Properties of nanofiltration membranes; - TU/e

Properties of nanofiltration membranes; model development and industrial application

PROEFSCHRIFT

ter verkrijging van de graad van doctor aan de Technische Universiteit Eindhoven, op gezag van de

Rector Magnificus, prof.dr. M. Rem, voor een commissie aangewezen door het College voor

Promoties in het openbaar te verdedigen op woensdag 20 juni 2001 om 16.00 uur

door

Johannes Martinus Koen Timmer

geboren te Delft

Dit proefschrift is goedgekeurd door de promotoren: prof.dr.ir. J.T.F. Keurentjes en prof.ir. J.A. Wesselingh Omslagfoto’s: met dank aan NIZO Food Research Omslagontwerp: Double Click Druk: Universiteitsdrukkerij T.U. Eindhoven CIP-DATA LIBRARY TECHNISCHE UNIVERSITEIT EINDHOVEN Timmer, Johannes M.K. Properties of nanofiltration membranes ; model development and industrial application / by Johannes M.K. Timmer. - Eindhoven : Technische Universiteit Eindhoven, 2001. Proefschrift. - ISBN 90-386-2872-2 NUGI 813 Trefwoorden: levensmiddelentechnologie ; membraantechnologie / nanofiltratie ; stofoverdracht / fysisch-chemische simulatie ; Maxwell- Stefan theorie Subject headings: food and feed chemistry ; membrane technology / nanofiltration ; mass transfer / physicochemical simulation ; Maxwell- Stefan theory

To Sophie,

a major driving force

ACKNOWLEDGEMENTS

Finishing a PhD work can take a lot of time. The first results were obtained in the early nineties

but surprisingly they are not outdated yet. What does this tell us? Was the idea too far ahead of

time? Do developments like this take so much time? Or do we spent research money for other

purposes? I’m not giving an answer to these questions. An advantage of taking so much time is

that I learned to know many people who are of major importance to the work and my personal

development.

First of all, I would like to thank the Netherlands Institute for Dairy Research, nowadays called

NIZO Food research, for the opportunity of making the research that is the core of this thesis.

Collaboration with world-famous experts in various areas of dairy research, made me aware of

the giant puzzle research generally is. I especially want to thank the current and former

Membrane Group members. Caroline, I think we pushed membrane science and process

understanding in the dairy industry forward. Your practical view on my theoretical whisperings

was of the utmost importance. It was the tie I needed to the real world. The result of our

collaboration is expressed in chapters 2 through 4. I hope we will continue to have Portwine

experiences, like in Oviedo. Jan Henk, I will remember you as the very flexible and hypercreative

scientist, who made it possible for me to start at NIZO. Janneke, Saskia, Jan, Teus, Lowie, Durita,

Monique, Hennie, Dick, Ton, Zeno, Johan, Nico, Anton, Jack, (probably I forgot a couple) it has

always been a pleasure working with you. Your expertise in membrane processes was

indispensable in the set up and performance of experiments, design of laboratory systems and

pilot-plants, and the quality of the work. Also the atmosphere within the group was excellent. I

think we showed what a team is capable of accomplishing. Han and Gerrald, I want to thank you

for focussing my attention on an omission in my original GMS model.

I want to thank my other colleagues at the various departments for the pleasant collaboration and

the way they contributed to my development. Ita, to me you will stay the face of NIZO, even now

you left. It was always a pleasure entering the Institute, seeing you in the fish-bowl. Thank you

for all the support you gave me in the past. Many others should be mentioned but a bookwork at

least the size of this thesis is necessary. I’m sorry if I overlooked you.

Reinoud, Frederik and Hans at the University of Groningen, I would like to thank you for the very

pleasant collaboration on the GMS theory and its application to NF processes. Frederik, I want to

thank you for making the first “jump” in the GMS theory at NIZO during your graduation work.

Four years later, your data are still the feed to our models. Reinoud, I really appreciated the time

you spent on serving as a sparring partner, even after you finished your PhD work and started at

Heineken. Our scientific discussions were very stimulating and still are. The results are presented

in the chapters 5 and 6 of this thesis. I hope you don’t suffer from a persistent mental damage

after experiencing my “Peugeot 309 going around the corner” technique.

And then there is Jos. By coincidence we met in 1988 in the US and developed a friendship.

Neither of us could have guessed at that time you were going to be my promotor. Our discussion

in February 1998 on how to get this PhD thesis a reality was a turning point. Our collaboration

since that time is very stimulating and I hope it continues. Anyone who needs an explanation on

narcoleptic behaviour can rely on your experience.

The staff members, PhD students and TWAIO’s of the Faculty of Chemical Engineering and

Chemistry, Section Process Development at the Eindhoven University of Technology, I want to

thank for the interest they showed in finishing this thesis and the relaxed working environment.

At NIZO I was fortunate to meet many people from different cultural background. I learned to

appreciate my fellow Europeans, their habits and their food, and learned more about the

Netherlands in the many trips to, what are considered to be, Dutch tourist attractions. Ana,

Raquel, Fatima, Raquel, Sofia, Ricardo, Eunice, Sonia, Celia, Anna, Maria, Olimpia, Maπ,

Anneli, Catherine and Nina. I want to thank you for making my private life more interesting and

for the hospitality you and your families offer, every time I’m around.

Being able to finish a PhD thesis is also dependent on “home base”. I want to thank my parents

for the education and guidance they gave me in my way to adulthood; my father for my concrete

constitution and mentality and my mother for the social touch. Thanks to the baseball gang,

especially Bert and Ruud, for looking after me in difficult moments, Henk, Ruben, Marieke and

Dick for many pleasant gatherings in the last two decades and the Carnival gang, especially

Marcel, for the annual mental sessions and the possibilities of getting matter of my chest.

Last but not least, there is my own seed: Sophie. You give life a meaning. Looking at you is

sufficient to reenergize my battery. How energetic would I be in your continuous presence?

CONTENTS

Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Summary Samenvatting Curriculum

Industrial membrane processes; perspectives of nanofiltration Transport of lactic acid through reverse osmosis and nanofiltration membranes Lactic acid separation from fermentation broths by reverse osmosis and nanofiltration Use of nanofiltration for concentration and demineralisation in the dairy industry: model for mass transport Determination of properties of nanofiltration membranes; Pore diameter from rejection measurements with a mixture of oligosaccharides Determination of properties of nanofiltration membranes; Charge properties from rejection measurements using NaCl and prediction of rejection of CaCl2 and NaH2PO4 General discussion and future research needs

1

19

39

61

87

103

123

1

CHAPTER 1

Industrial membrane processes; perspectives of nanofiltration

2 CHAPTER 1

1. INTRODUCTION Starting in the late sixties, membrane processes gradually have found their way into industrial

applications and serve as viable alternatives for more traditional processes like distillation,

evaporation or extraction. Based on the main driving force, which is applied to accomplish the

separation, many membrane processes can be distinguished. An overview of the driving forces

and the related membrane separation processes is given in Table 1.

Table 1: Driving forces and their related membrane separation processes

Driving force Membrane process pressure difference

chemical potential difference

electrical potential difference temperature difference

microfiltration, ultrafiltration, nanofiltration, reverse osmosis or hyperfiltration pervaporation, pertraction, dialysis, gas separation, vapor permeation, liquid membranes electrodialysis, membrane electrophoresis, membrane electrolysis membrane distillation

Many textbooks have been written on the basic mechanisms and the various applications of these

processes [1,2,3,4,5]. Pressure driven membrane separation processes, electrodialysis and gas

separation are industrially implemented and are generally considered as proven technology. Most

of the other processes, however, are still in the stage of development. As this thesis will focus on

pressure driven membrane separations, no further comments will be given on the other

techniques.

1.1 Pressure driven membrane processes Four pressure driven membrane processes are distinguished in practice:

1. Microfiltration (MF) is characterised by a membrane pore size between 0.05 and 2 µm and

operating pressures below 2 bar. MF is primarily used to separate particles and bacteria from

other smaller solutes.

2. Ultrafiltration (UF) is characterised by a membrane pore size between 2 nm and 0.05 µm and

operating pressures between 1 and 10 bar. UF is used to separate colloids like proteins from

small molecules like sugars and salts.

3. Nanofiltration (NF) is characterised by a membrane pore size between 0.5 and 2 nm and

operating pressures between 5 and 40 bar. NF is used to achieve a separation between sugars,

other organic molecules and multivalent salts on one hand and monovalent salts and water on

the other.

Industrial membrane processes; perspectives of nanofiltration 3

4. Reverse osmosis (RO) or hyperfiltration. RO membranes are considered not to have pores.

Transport of the solvent is accomplished through the free volume between the segments of

the polymer of which the membrane is constituted. The operating pressures in RO are

generally between 10 and 100 bar and this technique is mainly used to remove water.

The importance of these membrane processes can be judged from the membrane area installed in

the various industrial sectors.

Membrane area (1000 m2)

Figure 1: Total installed membrane area world-wide for RO of dairy liquids [6].

( whey: ■; milk:□; other:●; total:○)

1.2 Application areas 1.2.1 Dairy industry Figures 1 and 2 show the membrane area for RO and UF that has been installed in the dairy

industry [6]. After a stabilisation of the installed membrane area in the early nineties, a sudden

increase is apparent since 1994. This fact can be explained by lower prices for membrane

systems, replacement of old equipment and technology - the need for whey processing exists for

about 25 years, which might make dairy companies consider replacement -, increase of

1970 1980 1990 2000 Year

4 CHAPTER 1

processing capacity with the possibility of lowering the energy consumption per unit product, an

improving economic situation and the development of new markets.

Membrane area (1000 m2)

Figure 2: Total installed membrane area world-wide for UF of dairy liquids [6].

( whey: ■; milk:□; other:●; total:○)

1.2.2 Water and waste water treatment Since the early seventies a steady growth of various membrane processes in the manufacture of

drinking water is found [7]. In the beginning, membrane processes for drinking water production

were only applied in the US and the middle East. Nowadays the applications are rapidly

expanding all over the world. World-wide, 9.106 m3 of water is processed per day by RO and 106

m3 by NF and UF [7]. These capacities correspond to membrane areas of approximately 2.107,

2.106 and 4.105 m2, respectively.

In 1994 membrane techniques finally found their way on a large scale in waste water treatment.

Currently, about 0.8.106 m3 of waste water permeate is produced by MF and UF on a daily basis

[7]. An estimated membrane area related to this capacity is 3.105 m2. Many applications can be

found in membrane bioreactors, in which biological treatment of the waste water is made

simultaneously with membrane filtration.

1970 1980 1990 2000 Year


The dairy and drinking water industry correspond to a membrane sales value of about Dfl 1

billion annually, which is related to replacement only.

1.2.3 Possibilities of NF in water recovery New perspectives for membrane technology can be found in the reuse of water and the reduction

of energy consumption related to this reuse. In the reuse of water, membrane processes can either

be integrated in the process or used as an end-of-pipe treatment method. Integrated solutions seem

most advantageous with respect to the potential economic and energetic gain [8]. In addition to

water, other valuable auxiliaries can be recovered, thereby reducing effluent treatment costs.

However, a general assessment of the economics and the possibilities of reducing the water and

energy consumption is not possible because integrated solutions appear to be extremely case-

specific. However, for end-of-pipe application of NF boundary conditions for an economically

viable application can be derived [8]. It was found that a difference between the water inlet

temperature of a process and the main process temperature of 15°C already results in both

economic and energetic gain. Each m3 of water reduction results in an economic gain of at least

Dfl 0.25, while a reduction of energy consumption of 100 MJ per m3 water saved is apparent [8].

However, a sensitivity analysis showed that the economics of the process are very dependent on

the energy consumption of the NF process. The energy consumption can be directly related to the

applied transmembrane pressure. High transmembrane pressures are used when feed solutions

contain components that can create an osmotic pressure or that show a severe membrane fouling.

In waste water treatment and many food applications these conditions will occur. Therefore, a

clear understanding of the NF process is necessary. To solve this problem, predictive tools will be

of help to design or optimise the NF process. To start this tool development, the first step is to

establish the basic characteristics of NF processes and the mechanisms that are responsible for the

separation.

2. NANOFILTRATION

2.1 General In general NF has two distinct properties [9]:

• The pore size of the membrane corresponds to a molecular weight cut off value of

approximately 300-500 g/mole. Therefore, the separation of components with these molecular

weights from higher molecular weight components can be accomplished.

6 CHAPTER 1

• NF membranes have a slightly charged surface. Because the dimensions of the pores are less

than one order of magnitude larger than the size of ions, charge interaction plays a dominant

role. This effect can be used to separate ions with different valences.

Table 2: Overview of possible applications of nanofiltration in various industries.

Industry Application Food Textile Clothing and leather Paper and graphical Chemical Metal plating and product /electronic and optical Water production Landfills Agriculture

Demineralisation of whey [10-13] Demineralisation of sugar solutions [14] Recycle of nutrients in fermentation processes [15] Separation of sunflower oil from solvent [16,175] Recovery of Cleaning-In-Place solutions [18,19] Recovery of regeneration liquid from decolouring resins in sugar industry [20-23] Effluent treatment [24,25] Purification of organic acids [26-28] Separation of amino acids [6,30] Removal of dyes from waste water [31] Recovery of water and salts from waste water [32-39] Recovery and reuse of chromium(III) and chromium(II) [40-42] Recovery of water from waste water or waste water treatment effluent [43-47] Recovery of bleaching solution [48-50] Sulfate removal preceding chlorine and NaOH production [51-53] CO2-removal from process gasses [54] Preparation of bromide [55] Recovery of caustic solutions in cellulose and viscose production [56] CaSO4 precipitation [57] Separation of heavy metals from acid solutions [58,59] Removal of metal sulfates from waste water [60] Cleaning of machine rinsing solutions [61] Removal of Nickel [62] Recovery of Cu-ions from ore extraction liquids [12,62-65] Al3+ removal from canning industry waste water [66] Recovery of LiOH during treatment of battery waste [67] Removal of degreasing agents from water [68-71] Removal of precursors of disinfection byproducts [72,73] Hardness removal [74,75] Removal of natural organic matter (a.o. colour) [76-81] Removal of pesticides [82-84] Removal of heavy metals (As, Pb), Fe, Cu, Zn and silica [85,86] Treatment of brackish water [87] Removal of phosphate, sulphate, nitrate and fluoride [88-91] Removal of algal toxins [92,93] Purification of landfill leachate [94-104] Removal of selenium from drainage water [105]

With these properties the most important application areas can be defined:

• removal of monovalent ions from a.o. waste water, reaction mixtures in which NaCl is

formed and whey.


• separation between ions with different valences.

• separation of low- and high-molecular weight components.

An overview of the possible applications of NF in various industrial areas is given in Table 2. All

applications can be deduced to the three areas mentioned above. Except for the removal of

solvent from sunflower oil, all applications are in the treatment of aqueous systems. Table 2

shows the diversity of opportunities for nanofiltration and it can be expected that many are to

follow or already exist. However, most of the examples mentioned above are developed on a trial

and error basis and not from basic process knowledge. This means that these processes can run at

sub-optimal conditions and even membranes with better properties for the application might be

available. Improvement of these processes either by finding the optimal conditions or using better

membranes will result in economic gain. Additionally, current development times for new

pressure driven membrane processes are typically between one and two years, which is relatively

short and at this moment often results in sub-optimal solutions.

The major pitfall of this approach is that when unexpected problems occur in the process, there is

hardly any guideline to follow to come to a solution. From the above mentioned, it is obvious that

an understanding of the basic mechanisms underlying the separation is necessary. With this

understanding a translation to the development of industrial applications should be made, a step

which is currently omitted. With respect to the fundamentals of the nanofiltration process, major

progress has been made since the early nineties [106-110].

2.2 Mass transfer in nanofiltration A representation of the mass transfer process occurring in NF is given in Figure 3.

Boundarylayer MembraneBulk Permeate

ΔP

bC

ext1,mC

ext2,mC

int1,mC

int2,mC

Figure 3: Mass transfer in nanofiltration

8 CHAPTER 1

When an external pressure ΔP is imposed on a liquid which is adjacent to a semi-permeable

membrane, solvent will flow through the membrane. The general terms that are used in the

description of membrane separation processes are the solvent flux (J) and the rejection (R). The

solvent flux is given by:

totRPJ

η∆= (1)

in which ΔP is the effective transmembrane pressure [N/m2], η the permeate viscosity [Pa.s] and

Rtot the total resistance towards solvent flow [m-1].

A neutral solute dissolved in the solvent at a concentration level Cb will also flow towards the

membrane. If the membrane exhibits rejection for the solute, partial permeation will occur and

non-permeated solute accumulates in the boundary layer, and hence a concentration profile

develops. This phenomenon is called concentration polarisation [1,2]. The solute distributes at the

membrane/solution interface and will be transported through the membrane by convection and

diffusion. At the permeate side, a second distribution process will occur and a final concentration

of solute in the permeate, Cm,2ext, will be reached. For the characterisation of solute behaviour the

rejection is used, given by (see Figure 3):

b

ext2,m

CC

1R −= (2)

In nanofiltration, the distribution of a non-charged solute at the boundary layer/membrane

interface is considered to be determined by a steric exclusion mechanism. Steric exclusion is not

typical for nanofiltration but applies to ultrafiltration and microfiltration too. Due to its size a

solute only has access to a fraction of the total surface area of a pore. This causes a geometrical

exclusion of the solute from the membrane. A separation between solutes will only be

accomplished when the solutes have a difference in size.

For charged solutes two additional distribution mechanisms can be recognised:

1. Donnan exclusion, which compared to other pressure driven membrane processes has a

pronounced effect on the separation in NF. Due to the slightly charged nature of the

membrane, solutes with an opposite charge compared to the membrane (counter-ions) are


attracted, while solutes with a similar charge (co-ions) are repelled. At the membrane surface

a distribution of co- and counter-ions will occur, thereby causing an additional separation.

2. Dielectric exclusion, which generally does not play a role in ultrafiltration and microfiltration

but which is of major importance in electrodialysis [111]. Due to the charge of the membrane

and the dipole momentum of water, water molecules will show a polarisation in the pore.

This polarisation results in a decrease of the dielectric constant inside the pore, thereby

making it less favourable for a charged solute to enter. However, even in a situation that the

dielectric constant inside the pore is equal to the one of water, a change in electrostatic free

energy of the ion occurs when the ion is transferred from the bulk into the pore [112]. This

also results in exclusion.

The relative importance of the two mechanisms in NF is still point of debate in the scientific

community [109,113,114]. Most of the literature on NF uses Donnan exclusion as the distribution

mechanism [106-108,110]. In chapters 2, 3 and 4 of this thesis an approach has been chosen in

which the distribution mechanism is lumped into a mass transfer parameter and therefore the

nature of the distribution mechanisms is not of importance. In chapter 6, an analysis of the

importance of the Donnan exclusion and dielectric exclusion mechanisms is given.

For the mathematical description of the mass transfer process in nanofiltration the following

models have been used: Theorell Meyers Siever (TMS) model [107], Space Charge (SC) model

[107] and the Extended Nernst Planck (ENP) model [106-110], respectively.

In the SC-model a radial distribution of the electric potential and the ion concentration in the pore

is assumed, which is described by the Poisson-Boltzmann equation. For ion transport the Nernst-

Planck equation is used and the volumetric flow is described by the Navier-Stokes equation. The

TMS-model assumes a constant electric potential and ion concentration in the pore and is actually

a simplified SC-model. If, in addition to the assumption of a constant electric potential and ion

concentration, the volumetric flow is described by the Poiseuille equation, the model reduces to

the ENP-model. It is discussed by Wang et al. [107] that the calculated water velocity profiles

inside the pore do not differ significantly when either the Navier-Stokes equation or the Poiseuille

equation is used. This justifies the use of the Poiseuille equation for the description of solvent

flow. It has also been shown that the SC- and the TMS-model give similar results when the pore

diameter is less than 2 nm, so that the ENP-model can be used to describe the NF mass transfer

process. In NF, the applicability of the ENP-model has only been tested using results from

experiments with model solutions. The applicability of the model to describe NF of industrial

solutions has not been evaluated.

10 CHAPTER 1

The generalised Maxwell Stefan (GMS) model [115,116] has never been applied to the

description of nanofiltration processes but offers some advantages in the description of the

solvent transport. In the GMS-model, in addition to the pressure-related solvent transport,

transport caused by friction of the solvent with the solutes and in the case of charged solutes

transport by electrostatic effects is accounted for. Furthermore, the solvent transport is

mathematically treated in exactly the same manner as the solute transport. Another advantage of

the GMS model is that binary diffusion data can be used in contrast to effective diffusion

coefficients that are used in the other models.

3. SCOPE AND OUTLINE OF THE THESIS The short development times of membrane processes nowadays urges for methods that allow the

use of literature data to develop and optimise industrial NF processes. For this purpose, the

applicability of the ENP-model to industrial feed streams is tested. Two approaches are used that

differ in the level of complexity:

• A model in which boundary layer transport and membrane transport are treated separately,

which is an approach related to Figure 3. The concentration profile in each region is

calculated separately and the distribution of the solute at the membrane/boundary layer

interface connects both descriptions.

• A model in which boundary layer transport and membrane transport are lumped. This is an

approach in which the concentration polarisation layer and the membrane layer are

considered as one single layer. This is a first order treatment of the NF process.

A stepwise approach was followed which can serve as a starting point for a methodology to be

used for the development of industrial NF processes.

The ENP-model omits various contributions to the mass transfer process and is based on effective

diffusion coefficients. For a better process understanding and for descriptive and predictive

purposes, it can be advantageous to include the omitted contributions and use binary diffusion

data. The GMS-model incorporates the omitted mass transfer contributions and uses binary data

as a starting point. Therefore, the applicability of the GMS-model for the description of NF

processes is tested on model solutions.

In chapter 2 the laboratory scale separation of lactic acid from model solutions as a function of

pH and pressure using various RO and NF membranes is discussed. The experimental results are

described with the model in which boundary layer transport and membrane transport are lumped.

Chapter 3 discusses the use of the ENP-model derived from the previous chapter to results


obtained with lactic acid-containing fermentation broths. The influence of the proteins and

bacteria on the separation and the limitations of the ENP-model will be shown. A full description

of the batchwise concentration of a lactic acid fermentation broth by membranes will be given. In

addition, the fouling process is studied in more detail. Chapter 4 discusses the demineralisation of

whey and the applicability of the ENP-model in which boundary layer and membrane transport

are separated. Starting from laboratory scale experiments, the demineralisation of whey is

described using an approach in which a mixture of various salts is reduced to a system of three

ion-types.

Chapter 5 shows the use of the GMS-model in order to characterise the pore size of NF

membranes using a mixture of non-charged sugars. Chapter 6 is an extension to the GMS model

of chapter 5 in which charge effects are included and in which the charge properties of NF

membranes are established. The GMS approach will be compared with the ENP model for the

description of experimental data. Furthermore, an analysis of the relative importance of Donnan

and dielectric exclusion effects will be presented. This thesis finishes with chapter 7 in which

further comments on the previous chapters will be given. Ways of continuation of the work

described in this thesis will be discussed. A methodology for development of industrial NF

processes is presented, which allows the determination of the optimal process conditions, results

in a more founded selection of membranes and a better understanding of the process. An outlook

to future developments and needs is presented also.

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12 CHAPTER 1

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19

CHAPTER 2

Transport of lactic acid through

reverse osmosis and nanofiltration membranes1

SUMMARY

Model studies were performed with the aim of improving lactic acid separation from fermentation broths by

reverse osmosis and nanofiltration. A novel model, based on the extended Nernst-Planck equation, for the

description of mass transfer of lactic acid through these membranes was developed. The model can be used

to predict mass transfer of lactic acid under various pH and pressure conditions of the feed. The generalised

model allows a simple calculation of the separation efficiency not only of lactic acid but of other acids as

well.

1 This chapter has been published as J.M.K. Timmer, H.C. van der Horst, T. Robbertsen, “Transport of lactic acid through reverse osmosis and nanofiltration membranes”, Journal of Membrane Science 85 (1993) 205-216

20 CHAPTER 2

1. INTRODUCTION

Lactic acid is one of the major food preservatives and is also used for the manufacture of

derivatives such as stearoyl-2-lactylate, a dough conditioner [1]. In 1989 more than 30,000 tonnes

of lactic acid were produced world-wide, of which 50 to 60 percent was produced by

fermentation [2]. At the end of the fermentation, when the pH is kept between 5.5 and 6, lactate

concentrations between 12 and 15% are usually reached [1]. Further downstream processing

consists of a cell separation step, lactate precipitation and additional refining techniques to purify

the lactic acid product. Membrane processes like ultrafiltration and microfiltration can be used in

the cell separation step. Electrodialysis has also been applied to separate cells and,

simultaneously, to concentrate lactate from the fermentation broth. The application of these

membrane processes in membrane reactors for the continuous production of lactic acid is well

documented [3,4,5,6].

Another approach to the production of lactic acid is to carry out the fermentation without

adjustment of the pH. An advantage of this method is that due to the low pH obtained at the end

of fermentation, lactic acid can be removed selectively from the fermentation broth by using

cellulose acetate membranes and an initial purification of the lactic acid is achieved [7,8].

However, the lactic acid concentration (1-2%) obtained at the end of this batch process is

generally lower than for the batch fermentation process with pH control. Therefore additional

techniques to concentrate the dilute lactic acid stream are required. Reverse osmosis (RO) using

thin-film composite membranes has been applied to concentrate dilute (1%) lactic acid solutions

[9]. The lactic acid rejection of the composite and cellulose acetate RO membranes used was

found to be strongly dependent on pH [7,8,9]. This was explained by assuming that undissociated

lactic acid permeates freely with the water through the membrane while the dissociated form is

rejected. Lactic acid fermentation and simultaneous removal of lactic acid in a RO membrane

reactor has been studied also [8,10]. Because of the specific dynamic nature of this reactor and

the large influence of the membrane process on the economics of the process, a better understan-

ding of the mass transfer process of lactic acid through RO membranes is required. Further

improvements of the membrane reactor process were expected if a new membrane separation

technique, nanofiltration (NF), could be applied, because water permeability is higher and lactic

acid rejection of the membrane is lower [7]. There is no detailed information about mass transfer

through this type of membrane.

In this work we develop a mass transfer model in order to describe the separation of lactic acid

Transport of lactic acid through reverse osmosis and nanofiltration membranes 21

with the help of RO and NF membranes. In the following section we derive the pertinent

equations which are then applied for the description of the experimentally found lactic acid

rejection of different RO and NF membranes measured at various pH and pressure conditions.

2. THEORY

Mass transfer through RO membranes is usually described by the solution diffusion model [11].

The driving force for solvent flow is the pressure gradient across the membrane, with a linear

dependence of flow on the pressure gradient:

)P-.(A = J ww π∆∆ (1)

Jw :solvent flux [m.s-1]

ΔP :transmembrane pressure [Pa]

Δπ :osmotic pressure difference across the membrane [Pa]

Aw :solvent permeability [m.s-1.Pa-1]

For a clean membrane and with pure water as a feed Aw can be established by measuring the pure

water flux as a function of the pressure. Another method of determining Aw is by measuring the

flux as a function of the effective pressure (ΔP-Δπm).

Solute transport in RO, according to the solution diffusion model, is driven by the concentration

gradient of solute across the membrane and a linear relation between solute flux and

concentration gradient is assumed.

)C -C.(B = J ip,im,ii (2)

Ji :flux component i [mol.m-2.s-1]

Bi :mass transfer coefficient of component i [m.s-1]

Cm,i :concentration component i at membrane interface [mol.m-3]

Cp,i :concentration component i in permeate [mol.m-3]

In the solution diffusion model it is further assumed that no coupling between solute and solvent

transport is present [12]. However, this assumption is not always valid [13]. Drag by solvent flow

may cause additional transfer of solute through the membrane. In the case of charged solutes

electrical potential gradients cause transfer of solute also. Dresner [13] accounted for these

22 CHAPTER 2

additional mass transfer mechanisms by the extended Nernst-Planck equation. Vonk and Smit

[14] applied the extended Nernst-Planck equation to data obtained with uncharged RO

membranes and salt solutions. Equation (3) is the differential form of the extended Nernst-Planck

equation [14].

)-(x).(1C.J+] x(x).

.T.RF.z(x).C +

x(x)C.[P- = J iiw

iiiii σ

Ψ∂

∂∂

∂ (3)

Pi :permeability component i [m2.s-1]

Ci(x) :concentration component i at position x [mole.m-3]

zi :charge of component i [-]

F :Faraday constant [C.mole-1]

R :universal gas constant [J.mole-1.K-1]

T :absolute temperature [K]

Ψ :electrical potential [V]

σi :reflection coefficient component i [-]

We write equation (3) in a difference form and take the concentrations Cm,i = Ci(x = 0) where x =

0 is at the interface of the membrane at the concentrate side. Furthermore the gradients are taken

over the total thickness of the membrane Δx = l (l :thickness of the membrane) and when the

substitution Bi = Pi/l is made equation (3) transforms into

)-.(1C.J +] .T.R

F.C.z + C.[B- = J iim,wim,i

iii σ∆Ψ∆ (4)

For a system containing charged components the electroneutrality condition must be met

0 = C.z iiΣ (5)

In the case that there is no external charge transport there is also a restraint of zero electric

current through the membrane.

0 = J.z iiΣ (6)


When equations (4), (5) and (6) are applied to a binary system (i=1,2) we find for component 1

)F-.(1C.J + C.F- = J bm,1w1a1 ∆ (7)

where

)z.Bz.B-(1

).z.Bz.B-(

= F )

z.Bz.B-(1

)zz-.(1B

= F

22

11

222

111

b

22

11

2

11

a

σσ (8a,8b)

The concentration difference across the membrane is given by

C -C = C m,1p,11∆ (9)

Due to concentration polarisation effects there is an additional mass transfer resistance in the

boundary layer at the concentrate side of the membrane. From the mass balance across this

boundary layer the concentration at the membrane interface can be related to the concentration in

the bulk by [11]:

)kJ(exp).C-C( = )C-C(

i

wip,ic,ip,im, (10)

Cc,i :concentration component i in bulk [mol.m-3]

ki :mass transfer coefficient component i in boundary layer [m.s-1]

Substitution of equation (10) into equations (7) and (9) gives:

)F-).(1)kJ(exp).C -C(+C.(J + )

kJ(exp).C -C.(F = J b

1

wp,1c,1p,1w

1

wp,1c,1a1 (11)

The rejection of component i (Ri) is defined as:

24 CHAPTER 2

CC-1 = R

ic,

ip,i (12)

Furthermore, the flux of component i relates to the water flux as:

C.J = J ip,wi (13)

Combining equations (11), (12), (13) and taking i=1 results in

)J(B +JJ).J(R = R

w1sw

ww1s1 (14)

where

1)-)kJ).(exp(F-(1+1

F = )J(R

1

wb

bw1s (15)

1)-)kJ).(exp(F-(1+1

)kJexp(.F

= )J(B

1

wb

1

wa

w1s (16)

Rs1 :rejection parameter component 1 [-]

Bs1 :mass transfer parameter component 1 [m.s-1]

To develop the model for mass transfer of lactic acid it is assumed that dissociated and

undissociated lactic acid are independently permeating components. At pH <7 the system thus

contains five permeating components: water, Na+, H+, dissociated and undissociated lactic acid.

Water is considered the solvent.

Mass transfer of undissociated lactic acid is not influenced by the electrical potential gradient.

For undissociated lactic a relation similar to equation (7) can be derived. The rejection of


undissociated lactic acid can be described by equation (14).

In the system studied three charged components are present. However, because H+ concentration

is much lower than Na+ concentration it is assumed that transfer of H+ through the membrane can

be neglected. The system is considered as a binary system in charged components, which means

that equation (14) can be applied. When the system is considered a binary system the zero

electric current restraint (equation (6)) and equation (13) show that the Na+ concentration in the

permeate (Cp,Na) must be equal to the concentration of dissociated lactic acid in the permeate

(Cp,L). However, the dissociation equilibrium between dissociated lactic acid and undissociated

lactic acid plays a role also. The actual concentration of dissociated lactic acid in the permeate is

different from the Na+ concentration by an amount X, which then must be compensated by H+.

Transfer of H+ through the membrane was neglected, which means that H+ is only generated by

the dissociation of undissociated lactic acid and is equal to X. From these assumptions equation

(17) follows, which gives the equilibrium constant for the reaction between dissociated and

undissociated lactic acid.

X)-C(X)+C.(X

= KHLp,

Lp,a (17)

Ka :equilibrium constant for dissociation reaction of lactic acid

Cp,HL :undissociated lactic acid concentration in the permeate [mol.m-3]

For the model it is assumed that the equilibrium reaction is effectively established in the

permeate. The pH of the permeate (pHp) is given by:

log(X)- = pH p (18)

For the development of the model a zero order approach to equation (14) has been applied. This

means that both Rsi(Jw) and Bsi(Jw) are considered constant. The reason for this approach is that it

is very difficult to evaluate equations (15) and (16) and to obtain reliable values for the

parameters Fa, Fb and k1 because multiple solutions are possible.

To determine the independent mass transfer parameters BsHL, BsL, RsHL and RsL according to

equation (14) the influence of the equilibrium reaction must be accounted for. As already stated

the Na+ concentration gives the concentration of dissociated lactic acid without the effect of the

26 CHAPTER 2

equilibrium reaction. Therefore,

CC-1 = R

Lc,

p,NaL (19)

RL :rejection dissociated lactic acid [-]

Cc,L :dissociated lactic acid concentration in the concentrate [mol.m-3]

The rejection of undissociated lactic acid can be determined from:

CC -C-1 = R

HLc,

p,NaHLtotp,HL (20)

RHL :rejection undissociated lactic acid [-]

Cp,HLtot :total lactic acid concentration in the permeate [mol.m-3]

Cc,HL :undissociated lactic acid concentration in the concentrate [mol.m-3]

So using equation (14) the main transport parameters can be evaluated by measuring pH, CNa and

CHLtot.

3. EXPERIMENTAL

3.1 Reagents Lactic acid was of analytical grade and obtained from BDH Limited (Poole, England).

A 5 M sodium hydroxide solution was prepared from sodium hydroxide pellets (Analytical

grade, BDH Limited, Poole, England) and demineralised water. Feed solutions containing 1%

(w/v) lactic acid were prepared and pH was adjusted to 2.88, 3.45, 3.93, 4.43, and 4.93 by the

addition of sodium hydroxide solution.

3.2 Membranes The RO membranes (DDS HR95 and DDS CA995) and the NF membranes (DDS HC50 and

DDS CA960) were obtained from NIRO Atomizer (Apeldoorn, The Netherlands). The CA-type

membranes were made of cellulose acetate and the HC- and HR-type were thin-film composite

membranes composed of a polyamide separation layer on a polysulfone support.


3.3 Membrane system The experiments were done in a DDS Lab-20 unit (see chapter 4) in which the four membranes

were installed in series. For each membrane 0.036 m2 was installed. Experiments were performed

in batch circulation mode, which means that both the permeate and concentrate were carried back

to the feed vessel. The temperature during the experiments was 25°C and was maintained by a

cooling device present in the DDS Lab-20 unit. Outlet pressures used were 1, 1.5, 2, 2.5, 3, 3.5,

and 4 MPa. The pressure drop and concentration differences along the module were negligible.

The circulation velocity applied was 10 l.min-1. To test for concentration polarisation an

experiment with a lower circulation velocity of 4 l.min-1 with the solution at pH 2.88 was done.

3.4 Analyses The lactic acid concentration was determined by HPLC using an HPX-87 column (BioRad) and

refractive index detection. Na+ concentration was determined by flame emission photometry.

The osmotic pressure was calculated from freezing point depression measurements [15, 16].

3.5 Data treatment The water permeability, Aw, was determined from flux versus effective pressure data by linear

regression.

The parameters BsHL, BsL, RsHL and RsL using equation (14) were calculated from the rejection-flux

data (rejections determined by equations (19) and (20)) by a nonlinear regression method based

on a Marquardt algorithm using Statgraphics version 2.6 (Statistical Graphics Corporation,

Maryland, USA).

4. RESULTS

The water permeability parameter, Aw, for the different membranes at the two circulation

velocities are shown in Table 1. For the determination of Aw the osmotic pressure difference

measured between concentrate and permeate was used in equation (1). It is clear that both NF

membranes (CA960 and HC50) have a higher water permeability than the RO membranes, as

expected.

In order to see whether concentration polarisation effects could be neglected we made flux-

pressure measurements at two different circulation velocities (4 and 10 l.min-1). The results in

Figure 1 show that for both circulation velocities the flux through an HC50 membrane is directly

28 CHAPTER 2

proportional to the transmembrane pressure. This indicates that concentration polarisation

Table 1:Water permeability coefficient (Aw) of different membranes for two circulation capacities

at pH 2.88 and 25°C measured for a solution containing 1% lactic acid

Membrane

Circulation capacity [l.min-1]

Aw [10-12m.s-1.Pa-1]

CA960

HR95

CA995

HC50

4 10 4

10 4

10 4

10

6.51 6.63 4.31 4.71 2.44 2.46 5.40 5.11

Figure 1: Water flux, Jw, of an HC50 NF membrane (□,■) and an HR95 membrane (○,●) as a

function of pressure and at circulation velocities of 4 (open symbols) and 10 l.min-1 (closed

symbols) at pH 2.88 and 25°C using a solution containing 1% (w/v) lactic acid.

phenomena are of minor importance. This is confirmed by the fact that the fluxes are hardly

influenced by the circulation velocity, showing that the mass transfer resistance in the boundary

layer on the upstream side of the membrane is of minor importance to the overall mass transfer

resistance across the membrane. The same observations were made for the CA960 and the


CA995 membranes. These observations are in agreement with the results of Schlicher and

Cheryan [9]. The HR95 membrane showed a small dependence of the flux on the circulation

velocity, and for this membrane only concentration polarisation had a small effect on mass

transfer (Figure 1). The overall lactic acid rejections of an HC50 membrane at different fluxes

and pH values are given in Figure 2. An increase in either flux or pH gives an increase in overall

lactic acid rejection. The pH of the permeate at higher fluxes is, on average, 0.5 pH units lower

than the pH of the concentrate (Figure 3). The pH and flux dependence of organic acid rejection

was also found with the other membranes and was as expected [7,8,9,17]. The pH dependence is

caused by the fact that there is a preference for transport of undissociated lactic acid, which

results in a decrease in overall lactic acid rejection at low pH and a drop in pH of the permeate

caused by dissociation of undissociated lactic acid to meet the chemical equilibrium conditions.

From these findings it is justified that undissociated and dissociated lactic acid should be

considered as separate permeating components.

Figure 2: Overall lactic acid rejections of an HC50 NF membrane as a function of water flux, Jw,

and pH at 25°C using a solution containing 1% (w/v) lactic acid (◊:pH=4.86;■:pH=4.36;

□:pH=3.86;○:pH=3.36;●:pH=2.86). The lines are the results of the model calculation.

30 CHAPTER 2

Figure 3: pH of the permeate produced by NF of a solution containing 1% (w/v) lactic acid at

various fluxes and pH at 25°C using an HC50 membrane (◊:pH=4.86;■:pH=4.36;

□:pH=3.86;○:pH=3.36;●:pH=2.86). The lines are calculated using equations

(18) and (19).

Figure 4:Mass transfer parameter (BsL:□) and rejection parameter (RsL: ■) of an HC50 NF

membrane for dissociated lactic acid as a function of pH at 25°C. The dashed lines represent the

values used for the model calculation. (Error bars represent 95% confidence limits)


The result of the evaluation of BsHL, BsL, RsHL and RsL of the HC50 membrane is given in Figures 4

and 5 and Table 2. Figure 4 gives the values of BsL and RsL of an HC50 membrane at different pH

values. It is clear that the RsL is almost independent of pH and that BsL shows a linear dependence

on pH. The linear dependence between BsL and pH is in fact an indirect dependence. Sodium -

hydroxide is used to adjust pH, which causes an increase in Na+ concentration with increasing

pH.

Figure 5: Mass transfer parameter (BsHL: □) and rejection parameter (RsHL: ■) of an HC50 NF

membrane for undissociated lactic acid as a function of pH at 25°C. The dashed lines represent

the average values used in the model calculation. (Error bars represent 95% confidence limits)

The true linear dependence holds between Na+ concentration and BsL. Because in this system a

linear dependence between Na+ concentration and pH is observed, a linear dependence between

BsL and pH results. The amount of Na+ present in the concentrate determined the mass transfer

rate of dissociated lactic acid through an HC50 membrane. Figure 5 shows that both BsHL and

RsHL of an HC50 membrane are independent of pH. This means that pH has no effect on mass

transfer of undissociated lactic acid through HC50 membranes. Comparing the results in Figures

4 and 5 it is clear that the mass transfer parameter of undissociated lactic acid, BsHL, is at least 5

times larger then the mass transfer parameter of dissociated lactic acid, BsL, and that RsHL is lower

than RsL. This confirms quantitatively the preference for mass transfer of undissociated lactic

acid. The differences between BsHL and BsL, and between RsHL and RsL, are caused by charge

32 CHAPTER 2

effects. Membrane surfaces usually have a negative charge which causes negatively charged

molecules to be repelled. This results in a low partitioning of dissociated lactic acid between

membrane and concentrate compared to undissociated lactic acid, which causes a lower mass

transfer parameter, which is partly determined by the partition coefficient, and a higher Rs. To

use the model for mass transfer calculations of lactic acid through an HC50 membrane the

calculated values of BsHL and RsHL of different experiments were averaged (Table 2, BsHL =

15.98⋅10-6m.s-1, RsHL = 0.569). RsL was also averaged (RsL = 0.952) and a linear relation between

BsL and pH was used (BsL = (-3.607+1.262*pHc)⋅10-6m.s-1). Overall lactic acid rejections and the

pHp were calculated using equations (14), (17), and (18) for different values of pH and flux and

compared with the experiments.

From Figure 2 it is clear that the model gives a good description of the experimentally obtained

overall lactic acid rejections. The pHp also is predicted correctly (Figure 3). These results show

that the approach of treating dissociated and undissociated lactic acid as independently

permeating components, and assuming that the equilibrium reaction between both forms of lactic

acid is established in the permeate, can be used to predict overall lactic acid rejection of an HC50

membrane.

The same approach as above was applied to the results of the other membranes; the evaluated

parameters are given in Table 2. In general it can be said that RsHL and RsL of the different

membranes are constant and not dependent on the pH of the concentrate. However, BsHL and BsL

show different pH dependencies for the various membranes. The results obtained with the

CA995 membrane show a small decrease in BsHL while BsL remains constant. The HR95

membrane results show that both BsHL and BsL are independent of pH. For the CA960 membrane a

small decrease of BsL is observed with increasing pH while for BsHL it is difficult to find a trend in

the data because of the large uncertainty ranges. The negative values of BsHL found for some of

the experiments are caused by the method applied. The negative values are only found at high pH

values. The concentration of undissociated lactic acid is low at these pH values and small errors

in pH and Na+ concentration can cause errors in the corrected undissociated lactic acid con-

centration in the permeate. In the cases where negative BsHL values were calculated of course also

negative undissociated lactic acid rejections were found at low flux values. Values for BsHL and

RsHL found for the HC50 membrane at pH 2.88 are not reported because the parameters calculated

were unrealistic (>1012). The least residual sum of squares fitting procedure found this solution

for several starting values of BsHL and RsHL, which means that these unrealistic parameters are not


caused by the fitting procedure applied but by the data used.

Table 2:Mass transfer parameter (BsHL, BsL) and rejection parameter (RsHL, RsL) of different

membranes for undissociated and dissociated lactic acid at various pH and 25°C. (95%

confidence limits included)

Membrane pH Undissociated lactic acid Dissociated lactic acid

BsHL [10-6m.s-1] RsHL [-] BsL [10-6m.s-1] RsL [-]

CA960

HR95

CA995

HC50

2.88

3.45

3.93

4.43

4.93

2.88

3.45

3.93

4.43

4.93

2.88

3.45

3.93

4.43

4.93

2.88

3.45

3.93

4.43

4.93

9.65±2.43

0.32±2.12

0.45±1.63

-0.04±0.87

-1.11±0.60

0.21±0.01

0.38±0.02

0.37±0.03

0.24±0.03

-0.13±0.03

4.72±0.44

3.98±0.36

2.67±0.84

2.25±0.62

0.79±0.50

-

17.27±5.15

12.65±3.52

30.18±64.87

3.81±14.09

0.332±0.030

0.224±0.030

0.340±0.041

0.459±0.036

0.675±0.050

0.995±0.001

0.989±0.002

0.995±0.003

0.992±0.004

0.974±0.005

0.842±0.034

0.723±0.025

0.723±0.073

0.759±0.063

0.730±0.076

-

0.526±0.083

0.521±0.067

0.731±1.009

0.497±0.421

3.84±0.46

4.75±0.91

3.50±0.35

2.82±0.19

2.28±0.31

0.25±0.07

0.03±0.01

0.04±0.01

0.07±0.01

0.05±0.01

0.14±0.02

0.20±0.02

0.16±0.01

0.11±0.01

0.08±0.00

0.05±0.08

0.51±0.20

1.30±0.19

1.96±0.35

2.48±0.35

0.823±0.020

0.807±0.033

0.856±0.016

0.873±0.010

0.898±0.019

0.982±0.008

0.996±0.001

0.997±0.001

0.998±0.002

0.998±0.001

0.985±0.005

0.987±0.004

0.988±0.003

0.989±0.002

0.989±0.001

0.959±0.007

0.954±0.017

0.950±0.015

0.945±0.025

0.953±0.023

To verify the model an independent experiment was made in which a solution of approximately

0.6 % lactic acid was prepared and the lactic acid rejection of a HC50 membrane was determined

at different pressures (0.5 to 6 MPa). The lactic acid rejections for this experiment were

predicted with the data for BsHL, RsHL and RsL reported in Table 2 and a value for BsL of 0 was

used, because there is no Na+ in the solution. Figure 6 shows that the lactic acid rejection

34 CHAPTER 2

measured and the lactic acid rejection predicted are in good agreement. Also the pHp measured is

well predicted by the model. The small difference in pH is caused by a systematic error of

approximately 0.1 pH-unit caused by the pH electrode used in this experiment. These results

show that the model can be used to predict lactic acid rejection and that the assumptions made

lead to a valid model for the description of mass transfer of lactic acid through RO and NF

membranes.

Figure 6: Overall lactic acid rejections (■) of an HC50 NF membrane and the pH of the

permeate (□) as a function of water flux, Jw, and pHfeed 2.40 at 25°C using a solution containing

0.6% (w/v) lactic acid. The solid lines are predicted using the transport coefficients shown in

Table 2.

5. CONCLUSIONS

Mass transfer of lactic acid through RO and NF membranes can be described by the model

developed here, based on the extended Nernst-Planck equation. It can be concluded that con-

centration polarisation is of minor importance and that considering undissociated lactic acid and

dissociated lactic acid as separate components is a good approach. The model can be used to

determine mass transfer characteristics of different RO and NF membranes for the separation of

lactic acid. The model offers the possibility to predict and optimise lactic acid separation by RO

and NF. The model developed here for lactic acid can be applied to other acids as well.


6. LIST OF SYMBOLS

Aw :solvent permeability [m.s-1.Pa-1]

Bi :mass transfer coefficient of component i [m.s-1]


BsL :mass transfer parameter dissociated lactic acid [m.s-1]

BsHL :mass transfer parameter undissociated lactic acid [m.s-1]

Ci(x) :concentration component i at position x [mole.m-3]

Cm,i :concentration component i at membrane interface [mol.m-3]

Cp,i :concentration component i in permeate [mol.m-3]

Cc,i :concentration component i in bulk [mol.m-3]

Cp,HLtot :total lactic acid concentration in the permeate [mol.m-3]

Cp,HL :undissociated lactic acid concentration in the permeate [mol.m-3]

Cp,L :dissociated lactic acid concentration in the permeate [mol.m-3]

Cp,Na :sodium concentration in the permeate [mol.m-3]

Cc,HL :undissociated lactic acid concentration in the concentrate [mol.m-3]

Cc,L :dissociated lactic acid concentration in the concentrate [mol.m-3]

F :Faraday constant [C.mole-1]

Jw :solvent flux [m.s-1]

Ji :flux component i [mol.m-2.s-1]

ki :mass transfer coefficient component i in boundary layer [m.s-1]

Ka :equilibrium constant for dissociation reaction of lactic acid

pHp :pH of the permeate [-]

pHc :pH of the concentrate [-]

Pi :permeability component i [m2.s-1]

R :universal gas constant [J.mole-1.K-1]

Ri :rejection component i [-]

RL :rejection dissociated lactic acid [-]

RHL :rejection undissociated lactic acid [-]


RsL :rejection parameter dissociated lactic acid [-]

RsHL :rejection parameter undissociated lactic acid [-]

T :absolute temperature [K]

36 CHAPTER 2

zi :charge of component i [-]

ΔP :transmembrane pressure [Pa]


Ψ :electrical potential [V]

σi :reflection coefficient component i [-]

7. REFERENCES 1. T.B. Vick Roy, Lactic acid, in: H.W. Blanch, S. Drew, D.I.C. Wang, M. Moo-Young (eds.),

comprehensive Biotechnology Vol. 3, Pergamon Press, 1985, pp. 761

2. H. Benninga, A history of lactic acid making, Kluwer Academic Publishers, Dordrecht/Boston/London,

1990

3. E. Ohleyer, C.R. Wilke, H.W. Blanch, Continuous production of lactic acid from glucose and lactose in

a cell recycle reactor, Appl. Biochem. Biotechnol. 11 (1985) 457-463

4. T.B. Vick Roy, Lactic acid production in membrane reactors, Ph.D.Thesis, University of California,

Berkeley, 1983

5. B. Bibal, Y. Vassier, G. Goma, A. Pareilleux, High concentration cultivation of Lactococcus cremoris

in a cell recycle reactor, Biotechnol. Bioeng. 37 (1991) 746-754

6. M. Taniguchi, N. Kotani, T. Kobayashi, High concentration cultivation of lactic acid bacteria in

fermentor with cross-flow filtration, J. Ferment. Technol. 65 (1987) 179-

7. B.R. Smith, R.D. MacBean, G.C. Cox, Separation of lactic acid from lactose fermentation liquors by

reverse osmosis, Austr. J. Dairy Technol. 32 (1977) 23-36

8. J.H. Hanemaaijer, J.M.K. Timmer, T.J.M. Jeurnink, Continue produktie van melkzuur in

membraanreactoren, Voedingsmiddelentechnologie 21(9) (1988) 17-21

9. L.R. Schlicher, M. Cheryan, Reverse osmosis of lactic acid fermentation broths, J. Chem. Technol.

Biotechnol. 49 (1990) 129-140

10. D. Setti, Development of a new technology for lactic acid production from cheese whey, Proc. IV Int.

Congress Food Sci. Technol. Vol IV, 1974, 289

11. H. Strathmann, Trennung von molekularen Mischungen mit Hilfe synthetischer Membranen, Dr.

Dietrich Steinkopf Verlag, Darmstadt, 1979

12. W. Pusch, Measurements techniques of transport through membranes, Desalination 59 (1986) 105-198

13. L. Dresner, Some remarks on the integration of extended Nernst-Planck equations in the hyperfiltration

of multicomponent solutions, Desalination 10 (1972) 27-46

14. M.W. Vonk, J.A.M. Smit, Positive and negative ion retention curves of mixed electrolytes in reverse

osmosis with a cellulose acetate membrane. An analysis on the basis of the generalized Nernst-Planck

equation, J. Colloid Interface Sci. 96 (1983) 121-134


15. NEN 3462, Milk - Determination of the freezing point with a mercury thermometer (reference method),

Nederlands Normalisatie Instituut, Delft, The Netherlands, 1988

16. NEN 3463, Milk - Determination of the freezing point with a thermistor cryoscope, Nederlands

Normalisatie Instituut, Delft, The Netherlands, 1988

17. C. Peri, P. Battisti, D. Setti, Solute transport and permeability characteristics of reverse osmosis

membranes, Food Sci. Technol. 6 (1973) 127-132

38

39

CHAPTER 3

Lactic acid separation from fermentation broths by

reverse osmosis and nanofiltration1

SUMMARY

Laboratory scale and pilot plant nanofiltration (NF) and reverse osmosis (RO) experiments with fermentation

broths were performed with the following aims: (i) to quantify lactic acid rejection and to determine whether

the theoretical model developed in chapter 2 could be used to predict lactic acid rejection; (ii) to quantify

fouling of NF membranes and to determine the major fouling mechanism.

It is found that the rejection model developed, based on the extended Nernst-Planck equation, can be used to

quantify lactic acid rejection of RO and NF membranes. Especially at high fluxes, the prediction of lactic acid

rejection using parameters determined with lactic acid/water mixtures was quite good. At low fluxes, the

predicted rejection of lactic acid was usually lower.

Fouling of the membrane could be quantified in terms of three resistances: a membrane resistance, an initial

fouling resistance, and a time dependent fouling resistance. Empirical equations for the initial fouling

resistances were developed and time dependent fouling could be described either by a colloidal fouling model

(ultrafiltered fermentation broth) or a gel layer model (fermentation broth). Evaluation of the three resistances

by simulation of continuous and batch concentration experiments showed that during NF of an ultrafiltered

fermentation broth the initial fouling resistance, resulting from concentration polarisation effects, was the

predominant resistance. For a fermentation broth, the time dependent fouling becomes more important than the

initial fouling resistance. Protein fouling is the main cause of the time dependent fouling. Therefore, it is

recommended to remove proteins by ultrafiltration before NF.

1This chapter has been published as J.M.K. Timmer, J. Kromkamp, T. Robbertsen, “Lactic acid separation from fermentation broths by reverse osmosis and nanofiltration”, Journal of Membrane Science 92 (1994) 185-197

40 CHAPTER 3

1. INTRODUCTION

Lactic acid is one of the major food preservatives, and can be produced either by chemical synthesis

or by fermentation [1]. About 50 to 60 % of the annually produced lactic acid originates from

fermentation [2]. The fermentation process is carried out at a constant pH between 5.5 and 6.0 at

temperatures above 40°C. At the end of the fermentation, lactate concentrations between 12 and

15% are reached. In downstream processing of the fermentation broth, separation steps like

ultrafiltration, microfiltration, and electrodialysis can be applied.

Another approach to the production of lactic acid by fermentation is to carry out the process without

pH adjustment. An advantage of this method is that due to the low pH obtained at the end of

fermentation, lactic acid can be selectively removed from the fermentation broth by using cellulose

acetate RO membranes [3,4]. Another advantage is that a partial purification of lactic acid is

obtained. However, lactic acid concentrations at the end of fermentation are generally lower (1-2%)

than in the case of the pH-controlled fermentation. Therefore, additional techniques to concentrate

the dilute lactic acid stream are required. RO using thin-film composite membranes has been

applied to concentrate dilute (1%) lactic acid solutions. The lactic acid rejection of composite and

cellulose acetate membranes was found strongly dependent on pH [3,4,5,6]. This was explained by

a difference in rejection of the membrane for dissociated and undissociated lactic acid. In a previous

paper [6], we quantified these differences, and we were able to predict lactic acid rejection of RO

and NF membranes using 1% lactic acid solutions. It was shown that NF membranes in general

show lower rejection for lactic acid than RO membranes. For the selective separation of lactic acid

from a fermentation broth this is an advantage compared to RO.

For industrial applications, a predictive model for the lactic acid rejection of NF and RO

membranes that can be used for process development or optimisation is necessary. The model

described by Timmer et al. [6] can serve as a starting point to describe and predict lactic acid

rejection of NF and RO membranes using fermentation broths.

In addition to the description of the lactic acid rejection, a model, which describes the development

of flux in time, is needed to give a complete description of the NF or RO separation process.

Models like the osmotic pressure model or gel layer model [10] can be used to describe the flux

during RO and NF. However, these models do not consider all initial fouling phenomena and

describe a steady state situation in which no long-term fouling occurs. Hiddink et al. [8] discussed

the fouling observed during RO processing of whey in terms of initial and long-term fouling. Van

Boxtel [9] quantified this approach by developing a model that takes both initial and long-term

Lactic acid separation from fermentation broths by reverse osmosis and nanofiltration 41

fouling into consideration and they applied the model to the RO processing of cheese whey. They

showed that the model gave a good description of the fouling during the RO process and that it

could be used for control purposes [9]. This approach, applied to the NF separation of lactic acid

from fermentation broths, might improve the understanding of fouling, offer opportunities for

improving the NF separation process when the major fouling mechanism is known, and also give a

description of the process which can be used for process development and optimisation.

This paper focuses on the selective separation of lactic acid from fermentation broths by RO and

NF. The aims of this work were:

i: to quantify lactic acid rejection and verify if the model developed by Timmer et al. [6] can

be used for descriptive and predictive purposes.

ii: to quantify fouling of the membrane in terms of initial and long-term fouling.

In the theory section the equations used for quantifying lactic acid rejection and fouling will be

given. In the following sections these equations will be applied to the experimental results with a

laboratory unit containing RO and NF membranes, a pilot-plant NF system and whey based

fermentation media. It will be shown that the rejection model described by Timmer et al. [6] and the

flux model, following the approach of Hiddink et al.[8], can be used to give a description of the NF

separation of lactic acid from fermentation broths.

2. THEORY

2.1 Lactic acid rejection

Mass transfer of lactic acid through NF and RO membranes can be described by a model based on

the extended Nernst-Planck equation [6,7]. Two assumptions made in development of the model

were that dissociated and undissociated lactic acid permeate as separate components and that the

chemical equilibrium between dissociated and undissociated lactic acid is established in the

permeate. The dependence of rejection (R1) on water flux (Jw) is then found as:

)J(B + JJ).J(R = R

w1sw

ww1s1 (1)

In which

42 CHAPTER 3

1)-)kJ).(exp(F-(1+1

)kJexp(.F

= )J(B

1

w1b

1

w1a

w1s (2)

1)-)kJ).(exp(F-(1+1

F = )J(R

1

w1b

1bw1s (3)

Fa1 :overall rejection of the membrane for component 1 at infinite flux [-]

Fb1 :overall permeability of component 1 through the membrane [m.s-1]

k1 :mass transfer coefficient component 1 in boundary layer [m.s-1]



These equations hold for noncharged components and binary systems of charged components. It

was shown [6] that a first order approach, with Rs1(Jw) and Bs1(Jw) taken as a constant, could be

applied to describe lactic acid rejection of NF and RO membranes.

In this work equation (1) was applied to describe the overall lactic acid rejection data. A treatment

in dissociated and undissociated lactic acid applied in previous work [6] was not possible due to the

presence of other ions making it difficult to separate mass transfer phenomena from dissociation

reactions (the equilibrium reaction between dissociated and undissociated lactic acid).

For the theoretical prediction of the overall lactic acid rejection, numerical results from reference

[6] were used.

2.2 Fouling model In RO and NF the water flux through the membrane can be described by

R) - p( = J

totw

π∆∆ (4)

In which:

Jw :water flux [m.s-1]

Δp :pressure difference across the membrane [Pa]



Rtot :total resistance of the membrane to water permeation [Pa.s.m-1]

The total resistance of the membrane is composed of three separate resistances in series:

Rm :Resistance of a clean membrane to permeation of pure water. This resistance is time

independent,

Ri :Initial fouling resistance, caused by concentration polarisation phenomena and fouling of

the membrane during start up of the process [8,9]. This resistance is time independent also.

Van Boxtel [9] correlated Ri empirically with cross flow velocity (v), upstream pressure

(P), and concentration ratio (Cr) by

C.P.v.a = R dr

cbi (5)

a,b,c and d are empirical constants.

Rf :Time dependent fouling resistance

Precipitation of salts, deposition of colloidal particles, bacterial attachment or protein adsorption

can cause fouling. In general, fermentation broths contain salts, colloidal particles, bacterial cells

and proteins, so that each of these fouling mechanisms may occur. By treatment of the fermentation

broth by ultrafiltration, proteins and bacteria can be removed and fouling properties of the solution

can be changed. For the description of long-term fouling caused by proteins the gel layer model can

be used [9]. The following expression is described by van Boxtel [9] to describe this long-term

fouling:

0 = 0)=(tR B - J.A = t d

R dfw

f (6)

In which:

CCln.k.C. = B C. = A

prb,

prg,prprb,prb,

ρε

ρε

(7a,7b)

44 CHAPTER 3

ε :specific gel layer resistance [Pa.s.m-2]

Cb,pr :protein concentration in the bulk [kg.m-3]

Cg,pr :protein concentration in gel [kg.m-3]

ρ :density of the bulk solution [kg.m-3]

kpr :mass transfer coefficient of protein in boundary layer [m.s-1]

Equation (6) predicts a flux dependent increase of Rf with time. Equation (6) can only be applied

with a constant Cb,pr, as in continuous systems. In the case of a changing Cb,pr that occurs during

batchwise concentration of solutions, equation (6) can be transformed into

))C ln-CC.(lnk-J.(A.C =

t dR d

rpr,1b,

prg,prwr

f (8)

In which Cr is given by:

V0 :volume at time zero [m3]

Am :membrane surface area [m2]

The values for A and Cb,pr,1 are determined at Cr = 1. From equation (8), it can be seen that the time

dependent fouling is also dependent on the concentration ratio.

t d.A.J-VV = C

mw0

0r ∫

(9)

If proteins are absent, as in an ultrafiltered fermentation broth, the gel layer model can not be

applied. In this situation, a precipitation model or colloidal fouling model is more appropriate. Van

Boxtel [9] used a precipitation model to describe long-term fouling during RO treatment of whey. In

his experiments, it was very likely that calcium phosphate precipitation occurred because of the

neutral pH at which the experiments were performed. However, in our experiments the pH was

acidic, making it unlikely that calcium phosphate precipitation occurred. For this reason, we

preferred to apply the colloidal fouling model, because it is more general and does not need specific

information about the nature of the precipitant or colloid. Cohen and Probstein [11] developed a

model in which deposition of colloidal particles caused fouling. They showed that colloidal fouling

was convection controlled and using the law of mass conservation, they derived the following

expression:


)-(1R.J. =

t dR d

c

c0w0f

εΦ

(10)

In which:

Φ0 :foulant volume fraction in feed [-]

Jw0 :water flux determined by extrapolating the flux-time curve to time zero [m.s-1]

εc :effective foulant layer porosity [-]

Rc :specific foulant layer resistance [Pa.s.m-2]

The model shows that the increase in long-term fouling is constant and linearly dependent on the

foulant volume fraction. In the case of a given feed which is processed at different Cr and when it is

assumed that Jw0 shows the same pressure dependence as shown in equation (4), equation (10) can

be transformed into:

) - p.(C.RD =

t dR d

r0w

f π∆∆ (11)

In which:

)-(1R. = Dc

c0

εΦ

(12)

Rw0 :resistance at intercept of the flux-time curve at time zero [Pa.s.m-1]

The Rw0 put into the concept of initial and long-term fouling is equal to the sum of Rm and Ri.

By performing experiments at different Cr and Δp, the first factor on the right-hand side of equation

(11) can be evaluated. The factor D should be independent of process conditions. The pressure

dependence or Cr dependence of Ri can also be determined. Equation (11) can be used for

continuous experiments. In the case of batchwise concentration, the assumption of a quasi-steady

flux made by Cohen and Probstein [11] does not hold. In this situation Jw0 in equation (10) is

replaced by Jw. Evaluating batchwise concentration experiments should lead to the same results for

D and the pressure dependence or Cr dependence of Ri. In our case, we evaluated D and the pressure

dependence of Ri by continuous experiments. These results were used in order to determine the Cr

dependence of Ri by batchwise concentration experiments.

46 CHAPTER 3

3. EXPERIMENTAL

3.1 Media Fermentation broth (broth) was obtained by fermentation of a solution containing 4% delactosed

whey powder (Borculo, The Netherlands) using Lactobacillus helveticus 37N (NIZO, The

Netherlands). An ultrafiltrate of the fermentation broth (UF-broth) was obtained by batch

ultrafiltration using DDS GR61PP (cut off value:20,000 D) membranes. The pH of the broth and

the UF-broth was 3.3.

3.2 Membrane system For the laboratory scale RO and NF experiments a DDS Lab 20 unit was used in which four

membranes (RO: DDS HR95 and DDS CA995; NF: DDS HC50 and DDS CA960) were installed in

series. For each membrane, membrane area was 0.036 m2. Experiments were performed in batch

circulation mode, which means that both the permeate and the retentate were carried back to the

feed vessel. Broth and UF-broth were used as a feed. Temperature during the experiment was 37°C,

concentration ratio was approximately 1, and pressures applied varied between 1 and 4 MPa.

Maximum circulation velocity (10 l.min-1) of the system was applied.

For the pilot plant NF experiments a spiral wound Filmtec NF40 membrane module (4"-module, 6

m2) was used. Circulation capacity was 4.8 m3.h-1 at a temperature of 37°C. For the batchwise

concentration experiments, 1 m3 of either broth or UF-broth was processed at a feed pressure of 4

MPa. For the continuous experiments, 0.3 m3 of UF-broth was processed at 3, 4, and 5 MPa, and

concentration ratios of 4 and 8. Continuous experiments were performed in recycle mode, which

means that both permeate and retentate flows were returned to the feed vessel. Preconcentration of

the UF-broth was accomplished by NF in the same system. Samples of retentate and permeate were

taken at regular time intervals.

3.3 Analyses The lactic acid concentration was determined by HPLC using an HPX-87 column (BioRad) and

refractive index detection.

Osmotic pressure was measured at 37°C in a high-pressure osmometer [12] capable of measuring

pressures up to 5 MPa. A DDS CA995 membrane was used for the measurements. Osmotic

pressure was measured against pure water.

Protein concentration was determined by the method of Koops et al. [13]


3.4 Data treatment Clean membrane resistance, Rm, was determined from flux versus pressure data obtained with pure

water at different temperatures and applying linear regression.

Parameters Bs, and Rs of lactic acid for the membranes were calculated by using equation (1) and a

non-linear regression method based on a Marquardt algorithm using Statgraphics version 2.6

(Statistical Graphics Corporation, Maryland, USA).

For the batchwise concentration experiments with broth Ri = e.Crd was used. Parameters A, kpr, and

ln(Cg,pr/Cb,pr,1) in equation (8) and e and d were calculated simultaneously by non-linear regression

and a Runga-Kutta method for solving the differential equation.

For the continuous experiments with UF-broth Ri and D were determined simultaneously by non-

linear regression and a Runga-Kutta method for solving the differential equation. From the data

obtained at Cr = 4 and different pressures the dependence of Ri on P was determined. The parameter

c in equation (5) was determined by linear regression.

From the batchwise concentration experiments with UF-broth a.vb and d in equation (5) were

determined. In the calculation of these two parameters, the values of D and c determined from the

continuous experiments were used. The parameters were calculated by non-linear regression.

4. RESULTS

4.1 Lactic acid rejection The lactic acid rejections of an HC50 membrane for broth and UF-broth are shown in Figure 1. The

solid lines are calculated using equation (1). Furthermore, the predicted lactic acid rejection using

numerical results from [6] is given by the dashed line. The results show that lactic acid rejection of

the HC50 membrane is highest with the broth and almost constant. Comparing the lactic acid

rejection of the UF-broth with the predicted lactic acid rejection shows that the predicted rejection

is qualitatively and quantitatively correct. The increase in lactic acid rejection with the broth can be

explained by fouling of the membrane. From the increase in rejection it can be concluded that the

fouling layer acts as a membrane itself, having distribution properties for lactic acid. If the fouling

layer did not have its own distribution properties due to the increased diffusion length an increase in

concentration polarisation would be found, resulting in a decrease in rejection [14], which is not

observed. Electron microscopic pictures (not shown) showed considerable protein fouling on the

membrane in the case of the broth, while fouling of the membrane hardly occurred in the case of the

UF-broth.

48 CHAPTER 3

Figure 1:Lactic acid rejection of a flat sheet HC50 NF membrane at different water fluxes for a

UF-broth (∆) and a broth (+) measured at 37°C. Drawn lines are the fits using equation (1). The

dashed line is the predicted lactic acid rejection using literature data.

The calculated parameters for the HC50 membrane and the different feeds are given in Table 1.

Also the predicted lactic acid rejections were fitted using equation (1). The results of the other

membranes tested are treated in the same way and are also shown in Table 1. It can be seen that the

rejection parameters Rs are not significantly different for broth, UF-broth, and lactic acid/water

mixture. The mass transfer parameter Bs varies for broth, UF-broth, and the lactic acid/water

mixture. The effect of fouling is thus reflected in variations in Bs, which is lowest for the broth. A

comparison between Bs values from UF-broth and the lactic acid data can be made but should be

interpreted with care because during the experiments with UF-broth no results at very low flux were

obtained, which could result in errors in the calculation of Bs. From the comparison it can be

concluded the Bs values are similar between the UF-broth and the lactic acid/water system. These

results show that the rejection parameter Rs can be predicted by the model and that the mass transfer

parameter Bs can be predicted in the case of the UF-broth only. Prediction of Bs in the case of the

broth is not possible because of fouling phenomena. However, because the lactic acid rejection in

the case of the broth is almost constant only the rejection parameter is needed to make an estimate

of the rejection. Comparing the results of the NF membranes (CA960, HC50) and the RO


membranes (CA995, HR95) shows that the mass transfer parameters of the NF membranes are

higher than for the RO membranes, indicating that diffusivity of lactic acid in a NF membrane is

higher than in an RO membrane. The rejection parameter of the NF membranes is lower than for the

RO membranes. From this it can be concluded that the lactic acid separation characteristics of NF

membranes for treatment of UF-broth are better than for RO membranes. A comparison of the NF

membranes and the RO membranes in the case of the broth is difficult to make because the Bs for

the NF membranes is not very reliable since during the experiments with the broth and the NF

membranes no measurements in the lower flux region were made. However, the rejection

parameters show that also in the case of the broth separation characteristics of the NF membranes

are better.

Table 1: Calculated and measured overall mass transfer parameter (Bs) and rejection parameter

(Rs) of various RO and NF membranes for lactic acid for a fermentation broth and an ultrafiltrate

thereof at 37°C.

Membrane UF broth broth model predictions

Bs

[10-6m.s-1]

Rs

[-]

Bs

[10-6m.s-1]

Rs

[-]

Bs

[10-6m.s-1]

Rs

[-]

laboratory scale NF HC50 CA960 RO HR95 CA995 pilot plant NF NF40

9.87 4.96

0.14 2.51

1.29

0.67 0.54

0.99 0.78

0.46

0.01 0.07

0.12 0.58

0.86

0.56 0.57

0.99 0.74

0.47

3.79 5.79

0.24 1.82

3.79

0.51 0.51

0.99 0.78

0.51

To verify whether the trends in lactic acid rejection, Bs, and Rs found with the laboratory scale

experiments can be translated to pilot plant scale the lactic acid rejections of a NF40 membrane

were measured during batch concentration experiments of broth and UF-broth. Figure 2 presents the

measured rejections in the pilot plant experiment with the NF40 membrane. The predictions for the

lactic acid rejections were calculated by taking the model predictions for Bs and Rs for the HC50

membrane, given in Table 1. The separation characteristics of the NF40 and HC50 membranes were

identical (results not shown). The same trends in lactic acid rejection as during the laboratory scale

50 CHAPTER 3

experiments are observed. The lactic acid rejection of the broth is highest followed by the UF-broth.

The rejection parameters and mass transfer parameters for the NF40 membrane are given in Table

1.

Figure 2: Lactic acid rejection of a spiral wound NF40 membrane at different water fluxes for a

UF-broth (∆) and a broth (+) measured at 37°C. Drawn lines are the fits using equation (1). Dotted

line: predicted lactic acid rejection at pH 3.3 using literature data. Dashed line: lactic acid

rejection using the same data with the assumption that only undissociated lactic acid permeates.

The rejection parameters of the NF40 membrane are similar for the broth, the UF-broth and the

lactic acid/water mixture. However, as observed with the laboratory scale experiments the mass

transfer parameters are different. Fouling of the membrane and influence of the feed composition

play an important role at the pilot plant scale (as expected). The agreement between the results of

the UF-broth and the lactic acid water mixture is not as good as it was for the laboratory scale

experiments. In the case of the UF-broth the mass transfer parameter of the NF40 membrane is

lower than for the HC50 membrane. Increased levels of ions with higher diffusivities then

dissociated lactic acid result in a lowering of Bs, because charge transfer will always occur by the

most mobile couple of ion and counter-ion. For example when a Na+ ion passes through a

membrane it is more likely to have Cl- as a counter-ion than dissociated lactic acid because Cl- has

the highest diffusion coefficient. The influence of a decreased diffusivity of dissociated lactic acid

is calculated at pH 3.3. The dotted line in Figure 2 gives the calculated lactic acid rejection using


the lactic acid/water mixture data. The dashed line gives the lactic acid rejection when dissociated

lactic is not transported through the membrane by diffusion (equivalent to the presence of a faster

diffusing negative ion). The rejection of lactic acid increases when other negative ions are present,

showing the trend observed in Figure 2.

Concentration polarisation effects also can influence the determined mass transfer parameter. By

taking a spiral wound system instead of a plate and frame system, the hydrodynamic conditions

were changed. Based on the maximum in the rejection curves of the pilot plant experiments, which

is not present in the laboratory scale experiments, it is concluded that the mass transfer coefficient

of lactic acid in the spiral wound pilot plant system is lower then in the case of the plate and frame

laboratory scale system. This should result in a lower lactic acid rejection compared to the

laboratory scale experiments. However, this is not observed, meaning that the concentration effect

of ions is of more importance than concentration polarisation effects. A good comparison of the

NF40 and the HC50 membrane for the broth can not be made because of the uncertainty of the Bs of

the HC50 membrane.

It can be concluded that equation (1) can be used to describe lactic acid rejection of RO and NF

membranes for UF-broth and broth. The lactic acid rejection at high fluxes can be predicted based

on literature data obtained for lactic acid/water mixtures. A reasonable estimate for the mass

transfer parameter Bs can be calculated in the case of the UF-broth. Prediction of lactic acid

rejection at low fluxes in the case of the broth is not possible. For design purposes equation (1) can

be used with actual data or predicted values. In the case of the broth a worst case approach to the

design can be made by applying a flux invariable rejection equal to the calculated rejection

parameter.

4.2 Fouling

From the pure water flux experiments a Rm value of 8.6.104 MPa.s.m-1 at 37°C was determined for

the NF40 membrane. This value was used in equation (4) for the calculation of the various parame-

ters of Ri and the parameters of Rf as discussed in the materials and methods.

The osmotic pressure difference for the various experiments (both continuous and batch

experiments) was determined, and could be described by the following linear expression

(determined by linear regression of osmotic pressure and concentration ratio data):

[MPa] 0.033-C0.248. = rπ∆ (13)

52 CHAPTER 3

This expression was used in equation (4) for calculating Ri and Rf.

Figure 3: Initial fouling resistance, Ri, of a spiral wound NF40 membrane for UF-broth, measured

at 37°C, different pressures and concentration ratio Cr=4 (□) and Cr=8 (■). The drawn line is

calculated with Ri=4.18.105.P0.84.Cr0.47. Dashed lines give 95% confidence limits.

In Figure 3 the Ri of the NF40 membrane for the UF-broth calculated for the continuous

experiments are given. It can be seen that the initial fouling resistance Ri increases with pressure.

An increase in concentration ratio also gives a small increase in initial fouling resistance. From the

data at Cr = 4 the pressure dependence of Ri was determined.

P R 0.84i ≈ (14)

Figure 4 shows the parameter D for the continuous experiments. As can be seen the parameter D is

almost constant in the pressure range of 30 through 50 bar. An average value for D of 3.28.104

MPa.s.m-2 was determined. This value and the pressure dependence of Ri were used in calculating

the Cr dependence of Ri. Because measurements were only made at one cross flow


Figure 4: Parameter D of a spiral wound NF40 membrane for UF-broth measured at 37°C and

different pressures. Continuous experiments at Cr=4 (□) and Cr=8 (■). The drawn line is the

average value for D.

velocity the velocity dependence shown in equation (5) was lumped with the constant a in one

parameter. The batch concentration experiments with UF-broth were only performed at a pressure

of 4 MPa. From the results the following expression for Ri could be determined:

C.P.104.18. = R 0.47r

0.845i (15)

Equation (15) is shown as the drawn line in Figure 3. Equation (15) overestimates the Ri determined

during continuous experiments by about 50%. During the calculation of the exponent of Cr large

differences were found between the duplicate experiments. The dashed lines give the 95%

confidence limits of Ri solely based on the 95% confidence interval of the exponent of Cr. The

measured Ri values are not within these limits. A good explanation for these differences can not be

given and additional experiments are needed to investigate this. However, the order of magnitude of

Ri can be calculated so equation (15) can be used to make engineering calculations.

In the case of the broth only batchwise concentration experiments were performed. Equation (13) is

used to calculate the osmotic pressure difference at different Cr. Also a simplified version of

54 CHAPTER 3

equation (5), Ri = e.Crd, was used, because measurements were only performed at 4 MPa and one

circulation capacity. During calculations it appeared that d was very small (< 10-5). This means that

in the case of the broth the influence of Cr on Ri can be neglected. Therefore calculations were made

taking Ri constant, resulting in an Ri of 0.41 TPa.s.m-1.

The average values for A, kpr and ln(Cg,pr/Cb,pr,1) in equation (8) were 18.4 TPa.s.m-2,1.3.10-6 m.s-1

and 3.5, respectively. The magnitude of A found here agrees well with data obtained by van Boxtel

[9], who determined A for whey in a tubular membrane at different cross flow velocities (in our case

0.2 m.s-1). Average protein diffusion coefficients are 0.1-1.0.10-10 m2.s-1 [15]. Taking a value of

6.10-11 m2.s-1 results in a boundary layer thickness of 4.6.10-5 m, which is a reasonable value for a

boundary layer thickness in the laminar region (Reynolds number≈260, data from [16]). For the RO

of whey, mass transfer coefficients of 4-10.10-6 m.s-1 have been reported [17]. These values are

higher than in our case. We used a spiral wound module, while in [17] a flat sheet module was used.

The mass transfer coefficient in our spiral wound module was lower than in the flat sheet module,

which may explain the differences between our results and those reported in the literature [17].

The Cb,pr,1 was 0.74%; this means that the corresponding Cg,pr is 24.5%. This value is in the range of

16.6 - 30.5% reported by Suárez et al. [17]

4.3 Flow resistance calculations To gain insight into the determining fouling mechanisms during NF of the broth and the UF-broth,

calculations were made with the data obtained in the previous part of this paper.

The resistances Rm, Ri, and Rf were calculated for continuous experiments with broth and UF-broth

at 4 MPa, Cr = 4, and a processing time of 8 h, and for batch concentration experiments of both

media, starting with 1 m3, at 4 MPa and a processing time of 8 h.

The results for the continuous experiment with the broth and UF-broth are given in Figure 5. It can

be seen that during continuous NF of the UF-broth Ri is the largest resistance to water permeation.

Time dependent fouling (Rf) hardly contributes to the overall resistance to water permeation. This

shows that osmotic effects and concentration polarisation effects during continuous NF of UF-broth

cause the main mass transfer resistance. This is consistent with what was found for processing of

whey permeate [8]. The results of the continuous experiment with broth show that during NF after 1

h time dependent fouling is the predominant resistance.


Figure 5: Resistances as a function of time of a continuous experiment with UF-broth (Rm (▼), Ri

(●), Rf (■)) and broth (Ri (○), Rf (□)) at Cr=4, 4 MPa and 37°C. The resistances were calculated

using the fit of the experimental data to the theoretical model presented here.

Furthermore, the Ri is increased by a factor of 1.5 compared to the UF-broth. This shows that high

molecular weight compounds like proteins cause severe fouling of the NF-membrane in both the

initial stage of fouling and the time dependent fouling. Hence second to osmotic and concentration

polarisation effects protein fouling is very important, an observation made for whey also [8]. From

this it can be concluded that the NF process could be improved by removal of high molecular

weight compounds prior to NF. Also fouling can be better controlled because Ri can be influenced

by cross flow velocity.

During batch concentration of the UF-broth the increase in mass transfer resistance (Figure 6) is

mainly caused by the increase in Ri. A Cr of about 16 was reached after 8 h. As during continuous

NF of UF-broth osmotic and concentration polarisation effects are responsible for the increase in

mass transfer resistance. However, during NF concentration of the broth again time dependent

fouling becomes more important (Figure 6) at the end of the process (a Cr of 4 was reached after 8

h). Furthermore, it can be seen that initial fouling immediately results in a low capacity of the

membrane because Ri is high. Due to the fact that Ri is independent of Cr an increase in Ri, as was

found for UF-broth, does not occur.

56 CHAPTER 3

Figure 6: Resistances as a function of time of a batchwise concentration experiment with UF-broth

(Rm (▼), Ri (●), Rf (■)) and broth (Ri (○), Rf (□)) at 4 MPa and 37°C. The resistances were cal-

culated using the fit of the experimental data to the theoretical model.

4.4 Flux and rejection calculations With the results of the rejection studies and fouling studies the batchwise concentration of broth and

UF-broth were calculated. The results of the batchwise concentration of the UF-broth are shown in

Figure 7.

Both the flux and the overall lactic acid rejection can be calculated accurately. The same is

observed for the batchwise concentration of the broth (Figure 8). These calculations show that the

presented lactic acid rejection model and the flux model can be used to give a description of the NF

separation of lactic acid from fermentation broths.


Figure 7: Flux Jw (■) and overall lactic acid rejection (□) measured as a function of time during

batchwise concentration of UF-broth at 4 MPa and 37°C. Lines were calculated using the model.

Figure 8: Flux Jw (■) and overall lactic acid rejection (□) measured as a function of time during

batchwise concentration of broth at 4 MPa and 37°C. Lines were calculated using the model.

58 CHAPTER 3

5. CONCLUSIONS

From the lactic acid rejection measurements it can be concluded that prediction of the rejection

parameter of RO and NF membranes for lactic acid using broth or UF-broth is possible. The mass

transfer parameter can only be predicted in the case of the UF-broth. In the case of the broth

prediction is not possible because of system dependent fouling phenomena. Equation (1) can be

used with actual lactic acid rejection data to quantify lactic acid rejection.

Fouling of a spiral wound NF40 membrane can be quantified by a model in which three different

resistances (Rm, Ri, and Rf) are taken into account. In the case of a UF-broth a colloidal fouling

model can be used to describe the time dependent fouling, while for a broth a gel layer model was

used. From calculations using the parameters obtained it can be concluded that during NF of a broth

time dependent fouling caused by proteins causes the main resistance to water permeation. For a

UF-broth the initial resistance is the main resistance to water permeation, showing that

concentration polarisation phenomena are more predominant.

The descriptions of both the lactic acid rejection and the membrane fouling can be used to describe

lactic acid separation from fermentation broths and offer the possibility of optimising the NF

separation process. From the results it can be concluded that it is beneficial to remove the proteins

by ultrafiltration prior to NF.

6. LIST OF SYMBOLS

a,b,c, :empirical constants

d,e

Am :membrane surface area [m2]


Bs :mass transfer parameter lactic acid [m.s-1]

Cr :concentration ratio [-]

Cb,pr :protein concentration in the bulk [kg.m-3]

Cb,pr,1 :protein concentration in the bulk at Cr = 1 [kg.m-3]

Cg,pr :protein concentration in gel [kg.m-3]

D :parameter [Pa.s.m-2]

Fa1 :overall rejection of the membrane for component 1 at infinite flux [-]

Fb1 :overall permeability of component 1 through the membrane [m.s-1]

Jw :water flux [m.s-1]


Jw0 :water flux determined by extrapolating the flux-time curve to time zero [m.s-1]

k1 :mass transfer coefficient component 1 in boundary layer [m.s-1]

kpr :mass transfer coefficient of protein in boundary layer [m.s-1]


Rs :rejection parameter lactic acid [-]

R1 :rejection component 1 [-]

Rtot :total resistance of the membrane to water permeation [Pa.s.m-1]

Rm :resistance of a clean membrane to permeation of water [Pa.s.m-1]

Ri :initial fouling resistance to permeation of water [Pa.s.m-1]

Rf :time dependent fouling resistance permeation of water [Pa.s.m-1]

Rc :specific foulant layer resistance [Pa.s.m-2]

Rw0 :resistance at intercept of the flux-time curve at time zero [Pa.s.m-1]

V0 :volume at time zero [m3]

Δp :pressure difference across the membrane [Pa]


ε :specific gel layer resistance [Pa.s.m-2]

εc :effective foulant layer porosity [-]

ρ :density of the bulk solution [kg.m-3]

Φ0 :foulant volume fraction in the feed [-]

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60 CHAPTER 3



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16. G. Schock, A. Miquel , Mass transfer and pressure loss in spiral wound modules, Desalination 64 (1987)

339-352

17. E. Suárez , F. San Martín , R. Alvarez , J. Coca , Reverse osmosis of whey. Determination of mass transfer

coefficients, J. Membr. Sci. 68 (1992) 301-305

61

CHAPTER 4

Use of nanofiltration for concentration and demineralisation in

the dairy industry: model for mass transport1

SUMMARY

Models were developed, based on the extended Nernst-Planck equation, which describe the salt rejection as

a function of the flux for binary and ternary salt solutions. Effects of concentration polarisation,

composition of feed and concentration are incorporated in the model. In laboratory-scale experiments,

rejection-flux curves of four different commercial membranes were established for three different model

solutions (NaCl, CaCl2 and (NaCl + CaCl2)) and for ultrafiltration (UF) whey-permeate (pH 4.6, 5.8 and

6.6). The results indicated that the salt transport through all the NF membranes investigated depends on the

flux. At low flux, when the contribution of diffusive transport is the most important, permeability of

(especially monovalent) cations is high. At high flux, when transport by convection is the most important,

rejection reaches a maximum (constant) value. From this it follows that the salt transport can be controlled

by the flux.

For binary salt solutions (NaCl or CaCl2), rejection data could be described by the (two-parameter) model

for binary systems. For ternary systems (NaCl and CaCl2) the model was simplified from a model with four

transport parameters to a model with three transport parameters. Rejection data for a ternary system could

also be described adequately. Decoupling of transport parameters allowed that the model for the ternary

system could be reduced from a four-parameter model to a three-parameter model without losing accuracy.

For ultrafiltration (UF)-whey-permeate, a multi-component mixture, it is shown that an approach in which

monovalent cations, divalent cations and anions were grouped separately and lumped into one concentration

can be used to describe the rejection-flux data adequately. The experimental data for the (cumulative) anion

equivalent charges were predicted accurately only at pH 4.6 and 5.8. At pH 6.6, the rejection calculated for

the anions based on equivalent charges was somewhat lower than the rejection actually measured. About

half of the difference could be ascribed to lactate and carbonate, which were not determined separately. As

a result there was also a non-matching charge balance.

The transport parameters derived from the results with UF-whey-permeate can be used to predict the salt

rejection for similar multi-component systems like whey and UF-permeate in industrial systems.

1 This chapter has been published as H.C. van der Horst, J.M.K. Timmer, T. Robbertsen, J. Leenders, “Use of nanofiltration for concentration and demineralization in the dairy industry: model for mass transport”, Journal of Membrane Science 104 (1995) 205-218

62 CHAPTER 4

1. INTRODUCTION

World-wide an increasing amount of whey is industrially processed to whey powders and other

high-quality, protein-rich, products meant for nutritional use [1,2]. Whey intended for human or

animal consumption will increase in value if it is demineralised [3,4]. In a previous investigation

[5-8] it was established that by the use of spiral-wound reverse osmosis (RO) membranes for the

concentration of whey, energy savings of approximately 60% can be obtained as compared with

the energy consumption using evaporation (EV). Total costs for the concentration of whey to

50% total solids by RO (to 16.5% total solids) followed by EV by thermal vapour recompression

(TVR) (from 16.5 % to 50% total solids) are similar to those for concentration by EV only.

In industrial processes for whey demineralisation, whey is concentrated by EV, followed by

demineralisation of the concentrated whey using electrodialysis (EV + ED) and/or ion-exchange

(IE). ED is the most economical process for a demineralisation percentage of up to 60% [3,9,10].

Figure 1: Concentration and demineralisation of whey in two steps using evaporation (EV) or

reverse osmosis (RO) followed by electrodialysis and in one step using nanofiltration (NF)

Nanofiltration (NF) is an alternative for the concentration and demineralisation of whey by EV +

by ED [9]. NF-membranes (cut-off 200-1000) have a high permeability for (monovalent) salts

(NaCl, KCl) and have a very low permeability for organic compounds (lactose, proteins, urea).

The use of NF (also called ultra-osmosis [4]) instead of EV + ED has the advantage of

simultaneous concentration and demineralisation of whey [4] (Figure 1). This will lead to a

Use of nanofiltration for concentration and demineralisation in the dairy industry 63

considerable reduction of the costs for energy consumption, waste water disposal and total costs

[3,9].

The mineral reduction with respect to the monovalent ions during NF of sweet Gouda whey is

comparable with that obtained when whey is demineralised by ED (60%) (Table 1).

Table 1. Reduction in minerals in whey, partially demineralised by electrodialysis and nanofiltration.

Reduction

(%) Electrodialysis

(40%) Electrodialysis

(60%) Nanofiltration

(45%)

K+ + Na+ Ca2+ Cl-

42 24 71

64 35 89

65 6

54

The NF-permeate contains salts, nitrogen and some lactose. The loss of nitrogen and lactose in

the permeate depends on the membrane characteristics and can also be influenced by pre-

treatment of the feed and process conditions. With respect to the membrane characteristics the

following parameters are of importance: pore diameter, pore length, membrane material and

membrane charge. Membrane characteristics are difficult to establish or alter. The feed

characteristics, e.g. ionic strength, ion valence, salt composition, viscosity and pH, also affect the

separation and are easier to control.

In order to distinguish between the performance of different commercial membranes for feeds of

various origin (sweet and acid whey, ultrafiltration (UF)-permeate, sanitising solution), the

separation characteristics of the membranes must be quantified in one or more characteristic

membrane parameters. Also the effect of feed composition on the separation performance is of

interest to process technologists in the dairy industry.

From the literature [3,11-13] it is known that in multi-component salt solutions the rejection of

the solutes/components is different from that of the same components in a binary solution.

Furthermore rejection is related to the concentration of salt. Therefore it is difficult to predict

separation characteristics of a NF-membrane for complicated multi-component solutions like

dairy liquids using data derived from simple binary salt solutions. Vonk and Smit [14] and Tsuru

et al. [12,13] applied the extended Nernst-Planck equation, developed by Schlögl [15] and

Dresner [16], for the description of binary and multi-component salt mixtures. In the analysis of

their results, Vonk and Smit [14] were able to explain phenomena, like negative rejections, based

64 CHAPTER 4

on the existence of a electrical potential gradient, caused by the difference in mobilities of the

ions in the system, differences in partition properties and different ion reflections. They also

justified the idea that in salt systems the ions should be treated as separate components instead of

neutral species. In the treatment of their data, they applied the differential description of the

extended Nernst-Planck model. For industrial application this differential model is to

complicated and an accessible equation to calculate the rejection was not given.

The aims of this study were: (i) to develop an equation to describe the rejection in a binary and a

ternary salt system, based on a difference approach to the extended Nernst-Planck equation, (ii)

verify if the equations can be used for the description of binary and ternary systems, and (iii) to

characterise the salt transport through NF membranes. This information can be used to

understand and predict the performance of different NF membranes for feed of various origins

and gives insight into the contributions of different mass transfer processes (diffusion,

convection, boundary layer transport) to the overall transport of salts. From experiments with

model feed and UF-whey permeate, parameters are determined that can be used to predict solute

transport for clean membranes during NF of whey and other dairy streams.

2. THEORY The driving force in RO for solvent transport is the pressure difference across the membrane. The

solvent flux (Jw) during RO is usually described by the solution-diffusion model:

)P-(A= J ww π∆∆ (1)

For a clean membrane and with water as a feed Aw, the clean membrane solvent permeability

coefficient, can be established by measuring the water flux as a function of transmembrane

pressure (ΔP) (osmotic pressure difference Δπ = 0).

To set up a model for the solute transport in NF membranes we start with the extended Nernst-

Planck equation [14,17,18] in which there is a concentration-driven transport, an electrostatic

potential and a pressure-driven solute transport. This model has already been proven to give a

good description of the transport of lactic acid through NF membranes [17].

) -(x).(1C.J +] x

.T.R

F.z(x).C + x(x)C.[P- = J iiw

iiiii σ

Ψ∂∂

∂∂

(2)


Linearising the partial derivatives between the limits x = 0 (concentrate-side) and x = l

(permeate-side), and taking the concentrations at x = 0 leads to the following equation:

) - .(1C.J +] .T.R

F.z.C + C.[B- = J i0iwi0i

iii σ∆Ψ∆ (3)

in which Bi = Pi/l, l : membrane thickness.

For simplicity we will limit the calculations to two components (Na+(1) and Cl-(3)). The third

component (Ca2+ (2)) will be introduced later.

For a binary system (i=1,3) with two permeating components the following two equations hold:

) - .(1C.J +] .T.R

F.z.C + C.[B- = J 110w110

111 σ∆Ψ∆ (4)

) - .(1C.J +] .T.R

F.z.C + C.[B- = J 330w330

333 σ∆Ψ∆ (5)

From equation (5) an expression for the electrostatic potential can be derived

C.B.zJ - ) - .(1C.J + C.B- = .

T.RF

3033

3330w33 σ∆∆Ψ (6)

The electro-neutrality condition gives:

0 = C.z iiΣ ➔ 0 = C.z + C.z 3311 (7)

The no-current condition gives:

0 = J.z iiΣ ➔ 0 = J.z + J.z 3311 (8)

Combining equations (4), (6), (7) and (8) results in:

)R-.(1C.J + C.F- = J ,110w111 ∞∆ (9)

66 CHAPTER 4

in which:

))

z.Bz.B-(1

)zz-.(1B

( =F

33

11

3

11

1 (10)

and

)z.Bz.B-(1

).z.Bz.B-(

=R

33

11

333

111

,1

σσ∞ (11)

Figure 2. Concentration polarisation in the boundary layer.

By using the concentration difference across the membrane (Figure 2),

)C -C(- = C -C = C p,11,01,0p,11∆ (12)

and the equation for concentration polarisation,


)kJexp().C -C( = )C -C(

1

wp,1c,1p,11,0 (13)

in which k1 is the mass transfer coefficient (m.s-1), equation (9) can be transformed into:

)R - (1 . )kJ( exp . )C -C( + C . J + )

kJexp().C -C.(F = J ,1

1

Wp,1c,1p,1W

1

wp,1c,111 ∞

(14)

The rejection (Ri) of component i is defined by

CC - 1 = R

ic,

ip,i (15)

The flux of component i through the membrane is defined by

C.J = J ip,wi (16)

By using equations (14), (15) and (16) for component 1 the following expression for the rejection

can be derived

1)) - )kJ).(exp(R-(1 + .(1J+ )

kJexp(.F

J.R = R

1

w,1w

1

w1

w,11

∞

∞ (17)

Rearrangement of equation (17) gives

)J(B + JJ).J(R = R

w1sw

ww1s1 (18)

in which:

68 CHAPTER 4

1)-)kJ).(exp(R-(1+1

R = )J(R

1

w,1

,1w1s

∞

∞ (19)

and

1)-)kJ(exp).(R-(1+1

)kJ(exp.F

=)J(B

1

w,1

1

w1

ws1

∞

(20)

In order to establish the effects of concentration polarisation, the mass-transfer coefficient k1 is

calculated for laminar flow [19] using:

)Ld.Re.Sc.611.+66(3.=

Dd.k=Sh h33 3

1

i

hi (21)

in which:

µρ v.d.=Re ch (22)

and

ρµ.D

=Sci

(23)

Calculation of the mass transfer coefficient ki [19] shows that ki (≈50.10-6 m/s) is of the same

order of magnitude as the flux (10.10-6 - 40.10-6 m/s) and hence with respect to the calculation of

transport parameters, concentration polarisation has to be taken into account.

The derivation for a ternary system with three permeating components i.e. Na+, Ca2+ and Cl-, is

given in appendix I.


The final expression for the rejection of component i in a ternary system is given by equation 24.

j)i 1,2,=j 1,2,=(i )J(B + J

R.CC).J(B - J).J(R

= Rwsiw

jic,

jc,wijwwsi

i ≠ (24)

In equation 25 the rejection of component 3 (e.g. Cl-) is given:

))R-*(1C2+C

C2+)R-(1*C2+C

C(-1=R CaCaNa

CaNa

CaNa

Na3 (25)

The model will be validated by measuring the water flux versus the pressure. Membrane

permeability constant Aw (equation 1) can be calculated from the slope of the curve. By

measuring the solute rejection of e.g. Na+ and Cl- in a binary system and of Na+, Cl- and Ca2+ in a

ternary system as a function of the flux, the model can be tested to describe the experimental

results. Finally a UF-whey permeate will be considered as a ternary system in which Na+ and K+

are lumped as one component, Ca2+ is the second component and all the anions are lumped into

one imaginary third component with charge equivalent -1. Equivalent concentrations of the

anions will be calculated taking into account dissociation constants of weak acids [20]. The

transport parameters for the lumped monovalent cations, divalent cations and anions derived

from these results can then be used for similar ternary systems with different concentrations, pH,

mass transfer coefficients and non-permeating components (R = 1) in order to predict the

rejection-flux curves for each group of ions.

3. EXPERIMENTAL

3.1 Media

1. a 17 mM solution of NaCl (pro analysis, E. Merck, Darmstadt, FRG) in demineralised

water.

2. a 13.2 mM solution of CaCl2 (pro analysis, E. Merck, Darmstadt, FRG) in demineralised

water.

3. a 17 mM solution of NaCl and 13.2 mM CaCl2 in demineralised water.

4. UF-whey permeate, pH 4.6, 5.8 and 6.6. UF-whey permeate powder (NIZO, Netherlands)

70 CHAPTER 4

was dissolved in demineralised water (5%m/m) and pH was adjusted to 4.6 (5 N HCl) in

order to obtain a clear solution. Then the pH of the solution was set with 5 N NaOH. As

a result of this procedure the concentrations of Na+ were different for each pH as is

shown in Table 2. A typical composition of the UF-whey permeate at pH 4.6 is given in

Table 3.

5. water, demineralised by ion-exchange followed by RO.

Table 2. Concentration of sodium and chloride in a 5% solution of UF-whey permeate powder after pH adjustment.

pH whey permeate sodium (mg.g-1) chloride (mg.g-1)

4.6 361 1647

5.8 474 1660

6.6 707 1646

Table 3. Composition of UF-whey permeate (pH 4.6).

Component Concentration Component Concentration

Sodium (mg.g-1) 361 sulfate (mg.g-1) 117

potassium (mg.g-1) 2208 nitrate (mg.g-1) 49

Calcium (mg.g-1) 197 lactose (%) 4.0

phosphate (mg.g-1) 2030 protein (%) 0.18

chloride (mg.g-1) 1647 total solids (%) 5.0

citrate (mg.g-1) 1089

3.2 Membranes

Four different makes of commercial membranes were used. Names and properties are given in

Table 4.

3.3 Membrane system

The four membranes were placed in series and simultaneously tested in a laboratory unit LAB 20

(DDS, 360 cm2 per membrane type) (Figure 3). For the determination of the permeability

constant (Aw), clean water flux was measured at 5, 10, 20 and 30°C at pressures ranging from 2.5

to 40 bar.


Table 4. NF-membranes used in experiments.

Membrane Manufacturer/Source pH Temperature (°C) Material

FE 700-004 Filtration Engineering 2-11 50 PA/PS*1

NF 40 Filmtec 2-11 45 PA/PS*1

HC 50 Dow Chemical 2-10 60 PA/PS*1

CA 960 PP Dow Chemical 2-8 30 CA*2

*1PA/PS = polyamide on polysulfone support, *2CA = cellulose acetate

Experiments with the different solutions were performed in recirculation mode. Both the

permeate and the retentate were returned to the feed vessel. The experiments were carried out

with maximum circulation flow of 10 l/min at 20°C, corresponding to a mass transfer coefficient

ki of ≈ 50.10-6 m.s-1 at pressures ranging from 2.5 to 60 bar. The following parameters were

measured: temperature, pressure and permeate flow. The composition of retentate and permeate

was determined at each pressure level.

The cleaning procedure of the laboratory unit was as follows. After removing the feed from the

module, the system was rinsed with water. After rinsing, cleaning took place (30-35°C, 5 bar)

with 0.5% Ultrasil 50. After 45 minutes of cleaning the module was rinsed again with water and

water flux was measured to verify cleaning efficiency. In all cases original water flux was

restored.

Figure 3. Laboratory membrane unit for nanofiltration (Lab 20, DDS)

72 CHAPTER 4

3.4 Analyses

Total solids by drying at 105°C, 4 hours [21]; protein by micro-Kjeldahl [22], protein factor 6.38;

Na+, K+ and Ca2+ (flame emission spectrophotometry); Cl- (NEN 3761 and capillary ion analysis

(CIA)); phosphate (Griswald and CIA); lactose (Luff-Schoorl) [23]; citrate, nitrate and sulfate

(CIA).

Figure 4: Effect of temperature on the solvent permeability for four different NF-membranes.

(♦ NF 40; O HC 50; ▲ FE 700-004; ∇ CA 960)

4. RESULTS AND DISCUSSION

4.1 Water permeability, Aw

In Figure 4 the effect of temperature on the water permeability of the four different membranes is

shown. Theoretically [19] temperature should hardly affect the product of permeability (Aw) and

viscosity (μ) in this temperature range. From Figure 4 it can be seen that this is indeed the case

for all membranes. The results from the NF 40 and the HC 50 membrane are virtually the same,

which is expected because both membranes were produced by the same method. Permeability

constants are the lowest for these membranes. The CA 960 membrane has the highest

permeability constant. The differences in permeability can be caused by differences in the water

content of the membrane or differences in the separation layer thickness. In general CA

membranes have a higher water content than thin film composites, which can explain the highest

permeability for the CA membrane. The other three membranes have a skin layer made of


polyamide. It is not known whether the water content of the skin can be different for the three

membranes. From electron microscopic photographs it was not possible to see a clear difference

in the thickness of the skin layers. A conclusive remark about the reason for the difference in

water permeability for the three thin film composite membranes cannot be given.

Figure 5. Rejection-flux curve for sodium and chloride (feed 1).

▲ sodium(fit: full line); chloride(fit:dashed line)

4.2 Rejection-flux curves for NaCl, CaCl2

In Figure 5 the rejection for Na+ and Cl- (feed 1) versus flux is shown for the NF 40 membrane at

20 °C. The experimental data are fitted according to equation 18 (using DNa ≈ 1.48.10-9 and for

kNa 54.10-6 m/s). The differences between rejection of Na+ and Cl- are marginal, which is

according to expectations, because from the "electroneutrality"-condition it follows that RNa =

RCl. At low flux the rejection tends towards zero, while at high flux the rejection becomes almost

constant at a value of about 0.6. A high diffusive transport of Na+ and Cl- through the membrane

compared to convective transport is the reason that at a low flux a low rejection is found. With

increasing flux the contribution of convective transport becomes more important and rejection

will increase. However, concentration polarisation will also increase with an increase in flux,

which results in a decrease in rejection. The counteracting contributions of increased convective

transport and increased concentration polarisation result in a constant rejection at the fluxes

measured. The rejection-flux curves of the other membranes show the same behaviour.

74 CHAPTER 4

Figure 6. Rejection-flux curve for calcium and chloride (feed 2).

calcium (fit:full line); chloride(fit:dashed line)

In Figure 6 the rejection for Ca2+ and Cl- versus flux is shown for the NF 40 membrane at 20 °C

(feed 2, DCa ≈ 1.14.10-9 and kCa 46.10-6). Here again the difference between the rejection for Ca2+

and Cl- is negligible, as it should be, because of the electro neutrality condition. The average

rejection for both Ca2+ and Cl- as a function of the flux is higher than for Na+ and Cl-, indicating a

lower transport of Ca2+ and Cl- in this solution. This observation has been extensively discussed

by Vonk and Smit in terms of the existance of lyotropic series. The permeability of Ca2+ is lower

than the permeability of Na+, while the reflection of Ca2+ is higher than for Na+. By using these

inequalities in eqs. (10) and (11) it shows that the rejection of Ca2+ will be higher than the

rejection of Na+.

From the rejection-flux curves the transport parameters FNa, FCa, R∞, Na and R∞, Ca were calculated

for all membranes (Table 5). For Ca2+ the F-values, indicative of diffusive transport, are lower

than for Na+. The R∞-values indicative of convective transport are slightly higher. From this it

follows that the rejection of Ca2+ in a binary solution will be higher than for Na+. From the

transport parameters it can be seen that the membranes investigated show considerable

differences in their permeability to Na+ and Ca2+. A comment has to be made about the R∞-values


for the CA960 membrane. At the high experimental pressures the flux-pressure curve showed a

considerable deviation from linearity which was not found for the other membranes. This

indicated compaction of the membrane, which results in a change of properties of the membrane.

For this reason the values of R∞, which are statistically strongly influenced by measurements et

high pressures, should be handled with care.

Table 5. Transport parameters for the two-parameter model

Membrane Sodium Chloride Calcium Chloride F1

[10-6m.s-1] R∞,1 [-]

F1 [10-6m.s-1]

R∞,1 [-]

F2 [10-6m.s-1]

R∞,2 [-]

F2 [10-6m.s-1]

R∞,2 [-]

HC 50 Fe 700-004 CA 960 NF40

7.86 3.07

38.49 5.59

0.96 0.91 1.66 0.84

7.58 3.11

37.96 5.57

0.95 0.90 1.64 0.83

0.79 3.06 5.27 1.58

0.96 0.98 1.01 0.88

0.79 2.96 5.07 1.51

0.96 0.97 0.99 0.87

4.3 Validation of the model for a ternary system

From the derivation in appendix I it can be seen that a four-parameter model is obtained. In

equations A1.17 and A1.19 Rs1(Jw) is a function of the concentrations and B12(Jw) is a

complicated function of the flux. To simplify these parameters the X4-term in the flux-equation of

Na+, and the X3-term in the flux-equation of Ca2+, were neglected. Physically this means that the

contribution of drag by the other cation is neglected. This approach results in a concentration-

independent Rsi(Jw) and a simplified dependance of Bij(Jw) on the flux. Another advantage is that

the value of (1-F3,1) can be immediately compared with the value of R∞, i in equation 19. To

validate this simplification, R2-testing of the models according to Draper and Smith [23] was

applied. Table 6 shows that in all cases the R2 values of the four- and three-parameter model are

almost identical, showing that the decoupling is justified.

The results in Table 6 show that in the case of Na+, the presence of Ca2+ results in an increase in

transport of Na+, because of the positive sign of F2,1. In the case of Ca2+, a decrease of Ca2+

transport is obtained for the HC 50 and the NF 40 membrane. Furthermore, the (1-F3,1) and the

(1-F4,2) are very close to 1 except for the NF 40 membrane. This means that the contribution of

drag by the solvent to cation transport only will be noticed at high fluxes.

Comparing the four membranes shows that the diffusive contribution in mass transport of cations

(parameters F1,1, F2,1, F1,2 and F2,2) is highest for the Fe 700-04 membrane and lowest for the NF

40 and the HC 50. These differences might be explained by different surface properties of the

76 CHAPTER 4

Table 6. Transport parameters for the four- and three-parameter model

Membrane Parameters for sodium na R2 F1,1

[10-6m.s-1] F2,1

[10-6m.s-1] F3,1 [-]

F4,1 [-]

HC 50 Fe 700-004 CA 960 NF 40

4 3 4 3 4 3 4 3

0.999 0.997 0.998 0.999 0.994 0.996 0.988 0.987

6.17 4.09

13.82 17.29 3.67 7.50 4.85 4.08

6.02 5.55

12.80 14.02 9.85

10.16 8.74 8.48

-0.35 0.04 0.10 -0.06 0.29 -0.01 0.05 0.16

0.45

-0.10

-0.30

0.12

Membrane Parameters for calcium na R2 F1,2

[10-6m.s-1] F2,2

[10-6m.s-1] F3,2 [-]

F4,2 [-]

HC 50 Fe 700-004 CA 960 NF 40

4 3 4 3 4 3 4 3

0.998 0.997 0.999 0.999 0.989 0.991 0.998 0.998

-0.12 -0.03 -0.20 0.47 -1.52 1.10 -0.77 -0.43

0.76 0.73 1.92 2.15 2.31 2.50 1.75 1.86

-0.02

0.03

0.20

0.05

0.08 0.05 -0.01 0.00 -0.18 0.01 0.07 0.13

Figure 7. Rejection-flux curve for sodium, calcium and chloride (feed 3).

—▲— sodium; --- --- calcium; •• •• chloride


membranes. In Figure 7 the rejection for Ca2+, Na+ and Cl- is given versus flux for the NF 40

membrane at 20 °C (feed 3). The experimental data are described by the three parameter model

according to equations 24 and 25. We now see that the rejection-flux curve for Cl- is exactly the

same as it was during NF of the binary solution of NaCl but that the rejection for Na+ has

decreased as compared with the rejection for Na+ in a NaCl solution alone. So the rejection of Cl-

in a ternary solution is the same as it is in a binary solution of NaCl (as could be expected from

the values of the transport parameters: Tables 5 and 6); the absolute transport of Cl- is twice as

high due to the concentration of Cl- being twice as high in the ternary solution. The transport of

Na+ is higher and the transport of Ca2+ is as it was in the binary solution of CaCl2. This

observation is in accordance with results of Vonk and Smit [14], who found with a CA

membrane that only Na+ rejection was influenced when CaCl2 was added to the NaCl solution.

Also Tsuru et al. [12,13] had a similar observation with a mixture of Na2SO4 and NaCl using a

NTR7450 membrane. In this case the Cl- rejection decreased upon the addition of SO42-, while

SO42- rejection remained constant.

4.4 Rejection-flux curves for UF-permeate

In Figures 8a, b and c the rejection of monovalent cations (Na+ + K+), of divalent cations (Ca2+)

and of the cumulative anions (NO3-, SO4

2-, Cl-, Cit-1, Cit-2, Cit-3, Phos-1, Phos-2, Phos-3) is shown

versus the flux for UF-whey permeate (feed 4) at pH 4.6, 5.8 and 6.6 respectively. The system is

considered as a system with three permeating components: (Na+ + K+), Ca2+ and anions. The

lumping of the concentrations of (Na+ + K+) is allowed since the rejection (or permeability) for

both Na+ and K+ is very similar. The experimental anion rejection was calculated based on the

total cumulative negative charge in the permeate and the retentate. It is obvious that for all pH

values the rejection curves of (Na+ and K+) and the anions are closer to each other than in the

case of the model experiments with the ternary system. This difference is caused by a much

lower concentration of Ca2+ relative to Na+ and K+ in the UF-permeate as compared to the

NaCl/CaCl2 system. This results in a smaller decrease in rejection of Na+ and K+ as explained by

Vonk and Smit [14]. In the model experiments it was observed that Ca2+ rejection was hardly

influenced in the presence of Na+. Comparing Figures 8a-c to Figure 7, there is an unexpected

increase in Ca2+ rejection in the UF-permeate. The major reason for this increase is the

availability of free Ca2+ in the retentate. Ca-activity measurements in a simulated UF-permeate

showed that the free Ca2+ at pH 6.6 is about 15% of the amount measured by flame emission

78 CHAPTER 4

spectrophotometry. Calciumphosphate formatin or chelation by citrate can be the cause of the

reduced availability of Ca2+. When the Ca2+ rejection is calculated based on the Ca2+ activity,

rejections are much closer to the rejections of the NaCl/CaCl2 experiment.

Figure 8a. Rejection versus flux of cations and anions during NF of UF permeate at pH 4.6.

—▲— sodium + potassium; - - - - calcium; •• •• negative ions

For pH 4.6 and 5.8 the model describes all the experimental data very well. For pH 6.6 the data

for (Na+ + K+) and Ca2+ are described well by the three- parameter model. However, for these pH

values the calculated rejection-flux curve for the anions according to equation 25 does not

describe the measured values. The measured rejection values are lower than predicted. This is

probably caused by the fact that not all anions participating in the solute transport at these pH's

were analysed. This is indicated by a shortage of negative charge in the charge balance that

increases with increasing pH (Table 7). It was found that the shortage could be partly (50%)

ascribed to carbonate and lactate, the concentrations of which increase with increasing pH and

which then actively participate in the transport. Lactate and carbonate concentrations were not

determined. The remaining shortage could not be traced, but might be ascribed to errors in the

values of the dissociation constants of the weak acids that were used to calculate the negative

equivalents available for transport.


Figure 8b. Rejection versus flux of cations and anions during NF of UF permeate at pH 5.8.


Figure 8c. Rejection versus flux of cations and anions during NF of UF permeate at pH 6.6.


In a further investigation the transport parameters that are determined from the data of UF-whey

permeate, which is considered as a ternary system, will be used to predict the rejection of lumped

80 CHAPTER 4

monovalent cations, divalent cations and anions as a function of the flux for NF of whey.

Table 7. Charge balance for pH 4.6, 5.8 and 6.6 during NF of UF-whey permeate, NF 40, 20 °C, flux 11.2 10-6 m.s-1.

pH retentate permeate

cations (I)

anions (II)

(I) - (II) (equiv.m3)

(I) - (II) (%)

cations (I)

anions (II)

(I) - (II) (equiv.m3)

(I) - (II) (%)

4.6 5.8 6.6

93.7 95.6

106.0

96.8 89.3 95.7

-3.1 6.3

11.4

-3.3 6.6

10.7

33.2 33.9 36.6

32.5 33.8 35.4

0.7 0.03 1.2

2.3 0.1 3.4

Also for UF-whey-permeate one of the striking features in all the rejection flux curves is the low

solute rejection at low flux levels. This indicates that diffusive transport is the most important

transport mechanism at low flux. At higher flux, rejection reaches a constant value, indicating

that convective transport is then the major transport mechanism. Not taking into account the large

membrane area that is needed, the best removal of solutes (in our case salts) takes place at a low

flux level (thus at a low effective transmembrane pressure).

Table 8. Composition of concentration NF-permeate of UF-whey permeate (NF at 20 °C, pH 4.6, at a flux of 11.85 10-6 m.s-1, concentration factor 1).

Component Permeate concentration

NF 40 HC 50 FE 700-004 CA 960

sodium (mg.g-1) 154 117 179 53

potassium (mg.g-1) 1012 781 1002 406

calcium (mg.g-1) 11 5 6 10

phosphate (mg.g-1) 315 360 91 119

chloride (mg.g-1) 1008 771 1105 436

citrate (mg.g-1) 46 40 0 57

sulfate (mg.g-1) 0 0 0 7

nitrate (mg.g-1) 28 22 35 13

lactose (%) 0.11 0.03 0.00 0.17

The differences between the NF-membranes investigated here and established in the transport

parameters (Table 6) results in a difference in permeate composition, as is shown in Table 8.

Here the concentrations of components are given in NF-permeate from UF-whey-permeate after


NF at 20 °C, pH 4.6 at a flux of 11.85.10-6 m.s-1. It is obvious that the difference between the

various membranes as expressed in the transport parameters indeed results in a difference in

permeate salt composition.

5. CONCLUSIONS

The salt transport during NF of binary salt solutions like NaCl and CaCl2, and ternary salt

solutions like (NaCl + CaCl2) and UF-permeate, can be described by a model derived from the

extended Nernst-Planck equation. For the ternary system the model was simplified from a four-

to a three-parameter model. The neglecting of one transport parameter was validated by statistical

analysis. Furthermore the three-parameter model gave a good description of experimental results.

For a multi-component salt mixture like UF-whey-permeate, the rejection-flux behaviour of

mono- and divalent cations could be described accurately by the model at pH 4.6, 5.8 and 6.6.

However, only at pH 4.6 and 5.8 was the rejection of the anions calculated by the model

according to the experimental results. At pH 6.6, the calculated rejection of anions was higher

than the rejection actually found. The difference could be partly ascribed to incomplete analysis

of anions that participated in transport at pH 6.6. This was indicated by a shortage in the charge

balance at this pH.

Regarding a complex multi-component salt system like UF-whey permeate as a three-component

system with monovalent and divalent cations and anion equivalent charges seems to be a useful

approach for evaluating membrane performance and predicting salt transport for similar systems.

The salt rejections increase with increasing flux, indicating the importance of the contribution of

diffusive transport at low flux and convective transport at high flux. This finding may help to

increase demineralisation during NF of dairy streams.

As indicated by the transport parameters the membranes investigated differ with respect to the

permeation of salt.

6. LIST OF SYMBOLS

Aw :clean membrane solvent permeability constant (m.s-1.Pa-1)

Bi :membrane characteristic permeability coefficient of solute i (m.s-1)

Ci(x) :concentration component i (mole.m3)

Cp :solute concentration permeate (mole.m-3)

Cr :solute concentration concentrate (mole.m-3)

82 CHAPTER 4

D :diffusion coefficient (m2.s-1)

dh :hydraulic diameter (m)

F :Faraday constant (C.mole-1)

Ji :solute flux component i (mole.m-2.s-1)

Jw :pure water flux (m.s-1)

ki :mass transfer coefficient (m.s-1)

l :membrane thickness (m)

L :pathlength (m)

ΔP :transmembrane pressure difference (Pa)

Pi :permeability component i (m.s-1)

R :rejection coefficient (-)

R :gas constant (J.mole-1.K-1)

T :temperature (K)

TS :total solids content (w/w %)

vc :cross-flow velocity (m.s-1)

x :dimensionless membrane thickness (-)

zi :charge of component i (-)

ρ :density (kg.m-3)

σi :reflection coefficient (-)

Δπ :osmotic pressure difference (Pa)

μ :dynamic viscosity (Pa.s)

Ψ :electrostatic potential (V)

7. REFERENCES 1. W.S. Clark Jr., Status of whey and whey products in the USA today, in "Trends in whey utilization",

Bulletin IDF 212 (1987) 6-11

2. J.G. Zadow, Whey production and utilization in Oceania, in "Trends in whey utilization", Bulletin IDF

212 (1987) 12-16

3. P.M. Kelly, B.S. Horton, H. Burling, Partial demineralisation of whey by nanofiltration, Int. Dairy Fed.

Annual Sessions Tokyo, Group B47, B-Doc 213 (1991) 87

4. B.S. Horton, Anaerobic fermentation and ultra-osmosis, in "Trends in whey utilization", Bulletin IDF

212 (1987) 77-83

5. A. Morales, C.H. Amundson, D.G. Hill Jr., Comparative study of different reverse osmosis membranes


for processing dairy fluids. I. Permeate flux and total solids rejection studies, J. Food Processing

Preservation 14 (1990) 39-58

6. A. Morales, C.H. Amundson, C.G. Hill Jr., Comparative study of different reverse osmosis membranes

for processing dairy fluids, II. Specific solute effects-rejection coefficients for total nitrogen,

nonprotein nitrogen, lactose, COD, and ash, J. Food Processing Preservation 14 (1990) 59-83

7. C.J. Wright, Cost savings by using reverse osmosis to pre-concentrate whey or skim milk before

evaporation, Brief Communications of XXI Int. Dairy Congress, Moskou, Volume I, Book two, (1982)

478

8. H.C. van der Horst, S. Teerink, Application of spiral-wound composite reverse osmosis membranes for

the concentration of whey, Poster presented at the Int. Dairy Congress, Montpellier, 1990

9. A.G. Gregory, Desalination of sweet-type whey salt drippings for whey solids recovery, in "Trends in

whey utilization", Bulletin of the IDF 212 (1987) 38-49

10. H. Jönsson, Ion exchange for the demineralization of cheese whey, in "Trends in whey utilization",

Bulletin IDF 212 (1987) 91-98

11. M. Brusilovsky, D. Hasson, Prediction of reverse osmosis membrane salt rejection in multi-ionic

solutions from single-salt data, Desalination 71 (1989) 355-366

12. T. Tsuru, M. Urairi, S. Nakao, S. Kimura, Negative rejection of anions in the loose reverse osmosis

separation of mono- and divalent ion mixtures, Desalination 81 (1991) 219-227

13. T. Tsuru, M. Urairi, S. Nakao, S. Kimura, Reverse osmosis of single and mixed electrolytes with

charged membranes: experiment and analysis, J. Chem. Eng. Japan 24 (1991) 518-524

14. M.W. Vonk, J.A.M. Smit, Postitive and negative ion retention curves of mixed electrolytes in reverse



15. R.Schlögl, Ber. Bunsengesel. 70 (1966) 400

16. L. Dresner, Some remarks on the integration of extended Nernst-Planck equations in the hyperfiltration

of multicomponent solutions, Desalination 10 (1972) 27-46

17. J.M.K. Timmer, H.C. van der Horst, T. Robbertsen, Transport of lactic acid through reverse osmosis

and nanofiltration membranes, J. Membrane Sci. 85 (1993) 205-216

18. H.K. Lonsdale, W. Pusch, A. Walch, Donnan-membrane Effects in Hyperfiltration of Ternary systems,

J. Chem. Soc. Faraday Trans. 71 (1975) 501-514

19. R. Rautenbach, R. Albrecht, Membrane Processes, John Wiley & Sons Ltd., 1989

20. Handbook of chemistry and physics, 70th edition, CRC press, 1990

21. FIL IDF 15, Document of the International Dairy Federation 1961

22. J. Koops, H. Klomp and R.C.H. Elgersma, Rapid determination of nitrogen in milk and dairy products

by calorimetric estimation of ammonia following an accelerated digestion procedure, Neth. Milk Dairy

84 CHAPTER 4

J. 29 (1975) 169-180

23. N. Schoorl, Chem. Weekblad 26 (1929) 130

24. N.R. Draper, H. Smith, Applied regression analysis, 2nd edition, 1981

APPENDIX 1:

DERIVATION OF REJECTION EQUATION FOR A TERNARY SYSTEM When the extended Nernst-Planck equations for the three components Na+ (1), Ca2+ (2) and Cl−

(3) are manipulated, using the “no current” condition [ Eq. (8) ], the requirement of

electroneutrality [ Eq. (7) ] the following equation for Ji, the flux of component i, can be derived:

Ji = − F1,i ∆C1 − F2,i∆C2 + F3,i Jw C1,0 + F4,i JwC2,0 (i=1,2) (A1.1)

In which:

( ) ( )( ) ( )112212233

13221223311,1 zBzBQzBzB

zBzBQzBzBBF

−+−−+−

= (A1.2)

( )( ) ( )221121133

312122,1 zBzBQzBzB

BBQzBF

−+−−

= (A1.3)

( )( ) ( )112212233

321211,2 zBzBQzBzB

BBQzBF

−+−−

= (A1.4)

( ) ( )( ) ( )121121133

23112113322,2 zBzBQzBzB

zBzBQzBzBBF

−+−−+−

= (A1.5)

( )( ) ( ) ( )[ ]( ) ( )112212233

3111221223311,3 zBzBQzBzB

1zB1zBQzBzB1F

−+−−−−+−−

=σσσ

(A1.6)

( )( ) ( )221121133

312222,3 zBzBQzBzB

QzBF

−+−−

=σσ

(A1.7)


( )( ) ( )112212233

321111,4 zBzBQzBzB

QzBF

−+−−

=σσ

(A1.8)

( )( ) ( ) ( )[ ]( ) ( )221121133

3222112113322,4 zBzBQzBzB

1zB1zBQzBzB1F

−+−−−−+−−

=σσσ

(A1.9)

2,c21,c1

1,c11 CzCz

CzQ

+= 12 Q1Q −= (A1.10a,b)

When Eqs. (12) and (13) are combined with Eq. (A1.1) the following expression is obtained:

4i,43i,32i,21i,1i XFXFXFXFJ +++= (A1.11)

1,c1

w11 C

kJexpRX

= (A1.12)

2,c2

w22 C

kJ

expRX

= (A1.13)

( )

+−=

1

w111,cw3 k

JexpRR1CJX (A1.14)

( )

+−=

2

w222,cw4 k

JexpRR1CJX (A1.15)

When Eq. (A1.11) is put into the Eqs. (15) and (16) the following equation for the rejection of

component 1 can be established.

( ) ( )

( ) ww1s

21,c

2,cw12ww1s

1 JJB

RCC

JBJJRR

+

+= (A1.16)

86 CHAPTER 4

In which:

( )

−

+

−−=

1kJ

expF1

CC

FF1JR

1

w1,3

1,c

2,c1,41,3

w1s (A1.17)

( )

−

+

=

1kJexpF1

kJexpF

JB

1

w1,3

1

w1,1

w1s (A1.18)

( )

−

+

−

−

=

1kJexpF1

JkJ

expJF

kJ

exp1F

JB

1

w1,3

w2

w

w

1,2

2

w1,4

w12 (A1.19)

When the contribution of the X4-term is neglected the following expressions for Rs1(Jw), Bs1 (Jw)

and B12(Jw) are obtained:

( )

−

+

−=

1kJ

expF1

F1JR

1

w1,3

1,3w1s (A1.20)

( )

−

+

=

1kJ

expF1

kJ

expFJB

1

w1,3

1

w1,1

w1s (A1.21)

( )

−

+

−

=

1kJexpF1

kJexpF

JB

1

w1,3

2

w1,2

w12 (A1.22)

Similar equations can be derived for component 2.

87

CHAPTER 5

Determination of properties of nanofiltration membranes;

Pore diameter from rejection measurements with a mixture of

oligosaccharides1

SUMMARY

In this chapter a method is presented to determine pore diameters and effective transport lengths of

membranes by a single experiment with a dilute mixture of oligosaccharides. The experimental results are

compared with a theoretical model based upon the Maxwell-Stefan equations. The membrane friction

coefficients of the oligosaccharides are correlated to the pore diameter by analogy to falling velocities of

macroscopic spheres in narrow tubes. The partition coefficients of the solutes are a function of the pore

diameter according to the Ferry equation. Thus, with the pore diameter as the only unknown parameter,

rejection is described and the pore diameter is obtained by a Marquardt-Levenberg optimisation procedure.

.

1 This chapter has been submitted to the Journal of Membrane Science.

88 CHAPTER 5

1. INTRODUCTION

The separation characteristics of nanofiltration and ultrafiltration membranes are usually

expressed in terms of the NMWC (nominal molecular weight cut-off). This NMWC is supplied

by the manufacturer, usually without detailed information on the method of determination. It is

often unclear which solute is used or under which conditions the determinations have been

carried out. For this reason, it is not easy to obtain reliable information on the separation

characteristics of a membrane from the NMWC alone. Therefore, the user has to carry out

additional experiments to characterise the membrane. For an analysis of the separation

characteristics structural parameters of a membrane (pore diameter, effective pore length,

membrane porosity and charge density), which are independent of the applied conditions, need to

be established.

Nakao et al. [1] show that the pore diameter and the ratio of effective pore length to membrane

porosity (i.e. the effective transport length) can be obtained from rejection measurements with

uncharged solutes. Hanemaaijer et al. [2] show that filtration of oligosaccharides is a successful

method for the determination of mean effective pore sizes. Bowen et al. [3] compare pore

diameters determined from experiments with uncharged solutes with data from Atomic Force

Microscopy (AFM) analysis. The diameters obtained with AFM are about half of those as fitted

from experimental data. Both Bowen et al. [3] and Nakao et al. [1] report problems with the

determination of the effective transport length, τz/ε. This parameter is overpredicted when it is

calculated from the hydraulic permeability obtained from independent clean water flux

measurements. Only a simultaneous fit of the pore diameter and the effective transport length and

using the hydraulic permeability from the same experiment provides successful descriptions of

the experimental results.

In this paper it is shown that with a clean water flux experiment and one single experiment, using

a dilute mixture of oligosaccharides, the membrane characteristics can be determined. The

membrane characteristics are expressed in a mean effective pore diameter and the effective

transport length. From the clean water flux experiment the hydraulic permeability is determined,

while the other experiment is used to establish the pore diameter. The pore diameter determines

the distribution of solutes over liquid and membrane phase and the friction with the membrane

pore walls. The pore diameter is determined by comparing experimental results to predictions

based upon a Maxwell-Stefan representation of membrane filtration, which is described in the

theory section. The friction of solutes with the pore wall is estimated by analogy with the

Pore diameter from rejection measurements with a mixture of oligosaccharides 89

reduction in falling velocity of spheres in narrow tubes. From this analysis, pore diameter and the

effective transport length, τz/ε, are successfully obtained.

2. THEORY

To establish the pore diameter and the effective transport length, flux and solute rejections at

various transmembrane pressures have to be determined. For an analysis of the results we use a

theoretical model as described in [4,5]. In this model, the membrane is considered to be

heterogeneous, which means that pores are a separate phase next to the membrane phase. The

model is a combination of transport relations, mass balances, partition relations and constraint

relations.

2.1 Transport We start with a description of diffusive transport by the Generalised Maxwell Stefan equation

[6,7]. For an uncharged component i this equation is written as:

( ) iimik

kikikiiiiPTi uxuuxxPVxxετζ

ετζµ ,,, ∑ +−⋅=∇−∇− (1)

Equation (1) is a force balance, in which the driving force on component i is given on the left

hand side. The driving force is equal to the chemical potential gradient, separated into its

composition-dependent and pressure-dependent part. Due to this gradient, component i is

transported and will experience friction from the other components in the system, which is

described by the terms on the right hand side of equation (1). This friction is proportional to both

the mole fractions and the velocity difference of the components. The friction between solvent

and the membrane, and solute and the membrane also has to be considered. Therefore, the

membrane is taken as an extra component in the system. In the applied reference frame, the

membrane is immobile and its velocity equals zero. The mole fraction of the membrane cannot be

determined and for this reason is combined with the friction coefficient to obtain an overall

friction coeficient ζi,m.

In equation (1) the diffusive volume fluxes of the components are indicated by the symbol u and

are expressed in m3 per m2 of total membrane area. To obtain real component velocities these

90 CHAPTER 5

have to be divided by a factor ε/τ, in which ε is the porosity of the membrane and τ the tortuosity.

The diffusive friction coefficients, ζi,k , are related to the binary diffusivities by :

kiki D

RT,

, =ζ and mi

mi DRT

,, =ζ (2)

In pressure driven membrane processes both diffusive transport and viscous flow are important.

The viscous flow can be described by :

PBv f ∇−=ητ

ε 0 (3)

Bo is the permeability of the membrane. For Poiseuille flow through cylindrically shaped pores

Bo is equal to rp2 / 8. The total velocity of component i, wi, is equal to the sum of its diffusive

and viscous part : fii uw ν+= . We can substitute this in the Maxwell-Stefan equation, which

yields :

( ) iimik

kikikimiiiiPTi wxwwxxPBVxxετζ

ετζ

ηζµ ,,

0,, ∑ +−⋅=∇

+−∇− (4)

The component velocities wi are converted to molar fluxes Ni with the following equation :

totiii CwxN = (5)

We obtain the transport equation in terms of molar fluxes after substitution of eqn. (5) into eqn.

(4):

( )

ετζ+−

ετζ=∇

η

ζ+−µ∇− ∑ imik

kiikkitot

miiiiPTi NNxNxC

PBVxx ,,0

,,1

(6)


Concentration polarisation is important at high fluxes through the membrane. To incorporate this

in the model we need an additional relation for transport through the liquid boundary layer for

each solute, which is obtained from equation (6) by omission of the pressure dependent term on

the left hand side (no pressure gradient in the boundary layer) and the term related to friction

with the membrane on the right hand side:

( )∑ −=∇−k

kiikkitot

iPTi NxNxC

x ,,1 ζµ (7)

Equations (6) and (7) give the mass transfer description of the membrane separation process. To

complete the model mass balances, a description of the solute distribution between the membrane

and the liquid phase, a transition to absolute velocities, constraints and relationships to

determine the friction coefficients are necessary.

2.2 Mass balances, partitioning of solutes, bootstraps and constraint relations

In the transport equations, the component velocities only appear as differences. For the

calculation of absolute velocities additional relations are needed. These are provided by the mass

balances at the permeate side of the membrane:

pkx

pix

kNiN

= (8)

The partitioning of solutes is described by the following relation :

iii Kxy = (9)

For cylindrical pores the distribution coefficient, Ki is given by Ferry [8]:

( ) pii rrK /,1 2 =−= λλ (10)

92 CHAPTER 5

Partitioning of solvent causes an osmotic pressure jump at the membrane interface. In this work

we only deal with very dilute solutions and in our experiments no decrease in fluxes is observed

compared to clean water fluxes. Therefore, we ignore pressure jumps in our model and assume

the pressure at the entrance and the exit of the membrane to be equal to the pressure at the feed

and permeate side, respectively.

The model is completed by the constraint that the mole fractions have to add up to unity

everywhere in the system.

∑ =i

ix 1 , 1=∑i

iy (11)

2.3 Estimation of membrane friction coefficients.

For a complete description of transport of molecules through narrow pores, more information is

needed on the friction coefficients between permeating solutes and the membrane. We estimate

these by the analogy with the reduction of falling velocities of macroscopic spheres in narrow

tubes [9].

A Maxwell-Stefan form of the equation for the falling velocity of a single particle in a liquid,

which is bound by a surface, is written as:

( ) ( )a

tsfsss

a

msfs

a

fss N

uuN

uuN

F ,,,, ζζζζ +=+−= (12)

In a liquid, which is not bound, equation (12) reduces to :

∞= ,,

sa

fss u

NF

ζ (13)

From these equations, an expression for the friction factor between the particle and the surface,

ft, can be found :

tsfs

fs

s

st u

uf,,

,

, ζζζ

+==

∞

(14)


A relation for ft is presented by Lali et al. [9], having measured falling velocities in narrow tubes,

both in Newtonian and non-Newtonian liquids. The experimental data points on Newtonian

liquids are not presented, instead a correlation is given, which is valid within 10 % [9]. This

correlation reads:

( ) 2.2

,

1 λ−==∞s

st u

uf (15)

To find an expression for the friction of a large solute with a narrow membrane pore, assuming

cylindrical pores, in equation (14) we replace ζs,t and ζs,f by ζi,m and ζi,w, respectively. If we

assume the solute-solvent friction coefficient ζi,w to be the same in the membrane pores as in

free liquid we obtain the solute-membrane friction coefficient, ζi,m:

( )

−

−= 1

11

2,, λζζ wimi (16)

2.4 Other parameters.

The friction coefficients of the solutes with water are determined from the radius of the solute

with the Stokes-Einstein relation:

iwi rπηζ 6, = (17)

Friction between the different solutes is ignored as we work with very dilute solutions. The

partial molar volume of the different components is calculated from the molecular radius

according to:

3

34

iAi rNV π= (18)

94 CHAPTER 5

2.5 Solving the model For the ultrafiltration of a solution with n components the model consists of n equations of

transport through the membrane, n-1 equations of transport through the boundary layer, which

are needed if concentration polarisation is taken into account, n-1 mass balances, n-1 equilibrium

equations at both the upstream and the downstream side of the membrane, and a constraint

relation at each point in the system. Both the boundary layer and the membrane layer are divided

into 4 layers (with 5 grid points). The gradients in the Maxwell-Stefan equations are approached

by a central difference scheme according to the approach of Wesselingh and Krishna [10]. The

complete set of equations is solved for the molar fluxes, local mole fractions and pressures, using

the Newton-Raphson method [11]. All calculations are done ignoring the boundary layer except

where explicitly mentioned.

Model predictions are compared with experimental data, meanwhile optimising the pore diameter

as the only unknown parameter in the model, according to the Marquardt-Levenberg method

[11]. The pore diameter, which gives the best comparison of model description and experimental

results is considered to be the mean pore diameter of the particular membrane type. With this

pore diameter, the ratio of the effective pore length to the membrane porosity, τz/ε, should be

varied such that the overall hydraulic permeability (εrp2/8τz) remains constant.

3. EXPERIMENTAL

The experiments were done in a DDS Lab 20 system in which four different membranes were

installed. Further details of the system have been described elsewhere [12].

Solutions were prepared by dissolution of 1 g/L Paselli MD6 (AVEBE, Veendam, the

Netherlands) in reverse osmosis permeate which was obtained from demineralized water. Paselli

MD6 is a mixture of oligomers of glucose ranging from 2 to 40 units. The concentration

distribution is presented in Figure 1. The molecular radius of each oligomer was obtained from

the formula given by Aimar et al [13]:

46.033.0 ws Mr ⋅= (19)


Figure 1: Concentration distribution of glucose oligomers in a 1 g/l Paselli MD6 solution

The following membranes were tested: DDS CA960 (Dow Denmark), Nitto NTR7450 (Nitto

Denko) and Desal G10 and G20 (Desalination). The properties of these membranes are shown in

Table 1.

Table 1. Properties of the membranes used membrane type NMWC

(Dalton) Hydraulic Permeability #

(10-14 m) CA960 - 0.899

NTR7450 1000 0.929 G10 2500 0.699 G20 3500 1.27

# The hydraulic permeability is equal to εBo/τz

The hydraulic permeabilities of these membranes were determined from clean water flux

experiments with new membranes, which underwent an initial compression procedure, and

checked before each experiment with a control measurement at 10 bar. All control measurements

agreed closely to the initial clean water flux experiments (within 5%) except for the NTR

membrane. The hydraulic permeabilities of the NTR membrane varied as much as 30 % between

experiments. Therefore, for this membrane the clean water flux measured just before the

rejection experiment was used to obtain the hydraulic permeability.

96 CHAPTER 5

Experiments were carried out at 20 oC and transmembrane pressure drops upto 15 bar. Cross

flow velocity in all experiments was 0.9 m/s. Concentrations of the different oligosaccharides in

both permeate and concentrate were determined by anion exchange chromatography according to

the method of van Riel and Olieman [14].

4. RESULTS

4.1 Fluxes.

The fluxes, as measured during filtration of the oligosaccharide solutions, are shown in Figure 2.

The experimental data are indicated by symbols, the predictions based upon clean water flux

measurements by solid lines. They hardly differ, so we can safely assume that osmotic effects

due to the rejection of the components are negligible.

Figure 2: Measured and calculated fluxes as a function of effective pressure for 4 membranes

(CA 960:● ;NTR7450:○ ;G10:■ ;G20:□ )

Wang et al. [15] reported hydraulic permeabilities of the NTR7450 and G20 membranes of

1.78.10-14 and 1.34.10-14 m, respectively. Our result for the G20 membrane is in very good

agreement and the NTR7450 differs by almost a factor 2, which, however, is not an uncommon

difference for hydraulic permeabilities.


4.2 Rejection curves In Figure 3 the rejection of the different saccharides for an NTR7450 membrane is shown as a

function of permeate flux. The experimental results are indicated by symbols and the model

predictions by the solid lines. In most cases the model gives a good prediction of the

experimental data. Similar results are obtained with the G10 and the G20 membrane. In the case

of the CA membrane it is difficult to give an exact determination of the pore diameter from the

experiments, as the rejection data of only one oligosacharide are reliable, the others were very

close to unity. This means that the diameters of the saccharides are too close to or even higher

than the mean pore diameter.

Figure 3: Measured and calculated glucose oligomer rejection as a function of the flux for an

NTR7450 membrane (number of glucose units; 2:● ;3:○ ;4:■ ;5:□)

In the experiment with the more open G20 membrane, concentration polarisation seems to play a

role. Therefore, in the estimation of the pore diameter and the effective transport length, the

boundary layer is taken into account. The pore diameter is 7% lower as compared to the fit

omitting the boundary layer effects (Table 2). Concentration polarisation plays no role in the

other experiments.

98 CHAPTER 5

Table 2. Pore diameter and τz/ε as determined from the experiments

membrane type pore diameter (nm)

τz/ε (µm)

CA960 1.26 5.52 NTR7450 1.64 10.7

G10 1.81 14.6 G20 2.47* ; 2.65# 15.0 * ; 17.3 #

The values for the G20 membrane are determined accounting for (*), respectively ignoring (#) concentration polarisation effects.

The pore diameters and the effective transport length, τ∆z/ε, are presented in Table 2. We

observe an increase in pore diameter, which corresponds with an increase of the NMWC-values.

Our pore diameter for the NTR7450 membrane is slightly higher than the one found by Wang et

al. (1.4 nm, [15]), while for the G20 membrane it is considerably different from their value of 1.6

nm. The latter is curious because of the good agreement of the hydraulic permeabilities. The

effective transport lengths vary from 5.52 to 15 µm (or 17.3 µm, when ignoring concentration

polarisation). The effective transport lengths for the NTR7450 and G20 membrane, given by

Wang et al. [15] are dependent on the type of solute used. With neutral solutes they find values

of 0.74 and 1.82 µm, respectively, while using NaCl the effective transport lengths are 3.44 and

5.99 µm, respectively. This difference in transport lengths between neutral solutes and salts

found by Wang et al. [15], but also described by Nakao et al. [1] and Bowen et al. [3], is

explained by the fact that the main pores of the membrane are interconnected by smaller pores,

which are accessible for water but not for the larger solutes. Whereas the solutes are transported

just through the main pores water can flow through the smaller pores and thus experience a

longer transport length than the solutes. This mechanism could explain their difference in

transport length found for different solutes. However, we successfully describe our experiments

with only one parameter, i.e. the pore diameter. The ratio of effective pore length to membrane

porosity, τz/ε, is determined from the hydraulic permeability. An independent fitting of the pore

diameter and the effective transport length, as Nakao et al.[1], Bowen et al.[3] and Wang et al.

[15] apply, is not necessary. An independent estimation of the effective transport length can be

made from data of Cuperus [16] and Coster et al. [17]. Cuperus showed for a homogenous

asymmetric polysulfone membrane that the separation layer has a thickness of about 200 nm. For

a composite membrane this thickness generally is of the order of 1 or 2 µm [18]. By impedance

spectroscopy Coster et al. [17] determined porosities of skin layers of about 0.02 to 0.05. In a

first approximation, taking τ equal to 1, the effective transport length should then be at least 4


µm. For this reason, the value of the CA960 membrane, which is a homogeneous membrane is in

close accordance. In our opinion, the values of Wang et al. [15] seem to be too low. Our other

membranes are composites and for this reason values in the range of 15 to 20 µm should be

expected, in accordance with our results. The question might be raised why the transport length

of the solvent is so much larger than for the solutes as most of the solvent will also seek the route

with the lower resistance. An explanation for the observed difference can be found in the

statistics underlying the parameter estimation. Nakao et al. [1], Bowen et al. [3] and Wang et al.

[15] determine the quality of the fit on the residual sum of squares of the predicted and measured

rejections only. In our case, however, the quality of the fit is established on the flux and the

rejection simultaneously. An explanation for the difference in effective transport length between

neutral solutes on the one hand and salts on the other is the omission of the electric potential

induced solvent flow, which is opposite to the pressure induced flow (see chapter 6). Ignoring

this contribution will result in a larger transport length for salts as compared to neutral solutes.

As will be shown in chapter 6, good predictions of both the experimental flux and rejection can

be obtained also, using the pore radius and effective transport length from our single experiment

with an oligosaccharide mixture.

The method to determine pore sizes from experiments using a mixture of oligosaccharides is very

useful. One simple experiment provides enough information to determine accurately the pore size

of a particular membrane. Care should be taken in applying this method to very dense membranes

as only one or a few saccharides are partially permeated through these membranes and rejections

are above 0.9. This makes the determination of pore sizes for these dense membranes difficult.

5. CONCLUSIONS

Filtration of a dilute mixture of oligosaccharides is a successful experimental tool for the

determination of mean pore diameter and thereby the separation characteristics of nanofiltration

membranes. For very dense membranes, such as the CA membrane, the method can become

inaccurate because most sugars are larger than the mean pore diameter. To characterise this class

of membranes (NF with low NMWC or RO) a mixture of smaller solutes should be considered.

6. LIST OF SYMBOLS

B0 :membrane permeability [m2]

C :concentration [mol.m-3]

100 CHAPTER 5

D :diffusion coefficient [m2.s-1]

F :force on a component [N]

I :ionic strength [mol.m-3]

K :partition constant

La :Avogadro number

Mw :molecular weight [g.mol-1]

N :molar flux [mol.m-2.s-1]

P :pressure [Pa]

r :radius [m]

R :gas constant [J.mol-1.K-1]

T :temperature [K]

u :diffusive volume flux [m.s-1]

V :partial molar volume [m3.mol-1]

v :viscous volume flux [m.s-1]

w :overall volume flux [m.s-1]

x :mole fraction in boundary layer

y :mole fraction in membrane

z :thickness of the membrane [m]

ε :porosity of membrane

η :viscosity [Pa.s]

λ :ratio of solute to pore radius

µ :chemical potential [J.mol-1]

Φ :electrical potential [V]

P :osmotic pressure jump at entrance or exit of membrane [Pa]

τ :tortuosity of membrane

ζ :friction coefficient [J.mol-1.m-2.s-1]

subscripts

f :fluid

i,k :component index

m :membrane


p :pore

s :sphere

t :tube

tot :total

w :water

∞ :unbound fluid

superscripts

p :permeate

7. REFERENCES

1. S. Nakao and S. Kimura, Analysis of solutes rejection in ultrafiltration, J. Chem. Eng. Japan 14 (1981)

32-38

2. J.H. Hanemaaijer, T. Robbertsen, Th. van den Boomgaard, C. Olieman, C.Both and P. Schmidt,

Characterization of clean and fouled ultrafiltration membranes, Desalination 68 (1988) 93-108

3. W.R. Bowen, A.W. Mohammad and N. Hilal, Characterisation of nanofiltration membranes for

predictive purposes - use of salts uncharged solutes and atomic force microscopy, J.Membrane Sci. 126

(1997) 91-105

4. P.Vonk, T.R. Noordman, D. Schippers, B. Tilstra and J.A. Wesselingh, Ultrafiltration of a

polymer/electrolyte mixture, J. Membrane Sci. 130 (1997) 249-263

5. T.R. Noordman, P. Vonk, V.H.J.T. Damen, R. Brul, S.H. Schaafsma, M. de Haas and J.A. Wesselingh,

Rejection of Phosphates by a ZrO2 Ultrafiltration Membrane, J. Membrane Sci. 135 (1997) 203-210


7. R. Krishna, A unified theory of separation processes based on irreversible thermodynamics, Chem.

Eng. Comm. 59 (1987) 33-64

8. J.D. Ferry, Statistical evaluation of sieve constants in ultrafiltration, J. Gen. Physiol. 20 (1936) 95-104

9. A.M. Lali, A.S. Khare and J.B. Joshi, Behaviour of solid particles in viscous non-newtonian solutions:

settling velocity, wall effects and bed expansion in solid liquid fluidized beds, Powder Technol. 57

(1989) 39-50

10. J.A. Wesselingh and R. Krishna, Mass Transfer, Ellis Horwood, London 1990

11. W.H. Press, B.P. Flannery, S.A. Teukolsky and W.T. Vetterling, Numerical Recipes, Cambridge

University Press, Cambridge 1987

12. H.C. van der Horst, J.M.K. Timmer, T. Robbertsen and J. Leenders, Use of nanofiltration for

concentration and demineralisation in the dairy industry: model for mass transport, J. Membrane Sci.

104(1995) 205-218

102 CHAPTER 5

13. P. Aimar, M. meireles and V. Sanchez, A contribution to the translation of retention curves into pore

size distributions for sieving membranes, J. Membrane Sci. 54 (1990), 321-338

14. J. van Riel and C. Olieman, Selectivity control in the anion-exchange chromatographic determination of

saccharides in dairy products using pulsed amperometric detection, Carbohydrate Research 215 (1991)

39-46

15. X.-L. Wang, T. Tsuru, M. Togoh, S.-I. Nakao, S. Kimura, Evaluation of pore structure and electrical

properties of nanofiltration membranes, J. Chem. Eng. Japan 28 (1995) 186-192

16. F.P. Cuperus, Characterization of ultrafiltration membranes. Pore structure and top layer thickness,

PhD Thesis, University of Twente, 1990

17. H.G.L. Coster, K.J. Kim, K. Dahlan, J.R. Smith, C.J.D. Fell, Characterisation of ultrafiltration

membranes by impedance spectroscopy. I. Determination of the separate electrical parameters and

porosity of the skin and sublayers, J. Membr. Sci. 66 (1992) 19-26

18. J.M.K. Timmer, unpublished NIZO-results.

103

CHAPTER 6

Determination of properties of nanofiltration membranes;

Charge properties from rejection measurements using NaCl

and prediction of rejection of CaCl2 and NaH2PO41

SUMMARY

For the separation of charged solutes it is necessary to establish the charge density of the membrane. The

Generalised Maxwell Stefan (GMS) theory is applied to determine the charge density of various

membranes from NaCl-rejection measurements. A comparison is made with the Extended Nernst-Planck

(ENP) model, which is normally used. Generally, the distribution of ions between bulk phase and

membrane is described by a Donnan equilibrium. However, dielectric exclusion effects may have an

important effect but have hardly been considered in the past. In this chapter an analysis is made of the

relative importance of both distribution phenomena. Finally, the possibility of using NaCl charge density

data to predict the rejection and flux for CaCl2 and NaH2PO4 is investigated.

The results show that the GMS theory describes the experimental results equally well as the ENP model.

Best results are obtained when both dielectric and Donnan exclusion are considered. Due to the influence of

dielectric exclusion, the charge density as determined by the GMS theory are considerably lower than for

the ENP model. For this reason it is concluded that for engineering purposes the ENP model suffices but

for determination of the charge density the GMS theory is recommended.

Prediction of CaCl2 and NaH2PO4 rejection is not possible with either model. Therefore the membrane

charge density has to be determined for each salt individually. In the case of NaH2PO4 a considerable

increase in membrane charge density was determined, which is appointed to adsorption of phosphate ion to

the membrane surface.

1 This chapter has been submitted to the Journal of Membrane Science

CHAPTER 6

104

1. INTRODUCTION In chapter 5 it is shown that the pore diameter of nanofiltration (NF) membranes can be

determined by one single experiment with a dilute mixture of oligosaccharides [1]. The pore

diameter is calculated by a model based on the generalised Maxwell-Stefan (GMS) theory. For

the separation of charged solutes it is necessary to determine the charge density of the membrane.

Bowen et al. [2,3], Tsuru et al. [4,5] and Peeters [6], calculated the charge density from NaCl

rejection measurements using the extended Nernst-Planck (ENP) equation. Another possibility of

determining the charge density is by using the GMS theory. This model was successfully applied

to determine the charge density of ceramic ultrafiltration (UF) membranes with a NMWC

(nominal molecular weight cut-off) of 15000 Dalton [7]. This theory to our knowledge, however,

has never been applied to membranes with a low NMWC (<3500 Dalton). The advantage of this

theory is that the interactions between the different components (membrane/solvent,

membrane/solute, solute/solute, solute/solvent) are accounted for separately, whereas the ENP

model lumps these interactions into an effective diffusivity. In addition, the solvent flow is

described in a similar way as the solute flow, which is not the case for the ENP model, where a

Darcy-type relation is used. In addition, electrical-potential-induced solvent flow is also

accounted for in the model, which is not the case for the ENP model. The latter two properties

give distinct advantages when electro-kinetic and osmotic phenomena have to be accounted for.

To establish the charge density of the membrane, a model for the distribution of the ions between

the bulk and the membrane phase is necessary. A very common model for this is the model based

on Donnan equilibrium. This model is used throughout the literature [2,3,4,5,6]. However, from

literature on reverse osmosis processes [8,9] it is known that dielectric exclusion effects also

contribute to the distribution process. Recently, both Donnan and dielectric effects are considered

simultaneously [10] in the application of NF, but an analysis of their relative contributions has not

been published.

The aim of this work is to determine the applicability of the GMS theory for the determination of

the charge density of various membranes (NMWC <3500 Dalton) using NaCl solutions at

different concentrations, in analogy with Bowen and Mukhtar [2]. The results are compared with

the ENP approach with respect to the membrane charge properties, the description of the NaCl

results and the predictability of results obtained with CaCl2 and NaH2PO4 solutions. In addition,

the effect of taking dielectric exclusion into account is analysed.


105

2. THEORY Lightfoot [11] derived the GMS theory, which was originally published by Maxwell and Stefan

for diffusion in gases, on the basis of irreversible thermodynamics. The theory states that if a

driving force is imposed upon a component i, this force is counteracted by friction with other

components in the mixture. The application of this model to non-charged solute separation with

NF membranes is described in chapter 5.

2.1 Transport In the case of charged solutes, three driving forces can be distinguished:

• the chemical potential gradient (defined at constant temperature, pressure and electrical

potential):

i,P,Tµ

Φ∇ (1)

• the pressure gradient:

PiV ∇ (2)

• the electrical potential gradient:

Φ∇Fiz (3)

In chapter 5, it is shown that in the case of non-charged solutes the viscous flow through the

membrane can be described by:

P0Bfv ∇−=

ητε

(4)

However, in the case of charged solutes an additional electrical force on the bulk flow is present

[12,13]:

CHAPTER 6

106

∑ ∇−∇−=k

)FkzkxtotC1P(0B

fv Φητ

ε (5)

The description of combined diffusive and viscous transport for component i by the GMS

equation, as shown in chapter 5, is extended with the electrical potential gradient to give the

following result:

∑

∑

+−⋅=

=∇++∇++∇−

kiwixm,i)kwiw(kxixk,i

)k

F)kzkxCBm,iiz(P)B

m,iiV(i(ix tot00,P,T

ετζ

ετζ

Φη

ζη

ζµΦ

(6)

Conversion of the component velocities wi to molar fluxes Ni is accomplished by the expression:

totCiwixiN = (7)

Combining the previous two equations gives the GMS equation in terms of molar fluxes:

)k

iNm,i)kNixiNkx(k,i(totC1

)k

F)kzkxCB

m,iiz(P)B

m,iiV(i(ix tot00,P,T

∑

∑

+−⋅=

=∇++∇++∇−

ετζ

ετζ

Φη

ζη

ζµΦ

(8)

Concentration polarisation in the liquid boundary layer can be of importance at high fluxes and

for each component i is described by:

∑ −⋅=∇+∇−k

)kNixiNkx(k,iC1)Fizi(ixtot,P,T ε

τζΦµΦ

(9)


107

2.2 Mass balances, partitioning of solutes, bootstrap and constraint relations The component velocities only appear as differences in the transport equations and for the

calculation of absolute velocities additional relations are necessary. At the permeate side of the

membrane the following mass balance holds:

pk

pi

k

i

xx

NN

= (10)

The partitioning of a charged component is described by an equilibrium, in which Donnan,

dielectric and steric exclusion effects are accounted for [7,10]:

)iWRT

ANDonnanRT

Fzexp(iyyiixxiiK i ∆∆Φγγ += (11)

The validity of application of the Donnan equilibrium relation for membranes with pores less than

2 nm has been shown by Bowen et al. [3] and Wang et al. [14], who calculated that a radial

distribution of ion concentration and the potential in the pore can be neglected. However,

dielectric effects were omitted in their calculations. To describe the dielectric effects, the change

of the electrostatic free energy (ΔWi) of an ion between the bulk and a membrane phase is given

by the Born model [10]:

)b1

mp1(

ir08

2e2iz

iWεεπε

∆ −= (12)

in which zi is the valence of the ion, e the electron charge, ε0 the dielectric permitivity, ri the ion

radius, εb the dielectric constant of the bulk and εmp the dielectric constant of the membrane phase

(determined by the membrane material and the pore liquid). Hagmeyer and Gimbel [10] further

developed this model into:

)b1)2)

pm1(

mrr

393.0p1((

ir08

2e2iz

iW

i

p εεε

εεπε

∆ −−+= (13)

CHAPTER 6

108

in which εp is the dielectric constant of the pore liquid and εm is the dielectric constant of the

membrane material. This model applies to an ion which is passing through a liquid which is

contained within a cylindrical pore. For the steric exclusion coefficient Ki , the Ferry relation is

applied:

2)rr

1(iKp

i−= (14)

Partitioning of the solvent at the membrane/solution interfaces causes an osmotic pressure jump,

which is accounted for by:

intPiV)ixxiln(RT)iyyiln(RT ∆γγ += (15)

The Debije-Huckel theory is used for the determination of the activity of the ions in the solution

in analogy with Vonk [15]. For the model additional constraints are necessary. In the various

phases the sum of the mole fractions should be unity. In the feed, the permeate and in the

membrane the electroneutrality condition should be fulfilled. For the feed and the permeate it

reads as follows:

∑ =i

0ixiz (16)

and in the membrane:

∑ =+i

0mQixiz (17)

The membrane charge density, Qm, can be described by a Freundlich isotherm [2,6]:

∑ ⋅⋅−=i

K)ixiz(*QmQ s (18)


109

In previous descriptions of the Freundlich isotherm [2,6] the concentration was used, while here

we apply a mole fraction description.

2.3 Estimation of the friction coefficients.

In addition to the binary friction coefficients described in part 1 of this paper the friction between

ions of opposite charge can be determined from the following empirical relationship for the

diffusion coefficient [16]:

85.1

55.0

zzIwDwD8108.4D

−+ ⋅⋅−+⋅=−+ (18)

∑ ⋅⋅=i

ix2iz

21I (19)

The binary friction coefficient between two ions of opposite charge is linearly related to the

friction of each individual ion with water. The diffusion coefficients for the ions in water are

taken from literature [15,17] and are shown in Table 1. The friction between ions of the same

charge is neglected. Due to electrostatic repulsion, it is assumed that ions of like charge can not

approach in each others vicinity and therefore do not have a frictional interaction.

Table 1: Radius, molar volume and diffusion coefficient in water for the various ions used in this

study.

Component

Diw [10-9 m2/s]

Ion radius [10-9 m]

Vi [10-5 m3/mol]

Na+ Ca2+ Cl- H2PO4

- H2O

1.33 0.78 2.01 0.86

0.164 0.276 0.118 0.249

0.44 2.78 1.22 8.47 1.81

2.4 Solving the model The model was solved in the way as described in chapter 5. The pore diameter was determined

from the measurements using the mixture of oligosaccharides. The parameters Q* and Ks of the

Freundlich isotherm are determined by comparison of the theoretical model and the experimental

results at various NaCl concentrations. For iteration purposes, values of εmf (varied between 50

CHAPTER 6

110

and 78.3, minimum step size 2.5) were used as input variable and were considered concentration

independent. Parity plots and an analysis of the sum of residual squares of fluxes and rejections

lead to the optimal εmf.

3. EXPERIMENTAL The experiments were done in a DDS Lab 20 system in which four different membranes were

installed. Further details of the system are described elsewhere [18]. The membranes used and

their properties are reported in chapter 5.

Solutions of 10-3, 10-2, 10-1 and 0.5 M of NaCl, CaCl2 and NaH2PO4 were prepared by dissolving

NaCl, CaCl2·H2O or NaH2PO4·H2O at the desired concentration. The salts were obtained from

Merck, Germany and were all analytical grade. The water used for dissolving the salts was first

demineralised by ion-exchange and then treated by reverse osmosis. The pH of the solutions was

adjusted to 5.5. using the corresponding acids (HCl or H3PO4) and bases (NaOH or Ca(OH)2).

Experiments were carried out at 20°C and transmembrane pressures up to 15 bar. Cross flow

velocity was 0.9 m/s. The rejection (Rej) of the membranes for the various salts was determined

by conductivity measurements in the permeate (Ωp) and the retentate (Ωr) using a Radiometer

CDM80 conductivity meter and CDC114 electrode (cell constant: 1 cm-1) and using the following

relationship:

r

p

ΩΩ

1Rej −= (20)

4. RESULTS

4.1 Importance of Donnan and dielectric distribution effects To determine the relative importance of Donnan and dielectric effects on the distribution of ions,

estimations of the terms ziFΔΦDonnan and NAΔWi were made for an ion of radius 0.2 nm (Figure 1).

Both the Born model and the model described by Hagmeyer have been compared for different

values of the dielectric constant. In the case of the Born model the dielectric constant of the

membrane phase is taken as the x-axis, whereas in the case of the Hagmeyer model the dielectric

constant of the pore liquid is taken as the x-axis. Comparing the relative importance of the various

factors, it is obvious that for the Born model, dielectric effects start to play a role when the

dielectric constant of the membrane phase is less than 40. For the Hagmeyer model, pore radii of

0.5 and 1 nm always result in a dominance of the dielectric exclusion effects. For a pore radius of


111

2 nm, only at dielectric constants of the pore liquid above 60, Donnan exclusion will be

dominating. Considering the pore diameters determined in chapter 5, the Hagmeyer model

predicts that dielectric effects are determining the distribution of the ions between bulk and

membrane phase. It is not obvious whether the membrane and the pore liquid should be

considered as a single infinite membrane phase or as separate phases, according to the approach

of Hagmeyer. Therefore, both approaches were tested for fitting the experimental NaCl results.

Figure 1: comparison of the magnitude of Donnan exclusion term|ziF ΔΦDonnan| (-) and dielectric

exclusion terms |NAΔWi| for the Born model (▼) and the Hagmeyer model(rp=0.5 nm:■;rp=1

nm:□; rp=2nm:●). εb=78.3 [19], εm=4 [19], e=1.6021892*10-19 C, ε0=8.8541878*10-12 F.m-1 ,

NA=6.022045*1023 mol-1 , F=9.65*104 C.mol-1, ΔΦDonnan= -50 mV [6]

4.2 Comparison of the Born and the Hagmeyer dielectric model In Figure 2 the Born and the Hagmeyer model are compared for the description of NaCl rejection-

flux measurements. The fitted lines are based on using the pressure as the input variable. From

the pressure both the flux and the rejection are calculated. It is obvious that the Hagmeyer model

does not allow an accurate prediction of the results at high NaCl concentrations. The contribution

of dielectric exclusion in this model is such that concentration dependent phenomena hardly

occur. The Born model gives a good description of experimental results and is therefore used

throughout this chapter. This difference raises the question how the membrane phase should be

looked at in terms of dielectric phenomena. From this result the membrane phase might be

considered as a water phase with polymeric chains. Due to the presence of the polymeric chains

CHAPTER 6

112

the dielectric constant of this water phase will be lowered. The view of the Hagmeyer model as a

polymeric tube in which the ion has to pass through the water phase does not seem to be valid.

Figure 2: NaCl rejection curve as a function of the flux for a NTR7450 membrane at various

concentrations (10-3 M:□; 10-2 M:■; 0.1 M:○; 0.5 M:●). Born model fit,εmp=65 (-); Hagmeyer

model fit using εp=78.3 and εm=4 (--)

4.3 Comparison of the GMS model and the ENP model The ENP model used in the comparison is the model as described by Bowen et al. [3]. It has been

transferred into a mole fraction model instead of a concentration model. Furthermore, ionic

strength and the Freundlich isotherm are considered in mole fraction terms also, as described in

the theory section of this chapter. Dielectric effects were not accounted for in the ENP model.

Figure 3 shows that both models describe the experimental results very well. The only difference

is found at 0.5 M NaCl. It should be noted that the pore diameter and the effective transport

length are the same as used for the oligosaccharide experiment. It is not necessary to adjust these

parameters for the two models to come to a good description of the experimental results, as was

done by Bowen et al. [3] and Tsuru et al. [5].

The Freundlich parameters and the dielectric constant are given in Table 2. A correlation between

the Q* and the pore diameter is apparent, the smaller the pore size the higher is Q*. This trend is

visible in both modelling approaches. The values of Ks are similar for both models. The major

difference between the two models is found in the Q*. Due to the dielectric effect , Q* is lower for


113

the GMS model than for the ENP model. It is also obvious that the dielectric constant is not very

different from water and the larger the pore size the closer the dielectric constant approaches the

one of water. This comparison shows that for engineering purposes the ENP model is sufficient.

However, for determination of the charge properties of the membrane the GMS-model seems

more appropriate.


concentrations (10-3 M:□; 10-2 M:■; 0.1 M:○; 0.5 M:●). GMS model (-); ENP model (--)

Table 2: Freundlich parameters and dielectric constant of four membranes calculated for the

GMS model and the ENP model.

GMS model including dielectric exclusion ENP model Membrane Q* Ks εmp Q* Ks CA 960 NTR 7450 G10 G20

0.168 0.034 0.037 0.018

0.53 0.31 0.34 0.33

65 65 70

72.5

1.320 0.148 0.089 0.037

0.55 0.25 0.31 0.32

For a comparison of our results, Wang et el. [20] found values for Q* and Ks of 0.103 and 0.41,

respectively, for an NTR7450 membrane, using the ENP model. These values are in reasonable

accordance with our results. It results in a charge density which on average is about a factor of

two lower than in our case.

CHAPTER 6

114

4.4 Omitting dielectric phenomena in the GMS model As the dielectric constant of the membrane phase is close to the dielectric constant of water it is

investigated whether dielectric effects could be fully ignored in the model. A comparison is made

between the GMS model with dielectric exclusion and one without. It is obvious that especially at

higher NaCl concentrations the flux, in the case dielectric effects are omitted, is underpredicted

(Figure 4). Omitting the dielectric effect results in a too high estimation of the membrane charge

density. Therefore the contribution of the electric potential difference induced convective flow,

which is in the opposite direction as compared to the pressure difference induced convective flow,

is much larger than in the case when dielectric exclusion is considered. However, prediction of

flux and rejection at low NaCl concentration is very well possible with omission of dielectric

effects.


concentrations (10-3 M:□; 10-2 M:■; 0.1 M:○; 0.5 M:●). GMS model with dielectric exclusion (-);

GMS model without dielectric exclusion (--)

4.5 Prediction of the flux and the rejection, CaCl2 and NaH2PO4 experiments Using the parameters of Table 3, the rejection and the flux of the NTR7450 for NaH2PO4 (Figure

5) and CaCl2 (Figure 6) are predicted using the GMS and the ENP model.


115

Figure 5: NaH2PO4 rejection curve as a function of the flux for a NTR7450 membrane at various

concentrations (10-3 M:□; 10-2 M:■; 0.1 M:○; 0.5 M:●). GMS model prediction(-); ENP model

prediction(--)

Figure 6: CaCl2 rejection curve as a function of the flux for a NTR7450 membrane at various

concentrations (10-3 M:□; 10-2 M:■; 0.1 M:○; 0.5 M:●). GMS model prediction (-); ENP model

prediction (--)

CHAPTER 6

116

In the case of NaH2PO4, both models predict the flux range very well. However, prediction of the

rejection is very poor. The ENP model predicts a higher rejection at all concentrations, while the

GMS model underpredicts the rejection at high concentration and overpredicts at low

concentrations. In the case of CaCl2, neither the flux nor the rejection are predicted well with both

models. The ENP model underpredicts the rejection at all concentrations and overpredicts the

flux. For the GMS model, the rejections are overpredicted at all concentrations, while at high

concentrations the fluxes are underestimated. The GMS model predicts a much higher electrical

potential induced convective flow contribution than is actually measured. Similar observations

are found for the G10 membrane. Based on these observations, it is concluded that the charge

properties of the membranes differ when the ionic composition of the solution is changed.

Differences in charge densities of membranes are also reported by Tsuru et al. [5] and Peeters [6]

with various salts.

4.6 Determination of membrane properties, CaCl2 and NaH2PO4

Membrane properties of the NTR7450 and the G10 membrane are established using the procedure

as described in the materials and methods sections. Results of the NTR7450 membrane for

NaH2PO4 and CaCl2 are shown in Figures 7 and 8, respectively.

Figure 7: NaH2PO4 rejection curve as a function of the flux for a NTR7450 membrane at various

concentrations (10-3 M:□; 10-2 M:■; 0.1 M:○; 0.5 M:●). GMS model fit(-)


117

Figure 8: CaCl2 rejection curve as a function of the flux for a NTR7450 membrane at various

concentrations (10-3 M:□; 10-2 M:■; 0.1 M:○; 0.5 M:●). GMS model fit (-)

The GMS model describes both data sets well, except for the 0.5 M NaH2PO4 solution.

The membrane properties are shown in Table 3. A comparison of the parameters for the three

different salts shows that in case Na+ is the counter-ion, dielectric properties do not change.

However, the charge density of the membranes in case of NaH2PO4 is much larger than for NaCl.

This might indicate that adsorption of H2PO4- appears at the membrane surface, making it more

negatively charged. As a result, it becomes more rejecting to phosphate. Differences in adsorption

of the negative ions to the membrane surface have also been proposed by Peeters [6] as the

explanation for the differences found in the membrane charge densities between various salts.

Table 3: Freundlich parameters and dielectric constant of NTR 7450 and G10 membrane for

NaCl, NaH2PO4 and CaCl2

NaCl NaH2PO4 CaCl2 Membrane Q* Ks εmf Q* Ks εmf Q* Ks εmf NTR 7540 G10

0.034 0.037

0.31 0.34

65 70

0.965 0.267

0.76 0.66

65 70

0.113 0.052

0.45 0.47

75 70

5. CONCLUSIONS The GMS theory describes experimental NF results equally well as the ENP model. Therefore,

the use of the ENP model for engineering purposes is recommended, due to its simpler approach.

CHAPTER 6

118

However, in the case charge properties of membranes have to be established, the use of the GMS

theory is more appropriate because convective mass transfer due to an electrical potential gradient

is accounted for. In contrast to what is reported in literature, it is not necessary to adjust the pore

radius and the effective transport length, even in the case of the ENP model.

The contribution of dielectric exclusion has to be accounted for at high salt concentrations. The

approach followed by Hagmeyer results in an overprediction of dielectric exclusion, while the

simple Born model allows a good prediction of the experimental results. The dielectric constant

of the membrane phase is only slightly lower than for pure water.

Prediction of the rejection and the flux for NaH2PO4 and CaCl2 using the results of a NaCl

characterisation is not possible with either the GMS theory or the ENP model. The Freundlich

parameters indicate that in the case of NaH2PO4 a considerable increase of the charge density of

the membrane is occurring. This might be explained by adsorption of phosphate to the membrane

surface.

6. LIST OF SYMBOLS B0 :Membrane permeability [m2]

Ctot :Total molar concentration of the mixture [mol.m-3]

D+- :Maxwell Stefan diffusion coefficient for positive ion-negative ion interaction

[m2.s-1]

D+w :Maxwell Stefan diffusion coefficient for positive ion-water interaction [m2.s-1]

D-w :Maxwell Stefan diffusion coefficient for negative ion-water interaction [m2.s-1]

e :Electron charge [C]

F :Faraday’s constant {C.mol-1]

I :Mole fraction based ionic strength

Ki :Steric exclusion coefficient of component i

Ks :Exponential factor Freundlich isotherm

Ni :Molar flux of component i [mol.m-2.s-1]

P :Pressure [Pa]

Qm :Membrane charge density

Q* :Characteristic membrane charge

R :Gas constant [J.mol-1.K-1]

Rej :Rejection

ri :Radius of molecule i [m]


119

rp :Radius of membrane pore [m]

T :Absolute temperature [K]

Vi :Molar volume component i [m3.mol-1]

wi :Velocity of component i [m.s-1]

xi :Mole fraction of component i

yi :Mole fraction of component i in membrane

zi :Charge of component i

z+ :Charge of positive ion

z- :Charge of negative ion

γxi :Activity coefficient of component i in solution

γyi :Activity coefficient if component i in membrane phase

ΔΦDonnan :Donnan potential [V]

ΔPinterface :Pressure drop at membrane-solution interface [Pa]

ε :Membrane porosity

εm :Dielectric constant of the membrane

εmp :Dielectric constant of the membrane phase

ε0 :Dielectric permitivity [F.m-1]

εb :Dielectric constant of the bulk phase

εp :Dielectric constant of the pore liquid

Φ :Electrical potential [V]

μi :Chemical potential of component i [J.mol-1]

η :Permeate viscosity [Pa.s]

Ωp :Conductivity of the permeate [S.m-1]

Ωr :Conductivity of the retentate [S.m-1]

τ :Membrane tortuosity

ζi,j :Friction coefficient between component i and j [J.mol-1.m-2.s]

Subscripts

m :membrane

i,j,k :component index

T :constant temperature

P :constant pressure

CHAPTER 6

120

Φ :constant electrical potential

Superscript

p :permeate

7. REFERENCES 1. T.R. Noordman, J.M.K. Timmer, H.C. van der Horst, F.D. Donkers and J.A. Wesselingh,

Determination of properties of nanofiltration membranes. Part 1: Pore diameter from rejection

measurements with a mixture of oligosaccharides, submitted to J. Membrane Sci,

2. W.R. Bowen and H. Mukhtar, Characterisation and prediction of separation performance of

nanofiltration membranes, J. Membrane Sci. 112 (1996) 263-274

3. W.R. Bowen, A.W. Mohammad, N. Hilal, Characterisation of nanofiltration membranes for predictive

purposes- use of salts, uncharged solutes and atomic force microscopy, J. Membrane Sci. 126 (1997)

91-105

4. T. Tsuru, S. Nakao and S. Kimura, Calculation of ion rejection by extended Nernst-Planck equation

with charged reverse osmosis membranes for single and mixed electrolyte solutions, J. Chem. Eng. of

Japan 24 (1991) 511-517

5. T. Tsuru, M. Urairi, S. Nakao and S. Kimura, Reverse osmosis of single and mixed electrolytes with

charged membranes: experiment and analysis, J. Chem. Eng. of Japan 24 (1991) 518-524

6. J.M.M. Peeters, Characterization of nanofiltration membranes, PhD Thesis University of Twente, 1997

7. T.R. Noordman, P. Vonk, V.H.J.T. Damen, R. Brul, S.H. Schaafsma, M. de Haas and J.A. Wesselingh,

Rejection of phosphates by a ZrO2 ultrafiltration membrane, J. Membrane Sci. 135 (1997) 203-210

8. E. Glueckauf, The distribution of electrolytes between cellulose acetate membranes and aqueous

solutions, Desalination 18 (1976) 155-172

9. B.J. Mariñas, R.E. Selleck, Reverse osmosis treatment of multicomponent electrolyte solutions, J.

Membr. Sci. 72 (1992) 211-229

10. G. Hagmeyer, R. Gimbel, Modelling the salt rejection of nanofiltration membranes for ternary ion

mixtures and for single salts at different pH values, Desalination 117 (1998) 247-256


12. E.A. Mason, L.A. Viehland, Statistical-mechanical theory of membrane transport for multicomponent

systems: Passive transport through open membranes, J. Chem. Phys. 68 (1978) 3562-3572

13. T.R. Noordman, High flux ultrafiltration, PhD Thesis, University of Groningen, 2000

14. X.-L. Wang, T. Tsuru, S. Nakao and S. Kimura, Electrolyte transport through nanofiltration

membranes by the space-charge model and the comparison with the Teorell-Meyer-Sievers model, J.

Membr. Sci. 103 (1995) 117-133

15. P. Vonk, Diffusion of large molecules in porous structures, PhD thesis University of Groningen, 1994


121

16. J.A. Wesselingh and R. Krishna, Mass Transfer, Ellis Horwood Ltd, New York, 1990

17. J. Lyklema, Fundamentals of Interface and Colloid Science, Volume 1: Fundamentals, Academic

Press, London, 1991, chapter 6

18. H.C. van der Horst, J.M.K. Timmer, T. Robbertsen and J. Leenders, Use of nanofiltration for

concentration and demineralisation in the dairy industry: model for mass transport, J. Membrane Sci.

104 (1995) 205-218

19. R.C. Weast, M.J. Astle, CRC Handbook of chemistry and physics, 60th edition, 1981, CRC Press, Boca

Raton, Florida.

20. X.-L. Wang, T. Tsuru, M. Togoh, S. Nakao and S. Kimura, Evaluation of pore structure and electrical

properties of nanofiltration membranes, J. Chem. Eng. of Japan 28 (1995) 186-191

21. S.-I. Nakao, S. Kimura, Analysis of solute rejection in ultrafiltration, J. Chem. Eng Japan 14 (1981)

32-38

122

123

CHAPTER 7

General discussion and future research needs

124 CHAPTER 7

1. GENERAL DISCUSSION

In chapter 1 it is shown that there is a diversity of opportunities for NF. Also from an economic

point of view, NF is a viable alternative for the end-of-pipe treatment of waste water. Process

integrated applications can even make NF more beneficial. However, due to the very case-

specific nature of process-integrated solutions this is more difficult to quantify. Tools to analyse

process-integrated solutions are available, like e.g. pinch techniques [1,2,3]. This should allow for

identification of the opportunities for NF.

A major worry at the moment is the way NF processes, and industrial membrane processes in

general, are developed. From an analysis reported in literature [4], the importance of energy

consumption, expressed by the transmembrane pressure, on the economic viability is obvious.

Due to the trial and error basis of current membrane process development sub-optimal conditions

or less suited membranes might be applied. Improvement of these processes, either by finding the

optimal conditions or using better membranes, will result in economic gain. The short

development times of membrane processes, including NF, of about one to two years, and the

methodology applied will result in sub-optimal solutions also. The major pitfalls of the current

approach are that energy demand is too high and when unexpected problems occur in the process,

there is hardly any guideline to follow to come to a solution. From the above mentioned, it is

obvious that an understanding of the basic mechanisms underlying the separation is necessary.

With this understanding a translation to the development of industrial applications should be

made, a step which is currently omitted.

1.1 The description of NF of industrial feed by the ENP-model The first aim of the work described in this thesis was to determine whether the ENP-model could

be used for the development and the description of NF separation of industrial feed solutions.

Two approaches were used, which differed in the level of complexity: i) considering the

concentration polarisation layer and the membrane layer as one single layer (chapters 2 and 3), ii)

considering the concentration polarisation layer and the membrane layer as separate layers

(chapter 4). In both approaches no attention was paid to the actual distribution mechanism

occurring at the membrane/solution interface. The distribution coefficient and the diffusion

coefficient inside the membrane were lumped into one single mass transfer parameter.

General discussion and future research needs 125

1.1.1 Lactic acid separation In chapters 2 and 3, the separation of lactic acid from model and industrial feed solutions is

described. It is possible to use a model in which concentration polarisation and the membrane

layer are considered as one single layer. To tackle the separation problem, it was found that the

problem could be reduced by only taking dissociated and undissociated lactic acid into account.

During fermentation, lactose is converted into lactic acid, thereby reducing the pH by H+- and

dissociated lactic acid secretion. In this way excess of lactic acid was obtained in comparison to

the other components. Approximately 0.15 M undissociated lactic acid was present in the

fermentation broths. The mass transfer of this component is not affected by the presence of other

components. The dissociated lactic acid was present at a concentration of approximately 0.04 M,

which is about a five-fold excess compared to the other negative ions. Due to its slightly larger

size compared to chloride and a diffusion coefficient of about 1.10-9 m2.s-1 [5,6], the mass transfer

of dissociated lactic acid will just be slightly slower than for chloride. For these reasons the

prediction of the rejection data of the ultrafiltered fermentation broth was good. In the case of the

fermentation broth, protein fouling severely influenced the rejection-flux dependence. Due to an

increase of the diffusion path length, caused by the protein layer, it is expected that the overall

mass transfer parameter, Bs1 (eq. 16, chapter 2), is smaller. The finding that the rejection

parameter, Rs1 (eq. 15, chapter 2), is hardly influenced by the presence of the protein layer

indicates that the membrane is determinative. The question is whether this can be understood

from the underlying mechanisms. In the case of the undissociated lactic acid the rejection

parameter is mainly determined by size exclusion. Theoretical studies [7] and experimental

results [8,9] on UF and MF of protein containing solutions have shown that the irreversible

fouling layer is determinative for the rejective properties of the membrane process. In the

theoretical study, it was calculated that in the irreversible fouling layer, the separation distance

between spherical particles, composing the layer, are less than 1 nm, meaning that the irreversible

layer is a densely packed layer. From the analysis of the various contributions to the flow

resistance a considerable irreversible fouling was found. The theoretical findings and the presence

of irreversible fouling makes an estimation of the rejective properties of the fouling layer during

NF of lactic acid containing broth possible. The fermentation broth is prepared from a delactosed

whey powder, a feed that contains both whey proteins and protein aggregates. Especially the

aggregates can cause severe membrane fouling and are likely to be the cause of the irreversible

fouling [9]. The sizes of these aggregates can range from 10 to 100 nm. A pore in this layer can

thought to be presented as shown in Figure 1. Assuming the aggregates to be spherical, three

126 CHAPTER 7

adjacent aggregates surround a space which can be considered as the pore of the irreversible layer

(a separation distance between the aggregates of zero is assumed). An “apparant” pore diameter

can be calculated using the following equation:

aggregater134.0))6

cos(1(aggregaterapparantr ⋅=−⋅= π (1)

raggregate

raggregate+ rapparant

Figure 1: Definition of the “apparant” pore diameter

From the range of aggregate sizes, “apparant” pore sizes of 1.34 to 13.4 nm can be calculated. As

the pore diameter of NF membranes are close to 1.26 nm (results of CA960 membrane, chapter

6), it can be concluded that the membrane is determinative. As most of the lactic acid mass

transfer is by the undissociated form, it can be understood why the rejection parameters of the

model solution, the UF broth and the fermentation broth are the same. This brief analysis also

shows that in contrast to UF and MF the irreversible fouling layer is not determinative for the

rejective properties. There is only a small region of pore sizes in the lower UF-region (molecular

weight cut off values of approximately 1000 to 5000) in which both the membrane and the

irreversible fouling layer determine the rejective properties.

1.1.2 Demineralisation of whey In the case of demineralisation of whey, the situation is more complex. However, before

commenting on this another subject has to be dealt with. In the mass transfer model described in

chapter 4, a distinction between the mass transfer in the boundary layer and in the membrane is


made. Mass transfer in the membrane is described by the ENP-model while the mass transfer in

the boundary layer is described by a Fick model. A more appropriate approach is to describe the

boundary layer by the ENP-model as well. To get an impression of the difference between the

two models, the concentration profiles for Na+, Ca2+ and Cl- in the boundary layer were calculated

taking data from chapter 4 (medium 3, a flux of 30.10-6 m.s-1 and the corresponding rejections

from Figure 7, chapter 4). Only the concentration profiles of Na+ and Ca2+ were calculated, the Cl-

profile was determined from the charge balance.

From Figure 2, it is obvious that the diffusion-induced electrical potential gradient in the

boundary layer has a pronounced effect on the concentration profiles and the final concentrations

at the membrane interface. Omission of the electrical potential gradients in the concentration

polarisation layer results in a more than two-fold increase of the concentrations at the membrane

interface. The consequence of this is that the estimated parameters in chapter 4 are too low, as the

values calculated for ΔC1, ΔC2, C1,0 and C2,0 are higher when the potential gradient is not taken

into account.

Figure 2: Concentration profiles of Na+ (●,○), Cl- (■,□) and Ca2+ (▲,Δ) in the boundary layer.

Closed symbols: Fick-model, open symbols: ENP-model. Drawn line is potential.

The salt composition of whey is very complex. At least 12 ionic species can be distinguished, of

which 3 are positively charged and the others negatively. To simplify the system, the

128 CHAPTER 7

concentrations of the two monovalent cations Na+ and K+ were lumped and were considered as a

single monovalent cation, Ca2+ is the only divalent cation. All negatively charged ions were

considered as a single anion. In this way the system was reduced to a three component system.

This approach was very successful in the description of demineralisation of whey by NF.

Distinguishing between boundary layer and membrane transport allowed for the description of

concentration polarisation effects that were observed in the rejection-flux graphs using a defined

mixture of NaCl and CaCl2. From the results with the UF-whey permeate an important finding is

that one has to be aware of bound and unbound Ca2+. Bound Ca2+ does not contribute to the mass

transfer process. For a good description of the demineralisation of whey only the unbound Ca2+

should be considered.

1.2 The Generalised Maxwell Stefan description of NF The second aim of this work was to investigate the applicability of the GMS theory to describe

NF of model solutions and the relative importance of Donnan and dielectric exclusion in the

distribution of ions between the membrane pore and the bulk solution. In chapter 5 the GMS

description was used to characterise the membrane pore size and the effective transport length of

various NF membranes by using a dilute mixture of oligosaccharides. Charge effects are not of

importance in the model. The analogy to falling velocities of macroscopic spheres in narrow tubes

that was taken to correlate the membrane friction coefficients of the oligosaccharides to the pore

diameter was successful. The effective membrane path length determined from hydraulic

permeability measurements was sufficient to give a good description of the flux and rejection of

the oligosaccharides. This is in contrast with literature [10,11] where the effective membrane path

length seemed to be a function of component size. The explanation given in literature that larger

molecules have a longer transport length than small molecules, e.g. water, because not all free

volume in the membrane is accessible seems invalid. The reason for this is that water will look

for the path of least resistance also and therefore will have a similar transport length than larger

molecules.

In the case of the determination of the charge properties of the membranes, a much more complex

situation is found. From the analysis of the relative importance of the Donnan and dielectric

distribution it follows that both mechanisms have to be accounted for. For the description of the

results, the pore diameter and the effective transport length, established in the oligosaccharide

experiment, give very good results. Unlike stated in literature [10,11], adjustment of these

parameters was not necessary. This applies to the GMS theory as well as the ENP model. A


comparison showed that both models describe the results equally well. For engineering purposes

the ENP model is favoured due to its simplicity as compared to the GMS theory. However, for

determination of the charge density the GMS theory is recommended.

2. CONTINUATION OF THE PRESENT WORK The work on the application of the GMS theory, as presented in this thesis, is still incomplete.

Recently, two theoretical studies are published by Yaroshchuk [12,13] on the superpositioning of

Donnan and dielectric exclusion effects, stating that the Born model is not satisfactory for the

description of dielectric effects in membrane pores because solvation energies of ions are

underestimated. However, no experimental verification is made. In our case, the Born model

gives satisfactory results. In this area some questions remain. A good point made by Yaroshchuk

is that the current approach of using salt rejection measurements only is insufficient. An

independent estimation of the dielectric constant of the membrane and the pore liquid is

necessary. Further development of these theories and its experimental verification has to be made.

In addition, further studies on the adsorption of ions on membrane materials and their effect on

membrane charge density should be made. It seems plausible to expect that it is possible to put all

this in one framework and that a NaCl-characterisation of a membrane is sufficient as a starting

point to establish the charge density for other ions also.

3. GENERAL CONCLUSIONS The ENP-model can be used to describe NF of industrial feed. From an analysis of the feed, the

complexity of the separation problem can be reduced into a simple system, which allows a

modelling approach. Especially the correspondence between the rejection parameter that is

determined in model solutions and those obtained in industrial feed is of importance because it

allows the design of industrial NF-processes. Literature data or laboratory experiments can

provide this information.

The results also show that knowledge of the distribution mechanism is not necessary for a good

description of the experimental results and a prediction of NF separation. Lumping the

mechanism into a mass transfer parameter and a rejection parameter is a satisfactory approach.

Considering the concentration polarisation layer as a separate layer results in a more flexible

model, especially when geometries between membrane modules differ, like in our case.

The GMS model can serve as a good alternative to the ENP-model, despite its higher complexity.

To characterise a membrane pore size and the effective membrane path length, two experiments

130 CHAPTER 7

(clean water flux and oligosaccharide mixture) suffice. In the analysis of the membrane charge

properties it has been shown that dielectric effects and Donnan effects both have to be taken into

account. Prediction of the separation of other salts from a membrane characterisation by NaCl is

not possible at this moment. For this a further development of the models is necessary.

4. GENERAL APPROACH TO THE DEVELOPMENT OF INDUSTRIAL

NANOFILTRATION PROCESSES From the results presented in chapters two, three and four and recent literature [14] a general

approach can be deduced for the development of industrial nanofiltration processes. The

following steps in this approach can be distinguished:

1. Define the separation problem. What is the aim of the separation?

2. Analyse the feed composition. In this analysis attention should be paid to the non-charged

and charged species present in the mixture. In addition, the pH of the solution has to be

established to account for the behaviour of components that show pH-dependent dissociation,

like organic acids, amino acids, peptides and proteins.

3. Choose key components for the separation. This is a common approach in chemical

engineering and has been shown to be useful in chapter four. Lumping of components is a

second step to simplify the separation problem. In chapter 4 it has been shown that by

lumping monovalent and divalent positive ions as two single species, the UF-whey permeate

system could be fixed. The mass transfer of the negative ions (considered as species number

three) is completely determined by the mass transfer of the positive ions. In this case the data

can be well predicted by the model solution because most of the negative ions were chloride,

making the transition to a model system with three ionic species valid. If an industrial feed

solution cannot be reduced to a three component system, a reduction to the least number

should be made.

4. Redefine the separation problem in terms of these ionic species and select the proper model

components.

5. Based on these components and one of the mass transfer models presented in this thesis

calculations can be made. Two approaches can be followed: i) make calculations with an

optimisation routine, which determines the values of the membrane characteristics necessary

to get the best separation results of the key components. Select a membrane that comes

closest to these membrane characteristics. An overview of these data can be found in

literature [15]. Further data can be obtained from specification sheets of membrane


manufacturers, applying the methodology developed by Bowen et al. [15]. ii) Take the

extremes of the membrane characteristics for NF (pore size, charge density and membrane

path length) as given in literature [15] and make data sets. This will result in 8 (23) sets of

data for the membrane characteristics. Run the model for these 8 sets and determine which set

gives the best separation. From the calculations made by these two approaches a first

selection in membranes can be made.

6. Make experiments with the selected membranes and model solutions containing the key

components at the appropriate pH. These experiments can be used to verify the model

calculations and allow a further selection of the membranes.

7. Test the remaining membranes with the industrial feed solution and determine whether the

separation is acceptable for the given situation. In this stage it is necessary to focus on the

fouling process and the way it affects the separation. Generally, specific components in the

feed can be related to the fouling process and therefore ways to overcome the fouling (e.g. by

a pre-treatment) can be developed. The experimental results can be used to adjust the

parameters of the model when necessary. The need of adjustment was not present in the two

cases discussed in chapters three and four of this thesis.

8. Selection of membrane configuration. From an economic point of view, either hollow fibre or

spiral wound membranes are preferred. However, with a strongly fouling or a highly viscous

solution tubular or plate and frame systems have to be applied.

9. Make pilot tests and verify the outcome with predictions made by the model. Use the model

to optimise the process and verify these conditions. Concurrently laboratory tests can be made

to gain more information on the fouling process.

10. Design, built and start-up of the industrial system using the model.

This set up looks very time-consuming but it is not. It can easily be fit into the time-frame that is

currently applied in the development of NF-processes. For the person who has all necessary

equipment and analytical tools available, the first four steps can be made in a week. Step number

five will also take a week. The experimental testing in steps 6 and 7 take about three to four

weeks, the limit generally is determined by the time to analyse samples. Steps 8 and 9 will take

about 6 months to a year in cases where seasonal variations of the feed are of importance. Step 10

is dependent on the size of the plant, for a small size plant about 6 months will be necessary, in

the case of a large one, possibly two to three years. The interesting part of this time-frame is that

model-assisted laboratory testing takes a maximum of about five to six weeks. Unfortunately,

practice learns that hardly any attention is paid to the model-assisted laboratory testing or any

132 CHAPTER 7

laboratory testing at all. The importance of this stage should be recognised by membrane

manufacturers, engineering companies and industry. In the laboratory the basic insights in the

process are gathered, not in the pilot stage. Spending more time in the laboratory will potentially

save a lot of money later on.

5. FUTURE RESEARCH NEEDS Until this moment there are only four cases known in literature in which laboratory results and a

modelling approach are used to develop an industrial NF process. Two of them are described in

this thesis, the others are described by Bowen for the separation of a dye/salt/water system [14]

and salt removal from a dye solution by nanofiltration [16]. The methodology described above

should be tested for the development of other industrial NF processes, which are not related to the

areas mentioned above.

From a theoretical point of view further analysis of distribution phenomena, including dielectric

effects, should be made, in order to establish whether a NaCl-characterisation of an NF

membrane suffices to describe other salt separations. As a starting point, the work of Yaroshchuk

[12,13] can be used. For a better understanding and to establish the proper charge characteristics

of the membrane, dielectric properties of the pore liquid should be established experimentally.

Impedance spectroscopy might be a good technique for this [17,18]. It also gives more insight

into the diffusion and distribution processes.

The dynamics of NF processes is another topic, which did not receive any attention. Potential

applications bounce off on the wrong way of experimenting. E.g. for the demineralisation of

water, ion exchangers are used. During operation of the ion exchanger columns, the waste water

in a plant can contain low concentrations of NaCl (0.001 M). In this situation, NF can be applied

successfully to recover most of the water for other purposes. However, during the regeneration

step of the ion exchangers the NaCl concentration in the waste water can reach values of 1 M.

Steady state tests showed that NF was not appropriate for the separation, which can be understood

based on the results from chapters 4 and 6. It is not known, however, whether in a dynamic

situation, considering the increased NaCl concentration as a pulse load on the system, NF could

be the appropriate technique. To get an idea of the viability of NF in the case of a pulse load a

time constant analysis might give some insight. Three time constants should be compared: the

pulse duration, the residence time of the concentrate in the system and the time constant for mass

transfer. Based on a NaCl transport rate of 20 µm/s and a membrane thickness of 300 µm, a time

constant of 15 s is obtained. For an industrial membrane system a liquid residence time of 100 s is


found. The pulse duration is taken about the same order of magnitude as the liquid residence time.

From this brief analysis it can be concluded that the pulse will result in a severe permeation of

NaCl into the permeate. However, the difference in time constants is only one order of magnitude

and development of a buffer system can make NF a viable alternative for the waste water

treatment.

Most of the literature on NF considers aqueous feed. However, NF also shows a large potential in

non-aqueous separations. In the chemical industry, solvents are frequently used as a reactant, to

dissolve reactants or to dissolve products before further processing. Therefore, solvent recovery is

an area of major importance. Distillation is the most important technique for this but in analogy to

water removal in food industry, in which a membrane process and an evaporation process are

combined, NF as a first removal step should be considered to reduce energy consumption. The

major problem in NF of solvents is the material stability: polymeric membranes tend to swell and

lose their separation capabilities. Currently, a limited number of solvent-resistant membrane

materials are available [19,20,21,22]. A study of solvent transport through NF membranes, testing

n-alcohols, paraffins, ketones and acetate-esters, showed that, in addition to viscosity, surface

tension is a major parameter determining solvent flow [23,24]. For the paraffins, dielectric effects

also seem to play a role. This was not found for the other solvents. During filtration of solvent

mixtures the composition of the feed and the permeate were equal, indicating the absence of

solvent selectivity of the NF membrane. Only a limited number of these studies are currently

made and more research effort is necessary to gather the understanding of NF in non-aqueous

environments. Another important difference between aqueous and non-aqueous systems is the

concept of rejection. In addition to swelling of the membrane, macromolecules in solvents are

very flexible. This makes determination of the rejection of macromolecules very difficult [21].

While in aqueous systems macromolecules can be considered as rigid spheres, the shape of a

macromolecule in a solvent in the vicinity of a pore can change dependent on the structure of the

macromolecule and the applied pressure. A macromolecule can deform and can get an orientation

which allows it to flow through a pore. Even if the hydrodynamic size (size determined in free

solution, e.g. by light scattering) of the macromolecule is larger than the membrane pore size,

permeation can occur. De Gennes [25] developed a theoretical frame-work, which relates

permeability of a macromolecule to its structure, membrane properties and pressure conditions.

However, this theoretical frame-work still needs thorough experimental testing.

Two other important subjects in non-aqueous applications are membrane fouling and long-term

stability of the membranes. In the latter case, minor contaminants can be the cause of membrane

134 CHAPTER 7

break-down, while the membrane is very suited for the bulk solvent. From this it is obvious that

non-aqueous applications still need a substantial development effort.

6. FINAL COMMENTS This work shows that model approaches can be used to develop industrial NF processes.

However, more examples are necessary to confirm this. The procedure for process development

as described in this chapter structures the work to be done.

Also in the development of the theoretical frame work more effort is necessary, even though

major progress has been made. Especially, dielectric exclusion should be focussed upon. Non-

aqueous applications of NF in this respect are still to be considered in the virgin state.

7. REFERENCES 1. W.C.J. Kuo, R. Smith, Designing for the interaction between water-use and effluent treatment, Trans

IChemE 67 A (1998) 287-301

2. S.J. Doyle, R. Smith, Targeting water reuse with multiple contaminants, Trans IChemE 75 B (1997)

181-189

3. A. Alva-Argaez, A.C. Kokossis, R. Smith, Waste water minimisation of industrial systems using an

integrated approach, Computers Chem. Eng 22 Suppl. (1998) S741-S744

4. J.M.K. Timmer, J.T.F. Keurentjes, Mogelijkheden van energiebesparing in de industrie door

toepassing van membraanfiltratie, nanofiltratie in het bijzonder, report MINT-project 3385.02/04.83

Ontwikkeling van engineering-tools die de implementatie en optimalisatie van nanofiltratieprocessen

in de industrie op eenvoudige wijze ondersteunen, NOVEM, Utrecht, 1999

5. C.L.Chu, W.E.L. Spieβ, W. Wolf, Diffusion of lactic acid in gels, Lebensmit.-Wissenschaft und

Technologie 25 (1992) 470-475

6. C.L.Chu, W.E.L. Spieβ, W. Wolf, Diffusion of lactic acid and Na-lactate in a protein matrix,

Lebensmit.-Wissenschaft und Technologie 25 (1992) 476-481

7. P. Harmant, Controle de la structure de depots de particules colloidales en filtration frontale et

tangentielle, PhD Thesis, Université Paul Sabatier, Toulouse, 1996

8. A.D. Marshall, P.A. Munro, G. Tragardh, Influence of permeate flux on fouling during the

microfiltration of β-lactoglobulin solutions under cross-flow conditions, J. Membr. Sci. 130 (1997) 23-

30

9. J.M.K. Timmer, G. Daufin, Whey protein fractionation: membrane processes for production of high-

purity proteins, Final report AAIR-project AIR2-CT93-1207 (1997)


10. W.R. Bowen, A.W. Mohammed, N. Hilal, Characterisation of nanofiltration membranes for predictive

purposes-use of salts, uncharged solutes and atomic force microscopy, J. Membr. Sci. 126 (1997) 91-

105

11. T. Tsuru, M. Urairi, S.-I. Nakao, S. Kimura, Reverse osmosis of single and mixed electrolytes with

charged membranes: experiment and analysis, J. Chem. Eng. Japan 24 (1991) 518-524

12. A.E. Yaroshchuk, Non-steric mechanisms of nanofiltration: superposition of Donnan and dielectric

exclusion, accepted by Separation and Purification Technology

13. A.E. Yaroshchuk, Dielectric exclusion of ions from membranes, Adv. Coll. Int. Sci. 85 (2000) 193-230

14. W.R. Bowen, A theoretical basis for specifying nanofiltration membranes – dye/salt/water streams,

Desalination 117 (1998) 257-264

15. W.R. Bowen, A.W. Mohammad, Characterization and prediction of nanofiltration membrane

performance- a general assessment, Trans IChemE 76 A (1998) 885-893

16. W.R. Bowen, A.W. Mohammad, Diafiltration by nanofiltration: prediction and optimization, AIChE J.

44 (1998) 1799-1812

17. H.G.L. Coster, K.J. Kim, K. Dahlan, J.R. Smith, C.J.D. Fell, Characterisation of ultrafiltration

membranes by impedance spectroscopy. I. Determination of the separate electrical parameters and

porosity of the skin and sublayers, J. Membr. Sci. 66 (1992) 19-26

18. E.K. Zholkovskij, Irreversible thermodynamics and impedance spectroscopy of multilayer membranes,

J. Coll. Int. Sci. 169 (1995) 267-283

19. Koch, Chemically stable UF& Nanofiltration membranes, www.kochmembrane.com/

products/selro/selro.htm

20. SolSep, www.solsep.com

21. M.A.M. Beerlage, Polyimide ultrafiltration membranes for non-aqueous systems, PhD thesis,

University Twente, 1994

22. D.M. Koenhen, A.H.A. Tinnemans, Semipermeable composite membrane, a process for the

manufacture thereof, as well as application of such membranes for the separation of components in an

organic liquid phase or in the vapor phase, US Patent 5274047 (1993)

23. D.R. Machado, D. Hasson, R. Semiat, Effect of solvent properties on permeate flow through

nanofiltration membranes. Part I: Investigation of parameters affecting solvent flux, J. Membr. Sci. 163

(1999) 93-102

24. D.R. Machado, D. Hasson, R. Semiat, Effect of solvent properties on permeate flow through

nanofiltratin membranes. Part II. Transport model, J. Membr. Sci. 166 (2000) 63-69

25. C. Gay, P.G. de Gennes, E. Raphaël, F. Brochard-Wyart, Injection threshold for a statistically branched

polymer inside a nanopore, Macromolecules 29 (1996) 8379-8382

136 CHAPTER 7

SUMMARY Pressure-driven membrane processes, especially ultrafiltration and reverse osmosis, found their

way into industry since the late sixties. Advantages of these processes are the lower energy

consumption and the reduced environmental impact compared to conventional processes like

evaporation and extraction. Nanofiltration membranes became available in the eighties. They are

characterised by a pore diameter close to 1 nm and a slightly charged surface. These properties

make them suitable for the following applications:

i) Removal of monovalent ions, like sodium, potassium and chloride from waste water, reaction

mixtures or streams in the food industry.

ii) Separation of monovalent and multivalent ions, as is the case in the demineralisation of whey.

Here a separation of sodium and potassium from calcium is accomplished.

iii) Separation of small organic components from biological liquids, e.g. lactic acid separation

from fermentation broths, amino acid removal from protein hydrolysates, or the separation of

organic acids from municipal waste water.

In practice, nanofiltration processes are mainly developed on a “trial and error” basis. Only a few

examples exist in which the application of fundamental insights and laboratory results were used

for the development of industrial processes. The availability of methods to make the translation

from fundamental information into practice is essential to improve process development.

Additionally, better tools for optimisation and “trouble shooting” can be developed.

Due to its specific properties, nanofiltration is a complex process in which, next to a separation

based on size, a separation based on charge interaction occurs. Insight into size separation

originating from the field of ultrafiltration can immediately be applied to nanofiltration. However,

insight into charge-based separation evolves daily.

The Donnan equilibrium of the ions between water and the membrane phase is generally taken as

the starting point for a description. Besides the aspect of distribution of ions, mass transfer in

nanofiltration has mainly been described by the extended Nernst-Planck (ENP) model. The

disadvantage of this model is that no distinction is made between the individual interactions that

take place in the nanofiltration process. In addition, electrical potential-induced convective

transport of water is not taken into account. The generalised Maxwell-Stefan (GMS) approach

does take these interactions into account but has never been used to describe nanofiltration

processes.

The work described in this thesis has two major aims: gaining insight into the mass transfer

phenomena occurring in the nanofiltration process and the application thereof to industrially

relevant complex fluids.

In chapter 1, nanofiltration is positioned in the group of pressure-driven membrane processes.

Characteristics of the process are further defined and an overview of possible applications is

given.

In chapter 2, the development of an ENP-based model for the separation of lactic acid from

aqueous solution by nanofiltration is described. The core of the approach is that no distinction is

made between mass transfer in the boundary layer and mass transfer inside the membrane. The

influence of the flux and the pH of the solution on the rejection of various membranes for lactic

acid is established experimentally. In this chapter it is shown that a good process description is

obtained by splitting the mass transfer of lactic acid into transport of dissociated and

undissociated lactic acid.

In chapter 3, the model developed in chapter 2 is used to describe the removal of lactic acid from

fermentation broths. Additionally, attention is paid to the description of the membrane fouling

process. A distinction is made between resistances of the membrane, initial fouling and time-

dependent deposition of matter. With certain constraints the model can be used successfully for

the description of lactic acid rejection. Besides, it is observed that the fouling process in

nanofiltration in the presence of proteins is different from the one in which proteins are removed

upstream by ultrafiltration.

In chapter 4, the demineralisation of ultrafiltered whey by nanofiltration is studied. In analogy to

the methods described in chapters 2 and 3, a model for the demineralisation is developed. The

major difference with the model in chapters 2 and 3 is the distinction made between mass transfer

in the boundary layer and mass transfer inside the membrane. Furthermore, ultrafiltered whey is a

multicomponent mixture in which charge interactions can result in phenomena like negative

rejections. It is shown that an ENP-model in which only three components are defined results in a

good description of experimental results.

In chapter 5, the GMS approach is applied to characterise the pore diameter and the effective

transport length of various membranes using a mixture of uncharged oligosaccharides. The

friction between the oligosaccharides and the membrane was modelled using an analogy to falling

velocities of macroscopic spheres in narrow tubes. This approach results in a good description of

the oligosccharide rejection of the membranes.

In chapter 6, the GMS approach is applied to characterise the charge properties of nanofiltration

membranes. In the model, the electrical potential-induced convective flow is accounted for.

Secondly, an analysis is made of the contribution of dielectric exclusion in the distribution of ions

between membrane and water phase. To conclude, the frequently used ENP-model and the GMS

approach are compared. The analysis shows the importance of dielectric exclusion in addition to

the Donnan equilibrium. It is also shown that both the ENP-model and the GMS-model describe

experimental results equally well. The major difference is found in the calculated charge densities

of the membranes. Furthermore, it is established that a NaCl-characterisation of nanofiltration

membranes is insufficient to predict the rejection of CaCl2 and NaH2PO4.

Chapter 7 contains a general discussion of the findings in chapters 2 through 6 and describes a

methodology for the development of industrial nanofiltration processes. This chapter finishes

with highlighting subjects in nanofiltration that need attention in the near future.

SAMENVATTING

Drukgedreven membraanscheidingsprocessen, met name ultrafiltratie en omgekeerde osmose,

hebben sinds de jaren zestig steeds meer hun weg gevonden in de industrie. Voordelen van

membraanprocessen zijn dat ze in veel gevallen energiezuiniger en milievriendelijker zijn dan

conventionele processen zoals verdamping en extractie. Nanofiltratiemembranen zijn beschikbaar

gekomen in de jaren tachtig. Deze membranen hebben een poriediameter van ongeveer 1 nm en

zijn in beperkte mate geladen. Door deze eigenschappen zijn ze onder meer geschikt voor de

volgende toepassingen:

i) Het verwijderen van monovalente ionen zoals natrium, kalium en chloride uit afvalwater,

reactiemengsels of stromen in de levensmiddelenindustrie.

ii) Het scheiden van monovalente en meerwaardig geladen ionen. Dit vindt bijvoorbeeld plaats bij

het ontzouten van wei, waar natrium en kalium worden verwijderd uit een mengsel met calcium.

iii) De verwijdering van kleine organische componenten uit biologische vloeistoffen zoals

melkzuur uit fermentatievloeistoffen, aminozuren uit eiwithydrolysaten of organische zuren uit

afvalwater.

In de praktijk wordt er meestal op basis van een “trial and error” benadering een

nanofiltratieproces ontwikkeld. De beschikbaarheid van methoden om de vertaling van

fundamentele informatie naar de praktijk te maken is van essentieel belang voor een effectieve

procesontwikkeling. Tevens onstaan hierdoor betere mogelijkheden om processen te

optimaliseren en problemen op te lossen.

Nanofiltratie is een complex proces waarbij naast scheiding op grootte ook scheiding op basis van

lading plaatsvindt. Bij ultrafiltratie opgedane inzichten in scheiding op grootte kunnen direct

worden toegepast bij nanofiltratie. Het inzicht in het scheiden van geladen componenten groeit

echter nog steeds.

In het algemeen wordt het Donnan-evenwicht gebruikt voor de beschrijving van de verdeling van

ionen over water- en membraanfase. In de literatuur wordt voor de beschrijving van het transport

door het membraan gebruik gemaakt van de uitgebreide Nernst-Planck (ENP) beschrijving. Deze

beschrijving heeft echter als bezwaar dat er geen onderscheid wordt gemaakt tussen de

individuele processen die ten grondslag liggen aan het stofoverdrachtsproces. Daarnaast wordt er

geen rekening gehouden met het door elektrische potentiaalverschillen geïnduceerde convectieve

transport van water. De gegeneraliseerde Maxwell-Stefan (GMS) beschrijving houdt hier wel

rekening mee, maar is voor de beschrijving van nanofiltratieprocessen nog niet toegepast.

Het doel van het in dit proefschrift beschreven onderzoek is tweeledig: verkrijgen van inzicht in

de bij nanofiltratie optredende stofoverdrachtsprocessen en toepassen van de genoemde modellen

op industrieel relevante complexe vloeistoffen.

In hoofdstuk 1 wordt nanofiltratie geplaatst binnen de groep van drukgedreven

membraanfiltratieprocessen. De karakteristieken van het proces worden nader gedefinieerd en een

overzicht van mogelijke applicaties wordt gegeven.

Hoofdstuk 2 gaat in op de ontwikkeling van een model gebaseerd op de ENP-beschrijving voor

de scheiding van melkzuur uit waterige oplossingen. De kern van de gevolgde aanpak is dat er

geen onderscheid wordt gemaakt tussen stofoverdracht in de grenslaag en stofoverdracht in het

membraan. De invloed van de flux en de pH van de melkzuuroplossing op de retentie van

verschillende membranen voor melkzuur zijn experimenteel bepaald. In dit hoofdstuk wordt

aangetoond dat een goede beschrijving kan worden verkregen door het stofoverdrachtsproces van

melkzuur te splitsen in afzonderlijk transport van gedissocieerd en niet-gedissocieerd melkzuur.

In hoofdstuk 3 wordt het model dat in hoofdstuk 2 is beschreven toegepast voor de beschrijving

van de verwijdering van melkzuur uit fermentatievloeistoffen. In dit hoofdstuk wordt eveneens

aandacht besteed aan de beschrijving van het membraanvervuilingsproces. Hierbij is onderscheid

gemaakt tussen weerstanden als gevolg van het membraan, initiële vervuiling en tijdsafhankelijke

depositie van componenten. Er wordt aangetoond dat onder bepaalde aannamen het ontwikkelde

model kan worden toegepast voor de beschrijving van de melkzuurretentie. Daarnaast is er

geconstateerd dat het vervuilingsproces in de aanwezigheid van eiwitcomponenten anders

verloopt dan wanneer deze voorafgaand door ultrafiltratie zijn verwijderd.

In hoofdstuk 4 wordt de ontzouting van geültrafiltreerde wei middels nanofiltratie beschreven. In

analogie met de in hoofdstuk 2 en 3 beschreven werkwijze is voor de ontzouting van wei een

vergelijkbaar model opgesteld met dit verschil dat er onderscheid is gemaakt tussen transport in

de grenslaag en transport in het membraan. Wei is een multi-componentensysteem waarbij

verschillende ladingsinteracties kunnen resulteren in fenomenen als negatieve retenties. Er wordt

aangetoond dat met een ENP-beschrijving waarin drie componenten worden gedefinieerd een

goede beschrijving van de experimentele resultaten wordt verkregen.

In hoofdstuk 5 wordt de GMS-beschrijving toegepast voor de karakterisering van nanofiltratie-

membranen in termen van poriediameter en effectieve weglengte door gebruik te maken van een

waterige oplossing van ongeladen oligosachariden. De frictie tussen de suikers en het membraan

is benaderd in analogie met valsnelheden van macroscopische bollen in nauwe buizen. Deze

benadering resulteert in een goede beschrijving van de retentie van verschillende membranen

voor oligosachariden.

In hoofdstuk 6 wordt de GMS-beschrijving toegepast voor de karakterisering van de

ladingseigenschappen van nanofiltratiemembranen. Hierbij wordt convectief watertransport ten

gevolge van de ladingspotentiaal over het membraan meegenomen en wordt een analyse gemaakt

van de bijdrage van diëlektrische exclusie op het verdelingsproces van ionen over water- en

membraanfase. Ook wordt een vergelijking gemaakt tussen de GMS-beschrijving en het ENP-

model dat veelvuldig in de literatuur wordt toegepast. Uit de analyses volgt dat er terdege

rekening gehouden dient te worden met diëlektrische exclusie. Verder wordt aangetoond dat

zowel het ENP- als het GMS-model de resultaten goed beschrijven. Het grote verschil wordt

gevonden in de ladingseigenschappen die voor het membraan worden bepaald. Tevens is

vastgesteld dat een NaCl-karakterisering niet volstaat om de retentie van CaCl2 en NaH2PO4 te

voorspellen.

Hoofdstuk 7 bevat een algemene discussie over hetgeen in hoofdstukken 2 tot en met 6 is

gevonden en beschrijft een methodiek voor de ontwikkeling van industriële

nanofiltratieprocessen. Het hoofdstuk besluit met het aangeven van de problemen op het gebied

van nanofiltratieprocessen die in de toekomst aandacht verdienen.

CURRICULUM VITAE Martin Timmer is 17 september 1961 in Delft geboren. Na afronding van zijn Atheneum B aan

het Stanislascollege is hij in september 1979 begonnen aan de studie scheikundige technologie

aan de toenmalige Technische Hogeschool Delft. Deze studie rondde hij in augustus 1986 af bij

de vakgroep Bioprocestechnologie. In oktober 1986 begon hij bij de afdeling Technologie van het

Nederlands Instituut voor Zuivelonderzoek. Aan zijn verblijf bij het NIZO kwam in 1997 een

einde. Zijn volgende werkkring was de groep Procesontwikkeling van de faculteit Scheikundige

Technologie van de TU Eindhoven, waar hij tot juli 1999 werkzaam was. In november 1999 is hij

het bedrijf ETD&C gestart dat zich bezighoudt met technologieontwikkeling en advies.

Stellingen: 1. Diëlectrische exclusie is een essentieel mechanisme bij de scheiding van ionen middels

nanofiltratie. Dit proefschrift

2. Toepassing van het “Extended Nernst-Planck”-model bij de ontwikkeling van industriële

nanofiltratieprocessen is aan te bevelen. R. Rautenbach, M. Lohscheidt, “Einfluß der Kationen auf die Selectivität von Nanofiltrationsmembranen”, F&S Filtrieren und Separieren 12(4) (1998) 155-160

3. In tegenstelling tot hetgeen bij ultrafiltratie en microfiltratie wordt gevonden, heeft

irreversibele membraanvervuiling bij omgekeerde osmose en nanofiltratie een ondergeschikt effect op de retentie. Dit proefschrift

4. Het begrip retentie zal voor niet-waterige membraanprocessen moeten worden herzien.

M.A.M. Beerlage, “Polyimide ultrafiltration membranes for non-aqueous systems”, PhD Thesis, Twente University, 1994 C. Gay et al., “Injection threshold for a statistically branched polymer inside a nanopore”, Macromolecules 29 (1996) 8379-8382

5. Invoering van kennismanagementsystemen bij universitaire instellingen is een noodzaak

om ideeën-, kennis- en kapitaalvernietiging te voorkomen. 6. Welvaart is niet bevorderlijk voor kwaliteit. 7. In de toekomst mag de mensheid zich alleen nog met licentie voortplanten.

Bionieuws 26-2-2000 “Athersys maakte op 15 februari bekend dat het voorlopige octrooien heeft aangevraagd op 10.000 genen”.

8. De Westerse economie is er niet bij gebaat gewapende conflicten goed op te lossen.

9. De bij ontbinding van arbeidscontracten toegepaste kantonrechtersprocedure gaat volledig

voorbij aan de waarheidsvraag. 10. Wetenschappelijk onderzoek vertoont erg veel gelijkenis met de in de honkbalsport

bekende “nuckle” bal. De baan is sterk afhankelijk van omgevingsfactoren en eindigt vaak net naast het doel.

11. Het unieke van een goed gevoel is niet te beschrijven en wordt verpest als dat wordt

verlangd.

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