rapid sand fi lter back wash water. During operation periodically a water-air two-phase fl ow was used to remove the fouling layer. Filtration experiments have been done on a single tubular membrane (diameter 5,2 mm)

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to avoid effects of possible maldistribution of water and air over the cross sectional area of a membrane module. Also head loss experiments were performed. With the results of these head loss experiments the industrial relevance of the combined water and air ﬂ ow will be discussed.

In chapter 5 research on the effectiveness of the combined water and air fl ow in capillary nanofi ltration is presented. In capillary nanofi ltration membrane systems the concentration polarisation and fouling can be controlled by recirculation of the feed water at relatively high cross-fl ow velocities. Experiments on artifi cial water have been performed to evalu-ate whether wevalu-ater-air two-phase fl ow enhances the permeevalu-ate fl ux when concentration polarization is the fl ux limiting mechanism. Based on the experimental results the industrial relevance is demonstrated based on energy consumption calculations.

In chapter 6 the distribution of water and air over the cross sectional area of the membrane module is studied based on experimental research. An equal distribution of water and air over the cross section of the membrane module is essential for a good cleaning. In a test installation the inﬂ uence of superﬁ cial water and air velocities, air injection methods and membrane properties are investigated for membrane modules containing tubular and capillary membranes. Results of the experiments are presented in this chapter.

Finally, in chapter 7 some promising applications of water-air two-phase ﬂ ow are discussed and conclusions are made on the applicability of this technique. Also recommendations for further research are given.

Literature

Al Bastaki N., Abbas A. (2001). Use of ﬂ uid instabilities to enhance membrane performance: a review. Desalination, 136, 255-262.

Aptel P., Buckley C.A. (1996). Categories of membrane operations. In J. Mallevialle, P.E. Odendaal,M. Wiesner (Eds.) Water treatment membrane processes (2.1-2.24). New York: Mc Graw-Hill. Blume I, Koehnen D.M., Roesink H.D.W. (1995). Crossﬂ ow versus dead-end in large ultraﬁ ltration processes. In W.R. Bowen, R.W. Field, J.A. Howell (Eds.), Proceedings of Euromembranes 95, 2, 37-42. Bath, United Kingdom.

Frank M., Bargeman G., Zwijnenburg A., Wessling, M. (2001). Capillary hollow fi ber nanofi ltration membranes. Separation and Purifi cation Technology, 22-23, 499-506.

Gimbel R., Panglisch G., Dautzenberg W., Kiepke O. (1997). Erste Erfahrungen mit Pilotanlagen zur Ultra- und Mikroﬁ ltration der Trinkwasseraufbereitungsanlage Roetgen des Wasserwerkes des Kreises Aachen. In R. Rautenbach, T. Melin, M. Dohmann (Eds.), Möglichkeiten und Perspektiven der Membrantechnik bei der kommunalen Abwasserbehandlung und Trinkwasseraufbereitung (A13.1-A13.24). Aachen: Klenkes.

Heijman, S.G.J., Vantieghem, M., Raktoe, S., Verberk, J.Q.J.C., Dijk, J.C. van (submitted). Blocking of capillaries as fouling mechanism for dead-end ultraﬁ ltration. Submitted to: Journal of Membrane Science, 2004.

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Koros W.J., Ma Y.H., Shimizu T. (1996). Terminology for membrane processes - IUPAC recom-mendations. Journal of Membrane Science, 120, 149-159.

Kreutzer M. (2003). Hydrodynamcis of Taylor ﬂ ow in capillaries and monolith reactors. Delft: Ph. D. Thesis, Delft University of Technology.

Meer W. van der, Termeulen R., Moel P. de, Dalfsen H. van (1999). Luchtspoeling bij ultraﬁ ltratie. H₂O, 4, 20-22.

Meer W. van der, Efferen B. van, Dalfsen, H. van (2000). Air enhanced membrane fi ltration, de-velopments and fi rst full scale plant in the Netherlands. In R. Rautenbach, T. Melin, M. Dohmann (Eds.), Membrantechnik in der Wasseraufbereitung und Abwasserbehandlung: technische Neu-entwicklungen und Betriebserfahrungen im In- und Ausland (A12.1-A12.11). Aachen: Klenkes. Meer W.G.J. van der (2003). Mathematical modelling of NF and RO membrane fi ltration plants and modules. Delft: Ph. D. Thesis, Delft University of Technology.

Rautenbach R., Albrecht R. (1989). Membrane Processes. New York: John Wiley & Sons. Wallis G.B. (1969). One-dimensional two-phase ﬂ ow. New York: McGraw-Hill.

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Mass transfer in membrane ﬁ ltration and

in two-phase ﬂ ow

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2.1 Introduction

In membrane fi ltration convection of solvent to the membrane surface and the back transport of solutes and particles to the bulk fl ow are the main transport mechanisms. The convec-tive transport of solutes to the membrane surface is determined by the applied pressure and the permeability of the membrane. The back transport of solutes and particles from the membrane wall is infl uenced by the type of solute and the hydrodynamic conditions inside the membrane channel.

Hydrodynamics and mass transfer are coupled phenomena. Back transport becomes bet-ter when streamlines of fl uids are not straight but irregular. These irregular streamlines are found in turbulent fl ow. Turbulent fl ow conditions are therefore required for high mass transfer. However turbulent fl ow conditions are obtained at increased pressure drops, especially in narrow tubes like capillary membranes. This increased pressure drop results in a decrease in net driving pressure available for fi ltration and an increase in operational costs. In the design of industrial installations in general and membrane fi ltration installations more specifi cally it is a challenge to minimise the energy consumption while maintaining a high mass transfer rate. To achieve this goal hydrodynamic improvements in the design of installations are being developed.

Two-phase fl ow and more particular the two-phase fl ow pattern slug fl ow is reported to enhance the radial mass transport (Vrentas et al., 1978; Horvath et al., 1973). In small diameter tubes the overall fl ow pattern is laminar, the streamlines are straight and the pressure drop is limited, while in the liquid slugs vortices are present enhancing the radial mass transport to and from the membrane surface.

The use of two-phase fl ow in membrane fi ltration is not new. In protein fractionation ap-plications two-phase fl ow is used in cross-fl ow operated ultrafi ltration for the enhancement of permeate fl ux and retention (Cui, 1993; Cui and Wright, 1994). Also two-phase fl ow has been used to limit particle deposition in cross-fl ow operated ultrafi ltration systems treat-ing artifi cial waters containtreat-ing colloidal suspensions (Cabassud et al., 1997). In hybrid membrane processes like membrane bio reactors (MBR) two-phase fl ow is also used. In a MBR two-phase fl ow has a dual purpose, namely aeration of the biomass and creation of turbulence to limit fouling.

In this chapter ﬁ rst an analysis of hydrodynamics in membrane ﬁ ltration systems as used in water treatment will be given. Relevant hydrodynamic parameters will be introduced and

Figure 2.1 - Liquid slugs and Taylor bubble in two-phase ﬂ ow. In liquid slugs the streamlines in slug ﬂ ow are depicted.

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reviewed. In literature much information is available on operation of membrane installation. However a thorough evaluation of these installations based upon system hydrodynamics is lacking. Secondly two-phase fl ow will be introduced and the literature in industrial applica-tions on two-phase fl ow dealing with mass transfer and hydrodynamics will be reviewed. Thirdly the literature on two-phase fl ow in membrane fi ltration will be reviewed and possible new research topics on two-phase fl ow in membrane fi ltration will be addressed.

2.2 Hydrodynamics in membrane ﬁ ltration

2.2.1 Operation mode

The operation mode has a large infl uence on the hydrodynamics inside the membranes. In a cross-fl ow operated membrane system there will always be a back transport from the membrane wall to the bulk solution. This back transport is governed by diffusion and turbulence. The overall system performance can be easily adapted by changing the hy-draulic conditions during fi ltration.

In a dead-end membrane system there will be no back transport during the production run and a continuing decrease in system productivity will be observed. Therefore a frequent cleaning is necessary and the process is called semi dead-end ﬁ ltration. The overall sys-tem performance can only be inﬂ uenced by the hydraulic conditions during the cleaning phase.

Also a combination of the semi-dead end and cross-fl ow operation mode exists, viz. the semi-dead end system with cross-fl ow. This system is operated in cross-fl ow mode with recirculation. In time a build-up of solutes and particulate material in the system will occur and a permeate fl ux decrease is observed. Therefore a frequent hydraulic cleaning of the system is used. This operation mode is used in capillary nanofi ltration.

In the Netherlands micro- and ultrafi ltration installations are usually all operated in the semi dead-end mode. The raw water has a low fouling potential and only a small fl ux decrease in time occurs, compared to installations used in industry. Most nanofi ltration and reverse osmosis systems are based on the spiral wound membrane confi guration and operated in cross-fl ow mode. As a result of the high pressure needed to overcome the membrane resistance and the osmotic pressure, several modules containing several membrane ele-ments are placed in series. Only recently the capillary nanofi ltration membrane has been developed (Frank et al., 2001). More attention will be given to capillary nanofi ltration in chapter 5.

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2.2.2 Membrane performance

The membrane performance is expressed by the permeate ﬂ ux parameter. This parameter is given by the following general equation, valid for all membrane processes:

permeate flux = 1 dynamic viscosity driving force membrane r ⋅ e esistance (2.1)

For synthetic membranes used in water treatment the main driving force is a pressure gradient across the membrane and equation (2.1) is generally expressed by the following equation (Fane, 1986): J 1 R L m = ⋅ µ ∆p (2.2)

where J is the permeate ﬂ ux, ∆p is the pressure gradient across the membrane, µ_L is the liquid dynamic viscosity and R_m is the hydraulic membrane resistance. In general the inverse of the hydraulic membrane resistance (R_m-1_{) is used and deﬁ ned as the hydraulic}

permeability H_p. This hydraulic permeability depends on the pore size and structure, the porosity and the thickness of the membrane. The pressure gradient is defi ned as the trans membrane pressure (TMP) minus the osmotic pressure difference. The fl ux obtained when pure water is fi ltered is called clean water fl ux (CWF).

The presence of dissolved and particulate material in water will result in deviations from the linear relationship between permeate fl ux and pressure gradient as given in equation (2.2). Dissolved material results in a fl ux decrease due to the pressure needed to overcome the osmotic pressure gradient between feed and permeate side of the membrane. The effect of osmotic pressure is even enlarged by concentration polarization. Accumulation and deposition of colloidal particles and suspended solids near the membrane surface, at and in the membrane pores result in an additional resistance causing a fl ux decrease. Both processes, concentration polarization and fouling, thus result in a lower fl ux and can be limited by infl uencing the hydrodynamic conditions inside the membrane.

Concentration polarization occurs in all pressure driven membrane processes. However the effects of concentration polarization are only taken into consideration in nanofi ltration and reverse osmosis systems. In micro- and ultrafi ltration the permeate fl ux decrease is never attributed to concentration polarization. Particles and colloidal material do not cause an osmotic pressure difference.

2.2.3 Osmotic pressure and concentration polarization

Due to the retention of solutes by the membrane a difference between the concentration of solutes in feed and permeate exists. This difference in concentration is expressed by the parameter osmotic pressure difference. The osmotic pressure is calculated by the van ‘t Hoff equation for dilute solutions:

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πi = bπ,i⋅ ⋅ci Ru⋅T (2.3)

where π_i is the osmotic pressure of solute i, b_π,i is the number of ions formed from the solute, c_i is the concentration of solute i, R_u is the universal gas constant and T is the temperature. The osmotic pressure difference ∆π across the membrane is calculated from the concen-trations at the membrane surface c_m,i and the concentration in the permeate c_p,i:

∆πi πm,i - πp,i i

=

∑

(

)

(2.4)

Equation (2.2) can now be rewritten as:

J Hp (TMP )

L

= ⋅ −

µ ∆πi (2.5)

where TMP is the trans membrane pressure. The difference between TMP and ∆π is often expressed in the parameter Net Driving Pressure (NDP).

As a result of the pressure gradient across the membrane a convective transport of sol-utes to the boundary layer (J·c) is present (see ﬁ gure 2.2). This convective transport is balanced by back transport (D·dc/dx) and solute ﬂ ux through the membrane (J·c

p). Close

to the membrane wall the ﬂ ow is laminar and the concentration of solutes is higher than in the bulk. Due to the concentration gradient solutes will diffuse back from the boundary layer to the bulk. In steady state conditions the convective transport of solutes is equal to the sum of the permeate ﬂ ow and the diffusive back transport and the following mass balance for the boundary layer can be derived:

D FEED BOUNDARY CONCENTRATION CONVECTION * DIFFUSION $DC_DX CF PERMEATE *P CP

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J·c = D·dc dx + J·c

i

p,i _(2.6)

where D is the diffusion coefﬁ cient and x is the distance from the membrane surface. Integration of this mass balance with the boundary conditions:

x = 0 c = c_m,i and x = δ c = c_b,i results in: c - c c ,i - c = exp J· D = m,i p,i b p,i δ _β ⎛ ⎝⎜ ⎞ ⎠⎟ (2.7)

where δ is the thickness of the laminar boundary layer, c_b,i is the concentration of the solute in the bulk and β is the concentration polarization. The ratio between the thickness of the laminar boundary layer and the diffusion coefﬁ cient is called the mass transfer coefﬁ cient k, or:

k = D

δ (2.8)

The mass transfer coefﬁ cient can be expressed in an empirical Sherwood relationship taking into account the ﬂ ow conditions (expressed in the Reynolds number), the nature of the feed solution (expressed by the Schmidt number) and the geometry of the membrane system. The Sherwood relationship represents the relation between convective mass transport and the diffuse mass transport.

Sh = (Re, Sc, geometrical parameters) _(2.9) Sh = k·d D h (2.10) Re = u d⋅ h ν (2.11) Sc = D ν _(2.12)

where Sh is the Sherwood number, Re is the Reynolds number, Sc is the Schmidt number, d_his the hydraulic diameter of the membrane channel, u is the characteristic velocity and ν is the kinematic viscosity.

For spiral wound membranes modules different Sherwood relationships are available. The most used relationship was derived experimentally by Shock and Miquel (1987):

Sh = 0.065 Re_⋅ 7/8_⋅Sc1/4

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Empirical relationships are also available in literature for the Sherwood number for tubular and capillary membranes. For laminar ﬂ ow (Sieder and Tate, 1936)

Sh 1,62 Re Sc d L h 1/3 = ⋅⎛ ⋅ ⋅ ⎝⎜ ⎞ ⎠⎟ 30 Re Sc d L 10.000 h < ⋅ ⋅ < ⎛ ⎝⎜ ⎞ ⎠⎟ (2.14)

For turbulent ﬂ ow (Linton and Sherwood, 1950)

Sh=0,04 Re⋅ 3/4⋅Sc1/3 _Re_>_10.000_(2.15)

In membrane installations the Schmidt number and the membrane geometry are fi xed and the only operational parameter to control the concentration polarization is the cross-fl ow velocity. The cross-fl ow velocity can be used to control the concentration polarization. A higher cross-fl ow velocity will result in a higher pressure drop.

The pressure drop for spiral wound, tubular and capillary membranes is calculated by (Shock and Miquel, 1987):

dp dx = d u 2 h 2 λ ρ_{⋅ ⋅} for 140 < Re < 1.000 (2.16) where λ is the friction coefﬁ cient. For spiral wound membranes this friction coefﬁ cient is given by (Shock and Miquel, 1987):

λ = 6 23_. _⋅_Re−0 3.

(2.17)

and for tubular and capillary membranes by (Rautenbach and Albrecht, 1989):

λ = 64

Re for Re < 2.000 (2.18)

λ = 0.316 Re_⋅ -0.25

for 2.000 < Re < 100.000 (2.19) The use of the above presented theory of concentration polarization is limited because no precipitation of solutes (scaling) is taken into account. The above presented theory, well known as the solution-diffusion model, is therefore used for prediction of the fl ux in reverse osmosis and nanofi ltration membrane systems where the solubility products is not exceeded. Another disadvantage of this model is the assumption of a steady state situa-tion. Also no variation of the concentration profi le with time can be modelled.

Besides the impact of concentration polarization on the permeate productivity of a mem-brane ﬁ ltration installation, there are two other negative aspects associated with concen-tration polarization. First, the accumulation of solute on the membrane surface affects the retention. Secondly, an excessive concentration polarization may cause precipitation (i.e. scaling) as a result of an increase in wall concentration of the solute, thereby reducing both the water permeability and the life time of a membrane. In order to reduce these aspects the concentration polarization has to be limited. Membrane manufacturers use a maxi-mum value of 1,4 for the concentration polarization factor (Wilf, 1997). This concentration

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polarization factor is different from β and given by: CPF = exp A Q Q p f ⋅ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ (2.20)

where Q_p is the permeate productivity of the module, Q_f is the feed ﬂ ow and A a module speciﬁ c factor. Comparison between CPF and β for mono- and bivalent ions shows that a discrepancy of up to 100% can be observed. Therefore β-values up to 1,7 for monovalent ions and 2,2 for bivalent ions might be permitted based on the traditionally allowed CPF of 1,4 for plant design (van der Meer, 2003).

In the design of nanofi ltration and reverse osmosis installations the concentration po-larization is controlled by the module design and the staging of the membrane modules. When the installation has been built the concentration polarization can be infl uenced by the cross-fl ow velocity, permeate fl ux and recovery. In fi gure 2.3 the infl uence of the Rey-nolds number on the concentration polarization and pressure loss is given for different nanofi ltration systems. Calculations are based on empirical relationships (eq 2.7, 2.10, 2.13, 2.14 and 2.15). From this fi gure it becomes clear that in spiral wound membrane fi ltration systems the concentration polarization is low. However the operational range for cross-fl ow velocities is limited because high pressure losses occur at Reynolds numbers of about 300. Tubular nanofi ltration membranes have a concentration polarization which is higher than in spiral wound membranes but the pressure loss to obtain turbulent conditions is low. Tubular membrane nanofi ltration system have a low packing density and thus need a large footprint. Capillary membrane systems have a high susceptibility for concentra-tion polarizaconcentra-tion, due to the low degree of turbulence in the membranes. This observaconcentra-tion is in accordance with Frank et al. (2001). Also the pressure loss to obtain turbulent fl ow conditions is high.

Table 2.1 - Experimental calculated hydrodynamic conditions in different nanoﬁ ltration modules and estimated mass transport coefﬁ cients (Frank et al., 2001; Meer van der, 2003)

capillary NF tubular NF SPW NF

hydraulic diameter channel (mm) 1,0 5,2 1,0

trans membrane pressure (bar) 5,1 5,0 15,9

clean water ﬂ ux (l·m-2_·h-1_·bar-1₎ ₂₀ ₁₆ ₇

Q_f (m3_·h-1₎ _4,8 ₁₅ ₁

u_L (m·s-1₎ _1,7 _0,3 _0,1

mass transfer coefﬁ cient (m·s-1₎ _2,5 _{not calculated} _4,7

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2.2.4 Fouling

A direct result of the separation of water and particulate material is the accumulation, deposition and adsorption of material on the membrane surface and in the membrane pores. These processes are known as fouling. Fouling is the result of concentration po-larization of particulate material and dissolved solutes. Fouling is a complex process and occurs mostly due to colloidal and scale precipitation as well as microbial growth. In the literature much attention is given to the mechanisms and prevention of fouling (Mulder, 1991; Nyström et al., 1995; Hong and Elimelech, 1997; Siedel and Elimelech, 2002; Cho et al., 2002). Different types of fouling are distinguished, its presence largely affected by the type of membrane, materials to be removed and chemical water composition: - scaling/precipative fouling;

- particulate fouling; - adsorptive fouling;

- biofouling/biological fouling.

Figure 2.3 - Theoretical concentration polarization for MgSO₄ and pressure drop as function of the Reynolds number for different nanoﬁ ltration systems (permeate ﬂ ux = 42,5 l·m-2_·h-1_{), D = 1,35·10}-9 m2_·s-1_{, T = 20°C, L = 1 m).} 1 2 3 Reynolds number (-) concentration polarization B 101 102 103 104 0 2,5 5 7,5 10 x 104 $ p (Pa) B_h B_h B_h = 1 mm) $p SPW NF (d h $p Tubular NF (d_h $p Capillary NF (d_h

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Fouling results in an additional resistance for transport of water across the membrane, propagates in time and results in a ﬂ ux decrease. Fouling can be either reversible or ir-reversible. Reversible fouling can be removed from the membrane by different rinsing methods. Irreversible fouling is hard to remove. The only possibility to remove irreversible fouling is the use of chemicals. However, even not all irreversible fouling is removed when chemicals are used.

The mass transfer principle for fouling is identical to the mass transfer principle of concen-tration polarization. Due to the driving force solvent permeates through the membrane, while particles are retained. A build-up of concentration of particles is found at the mem-brane surface (see ﬁ gure 2.5). The convective transport to the memmem-brane is counter bal-anced by a back transport to the bulk ﬂ ow. This back transport is based on diffusivity or hydrodynamics. However, the diffusivity of retained suspended material is low and a build up of material as a cake layer on the membrane surface is observed. When particles are larger than 0.1 µm the hydrodynamic effects are dominant over the diffusion (Melin and Rautenbach, 2003). The main back transport mechanism for particles is thus caused by hydrodynamic effects due to shear stresses at the membrane surface.

The shear stress on a particle is calculated with the equation:

τw ρL L 2

= 1

2⋅ ⋅ ⋅f u (2.21)

where τ_w is the wall shear stress, f is the friction factor which is a function of the Reynolds number, ρ_L is the liquid density and u_L the liquid velocity.

In literature almost no clear guidelines are available on the value of the shear stress to limit particle deposition. Elmaleh and Abdelmoummi (1998) advise in a cross-fl ow operated tubular membrane with a diameter of 6 mm a shear stress between 20 and 30 Pa to obtain optimal removal of accumulated bio mass from the membrane surface. This latter value corresponds to a cross-fl ow velocity of 3,5 m·s-1_{. Above a cross-fl ow velocity of 3 m·s}-1_no

fouling resistance was observed. Cabassud et al. (1997) calculated a shear stress of 5,7 Pa in hollow ﬁ bres with a diameter of nearly 1 mm at a cross-ﬂ ow velocity of 0,71 m·s-1_.

Figure 2.4 - Typical graph depicting reversible and irreversible fouling in an ultraﬁ ltration system. Clean water flux

Irreversible fouling Reversible fouling Chemical cleaning Time Hydraulic cleaning Flux

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Kennedy et al. (2001) calculated a shear stress of 16 Pa in capillary membranes with a diameter of 1,5 mm at a cross-ﬂ ow velocity of 1,63 m·s-1_{. In general it can be said that at}

high cross-ﬂ ow velocities shear stresses of some 10 Pa are obtained.

The objective of the cross-fl ow is to maintain particulate material in suspension in the bulk water in order to prevent their deposition on the membrane. As the cross-fl ow velocity increases, the fouling potential is reduced, but the energy consumption will increase. For commercial available capillary membranes (diameter up to 1,5 mm) the cross-fl ow velocity is limited by the pressure head loss. For capillary membranes the pressure head loss is up to 1 bar·m-1_{at 20°C at velocities of 1 m·s}-1_{. This appears to be the optimum between the}

pressure drop and the membrane compactness, since the membrane ﬁ ber diameters will dictate the number of membranes which can be ﬁ tted in a membrane module (Anselme and Jacobs, 1996).

Besides a high cross-ﬂ ow velocity to improve the back transport other methods are avail-able to improve the back transport of material to the bulk ﬂ ow. Membranes can be cleaned by inserting sponge balls in the membrane tubes. The membrane surface is cleaned by the scouring effect of the sponge balls. This method is only used in large diameter mem-branes.

Another commonly used method the improve the back transport is to use intermittent and high-frequency backwashing. In this method the direction of fl ow though the membrane is periodically reversed by applying a negative pressure gradient across the membrane. In this way particulate material is fl ushed out of the membrane pores and from the membrane surface. During the back wash or back fl ush even chemicals (acid, base, disinfectant) can be added to achieve additional cleaning of the membranes. Backwashing is performed

FEED CAKE

CONVECTION

SHEAR

VELOCITY

CONCENTRATION

Figure 2.5 - Schematic representation of velocity and concentration proﬁ le in ultraﬁ ltration mem-brane.

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with permeate and during back washing the installation is taken out of production, result-ing in a lower overall recovery. The effi ciency of backwashresult-ing is dependent on the fl ux, the frequency, duration and applied pressure of the backwashing, on the type of fouling and on the membrane geometry. In cross-fl ow operated membrane systems a back wash is used less frequently than in a dead-end operated membrane system. To minimize the loss of permeate a backwash can be combined with an increased cross-fl ow (also called forward fl ush or cross-fl ush).

The set points for backwashing are usually obtained by extensive pilot plant research on location because of the complex behaviour of fouling. It is diffi cult to give uniform rules for cleaning methods as became clear from a survey of the Dutch membrane fi eld installations (Kiwa BTO 2004.016, 2004). All installations were operated and cleaned in a different way. In literature only limited information on set points for the different cleaning methods are available. Kennedy et al. (1998) reported an optimum back wash to fi ltration ratio of 2,5 when canal water was fi ltered. This ratio is in correspondence with the ratio given by Howell and Finnigan (1991). The optimum back wash time in the study of Kennedy et al. (1998) was 2 minutes. This quite long time was needed to remove all accumulated material from the membrane module. For forward or cross-fl ushing Kennedy et al. (1998) found that this method was effective when the cross-fl ow velocity was in the turbulent regime (Reynolds number > 2.300). The duration of the cross-fl ush did not have much infl uence on the fl ux restoration. However the module should at least be totally fl ushed.

In contrast to reverse osmosis and nanofi ltration systems almost no (dimensionless) parameters are used to design ultrafi ltration systems in water applications or to evaluate their performance. However in table 2.2 a fi rst attempt is made to use (dimensionless) parameters to evaluate the system performance. Assumptions made for these calculations were a permeate fl ux of 100 l·(m-2_·h-1_{), a length of the membrane of 1 m, turbulent fl ow}

conditions starting at a Reynolds number of 2.300, a back fl ush to fi ltration ratio of 2,5 and a temperature of 20°C. From this table it can be concluded that for capillary and tubular membranes operated in dead-end mode the Reynolds number inside the membrane lu-men is insuffi cient is to create turbulent fl ow conditions during a back wash. Also the shear stress during a back wash is insuffi cient to clean the membrane. However, a back wash is used in almost all installations. Apparently most of the membrane resistance is caused by pore blocking which can be removed by a back wash only. As result of the back wash the cake layer is (locally) lifted from the membrane surface and the particulate material is slowly transported out of the membranes, especially in tubular membranes. The pressure loss during a back wash is limited.

The hydrodynamic conditions inside the membrane during a forward fl ush are quite dif-ferent. A forward fl ush is performed with turbulent fl ow conditions. To achieve this high velocities are necessary. Especially in capillary membranes these high velocities result in undesired pressure losses due to friction. Therefore a forward fl ush is even not pos-sible in some membrane systems with membrane modules placed in series. In capillary membranes the shear forces during a forward fl ush meet the required values, in tubular membranes the shear forces are still below the required values.

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2.3 Two-phase ﬂ ow in large diameter tubes

In liquid-gas two-phase fl ow the mixture adopts different confi gurations, better known as fl ow patterns or fl ow regimes. Flow patterns are identifi ed by different techniques. The most widely used technique is fl ow visualization by eye or photographic observations. In literature many different two-phase fl ow patterns have been determined and the classifi cation is gen-erally based on subjective grounds. The two-phase fl ow is often very chaotic and diffi cult to describe, which leaves room for personal judgment and interpretation. For vertical and horizontal two-phase fl ow it is necessary to defi ne the regimes independently, because in horizontal two-phase fl ow gravity causes an asymmetric distribution of the phases. 2.3.1 Flow regimes in vertical upward two-phase fl ow in large diameter tubes

For vertical two-phase fl ow the classifi cation of Hewitt and Hall-Taylor (1970) will be fol-lowed describing four basic fl ow patterns for vertical upward two-phase fl ow in a 5-10 cm diameter column. The liquid viscosity is low (water) and the volume changes due to de-compression are neglected.

At low gas and liquid fl ow rates small discrete air bubbles are present in the liquid. When the bubbles are very small they behave as rigid spheres rising vertically in rectilinear motion. However, above a critical size (about 0,15 cm for air-water at low pressure) the bubbles begin to deform, and the upward motion is a zig-zag path with considerable randomness. When the turbulence level is low the name laminar bubbly fl ow is used. When the liquid fl ow rate and thus turbulence become higher, pressure fl uctuations become stronger than the surface tension and the bubbles will break into smaller spherical bubbles (Clift et al., Table 2.2 - Theoretical calculated hydrodynamics in ultrafi ltration membrane (L = 1 m, T = 20°C).

dead-end operation cross-fl ow operation diameter channel (mm) 1,0 5,0 1,0 5,0 fi ltration u (m·s-1₎ Re (-) p (bar) τw (Pa) 0,11 110 0,036 0,45 0,02 110 0,0003 0,02 4,02 4.000 3,21 40,20 0.8 4.000 0,025 1,61 back fl ush u (m·s-1₎ Re (-) p (bar) τw (Pa) 0,28 276 0,089 1,12 0,06 276 0,0007 0,04 0,28 276 0,089 1,12 0,06 276 0,0007 0,04 forward fl ush u (m·s-1₎ Re (-) p (bar) τw (Pa) 2,31 2.300 1,22 15,3 0,46 2.300 0,010 0,61

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1978). This pattern is called dispersed bubble ﬂ ow. When the gas ﬂ ow rate is increased the volumetric gas concentration (α_G) will become larger and bubbles will collide and coalesce forming a number of somewhat larger individual bubbles with a umbrella shaped spherical cap, but with diameters smaller than the pipe (Taitel et al., 1980). The void fraction where umbrella shaped bubble are formed is about 0,2. These umbrella shaped bubbles have a rise velocity larger than the smaller bubbles and break up easily by turbulence.

When the void fraction becomes larger the spherical cap bubbles will collide with smaller air bubbles and coalesce, forming larger bubbles. When the diameter of the gas bubbles is about half the tube diameter they are called Taylor bubbles (Davies and Taylor, 1949). Taylor bubbles occupy most of the pipe cross sectional area and are infl uenced by the tube wall. Their motion is no longer free in the radial direction. Taylor bubbles are axially separated from each other by water packages, the so called liquid slugs. In these liquid slugs small air bubbles are dispersed. The rise velocity of a Taylor bubble is larger than of the small discrete bubbles, and these small bubbles are overtaken by the Taylor bubble. Due to the high velocity of the liquid slug, these small bubbles coalesce with the large Taylor bubble in the wake zone of the slug bubble. When the length of a Taylor bubble becomes larger than a few times the tube diameter the liquid fi lm next to the Taylor bubble becomes very thin. The liquid next to the gas bubble fl ows downward as a falling fi lm. Part of the small

bubble slug churn annular

uG,s

water

air

Figure 2.6 – Flow regimes in vertical upward two-phase ﬂ ow in large diamter tubes at constant superﬁ cial liquid velocity.

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discrete bubbles already coalesce in this liquid fi lm with the Taylor bubble. At the bottom of the Taylor bubble small gas bubbles are separated from the Taylor bubble by an en-trainment process. The fl ow in liquid fi lm torns small bubbles free from the Taylor bubble. When the process of growth by coalescence and loss by entrainment is equal, the fl ow is fully developed. A fully developed Taylor fl ow is called slug fl ow. In slug fl ow most of the gas is located in large bullet shaped bubbles having a diameter almost equal to the pipe diameter. These bubbles move uniformly upward. Different researchers suggest a length of 60 - 200 pipe diameters to obtain a stable slug fl ow to develop (Lin et al., 1987). Increasing the air fl ow results in longer air bubbles. Liquid is now torn apart form the liquid fi lm next to the air bubble by the friction with the gas velocity. This process is better known as fl ooding. The bullet-shaped Taylor bubble becomes narrow, and its shape is distorted by the liquid entrained from the liquid fi lm. The continuity of the liquid in the slug between successive Taylor bubbles is repeatedly destroyed by a high local gas concentration in the slug. As this happens the liquid slug falls. This liquid accumulates, forms a bridge and is again lifted by the gas. This fl ow pattern is called churn fl ow. Typical for churn fl ow is the oscillatory or alternating direction of motion of the liquid.

Increasing the gas fl ow even further results in continuity of the gas phase along the pipe in the core. The liquid phase moves upwards partly as wavy liquid fi lm and partially in the form of drops entrained in the gas core. This fl ow pattern is called annular fl ow.

2.3.2 Flow regimes in horizontal two-phase ﬂ ow in large diameter tubes

In horizontally orientated tubes at low air fl ow rates small air bubbles are formed. These air bubbles tend to fl ow in the upper part of the tube. The fl ow pattern is called bubble fl ow. Increasing the gas fl ow rates results in a fl ow pattern almost similar to slug fl ow in vertical tubes. However the liquid layer separating the gas bubble from the wall tends to be thicker at the bottom of the tube than at the top. Also the nose of the gas bubble is asymmetric. This fl ow pattern is called plug fl ow. Further increase of the air fl ow rate results in a com-plete separation of liquid and gas, the fl ow pattern is therefore called stratifi ed fl ow. Liquid is fl owing at the bottom of the tube, gas is fl owing at the top. A further increase in gas fl ow rate results in large surface waves on top of the liquid layer. Due to the wavy character this fl ow pattern is called wavy fl ow. Further increase of the gas fl ow rate results in large waves. Eventually, the waves become big enough to reach the top of the channel. The waves propagate at high velocities and wet the whole channel surface leaving a liquid fi lm covering the surface in between the bridging waves or slugs. This fl ow pattern is called slug fl ow. The fl ow during slug fl ow is asymmetrical, on top of the channel the slugs are found, liquid is fl owing on the bottom of the channel. Further increase in gas fl ow results in annular fl ow. The gas is fl owing in the centre of the tube and the liquid next to the wall. At the bottom of the tube the liquid fi lm is thicker than at the top.

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2.3.3 Flow pattern maps

Results of observations of two-phase fl ow experiments are usually presented in fl ow pattern maps. A fl ow pattern map depicts data from experimental observations on a two-dimensional plot (fi gure 2.8). The coordinates used are the two-dimensional superfi cial liquid and gas velocities (Wallis, 1969). In fl ow pattern maps areas where the fl ow patterns are similar are separated from each other by so-called transition lines. By means of fl ow pat-tern maps the fl ow patpat-tern at a certain liquid and air velocity for a specifi c pipe geometry can easily be deduced. However there is no reason to expect that an experimental fl ow pattern map can be used for other pipe geometries.

To prevent extensive experimental research on fl ow patterns in pipes with a different di-ameter, models have been developed predicting the theoretically boundaries for upward two-phase fl ow. These models are always verifi ed with experimental data. Taitel et al. (1980) presented a physical model describing transitions between the fl ow regimes and used this model to develop theoretically based transition equations to construct fl ow pattern maps independent of pipe geometry or fl uid properties. The model of Taitel is valid for pipes with diameters of 2 – 6 cm at low pressures. For a derivation of the transition equations see Taitel et al. (1980). Here the most important equations are summarized:

bubbly flow plug flow stratified flow wavy flow slug flow annular flow

Figure 2.7 - Flow regimes in horizontal two-phase ﬂ ow in large diameter tubes (Hewitt and Hall-Taylor, 1970).

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Existence of bubble ﬂ ow: ρ ρ ρ σ L h L G g d 2 2 0 25 4 36 ⋅ ⋅ −

(

)

⋅ ⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ≤ . , (2.22) Bubble to slug: u_{L s} u_{G s} g L G L , , , , = ⋅ − ⋅⎡ ⋅

(

−

)

⋅ ⎣ ⎢ ⎤ ⎦ ⎥ 3 115 ₂ 0 25 ρ ρ σ ρ (2.23)

Bubble to dispersed bubble: u u

d g L s G s h L L L G L , , , , , , + = ⋅ ⋅⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ⋅⎡ ⋅

(

−

)

⎣ ⎢ 4 0 0 429 0 089 0 072 σ ρ ν ρ ρ ρ ⎤⎤ ⎦ ⎥ ⎛ ⎝ ⎜ ⎜ ⎜ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ ⎟ ⎟ ⎟ 0 446, (2.24)

Slug to churn transition:

L d u g d E h M h = ⋅ ⋅ + ⎛ ⎝ ⎜⎜ ⎞_⎠⎟⎟ 40 6, 0 22, (2.25) Annular ﬂ ow: u g G s G L G , , , , ⋅ ⋅ ⋅

(

−

)

⎡⎣ ⎤⎦ = ρ σ ρ ρ 0 5 0 25 3 1 _(2.26) 10-2 10-1 100 101 102 10-3 10-2 10-1 100 101 u G.s (m·s -1 ) u L.s (m·s -1 ) intermittent flow churn flow slug flow

dispersed bubble flow annular flow

Figure 2.8 - Experimental ﬂ ow pattern map for a vertically orientated tube with diameter of 12,3 mm (Barnea et al., 1983).

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Based on the transition equation theoretical ﬂ ow pattern maps can be constructed. Barnea et al. (1983) reported that the theoretical predicted transition boundaries for a two-phase upward ﬂ ow as predicted by Taitel were valid for small diameter pipes.

2.3.4 Fundamentals of slug ﬂ ow in a vertical tube

In the following chapters experimental results will be presented based on application of phase fl ow in membranes. To understand these experiments some theory of two-phase fl ow and measuring techniques is necessary. Sometimes this theory is explained in the appropriate chapters. However some theory of two-phase fl ow and more specifi c the fl ow pattern slug fl ow is too important not to devote special attention to it in a special paragraph. This brief overview of the fundamentals of two-phase fl ow is not intended to be complete, but offers a fi rst introduction into two-phase fl ow.

When air is introduced in a stationary liquid without walls, air bubbles will be formed and move upward due to their buoyancy. In tubes the shape and rise velocity of the air bubbles is determined by different parameters, viz. speciﬁ c gravity, surface tension, viscosity, pipe diameter, liquid and air velocities. From these parameters different forces can be deduced, like the inertia force (ρ·u2_·L2_{), the gravitational force (}ρ·g·L3_{), the viscous force (µ·u·L) and}

the surface tension force (σ·L). Different dimensionless numbers can be constructed with these forces.

The Reynolds number represents the relation between the inertial force and the viscous force and is given by the relationship:

Re = u d⋅ h

ν (2.27)

where u is the velocity, ρ_L is the density of the liquid, d_h is the hydraulic diameter of the tube and ν is the dynamic liquid viscosity. The Reynolds number is indicating the fl ow condi-tions. At Reynolds numbers smaller than 2.300 the fl ow through a tube is called laminar. The fl uid fl ows smoothly trough the tube in straight streamlines at constant velocity with-out vortices or other turbulence. At Reynolds number larger than 4.000 the fl ow is called turbulent. Eddies and vortices are visible in the fl owing water, no straight fl ow lines are observed. The fl ow type in the region 2.300 < Re < 4.000 has no clear name, but is often referred to as the fl ow type in the transition area.

The Eötvös number represents the relation between the gravitational force and the surface tension force and is given by the relationship:

Eo =

(

ρL−ρG

)

⋅ ⋅g L

σ

2

(2.28)

where ρ_g is the gas density and σ is the surface tension. The surface tension keeps the pipe wall wet and tends to make small liquid drops and small gas bubbles spherical. The

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gravity tends to pull the liquid to the bottom of the pipes in case of non-vertical ﬂ ow. The surface tension dominates when the bubble in a vertical pipe does not move at all. The static interface adopts a particular shape so that gravitational forces are completely bal-anced by surface forces. According to Bretherton (1961) a bubble does not have a rise velocity when the Eötvös number is smaller than 3,37.

The capillary number represents the relation between the viscosity force and the surface tension force and is given by the relationship:

Ca = µ uTB

σ

⋅ (2.29)

where u_TB is the velocity of a Taylor bubble. The capillary number characterises the ﬂ ow ﬁ eld in the liquid slug within a pipe. When the capillary number is smaller than 0,47 a toroidal rotating vortex creates mixing inside the liquid slug. When the capillary number is higher than 0,47 the liquid slugs bypass the gas bubbles (Thulasidas et al, 1997).

The Morton number is the ratio of gravitational and capillary forces and is given by:

Mo = g· - · 4 L G L 2 3 µ ρ ρ ρ σ ⋅

(

)

(2.30) For bubbles rising freely in inﬁ nite media it is possible to prepare a generalized graphical correlation in terms of the mentioned dimensionless numbers. This graphical representa-tion is depicted in ﬁ gure 2.9. Relarepresenta-tionships for these freely rising air bubbles have been

-12 -10 -8 -6 -4 -2 0 2 4 6 ₈ 10-1 1 10 102 103 104 105 10-2 10-1 1 10 102 103

Eötvös number Eö

Reynolds number Re

Log Mo

Figure 2.9 - Shape regimes for bubbles and drops in unhindered gravitational motion through liquids (Clift et al, 1978).