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JOHANNES KEPLER UNIVERSITÄT LINZ Netzwerk für Forschung, Lehre und Praxis Separation of Amino Acids with Nanofiltration: Permeation Modelling and Batch System Design Dissertation zur Erlangung des akademischen Grades Doktor der Technischen Wissenschaften Angefertigt am Institut für Verfahrenstechnik Eingereicht von: Dipl.-Ing. Zoltán Kovács Beurteilung: O. Univ.-Prof. Dr. Wolfgang Samhaber Ao. Univ.-Prof. Dr. Anton Friedl Linz, August 28, 2008 Johannes Kepler Universität A-4040 Linz · Altenbergerstraße 69 · Internet: http://www.jku.at/ · DVR 0093696
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Page 1: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

J O H A N N E S K E P L E RU N I V E R S I T Ä T L I N Z

N e t z w e r k f ü r F o r s c h u n g , L e h r e u n d P r a x i s

Separation of Amino Acids with Nanofiltration:

Permeation Modelling and Batch System Design

Dissertation zur Erlangung des akademischen Grades

Doktor der Technischen Wissenschaften

Angefertigt amInstitut für Verfahrenstechnik

Eingereicht von:

Dipl.-Ing. Zoltán Kovács

Beurteilung:

O. Univ.-Prof. Dr. Wolfgang Samhaber

Ao. Univ.-Prof. Dr. Anton Friedl

Linz, August 28, 2008

Johannes Kepler UniversitätA-4040 Linz · Altenbergerstraße 69 · Internet: http://www.jku.at/ · DVR 0093696

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ABSTRACT

The annual worldwide consumption of amino acids in the pharmaceutical, chem-

ical and food industries exceeds three million tons. Nanofiltration (NF) is the

most recently developed pressure-driven membrane process, and its application

for the purification and the recovery of amino acids is a viable alternative over

traditional separation processes.

The principal objective of this thesis is to gain insight into the mass transfer phe-

nomena occurring in the NF process, and the application thereof to industrially

relevant batch filtration processes.

Within this work several aspects of amino acid NF are considered. First, the

basic characteristics of numerous commercial polymeric NFand tight ultrafil-

tration membranes are investigated by applying space-charge transport models

and irreversible thermodynamics models. Further, the membrane separation

performance is analyzed based on data obtained from systematic permeation

experiments using diprotic amino acids. A particular attention is paid to con-

centrated systems, since such systems possess considerable industrial interests.

A concept is presented to determine the osmotic pressure of amino acid so-

lutions by altering the stoichiometric coefficient of the van’t Hoff law corre-

sponding to the dissociation state of the amino acids. Starting from the classical

Kedem-Katchalsky equations, a model is developed that allows a simple quan-

tification of the governing phenomena.

Finally, a novel numerical method is introduced for modelling the separation

performance of batch and semi-batch filtration systems, highlighting its main

advantages over analytic solutions. Also optimization techniques are presented

for multi-step batch processes considering economical aspects and technologi-

cal demands.

Keywords: separation, nanofiltration, amino acid, membrane filtration, mass transfer,

modelling, batch process, simulation.

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ZUSAMMENFASSUNG

Der weltweite Verbrauch von Aminosäuren liegt in der Pharma-, Chemie- und

Lebensmittelindustrie bei mehr als drei Millionen Tonnen jährlich. Die Nanofil-

tration (NF) ist das jüngst-entwickelte, druckgetriebeneMembrantrennverfah-

ren. Ihre Anwendung für die Reinigung und die Rückgewinnungvon Amino-

säuren ist eine Alternative gegenüber traditionellen Trennprozesse.

Das Hauptziel dieser Arbeit ist die Ermittlung und modellmässige Beschreibung

der massgeblichen Stofftransportmechanismen im NF-Prozess sowie deren An-

wendung auf industriell relevante Batch-Filtrationsprozesse.

In dieser Arbeit werden verschiedene Aspekte der Separation von Aminosäuren

durch NF behandelt. Durch die Anwendung von Space-Charge Transport Mod-

ellen und Irreversiblen Thermodynamik Modellen werden diegrundlegenden

Eigenschaften der zahlreichen kommerziellen polymeren Nanofiltrations- und

dichten Ultrafiltrationsmembrane untersucht. Mit der Hilfe von Permeation-

sexperimente mit diprotischen Aminosäuren werden Membrane charakterisiert.

Ein besonderes Augenmerk liegt dabei auf konzentrierte Lösungen, da solche

Systeme über beträchtliches industrielles Interesse verfügen.

Ein Konzept für die Berechnung des osmotischen Druck der Aminosäure-Lö-

sungen wird vorgestellt. Dieses basiert auf der Veränderung des stöchiomet-

rischen Koeffizient der van’t Hoff Gleichung, entsprechendder Dissoziation

der Aminosäuren. Ausgehend von den klassischen Kedem-Katchalsky Gle-

ichungen wird ein Modell entwickelt, das eine einfache Quantifizierung des

Stofftransportes durch die Membran ermöglicht.

Schlussendlich wird eine neuartige Methode zur numerischen Modellierung

des Trennverhaltens von Batch und Semi-Batch Filtrationssysteme konzipiert,

wobei die wichtigsten Vorteile gegenüber analytischen Lösungen gezeigt wer-

den. Darauf basierend werden Optimierungsmethode für Multi-Step-Memb-

rantrennverfahren, unter Berücksichtigung ökonomischerAspekte und technol-

ogischen Anforderungen, betrachtet.

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Preface

All the contributions presented in this thesis have previously been accepted or

submitted to leading journals. The papers accepted for publication, in press or

in print are included in the thesis without alteration of content.

⊲ Z. Kovács, W. Samhaber, “Characterization of nanofiltration mem-

branes with uncharged solutes,” inMembrantechnika, 12 (2) (2008)

22–36.

⊲ Z. Kovács, W. Samhaber, “Contribution of pH dependent osmotic

pressure to amino acid transport through nanofiltration membranes,”

in Separation and Purification Technology,, 61 (2008) 243–248.

⊲ Z. Kovács, W. Samhaber, “Nanofiltration of concentrated amino

acid solutions,” inDesalination,, Accepted Manuscript, To appear,

2008.

⊲ Z. Kovács, M. Discacciati, W. Samhaber, “Modeling of amino acid

nanofiltration by irreversible thermodynamics,” inJournal of Mem-

brane Science,, Submitted, 2008.

⊲ Z. Kovács, M. Discacciati, W. Samhaber, “Numerical simulation

and optimization of multi-step batch membrane processes,”in Jour-

nal of Membrane Science,, Accepted Manuscript, Available online

10 July 2008.

⊲ Z. Kovács, M. Discacciati, W. Samhaber, “Mathematical mod-

elling of batch and semi-batch membrane filtration processes,” in

Journal of Membrane Science, Submitted, 2008.

v

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Contents

Abstract i

Preface v

I INTRODUCTION 1Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

II APPENDED PAPERS 21

1 Characterization of nanofiltration membranes with uncharged so-

lutes 23

1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

1.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

1.2.1 Spiegler–Kedem model . . . . . . . . . . . . . . . . . . 27

1.2.2 Models of hindered transport . . . . . . . . . . . . . . . 28

1.2.3 Molecular size . . . . . . . . . . . . . . . . . . . . . . 30

1.3 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

1.4 Results and discussion . . . . . . . . . . . . . . . . . . . . . . 32

1.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

vii

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viii CONTENTS

2 Contribution of pH dependent osmotic pressure to amino acid trans-

port through nanofiltration membranes 43

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

2.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

2.2.1 Osmotic pressure of amino acid solutions . . . . . . . . 46

2.2.2 Permeability equations . . . . . . . . . . . . . . . . . . 48

2.3 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

2.3.1 Materials . . . . . . . . . . . . . . . . . . . . . . . . . 49

2.3.2 Experimental set-up . . . . . . . . . . . . . . . . . . . 50

2.3.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . 51

2.4 Results and discussion . . . . . . . . . . . . . . . . . . . . . . 51

2.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

3 Nanofiltration of concentrated amino acid solutions 59

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

3.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

3.3 Experimental design and procedures . . . . . . . . . . . . . . . 65

3.3.1 Materials . . . . . . . . . . . . . . . . . . . . . . . . . 65

3.3.2 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 66

3.3.3 Vapor pressure osmometry . . . . . . . . . . . . . . . . 66

3.3.4 Membrane permeation procedures . . . . . . . . . . . . 67

3.4 Results and discussion . . . . . . . . . . . . . . . . . . . . . . 68

3.4.1 Vapor pressure osmometry . . . . . . . . . . . . . . . . 68

3.4.2 RO investigations . . . . . . . . . . . . . . . . . . . . . 69

3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

4 Modeling of amino acid nanofiltration by irreversible thermody-

namics 79

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

4.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

4.2.1 Fundamentals of IT theory . . . . . . . . . . . . . . . . 82

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CONTENTS ix

4.2.2 Effect of pH on the osmotic pressure . . . . . . . . . . . 82

4.2.3 Manipulation of the Kedem-Katchalsky (KK) equations83

4.2.4 Estimates of the membrane parameters . . . . . . . . . 86

4.2.5 Development of possible NF models . . . . . . . . . . . 88

4.3 Experimental setting . . . . . . . . . . . . . . . . . . . . . . . 91

4.3.1 Materials . . . . . . . . . . . . . . . . . . . . . . . . . 91

4.3.2 Analyses . . . . . . . . . . . . . . . . . . . . . . . . . 92

4.3.3 Experimental set-up and procedures . . . . . . . . . . . 92

4.4 Results and discussion . . . . . . . . . . . . . . . . . . . . . . 94

4.4.1 Membrane GH: estimate of the transport parameters . . 94

4.4.2 Simulation of separation for the membrane GH . . . . . 95

4.4.3 Estimate of the transport parameters for the membrane

DK . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

4.4.4 Simulation of separation for the membrane DK . . . . . 100

4.4.5 Simulations for the membrane GH with direct parame-

ter estimation . . . . . . . . . . . . . . . . . . . . . . . 100

4.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

5 Numerical simulation and optimization of multi-step batch mem-

brane processes 111

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

5.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

5.2.1 Batch system design . . . . . . . . . . . . . . . . . . . 114

5.2.2 Classical mathematical treatment . . . . . . . . . . . . 116

5.2.3 Development of computational algorithm . . . . . . . . 117

5.2.4 Rejection and flux as functions of feed composition . . .119

5.3 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

5.3.1 Materials . . . . . . . . . . . . . . . . . . . . . . . . . 121

5.3.2 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 121

5.3.3 Experimental set-up and procedure . . . . . . . . . . . 121

5.4 Results and discussion . . . . . . . . . . . . . . . . . . . . . . 123

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5.4.1 Classical mathematical treatment . . . . . . . . . . . . 126

5.4.2 Rejection and flux as function of feed composition . . . 126

5.4.3 Simulation . . . . . . . . . . . . . . . . . . . . . . . . 128

5.4.4 Optimization . . . . . . . . . . . . . . . . . . . . . . . 129

5.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

6 Modeling of batch and semi-batch membrane filtration processes 137

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

6.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140

6.2.1 Batch and semi-batch operations . . . . . . . . . . . . . 140

6.2.2 Mathematical modeling . . . . . . . . . . . . . . . . . 141

6.2.3 Computational algorithm . . . . . . . . . . . . . . . . . 144

6.2.4 Permeate flux and rejection . . . . . . . . . . . . . . . . 145

6.3 Materials and methods . . . . . . . . . . . . . . . . . . . . . . 150

6.3.1 Solution procedure for the IT model . . . . . . . . . . . 152

6.3.2 Solution procedure for the DSPM-DE model . . . . . . 152

6.4 Results and discussion . . . . . . . . . . . . . . . . . . . . . . 154

6.4.1 Empirical approach . . . . . . . . . . . . . . . . . . . . 154

6.4.2 Model validation . . . . . . . . . . . . . . . . . . . . . 157

6.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160

.1 Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . 161

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

III SYNOPSYS 169Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182

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Part I

INTRODUCTION

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Introduction

Membrane filtration is a rapidly emerging technology. Although it was not con-

sidered a technically relevant separation process until approximately 40 years

ago [1], nowadays membranes are widely used for industrial separations. A

broad range of membranes with different specifications are offered by various

manufactures, which makes membrane filtration suitable forspecific industrial

separation demands. Since pressure driven membrane processes constitute a

separation without phase or temperature change, they can becharacterized by

their low specific energy consumption. It might offer potential advantages over

more conventional separation processes in respect to modular construction, low

maintenance, simple integration in existing processes, low running costs and

economical operation also in small scale [2]. Many textbooks have been written

on the basic mechanisms and various applications of membrane-based separa-

tion processes [1, 3–5] including description of membrane materials, membrane

preparation, element types and module design, etc. A state-of-the-art review of

these aspects is beyond the scope of this thesis.

Nanofiltration (NF) is the most recently developed conventional pressure driven

membrane process, and its properties lie between ultrafiltration (UF) and re-

verse osmosis (RO). The termnanofiltration itself was introduced by the mem-

brane manufacturer FilmTec highlighting that such membranes are capable to

retain uncharged molecules with the size of about 1 nm, and which corre-

sponded well with the early predictions of Sourirajan and Matsuura about the

membranes’ hypothetical capillary pore size [6]. With NF membranes, selec-

tive solute separations based on charge and molecular size differences are pos-

3

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sible. Due to its potential advantages, NF has gained a strong market position,

brought about a number of patents, industrial research projects and commercial

installations [7]. NF systems are usually operated at medium pressures in the

range of 10-40 bar, and have much higher water fluxes comparedto RO mem-

branes. NF can be applied for separation between ions with different valences

and for separation of low- and high-molecular weight components. Polymeric

NF membranes show diversity in separation behaviour but they are common in

rejecting highly charged ions (such asSO2−4 ,CO2−

3 ,PO3−4 ) in a higher degree,

while in comparison, rejection of single charge ions (Cl−, Na+, K+) is much

less. NF also rejects uncharged, dissolved material and positively charged ions

according to the size and shape of the molecule in question [4]. The transporta-

tion of non-charged solutes through an NF membrane is usually characterized

by the term of molecular weight cut-off, which is in the rangeof about 200-

1000 Dalton. These important features qualify NF for the separation of small

charged biomolecules, such as amino acids.

NF separation is industrially implemented, and is generally considered as proven

technology. However, despite the extensive use of NF, the mechanism of trans-

port through NF membranes has not been yet explored in details [8, 9]. At a

fundamental level, NF is a very complex process. Several models have been

proposed for NF so far, which can be divided into two main types: transport

mechanism models and irreversible thermodynamics models (IT).

The fundamental models derived from the irreversible thermodynamics are the

Kedem-Katchalsky model [10, 11] and the Spiegler-Kedem model [12]. This

phenomenological approach treats the membrane as a black box. Thus, the

mechanism of transport and the structure of the membrane areignored. IT

models have been applied in predicting transport through NFmembranes for

single and binary solute systems [13, 14], most recently formultiple systems

[15, 16] and also for industrial feeds [17–20].

As far as transport mechanism models are concerned, a conceptual difference

in the modelling approach is taken. With respect to the fundamentals of the NF

process, major progress has been made since the early nineties [24]. The main

advantage of this type of models is that the model parametersare better related

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to the structural and electrical properties of the membranes. Many charged

transport theories have been proposed so far [21]. These models account for

electrostatic effects as well as for diffusive and convective flows. The early

investigators Lakshminarayanaiah [22] and Dresner [23] described the possible

utilisation of the extended Nernst-Planck equations for the prediction of solute

ion fluxes. Since then, various possible approaches to the description of NF

using the extended Nernst-Planck equation [25–29] have been presented. The

extended Nernst-Planck model is able to predict correctly the trends expected

for ionic solute rejection, including conditions under which a negative rejection

is obtained. In the last ca. 10 years many papers were published on modeling of

different solute-systems [30–36]. The model is still in thestage of development

and requires direct methods to estimate model parameters instead of collecting

experimental data, however, it has became an important toolfor the quantitative

prediction of NF.

As for all current descriptions of NF, the modelling approaches are more de-

scriptive than truly predictive due to the utilisation of empirical fitting param-

eters [6]. Despite the considerable progress in the development of transport

models, at present, it is difficult to accurately predict theperformance of NF

membranes when complex solutions consisting of more solutes are to be pro-

cessed, since the mass transfer through the membrane is influenced by the size,

the charge, the nature of the components and their interactions with each other

and with the membrane. As a result, currently piloting is highly recommended

for NF applications.

Since the mid eighties, NF processes have gradually found their way into in-

dustrial applications in various fields such as food [37, 38], paper [39], tex-

tile [40], (bio-)pharmaceutical [41, 42] and chemical industry [43]. Compre-

hensive description of NF applications can be found in textbooks and review

articles [6, 24, 37, 44], here we only collect some relevant perspectives of NF

utilization. Typical NF applications include desalination of dyestuffs [45], reuse

of CIP solutions [46], concentration of thin sugar liquor [47], treatment of alka-

line process liquors [48], pulp-bleaching effluents from the textile industry [40],

demineralization of whey [49], metal and acid recovery [50], trace contaminant

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removal [51], non-aqueous NF applications [52], etc. NF membranes can re-

move hardness, organics and particulate contaminants fromwater [44], thus it

can be used to treat all kinds of water including ground water[53, 54], surface

water [55, 56], and wastewater [57, 58]. In addition, NF is used as a pretreat-

ment in desalination processes to lower the required operational pressure in sea

water RO plants, and to prevent fouling and scaling [59, 60].

Amino acids are used in large quantities as raw material and active ingredients

in the pharmaceutical, food and chemical industry. In the area of biotechnol-

ogy they are also essential compounds in most fermentation and cell cultivation

processes. There are 20 DNA-encoded amino acids but the number of man-

made unnatural amino acids is over a few hundred. With the exploitation of

new uses of amino acids and the large progress in production technology, the

market for amino acids in general is said to double every decade [61]. The

worldwide annual consumption of amino acids in the pharmaceutical, cosmetic,

and food industries was 3.3 million tons in 2005 [62]. Due to the diverse oc-

currence of amino acids in such industrial processes, downstream and upstream

systems with various composition of these species in aqueous media or in differ-

ent solvents are present, where the purification of intermediates, side and final

products is a considerable challenge. The growing interestin the utilization

of NF membranes mainly stems from their unique physical properties, making

them especially well suited for applications separating small biomolecules, like

amino acids. Chromatography, evaporation, ion-exchange,distillation and ex-

traction techniques are commonly used in the purification step, which are often

the bottle-neck of the synthesis processes, due their limitations in high yield and

economical efficiency. The utilization of NF for the purification and recovery

of amino acids is a viable alternative over more traditionalseparation processes.

The potential use of NF for amino acid processing has been recently studied

and discussed by several authors, which had covered the fieldof enzymatic glu-

tathion synthesis [63], separation of glutamine from fermentation broth [64], as-

partame production [17], fractionation of protein hydrolysates [65–67], cofactor

regeneration in L-tert-leucine enzymatic synthesis [68].A number of inventions

related to amino acid NF are patented. These include processes to improve clar-

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ity and color of green tea extract [69], to purify dipeptide from its monomeric

amino acid building blocks [70], to treat protein hydrolyzates [71–73], and to

recover betaine from sugar beet-derived solution [74].

Although in industrial processes mostly concentrated systems are processed,

most of the NF studies in the open literature are dealing withhighly diluted

aqueous amino acid solutions, and only a little effort was made trying to clarify

the effect of increasing feed concentration in respect to the charged state of

amino acids. In particular, very few reports are available on diprotic amino

acids. Moreover, no quantitative description of amino acidtransport through

NF has been given so far. Obviously, the formulation of such amathematically

consistent description of rejection and permeate flux is an essential step towards

practical applications.

The operating concept of NF plants can be continuous or batch. The latter

strategy is considered in this thesis. Batch system design is of both industrial

and academic interest. It is a well established technique and has found many

applications in the food and beverage, chemical, biotechnological and pharma-

ceutical industries [75]. In comparison with continuous processes, batch oper-

ations are particularly suited to small-scale operations,require less expensive

automatic controls, and allow a reduced membrane area in order to reach the

target [3].

In batch membrane system design, a common separation strategy for selective

removal of components with low retentions is to employ a multi-step membrane

process. A multi-step batch process is a chain of operationsof defined number

and order, which are carried out consecutively using the same membrane mod-

ule. There are two basic operation modes: the concentrationand the dilution

mode. In general, a multi-step process consists of three steps (or operations):

(1) pre-concentration, (2) dilution mode and (3) post-concentration. This con-

cept is one of the conventional process techniques to achieve high purification

of macro-solutes with an economically acceptable flux [76].

Among the various batch design modes, the concentration mode and the con-

stant volume dilution mode (or the combination of the two which is usually

referred as diafiltration) have been in the center of scientific interest and ana-

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lyzed in detail by many authors [30, 35, 75, 77–83]. Most recently, attention

has been raised on the mathematical modelling aspects of thevariable volume

dilution mode, as an alternative way for concentration of macrosolute and si-

multaneous removal of microsolute [84–86]. In contrary, much less literature

are available on semi-batch process performances.

Many studies have provided mathematical descriptions of batch processes. The

computation of the changes of solutes and volume in the feed tank during the

process is based on mass balance. This results in a set of equations involving

coefficients which describe the rejection of the solutes. Such coefficients are

usually determined from experiments with the process liquor, and based on the

experimental results, mean rejection values are calculated which characterize a

whole process step. Apart from a few studies [30, 87], the reflection coefficients

are considered to be constant in the mathematical handling.In the cases where

the rejections of the solutes are strongly varying in the function of their feed

concentrations, and a considerably interdependence in their permeation occurs,

the simulation based on constant coefficients and the subsequent optimization

might lead to inaccurate results. In order to express the rejections as state func-

tions of the actual feed concentrations and incorporate them in unit operation

design, numerical techniques have to be applied. A further description of this

aspect will be given in the thesis.

The scope of the thesis

The principal objective of this thesis is to gain insight into the mass transfer phe-

nomena occurring in the NF process, and the application thereof to industrially

relevant batch filtration processes.

Within this work several aspects of amino acid NF are considered. Both basic

research and applied research related problems are discussed. It comprises the

following main components:

(i) Characterization of the basic properties of NF membranes with neutral

solutes and electrolytes.

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9

(ii) Experimental investigation of amino acid permeation.

(ii) Mathematical modeling of transport phenomena.

(iv) Simulation and optimization of industrially relevantbatch and semi-batch

filtration processes.

This dissertation project comprises a series of scientific papers. The papers

submitted or accepted for publication, in press or in print,are included in the

thesis without alteration of the original content. The research itself primarily

focuses on innovative ideas and experimental work which advance the field of

NF separation and lead to conclusive and publishable results. A brief overview

of the chapters focusing on internal coherence is presentedin the next section.

Thesis outline

This thesis addresses several aspects of amino acid nanofiltration. Essentially,

amino acids are ionizable organic compounds of different molecular sizes. Their

electrical properties can be controlled by the pH. Thus, they show similarities

with the properties of both electrolytes and neutral molecules. Since the solute

permeation through NF membranes is predominantly influenced by the size and

the charged state of the solutes, it is of great importance tounderstand the NF

separation mechanism of such species, and to gain information which is trans-

ferable to describe amino acid transport. Therefore, the basic characteristics of

NF membranes are investigated using different neutral solutes and electrolytes.

Electrokinetic space-charge models and irreversible thermodynamics models

were applied to characterize numerous commercial polymeric NF and tight UF

membranes.

In Chapter I we investigate the separation behaviour of NF membranes us-

ing experimental permeation data of six noncharged solutes. For this purpose,

an indirect characterization method is applied using two types of steric pore

flow models. Five commercial polymeric NF and dense UF membranes are

characterized with their hypothetical pore sizes, and their molecular cut-off

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10

values are determined. As far as charged components are considered, many

studies have been examined their transport through NF membranes, and it is

a relatively well-established field of the discipline. We examine the relevant

models later inChapter VI . The principle aim of this investigation is to com-

pare two mainstream models on the basis of their applicability for simulation

of industry-related separation processes. The two models are the irreversibly

thermodynamics models originally introduced by Kedem and Katchalsky [11],

and the linearized Donnan-steric-pore-dielectric-exclusion model pioneered by

Bowen et. al [29]. These models are compared on the basis of complexity,

required input data, necessary a-priori experiments, quality of the representa-

tion of the observed transport phenomena, and constancy of fitting parameters

(especially their concentration-dependence). The main objective is to examine

how the transport parameters are related to structural and electrical properties

of the membrane, and whether the information gained is transferable for other

solute systems. Although there might be no straightforwardrelation between

amino acid transport and the permeation of the examined salts and noncharged

compounds, it should be pointed out, that NF is unlikely to beapplied only for

solvent removal from amino acids, but rather for separatingamino acids from

other components which differ in size or electrical sign. Thus, the evaluation of

transport mechanism of such solutes and the examination of modeling method-

ologies have considerable relevance for future applications.

The core of this thesis includingChapters II, III and IV deals with amino

acids, and targets the evaluation of the major factors affecting the separation.

Chapter II presents permeation experiments using aqueous alanine solutions.

A concept is delivered to determine the osmotic pressure of amino acid solutions

by altering the stoichiometric coefficient of the vant’t Hoff law corresponding to

the dissociation state of the amino acids. The effect of pH onthe osmotic pres-

sure, and thus, on the separation is pointed out. Building onthe achievements

of this chapter,Chapter III comprises further investigations of the underlying

transport phenomena. Systematic permeation experiments of aqueous solutions

of diprotic amino acids (L-glutamine and glycine) were carried out in order to

determine the permeate flux and the rejection as a function ofincreasing feed

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11

concentration and ionization state. While the experimentspresented inChapter

II were carried out in concentration mode, here steady state total-recycle-mode

operations are provided. Differences in the separation behavior of numerous

membranes, as well as differences in the filtration of highlyconcentrated and

diluted systems are discussed. So far, apart from a few limited studies, only

highly diluted solutions have been considered in the literature, although sep-

aration and purification of concentrated systems possess particular industrial

interests. Thus, the concentration of amino acids in the whole range of their sol-

ubility is studied, and the effect of dissociation state related to the feed concen-

tration is discussed in detail. Moreover, the osmotic pressure model is verified

by vapor pressure osmometry and reverse osmosis experiments. Chapter IV is

a theoretical analysis of the results obtained from the permeation experiments.

Starting from the classical Kedem-Katchalsky model, an equation is derived to

compute the permeate flux and the rejection of diprotic aminoacid compounds.

We discuss the influence of the pH and the feed concentration of the solution

on the transport parameters which characterize the membrane, and we improve

the basic equation by accounting for these dependencies. Two possible strate-

gies are proposed to estimate the transport parameters fromexperimental data.

Finally, we compare the numerical simulations that we obtained using the pre-

dictive models with the experimental data measured in our laboratory.

Chapter V and VI moves away from basic research oriented problems towards

applied research related fields. These chapters primary focus on the devel-

opment of a novel numerical technique for batch system design. The simu-

lation and optimization of the classical multi-step batch processes including

pre-concentration, dilution mode and post-concentrationsteps is presented in

Chapter V, andChapter VI provides a global model which can be used for

quantitative prediction of all batch and semi-batch operations. The permeation

experiments were carried out using a synthetic test solution prepared with an

organic molecule and an inorganic salt. It should be pointedout, that these

chapters strictly focus on an innovative mathematical approach for attacking the

chemical engineering problem, and the essential role of thepermeation exper-

iments is to prove the validity of the investigated mathematical models. How-

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12

ever, the studied system shows considerably similarities between amino acid

solutions, and obviously, the application of the provided methods to amino acid

solutions is trivial. The presented simulation technique accounts for variable

solute rejection coefficients, and uses the feed concentrations as a basis for the

calculations, rather than the concentration factor. The approach presented in

these chapters has a modular structure. The design equations describing the en-

gineering aspects of batch and semi-batch systems are handled separately from

the estimation methods describing the mass transfer through the membrane.

Chapter VI shows how the achievements in basic research can be integrated

and used for batch and semi-batch system design. Thus, the theoretical models

analyzed in the previous chapters, such as irreversible thermodynamics models

and electrokinetic space-charge models, can be applied in the proposed sim-

ulation technique and used for the design of industrially relevant membrane

filtration processes.

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20

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Part II

APPENDED PAPERS

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Page 35: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

1Characterization of nanofiltration

membranes with uncharged solutes

Reprinted from: Z. Kovács, W. Samhaber, Characterization of nanofiltration

membranes with uncharged solutes, Membrántechnika 12(2),22–36, 2008.

The transportation of non-charged solutes through nanofiltration (NF) mem-

branes is usually characterized by the term of molecular weight cut-off (MWCO)

that is in the range of about 200-1500 Dalton. However, thereare currently

no standard methods for characterizing and reporting MWCO.The meaning

of this information can vary between different membrane manufactures, and

the applied experimental technique has a significant impacton the measured

MWCO value. In this study, the separation performances of five commercial

NF and tight ultrafiltration membranes (DK, GE, GH, NP030, NP010) were in-

23

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24 CHAPTER 1.

vestigated using experimental permeation data of six noncharged solutes with

various molecular weights. The membranes were characterized with their hy-

pothetical pore sizes and their MWCO values were determinedusing two types

of steric pore flow models, the steric-hindrance-pore (SHP)and the Donnan-

steric-pore (DSP) model. Thermodynamical analysis of the experimental data

was performed in order to obtain the reflection coefficients of the solutes, and

the obtained phenomenological parameters were then linkedto the membrane

structural parameters. The overall best-fitting pore size radii in a least-squares

sense were computed for each membrane by fitting to the sets ofexperimental

data of reflection coefficients and solute radii. The predictions of both DSP and

SHP models were found to be in a good agreement with the experimental data.

However, a significant difference was found in the estimatedpore size values

depending on which measure of the solute size was employed and depending

on the applied models. The provided values of membrane pore size can be used

to predict the rejection of any noncharged solute for a givenapplied pressure.

1.1 Introduction

Nanofiltration (NF) membranes are a relatively recent development in the field

of pressure-driven membrane separations, and their properties lie between ul-

trafiltration (UF) and reverse osmosis (RO). Due to its potential advantages, NF

has gained a strong market position, brought about a number of patents, in-

dustrial research projects and commercial installations [1]. Starting in the late

sixties, NF membrane processes have gradually found their way into industrial

applications in various fields such as water softening, dye recovery, treatment of

metal contained waste waters, oil-water separation, demineralization of whey,

recycle of nutrients in fermentation processes, purification of landfill leachate,

removal of sulfates from sea-water, bioproduct separation[2].

NF systems are usually operated at medium pressures in the range of 10-50

bar, and have much higher water fluxes compared to RO membranes. NF can

be applied for separation between ions with different valences and for separa-

tion of low- and high-molecular weight components. Polymeric NF membranes

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1.1. INTRODUCTION 25

show diversity in separation behaviour but they are common in rejecting highly

charged ions (such asSO2−4 , CO2−

3 , PO3−4 , Mg2+) in a higher degree, while

in comparison, rejection of single charge ions (Cl−, Na+, K+) is much less. NF

also rejects uncharged, dissolved material and positivelycharged ions according

to the size and shape of the molecule in question [3].

The transportation of non-charged solutes through an NF membrane is usually

characterized by the term of molecular weight cut-off (MWCO), which is a

number expressed in Dalton indicating the molecular weightof a hypothetical

non-charged solute that is in 90% rejected. The MWCO of NF membranes is

usually given by the manufacturers and typically in the range of about 200-

1500 Dalton. However, there are currently no standard methods for character-

izing and reporting MWCO. The meaning of this information can vary between

different membrane manufactures, thus limiting its value.The applied experi-

mental technique has a significant impact on the measured MWCO. The exper-

imental conditions, such as the hydrodynamic flow conditions, the temperature,

the applied pressure or the range of the applied pressure-scan, the type of so-

lute(s), are often not reported. Besides, the different techniques for MWCO

make membranes from different manufacturers hardly comparable without fur-

ther experimental investigations. Moreover, the concept of MWCO does not

address the question of how great the permeation of solutes smaller and larger

than the indicated MWCO can be.

Membranes have been historically characterized by MWCO rather than by mem-

brane pore size [4]. It should be noted that this concept is based on practi-

cal aspects and has no true physical meaning. The molecular weight is not a

straightforward meausre of the size and it ignores the shapeof the permeating

molecule, and thus, it gives only a rough estimation of the membrane’s ability

to remove dissolved uncharged components.

The termnanofiltration was introduced by the membrane manufacturer FilmTec

highlighting that such membranes are capable to retain uncharged molecules

with the size of about 1 nm, and which corresponded well with the early predic-

tions of Sourirajan and Matsuura about the membranes’ hypothetical capillary

pore size [5]. However, it is still the subject of scientific debates whether NF

Page 38: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

26 CHAPTER 1.

membranes can be considered as porous or nonporous media.

Several direct characterization methods are known for NF membranes such as

permporometry, gas adsorption-desorption and microscopytechniques. How-

ever, the pore size determination of polymeric membranes seems to be still an

unsolved problem. Permporometry analysis requires pores larger than 2 nm [6],

and the nitrogen adsorption-desorption method only for inorganic membranes

can be effectively applied. As far as microscopy is concerned, Bowen et al. [7]

analysed the structural parameters of NF membranes with atomic force mi-

croscopy (AFM) and claimed that AFM images provide direct confirmation of

the presence of discrete pores of nanometre dimensions in such membranes.

However, the authors reported that AFM can only give information of the sur-

face pore dimensions as the tip cannot probe into the depth ofthe pore. Singh

et al. [8] also pointed out that an important requirement forAFM pore size de-

termination is a very low surface roughness, hence it is difficult to distinguish

between the pores and the depressions in the membrane surface.

Models that adequately describe the separation behaviour of membranes are

important since these are needed in the design of NF processes. NF is a complex

process lying between UF and RO, thus models from both these areas and their

combinations can be used to describe NF performance. These models rely on

fundamentally different concepts and can be divided into the following types:

irreversible thermodynamics models, nonporous or homogenous models, and

pore models.

The properties of dry membranes are subject to changes in thepresence of wa-

ter. Thus, during the filtration, a swollen polymeric network is obtained which

likely does not contain discrete pores. [5] In contrary to polymers, the morphol-

ogy of inorganic membranes does not change by contacting with water. Well

established characterization methods prove that inorganic NF membranes con-

tain discrete pores in the order of 0.5 to 2 nm. Despite this morphological dif-

ference, both type of membranes show very similar separation behaviours, and

their performance can be predicted with the same models assuming hypotheti-

cal pores in the near- or sub-nanometre range. However, in the pore models, the

terms ’pore’ or ’capillary’ refer to any connecting polymermaterial-free void

Page 39: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

1.2. THEORY 27

space through which fluid transport can take place under a driving force [9].

In this paper we investigate the separation behaviour of NF membranes using

experimental permeation data of six noncharged solutes. Weuse an indirect

characterization method employing two types of steric poreflow models which

are described in Sect.1.2.2, and we discuss possible concepts for solute size

determination in Sect.1.2.3. We characterize five NF and tight UF membranes

with their hypothetical pore sizes and determine their MWCOvalues with the

different models.

1.2 Theory

1.2.1 Spiegler–Kedem model

The Spiegler–Kedem model (SK) [10] is based on the principles of irreversible

thermodynamics and has found a wide use for the description of RO and NF

membrane separations. This phenomenological approach treats the membrane

as a black box, and no insight is given into the membrane structure and mor-

phology. The relation between the rejectionR and the solvent volume fluxJv

is given by the expression:

R =

σ

(

1 − exp

(

σ − 1

PsJv

))

1 − σ exp

(

σ − 1

PsJv

) , (1.1)

where the two membrane parameters are the reflection coefficient σ and the

solute permeability coefficientPs.

The rejection is defined as

R = 1 − cp/cr, (1.2)

wherecp andcr represent, respectively, the solute concentrations in theperme-

ate and retentate streams.

Page 40: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

28 CHAPTER 1.

1.2.2 Models of hindered transport

The modelling of solute transport through the membrane is based on the ex-

tended Nernst–Planck equation accounting for diffusion, convection and elec-

tromigration. For uncharged species, when electrostatic effects are negligible,

the transport equation for the molar solute fluxjs is given as the sum of the

diffusive and the convective terms as follows

js = KccV −Dpdc

dx, (1.3)

whereV is the solvent velocity,Kc is the convective hindrance factor andDp is

the hindered solute diffusivity in the membrane pores. Thislatter is given as the

product of the bulk diffusivityD∞ and the diffusive hindrance factorKd, and

corrected with the factorη0/ηp which accounts for the solvent pore viscosityηp

versus the bulk viscosityη0. There it holds:

Dp = KdD∞

η0ηp. (1.4)

The Donnan-steric-pore-model (DSP) was originally developed by Bowen et

al. [7]. They have introduced the following relationships between the ratio of

solute to pore radiusλ and the hindrance factorsKc andKd:

Kc = (2 − Φ)(

1 + 0.054λ− 0.988λ2 + 0.441λ3)

, (1.5)

Kd = 1 − 2.30λ+ 1.154λ2 + 0.224λ3, (1.6)

where the steric partitioning coefficientΦ (neglecting concentration polarisaton)

is given as

Φ = (1 − λ)2. (1.7)

The model assumes a fully developed solute velocity inside the pores and as-

sumes a Hagen-Poiseuille type parabolic profile. The solvent velocity in cylin-

drical pores with constant circular cross-sections can be obtained from the Hagen-

Poiseuille law:

V =r2p (∆P − ∆π)

8ηp (∆x/Ak)(1.8)

Page 41: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

1.2. THEORY 29

wherex/Ak is the ratio of effective membrane thickness to membrane porosity,

ηp is the solvent viscosity in the pore,∆P is the applied pressure, and∆π is

the osmotic pressure difference across the pore.

The bulk solvent properties can significantly differ from the properties of thin

liquid layers present in narrow pores. In a recent study of Bowen et al. [11],

the ratio of bulk solvent viscosityη0 and pore viscosityηp was expressed as a

function of pore sizerp in the following form:

ηp

η0= 1 + 18 (d/rp) − 9 (d/rp)

2, (1.9)

whered is the thickness of oriented solvent layer.

Eq.(1.8) can be introduced into Eq(1.3), and since the solute flux can be rewrit-

ten asjs = cpV , the integration of the concentration gradient across the mem-

brane thickness yields:

R = 1 − KcΦ

1 − (1 −KcΦ) exp (−Pem), (1.10)

where the modified dimensionless Peclet numberPem is defined as

Pem =KcV∆x

KdDpAk, (1.11)

and indicates the relative importance of convection over diffusion.

Thus, Eq. (1.10) allows us to determine the limiting rejection:

Rlim = 1 −KcΦ. (1.12)

A similar approach to Bowen et al. [7] was used by Nakao et al. [12] to develop

the steric-hindrance pore (SHP) model, which was later applied by Wang et

al. [13] to predict the separation performance of NF membranes. In the SHP

model, the phenomenological coefficientσ obtained from the Spiegler–Kedem

analysis is linked to the membrane morphological parameterλ as follows:

σ = 1 −(

1 +16

9λ2

)

(1 − λ)2[

2 − (1 − λ)2]

(1.13)

Note that as far as neutral solutes are considered, Eq.(1.13) only differ from

Eq.(1.12) in the analytical expressions forKc andKd described in Eqs. (1.5).

Page 42: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

30 CHAPTER 1.

More detailed description of the SHP model can be found in other studies [12–

14].

It should be pointed out that these models assume a sphericalsolute transport in

paralel cylindrical membrane pores with identical and constant circular cross-

sections. Pore size distribution is not considered in this paper.

1.2.3 Molecular size

Several measures of the molecular size are known such as the Stokes radius, the

diameter derived from the hydrodynamic volume or from molarvolume, the

effective diameter, and the molecular width [15]. Among them, the effective

diameter was found by Van der Bruggen et al. [16] to be the mostsuitable for

describing filtration phenomena, as it reflects the projection of the molecule on

the membrane. An empirical correlation between the effective radiusrE and

the molecular weightMw was determined as follows [15]:

rE = 0.0325(Mw)0.438. (1.14)

The Stokes radiusrS for the uncharged molecules at a given molecular weight

Mw can be determined by using the following empirical relationgiven by

Bowan et. al. [17]:

log rS = −1.4854 + 0.461 log(Mw). (1.15)

Finally, the relation between the diffusivity and molecular size can be calculated

with the Stokes–Einstein equation:

D∞ =kT

6rSπη. (1.16)

1.3 Experimental

Five commercial polymeric NF and tight UF membranes were employed in this

study. The membrane specifications given by the manufacturers are shown in

Table 1.1.

Page 43: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

1.3. EXPERIMENTAL 31

Table 1.1: Membrane specifications given by the manufacturers

Name DK GE (G-5) GH (G-10) NP030 NP010

Manufacturer GE W&P Technologies Microdyn-Nadir

Internet http://www.geawater.com http://www.microdyn-nadir.com

Material of separa-

tion layer

proprietary permanently hydrophilic PES

Retention of un-

charged solutes

150-3001 10002 25002 70–903 25-453

Pure water flux

[L/h/m2/bar]

5.5± 25% 1.2± 25% 3.2± 25% 1–1.8 5–10

Classification NF UF UF NF NF1 MWCO [Da] characterized on glucose and sucrose

2 MWCO [Da] characterized on polyethylene glycol

3 Lactose rejecton [%] (test conditions: 4% solution, 40 bar,stirred cell (700 rpm), 20oC)

Chemicals of analytical degree used in the experiments werepurchased from

Sigma–Aldrich and Serva–Feinbiochemica. Their properties are shown in Table

1.3. Membrane filtration was performed using the experimental set-up shown

Table 1.2: Molecular weights, effective and Stokes radii, and diffusivities of neutral

solutes in aqueous solutions at 25oC.

Solute Mw [g/mol] rE1 [nm] rS

2 [nm] D∞

3 [10−9m2/s]

n–Butanol 74.1 0.21 0.24 1.03

D–Ribose 150.1 0.29 0.33 0.74

D–Glucose 180.2 0.32 0.36 0.68

D–Lactose Monohydrate 360.3 0.43 0.49 0.50

Polyethylene glycol 570–630 0.54 0.62 0.39

Dextran ≈ 900 0.64 0.75 0.331 calculated with Eq.(1.14);2 calculated with Eq.(1.15);3 calculated with Eq.(1.16)

in Fig.1.1. The membrane unit is equipped with a DDS LAB20 plate-and-frame

module. Membrane discs with the effective membrane surfacearea of 350 cm2

were placed in series and simultaneously tested. Single-component solutions of

100 ppm concentration were used. Both permeate and retentate streams were

recycled into the feed tank. The cross-flow rate was set to 500L/h which en-

sures a negligible concentration polarisation effect [18]. During the filtration

Page 44: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

32 CHAPTER 1.

Figure 1.1: Schematic diagram of the lab-scale membrane system

experiments the applied trans-membrane pressure was changed between 0 and

40 bar. In all runs, stabilization time of 30 minutes was usedbefore taking sam-

ples. Permeate flux was manually measured by using a calibrated cylinder and

a stopwatch. Concentrations of solutes were determined by total organic carbon

analyzer (TOC 500, Shimadzu). All experiments were carriedout at 25oC.

1.4 Results and discussion

The measured permeate fluxes versus applied pressure for thefive membranes

are shown in Fig.1.2. The slopes of the curves are equal to thehydraulic perme-

ability of the respective membranes, which indicates that the osmotic pressure

effects of the solutes are negligible due to the low feed concentrations. For

each sets of measured data of fluxJv and the rejectionR, Eq.(1.1) was used to

compute the values of the membrane parametersσ andPs with nonlinear two-

parameter fitting in a least-squares sense. Theσ corresponds to the maximum

rejection at infinite volume flux. The results of the SK analysis are illustrated

Page 45: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

1.4. RESULTS AND DISCUSSION 33

0 0.5 1 1.5 2 2.5 3

x 106

0

0.2

0.4

0.6

0.8

1x 10

−4

trans−membrane pressure [Pa]

perm

eate

flux

[m/s

]

DKGEGHNP030NP010

Figure 1.2: Measured fluxes of lactose solution (symbols) and predictedfluxes based on

pure water permeability (solid lines) for the 5 membranes.

in Fig.1.3 using the permeation data of lactose as an example.

0 2 4 6 8

x 10−5

0

0.2

0.4

0.6

0.8

1

permeate flux [m/s]

reje

ctio

n [−

]

DKGEGHNP030NP010

Figure 1.3: Experimental data (symbols) of lactose rejection as function of flux for the

5 membranes. Solid lines were fitted using the SK model.

Page 46: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

34 CHAPTER 1.

Prior to the steric pore model analysis, two main steps were performed. First,

the reflection coefficients of the 6 solutes were determined for the 5 membranes

using the SK model. Second, the Stokes radiirS and the effective radiirE of all

solutes were calculated from Eq.(1.15) and Eq.(1.14), respectively. Thus, using

the solute radius and the respective reflection coefficient allow us to determine

the hypothetical pore size for each membrane.

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

Stokes radius [nm]

σ [−

]

DKGEGHNP030NP010

Figure 1.4: Relationship between reflection coefficient (e.g. limitingrejection) and

Stokes radii of solutes. The optimal estimates for the pore radii of the five membranes

were provided from the model proposed by Bowen et al. using Eq(1.12). Solid lines

illustrate model predictions with the best fittingrp values.

The DSP model using Eq.(1.10) or alternatively, the SHP model using Eq.(1.13)

can be fitted to the reflection coefficient of each uncharged solute individually

in order to estimate the pore size. This would result in slightly different esti-

mated pore size values for each solute and an average value could be calculated

to characterize each membrane. Nevertheless, in this study, the reflection coef-

ficients of all solutes were considered to compute the pore size of each mem-

brane, which gives the overall best-fitting solution in a least-squares sense.

The predictions of the DSP and the SHP models compared with the experimen-

tal data are shown in Fig.1.4 and Fig.1.5, respectively. Thequality of the fit can

Page 47: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

1.4. RESULTS AND DISCUSSION 35

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

0.2

0.4

0.6

0.8

1

effective radius [nm]

σ [−

]

DKGEGHNP030NP010

Figure 1.5: Relationship between reflection coefficient (e.g. limitingrejection) and ef-

fective radii of solutes. The optimal estimates for the poreradii of the five membranes

were provided from the SHP model using Eq(1.13). Solid linesillustrate model predic-

tions with the best fittingrp values.

be described with the coefficient of determinationR2 defined as

R2 = 1 −∑

i

(σi − σ∗

i )2/∑

i

(σi − σ)2, (1.17)

whereσ, σ∗ and σ are the experimental, the modelled, and the mean of the

experimental values, respectively. Using the determined pore sizes in the mod-

els allows us to compute the size of the molecule that has a limiting rejection

of 90% and thus, the empirical relations described in Sect.1.2.3 can be used to

calculate the MWCO from the solute radius. The obtained dataof rp, MWCO

andR2 are listed in Table 1.4 for three different approaches. Overall, very good

approximates of the measured data are given by both models. However, the

pore sizes estimated by the DSP model are considerably bigger than the SHP

model predictions. There is also a significant difference inthe estimated pore

size values depending on which measure of the solute size wasemployed in

the SHP model. The overall fittings of the studied two models are shown in

Fig. 1.6 and Fig. 1.7. The estimated pore radii of the membranes listed in Table

Page 48: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

36 CHAPTER 1.

Table 1.3: Estimated hypothetical pore sizes of the five membranes obtained from SHP

and DSP models using experimental data of neutral solutes.

SHP model DSP model

using effective radius using Stokes radius using Stokes radius

membrane rp[nm] MWCO R2 rp[nm] MWCO R2 rp[nm] MWCO R2

GE 0.46 290 0.954 0.52 280 0.951 0.70 380 0.912

DK 0.39 200 0.940 0.44 200 0.925 0.55 230 0.807

GH 0.73 840 0.980 0.85 820 0.976 1.14 1100 0.923

NP030 0.59 520 0.915 0.68 500 0.917 0.93 700 0.934

NP010 0.80 1040 0.973 0.93 1010 0.976 1.29 1400 0.949

0 0.2 0.4 0.6 0.8 1 1.20

0.2

0.4

0.6

0.8

1

λ [−]

σ [−

]

DKGEGHNP030NP010SHP

R2=0.9613

Figure 1.6: Reflection coefficients of all solutes as a function of ratio of Stokes radii of

the solutes to the pore radii of the five membranes. The curve was calculated from the

SHP model with Eq.(1.13) using the pore radiirp reported in Table 1.4.

1.4 and the Stokes radii as the measure of solute size were used to computeσ

for each solute and for each membrane. Then,σ was plotted as a function of

λ. As shown in Fig. 1.6 and Fig. 1.7, the experimental values ofσ are in good

agreement with the estimatedσ values irrespective of which solute and mem-

brane was applied. It is important to note that combining Eq.1.8, Eq. 1.10 and

Page 49: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

1.4. RESULTS AND DISCUSSION 37

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

λ [−]

σ [−

]

DKGEGHNP030NP010after Bowen et al.

R2=0.9419

Figure 1.7: Reflection coefficients of all solutes as a function of ratio of Stokes radii to

the pore radii of the five membranes. The curve was calculatedfrom the DSP model with

Eq.(1.12) using the pore radiirp reported in Table 1.4.

Eq. 1.11 provides a direct estimation of the pore size without the necessity of

a prior SK analysis. The pore size can be obtained by fitting tothe experimen-

tally determined set of applied pressure and rejection data, or vice versa, the

rejection of a noncharged solute for a given applied pressure can be calculated

if the pore size of the membrane is known. This latter conceptwas applied to

estimate theR of the different solutes as a function of∆P using the prior deter-

mined pore radius listed in Table 1.4. The model prediction is plotted together

with the experimental data in Fig. 1.8 for the membrane GE as arepresentative

membrane.

Page 50: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

38 CHAPTER 1.

0 1 2 3 4

x 106

0

0.2

0.4

0.6

0.8

1

∆P [Pa]

reje

ctio

n [−

]

lactose glucose ribose butanol

Figure 1.8: Rejection of solutes as a function of permeate flux for the membrane GE. The

curves were computed using Eq.(1.10) and assuming membranepore radiusrp = 0.70

nm.

1.5 Conclusions

The hypothetical pore radii of five commercial NF membranes (DK, GE, GH,

NP030, NP010) were evaluated from permeation experiments using different

noncharged solutes. Thermodynamical analysis of experimental data was per-

formed in order to obtain the reflection coefficients of each solute. This phe-

nomenological parameter was linked to the membrane structural parameter us-

ing two steric pore flow models. The overall best-fitting solution in a least-

squares sense was computed for each membrane by fitting the pore size radii

to the sets of experimental data of reflection coefficients and solute radii. Pre-

dictions of both DSP and SHP models were found to be in a good agreement

with the experimental data. However, there is a significant difference in the es-

timated pore size values depending on which model is used andalso on which

measure of the solute size is employed. The provided values of membrane pore

Page 51: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

BIBLIOGRAPHY 39

size can be applied to predict the rejection of any noncharged solute for a given

applied pressure.

Bibliography

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spectives, Mem. Technol. 9 (2002) 6–9.

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[3] J. Wagner, Membrane Filtration Handbook - Practical Tips and Hints, Osmonics,

Inc., Minnetonka USA, 2001.

[4] S. Allgeier, Membrane filtration guidance manual, Tech.Rep. EPA 815-R-06-009,

United States Environmental Protection Agency, Office of Water (2005).

[5] A. Scaefer, A. Fane, T. Waite, Nanofiltration – Principles and Applications, Else-

vier Advanced Technology, Oxford UK, 2005.

[6] F. P. Cuperus, D. Bargeman, C. A. Smolders, Permporometry: the determination

of the size distribution of active pores in uf membranes, J. Mem. Sci. 71 (1992)

57–67.

[7] W. Bowen, A. Mohammad, N. Hilal, Characterization of nanofiltration membranes

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croscopy, J. Membr. Sci. 126 (1997) 91–105.

[8] S. Singh, K. C. Khulbe, T. Matsuura, P. Ramamurthy, Membrane characterization

by solute transport and atomic force microscopy, J. Mem. Sci. 142 (1998) 111–127.

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[10] K. Spiegler, O. Kedem, Thermodynamics of hyperfiltration (reverse osmosis): cri-

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[11] W. Bowen, J. Welfoot, Modelling the performance of membrane nanofiltrationU-

critical assessment and model development, Chem. Eng. Sci.57 (2002) 1121–

1137.

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40 CHAPTER 1.

[12] S. Nakao, S. Kimura, Models of membrane transport ohenomena and their appli-

cations for ultrafiltration data, Chem. Etg. Japan 15 (2) (1982) 200.

[13] X. Wang, T. Tsuru, M. Togoh, S. Nakao, S. Kimura, Evaluation of pore structure

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28 (2) (1995) 186–192.

[14] X. Wang, T. Tsuru, S. Nakao, S. Kimura, The electrostatic and steric-hindrance

model for the transport of charged solutes through nanofiltration membranes, J.

Membr. Sci. 135 (1997) 19–32.

[15] B. V. der Bruggen, C. Vandecasteele, Modelling of the retention of uncharged

molecules with nanoiltration, Water Research 36 (2002) 1360–1368.

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BIBLIOGRAPHY 41

Table 1.4: Nomenclature

Symbol Name Unit

cp Permeate concentration mol/m3

cr Retentate concentration mol/m3

d Thikness of oriented solvent layer m

D∞ Diffusion coefficient at infinite dilution m2/s

Dp Hindered diffusion coefficient within the pore m2/s

js Molar solute flux mol/m2/s

Jv Volumetric permeate flux m/s

k Boltzmann constant (1.38 · 10−23) J/K

Kc Convective hindrance factor –

Kd Diffusive hindrance factor –

Mw Molecular weight g/mol

Pem Modified Peclet number –

Ps Solute permeability m/s

R Rejection –

Rlim Limiting rejection –

rE Effective radius of solute m

rp Pore radius m

rS Stokes radius of solute m

T Temperature K

V Solvent velocity m/s

x Axial position within the pore m

Greek symbols

∆P Applied pressure Pa

∆π Osmotic pressure difference across the pore Pa

∆x Membrane thickness m

Φ Steric partitioning coefficient –

η0 Bulk dynamic viscosity Pas

ηp Dynamic viscosity within pores Pas

λ Ratio of solute to pore radius –

σ Reflection coefficient –

Page 54: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

42 CHAPTER 1.

Page 55: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

2Contribution of pH dependent

osmotic pressure to amino acid

transport through nanofiltration

membranes

Reprinted from: Z. Kovács, W. Samhaber, Contribution of pH dependent os-

motic pressure to amino acid transport through nanofiltration membranes, Sep-

aration and Purification Technology 61, 243–248, 2008.

A concept is presented to determine the osmotic pressure of amino acid solu-

tions by altering the stoichiometric coefficient of the van’t Hoff law correspond-

ing to the dissociation state of the amino acids. The osmoticpressure is greatly

43

Page 56: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

44 CHAPTER 2.

affected by the feed pH, which significance has been overseenin membrane per-

meation studies. Nanofiltration experiments were carried out in order to inves-

tigate the effect of osmotic pressure on the permeation of amino acids through

polymeric membrane. L-alanine aqueous solutions of various feed pH (6.0, 9.7,

11.1) were concentrated in discontinuous operation mode with complete reten-

tate recycle. It has been stated by many authors, that polymeric nanofiltration

membranes possess higher rejection for amino acids in negatively charged form

than for zwitterions. In our study we demonstrate that this tendency can be

reversed in higher concentration range.

2.1 Introduction

Nanofiltration (NF) is a relatively new class of pressure-driven membrane tech-

niques that lies between ultrafiltration and reverse osmosis. NF is operated at

medium pressures in the range of 5-50 bar. Both size and charge of solute play

an important role in the separation behaviour of NF membranes. The transporta-

tion of non-charged solutes through an NF membrane is usually characterized

by the term of molecular weight cut-off, which is in the rangeof about 200-

1000 Dalton. Polymeric NF membranes are known to have considerably higher

rejection for ionic species than for neutral solutes of the same molecular weight

due to the properties of electrostatic repulsion as well as size exclusion.

NF membrane processes have found their way into industrial applications of

various fields as viable alternatives to more traditional separation processes

like extraction, ion-exchange, evaporation and distillation. In the synthesis and

down-stream processing of amino acids (AA), the purification and recovery is

a challenge, where NF is a promising separation tool. The potential use of NF

for such purposes has been recently studied and discussed byseveral authors,

which had covered the field of enzymatic glutathion synthesis [1], separation of

glutamine from fermentation broth [2], aspartame production [3], fractionation

of protein hydrolysates [4–6], cofactor regeneration in L-tert-leucine enzymatic

synthesis [7].

Amino acids are ionisable compounds. In neutral aqueous media, diprotic AA

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2.1. INTRODUCTION 45

with non-ionisable residual group are predominantly present in zwitterionic

form as a result of intermolecular proton transfer. If the pHof the solution is

higher than their isoelectric point, dissociation takes place, which results the an-

ionic form. It has been reported in several studies, that a considerably higher re-

jection can be observed for AA of anionic form than for zwitterions [1, 3, 8, 9].

It should be noted, that these studies have been focused on highly diluted sys-

tems of10−2−10−3 molar feed concentration range. Wang et al. simulated NF

process for concentration and diafiltration of L-phenylalanine/L-aspartic acid

solution based on rejection data achieved from laboratory measurements using

highly diluted systems [3]. Fairly less experimental data are available on con-

centrated solutions. Timmer et al. [10] demonstrated the effect of 0.1 molar feed

concentration on NF and also Li et al. [2] studied the rejection of L-glutamine

and L-glutamic acid single solutions with the variation of feed concentration up

to their solubility limit. It was concluded, that the rejection of charged AA is de-

creasing much more with increasing feed concentration thanin the case of AA

of zwitterionic form. Such a finding was interpreted by the authors as a result

of a change in the charged nature of the membranes. Namely, the saturation of

the charged sites on the membrane is claimed by the authors toprovoke a more

permeable medium for charged components due to charge shielding. Estima-

tion and use of effective membrane charge density for practical applications is

rather complex and no quantitative description of the transport phenomena of

amino acids has been reported so far. For the sake of completeness we have to

mention, that an increase in the rejection of L-glutamine with increasing feed

concentration was found by Li et al [2]. This unusual behaviour has been ex-

plained by the authors as the result of association of L-glutamine into dimers

and polymers. On the basis of the current state of research, no definite conclu-

sion on the concentration dependency of rejection can be drawn. Since NF is

a pressure driven process, information on the osmotic pressure of the feed is

essential. The pH dependency of the osmotic pressure exerted by AA solutions

and the impact of this phenomenon on the separation behaviour seem to be left

out of consideration in the literature yet.

In the following, we report the concept for calculating the osmotic pressure of

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46 CHAPTER 2.

diprotic amino acid solutions highlighting the role of feedpH and discuss the

impact of it on membrane permeation behaviour based on experimental results.

The following discourse will deal with the case of alanine and its permeation

studies through an NF membrane, which will, however, be sufficient to indicate

the general nature of the relevant phenomena.

2.2 Theory

2.2.1 Osmotic pressure of amino acid solutions

There is a lack of available information on osmotic pressuredata of amino acid

solutions in the open literature, although it is expected tobe of special signifi-

cance in several disciplines of science.

The dissociated species of a diprotic amino acid in aqueous solution occur in

equilibrium as follows:

HOOC–R–NH+3 ⇋−OOC–R–NH+3 ⇋

−OOC–R–NH2

We consider a cation fractionfA+ , an anion fractionfA− and a zwitterionic

fraction fA0 of the total amino acid concentration. The equilibrium can be

expressed withK1 andK2 dissociation constants:

1 = fA+ + fA− + fA0 (2.1)

K1 =cH+ · cA0

cA+

(2.2)

K2 =cH+ · cA−

cA0

(2.3)

Using the identities of pK1 =− log K1, pK2 =− log K2, pH=− log cH+ , and

combining with (2.1), (2.2) and (2.3), the following relations can be delivered:

fA+ =1

1 + 10pH−pK1 + 102pH−pK1−pK2

, (2.4)

fA− =1

1 + 10pK2−pH + 10pK1+pK2−2pH , (2.5)

The osmotic pressure can be determined by van’t Hoff law:

π = iRT cA (2.6)

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2.2. THEORY 47

0 2 4 6 8 10 12 140

10

20

30

40

50

π [b

ar]

pH

0.1 mol/L 0.5 mol/L 1 mol/L

Figure 2.1: Estimated osmotic pressure in the function of pH for alaninesolutions of

different concentrations at 25 °C.

The factori is evidently equal to the sum of the number of inactive molecules,

plus the number of ions, divided by the sum of the inactive andactive molecules

[11]. For a diprotic amino acid this gives

i =fA0 + 2fA+ + 2fA−

fA0 + fA+ + fA−

(2.7)

which can be converted into the equivalent form ofi = 1 + fA+ + fA− .

Combining (2.4, 2.5) and (2.6) results in

π = RTcA[1 +1

1 + 10pH−pK1 + 102pH−pK1−pK2

+

+1

1 + 10pK2−pH + 10pK1+pK2−2pH ]

(2.8)

Equation (2.8) expresses the pH dependency of the osmotic pressure of a dipro-

tic amino acid, which is graphically illustrated in Fig.2.1. The net chargez

is given byz = (+1) · fA+ + (−1) · fA− + (0) · fA0 . Fig.2.1 shows that

complete ionisation (z = +1 or z = −1) results a two fold increase in the

osmotic pressure compared with the non-charged state (z = 0). This difference

in the osmotic pressure can cause remarkable consequences on the permeation

through the membrane especially in higher concentration ranges, where the ex-

erted osmotic pressure of the feed is in the same order of magnitude with the

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48 CHAPTER 2.

applied pressure. Compare with the generally applied 10–40bar pressure in

NF, considering for instance a 1 mol/L solution, the exertedosmotic pressure

for neutral and alkaline regime is ca. 25 and 50 bar. Since thesolution prop-

erty is expressed in term of pressure, it can be used in practical calculations and

readily applied in predictive models.

2.2.2 Permeability equations

Many models have been proposed for NF so far, which can be divided into

two main types: transport mechanism models and irreversible thermodynamics

models (IT).

The models based on phenomenological relationships of the thermodynamics

of irreversible processes have been widely used in predicting transport through

NF membranes for single and binary solute systems [12, 13], most recently for

multiple systems [14] and also for industrial feeds [3, 15–17].

The set of basic equations is given by Kedem and Katchalsky (KK) for jv total

volume flux andjs molar solute flux [18]:

Jv = Lp(∆P − σ∆π), (2.9)

js = ω∆π + (1 − σ)Jvc, (2.10)

whereLp, ω andσ are membrane transport coefficients;c is the mean solute

concentration within the membrane;∆P is the transmembrane pressure; and

∆π is the osmotic pressure difference.

In non-equilibrium thermodynamics, the membrane is treated as a "‘black box"’,

so no insight into the transport mechanisms is provided. TheKK model neglects

the effect of membrane charge. It is generally true, that polymeric NF mem-

branes have higher rejection for negatively charged than for zwitterionic amino

acids in diluted systems. The reason of this difference in the solute permeabil-

ity in such diluted systems, as well as the inner mechanism ofthe membrane

effect itself would require a more complex theoretical description, which will

at this stage be left aside. Our objective is to demonstrate the effect of the os-

motic pressure. According to our prior hypothesis, the osmotic pressure as a

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2.3. EXPERIMENTAL 49

function of ionization can be described by Eq. (2.8). In diluted systems and

at adequately high transmembrane pressure, whereσ∆π ≪ ∆P , the osmotic

pressure difference between charged and uncharged solutesis less pronounced.

In contrary, at higher concentration range, the pH dependency of the osmotic

pressure can result a significant change in the volume flux andhas a greater

overall influence on solute permeability according to Eq. (2.9, 2.10).

2.3 Experimental

2.3.1 Materials

L-alanine of analytical degree used in the experiments was purchased from

Merck. The properties are shown in Table 2.1.

Table 2.1: Characteristics of alanine

Item Alanine

Symbol Ala

Molecular formula C3H7NO2

Molecular weight, g/mol 89.09

pK, α–COOH group 2.34

pK, α–NH+3 group 9.69

pK, side chain -

Solubility in water at 25 °C, g/L 167

Commercial polymeric DK nanofiltration membrane is used in this study. This

thin film composite membrane was supplied by GE W&P Technologies, char-

acterized by an approximate molecular weight cut-off of 150-300 Da.

Concentration of Ala was determined in pre-diluted solutions using a total or-

ganic carbon analyzer (TOC 500, Shimadzu). Adjustment of pHwas made

with a low ionic double junction pH electrode by adding 5 molar NaOH. Os-

motic pressure of Ala solutions was determined by vapour pressure osmometry

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50 CHAPTER 2.

Figure 2.2: Schematic diagram of the lab-scale membrane system

with Knauer K-7000 osmometer using standard NaCl solutionsof known os-

molalities for calibration.

2.3.2 Experimental set-up

Nanofiltration was performed using the experimental set-upshown in Fig.2.2.

The membrane unit is equipped with a LAB20 type plate-and-frame module

manufactured by DDS (De Danske Sukkerfabrikker, Denmark).Two flat-sheet

discs of DK membrane with the effective membrane surface area of 350 cm2

were placed in the module. Retentate stream was recycled to the feed tank and

permeate was collected in a separate vessel during the process. The circulating

velocity was set to 500 L/h, which is the recommended value bythe manufac-

turer, as necessary for restrained concentration polarization, corresponding to a

Reynolds number of 965 [19]. Applied trans-membrane pressure was adjusted

to 30 bar with a pressure valve at the retentate side. All experiments were car-

ried out at 25 +/- 0.2 °C.

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2.4. RESULTS AND DISCUSSION 51

2.3.3 Methods

The experimental work was carried out in three batches, all of them follow-

ing the same procedure and under the same conditions but at different feed pH.

First, an aqueous 0.2 molar solution of Ala was fed in the feedtank and con-

centrated in discontinuous operation mode with complete retentate recycle. The

total volume of the permeate was measured in order to calculate the volumet-

ric concentration factor of the feed solution (n = Vfeed/Vconcentrate). During

the process, permeate and retentate samples were periodically taken from the

permeate pipe and from the feed tank, respectively. Ala rejection was then cal-

culated using the formula

R = 1 − cpcr, (2.11)

wherecp andcr are the solute concentrations of permeate and retentate, respec-

tively. The permeate flux was manually measured by using a calibrated cylin-

der and a stopwatch. Volume of collected permeate and operation time was

recorded. The concentration process was stopped, when the Ala concentration

of approximately 0.9 mol/L had been achieved. Then the collected permeate

was recycled and mixed again with the concentrate in the feedtank. There-

after, the pH was adjusted to 9.7, which corresponds to 50% dissociation, and

the concentration process was repeated in the same way than as was before at

neutral pH. Finally, in the third batch, the operation was carried out by setting

the pH to11.1, which results a close to complete ionisation of the Ala.

After the experimental part, deionised water permeabilityof the membrane was

checked and complete recovery of the initial permeability was verified.

2.4 Results and discussion

Results of the batch-mode NF experiments of pH 6.0, 9.7 and 11.1 are sum-

marised in Table 2.2. The initial feed solutions were concentrated up to about

0.9 mol/L, which required 4.7, 5.7 and 9.3 hours of operationtime for the re-

spective batches. Rejection and flux data plotted against the concentration factor

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52 CHAPTER 2.

1 2 3 4 5 6 7 840

50

60

70

80

90

100

n [−]

Rej

ectio

n [%

]

pH=11.1pH=9.7pH=6.0

Figure 2.3: Rejection in the function of concentration factor for the different batches

1 2 3 4 5 6 7 80

20

40

60

80

100

n [−]

perm

eate

flux

[L/h

/m²]

pH=6.0pH=9.7pH=11.1

Figure 2.4: Permeate flux in the function of concentration factor for thedifferent batches

Page 65: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

2.4. RESULTS AND DISCUSSION 53

Table 2.2: Summary of batch NF operations carried out at different pH values

pH 6.0 9.7 11.1

operation time, h 4.7 5.7 9.3

concentration factor, - 7.5 7.1 5.5

final concentration, mol/L 0.89 0.90 0.86

flux decrease during operation, %a 58 72 81

rejection decrease during operation, %b 12 27 39

adefined as(1 − Jfinal/Jinitial) · 100%bdefined as(1 − Rfinal/Rinitial) · 100%

are shown in Fig. 2.3 and 2.4. At low concentration range, an increase in the

ionisation degree results increasing rejection. Initial rejections were 72%, 78%

and 89% at pH 6.0, 9.7 and 11.1, respectively. This tendency is in a good agree-

ment with literature data of diluted diprotic amino acid solutions [1–3, 8] and in

particular, confirms the observations on permeability ofβ-Alanine through cel-

lulose acetate membranes demonstrated by Matsuura and Sourirajan [9]. While

the rejection of zwitterionic Ala decreases only slightly (with a total of 12%)

during the process, a substantially larger drop can be observed in the batches

where Ala has the net charge ofz = −0.5 (27%) orz = −1 (39%). The rejec-

tion of charged Ala molecules decreases by increasing retentate concentration

and not only reaches the rejection value of zwitterionic form, but even lower

values were measured at the final stage of the process. This phenomenon is

shown in Fig. 2.5. Rejection of zwitterionic form decreasedfrom 72% to 63%,

whereas, on the other hand, the rejection drop for anionic form was from 89%

to 54%. Such behaviour has been interpreted by the saturation of the charged

sites of NF membranes. This saturation results weaker electrostatic repulsion

and it is claimed to explain a large rejection drop for charged solutes by in-

creasing feed concentration, but so far, no sufficient explanation was reported

on why charged AA is more permeable in comparison with non-charged AA at

high feed concentration regime.

Rejection can not be discussed independently of flux data. Asit is shown in

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54 CHAPTER 2.

0.2 0.4 0.6 0.8 140

50

60

70

80

90

100

cR [mol/L]

Rej

ectio

n [%

]

pH=6.0pH=9.7pH=11.1

Figure 2.5: Rejection in the function of retentate concentration for the different batches

Fig.2.4, high flux differences between the batches were found even at the pro-

cess begin, although these flux data refer to the same, 0.2 mol/L Ala feed con-

centrations. The initial permeate fluxes were 92, 83 and 64 L/h/m2 for the

batches pH 6.0, 9.7 and 11.1, respectively. These differences can be explained

by taking into account the osmotic pressure of the feed solutions. Increasing

degree of ionisation results an increase in the osmotic pressure as it is shown in

Fig.2.6. At the initial feed concentration, it is approximately 5 bar for zwitte-

rionic, 7.5 bar for half-dissociated and about 10 bar for practically completely

dissociated molecules. The experimental values measured by vapour pressure

osmometry are in a good agreement with the estimated values.Hereby we have

to remark, that because of amino acids act as buffers, a smallinaccuracy in

adjusting the feed pH to the pK value of Ala can cause a relatively great differ-

ence in the exerted osmotic pressure values, which can gain major importance in

membrane process control. Stable, less pH dependent osmotic pressure values

can be adjusted around the isoelectric point and at the dissociation level of close

to unity. The osmotic pressure of the solution still could beraised after all Ala

molecules are converted into anionic form by further addition of NaOH. In this

case, no extra osmotic pressure gradient across the membrane would be built,

since the membrane is virtually freely permeable for ionic species produced by

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2.4. RESULTS AND DISCUSSION 55

0 0.2 0.4 0.6 0.8 10

10

20

30

40

50

concentration [mol/L]

π [b

ar]

estimated pH=6.0estimated pH=9.7estimated pH=11.1pH=6.0 measuredpH=9.7 measuredpH=11.1 measured

Figure 2.6: Estimated osmotic pressure (Eq. 2.8) versus Ala concentration curves with

the experimental results of vapor pressure osmometry (at 25°C) .

the dissociation of the excessive NaOH. The permeate flux decreases during the

concentration process. As it is shown in Fig.2.7, the relative decrease of flux

(i.e., Jactual/Jinitial · 100%) within the process was found to be unequal for

the batches. The greatest decrease (81%) of the initial flux by the end of the

process was achieved in batch pH 11.1, in contrary, medium (72%) for pH 9.7,

and low (58%) for pH 6.0 were measured. Considering a final concentration

of 0.9 mol/L on the feed side for osmotic pressure calculation, it results about

22, 33 and 44 bar for net charge ofz = 0 z = −0.5 andz = −1, respec-

tively. These values are of the order of the applied transmembrane pressure,

which is 30 bar. It is to be noted, that for a completely rejecting membrane, in

the case of completely dissociated molecules we would require more than 44

bar external pressure to gain permeate flux as it is the basis of reverse osmosis.

Based on Eq.(2.9) we see that positive flux for a partially retentive NF mem-

brane is the result of the lower osmotic pressure gradient across the membrane

(∆π = R · πfeed, withR < 1) and of the convective interaction between solute

and solvent (σ < 1). The rejection in the function of permeate flux is shown in

Fig.2.8. One can clearly see, that a decreasing permeate fluxresults a decrease

in the rejection. Since the anionic Ala exerts two fold the osmotic pressure of

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56 CHAPTER 2.

0.2 0.4 0.6 0.8 10

20

40

60

80

100

cR [mol/L]

rela

tive

flux

chan

ge [%

]

pH=6.0pH=9.7pH=11.1

Figure 2.7: Relative flux decrease in percentage defined asJactual/Jinitial · 100%

versus retentate concentration for the different batches

0 20 40 60 80 1000

20

40

60

80

100

J [L/h/m²]

Rej

ectio

n [%

]

pH=11.1pH=9.7pH=6.0

Figure 2.8: Rejection in the function of permeate flux for the different batches

the zwitterionic Ala, this difference in the feed side can beidentified as a major

factor for the extensively pronounced permeate flux decrease. This enhanced

drop in the flux between the differently charged solutes in highly concentrated

solutions can result lower observed rejection for anionic than for zwitterionic

solutes of the same feed concentration.

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2.5. CONCLUSIONS 57

2.5 Conclusions

1. A quantitative and simple theory of pH dependence of the osmotic pres-

sure exerted by diprotic amino acids is presented.

2. The pH dependency of osmotic pressure was verified experimentally by

vapour pressure osmometry.

3. The significance of such phenomenon in membrane transportis pointed

out.

Bibliography

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acids by nanofiltration, Biochem. Eng. 19 (2004) 165–170.

[2] S. Li, C. Li, Y. Liu, X. Wang, Z. Cao, Separation of L–glutamine from fermentation

broth by nanofiltration, J. Membr. Sci. 222 (2003) 191–201.

[3] X. Wang, A. Ying, W. Wang, Nanofiltration of L-phenylalanine and L-aspartic acid

aqueous solutions, J. Membr. Sci. 196 (2002) 59–67.

[4] C. Martin-Orue, S. Bouhallab, A. Garem, Nanofiltration of amino acid and peptide

solutions: mechanisms of separation, J. Membr. Sci. 142 (1998) 225–233.

[5] A. Garem, G. Daufin, J. Maubois, J. Leonil, Selective separation of amino acids

with charged inorganic nanofiltration membrae: effect of physicochemical param-

eters on selectivity, Biotech. Bioeng. 54 (4).

[6] Y. Pouliot, S. Gauthier, C. Bard, Fractionation of casein hydrolysates using poly-

sulfone ultrafiltration hollow fiber membranes, J. Membr. Sci. 80 (1993) 257–264.

[7] K. Seelbach, U. Kragl, Nanofiltration membranes for cofactor retention in contin-

uous enzymatic synthesis, Enzyme Microb. Technol. 20 (1997) 389–392.

[8] T. Tsuru, T. Shutou, S. Nakao, S. Kimura, Peptide and amino acid separation with

nanofiltration membranes, Sep. Sci. Technol. 29 (8) (1994) 971–984.

[9] T. Matsuura, S. Sourirajan, Reverse osmosis separationof amino acids in aqueous

solutions using porous cellulose acetate membranes, J. Appl. Polym. Sci. 18 (1974)

3593–3620.

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58 CHAPTER 2.

[10] J. Timmer, M. Speelmans, H. van der Horst, Separation ofamino acids by nanofil-

tration and ultrafiltration membranes, Sep. Purif. Technol. 14 (1998) 134–144.

[11] S. Arrhenius, On the dissociation of substances dissolved in water, Zeitschrift für

Physikalische Chemie 1 (1887) 631.

[12] S. Koter, Determination of the parameters of the spieglerUkedemUkatchalsky

model for nanofiltration of single electrolyte solutions, Desalination 198 (2006)

335–345.

[13] A. Kargol, Modified Kedem-Katchalsky equations and their applications, J.

Membr. Sci. 174 (2000) 43–53.

[14] A. Ahmad, M. Chong, S. Bhatia, Mathematical modeling and simulation of the

multiple solutes system for nanofiltration process, J. Membr. Sci. 253 (2005) 103–

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[15] C. Bhattacharjee, P. Sarkar, S. Datta, B. Gupta, P. Bhattacharya, Parameter estima-

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[16] M. Moresi, B. Ceccantoni, S. L. Presti, Modelling of ammonium fumarate recovery

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[17] M. Pontie, H. Buisson, C. K. Diawara, H. Essis-Tome, Studies of halide ions mass

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Page 71: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

3Nanofiltration of concentrated amino

acid solutions

Reprinted from: Z. Kovács, W. Samhaber, Nanofiltration of concentrated amino

acid solutions, Desalination, Accepted, To Appear, 2008.

Permeation experiments of aqueous solutions of diprotic amino acids (L-glutamine

and glycine) were carried out with numerous commercial polymeric nanofiltra-

tion (NF) and tight ultrafiltration (UF) membranes. The aim of this study was

to determine the permeate flux and the amino acid rejection asa function of in-

creasing feed concentration and ionization state of the amino acids. So far, apart

from a few limited studies, highly diluted solutions have been considered in the

literature, although separation and purification of concentrated systems possess

particular industrial interests. The concentration of amino acids in the whole

59

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60 CHAPTER 3.

range of their solubility was studied with a stepwise pH scanranging from0 to

−1 total net charge. Considerable higher rejection and flux drop over the con-

centration was observed in higher pH range, where amino acids are present in

dissociated form. Membranes with different type of active layer material show

similar concentration dependent tendency in the permeation behaviour. This

phenomenon can be explained by the dissociation dependencyof the osmotic

pressure. An altered form of the van’t Hoff law is reported tocalculate the pH

dependency of the osmotic pressure and verified by vapor pressure osmometry

and reverse osmosis (RO) experiments.

3.1 Introduction

With the exploitation of new uses of amino acids and the largeprogress in pro-

duction technology, the market for amino acids in general issaid to double every

decade [1]. Purification and recovery of amino acids plays animportant role in

many chemical, pharmaceutical, food and biotechnologicalprocesses. NF is a

relatively new class of the pressure-driven membrane processes and its appli-

cation for such purposes is a viable alternative over more traditional separation

processes like extraction, ion-exchange, evaporation anddistillation.

Amino acids are amphoteric electrolytes. The ionisation state can be controlled

by pH of the feed solution, which causes considerably changes in the mass

transfer through the membrane. It has been proved, that an increase in the ion-

ization degree of amino acids results increasing rejectionof polymeric mem-

branes [2–5].

Although in industrial processes mostly concentrated systems are processed,

most of the NF studies in the open literature are dealing withhighly diluted

aqueous amino acid solutions, and only a little effort was made trying to clar-

ify the effect of increasing feed concentration in respect to the charged state

of amino acids. In particular, very few reports are available on diprotic amino

acids. In the next two paragraphs, first we emphasize the literature results on

concentrated diprotic amino acid solutions, which is the subject of our experi-

mental study, and then align the related achievements on concentrated basic and

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3.1. INTRODUCTION 61

acidic amino acids.

Timmer at al. [6] determined the rejection of leucine for several polymeric

membranes, although the adjusted feed concentration of studied amino acids

was limited to 0.01 mol/L and 0.1 mol/L, and pH was adjusted to5.5, where the

zwitterionic form is predominant. At this feed pH, for the given concentration

difference, no change neither in rejection nor permeate fluxwas observed. Li

et al. [7] studied the rejection of NTR 7450 membrane for glutamine in single

solutions. Full scan of concentration up to the solubility limit was investigated,

but restricted to the pH range of5.5−7.5, where glutamine is practically undis-

sociated. Permeate flux is not reported, but surprisingly, the rejection increased

with increasing feed concentration. This phenomenon is explained by the au-

thors, that at higher concentration range L-glutamine associates into dimers and

polymers and so, the increasing rejection is the result of size effects.

Timmer at al. and also Li et al. [6, 7] carried out experimentswith non-diprotic

amino acids under the above mentioned experimental circumstances. A sig-

nificantly higher rejection drop with increasing concentration was observed for

charged amino acids than for non-charged. Although non-diprotic amino acids

were used, this statement likely can be generalized for diprotic amino acids.

Such a phenomenon is explained by both authors with the saturation of the

charged sites on the membrane, which makes the membranes more permeable

to charged components in higher concentration range. No quantitative analy-

sis of this charge shielding has been investigated yet. It isconflicting, that a

converse behaviour was observed with glutamic acid [7]. At pH 8, where the

net charge is−1, a less pronounced rejection drop (from95% to 75%) was

measured over the concentration than close to its isoelectric point (from90% to

5%).

Apart from these limited investigations, no systematic evaluation of concentra-

tion dependency of amino acid mass transfer through NF membranes has been

performed. Therefore, systematic permeation experimentswere investigated

with stepwise increase of the ionization state from0 to−1 total net charge, and

with a gradual increase of the amino acid feed concentrationin the whole range

of its solubility.

Page 74: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

62 CHAPTER 3.

3.2 Theory

The osmotic pressure of amino acid solutions is strongly dissociation depen-

dent. The importance of this fact seems to be overseen in the literature. Hereby,

we make an attempt to derive the pH dependency of osmotic pressure for dipro-

tic amino acids.

Diprotic amino acids have two ionising groups: alpha-carboxylicacid and alpha-

amino group. The dissociation in aqueous solution occurs inequilibrium as

follows:

HOOC−CR−NH+3 −−⇀↽−− –OOC−CR−NH+

3 −−⇀↽−− –OOC−CR−NH2

The total amino acid concentration is equal to the sum of all its ionic forms

cA = cA0 + cA+ + cA− , (3.1)

wherecA0 represents the zwitterionic,cA+ the cationic andcA− the anionic

form. The dissociation of carboxyl group is represented by the reaction

−COOHK1−−⇀↽−− −COO– + H+

with a dissociation constant

K1 =cA0cH+

cA+

. (3.2)

On the other hand, the dissociation of amino group is described by the reaction

−NH+3

K2−−⇀↽−− −NH2 + H+

with a dissociation constant

K2 =cA−cH+

cA0

. (3.3)

Using the identities of pK1 =− log K1, pK2 =− log K2, pH=− log cH+ , and

combining with (3.1–3.3), the amino acid ionic fractions can be expressed as

fA+ =cA+

cA=

1

1 + 10pH−pK1 + 102pH−pK1−pK2

, (3.4)

fA− =cA−

cA=

1

1 + 10pK2−pH + 10pK1+pK2−2pH . (3.5)

Page 75: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

3.2. THEORY 63

The net charge (z) of the amino acid can be calculated by

z = (+1)fA+ + (−1)fA− , (3.6)

and with the respective pK values for Gln and Gly plotted against pH in Fig.3.1.

The osmotic pressure can be determined by van’t Hoff law:

6 7 8 9 10 11 12

−1

−0.8

−0.6

−0.4

−0.2

0

pH

tota

l net

cha

rge

GlyGln

Figure 3.1: The change in net charge of glycine and L-glutamine for the studied pH

range

π = iRT cA (3.7)

The factor i is the relation between the osmotic pressure actu-

ally exerted by a substance and the osmotic pressure which itwould

exert if it consisted only of inactive (undissociated) molecules. i is

evidently equal to the sum of the number of inactive molecules,

plus the number of ions, divided by the sum of the inactive and

active molecules. [8]

For a diprotic amino acid this gives

i =fA0 + 2fA+ + 2fA−

fA0 + fA+ + fA+

(3.8)

Page 76: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

64 CHAPTER 3.

which can be converted into the equivalent form ofi = 1 + fA+ + fA− .

Combining (3.4, 3.5) and (3.6) results in

π = RTcA[1 +1

1 + 10pH−pK1 + 102pH−pK1−pK2

+

+1

1 + 10pK2−pH + 10pK1+pK2−2pH ]

(3.9)

Eq.3.9 can be practically useful for quantitative NF process description. Since

it expresses the underlying physical property of the solution in term of osmotic

pressure, it can be readily employed in models, such as irreversible thermody-

namics models (IT).

The IT models are based on linear phenomenological relationships and have

the advantage over transport mechanism models, that no detailed knowledge on

the structure of the membrane and no insight into the complextransport mech-

anisms is required. IT models have already been used in predicting transport

through NF membranes for single and binary solute systems [9, 10], most re-

cently for multiple systems [11] and also for industrial feeds [5, 12–14].

The relationship betweenJv total volume flux andjs molar solute flux [15] was

derived by Kedem and Katchalsky (KK):

Jv = Lp(∆P − σ∆π), (3.10)

js = ω∆π + (1 − σ)Jvc, (3.11)

whereLp the hydraulic permeability,ω the solute permeability andσ the re-

flection coefficient are the three membrane transport coefficients;c is the mean

solute concentration within the membrane;∆P is the transmembrane pressure;

and∆π is the osmotic pressure difference.

Page 77: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

3.3. EXPERIMENTAL DESIGN AND PROCEDURES 65

3.3 Experimental design and procedures

3.3.1 Materials

Membranes

Commercial polymeric NF and tight UF membranes employed areshown in

Table 3.1.

Table 3.1: Membrane specifications

Name DK GE (G-5) GH (G-10) NP030 NP010

Manufacturer GE W&P Technologies Microdyn-Nadir

Internet http://www.geawater.com http://www.microdyn-nadir.com

Material of sepa-

ration layer

proprietary permanently hydrophilic PES

MWCO 150-300 1000 2500 150-300 1000

Pure water flux

[L/h/m2/bar]

5.5± 25% 1.2± 25% 3.2± 25% >1 >5

Classification NF UF UF NF NF

Amino acids

The amino acids of analytical degree used in the experimentswere glycine and

L-glutamine purchased from Merck. Their properties are shown in Table 3.3.1.

Membrane filtration unit

Membrane filtration was performed using the experimental set-up shown in

Fig.3.2. The membrane unit is equipped with a DDS LAB20 plate-and-frame

module. Membrane discs with the effective membrane surfacearea of 350 cm2

were placed in series and simultaneously tested. Both permeate and retentate

streams were recycled to the feed tank to keep the feed concentration constant.

The circulating velocity was set to 500 L/h, which is the recommended value

by the manufacturer as necessary to avoid excessive concentration polarisation,

Page 78: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

66 CHAPTER 3.

Table 3.2: Characteristics of amino acids

Item glycine glutamine

Symbol Gly Gln

Molecular formula C2H5NO2 C5H10N2O3

Molecular weight [g/mol] 75.07 146.15

pK11 2.34 2.17

pK21 9.60 9.13

Solubility1[g/L] 251 421data refer to aqueous solution at 25 °C [16]

corresponding to a Reynolds number of 965 [17]. All experiments were carried

out at 25±0.2 °C.

3.3.2 Analysis

Concentration of amino acid single-component solutions was measured with a

total organic carbon analyzer (TOC 500, Shimadzu).

3.3.3 Vapor pressure osmometry

The vapour pressure osmometry measurements were carried out with a Knauer

K-7000 vapor pressure osmometer at 25 °C. The osmometer is equipped with

two thermistors. Droplets of high-purity water as reference were introduced on

both thermistors and then it was replaced by the amino acid solution on one of

the thermistors. The difference in vapour pressure of waterand the amino acid

solution was measured indirectly in terms of difference in the resistances of

the two thermistors. The calibration of the osmometer was done with standard

NaCl solutions using the relation between osmolality and molality data given

by the supplier. The pH of the solutions was adjusted either with concentrated

HCl or NaOH using low ionic double junction pH electrode. Each sample was

measured a minimum of three times. The maximum variation of the results was

Page 79: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

3.3. EXPERIMENTAL DESIGN AND PROCEDURES 67

Figure 3.2: Schematic diagram of the lab-scale membrane system

allowed to be withins3% of the mean value, otherwise the abnormal value was

eliminated and the measurement repeated.

3.3.4 Membrane permeation procedures

RO procedure

RO experiments were carried out using 0.5 mol/L glycine solution. The perme-

ate flux of SE type RO membrane (purchased from GE W&P Technologies) was

monitored at constant temperature of 25 °C by increasing thetransmembrane

pressure up to 40 bar. Then the pH was adjusted with NaOH to 9.6, which cor-

responds to−0.5 net charge and the experiment was repeated. Finally, pH of

11.8 was set, where99.4% of the amino acid is present in a negatively charged

form.

Page 80: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

68 CHAPTER 3.

NF procedure

Amino acids of certain concentration in single-component system were pre-

pared and then adjustment of pH was made in the feed tank with the addition

of NaOH using VWR low ionic double junction pH electrode. Applied trans-

membrane pressure was set to 30 bar. In all runs, stabilization time of 30 min-

utes was used before taking samples. Permeate flux was manually measured

by using a calibrated cylinder and a stopwatch. After the complete pH scan

(pH 3-11), the feed solution was drained and the above mentioned procedure

was repeated with another feed of different concentration.The amino acid con-

centration was varied from 0.001 mol/L to their solubility limit. After each

run, deionised water permeability was checked to ensure a complete recovery

of the initial permeability of the membranes. After each trial with the certain

amino acid, salt rejection was measured to detect possible changes in membrane

characteristic. During the experimental part, no significant change in water per-

meability nor in salt rejection was observed.

3.4 Results and discussion

3.4.1 Vapor pressure osmometry

The theoretical determination of the pH dependency of the osmotic pressure

was confirmed by experimental results of vapor pressure osmometry. Eq.3.9

implies that the osmotic pressure of a diprotic amino acid solution for any given

concentration and temperature is twice so high for completedissociation than

for pH=pI. It is to be noted, that principally the osmotic pressure of the solution

still can be increased after achieving a complete dissociation of the amino acids

by further addition of strong base/acid. The excessive presence of dissociated

NaOH molecules would result in additive osmotic pressure. NF membranes

possess low rejection for excessive NaOH. Thus, this excessive osmotic pres-

sure on the feed side would lead to a less pronounced osmotic pressure differ-

ence across the membrane. Besides, this would occur at extreme high (or ex-

treme low) pH values, which are out of our interests. Fittingof estimated curves

Page 81: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

3.4. RESULTS AND DISCUSSION 69

2 4 6 8 10 120

10

20

30

40

50

pH

π [b

ar]

0.1 M 0.5 M 1 M estimated

2 4 6 8 10 120

2

4

6

8

10

pH

π [b

ar]

0.05 M 0.1 M 0.2 M estimated

Figure 3.3: Predicted and experimentally determined osmotic pressurefor Gly (illus-

trated with closed symbols) and Gln solutions (open symbols) of different concentrations

in function of pH at25 ◦C. (Knauer K-7000 vapor pressure osmometer). Continuous

lines are calculated using Eq.3.9.

to the experimental data for Gly and Gln solutions of different concentrations

and pH values are shown in Fig.3.3. The experimental resultscorrespond very

well with the predicted values. The results of vapor pressure osmometry do

not seem to confirm the speculation of Li et al. [7]. A hypothetical association

of L-glutamine into dimers or polymers would cause a decrease in the exerted

osmotic pressure, which is not the case.

3.4.2 RO investigations

The solute rejection of the RO membrane is virtually complete (σ = 1), which

reduces Eq.3.10 to

Jv = Lp(∆P − ∆π). (3.12)

The hydraulic permeability can be determined from deionized water measure-

ment, since∆π = 0. The osmotic pressure of glycine solutions respective to

the feed pH can be calculated using Eq.3.9.

As it is shown in Fig.3.4, an increase in the feed pH causes a permeate flux

drop, which can be explained by the dissociation dependencyof the osmotic

Page 82: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

70 CHAPTER 3.

pressure according to Eq.3.9. The estimated data are in a good agreement with

the experimental values.

10 15 20 25 30 35 400

5

10

15

20

pressure [bar]

perm

eate

flux

[L/h

]

waterpH 6.0pH 9.6pH 11.8

Figure 3.4: Permeate flux in the function of transmembrane pressure for different feed

pH using 0.5 mol/L glycine solution and deionized water. (SEmembrae,25 ◦C) Contin-

uous lines are calculated using Eq.3.12 combining with Eq.3.9.

.

Glycine permeation

The amino acid permeation through the five tested NF membranes was experi-

mentally determined with feed solutions of 0.001, 0.1, 0.5,1 and 2 mol/L. The

measured data of rejection and permeate flux for the respective Gly concen-

trations are plotted versus pH in Fig.3.5. This systematic experimental design

allow us to investigate the influence of both concentration and pH on the rejec-

tion and on the permeate flux. Besides, we can compare the performances of

membranes with different active-layer materials. Trends observed with diluted

and concentrated solutions differ markedly.

Let us first the low concentration regime and analyze the rejection-versus-pH

data of the 0.001 M solution. With respect to each membrane polymer, the

solute separation data varied only within a very narrow range up to pH 8-9. In

Page 83: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

3.4. RESULTS AND DISCUSSION 71

this pH range, as it illustrated in Fig.3.1, Gly exists in solution predominantly as

zwitterion. From this pH, the rejection grows with increasing pH. In all cases,

the greatest rejections were observed at strongly alkalineconditions, where Gly

is completely dissociated. The rejection profiles of all membranes correspond

very well to the ratio of anionic species of Gly. These results indicate that

the rejection of Gly can be influenced by manipulating the pH.However, this

statement is only valid for diluted solutions. Here, it may be pointed out here

that the osmotic pressure of such diluted solutions is very low in comparison

to the applied transmembrane pressure. The osmotic pressure of a 0.001 M

feed solution varies only ca. 0.02 bar by changing the pH, which obviously has

a negligible contribution to the separation. Therefore, nodistinct variation in

permeate flux can be obtained in low concentration range.

The object of this research was to investigate the effect of an increase in feed

concentration with respect to pH. Concerning concentratedsolutions, the ex-

perimental results, plotted in Fig.3.5, show that the rejection of charged com-

ponents can be equal or even less than the rejection of zwitterionic species. It

should be recalled that, in this concentration regime, the osmotic pressure and

the external pressure are comparable driving forces. Choosing for illustration

a 2 molar solution as a reference point, the feed-side osmotic pressure values

are ca. 48 bar for pH 6 and 96 bar for pH 11. This means a huge, ca.50 bar

feed-side osmotic pressure difference depending on the adjusted pH. Thus, the

pH dependency of the osmotic pressure on the overall separation is more pro-

nounced in higher concentration range than in lower concentration range. The

experimental results support this general conclusion. An increase in the feed

concentration gives the following general results for NF membranes with re-

flection coefficients lower than unity: (i) decrease in rejection and (ii) decrease

in flux, however, they are interdependent quantities. A dropin rejection and

in flux was found to be more stressed for anionic species than for zwitterions,

which is in a good agreement with the dissociation-dependent pattern of the

osmotic pressure.

Page 84: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

72 CHAPTER 3.

3.5(a) − GE

5 6 7 8 9 10 11 120

0.2

0.4

0.6

0.8

1

pH

R [−

]

0.001 M0.1 M0.5 M1 M2 M

5 6 7 8 9 10 11 120

5

10

15

20

25

30

pH

perm

eate

flux

[L/h

/m²]

3.5(b) − DK

5 6 7 8 9 10 11 120

0.2

0.4

0.6

0.8

1

pH

R [−

]

0.001 M0.1 M0.5 M1 M2 M

5 6 7 8 9 10 11 120

20

40

60

80

100

120

pH

perm

eate

flux

[L/h

/m²]

3.5(c) − GH

5 6 7 8 9 10 11 120

0.2

0.4

0.6

0.8

1

pH

R [−

]

0.001 M0.1 M0.5 M1 M2 M

5 6 7 8 9 10 11 120

20

40

60

80

100

120

pH

perm

eate

flux

[L/h

/m²]

Page 85: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

3.4. RESULTS AND DISCUSSION 73

3.5(d) − NP030

5 6 7 8 9 10 11 120

0.2

0.4

0.6

0.8

1

pH

R [−

]

0.001 M0.1 M0.5 M1 M2 M

5 6 7 8 9 10 11 120

10

20

30

40

pH

perm

eate

flux

[L/h

/m²]

3.5(e) − NP010

5 6 7 8 9 10 11 120

0.2

0.4

0.6

0.8

1

pH

R [−

]

0.001 M0.1 M0.5 M1 M2 M

5 6 7 8 9 10 11 120

20

40

60

80

pH

perm

eate

flux

[L/h

/m²]

Figure 3.5: Rejection of glycine and permeate flux in function of feed pH for the different

membranes. (Solid lines are to guide eyes)

Glutamine permeation

Experimental results with Gln show the same tendency like with Gly, although

less pronounced, since the highest feed concentration was restricted to 0.2 mol/L

because of the solubility of Gln. The osmotic pressure of the0.2 molar feed so-

lution is app. 5 bar for zwitterionic and 10 bar for dissociated Gln solutions.

Slight decrease in the rejection for GE, none for DK and greater for GH, NP030

and NP010 membranes were observed. At higher concentrationrange, the per-

meate flux decreased with increasing pH analogously to the Gly measurements.

The permeation behaviour of the studied five membranes do notmatch with the

Page 86: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

74 CHAPTER 3.

behaviour of NTR7450 membrane studied by Li et al [7]. Based on our perme-

ation experiments, possible association of Gln into dimersand polymers could

not be identified as separation influencing parameter.

3.6(a) − GE

5 6 7 8 9 10 11 120

0.2

0.4

0.6

0.8

1

pH

R [−

]

0.001 M

0.01 M

0.1 M

0.2 M

5 6 7 8 9 10 11 120

5

10

15

20

25

30

pHpe

rmea

te fl

ux [L

/h/m

²]

3.6(b) − DK

5 6 7 8 9 10 11 120

0.2

0.4

0.6

0.8

1

pH

R [−

]

0.001 M

0.01 M

0.1 M

0.2 M

5 6 7 8 9 10 11 120

20

40

60

80

100

120

pH

perm

eate

flux

[L/h

/m²]

3.6(c) − GH

5 6 7 8 9 10 11 120

0.2

0.4

0.6

0.8

1

pH

R [−

]

0.001 M

0.01 M

0.1 M

0.2 M

5 6 7 8 9 10 11 120

20

40

60

80

100

pH

perm

eate

flux

[L/h

/m²]

Page 87: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

3.5. CONCLUSIONS 75

3.6(d) − NP030

5 6 7 8 9 10 11 120

0.2

0.4

0.6

0.8

1

pH

R [−

]

0.001 M

0.01 M

0.1 M

0.2 M

5 6 7 8 9 10 11 120

10

20

30

40

pH

perm

eate

flux

[L/h

/m²]

3.6(e) − NP010

5 6 7 8 9 10 11 120

0.2

0.4

0.6

0.8

1

pH

R [−

]

0.001 M

0.01 M

0.1 M

0.2 M

5 6 7 8 9 10 11 120

25

50

75

100

125

150

pH

perm

eate

flux

[L/h

/m²]

Figure 3.6: Rejection of L-glutamine and permeate flux in function of feed pH for the

different membranes. (Solid lines are to guide eyes)

3.5 Conclusions

Permeation experiments using several polymeric NF and tight UF membranes

were carried out with diprotic amino acids for a wide range offeed concentra-

tion and for total net charge ranging from0 to −1.

1. At low concentration range, commonly below app. 0.2 mol/L, a consider-

ably higher rejection for charged than for zwitterionic amino acids were

measured.

Page 88: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

76 CHAPTER 3.

2. At higher concentration range, charged amino acids have amuch pro-

nounced rejection drop over the concentration than zwitterions. As a re-

sult, even lower rejections for anionic amino acids were observed at the

applied transmembrane pressure.

3. At low concentration range, depending on the rejection generally below

app. 0.1-0.2 mol/L, no flux difference was observed. Above this concen-

tration range, more stressed decrease in flux with increasing concentra-

tion occurs for negatively charged amino acids than for zwitterions.

4. The pH dependency of osmotic pressure have not been taken into account

in the literature yet. Membranes with different active layer material show

identical tendency according to their response for increasing feed con-

centration. The pH dependency of osmotic pressure is identified as ma-

jor parameter affecting the separation behaviour in higherconcentration

regime.

5. Altered form of van’t Hoff law is reported for the pH dependency of the

osmotic pressure of diprotic amino acids and was confirmed experimen-

tally with vapor pressure osmometry and reverse osmosis.

Based on the series of our permeation experiments, we can conclude, that a

great care in NF process design for concentrating amino acids is needed if it is

based on experimental results of diluted systems, because the separation perfor-

mance in more concentrated systems is notably influenced by the osmotic pres-

sure, which is a strongly ionisation (i.e. pH) dependent quantity. The altered

form of the van’t Hoff law can be used for practical engineering calculations, it

can be favourable applied for instance in irreversible thermodynamics models.

Simulations with Kedem-Katchalsky equations are under investigations in our

laboratory.

Bibliography

[1] R. Faurie, J. Tommel, Microbial Production of L-Amino Acids, Vol. 79 of Ad-

vances in Biochemical Engineering/Biotechnology, Springer, Berlin and Heidel-

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BIBLIOGRAPHY 77

berg, 2002.

[2] T. Gotoh, H. Iguci, K. Kikuchi, Separation of gluthatione and ist related amino

acids by nanofiltration, Biochem. Eng. 19 (2004) 165–170.

[3] T. Tsuru, T. Shutou, S. Nakao, S. Kimura, Peptide and amino acid separation with

nanofiltration membranes, Sep. Sci. Technol. 29 (8) (1994) 971–984.

[4] T. Matsuura, S. Sourirajan, Reverse osmosis separationof amino acids in aqueous

solutions using porous cellulose acetate membranes, J. Appl. Polym. Sci. 18 (1974)

3593–3620.

[5] X. Wang, A. Ying, W. Wang, Nanofiltration of L-phenylalanine and L-aspartic acid

aqueous solutions, J. Membr. Sci. 196 (2002) 59–67.

[6] J. Timmer, M. Speelmans, H. van der Horst, Separation of amino acids by nanofil-

tration and ultrafiltration membranes, Sep. Purif. Technol. 14 (1998) 134–144.

[7] S. Li, C. Li, Y. Liu, X. Wang, Z. Cao, Separation of L–glutamine from fermentation

broth by nanofiltration, J. Membr. Sci. 222 (2003) 191–201.

[8] S. Arrhenius, On the dissociation of substances dissolved in water, Zeitschrift für

Physikalische Chemie 1 (1887) 631.

[9] S. Koter, Determination of the parameters of the spieglerUkedemUkatchalsky

model for nanofiltration of single electrolyte solutions, Desalination 198 (2006)

335–345.

[10] A. Kargol, Modified Kedem-Katchalsky equations and their applications, J.

Membr. Sci. 174 (2000) 43–53.

[11] A. Ahmad, M. Chong, S. Bhatia, Mathematical modeling and simulation of the

multiple solutes system for nanofiltration process, J. Membr. Sci. 253 (2005) 103–

115.

[12] C. Bhattacharjee, P. Sarkar, S. Datta, B. Gupta, P. Bhattacharya, Parameter estima-

tion and performance study during ultrafiltration of kraft black liquor, Sep. Purif.

Technol. 51 (2006) 247–257.

[13] M. Moresi, B. Ceccantoni, S. L. Presti, Modelling of ammonium fumarate recovery

from model solutions by nanofiltration and reverse osmosis,J. Membr. Sci. 209

(2002) 405–420.

[14] M. Pontie, H. Buisson, C. K. Diawara, H. Essis-Tome, Studies of halide ions mass

transfer in nanofiltration - application to selective defluorination of brackish drink-

ing water, Desalination 157 (2003) 127–134.

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78 CHAPTER 3.

[15] O. Kedem, A. Katchalsky, Thermodynamical analysis of the permability of biolog-

ical membranes to non-electrolytes, Biochim. Biophys. Acta 27 (1958) 229–246.

[16] D. Lide, Handbook of Chemistry and Physics, CRC Press, Boca Raton, FL, 1997,

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Page 91: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

4Modeling of amino acid nanofiltration

by irreversible thermodynamics

Reprinted from: Z. Kovács, M. Discacciati, W. Samhaber, Modeling of amino

acid nanofiltration by irreversible thermodynamics, Technical Report submitted

to Journal of Membrane Science, 2008.

Starting from the classical Kedem-Katchalsky model for filtration through mem-

branes, we derive an equation to compute the permeate flux andthe rejection

of diprotic amino acid compounds. We discuss the influence ofthe pH, the

viscosity and the feed concentration of the solution on the transport parame-

ters which characterize the membrane, and we improve the basic equation by

accounting for these dependencies. We propose two possiblestrategies to esti-

mate the transport parameters from experimental data. Finally, we compare our

79

Page 92: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

80 CHAPTER 4.

simulation results with experiments of tight ultrafiltration (UF) and nanofiltra-

tion (NF).

4.1 Introduction

Amino acids are widely used for human and animal nutrition, as pharmaceuti-

cals, cosmetics, agrochemicals and as other derivates for industrial uses. The

estimated world market is in the order of magnitude of106 tons/year and the

production is said to double every decade [1, 2]. Protein hydrolysis, microbi-

ological fermentation, chemical synthesis and enzymatic route can be used to

produce amino acids. In these diverse fields, NF can be applied for separation

and purification purposes. For the design of appropriate membrane filtration

processes, experimental studies on amino acid permeation and predictive mod-

els are needed.

Amino acids are amphoteric electrolytes. In aqueous media they are predom-

inantly present in zwitterionic form at their isoelectric point (pI). Adjusting

the pH of the solution to a level higher than pI results in negatively charged

molecules due to the deprotonation of the carboxyl group. Ithas been shown

that polymeric NF membranes have a considerably higher rejection for nega-

tively charged amino acids than for zwitterions [3–6]. Thisstatement is true

in low concentration regime. Most of NF studies focus on highly diluted sys-

tems, although concentration increase has a particular interest in industrial ap-

plications. Limited experimental data are available on concentrated systems. A

greater rejection drop over concentration was measured forcharged solutes than

for zwitterions and this was explained by charge-shieldingphenomena [7, 8].

Such a finding has been interpreted as a saturation of the charged sites of the

membrane due to the increasing concentration of charged solutes, which results

in a more permeable medium for charged components. No quantitative descrip-

tion of the transport phenomena has been reported so far.

Recently, a concept has beed presented to calculate the osmotic pressure of

amino acid solutions by altering the stoichiometric coefficient of the van’t Hoff

law corresponding to the dissociation state of the amino acids [9]. NF exper-

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4.1. INTRODUCTION 81

iments were carried out with L-alanine solutions in batch operation mode and

the dependency of osmotic pressure on pH has been identified as a major factor

affecting the separation behavior in high concentration regime.

The permeation of diprotic amino acid through several NF andtight ultrafiltra-

tion (UF) membranes was experimentally studied in our laboratory [10]. Sys-

tematic permeation experiments with glycine (Gly) and L-glutamine (Gln) were

investigated with stepwise increase of the ionization state from0 to−1 total net

charge, and with a gradual increase of the amino acid feed concentration in the

whole range of its solubility. It has been demonstrated, that membranes pur-

chased from different manufacturers with different activelayer materials show

an identical tendency as concerns their response to increasing feed concentra-

tion.

In this paper we study possible models based on the classicaltheory of irre-

versible thermodynamics (IT) to describe the transport of amino acids through

membranes. IT models have been applied in predicting transport through NF

membranes for single and binary solute systems [11, 12], most recently for

multiple systems [13, 14] and also for industrial feeds [6, 15–17].

We consider the Kedem-Katchalsky equations and, after introducing the effect

of pH on the osmotic pressure, we derive an equation to compute the rejec-

tion of the solute at any fixed concentration, pH and trans-membrane pressure

(Sects. 4.2.1–4.2.3). In Sect. 4.2.4, we present two possible ways to estimate

the transport parameters which characterize the membrane from experimental

data. The basic model is improved in Sect. 4.2.5 accounting for the depen-

dency of the transport parameters on the concentration and on the viscosity of

the solution. Finally, in Sect. 4.4 we compare the numericalsimulations that

we obtained using our predictive models with the experimental data measured

in our laboratory (see Sect. 4.3).

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82 CHAPTER 4.

4.2 Theory

4.2.1 Fundamentals of IT theory

The IT approach assumes a linear dependency of fluxes and related forces. In

transport phenomena through membranes, the driving forcesare the osmotic

pressure gradient∆π and the trans-membrane pressure gradient∆P , which

represents the applied pressure difference between the retentate and permeate

side of the membrane. The associated fluxes are the total volume fluxJv and

the relative velocity versus solventJD which are defined, respectively, as:

Jv = Lp ∆P + LpD ∆π, (4.1)

JD = LDp ∆P + LD ∆π. (4.2)

Lp, LpD, LDp, LD are suitable coefficients withLDp = LpD (Onsanger reci-

procity).

By convention, we use the symbol∆ to denote the difference of a quantity in

the retentate side and in the permeate side: e.g.,∆π = πr −πp, the sub-indices

r andp standing for “retentate” and “permeate”, respectively.

For practical use, Kedem and Katchalsky [18, 19] proposed toreplaceJD by

the solute fluxjs and they restated (4.1)-(4.2) as:

Jv = Lp(△P − σ△π), (4.3)

js = ω△π + (1 − σ)Jvc, (4.4)

whereLp is the hydraulic permeability of the membrane,σ is the reflection

coefficient, andω is the solute permeability coefficient.c represents the mean

concentration of the solute.

4.2.2 Effect of pH on the osmotic pressure

The osmotic pressure gradient△π is related to the difference of the concentra-

tion ∆c by the van’t Hoff law:

△π = νRT△c, (4.5)

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4.2. THEORY 83

whereT is the temperature,R is the gas constant, andν is the stoichiometric

coefficient.

We remind that for a diprotic amino acid it holdsν = 1 + fA+ + fA− , where

fA+ andfA− are the cation and the anion fractions, respectively, whichare

functions of pH as follows:

fA+ =1

1 + 10pH−pK1 + 102pH−pK1−pK2

,

fA− =1

1 + 10pK2−pH + 10pK1+pK2−2pH .

pK1 and pK2 are the dissociation constants of the amino acid. Thus, we have

ν = 1+1

1 + 10pH−pK1 + 102pH−pK1−pK2

+1

1 + 10pK2−pH + 10pK1+pK2−2pH .

(4.6)

From (4.5) and (4.6), it can be seen that the pH has an important contribution to

the osmotic pressure for amino acid permeation. In two recent works [9, 10], we

have shown experimentally the strong dependency between osmotic pressure

and pH.

Finally, let us recall the relationship between the net charge of an amino acid

and its pH. Indeed, sincez = (+1) · fA+ + (−1) · fA− + (0) · fA0 , fA0 being

the zwitterionic fraction, there holds

z =1

1 + 10pH−pK1 + 102pH−pK1−pK2

− 1

1 + 10pK2−pH + 10pK1+pK2−2pH .

(4.7)

In the following, owing to (4.7), we will often refer to the chargez or to the pH

as two equivalent quantities.

4.2.3 Manipulation of the Kedem-Katchalsky (KK) equations

In this section, we use the Kedem-Katchalsky (KK) model (4.3)-(4.4) to derive

an equation where the only unknown is the rejection of the solute through the

membrane. In this way, we will be able to determine the rejection for any

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84 CHAPTER 4.

given feed concentrationcr, pH and trans-membrane pressure∆P , once the

membrane transport parametersLp, σ andPs are known.

To obtain such equation, thanks to (4.5), we can firstly write:

Jv = Lp△P − LpσνRT (cr − cp), (4.8)

js = Ps(cr − cp) + (1 − σ)Jvc, (4.9)

where we have denoted byPs = ωνRT the solute permeability of the mem-

brane.

Then, since we assume thatJv > 0, we can divide (4.9) byJv, and recalling

that it holds:

cp =jsJv

, (4.10)

we obtain

cp =Ps(cr − cp)

Lp△P − LpσνRT (cr − cp)+ (1 − σ)c . (4.11)

Now, let us introduce the rejectionR:

R = 1 − cpcr. (4.12)

Obviously,cp = cr(1 −R), so that we can rewrite (4.11) as

cr(1 −R) =PscrR

Lp△P − LpσνRTcrR+ (1 − σ)c . (4.13)

The mean concentration across the membranec can be estimated using different

models based on physical considerations. The simplest approach is to consider

a linear model which representsc as the arithmetic average of the retentate and

permeate concentrations, i.e.

c =cr + cp

2. (4.14)

However, a more widely adopted model is thelogarithmicone which describes

c via the logarithmic average

c =cr − cp

ln cr − ln cp. (4.15)

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4.2. THEORY 85

For our simulations, we will adopt (4.15). Notice that, thanks to (4.12), the

logarithmic average (4.15) can be rewritten as

c = − crRln(1 −R)

, (4.16)

so that (4.13) becomes:

cr(1 −R) − PscrRLp△P − LpσνRTcrR

+ (1 − σ)crR

ln(1 −R)= 0 . (4.17)

After assigning the transport parameters of the membraneLp, Ps andσ, (4.17)

allows us to compute the value ofR corresponding to any set of variablescr,

ν and∆P . Let us point out that in order to ensure that the computed rejection

is physically significant,R must be a value between zero andmin(1,R∗), with

R∗ = ∆P/(σνRTcr). Indeed, this guarantees that the computed valueR is

such that0 < R < 1, and that the corresponding volume fluxJv is positive.

Remark 4.2.1 Should we consider the arithmetic average (4.14) instead of

(4.15), thanks to (4.12) we would havec = cr(1 − R/2), so that (4.13) would

become

cr(1−R)− PscrRLp△P − LpσνRTcrR

− (1− σ)cr

(

1 − R2

)

= 0 . (4.18)

This is a quadratic equation forR, whose solution can be immediately obtained

by the formula

R =−B +

√B2 − 4AC

2A, (4.19)

where we have denoted byA, B andC the (known) coefficients

A = (1 + σ)σLpνRTc2r,

B = −(

2Lpσ2νRTc2r + (1 + σ)crLp△P + 2Pscr

)

,

C = 2σcrLp△P.

An analogous formula for the permeate concentration has been proposed by

Kargol [20], and it was used to study the effect of increasingmechanical pres-

sure.

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86 CHAPTER 4.

Finally, we point out that the other solution of (4.18):(−B−√B2 − 4AC)/(2A)

would correspond to a negative total volume fluxJv < 0. As this is not mean-

ingful from the physical point of view, we consider (4.19) asthe sole solution of

(4.18).

4.2.4 Estimates of the membrane parameters

Equation (4.17) involves several physical parameters to describe the transport

properties of the membrane. Indeed, to computeR, we need to provide esti-

mates forLp, Ps andσ.

In the case of filtration of pure water, the osmotic pressure difference is∆π = 0.

Thus, we can compute the hydraulic permeability of the membrane with respect

to water, sayLpW , using the linear relationship

LpW =Jv

∆P. (4.20)

Usually, the dependency of the hydraulic permeabilityLp on the concentration

of the solution is neglected in the IT models of NF, and it is common practice

to setLp = LpW . However, an increase in concentration can cause significa-

tive changes in the viscosity and a consequent modification of the hydraulic

permeability. In the UF and reverse osmosis theory, viscosity changes are in-

corporated in the permeate flux by defining the latter asJv = △P/(µRm),

whereRm is the membrane resistance andµ is the viscosity of the solution.

Niemi and Palosaari [21] and, more recently, Moresi et al. [16] proposed mod-

els to account for the viscosity of the solution also in NF. Following [16], we

assumeLp to be inversely proportional to the viscosity of the solution:

Lp =LpW

µr, (4.21)

whereLpW is the hydraulic permeability with respect to pure water (4.20), and

µr is the relative viscosity of the feed solution to pure water,which in our case

is influenced by both the concentration and the feed pH.

The reflection coefficientσ and the solute permeabilityPs can be estimated

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4.2. THEORY 87

considering the Spiegler-Kedem (SK) model [22]:

R =

σ

(

1 − exp

(

σ − 1

PsJv

))

1 − σ exp

(

σ − 1

PsJv

) . (4.22)

More precisely, provided measurements of the fluxJv and the rejectionR for

a very diluted solution at different trans-membrane pressures∆P , the values of

the parametersσ andPs can be computed to fit (4.22) in a least-squares sense.

The reflection coefficientσ and the solute permeabilityPs are functions of

the pH (or, equivalently, of the net chargez). It has been shown by several

authors [3, 5, 6], that polymeric membranes in contact with diluted solutions

feature high permeability to zwitterionic amino acids, andlow permeability to

negatively charged amino acids. In this work, we treat aminoacid molecules

of different ionization state as species with different coefficientsPs andσ. So,

low σ and highPs can be assigned to a zwitterionic amino acid, while highσ

and lowPs correspond to a negatively charged amino acid. An analytic repre-

sentation ofσ andPs with respect toz is not currently known. However, we

can provide some elementary relations based on experimental measurements.

In particular, as we will illustrate more precisely in Sect.4.4.1, after estimating

σ andPs for some values of pH, we will expressσ = σ(z) andPs = Ps(z) as

affine maps ofz.

Concerning the dependency ofσ andPs on the feed concentration, no definite

conclusion can be drawn on the basis of the literature. Indeed, constant trans-

port parameters have been found by several authors [21, 23–25], while others

have described a considerable influence of the feed concentration [16, 26–28].

Empirical relationships can be determined by fittingσ andPs using (4.22) con-

sidering experimental values ofJv andR for a complete pressure scan and for

several feed concentrations. However, although this is a commonly used tech-

nique (see, e.g., [26, 29, 30]), due to its strong dependencyon experimental

data, it does not permit to set up a predictive model.

Finally, let us point out that experimental data of amino acid rejection as a func-

tion of volume flux for different pH values are rarely available in the literature.

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88 CHAPTER 4.

However, many studies reported experimental results on therejection as a func-

tion of pH corresponding to a single constant pressure gradient∆P [3, 4, 6, 7].

The Spiegler-Kedem model (4.22) cannot be used to estimate the transport pa-

rameters with such data, but an alternative strategy can be pursued.

Indeed, if the retentate concentration is sufficiently low and the applied trans-

membrane pressure is sufficiently high, the osmotic pressure becomes negligi-

ble because△P ≫ σ△π. Since in this caseµr ≈ 1, LpW can be estimated

by

LpW ≈ Jv

△P , (4.23)

whereJv is the mean value of the provided flux data.

Moreover, the reflection coefficient can be estimated directly from the rejection,

sinceR ≈ σ at sufficiently high pressure.

Finally, from (4.17) we can get the expression

Ps = −(

1

R − 1 +1 − σ

ln(1 −R)

)

Lp (σνRTRcr −△P ) , (4.24)

which allows us to estimatePs for any given pH.

The advantage of this technique is that all transport parameters can be estimated

with a minimum number of experimental data. Indeed, one needs only to mea-

sure the flux and rejection of a solution at neutral and at highpH, at low and high

concentration keeping a constant high pressure gradient∆P . In the following,

we refer to this technique asdirect parameter estimation.

4.2.5 Development of possible NF models

In this section, we present possible models to predict the filtration of amino

acids through membranes. The basic model is the one by Kedem and Katchal-

sky (4.3)-(4.4) which assumes constant transport parameters. However, on the

basis of the considerations that we made in Sect. 4.2.4 aboutthe dependencies

of transport parameters on pH, viscosity and concentrationof the aqueous so-

lution, we propose two slightly modified models which will allow us to better

represent the experimental evidence, as we will see in Sect.4.4.

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4.2. THEORY 89

The Kedem-Katchalsky (KK) model: description and algorithmic aspects

The basic model for NF is (4.3)-(4.4), which leads to the equation (4.17) for the

rejectionR. This model assumes that

i) Lp is constant andLp = LpW ;

ii) σ andPs are constant with respect to the feed concentrationcr, but de-

pend on the pH (equivalently, on the net chargez) of the solution.

To estimate the rejectionR using this model, we proceed as follows.

Considering a suitable set of experimental dataJv andR for a diluted solution

at several values of pH and∆P ,

1. we estimateLpW using (4.20) and we setLp = LpW ;

2. we estimateσ andPs using the SK model (4.22) for each value of pH;

3. we interpolate the values ofσ andPs obtained at each pH in order to have

functions relating them to pH (equivalently, to the net chargez).

Recall that (4.23)-(4.24) might be used instead of (4.22).

Once these quantities are known, for any assigned pressure∆P , pH, and feed

concentrationcr,

4. we computeν using (4.6);

5. we computeσ andPs using the relations obtained at point 3;

6. we plug these quantities into (4.17) and we solve the equation to compute

R;

7. we use (4.3) to compute the corresponding fluxJv.

From the numerical point of view, let us point out that the estimate (4.22) re-

quired at point 2 can be carried out using the Levenberg-Marquardt method

(see, e.g., [31]), while equation (4.17) can be solved usingthe Newton method

(see, e.g., [32]).

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90 CHAPTER 4.

A model accounting for the viscosity of the solution

In this model we would like to account for the viscosity of thesolution as indi-

cated in [16]. Thus, we will not setLp = LpW , like in KK, but use (4.21). This

requires a preliminary study of the viscosityµr depending on the concentration

and the pH of the solution. In particular, after measuring experimentallyµr for

a few sample concentrations at different pH, we interpolatethese data to obtain

a function which relatesµr to cr and pH (or, equivalently,z): µr = µr(cr, z).

Then, we perform the following steps:

1. we estimateLpW using (4.20);

2. we do steps 2–5 of the KK model (Sect. 4.2.5);

3. we computeµr for the assignedcr and pH using the functionµr =

µr(cr, z), and we estimateLp using (4.21);

4. we do steps 6–7 of the model KK.

We indicate this model as KKµ.

Solute permeabilityPs depending on the concentrationcr

In the third model that we propose, we consider the parameterPs depending not

only on the chargez like in the previous two models, but also on the feed con-

centrationcr. This idea is issued from (6.24) where we can remark an explicit

linear dependency ofPs on cr. We assumeσ to be independent ofcr.

To establish the dependencyPs = Ps(cr, z) we proceed as follows. We con-

sider suitable experimental values of rejection and flux at high concentration

for different pH, and we use (6.24) to compute the corresponding Ps. Then,

we interpolate linearly these values in order to expressPs as a function ofz

at high concentration. Finally, we interpolate linearly between this function at

high concentration and the one obtained at low concentration via the SK model

(4.22) (see step 3 of KK).

We indicate this model as KKcµ, and we can resume it through the following

steps.

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4.3. EXPERIMENTAL SETTING 91

1. We estimateLpW using (4.20);

2. we do steps 2–3 of KK (Sect. 4.2.5);

3. we establish a linear relationshipPs = Ps(cr, z) as explained here above;

4. we estimateν using (4.6);

5. we estimateσ using the relation obtained at point 2, andPs using the

function of point 3;

6. we do steps 3–4 of KKµ (see Sect. 4.2.5).

For the sake of clarity, in table 4.1 we resume the three models that we have

presented pointing out on which quantities the parametersLp, σ andPs depend

in each case.

Table 4.1: Dependency ofLp, σ andPs on the physical quantitiesz, cr andµr for the

three models described in Sect. 4.2.5.

Parameter KK (Sect. 4.2.5) KKµ (Sect. 4.2.5) KKcµ (Sect. 4.2.5)

Lp constant µr µr

σ z z z

Ps z z cr, z

4.3 Experimental setting

In our experiments we considered Gycine (Gly) and two different membranes.

4.3.1 Materials

Glycine (Gly) of analytical degree used in the experiments was purchased from

Merck. Its properties are shown in table 4.2.

In a previous work [10], we studied the transport propertiesof several com-

mercial polymeric membranes. On the basis of those results,here we chose

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92 CHAPTER 4.

Table 4.2: Characteristics of Glycine.

Item Glycine

Symbol Gly

Molecular formula C2H5NO2

Molecular weight [g/mol] 75.07

pH at the isoelectric point 5.97

pK, α–COOH group 2.34

pK, α–NH+3 group 9.60

Solubility in water at 25 °C [g/L] 251

to consider the membrane GH (G10) as a representative membrane, and the

membrane DK which seemed to show a different response to increasing feed

concentration than the other four membranes used in [10]. GHand DK are thin

film composite membranes supplied by GE W&P Technologies. They are char-

acterized by a molecular weight cut-off for non-charged components of approx

2500 Da and approx 150-300 Da, respectively, and they are classified as tight

UF and NF membrane, respectively.

4.3.2 Analyses

The concentration of Gly was measured with a total organic carbon analyzer

(Shimadzu TOC 500). The kinematic viscosity and the densityof Gly solutions

of different concentration and pH were measured at 25 °C withUbbelohde cap-

illary viscometer (technical details: Schott, Type 530/10, 0.63 mm diameter

capillary tube) and density meter (technical details: Antoon Paar DMA 35N

harmonic oscillator technology density meter), respectively. Dynamic viscosity

was obtained as product of kinematic viscosity and density.

4.3.3 Experimental set-up and procedures

Membrane filtration was performed using the experimental set-up shown in

Fig. 4.1. The membrane unit is equipped with a DDS LAB20 plate-and-frame

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4.3. EXPERIMENTAL SETTING 93

Figure 4.1: Schematic diagram of the lab-scale membrane system.

module. Membrane discs with effective membrane surface area of 350 cm2

were applied and tested in parallel. Both permeate and retentate streams were

recycled to the feed tank to keep the feed concentration constant. The circulat-

ing velocity was set to 0.5 m3/h, corresponding to Reynolds number 965, which

is the recommended value by the manufacturer to avoid excessive concentration

polarization [33]. All experiments were carried out at 25±0.2 °C.

In order to study the effect of concentration and pH on the separation behavior,

systematic measurements were carried out. First, a solution with a certain con-

centration of Gly was prepared and its pH was adjusted by adding NaOH using

a VWR low ionic double junction pH electrode. The applied trans-membrane

pressure was set to 3·106 Pa. In all runs, a stabilization time of 30 minutes

passed before taking sample. The permeate flux was manually measured by

using a calibrated cylinder and a stopwatch. After the complete pH scan (pH

5÷12), the feed solution was drained and the above mentioned procedure was

repeated with another feed of different concentration. TheGly concentration

was increased from 10 mol/m3 to its solubility limit. After each run, the per-

meability of deionised water was checked to ensure a complete recovery of the

initial permeability of the membranes. Before and after theexperimental work

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94 CHAPTER 4.

with Gly, salt rejection was measured to detect possible changes in the charac-

teristics of the membrane. During the experiments, no significant changes in

water permeability nor in salt rejection were observed.

4.4 Results and discussion

4.4.1 Membrane GH: estimate of the transport parameters

In order to estimate the transport parameters of the membrane GH, experiments

with a stepwise increase in the trans-membrane pressure∆P up to 4·106 Pa

were carried out using a 10 mol/m3 Gly solution. The permeate flux and the

rejection were monitored at neutral pH of the isoelectric point. Then, the pH

was adjusted with NaOH to 9.75, which corresponds to ca.−0.59 net chargez,

and the experiment was repeated. Finally, the pH was set to 11.3, in which case

98% of Gly is present in a negatively charged form.

From the experimental data, we estimatedLpW = 1.0262·10−11 m/(Pa s) using

(4.20). The stoichiometric coefficientν and the net chargez for the assigned

pH were computed from (4.6) and (4.7), respectively. Moreover, we used (4.22)

to estimateσ andPs. The computed values are reported in table 4.3, while

Fig. 4.2 shows the curves obtained through (4.22) to fit the data at different pH.

Finally, we interpolated linearly (in a least-squares sense) the estimated values

Table 4.3: Estimatedν, z, σ and Ps for the membrane GH using a 10 mol/m3 Gly

solution.

pH ν z σ Ps [m/s]

6.0 1.0005 -3.2397·10−5 0.1826 1.0103 · 10−5

9.75 1.5855 -0.5855 0.38523.9169 · 10−6

11.3 1.9804 -0.9804 0.75121.5088 · 10−6

of σ andPs versusz, as shown in Fig. 4.3. In order to use the models KKµ and

KK cµ we need to estimateµr. The relative viscosity to deionized waterµr was

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4.4. RESULTS AND DISCUSSION 95

0 1 2 3 4 5

x 10−5

0

0.2

0.4

0.6

0.8

1

Jv [m/s]

R

pH=6.0

pH=9.75

pH=11.3

Figure 4.2: Fitting of the experimental values for a 10 mol/m3 Gly solution at different

pH.

expressed as a function of pH and Gly concentration by fittingthe experimental

data ofµr in a least-squares sense. The estimated functionµr = µr(cr, z)

is reported in Fig. 4.4, while in Fig. 4.5 we show the values ofLp obtained

by (4.21). Finally, for KKcµ we have to study the dependency ofPs on the

concentration. To this aim, we considered a set of experimental valuesR and

Jv for a 2000 mol/m3 Gly solution at different pH and∆P = 3 · 106 Pa, and

we proceeded as explained in Sect. 4.2.5. The dependency ofPs on z andcrthat we obtained is shown in Fig. 4.6.

4.4.2 Simulation of separation for the membrane GH

Using the values of the transport parameters obtained in Sect. 4.4.1, we simu-

lated the filtration of a Gly solution through the membrane GH. We took several

feed concentrations:cr = 10, 100, 500, 1000, 2000 mol/m3, and we considered

the pH range6 ÷ 12.

First, we considered the basic KK model (see Sect. 4.2.5). Secondly, we adopted

the modified KKµ model (see Sect. 4.2.5) including the relative viscosityµr in

the hydraulic permeabilityLp (4.21) (see also Fig. 4.5). Finally, we considered

the KKcµ model (see Sect. 4.2.5) accounting also for the dependency of Ps on the

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96 CHAPTER 4.

−1−0.8−0.6−0.4−0.200

0.2

0.4

0.6

0.8

1

σ

z−1−0.8−0.6−0.4−0.20

0

0.2

0.4

0.6

0.8

1

1.2x 10

−5

Ps

[m/s

]

z

Figure 4.3: Membrane GH: linear dependency of the estimated reflection coefficientσ

(left) and of the solute permeabilityPs (right) with respect to the net chargez.

feed concentrationcr (Fig. 4.6). In Fig. 4.11, we compare the numerical results

obtained using the three models with the experimental data.The predictions of

the KK model are consistent with the trend of our experimental observations in

the sense that this model predicts a low rejection drop for zwitterions and a high

rejection drop for anions, and it indicates a pronounced decline of the permeate

flux over the pH for concentrated solutions. Moreover, it predicts the maxi-

mum of rejection at moderate pH for concentrated solutions.This means that

at sufficiently high feed concentration, a slightly greaterrejection can be found

for partially charged compounds than for completely charged compounds. This

remarkable phenomenon was experimentally observed for themembranes GE,

GH, NP030 and NP010 in our previous study [10].

The KK model is only able to predict the overall pattern of theseparation behav-

ior, indicating the general tendencies of fluxes and rejections. The simulation

results are inaccurate in comparison with the experimentaldata, especially at

high pH and high concentration range, where the rejection isoverestimated,

while the flux is underestimated due to their interdependency. However, con-

sidering that only a few input data are needed for this model and that no insight

into the transport phenomena nor special knowledge on the membrane structure

and material are involved, the results that it provides are appreciable.

The measured flux decline for non-charged Gly is greater thanwhat can be

Page 109: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

4.4. RESULTS AND DISCUSSION 97

0

500

1000

1500

2000

−1

−0.8

−0.6

−0.4

−0.2

0

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

µr

z cr [mol/m3]

Figure 4.4: Estimated relative viscosityµr of a Gly solution as function of pH and

concentration at 25 °C.

predicted with the KK model. This can be explained due to the fact that, since

zwitterions are low-rejected components,σ∆π is small, and (4.3) overestimates

Jv. The low experimental values of the flux could be retrieved accounting for

the dependency ofLp on the viscosity. Indeed, we can see that, although the

fluxes remain underestimated for high pH, the KKµ model greatly improves the

flux prediction for the low pH area, as shown in Fig. 4.11.

On the other hand, the model KKcµ successfully predicts the behavior of rejec-

tion and flux. Involving the dependency of the solute permeability on concen-

tration seems to be an adequate strategy for simulation purposes.

4.4.3 Estimate of the transport parameters for the membrane

DK

To estimate the transport parameters of the membrane DK, we use the data taken

from [10] and reported in table 4.4. Since these data refer toa sole value∆P ,

we cannot use (4.22). Thus, we follow the direct parameter estimation approach

described at the end of Sect. 4.2.4. More precisely, we apply(4.23) to estimate

LpW using the mean value of the fluxesJv reported in table 4.4. Thus, we get

Page 110: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

98 CHAPTER 4.

0500

10001500

2000−1

−0.5

05

6

7

8

9

10

11

12

x 10−12

z cr [mol/m3]

Lp

[m/(

Pa

s)]

Figure 4.5: Hydraulic permeabilityLp as function of charge and concentration.

Table 4.4: Experimental data for the membrane DK measured for a 10 mol/m3 Gly

solution, at∆P = 3 · 106 Pa, andT = 25 °C.

pH Jv · 10−5 [m/s] R6.0 2.97 0.7355

6.6 2.81 0.7500

7.9 2.69 0.7479

8.9 2.60 0.7603

9.9 2.85 0.8386

10.8 2.88 0.9180

LpW = 9.3371 · 10−12 m/(Pa s).

Moreover, considering the approximationR ≈ σ at high pressure, we plot the

given values ofR versusz, and we interpolate them linearly in a least-squares

sense to get a functionσ = σ(z) as shown in Fig. 4.7 (left).

Finally, we compute by (6.24) the values ofPs corresponding to the assigned

data still settingR ≈ σ, and we interpolate them linearly to get the dependency

onz shown in Fig. 4.7 (right). In order to incorporate also the dependency on the

Page 111: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

4.4. RESULTS AND DISCUSSION 99

0500

10001500

2000

−1

−0.5

0

0

1

2

3

4

5

6

x 10−5

Ps

[m/s

]

zcr [mol/m3]

Figure 4.6: Solute permeabilityPs = Ps(cr, z) for the membrane GH as function of

charge and concentration. The black triangles represent the values ofPs calculated by

(6.24) using the experimental data ofR for different pH atcr = 2000 mol/m3.

concentrationcr, we consider another set of dataR andJv for a 2000 mol/m3

Gly solution at∆P = 3 · 106 Pa with different pH, and we proceed as for

the membrane GH. The solute permeabilityPs = Ps(cr, z) that we obtain is

reported in Fig. 4.8.

−1−0.8−0.6−0.4−0.200

0.2

0.4

0.6

0.8

1

σ(≈

R)

z−1−0.8−0.6−0.4−0.20

1.5

2

2.5

3

3.5

4

4.5x 10

−6

Ps

[m/s

]

z

Figure 4.7: Membrane DK: linear dependency of the estimated reflection coefficientσ

(left) and of the solute permeabilityPs (right) with respect to the net chargez.

Page 112: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

100 CHAPTER 4.

0500

10001500

2000

−1

−0.8

−0.6

−0.4

−0.2

0

1

2

3

4

5

x 10−6

Ps

[m/s

]

zcr [mol/m3]

Figure 4.8: Solute permeabilityPs = Ps(cr, z) for the membrane DK as function of

charge and concentration. The black triangles represent the values ofPs calculated by

(6.24) using the experimental data for this membrane atcr = 2000 mol/m3.

4.4.4 Simulation of separation for the membrane DK

We proceed now similarly to Sect. 4.4.2 using the parametersestimated in

Sect. 4.4.3 to compute rejection and fluxes considering the models KK, KKµ

and KKcµ. The results of our computations are shown in Fig. 4.12 together with

the corresponding experimental data. In contrast to the case of the membrane

GH, here the KK model gives a good prediction for the rejection, and a suffi-

ciently good estimation for the flux. A slightly better fitting was obtained using

KKµ which was further improved applying KKcµ.

4.4.5 Simulations for the membrane GH with direct param-

eter estimation

In this section, we would like to compare the results of Sects. 4.4.1-4.4.2 with

those that one would obtain estimating the transport parametersLpW , Lp, σ

andPs using the direct estimation technique adopted for the membrane DK in

Page 113: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

4.4. RESULTS AND DISCUSSION 101

Sect. 4.4.3 instead of that followed in Sect. 4.4.1. This would allow us to check

how possible errors in the estimates of the transport parameters would influence

the numerical simulations.

We consider the experimental data reported in table 4.5. After computing the

Table 4.5: Experimental data for the membrane GH measured for a 10 mol/m3 Gly

solution, at∆P = 3 · 106 Pa, andT = 25 °C.

pH Jv · 10−5 [m/s] R6.0 3.25 0.1157

6.6 3.15 0.1452

7.9 3.08 0.1261

8.9 3.01 0.1736

9.9 3.14 0.4646

10.8 3.07 0.7344

mean value of the fluxesJv reported in table 4.5, we apply (4.23) and we

getLpW = 1.0391 · 10−11 m/(Pa s). Then, we consider again the approxi-

mationR ≈ σ and we interpolate the values ofR to obtain a linear depen-

dencyσ = σ(z) as shown in Fig. 4.9 (left). Under the same approxima-

tion, we use (6.24) to compute the values ofPs corresponding to the exper-

imental data and we interpolate them to get the linear dependency onz re-

ported in Fig. 4.9 (right). Finally, the dependency ofPs on the concentration,

Ps = Ps(cr, z), is investigated considering the same set of experimental data

for a 2000 mol/m3 Gly solution that was already used in Sect. 4.4.1. The result

is shown in Fig. 4.10. We can now perform the simulations analogous to those

of Sect. 4.4.2 using the models KK, KKµ and KKcµ. The results are reported in

Fig. 4.13 and compared with the related experimental data.

The simulation results obtained with direct parameter estimation are compa-

rable with those that we had computed using SK to determine the transport

parameters. Let us point out once more that the advantage of this technique

is the smaller amount of experimental data needed to computethe parameters.

Moreover, all the data required by the KKcµ model could be obtained adequately

Page 114: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

102 CHAPTER 4.

−1−0.8−0.6−0.4−0.200

0.2

0.4

0.6

0.8

1σ(≈

R)

z−1−0.8−0.6−0.4−0.20

0.4

0.6

0.8

1

1.2

1.4

1.6x 10

−5

Ps

[m/s

]

z

Figure 4.9: Linear dependency of the estimated reflection coefficientσ (left) and of the

solute permeabilityPs (right) with respect to the net chargez for the membrane GH

using the approach in Sect. 4.4.5.

0500100015002000

−1

−0.5

0

0

2

4

6

8

x 10−5

Ps

[m/s

]

z cr [mol/m3]

Figure 4.10: Solute permeabilityPs as function of charge and concentration for the

membrane GH following the approach in Sect. 4.4.5.

interpolating only four experimental points: two at low andtwo at high concen-

tration, each pair corresponding to low and high pH.

Page 115: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

4.5. CONCLUSIONS 103

4.5 Conclusions

We have provided a modified form (4.17) of the Kedem-Katchalsky equations

which can be used to computeR andJv for any∆P , pH, andcr. We discussed

two different techniques to estimate the transport parameters of the membranes,

namely, the SK approach and the direct parameter technique.We investigated

the dependency of the transport parameters on pH, viscosityand feed concen-

tration, and we included them into models to simulate the separation behavior

of NF membranes.

Finally, we compared the results that we obtained through our models with

experimental data of two membranes with different separation behaviors.

On the basis of this study, we can conclude that the models that we have in-

vestigated allow us to predict the flux and rejection with satisfactory accuracy.

The main advantage of these models is that they require very few input data,

which can be easily obtained from a simple experimental design. On the other

hand, the major shortcoming of these techniques is that theygreatly rely on em-

pirical relations between transport parameters and physical quantities like pH,

concentration or viscosity. An accurate evaluation of these relations is a crucial

step in the developement of the model. However, they can not be derived in a

straightforward way from the fundamentals of the irreversible thermodinamics

models.

Another possible strategy would be to adopt more involved models like the

DSPM-DE model [34, 35], which gives a deeper insight of the transport mech-

anism of the membrane. This approach is currently under investigation.

Acknowledgements.The second author acknowledges the Radon Institute for

Computational and Applied Mathematics (RICAM) in Linz, Austria, for par-

tially supporting this research.

Page 116: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

104 CHAPTER 4.

Table 4.6: Nomenclature

Symbol Name Unit

cp Permeate concentration mol/m3

cr Retentate concentration mol/m3

c Mean solute concentration across the membrane mol/m3

fA+ Cation fraction of the amino acid –

fA− Anion fraction of the amino acid –

fA0 Zwitterionic fraction of the amino acid –

js Molar solute flux mol/(m2 s)

Jv Total volume flux m/s

Lp Hydraulic permeability m/(Pa s)

Ps Solute permeability m/s

∆P Trans-membrane pressure Pa

R Rejection –

R Gas constant J/(°Cmol)

T Temperature °C

z Net charge of the amino acid –

µr Relative dynamic viscosity to water –

ν Stoichiometric coefficient –

π Osmotic pressure Pa

ω Solute permeability coefficient mol/(m2 s Pa)

σ Reflection coefficient –

Page 117: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

4.5. CONCLUSIONS 105

Membrane GH: simulations using the KK model

6 7 8 9 10 11 120

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

pH

R

cr = 10 mol/m3

cr = 100 mol/m3

cr = 500 mol/m3

cr = 1000 mol/m3

cr = 2000 mol/m3

6 7 8 9 10 11 120

0.5

1

1.5

2

2.5

3

3.5x 10

−5

pH

Jv

[m/s

]

cr = 10 mol/m3

cr = 100 mol/m3

cr = 500 mol/m3

cr = 1000 mol/m3

cr = 2000 mol/m3

Membrane GH: simulations using the KKµ model

6 7 8 9 10 11 120

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

pH

R

cr = 10 mol/m3

cr = 100 mol/m3

cr = 500 mol/m3

cr = 1000 mol/m3

cr = 2000 mol/m3

6 7 8 9 10 11 120

0.5

1

1.5

2

2.5

3

3.5x 10

−5

pH

Jv

[m/s

]

cr = 10 mol/m3

cr = 100 mol/m3

cr = 500 mol/m3

cr = 1000 mol/m3

cr = 2000 mol/m3

Membrane GH: simulations using the KKcµ model

6 7 8 9 10 11 120

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

pH

R

cr = 10 mol/m3

cr = 100 mol/m3

cr = 500 mol/m3

cr = 1000 mol/m3

cr = 2000 mol/m3

6 7 8 9 10 11 120

0.5

1

1.5

2

2.5

3

3.5x 10

−5

pH

Jv

[m/s

]

cr = 10 mol/m3

cr = 100 mol/m3

cr = 500 mol/m3

cr = 1000 mol/m3

cr = 2000 mol/m3

Figure 4.11: Simulations for membrane GH using the models KK (top), KKµ (middle)

and KKcµ (bottom). Continuous lines represent the estimated rejection R (left) and vol-

ume fluxJv (right) versus pH for a Gly solution at different feed concentrations. Dotted

lines report the experimental data. (∆P = 3 · 106 Pa,T=25 °C.)

Page 118: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

106 CHAPTER 4.

Membrane DK: simulations using the KK model

6 7 8 9 10 11 120

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

pH

R

cr = 10 mol/m3

cr = 100 mol/m3

cr = 500 mol/m3

cr = 1000 mol/m3

cr = 2000 mol/m3

6 7 8 9 10 11 120

0.5

1

1.5

2

2.5

3x 10

−5

pH

Jv

[m/s

]

Membrane DK: simulations using the KKµ model

6 7 8 9 10 11 120

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

pH

R

cr = 10 mol/m3

cr = 100 mol/m3

cr = 500 mol/m3

cr = 1000 mol/m3

cr = 2000 mol/m3

6 7 8 9 10 11 120

0.5

1

1.5

2

2.5

3x 10

−5

pH

Jv

[m/s

]

Membrane DK: simulations using the KKcµ model

6 7 8 9 10 11 120

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

pH

R

cr = 10 mol/m3

cr = 100 mol/m3

cr = 500 mol/m3

cr = 1000 mol/m3

cr = 2000 mol/m3

6 7 8 9 10 11 120

0.5

1

1.5

2

2.5

3x 10

−5

pH

Jv

[m/s

]

Figure 4.12: Simulations for membrane DK using the models KK (top), KKµ (middle)

and KKcµ (bottom). Continuous lines represent the estimated rejection R (left) and vol-

ume fluxJv (right) versus pH for a Gly solution at different feed concentrations. Dotted

lines report the experimental data. (∆P = 3 · 106 Pa,T=25 °C.)

Page 119: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

4.5. CONCLUSIONS 107

Membrane GH: simulations using the KK model

6 7 8 9 10 11 120

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

pH

R

cr = 10 mol/m3

cr = 100 mol/m3

cr = 500 mol/m3

cr = 1000 mol/m3

cr = 2000 mol/m3

6 7 8 9 10 11 120

0.5

1

1.5

2

2.5

3

3.5x 10

−5

pH

Jv

[m/s

]

cr = 10 mol/m3

cr = 100 mol/m3

cr = 500 mol/m3

cr = 1000 mol/m3

cr = 2000 mol/m3

Membrane GH: simulations using the KKµ model

6 7 8 9 10 11 120

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

pH

R

cr = 10 mol/m3

cr = 100 mol/m3

cr = 500 mol/m3

cr = 1000 mol/m3

cr = 2000 mol/m3

6 7 8 9 10 11 120

0.5

1

1.5

2

2.5

3

3.5x 10

−5

pH

Jv

[m/s

]

cr = 10 mol/m3

cr = 100 mol/m3

cr = 500 mol/m3

cr = 1000 mol/m3

cr = 2000 mol/m3

Membrane GH: simulations using the KKcµ model

6 7 8 9 10 11 120

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

pH

R

cr = 10 mol/m3

cr = 100 mol/m3

cr = 500 mol/m3

cr = 1000 mol/m3

cr = 2000 mol/m3

6 7 8 9 10 11 120

0.5

1

1.5

2

2.5

3

3.5x 10

−5

pH

Jv

[m/s

]

cr = 10 mol/m3

cr = 100 mol/m3

cr = 500 mol/m3

cr = 1000 mol/m3

cr = 2000 mol/m3

Figure 4.13: Simulations for the membrane GH using the models KK (top), KKµ (mid-

dle) and KKcµ (bottom). Continuous lines represent the estimated rejection R (left) and

volume fluxJv (right) versus pH for a Gly solution at different feed concentrations

(∆P = 3 · 106 Pa, T=25 °C). Dotted lines report the experimental data. The trans-

port parameters of the membrane were estimated as describedin Sect. 4.4.5

Page 120: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

108 CHAPTER 4.

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110 CHAPTER 4.

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Page 123: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

5Numerical simulation and

optimization of multi-step batch

membrane processes

Reprinted from: Z. Kovács, M. Discacciati, W. Samhaber, Numerical simulation

and optimization of multi-step batch membrane processes, To appear in Journal

of Membrane Science, 2008.

A simple numerical technique is presented for batch membrane filtration de-

sign. The underlying model accounts for variable solute rejection coefficients,

and it has a modular structure which permits to easily describe the batch pro-

cess involving different arrangements of the three typicalbasic steps: pre-

concentration, dilution-mode and final concentration. Theexperimental design

111

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112 CHAPTER 5.

required to set up the model is discussed, together with the necessary sampling

procedure. In order to validate the technique, multi-step nanofiltration experi-

ments were carried out using a binary test solution containing organic and in-

organic substances. The objective of the process is to remove the electrolyte

from the solution and concentrate the organic component. The predictions for

the multi-step process performances were found to be in goodagreement with

the experimental results. Finally, optimum-search techniques for the overall

multi-step process are discussed, considering economicalaspects and techno-

logical demands. The presented optimization procedure canbe useful to find

the optimum pre-concentration and dilution factors for a membrane plant with

a defined module configuration and membrane area.

5.1 Introduction

In batch membrane system design, a common separation strategy for selective

removal of components with low retentions is to employ a multi-step membrane

process. A multi-step batch process is a chain of operationsof defined number

and order, which are carried out consecutively using the same membrane mod-

ule. There are two basic operation modes: the concentrationand the dilution

mode. In general, a multi-step process consists of three steps (or operations):

(1) pre-concentration, (2) dilution mode and (3) post-concentration. This con-

cept is one of the conventional process techniques to achieve high purification

of macro-solutes with an economically acceptable flux [1].

It is widely accepted to use the term “diafiltration” insteadof “dilution mode”,

to refer to amodeof operation. However, according to the terminology recom-

mendation of the former European Society of Membrane Science and Technol-

ogy (now known as the European Membrane Society), the term “diafiltration”

should be replaced by “dilution mode” [2]. It also should be noted that the term

“diafiltration” is often used in a misleading way, denoting the whole process

involving both concentration and dilution mode operations.

Membrane diafiltration is a well established technique and has found many

applications in the food and beverage, chemical, biotechnological and phar-

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5.1. INTRODUCTION 113

maceutical industries [3]. Batch system design is of both industrial and aca-

demic interest, including active areas on purification of oligosaccharides [4, 5],

recovery of high-value product from process waste stream [6], fractionation

of whey proteins [7, 8], diafiltration of milk [9], desaltingof dye and pig-

ments [10, 11], recovery of products from fermentation broth [12], removal

of humic substances [13], etc.

Many studies have provided mathematical descriptions of multi-step processes.

Usually, the computation of the changes of solutes and volume in the feed

tank during the process is based on mass balance. This results in a set of

equations involving coefficients which describe the rejection of the solutes.

Such coefficients are usually determined from experiments with the process

solution, and they are considered to be constant in the mathematical handling

[4, 5, 7, 8, 11–16]. Assuming non-constant coefficients (e.g., feed-composition

dependent) would lead to a complex system of algebraic equations which has re-

ceived much less attention so far. Bowen et al. [10] and recently Oatley et al. [6]

have developed predictive models using the extended Nernst-Planck equation,

and they have applied them to concentration and dilution mode processes. This

approach resulted in a set of differential equations which only partly could be

solved exactly, and numerical integration methods had to beemployed for the

simulation of the feed concentration of the permeating component. Also Fo-

ley [14] had to introduce numerical integration techniquesin order to adequately

simulate membrane process with non-perfect macro-solute rejection. However,

the rejection coefficients were kept constant during all thesteps of the process,

which might not be generally true for all applications.

Considerable progress in the application of numerical techniques has been a-

chieved for continuous membrane processes [17–19]. Driscoll [20] developed

a FORTRAN code to simulate various configurations of the ultrafiltration/dia-

filtration process including batch, semi-batch, feed-and-bleed and single pass

operations. The approach followed in his work did not use theconcentration

factor as a basis for the calculations, but rather the component concentrations.

The main design equations (with the additional assumption that the rejections

are constant) of the computer program are summarized by Cross [21]. The

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114 CHAPTER 5.

simulator is capable of determining the required membrane area and the optimal

area distribution for a multi-stage system.

In this study, we present a simple computational method which can be used as

a basis for batch process simulations. The presented technique can find appli-

cations where the optimal settings of a multi-step process are to be determined

for a membrane plant with a given membrane area. After discussing the re-

quired input data and the corresponding experimental design with the necessary

sampling procedure, we use permeation data of a two-component test system to

validate the numerical method. Finally, we discuss optimum-search techniques

considering economical aspects and technological demands.

5.2 Theory

5.2.1 Batch system design

A schematic flow diagram of the batch filtration system considered in this study

is shown in Fig. 5.1. In both concentration and dilution operation modes, the

M e m b r a n e m o d u l e

P e r m e a t e

R e t e n t a t e

F e e d t a n k

P u m p

F i n a l v o l u m e

P e r m e a t e t a n k

D i l u a n t

D i l u t i o n v o l u m e

I n i t i a l v o l u m e

Figure 5.1: Schematic representation of batch membrane filtration settings.

feed solution is circulated through a membrane module at high flow rate. The re-

tentate stream is completely recycled into the feed tank, and the permeate stream

is collected separately. In the concentration mode no wash-water is added, thus

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5.2. THEORY 115

resulting in a continuous volume decrease in the feed tank. The concentration

mode process is described by the concentration factorn, which is the ratio of

the initial volume to the final volume. The dilution mode is described by the di-

lution factorD, which is the ratio of the applied wash-water volume to the feed

volume. In this study, we consider a constant-level continuous dilution mode,

which means that a level sensor is activated to keep a constant feed volume by

continuously adding the diluant at a rate equal to the permeation rate.

In the following, we consider a solution consisting of two compounds. To iden-

tify the substances and the stages we use two subscripts: thefirst one,f , p or

d, stands for ‘feed’, ‘permeate’ or ‘diluant’, respectively; the second subscript

denotes the actual step of the process. If a third subscript appears, it denotes

component ‘1’ or ‘2’. The initial feed solution has a volumeVf,0 and the initial

concentrations of the two components arecf,0,1 andcf,0,2, respectively. The so-

lution is processed in a multi-step batch process involving(1) pre-concentration,

(2) dilution-mode and (3) post-concentration steps as it isschematically shown

in Fig. 5.2. Each step can be described by the operation timet and the cor-

Vf,0, cf,0,1, cf,0,2

Step 1 ↓ Pre-concentrationn1, t1

Vf,1, cf,1,1, cf,1,2

Step 2 ↓ Dilution mode D2, t2

Vf,2, cf,2,1, cf,2,2

Step 3 ↓ Post-concentrationn3, t3

Vf,3, cf,3,1, cf,3,2

Figure 5.2: Schematic summary of the multi-step process.

responding concentration or dilution factorsn or D, respectively. Thus, for

exampleVf,1 is the volume in the feed tank after Step 1, which was achieved

in the operation timet1 by reducing the initial feed volumeVf,0 by the con-

centration factorn1, resulting in the concentrationscf,1,1 andcf,1,2 in the feed

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116 CHAPTER 5.

tank.

5.2.2 Classical mathematical treatment

The performance of batch systems has been studied by severalauthors [4, 5, 7,

8, 11–16]. Here, we briefly summarize the basic equations of the mathemat-

ical models, and in Sect. 5.4.1 we discuss the cases where they have limited

applicability. Membrane fouling is not considered in this paper.

The operation time for the pre-concentration step can be calculated by

t1 =

∫ Vf,0

Vf,1

dVf

J(t)A(5.1)

whereA is the membrane area andJ(t) is the permeate flux.

Mass balance is used to relate the concentrations of the solutes at the end of this

operation,cf,1,i, i = 1, 2, to the pre-concentration factorn1 as follows:

cf,1,i = cf,0,i · (n1)σi i = 1, 2 (5.2)

whereσi is the solute rejection coefficient, and the concentration factorn1 is

given byn1 = Vf,0/Vf,1.

For the dilution mode, the operation timet2 and the change in the solute con-

centrations in the feed tank is given by

t2 =

∫ Vp,2

0

dVp

J(t)Aand cf,2,i = cf,2,i · eD2(σi−1) i = 1, 2 (5.3)

where the dilution factorD2 is related to the volume of the total permeateVp,2

collected in Step 2:D2 = Vp,2/Vf,1.

Similarly to (5.1) and (5.2), for the post-concentration step there holds

t3 =

∫ Vf,2

Vf,3

dVf

J(t)Aand cf,3,i = cf,2,i · (n3)

σi i = 1, 2. (5.4)

Eqs. (5.2)-(5.4) are derived assuming that the recirculation rate is very high

compared to the permeate rate.

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5.2. THEORY 117

5.2.3 Development of computational algorithm

The multi-step process is carried out at constant pressure and temperature, and

the same hydrodynamic conditions are maintained during theoperation. Thus,

at any time and at any step of the process, the permeate flux andthe rejections of

the components depend solely on the actual feed composition. We will describe

the flux and the rejections as functions of the feed composition in Sect. 5.2.4.

Here, we assume that these functions are known, and we derivea computational

method to simulate the feed concentration of the componentsand the feed vol-

ume over the operation time.

In the following we consider a single-step process which canbe either concen-

tration mode or dilution mode, thus, the process step numberis not indicated

with subscripts. The feed solution has an initial volumeV 0f and initial concen-

tration of the solutesc0f,i, i = 1, 2. At each stepk of the process, independently

of whether it operates in concentration or in dilution mode,we collect the per-

meate until the final permeate volumeV finalp is reached. Let us split the perme-

ate volume interval [0,V finalp ] in subintervals[V k

p , Vk+1p ], k = 0, . . . , N − 1,

with V 0p = 0 andV N

p = V finalp . Let∆V k+1

p = V k+1p −V k

p , and denote by the

upper-indexk the value of any quantity in the collected permeate volumeV kp :

e.g.,ckf,i = cf,i(Vkp ).

We fix a-priori a sufficiently small volume∆Vp which permeates through the

membrane. Since the initial feed composition is given, using the relationship

Jk = J(ckf,1, ckf,2), the permeate flux and the corresponding permeation time

can be estimated. The known rejection of the compounds,

Rki = Ri(c

kf,1, c

kf,2) i = 1, 2, (5.5)

allows us to compute the permeated mass of each component in the volume

∆Vp. Thereafter, mass and component balances for both permeateand feed

tank can be used to determine the new compositions and total masses.

This procedure can be repeated with the new values. Obviously, in dilution

mode operation, we assume a wash-water volume inlet into thefeed tank, which

is equal to the volume permeated through the membrane. The exit condition of

the cycle can be an a-priori defined volume to be collected in the permeate tank,

Page 130: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

118 CHAPTER 5.

or, alternatively, either a collapsed time or a pre-defined feed concentration of

one of the solutes.

The proposed algorithm can be summarized in the following steps.

1. For the collected permeate volumeV kp , calculate the fluxJk and the re-

jectionRki , i = 1, 2, of the two solutes.

2. The time needed for obtaining the fixed permeate volume∆Vp is

∆tk =∆Vp

Jk ·A . (5.6)

The total collapsed time is given by

tk+1 = tk + ∆tk. (5.7)

Notice that (5.6) corresponds to a discretization of the integral expression

(5.1).

3. The volume in the feed tank becomes

V k+1f = V k

f − ∆Vp + ∆Vd (5.8)

where∆Vd is the volume of diluant added into the feed tank while the

permeate volume∆Vp is collected. Obviously,∆Vd = 0 in concentration

mode. In dilution mode, the volumeV kf remains constant for allk since

∆Vp = ∆Vd.

4. Finally, the concentrations in the feed tank can be obtained as

V k+1f ck+1

f,i = V kf c

kf,i − ∆Vpc

kp,i + ∆Vdc

kd,i i = 1, 2. (5.9)

The permeate concentrationckp,i is given byckp,i = ckf,i(1−Rki ), where the

rejectionRki changes at each stepk. This improves the model illustrated

in Sect. 5.2.2 where the rejection coefficientσi is always kept constant

through the whole process. Recall also thatRki , i = 1, 2, depends at each

discretization stepk on the actual concentration of all components as it is

expressed in (5.5).

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5.2. THEORY 119

Using this computational technique, one can simulate diverse processes. The al-

gorithm can be run either in concentration or in dilution mode, and a multi-step

process can be built up from individual blocks by defining theinput arguments

of a latter step as the output arguments of the previous step.The number and

the order of the individual steps can be freely chosen. Furthermore, also the

solute concentration of the diluant can be set, so that the simulation of dilution

mode is not restricted to pure water utilization. This can bea useful feature for

numerous applications, where diluted process-liquids arealso produced and the

utilization of these liquids as diluants has to be considered.

In this study, we consider constant level dilution mode withcontinuous addition

of the washing solution. However, a simple modification of Eqs. (5.8)-(5.9)

would permit to simulate both constant and variable volume level dilution mode

with continuous as well as intermittent addition of washingsolution.

Let us point out that a similar algorithm can be established if one fixed a-priori

a time step∆t instead of the permeate volume∆Vp. In this case, (5.6) becomes

∆V kp = Jk ·A · ∆t (5.10)

and the collected volume at timetk+1 = (k + 1) · ∆t is

V k+1p = V k

p + ∆V kp . (5.11)

Moreover, the volume and the concentrations in the feed tankcan be obtained

by the following equations, respectively:

V k+1f = V k

f − ∆V kp + ∆V k

d (5.12)

V k+1f ck+1

f,i = V kf c

kf,i − ∆V k

p ckp,i + ∆V k

d ckd,i i = 1, 2. (5.13)

Both approaches (with fixed∆Vp or ∆t) lead to the same final results at the end

of the simulation.

5.2.4 Rejection and flux as functions of feed composition

Several approaches can be applied in order to evaluate the separation behavior

of the membrane required in the Step (1) of the algorithm. Forexample, the esti-

mation of the permeate flux and the rejections of the compounds can be obtained

Page 132: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

120 CHAPTER 5.

by transport or irreversible thermodynamics models. However, in this study, we

adopt a practical approach based on experimental data. The classical mathemat-

ical treatment (see Sect. 5.2.2) requires analysis of samples taken from the feed

tank in order to estimate the flux behavior and the rejection coefficients of the

compounds.In our case, we need to provide the relationsJk = J(ckf,1, ckf,2) and

Rki = Ri(c

kf,1, c

kf,2), i = 1, 2, which require a different sampling technique to

be established. Indeed, not only samples from the feed tank,but also from the

permeate stream need to be taken at the same time. These data can be directly

achieved from one well-prepared test run with the real process solution. We

assume that the samples are taken from the membrane plant whose operation

is to be optimized. Scale-up calculations, where a change inthe hydrodynamic

conditions needs to be taken into account, are out of the scope of this work.

The advantage of this empirical approach in comparison to the transport and

irreversible thermodynamics models is that reliable relations can be obtained

from a limited number of experimental data without prior approximations. This

strategy can find applications in engineering calculationsdealing with complex

systems, where theoretical approaches might give poor predictions if not prop-

erly tuned. However, if a reliable theoretical prediction of flux and rejection

is available, it can be directly inserted in Step (1) withouthaving to reformu-

late the mathematical framework. It should be pointed out that the flux and

the rejections depend on many other factors in addition to the feed composi-

tion, such as temperature, pressure and cross-flow velocity. A complete study

accounting for all these factors would rapidly increase thenumber of required

prior-experiments. Thus, further advances in diafiltration should address the

development of mass transfer models inside nanofiltration membranes, in order

to develop better prediction methods for the solute rejections.

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5.3. EXPERIMENTAL 121

5.3 Experimental

5.3.1 Materials

A commercial polymeric GE (G-5) NF membrane obtained from GEWater &

Process Technologies was applied in this study. For our experiments we used

mill white table beet sugar (Wiener Zucker) purchased fromAGRANA AUSTRIA,

fine industrial sodium chloride fromSALINE AUSTRIA, and deionized water.

5.3.2 Analysis

The conductivityr and the refractive indexχ of calibration solutions were deter-

mined for sugar and salt concentrations up to 0.6 mol/L and 0.3 mol/L, respec-

tively. The refractive index was measured with Atago PR-101digital refrac-

tometer, the conductivity with WTW LF 95 conductivity meterand the density

with Antoon Paar DMA 35N harmonic oscillator technology density meter. The

concentrations can be expressed in terms ofr andχ by fitting the experimental

data in a least-squares sense to the equation:

c = (a1χ2 +a2χ+a3)r

2 +(a4χ2 +a5χ+a6)r+(a7χ

2 +a8χ+a9) (5.14)

wherea1, . . . , a9 are the (unknown) empirical coefficients. The estimated func-

tionsc = c(χ, r) for sucrose and salt are reported in Fig. 5.3.

5.3.3 Experimental set-up and procedure

The NF plant is shown in Fig. 5.4. A filtration area of 0.55 m2 spiral-wound

membrane element was installed in the membrane module. The applied trans-

membrane pressure was kept at 30 bar. All experiments were carried out at

25±0.2 °C. Before starting the operation, the plant was run by recycling both

retentate and permeate into the feed tank in order to achievesteady state condi-

tions. Then, sampling was carried out for the analysis of theinitial component

and the operation was started. During the operation, the retentate stream was

recycled to the feed tank with the circulation flow-rate of 1000 L/h, and the per-

meate stream was collected in a permeate tank. Permeate and retentate samples

Page 134: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

122 CHAPTER 5.

010

2030

40

0

10

20

30

0

0.2

0.4

0.6

0.8

1

conductivity [mS/cm]refraction [Bx°]

sucr

ose

conc

entr

atio

n ×

10−

3 [mol

/L]

010

2030

0

10

20

30

0

0.2

0.4

0.6

conductivity [mS/cm]refraction [Bx°]

NaC

l con

cent

ratio

n ×

10−

3 [mol

/L]

Figure 5.3: Estimated plane (solid lines) and experimental data (closed symbols) of

sucrose (left) and salt (right) concentration as functionsof conductivity and refractive

index at25 ◦C.

Figure 5.4: Schematic figure of the experimental set-up.

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5.4. RESULTS AND DISCUSSION 123

were taken periodically always at the same time from the permeate pipe and

from the feed tank, respectively. The density, the conductivity and the refrac-

tive index of both permeate and feed samples were monitored.The permeate

flux was measured with a mass flow meter and the weight of the collected per-

meate was monitored with a balance placed under the permeatetank. The high

flow rate of the recycled retentate caused perfect mixing in the feed tank. The

concentration of the compounds in the feed tank and in the retentate stream

were practically equal at any time of the process due to the orders of magnitude

difference between the feed flow-rate and the permeate flow-rate. After each

run, the permeability of deionised water was checked, and complete recovery

of the initial permeability of the membranes was ensured.

5.4 Results and discussion

Six batches were processed applying various concentrationand dilution factors.

The multi-step batch experiments are summarized in Table 5.1. In the last two

column,n = n1 ·n3 is the total concentration factor, whilet is the total elapsed

time.

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12

4C

HA

PT

ER

5.

Table 5.1: Experimental data for membrane GE, 30 bar, 25°C, initial feed volume and concentrations in all cases:Vf,0 = 25 L,

cf,0,1 = 0.150 mol/L andcf,0,2 = 0.300 mol/L.

Pre-concentration Dilution mode Post-concentration

run n1 t1 cf,1,1 cf,1,2 D2 t2 cf,2,1 cf,2,2 n3 t3 cf,3,1 cf,3,2 n t

No. [-] [h] [mol/L] [mol/L] [-] [h] [mol/L] [mol/L] [-] [h] [m ol/L] [mol/L] [-] [h]

#1 1.00 0.00 0.150 0.300 0.92 2.93 0.128 0.175 2.47 2.05 0.2820.262 2.5 5.0

#2 1.25 0.64 0.182 0.326 1.20 3.05 0.140 0.157 1.98 1.28 0.2480.215 2.5 5.0

#3 1.43 1.00 0.198 0.341 1.36 3.17 0.148 0.150 1.76 0.98 0.2340.192 2.5 5.2

#4 1.42 0.98 0.199 0.337 0.85 1.83 0.158 0.212 1.73 1.00 0.2440.259 2.5 3.8

#5 1.65 1.33 0.219 0.349 1.62 3.17 0.159 0.140 1.49 0.65 0.2330.176 2.5 5.2

#6 2.46 2.28 0.337 0.404 1.66 2.75 0.234 0.123 1.00 0.00 0.2340.123 2.5 5.0

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5.4.R

ES

ULT

SA

ND

DIS

CU

SS

ION

12

5

Table 5.2: Simulation results with corresponding prediction errors (in brackets) for membrane GE, 30 bar, 25°C, initial feed volume

and concentrations in all cases:Vf,0 = 25 L, cf,0,1 = 0.150 mol/L andcf,0,2 = 0.300 mol/L.

Pre-concentration Dilution mode Post-concentration

run t1 cf,1,1 cf,1,2 t2 cf,2,1 cf,2,2 t3 cf,3,1 cf,3,2 t

No. [h] [mol/L] [mol/L] [h] [mol/L] [mol/L] [h] [mol/L] [mol /L] [h]

#1 0.00 (0%) 0.150 (0%) 0.300 (0%) 2.79 (-5%) 0.126 (-1%) 0.176 (0%) 1.93 (-6%) 0.262 (-7%) 0.256 (-3%) 4.7 (-5%)

#2 0.66 (4%) 0.180 (-1%) 0.323 (-1%) 3.04 (-0%) 0.143 (2%) 0.159 (1%) 1.29 (1%) 0.249 (0%) 0.215 (0%) 5.0 (1%)

#3 1.01 (1%) 0.200 (1%) 0.336 (-1%) 3.09 (-2%) 0.154 (4%) 0.150 (0%) 0.99 (1%) 0.244 (4%) 0.194 (1%) 5.1 (-1%)

#4 0.99 (2%) 0.199 (0%) 0.335 (0%) 1.99 (-8%) 0.169 (7%) 0.197(-8%) 1.03 (2%) 0.263 (7%) 0.245 (-6%) 4.0 (5%)

#5 1.35 (1%) 0.225 (2%) 0.350 (0%) 3.28 (3%) 0.165 (3%) 0.134 (-4%) 0.65 (0%) 0.228 (-2%) 0.162 (-8%) 5.3 (2%)

#6 2.14 (-6%) 0.308 (-9%) 0.387 (-5%) 2.62 (-5%) 0.223 (-5%) 0.136 (10%) 0.00 (0%) 0.223 (-5%) 0.136 (10%) 4.8 (-6%)

Prediction error [%]= (1 − Estimated value/Measured value) · 100%

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126 CHAPTER 5.

5.4.1 Classical mathematical treatment

One important assumption of Eqs. (5.2)-(5.4) is that for allcomponents a con-

stantσ is employed for all steps. This is only applicable when the rejection rates

of the solutes remain constant through the process. Moreover, this formulation

is only valid when the interdependence between the micro andmacro-solute

feed concentrations on their rejections is negligible. In amore general case,

the rejection coefficients of both micro-solute and macro-solute in the dilution

mode step are affected by the extent to which the micro-solute concentration

was reduced and also to which the macro-solute was concentrated in the pre-

concentration step. Thus, the rejection coefficients of Step 2 are functions of

the applied pre-concentration factorn1, and in the post-concentration step they

are functions of bothn1 andD2. Similarly, the feed concentrations of both

components can influence the permeate flux. Obviously, employing more steps

increases the difficulty of the problem.

The rejection coefficients were calculated using Eqs. (5.2)-(5.4) for both com-

ponents using the experimental results. The rejection coefficient of sugar was

found to be practically independent of the applied pre-concentration and dilu-

tion factors with mean value≈ 0.8. On the contrary, the salt rejection coef-

ficient was greatly influenced by the feed composition, as shown in Table 5.3.

This provides an example of the limited practical significance of the approxi-

mationσ =constant.

5.4.2 Rejection and flux as function of feed composition

The experimental data of permeate flux and rejections are plotted in the function

of feed composition in Fig. 5.5 and Fig. 5.6. A high and fairlycomposition-

independent rejection (77-84%) was measured for the sugar.On the contrary,

the rejection of salt strongly depends on the feed concentrations of both com-

ponents varying between 20 and 63%. Moreover, both components have great

contributions to the permeate flux.

Empirical planes were fitted to the experimental data expressing the flux and

the rejections in terms ofcf,1 andcf,2. In our specific application, very good

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5.4. RESULTS AND DISCUSSION 127

Table 5.3: Rejection coefficients of salt for the six batch operations.Values are calcu-

lated from experimental measurements.

Batch Step 1 Step 2 Step 3

#1 – 0.41 0.45

#2 0.36 0.39 0.46

#3 0.36 0.39 0.44

#4 0.33 0.45 0.36

#5 0.30 0.44 0.57

#6 0.33 0.28 –

fittings were achieved using the plane

P(cf,1, cf,2) = (x1cf,1 + x2)cf,2 + (x3cf,1 + x4), (5.15)

wherex1, . . . , x4 are the unknown empirical coefficients andP represents one

of the dependent variables:J ,R1 orR2.

The data-fitting problem was solved in a least-squares sense. This simple linear

fitting gives good estimation of flux and rejections for the studied feed com-

position range; however, it has limited usage for data extrapolation. Many

experiments were carried out in order to check the validity and the accuracy

of the simulation technique and also to compare with classical models’ predic-

tions. In Fig. 5.5-5.6 we plot all measured values. However,it should be noted

that fewer experimental points are sufficient to explore themathematical rela-

tions relatingJ , R1, R2 to cf,1, cf,2. Thus, the numerical approach does not

need significantly more input data than the classical modeling technique, but it

requires taking samples from the feed tank and the permeate stream at the same

time. In fact, the necessary input data can be gained from onewell-prepared

batch experiment.

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128 CHAPTER 5.

00.1

0.20.3

0.4

00.1

0.20.3

0.40.5

0

0.2

0.4

0.6

0.8

1

cf,1

[mol/L]cf,2

[mol/L]

R1 [−

]

00.1

0.20.3

0.4

00.1

0.20.3

0.40.5

0

0.2

0.4

0.6

0.8

1

cf,1

[mol/L]cf,2

[mol/L]

R2 [−

]

Figure 5.5: Rejection of sugar (left side) and salt (right side) as functions of feed com-

position for GE membrane. Experimental data are illustrated with open circles and fitted

empirical planes with continuous lines. (25 °C, 30 bar.)

5.4.3 Simulation

The empirically determined relation (5.15) betweenJ ,R1,R2 andcf,1, cf,2 can

be applied in the algorithm explained in Sect. 5.2.3, and theseparation behavior

can be simulated for a single-step process with pre-defined exit condition. Then,

the output values can be used as input values for the next step. Thus, multi-step

process simulations can be built with optional step number and order. We can

validate the simulation technique by reproducing the results of the experiments.

In Fig. 5.7, the simulated separation performance is illustrated together with the

experimental data of the batch No. 3. As shown in Table 5.2, very good predic-

tion accuracy was achieved in all cases. The greatest error of 10% was found in

the final salt concentration of batch No.6. However, the finalsalt concentration

was very low and the difference between the predicted and themeasured value

of the salt mass in the final product is7.6 g, which is only1.7% of the initial

438.4 g mass.

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5.4. RESULTS AND DISCUSSION 129

00.1

0.20.3

0.4

00.1

0.20.3

0.40.5

0

2

4

6

8

10

12

cf,1

[mol/L]cf,2

[mol/L]

J [L

/h/0

.5 m

2 ]

Figure 5.6: Permeate flux of the membrane GE as function of feed composition. Exper-

imental data of the 0.5 m2 element are illustrated with open circles and fitted empirical

plane with continuous lines. (25 °C, 30 bar.)

5.4.4 Optimization

The purpose of the optimization is to find the set of operationparameters which

result in the most economical process and satisfy the given technological de-

mands of the final product. Thus, the total processing cost isthe objective func-

tion which has to be minimized; the operational parameters of n1 andD2 are the

decision variables, and the given technological requirements are the constraints

of the optimization. We define a product quality and a productvolume con-

straint, e.g. the final salt concentrationcf,3,2 must be less than a limit value of

climit = 0.2 mol/L and the total concentration factorn = 2.5 must be achieved.

In the following, we use the processing conditions and the specifications of our

laboratory system for the optimization task. However, the concept can find a

general interest, and industrial problems can be handled inan analogous way.

This technique can be useful to find the optimal operational parameters of an

existing membrane plant with a defined membrane area.

The objective function can be defined as the total cost per unit of product pro-

duced. The total cost is a sum of three terms, which are the operational cost of

the pump, the cost of the valuable component loss, and the cost of the utilized

dilution water.

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130 CHAPTER 5.

0 1 2 3 4 5 65

6

7

8

9

10pe

rmea

te fl

ux [L

/h/0

.5 m

2 ]

time [h]0 1 2 3 4 5 6

0

0.05

0.1

0.15

0.2

0.25

0.3

time [h]

conc

entr

atio

n [m

ol/L

]

cf,1

cf,2

Figure 5.7: Predicted (solid lines) and experimental data (symbols) ofmembrane GE

for run No. 3. Permeate flux of the membrane element (left) andconcentrations of the

compounds (right) in the feed tank are plotted versus operation time. Concentrations of

sugar and salt are illustrated with open squares and filled circles, respectively.

We can describe the mathematical problem as follows:

minimizef(n1, D2) = (k1t+ k2mloss + k3Vd,2)/(cf,3,1Vf,3) (5.16)

subject to the constraints

n = n1 · n3 = 2.5 and cf,3,2 ≤ climit (5.17)

wheref(n1, D2) is the objective function,t is the total operation time,mloss

is the total product loss defined as the difference between the initial and the

final mass of sugar:mloss = Vf,0cf,0,1 − Vf,3cf,3,1, Vd,2 is the dilution water

consumption, andk1, k2 andk3 are constants.

The constantk1 is a product of the power consumption of the pump and the

electricity price, which givesk1=7.5 kW · 0.007e/kWh=0.525e/h. The price

of commercial table sugar was used to determine the constantk2 resulting in

k2=0.001e/g, andk3= 0.008e/L was taken as unit price of the utilized dilution

water.

The technique described in Sect. 5.4.3 was applied to simulate multi-step pro-

cesses using a series of operational parametersn1,D2, n3 = n/n1. The objec-

tive function was computed for each batch. The results of thecost estimations,

Page 143: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

5.4. RESULTS AND DISCUSSION 131

which meet the product quality requirement, are illustrated in Fig. 5.8. The total

elapsed CPU time for the cost calculations of the (n1, D2) matrix was≈ 0.5

second (AMD 1.8 Ghz processor). The matrix has an order of30 × 40, and

each element corresponds to a complete multi-step process simulation with a

discretization step of∆Vp = Vf,0/1000. There are two distinct areas in Fig. 5.8

based on whether the product quality constraintcf,3,2 ≤ climit was achieved by

the applied operational parameters. The two areas are separated by the optimal

trajectory of the objective function which corresponds tocf,3,2 = climit final

salt concentration. For each fixedn1, an optimal valueD2 can be found, which

00.5

11.5

2

1

1.5

2

2.50

1

2

3

D2 [−]n

1 [−]

obje

ctiv

e fu

nctio

n [E

UR

/mol

]

0 0.5 1 1.5 21

1.5

2

2.5

D2 [−]

n 1 [−]

cf,3,2

≤ c limit

cf,3,2

≥ c limit

Figure 5.8: Computed objective function versus pre-concentration factor n1 and dilu-

tion factorD2 which satisfy the constraints (left-hand-side figure). Top-view of the ob-

jective function surface (right-hand-side figure) with twodistinct areas ofcf,3,2 ≥ climit

(dark blue color) andcf,3,2 ≤ climit (faceted pattern).

would ensure the desired product quality. To compute such optimal values of

D2, we develop an iterative method to find the optimal trajectory. This tech-

nique allows a quick sensitivity analysis of the objective function with respect

to the constantsk1, k2, k3. The optimization method is illustrated through the

flow-chart in Fig. 5.9. Figure 5.10 shows the estimated cost functions. We

can see that for the specific problem that we are studying, allthree terms of the

objective function have minimum values atn1 = 2.5, which corresponds to an

optimal dilution factor ofD2 = 0.98.

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132 CHAPTER 5.

Figure 5.9: Flow-chart of the optimization technique.

Obviously, this outcome is not generally valid. However, the optimization tech-

nique can be applied in other contexts assigning different values to the constants

in the objective function and/or redefining the unique features of the membrane

permeation (J = J(cf,1, cf,2) andRi = Ri(cf,1, cf,2), i = 1, 2). This would

lead to different solutions for each specific application.

5.5 Conclusions

A simple computational technique is proposed for the simulation of batch mem-

brane filtration processes. The technique has the followingcharacteristics:

• Either transport models or real-life experimental data can be used in the

algorithm to describe the permeation properties of the membrane, without

having to modify the governing equations.

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5.5. CONCLUSIONS 133

1 1.5 2 2.50

0.5

1

1.5

2

obje

ctiv

e fu

nctio

n [E

UR

/mol

]

n1 [−]

total costspump operationproduct lossdilution water

Figure 5.10: Contribution of the sub-costs to the total costs in the function of the pre-

concentration factorn1 for the cases which satisfy the given constraintscf,3,2 = climit

andn = 2.5.

• It can be employed for systems where the classical mathematical model-

ing has limited applicability, in particular, in the cases whereσ is strongly

varying and the assumptionσ=constant fails.

• The simulation of dilution mode can be performed also considering a

diluant which contains solutes.

• Both constant- and variable-volume dilution-mode operations, as well as

continuous and step-wise addition of diluant can be simulated with minor

adjustments to the proposed algorithm.

In this study, the simulations were performed using empirical relations delivered

from permeation experiments with a binary model solution. The predictions of

the multi-step process performances were found to be in goodagreement with

the experimental results. Finally, we reported an optimum-search technique

considering economical aspects and technological demands. This method can

be used to find optimum process settings of a membrane plant with a given

filtration area.

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134 CHAPTER 5.

Table 5.4: Nomenclature

Symbol Name Unit

A Membrane area m2

J Volumetric permeate flux L/(h m2)

t Operation time h

V Volume L

mloss Total product loss g

climit salt concentration constraint mol/L

c Concentration mol/L

χ Conductivity mS/cm

r Refractive index Bx◦

P Applied pressure bar

R Rejection –

D Dilution factor –

n concentration factor –

T Temperature °C

ρ Density kg/m3

σ Rejection coefficient –

Subscripts

f feed

r retentate

p permeate

d dilution water

i component (in the experimental part:i=1 sucrose, andi=2 salt)

Superscripts

k discretization step

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BIBLIOGRAPHY 135

Bibliography

[1] W. Blatt, S. Robinson, Membrane ultrafiltration: the diafiltration technique and its

application to microsolute exchange and binding phenomena, Anal. Biochem. 26

(1968) 151–173.

[2] V. Gekas, Terminology for pressure driven membrane operations, Tech. rep., The

European Society of Membrane Science and Technology (1986).

[3] F. Lipnizki, J. Boelsmand, R. Madsen, Concept of industrial-scale diafiltration sys-

tems, Desalination 144 (2002) 179–184.

[4] A. Goulas, P. Kapasakalidis, H. Sinclair, R. Rastall, A.Grandison, Purification of

oligosaccharides by nanofiltration, J. Mem. Sci. 209 (2002)321–335.

[5] W. Li, J. Li, T. Chen, C. Chen, Study on nanofiltration for purifying fructo-

oligosaccharides. I. Operation modes, J. Mem. Sci. 245 (2004) 123–129.

[6] D. Oatley, B. Cassey, P. Jones, W. Bowen, Modelling the performance of mem-

brane nanofiltrationUrecovery of a high-value product from a processwaste stream,

Chem. Eng. Sci. 60 (2005) 1953–1964.

[7] B. Cheang, A. Zydney, A two-stage ultrafiltration process for fractionation of whey

protein isolate, J. Mem. Sci. 231 (2004) 159–167.

[8] L. Wang, G. Yang, W. Xing, N. Xu, Mathematic model of the yield for diafiltration

processes, Sep. Purif. Technol. 59 (2008) 206–213.

[9] N. Rajagopalan, M. Cheryan, Process optimization in ultrafiltration: flux-time

considerations in the purification of macromolecules, Chem. Eng. Commun. 106

(1991) 57–69.

[10] W. Bowen, A. Mohammad, Diafiltration by nanofiltration:Prediction and opti-

mization, AIChE Journal 44 (8) (1998) 1799–1812.

[11] A. Simon, L. Vandanjon, G. Levesque, P. Bourseau, Concentration and desalination

of fish gelatin by ultrafiltration and continuous diafiltration processes, J. Biotech-

nol. 70 (1999) 393–402.

[12] A. Muller, G. Daufin, B. Chaufer, Ultrafiltration modes of operation for the sepa-

ration of a-lactalbumin from acid casein whey, J. Mem. Sci. 153 (1999) 9–21.

[13] R. Duarte, E. Santos, A. Duarte, Comparison between diafiltration and concen-

tration operation modes for the determination of permeation coefficients of humic

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136 CHAPTER 5.

substances through ultrafiltration membranes, Anal. Chim.Acta 442 (2001) 155–

164.

[14] G. Foley, Minimisation of process time in ultrafiltration and continuous diafiltra-

tion: the effect of incomplete macrosolute rejection, J. Mem. Sci. 163 (1999) 349–

355.

[15] R. Baker, Membrane Technology and Applications, Wiley, West Sussex, 2004.

[16] M. Mulder, Basic Principles of Membrane Technology, Kluwer Academic Publish-

ers, Dordrecht, 2000.

[17] H. Niemi, S. Palosaari, Flowsheet simulation of ultrafiltration and reverse osmosis

processes, J. Mem. Sci. 91 (1994) 111–124.

[18] N. Voros, Z. Maroulis, D. Kouris, Optimization of reverse osmosis networks for

seawater desalination, Computers Chem. Engrg. 20 (1996) 345–350.

[19] K. Morison, X.She, Optimisation and graphical representation of multi-stage mem-

brane plants, J. Mem. Sci. 211 (2003) 59–70.

[20] K. Driscoll, Development of a Process Simulator for theUltrafiltration/ Diafiltra-

tion Process, Ph.D. thesis, University of Arkansas, Fayetteville, US (2001).

[21] R. A. Cross, Optimum process design for ultrafiltrationand crossflow micro-

filtration systems, Desalination 145 (2002) 159–163.

Page 149: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

6Modeling of batch and semi-batch

membrane filtration processes

Reprinted from: Z. Kovács, M. Discacciati, W. Samhaber, Modeling of batch

and semi-batch membrane filtration processes, Technical Report submitted to

Journal of Membrane Science, 2008.

A mathematical frame for modeling batch and semi-batch membrane filtration

processes is provided. The approach followed in this work uses the feed con-

centrations as a basis for the calculations, rather than theconcentration factor.

A practical computational algorithm is proposed. Our method hands separately

the design equations describing the engineering aspects ofbatch and semi-batch

systems and the models of mass transfer through the membrane. Thus, differ-

ent methods can be applied to compute the permeate flux and rejection without

137

Page 150: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

138 CHAPTER 6.

having to modify the general framework. In particular, we present an empirical

approach to characterize the membrane separation behaviorbased on a minimal

number of experiments. Moreover, we consider irreversiblethermodynamics

models and a transport model based on the extended Nernst-Planck equations.

Finally, various batch and semi-batch NF operations are carried out with an

organic/electrolyte binary test solution to validate the proposed algorithms.

6.1 Introduction

Batch membrane filtration has a considerable industrial interest with many ap-

plications in the food and beverage, chemical, biotechnological and pharmaceu-

tical industry. In comparison with continuous processes, batch operations are

particularly suited to small-scale operations, require less expensive automatic

controls, and allow to use membranes with reduced area in order to reach the

target [1].

Improving batch operation performances is an active field ofscientific research.

Among the various batch design modes, the concentration mode and the con-

stant volume dilution mode (or the combination of the two which is usually

referred as diafiltration) have been studied in detail by many authors [2–11].

Most recently, attention has been paid to variable volume dilution mode, as

an alternative way for macrosolute concentration and simultaneous microsolute

removal [12–14]. Assuming constant solute rejection coefficients, Foley devel-

oped a mathematical model and compared the variable volume dilution with the

traditional two-step diafiltration process in terms of water usage and operational

time [12]. Much less literature is available on semi-batch process performances.

Research has been conducted on the recovery of used cleaning-in-place solu-

tions in the dairy industry [15], immersed membrane systemsfor removing sus-

pended solids [16], the treatment of waste oil/water emulsions [17], and on the

performance of semi-batch filtration system for treating waste metal-working

fluids [18].

A very common approach in mathematical modeling is to assumeconstant re-

jection coefficients and to use the concentration factor as abasis for the calcu-

Page 151: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

6.1. INTRODUCTION 139

lations. The rejection coefficients are usually empirically determined from per-

meation experiments with the process liquor, and a mean rejection value char-

acterizing a whole process step can be calculated. In our previous study [19],

it was shown that this approach can only be applied when the rejection rates of

the solutes remain constant throughout the process. In fact, when the rejections

of the solutes strongly vary depending on their feed concentrations and there

is a considerable interdependence in their permeation, thesimulation and op-

timization might lead to inaccurate results. In order to express the rejections

as state functions of the actual feed concentrations and incorporate them in unit

operation design, numerical techniques have to be applied.Major achievements

have been obtained by Cross [20] and Driscoll [21]. The approach followed in

their work did not use the concentration factor as a basis forthe calculations, but

rather the component concentrations. They developed a simulation tool capable

of determining the membrane area and the optimal area distribution required for

a multi-stage system. Besides continuous operation design, their software can

be used to simulate concentration mode, constant-volume dilution mode and

constant volume type semi-batch operations.

Transport mechanisms through membranes have also been studied thoroughly.

Bowen and Mohammad [8] developed a predictive model based onthe ex-

tended Nernst-Planck equations for the performance of dilution and concen-

tration mode NF in separating dye/salt solution. Excellentagreements between

predicted and experimental rejections were achieved assuming a linear rela-

tionship between the charge density of the membrane and the ionic strength of

the salt solution. Similar methodologies for studying the diafiltration for the

removal of pyruvate from process stream were applied by Bowen et al. [22].

The simulations are developed on the basis of a transport model and, obviously,

non-constant rejections are considered.

The main aim of the present paper is to provide a simple but general mathe-

matical framework for modeling batch and semi-batch membrane filtration op-

erations. In Sect. 6.2.2, we propose a system of ordinary differential equations,

while in Sect. 6.2.3 we illustrate a possible computationalalgorithm. The de-

sign equations describing the engineering aspects of batchand semi-batch sys-

Page 152: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

140 CHAPTER 6.

tems are handled separately from the models of permeation through the mem-

brane. Therefore, our approach is valid for all pressure-driven membrane fil-

tration processes. The estimation strategies for flux and rejection are presented

in Sect. 6.2.4. We discuss the minimum experimental design necessary for an

empirical approach in Sect. 6.2.4, while we study two theoretical NF models in

Sect. 6.2.4. Finally, we compare the predicted values with data obtained from

NF permeation experiments with an organic/electrolyte binary solution.

6.2 Theory

6.2.1 Batch and semi-batch operations

A schematic flow diagram of the batch and semi-batch filtration systems con-

sidered in this study is shown in Fig. 6.1. In all batch and semi-batch oper-

M e m b r a n e m o d u l e

P e r m e a t e

R e t e n t a t e

F e e d t a n k

P u m p

D i l u a n t

Figure 6.1: Schematic representation of batch membrane filtration settings.

ations, the retentate stream is recirculated to the feed tank and the permeate

stream is collected separately. The main difference between the various types

of operational modes is due to the quality and the quantity ofthe diluant stream

introduced in the feed tank during the operation. In this context, the simplest

Page 153: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

6.2. THEORY 141

operational mode is the concentration mode since no diluantis applied. The

diluant can be added to the feed tank with a constant flow rateQ supplied by an

external pump. Alternatively, the flow rate of the diluant can be equal or propor-

tional to the permeate flow rate: in the former case we speak ofconstant-volume

operational mode, while in the latter of variable-volume operational mode. In

general, the diluant streamD can be described as the sum of two terms

D = αJA+Q (6.1)

whereα is a proportionality factor,J is the permeate flux,A is the membrane

area, andQ is the flow-rate of the diluant supplied by an external pump. One

of the two terms in (6.1) can be set to zero to represent eithera constant or a

flux-dependent diluant flow rate.

The diluant can be pure solvent, fresh process liquor, or a solution containing

low concentration of solutes. The latter case is important in numerous industrial

applications, where diluted process-liquors are producedand used as diluants.

When fresh process water is used as diluant, the process is considered as semi-

batch (or fed-batch) operation. (Notice that in this case noreal washing-out

effect of the micro-solute occurs.)

Thus, all the possible operational modes can be characterized by convenient

values ofQ, α, and the concentrationcd,i of componenti in the diluant as

illustrated in Table 6.1.

6.2.2 Mathematical modeling

The permeate flow-rate at any timet of the operation is given as the product of

the permeate fluxJ(t) and of the membrane areaA:

dVp

dt(t) = J(t)A. (6.2)

The volume flow entering the feed tank can be expressed as the sum of the

constant and the flux-dependent term as

dVd

dt(t) = Q+ α

dVp

dt(t). (6.3)

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142 CHAPTER 6.

Table 6.1: Design of commonly used batch and semi-batch operatons.

Operational mode Q α cd,i

Concentration mode 0 0 0

Constant-volume dilution mode with pure

solvent as diluant

0 1 0

Variable-volume dilution mode with pure

solvent as diluant

0 0 < α < 1 0

Constant-volume dilution mode with diluted

process liquor as diluant

0 1 0 < cd,i < cf,i

Variable-volume dilution mode with diluted

process liquor as diluant

0 0 < α < 1 0 < cd,i < cf,i

Constant-volume fed-batch with process

liquor

0 1 cf,i

Variable-volume fed-batch with process

liquor

0 0 < α < 1 cf,i

Constant inlet-rate dilution with pure solvent

as diluant

Q 0 0

Constant inlet-rate dilution with diluted pro-

cess liquor as diluant

Q 0 0 < cd,i < cf,i

Constant inlet-rate fed-batch with process

liquor

Q 0 cf,i

The change in the volume in the feed tank during the operationis given as

dVf

dt(t) =

dVd

dt(t) − dVp

dt(t). (6.4)

Finally, assuming to consider two solutes, the mass balancefor the solute con-

centrations yields

d

dtVf (t)cf,i(t) = −dVp

dt(t) cp,i(t) +

dVd

dt(t)cd,i(t) i = 1, 2 (6.5)

wherecp,i(t) denotes the permeate concentration of solutei at timet. Substi-

tuting (6.2) in (6.3) we obtain

dVd

dt(t) = Q+ αJ(t)A (6.6)

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6.2. THEORY 143

while using (6.2) and (6.6) in (6.4) we get

dVf

dt(t) = Q− (1 − α)J(t)A . (6.7)

Equation (6.5) can be rewritten in the following way:

dVf

dt(t)cf,i(t)+Vf (t)

dcf,i

dt(t) = −dVp

dt(t)cp,i(t)+

dVd

dt(t)cd,i(t) i = 1, 2

and using (6.2), (6.6) and (6.7), we obtain, fori = 1, 2,

Vf (t)dcf,i

dt(t) = J(t)A[αcd,i(t)−cp,i(t)+(1−α)cf,i(t)]+Q(cd,i(t)−cf,i(t)).

Recalling thatcp,i(t) = cf,i(t)(1 − Ri(t)), whereRi(t) is the rejection of

solutei at timet, we can write

Vf (t)dcf,i

dt(t) = J(t)A[αcd,i(t)+cf,i(t)(Ri(t)−α)]+Q(cd,i(t)−cf,i(t)).

Thus, we have the following initial-value problems:

dVf

dt(t) = Q− (1 − α)J(t)A

Vf (0) = V 0f

(6.8)

and, fori = 1, 2,

Vf (t)dcf,i

dt(t) = J(t)A[αcd,i(t) + cf,i(t)(Ri(t) − α)] +Q(cd,i(t) − cf,i(t))

cf,i(0) = c0f,i .

(6.9)

V 0f andc0f,i denote respectively the initial feed volume and the initialfeed con-

centration of the solutei. Remark that problems (6.8) and (6.9) are valid for all

batch and semi batch processes described in Sect. 6.2.1. Moreover, notice that

the estimation of the fluxJ(t) and of the rejectionRi(t) can be carried out sep-

arately using the most convenient approach for the problem at hand. Possible

strategies to compute flux and rejection are presented in Sect. 6.2.4.

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144 CHAPTER 6.

6.2.3 Computational algorithm

Let us split the interval of the operation time[0, tfinal] in subintervals[tn, tn+1],

n = 0, . . . , N − 1, with t0 = 0 andtN = tfinal. Let ∆tn+1 = tn+1 − tn, and

denote by the upper-indexn an approximation of the value of any quantity at

time tn: e.g.,cnf,i ≈ cf,i(tn).

The relevant quantities for batch and semi-batch operationmodes can be com-

puted using the following algorithm.

1. At time tn, calculate the fluxJn and the rejectionRni (i = 1, 2) of the

two solutes.

2. The volume of permeate∆V np obtained in the time interval∆tn+1 is:

∆V np = JnA∆tn+1 (6.10)

3. The diluant volume∆V nd which enters in the feed tank in the time interval

∆tn+1 is given by

∆V nd = Q∆tn+1 + α∆V n

p (6.11)

4. At timetn+1 the volume in the tank becomes:

V n+1f = V n

f − ∆V np + ∆V n

d (6.12)

5. Finally, the concentrations at timetn+1 can be computed as follows:

V n+1f cn+1

f,i = V nf c

nf,i − ∆V n

p cnp,i + ∆V n

d cnd,i i = 1, 2. (6.13)

Notice that equations (6.10)-(6.13) correspond to a discretization in time of

(6.2)-(6.5) using the forward Euler method. Moreover, theyprovide approxi-

mate solutions to problems (6.8) and (6.9). To solve (6.12)-(6.13), the following

input data are required:

• initial volume in feed tankV 0f

• initial concentration of macrosolute in feed tank:c0f,1

Page 157: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

6.2. THEORY 145

• initial concentration of microsolute in feed tank:c0f,2

• constant diluant inlet-rateQ, or ratio of permeate flow to diluant flowα

• concentration of macrosolute in diluant:cd,1

• concentration of microsolute in diluant:cd,2

• exit condition (operation time, feed volume, collected permeate volume,

or applied diluant volume)

6.2.4 Permeate flux and rejection

The flux and the rejections depend on many independent variables such as feed

concentrations, temperature, applied pressure, hydrodynamic conditions, and

state of fouling. In Sects. 6.2.2 and 6.2.3, we have not considered any specific

model to express flux and rejection. However, any suitable empirical or theo-

retical method can be inserted in the framework that we have presented without

having to change it. We provide two examples in the followingsections.

Empirical approach

Assuming that the applied pressure, the temperature, and the hydrodynamic

conditions are kept constant, flux and rejection are functions only of the feed

concentrations. The objective is to determine these relationships from a mini-

mum number of experiments. Reliable relations can be obtained when experi-

mental data are available in the whole range ofcf,1 andcf,2, or, at least, in the

extreme points of thecf,1-by-cf,2 matrix. An effective technique for this pur-

pose is to concentrate the initial feed solution, then to addpure water to obtain

the initial volume, and to repeat this procedure several times. The operational

conditions of such experimental run are described in Sect. 6.3 and the results are

discussed in Sect. 6.4.1. We assume that the samples are taken from the mem-

brane plant whose operation is to be simulated. Scale-up calculations, where

an increased membrane area and a corresponding change in thehydrodynamic

Page 158: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

146 CHAPTER 6.

conditions need to be taken into account, are out of the scopeof this work. Such

aspects are described in [21, 23–26].

Irreversible thermodynamics models

The fundamental models derived from irreversible thermodynamics (IT) are the

Kedem-Katchalsky and the Spiegler-Kedem models [27–29]. According to Ke-

dem and Katchalsky, the volume fluxJ and the molar solute fluxjs for a single

solute through a membrane are given by:

J = Lp△P − LpσνRT (cf − cp) (6.14)

js = Ps(cf − cp) + (1 − σ)Jc (6.15)

whereLp is the hydraulic permeability of the membrane,σ is the reflection

coefficient,Ps is the solute permeability of the membrane,ν is the dissociation

coefficient, whilec represents the mean concentration of the solute.

In this model the membrane is treated as a black box: the transport mecha-

nisms and the structure of the membrane are ignored. IT models have been

applied in predicting transport through NF membranes for single and binary

solute systems [30, 31], for multiple systems [32, 33] and also for industrial

feeds [34–37].

Assuming thatJ > 0, we can divide (6.15) byJ , and recalling that there holds:

cp =jsJ

(6.16)

we obtain

cp =Ps(cf − cp)

Lp△P − LpσνRT (cf − cp)+ (1 − σ)c . (6.17)

Recalling thatcp = cf (1 −R), we can rewrite (6.13) as

cf (1 −R) =PscfR

Lp△P − LpσνRTcfR+ (1 − σ)c . (6.18)

The mean concentration across the membranec can be estimated using the log-

arithmic average

c =cf − cp

ln cf − ln cp= − cfR

ln(1 −R)(6.19)

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6.2. THEORY 147

so that (6.18) becomes

cf (1 −R) − PscfRLp△P − LpσνRTcfR

+ (1 − σ)cfR

ln(1 −R)= 0 . (6.20)

After assigning the transport parameters of the membraneLp,Ps andσ, Eq. (6.20)

allows us to compute the rejectionR corresponding to any set of valuescf and

∆P . For more details, we refer to [38].

Generalizing (6.20), the rejections at timet of solutes for a binary system can

be calculated solving, fori = 1, 2,

cf,i(t)(1 −Ri(t)) =∑2

k=1 Ps,kcf,k(t)Rk(t)

Lp

[

∆P −RT∑2

k=1 σkνkcf,k(t)Rk(t)] + (1 − σi)

cf,i(t)Ri(t)

ln(1 −Ri(t)).

(6.21)

The permeate flux can be then recovered as:

J(t) = Lp

[

∆P −RT

2∑

k=1

σkνkcf,k(t)Rk(t)

]

. (6.22)

Finally, let is recall that the Spiegler-Kedem (SK) model [29] states that

R =

σ

(

1 − exp

(

σ − 1

PsJ

))

1 − σ exp

(

σ − 1

PsJ

) . (6.23)

The effect of membrane charge density on the permeation of charged compo-

nents is not taken into account in these models. However, many authors [39–42]

established relationships between the transport parameters (σ andPs) and the

membrane electrical and structural properties and used IT models to describe

permeation of electrolytes through NF membranes.

Finally, let us point out that the electrolyte permeabilitycoefficientPs is pro-

portional to the partition coefficient of the electrolyte [31], and its concentration

dependence can be expressed as

Ps = P ∗

s

(

cfc∗f

)m

(6.24)

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148 CHAPTER 6.

whereP ∗

s is the solute permeability for a reference feed concentration c∗f , and

m is a suitable parameter.

Transport models

Solute transport across NF membrane pores can be described using the extended

Nernst-Planck model. The solute molar flux of an ionj is given as a sum of

three terms (diffusion, electromigration and convection)as follows:

ji = −Dj,pdcjdx

− zjcjDj , p

RTFdψ

dx+Kj,ccj V (6.25)

The transport equation for non-charged compounds is given as the sum of the

diffusive and the convective terms due to negligible electrostatic effects. The

model assumes a Hagen-Poiseuille-type solvent velocity inuniform, straight,

cylindrical membrane pores. The hindered nature of diffusion and convection

is accounted by incorporating steric hindrance factors (Kj,d andKj,c).

Such elektokinetic space-charge modelling systems based on the extended Nernst-

Planck equation have been successfully applied by many researchers [43–47].

However, calculations of membrane performance using such amodel can be

very demanding in computational time [48]. Starting from the DSPM-DE model

[49, 50], a useful approach for engineering calculations has been developed by

Bowen et al. [51]. The system of differential equations was reduced to a sys-

tem of algebraic equations denoted at DSPM-DE model by finitedifference

linearization of pore concentration gradients.

Let us summarize the governing equations of the linearized DSPM-DE model

that we will use in the following. We consider an aqueous solution of a 1:1

type electrolyte. Supscriptj = 1, 2 denotes the coion and counterion of the

electrolyte, respectively. In Sect. 6.3.2 we extend the model accounting for an

aqueous ternary system consisting of a neutral compound anda dissociated 1:1

type electrolyte.

The concentrations within pore entrance and outlet are given by, respectively,

centj =

−Xd +√

X2d + 4Φ′

1Φ′

2c2f,j

2coutj =

−Xd +√

X2d + 4Φ′

1Φ′

2c2p,j

2

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6.2. THEORY 149

(6.26)

whereXd is the effective charge density of the membrane.Φ′

j (j = 1, 2) is

the dimensionless partial partition coefficientΦ′

j = Φje−∆Wj/kT , Φj being

the steric partitioningΦj = (1 − λj)2, whereλj = rj/rp is the ratio between

the ion and the membrane pore radii. Finally,∆Wj is the so-called solvation

energy barrier:

∆Wj =z2

j e2

8πǫ0aj

(

1

ǫp− 1

ǫb

)

with the dimensionless pore dielectric constant:

ǫp = 80 − 2(80 − ǫ∗)

(

d

rp

)

+ (80 − ǫ∗)

(

d

rp

)2

.

For the meaning of the other symbols we refer to Appendix .1.

Finally, the permeate concentration for a 1:1 type electrolyte is given by

cp =(Pe1 + Pe2)c

2av,1 + (Pe1 + Pe2)Xdcav,1 − (2cav,1 +Xd)∆c1(

Pe1

Kc,1+Pe2Kc,2

)

cav,1 + Pe1

Kc,1Xd

(6.27)

cav,i is the average concentration within the pores

cav,j =centj + cout

j

2(6.28)

while Pej is the Peclet number

Pej =Kc,jr

2p∆Pe

Kd,jD∞,jη0

which depends on the hindrance factors

Kc,j = (2 − Φj)(

1.0 + 0.054λj − 0.988λ2j + 0.441λ3

j

)

Kd,j = 1 − 2.30λj + 1.154λ2j + 0.224λ3

j

on the effective pressure

∆Pe = ∆P − ∆π = ∆P −RT

2∑

j=1

(cf,j − cp,j) (6.29)

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150 CHAPTER 6.

on the diffusion coefficient at infinite dilutionD∞,j and on the bulk dynamic

viscosityη0.

To our knowledge, there is no direct method to estimate the membrane charge

densityXd which depends on the membrane chemistry and on the specific ad-

sorption of ions [52]. Therefore, estimates are based on experimental isotherm

data.

In this work we assume that the flux and rejections are sole functions of the

actual feed concentrations, and that the concentration polarization is negligi-

ble. However, the model can be extended to account for other parameters like

temperature [53], pore-size distribution [54], pH [8] or concentration polariza-

tion [8].

More recently, Geraldes [55] has developed a computer program called NanoFil-

tran for the simulation of mass transfer in NF based on the extended Nernst-

Planck equation. The program can run in two modes: system prediction mode

and membrane characterization mode. In the first mode, the rejection of solutes

in single or multi-component systems can be estimated for a given permeate

flux accounting for concentration polarization. In the second mode, the mem-

brane properties can be evaluated using experimental data for the fitting. Such

a program with minor changes could be applied as a subroutinefor the batch

system simulations described in this work.

6.3 Materials and methods

The NF apparatus used in this study, the applied chemicals and the sample anal-

ysis have been described in details in the previous work [19]. In brief, techni-

cal grade sucrose and sodium chloride were used to prepare the aqueous solu-

tions, and then cross-flow filtration experiments were carried out using a 0.45

m2 spiral-wound membrane element. The recirculation flow-rate was very high

(1000 L/h) in comparison with the permeate flux, so that the effect of concentra-

tion polarisation on the overall membrane separation can beneglected. During

the filtration experiments, permeate and retentate sampleswere taken periodi-

cally always at the same time from the permeate pipe and from the feed tank,

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6.3. MATERIALS AND METHODS 151

respectively. The NF membrane used in this study was Desal-DK purchased

from Osmonics (today GE Water & Process Technologies). In all five experi-

ments, the applied pressure was kept at 30 bar and the temperature at 25°C. The

first experiment was needed to determine the relations betweenJ , R and the

feed concentration. The additional four experiments were used to validate our

model. These experiments are described in more details hereafter.

1. Experimental run for parameter fitting. The feed solution (30 L, 0.15

mol/L sucrose and 0.3 mol/L NaCl) was concentrated to 10 L. Then, 20

L deionized water was added into the feed tank, and it was concentrated

again to 10 L. This procedure was repeated four times.

2. Validation run no. 1. Constant-volume dilution mode was performed with

15 L initial feed solution containing 0.3 mol/L sucrose and 0.3 mol/L

NaCl. A level sensor was employed to keep the constant feed volume

by continuously adding deionized water as diluant at a rate equal to the

permeation rate. The process was stopped after 4 hours of operation.

3. Validation run no. 2. Variable-volume dilution mode with pure water as

diluant was performed. The initial feed was 30 L containing 0.15 mol/L

sucrose and 0.3 mol/L NaCl. The ratio of diluant inlet rate topermeate

flow rate was kept atα = 0.75 in a quasi-continuous way: after every

2 liters of collected permeate, 1.5 L pure water was added into the feed

tank. The operation was stopped when the feed solution was reduced to

10 L.

4. Validation run no. 3. Constant-volume dilution mode was performed us-

ing diluted process liquor as diluant. The volume in the feedtank was

kept at 10 L. The initial sucrose and salt concentrations were 0.15 mol/L

and 0.3 mol/L, respectively. The total volume of the diluantused dur-

ing the operation was 60 L, and it contained 0.05 mol/L sucrose and 0.1

mol/L NaCl.

5. Validation run no. 4. A fed-batch process was performed. 10 L initial

feed solution containing 0.15 mol/L sucrose and 0.3 mol/L salt was in-

Page 164: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

152 CHAPTER 6.

troduced in the feed tank. During the operation, the permeate stream was

collected separately, the retentate was recycled, and fresh process liquor

was continuously added to the feed tank with a constant inletrate ofQ =

9.64 L/h.

6.3.1 Solution procedure for the IT model

The values of the transport parameters for the membrane DK and for NaCl are

taken from Yaroshchuk [56]:c∗f = 1 mol/m3, σ = 0.9259, P ∗

s = 3.319 ·10−6 m/s, andm = 0.4569.

The Spiegler-Kedem analysis of different neutral solutes is provided in [57].

The transport parameters of lactose (σ = 0.9935,Ps = 3.5 ·10−9) were chosen

for modeling the sucrose permeation, since the physiochemical nature and the

size of the two neutral molecules are practically identical. We assumed constant

transport parameters for sucrose over the whole range of feed concentration.

Finally, the pure water permeability of the membrane was taken asLp = 3.68 ·10−12 [m/s/Pa].

The rejection of the solutes can be estimated for a given feedcomposition by

solving (6.21) or using the SK approach. In this case,

1. Calculate salt permeability using (6.24).

2. Consider a guess for the permeate fluxJ .

3. Calculate rejections for both components using (6.23).

4. Calculate the permeate flux using (6.22).

5. Iterate steps (3)-(4) until convergence.

6.3.2 Solution procedure for the DSPM-DE model

The model parameters used in this study were taken from Bowenet al. [51] who

applied the linearized DSPM-DE model to characterize the Desal-DK mem-

brane. The estimated value of the dielectric constant for the oriented water layer

Page 165: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

6.3. MATERIALS AND METHODS 153

is ǫ∗ ≈ 31, and the predicted average pore size of the membrane isrp = 0.45

nm. The effective charge density of the membraneXd as function of the NaCl

concentration in the wall is reported in Table 6.2. We assumea negligible con-

centration polarization effect so that the feed and the wallconcentrations are

practically equal. The diffusivity, charge and Stokes radius of sodium and chlo-

ride ions are also taken from [51]. The value ofXd was assumed to be null

Table 6.2: Effective charge density of the Desal-DK membrane from analysis of NaCl

permeation data with linearized model given by Bowen et al. [51]

cf,2 (mol/m3) Xd (mol/m3)

1.4 -0.50

3.7 -1.07

11.0 -2.05

37.6 -5.75

111.8 -1.85

for a concentration of NaCl greater than 120 mol/m3. For less concentrated

solutions, we interpolated the values ofXd given in Table 6.2 to get a suitable

function ofcf,2.

Since the Stokes radius of sucrose is greater than the estimated pore radius

of the membrane DK, complete sucrose rejection was assumed.However, the

actual feed concentration of sucrose influences the permeate flux and the salt

rejection during the process. We calculate the osmotic pressure exerted by the

feed solution as follows

∆π = RT (cf,1 + νcf,2), (6.30)

where cf,1 is the sugar, and cf,2 is the salt concentration in the feed. Thus, the

effective pressure becomes

∆Pe = ∆P − ∆π = ∆P −RT

2∑

i=1

(cf,i − νcp,i) (6.31)

Page 166: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

154 CHAPTER 6.

where subscripti = 1 stands for sugar andi = 2 for salt. In the followings,

instead of (6.29) that accounts only for an aqueous salt solution, we consider

(6.31) which describes an aqueous sugar/salt system. Sincewe assume a com-

plete sugar rejection, all further equations for the determination of the salt per-

meate concentration, that are presented in Sect. 6.2.4, remain unchanged.

The following calculation procedure was applied to determine flux and salt re-

jection.

1. Estimate the effective membrane charge densityXd corresponding to a

given salt concentrationcf,2 on the basis of the experimental data of Table

6.2.

2. Consider an initial guess for the permeate salt concentration cp,2 and es-

timatecoutj using (6.26).

3. Calculatecentj andcav,j using (6.26) and (6.28).

4. Calculate effective pressure driving force using Eq. 6.31 accounting for

the osmotic pressure difference caused by both sugar and salt concentra-

tion differences across the membrane.

5. Calculate the permeate salt concentrationcp,2 using (6.27) and compare

with the guess of point (2).

6. Iterate (2)-(5) until convergence with respect tocp,2.

7. Calculate the salt rejection asR = 1 − cp,2/cf,2 and the permeate flux

with V = Lp∆Pe.

6.4 Results and discussion

6.4.1 Empirical approach

The feed concentrations versus the operation time obtainedfrom the first ex-

perimental run are illustrated in Fig. 6.2. The change in theconcentrations in

the feed tank during the experimental run is shown in Fig. 6.3. Experimental

Page 167: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

6.4. RESULTS AND DISCUSSION 155

0 1 2 3 4 5 60

0.1

0.2

0.3

0.4

0.5

0.6

0.7

time [h]

conc

entr

atio

n [m

ol/L

]

cf,1

cf,2

Figure 6.2: Measured data of feed concentration as a function of operation time for the

experimental run.

data in the wholecf,1-by-cf,2 matrix are available through the proposed exper-

imental design. This allows an effective parameter estimation by data-fitting on

the measured data ofR andJ . The measured data obtained from validation

run no. 2 are also illustrated in Fig. 6.3. Comparing the two operational modes,

one can see that the variable volume dilution mode is not sufficient to obtain

the relation between the rejection and the feed compositiondue to the limited

date oncf,1 andcf,2. The experimental data of permeate flux and rejections ob-

tained from the experimental run are plotted as functions offeed composition

in Figs. 6.4 and 6.5. The surfaces shown in Figs. 6.4 and 6.5 were fitted to the

experimental data in a least-squares sense. In particular,we have found a very

good fitting using

J = (x1c2f,2 + x2cf,2 + x3) · exp((x4c

2f,2 + x5cf,2 + x6)cf,1)(6.32)

R1 = (y1cf,2 + y2)cf,1 + (y3cf,2 + y4) (6.33)

R2 = (w1c2f,2 + w2cf,2 + w3) · exp((w4c

2f,2 + w5cf,2 + w6)cf,1)(6.34)

Page 168: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

156 CHAPTER 6.

0.2 0.3 0.4 0.50

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

cf,1

[mol/L]

c f,2 [m

ol/L

]

experimental run validation run no. 2

Figure 6.3: Change in the feed composition during the experimental run.

0

0.2

0.4

0.6 0

0.2

0.4

0

0.2

0.4

0.6

0.8

1

cf,2

[mol/L]cf,1

[mol/L]

R1 [−

]

00.2

0.40.6

0

0.2

0.4

0

0.2

0.4

0.6

0.8

1

cf,1

[mol/L]cf,2

[mol/L]

R2 [−

]

Figure 6.4: Rejection of sugar (left side) and salt (right side) as functions of feed com-

position for membrane DK. Experimental data are illustrated with open circles and fitted

empirical planes with continuous lines. (25 °C, 30 bar.)

wherex1, . . . , x6, y1, . . . , y4, w1, . . . , w6 are suitable coefficients.

An almost total and composition-independent rejection wasmeasured for sugar.

Page 169: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

6.4. RESULTS AND DISCUSSION 157

00.2

0.40.6 0

0.20.40

10

20

30

cf,2

[mol/L]c

f,1 [mol/L]

perm

eate

flux

[L/h

/0.5

m2 ]

Figure 6.5: Permeate flux of the membrane DK as function of feed composition. Exper-

imental data of the 0.5 m2 element are illustrated with open circles and fitted empirical

plane with continuous lines. (25 °C, 30 bar.)

On the contrary, the rejection of salt strongly depends on the feed concentrations

of both components varying between 14 and 70%. Moreover, both components

have great contributions to the permeate flux. It should be pointed out that great

care is needed when the empirical relations are employed forextrapolation out

of the range of the experimentalcf,1-by-cf,2 matrix.

6.4.2 Model validation

The simulation technique discussed in Sects. 6.2 and 6.3 allows a quick com-

parison of the performances of different batch and semi-batch operations, and

also of multi-step processes involving different combinations of the basic oper-

ations.

After estimating the flux and rejection as functions of concentration from the

first experiment, four more experiments were carried out in order to validate

the model. In each test the flux and rejection required in (6.10) and (6.13)

were computed using the empirical and the theoretical approaches discussed

in Sects. 6.2.4-6.2.4 (see also Sects. 6.3.1 and 6.3.2). Thepredicted and the

measured data of the membrane DK for the different operations are shown in

Fig. 6.6-6.9. The permeate fluxJ of the membrane element (left-side figures)

Page 170: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

158 CHAPTER 6.

and the concentrations of the compounds (right-side figures) in the feed tank are

plotted versus operation time. Concentrations of sugar andsalt are illustrated

with open and closed circles, respectively.

0 1 2 3 40

2

4

6

8

10

12

14

16

18

time [h]

perm

eate

flux

[L/h

/0.5

m2 ]

measuredEMPITDSPM−DE

0 1 2 3 40

0.05

0.1

0.15

0.2

0.25

0.3

0.35

time [h]co

ncen

trat

ion

[mol

/L]

Figure 6.6: Validation run no. 1: constant-volume dilution mode with pure solvent as

diluant.

0 2 4 6 80

2

4

6

8

10

12

14

16

18

time [h]

perm

eate

flux

[L/h

/0.5

m2 ]

measuredEMPITDSPM−DE

0 2 4 6 80

0.1

0.2

0.3

0.4

0.5

time [h]

conc

entr

atio

n [m

ol/L

]

Figure 6.7: Validation run no. 2: variable-volume dilution mode with pure solvent as

diluant (α = 0.75).

In general, good predictions were obtained using the theoretical models. The

permeate flux of the membrane element is under-estimated to acertain extend

with both models thus giving inaccurate predictions for thevalidation run no. 4

shown in Fig. 6.9. In this case, since the change in the volumein the feed tank is

Page 171: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

6.4. RESULTS AND DISCUSSION 159

0 1 2 3 4 50

2

4

6

8

10

12

14

16

18

time [h]

perm

eate

flux

[L/h

/0.5

m2 ]

measuredEMPITDSPM−DE

0 1 2 3 4 50

0.1

0.2

0.3

0.4

0.5

time [h]

conc

entr

atio

n [m

ol/L

]

Figure 6.8: Validation run no. 3: constant-volume dilution mode with diluted process

liquor as diluant.

0 0.5 1 1.5 2 2.50

2

4

6

8

10

12

14

16

18

time [h]

perm

eate

flux

[L/h

/0.5

m2 ]

measuredEMPITDSPM−DE

0 0.5 1 1.5 2 2.50

0.1

0.2

0.3

0.4

0.5

0.6

time [h]

conc

entr

atio

n [m

ol/L

]

Figure 6.9: Validation run no. 4: constant inlet-rate fed-batch process employing pro-

cess liquor as inlet (Q = 9.64 L/h).

given by the difference of the constant inlet and the permeate outlet, a relatively

small estimation error in the permeate flux can cause inaccurate prediction for

the actual volume in the feed tank, and thus for the feed concentrations.

In the case of the IT model,σ andPs need to be estimated for each component

either from literature data or from previous experiments with single-solute sys-

tems. It should be pointed out that these transport parameters implicitly account

for the interaction between the given membrane and the specific solute, which

Page 172: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

160 CHAPTER 6.

can not be directly inferred from the IT model on a physical basis. Moreover,

their dependence on the concentration should be evaluated in order to improve

the model.

The DSPM-DE model requires more input parameters related toboth the mem-

brane structural and electrical properties and the characteristics of the solute.

However, the increased computational cost with respect to the IT model is paid

back by the good representation of the properties of the membrane.

The simulations based on the empirical approach fit better the experimental data

than those based on theoretical models. However, the latterare quite satisfac-

tory considering the simplifications used to derive the theoretical models and

the fact that we used parameters taken from literature without evaluating the

differences in the test conditions and equipments as well asin the properties of

the individual elements or membranes. Moreover, the theoretical models can

be readily used for analyzing the sensitivity of the separation with respect to

the applied pressure, and they can be extended on a physical basis accounting

for cross-flow velocities. On the other hand, the empirical approach would de-

mand a rapidly increasing amount of experiments to estimatefurther parameters

that would enrich the model, like applied pressure, cross-flow velocity, another

solute or temperature.

6.5 Conclusion

A mathematical frame is provided for modeling batch and semi-batch mem-

brane filtration processes. The approach followed in this work uses the the feed

concentrations as basis for the calculations, rather than the concentration fac-

tor. A model based on a system of ordinary differential equations and a practical

computational algorithm are presented. The design equations describing the en-

gineering aspects of batch and semi-batch systems are handled separately from

the estimation methods describing the mass transfer through the membrane.

Thus, the permeate flux and rejection can be estimated eitherby empirical equa-

tions fitted to the experimental data or by equations based ontheoretical models.

In particular, we compared an experimental approach requiring a minimal num-

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.1. NOMENCLATURE 161

ber of experiments to the IT model and the linearized DSPM-DEmodel. The

theoretical models might be advantageous over the empirical approach when

many parameters are involved. Finally, various batch and semi-batch NF oper-

ations and simulations were carried out with an organic/electrolyte binary test

solution. In all cases, good agreements were found between predicted and ex-

perimental data.

.1 Nomenclature

aj Stokes radius of ionj (m)

A membrane area (m2)

c concentration (mol m−3)

d thickness of oriented solvent layer (0.28−9 m)

D diluant flow-rate (m3 s−1)

Di,∞ diffusion coefficient at infinite dilution (m2 s−1)

Di,p hindered diffusion coefficient within the pore (m2 s−1)

e electronic charge (1.602177 · 10−19 C)

F Faraday constant (96487 C mol−1)

j molar solute flux (mol m−2 s−1)

J permeate flux (m3 s−1 m−2)

k Boltzmann constant (1.38066 · 10−23 J K−1)

Kc convective hindrance factor

Kd diffusive hindrance factor

Lp hydraulic permeability (m s−1 Pa−1)

Pe Peclet number

Ps solute permeability (m s−1)

Q inlet into the feed tank supplied by external pump (m3 s−1)

ri solute radius (m)

rp pore radius (m)

R gas constant (8.31447 J T−1 mol−1)

R rejection

t operation time (h)

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162 CHAPTER 6.

T temperature (K)

V volume (L)

V solvent velocity (m s−1)

x axial position within the pore (m)

Xd effective membrane charge (mol m−3)

zj valence of ionj

Greek symbols

∆cj concentration difference of ionj across the pore thickness (mol m−3)

∆P applied pressure (Pa)

∆π osmotic pressure difference across the membrane (Pa)

∆Wi Born solvation energy barrier (J)

∆x membrane thickness (m)

ǫb bulk dielectric constant

ǫp pore dielectric constant

ǫ∗ dielectric constant of oriented water layer

ǫ0 vacuum permittivity (8.854· 10−12 J−1 C2 m−1)

Φi steric partitioning coefficient

Φ′

i partial partition coefficient

η0 dynamic viscosity of solvent (Pa s)

λ ratio of solute to pore radius

σ reflection coefficient

ψ potential within the pore (V)

ν dissociation constant

Subscripts

f feed

p permeate

d diluant

i component (in the experimental part:i=1 sucrose, andi=2 salt)

j ion (in the experimental part:j=1 Na+, andj=2 Cl−)

Superscripts

n time discretization step

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BIBLIOGRAPHY 163

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168 CHAPTER 6.

Page 181: Separation of Amino Acids with Nanofiltration: Permeation Modelling ...

Part III

SYNOPSYS

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Synopsys

This chapter is a concise drawing together of the original findings and main

conclusions of the substantive chapters as well as a critical assessment of this

thesis. It also focuses on describing the continuation of the present work and

further research needs.

This research project makes an original contribution in thefield of amino acid

nanofiltration. Since concentrated systems are usually thetargets of industrial

separations, the first main challenge in this work was to clarify the effect of

increasing feed concentration on the separation. Many papers have been pub-

lished dealing with diluted solutions [1–4], but only a few works are available on

concentrated systems. Besides, as we indicated in Chapter II and III, there are

certain inconsistencies in the results and in their explanations between the dif-

ferent studies. On the basis of the current state of research, no definite conclu-

sion on the effect of increasing concentration could be drawn. These concerns

and the gap in the scientific research on this field have openedthe opportunity

for publication. Focusing on this issue, we present experimental evaluation of

amino acid permeation in Chapter II and IV. These experimental investigations

have led to the conclusion that the rejection dependence on the concentration is

more expressed for dissociated amino acids than for zwitterions. An other im-

portant finding is that membranes purchased from different manufacturers with

different active layer materials show an identical tendency as concerns their re-

sponse to increasing feed concentration. Based on these achievements one can

assume that, although NF is a very complex process at fundamental level in-

fluenced by many factors, one of the major effects on amino acid transport is

171

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172

actually related to the physico-chemical properties of thetarget substance rather

than the membrane. In an attempt to prove this hypothesis, wedelivered a con-

cept to calculate the osmotic pressure of amino acid solutions starting from the

van’t Hoff law and incorporating the ionisation state of amino acids. Thus, the

pH dependency of a diprotic amino acid can be described as follows:

π = RTcA[1 +1

1 + 10pH−pK1 + 102pH−pK1−pK2

+

+1

1 + 10pK2−pH + 10pK1+pK2−2pH ]

(35)

where the dissociation coefficientspK1 andpK2 are basic properties of amino

acids and can be taken from literature.

By changing the pH of an amino acid solution, the physico-chemical properties

of the system are modified. Expressing this change with a physical term is

a major step in model building. Eq. 35 allows us to quantify the underlying

phenomena, and since it is in term of pressure, it can be employed for practical

engineering calculations.

Eq. 2.8 describes the effect of pH on osmotic pressure. Choosing for illustra-

tion a 1 molar diprotic amino acid solution as a reference, the calculated osmotic

pressure is ca. 24 bar at the isoelectric point and 48 bar for completely disso-

ciated amino acids. This means a huge pH-dependent difference, which has a

major impact on the NF separation, since the applied pressure in NF is usually

in the range of 5 to 40 bar. The importance of this fact seems tobe overlooked

in the literature. We refer here to an often quoted common wisdom that “mem-

branes do not lie”, meaning that they always do what they can do under the

given circumstances [5]. In our case, the dissociation-dependent pattern of the

osmotic pressure explains the stressed rejection and flux drop for the ionized

amino acids at high concentration ranges. The impact of thisphenomena on NF

separation was experimentally shown in Chapter II and III.

A pronounced flux and rejection drop for dissociated amino acids at high con-

centrated ranges has been reported earlier [6, 7], and such phenomenon is ex-

plained with the saturation of the charged sites on the membrane. This satu-

ration is said to make the membranes more permeable to charged components

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173

in higher concentration range due to charge shielding. We should also point

out that no quantitative analysis of this charge shielding has been investigated

yet. Our findings on the pH dependence of osmotic pressure putthis hypoth-

esis in doubt. The threat arises related to the internal validity of the charge

shielding phenomena. Namely, it is questionable whether the change in the de-

pendent variables (flux and rejection) may produced solely by the independent

one (decreasing membrane charge density). In fact, our findings show that the

pH dependent osmotic pressure of the amino acid solution is greatly responsible

for the observed effects.

Indirect and direct experimental verification of the concept for osmotic pres-

sure determination was made with RO measurements and with vapor pressure

osmometry. The validity of the model was checked with three diprotic amino

acids over a wide range of concentration and pH with good agreement between

predicted and experimental data. Although Eq. 2.8 can be used only for diprotic

amino acids, the utilization of the presented concept to develop similar equa-

tions for basic and acidic amino acids is trivial. The theoryis most likely

generally-valid for all amino acids, but it is still a question whether it could

be applied for di-, tri-, or longer–chain peptides. Furtherexperimental analy-

ses is needed to explore the limitations of the provided model elaborating also

aspects of non-ideality of the system. Eq. 2.8 is directly derived from the first

principles using the van’t Hoff law and Arrhenius’ hints combining with some

well-established and well-known laws of acid/base dissociation. Such deriva-

tion combining two related fields of science is straightforward and simple. Nev-

ertheless, Eq. 2.8 is our own product, and to the best of our knowledge, it has

been never published in this compact form yet. Moreover, no literature on os-

motic pressure data exerted by amino acid solutions of different pH has been

found. We believe that the presented osmotic pressure modelcould find general

interest in several other disciplines of science dealing with amino acids. As far

as membrane filtration is concerned, the importance of the pHon the osmotic

pressure and thus, on the separation performance has been neglected so far, al-

though our theoretical and experimental investigations clearly prove that it is a

major governing factor.

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174

Building on the achievements of Chapter II and III, a quantitative description of

amino acid transport is possible. The Kedem-Katchalsky (KK) model was em-

ployed to compute the permeate flux and rejection of amino acid compounds.

For engineering purposes this phenomenological model might be favoured due

to its simplicity as compared with models based on transportmechanism. How-

ever, the model suffers from some pitfalls. First, the modelin its original form is

not capable for the direct determination of rejection and flux. Second, as stated

in literature dealing with other solute-systems, the modelparameters might not

be constant over concentration.

In order to overcome the first problem, starting from the KK model we derived

an equation where the only unknown is the rejection. Thus, after assigning

the transport parameters of the membraneLp, Ps andσ, the rejection can be

calculated for any set of variablescr, ν and∆P with the following equation:

cr(1 −R) − PscrRLp△P − LpσνRTcrR

+ (1 − σ)crR

ln(1 −R)= 0 . (36)

This form of the KK model is not restricted to NF membranes or amino acids,

in fact, a generally-valid an analytic tool is provided. Eq.36 was derived by

assuming a logarithmic solute concentration profile acrossthe membrane thick-

ness. In a simpler case, when a linear profile is assumed, an algebraic solution

of the model exists. Such assumption resulting a quadratic equation has been

already examined by Kargol [8], however, it was only used to study the effect

of increasing mechanical pressure.

The second difficulty is related to the concentration dependence of transport

parameters. We should point out that the presented model with the assump-

tion of constant transport parameters is able to predict theoverall pattern of the

separation behaviour, indicating the general tendencies of fluxes and rejections

correctly. However, the actual values of the simulations are somewhat inaccu-

rate in comparison with the experimental data. The relationbetween transport

parameters and feed concentration can not be derived in a straightforward way

from the fundamentals of the irreversible thermodynamics models. For this

purpose, empirical relations have to be evaluated. In Chapter IV we analyse

different methodologies for improving the basic model. In our case, assum-

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175

ing a linear relationship between the solute permeability parameter and the feed

concentration resulted in good predictions, however, the external validity of this

observation is not proved. One of the threats to the externalvalidity of the model

is that this linear relation is not proved for basic or acidicamino acids. We can

conclude that an accurate evaluation of these relations is acrucial step in the

model development, and currently also the greatest limitation of the model.

To estimate the transport parametersσ andPs, the Spiegler–Kedem model is

used. This model needs a set of rejection and corresponding flux data as input.

Starting for the original KK model, we have developed a strategy to estimate

the transport parameters from experimental data, which does not require a com-

plete pressure scan. We call this method as direct parameterestimation, and the

advantage of this technique is the smaller amount of experimental data needed

to compute the parameters. The simulation results obtainedwith direct param-

eter estimation are comparable with those that we had computed using SK to

determine the transport parameters.

The ability to predict the separation performance of NF is very useful for the

planning and optimization of such processes. Eq. 36 together with Eq. 35 gives

a quantitative description of amino acid transport throughNF membranes. The

quantification of such phenomena has not been presented before.

The development of models based on transport phenomena has gone through a

major progress in the last decade. Recently, a modelling approach based on the

extended Nernst-Plack has been developed, that has the potential for industrial

applications [9–11]. Such model would ideally utilize available physical prop-

erty data of a process stream and a membrane. In Chapter IV we point out that

models based on the extended Nernst-Plank equation could gain an important

role in the modelling of amino acid separation in the future.The modelling of

amino acid separation using transport mechanism models is beyond the scope of

this thesis. Analysis of permeation with the DSPM-DE model is currently un-

der investigation in our laboratory. The utilization of this model to amino acids

is complex and not straightforward. A possible strategy formodelling purposes

is to consider an amino acid solution as a mixture of neutral compounds and

ions, rather than consider amino acid compounds with different ionization state.

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176

Thus, let us consider a diprotic amino acid solution. When the pH of this solu-

tion is equal with the isoelectric point of the given amino acid, the molecule is

present in a zwitterionic, e.g. quasi neutral, form. When the pH is set to a high

value where the amino acid is completely dissociated, then the solution can be

considered as a 1:1 type electrolyte. Here the coion is the amino acid anion,

and the counter ion is the cation of the alkaline used for adjusting the pH (for

instance Na+ when NaOH is used). Following this logic, at pH=pK a mixture

is given consisting of neutral solutes and ions (amino acid anion accompanied

by Na+) where the ratio of neutral compounds to ions is 1:2. Thus, this system

is analogue to the organic molecule/electrolyte system that have been studied in

Chapter VI. An other possible interpretation is to assume amino acid molecules

with ionization state ranging from 0 to -1. In both cases, several difficulties

arise when applying the DSPM-DE model. The most relevant problems that

have to be solved are summarized hereafter.

• The model requires the diffusivity values of the species. It is difficult to

obtain diffusion coefficients of amino acids respect to their dissociation

state [12, 13], and conceptual problems might occur applying them in the

model.

• It has been stated by several authors that zwitterionic amino acids re-

jections are greater than strictly neutral organic solutesof similar size

potentially [7, 14, 15]. Zwitterionic amino acids are not a truly neutral

molecules, but have two opposite charged sites as dipolar ions. Despite

their null net charge, their transmission is greater than the expected, indi-

cating that size is not the sole parameter that governs transmission. There-

fore, the permeation of zwitterions is not solely dependenton the ratio

of molecule radius to pore radius. So far, the underlying physical phe-

nomenon is not known in details, and no quantitative trends have been

drawn between truly neutral compounds and zwitterions. It follows that

the model would underestimate the real rejection, and empirical correc-

tion factors should be evaluated.

• Different amino acids show different affinity to water. This phenomenon

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177

is expressed in terms of hydrophobicity which is often correlated to mem-

brane retention [15–17]. The DSMP-DE model does not incorporate such

considerations. It has been reported that a high hydrophobicity lowers the

retention, but the influence of hydrophobicity decreases ifthe molecular

size (compared to the MWCO of the membrane) increases [17]. The ef-

fect of hydrophobicity on retention for charged and uncharged organic

molecules was extensively studied by Boussu et. al. [18], and empirical

relation between rejection and hydrophobicity was determined by means

of linear regression. However, under conditions where the dissociation

of amino acids has to be considered, the situation is more complex, since

the retention is influenced by the interplay between membrane and com-

ponent hydrophobicity, charge, and size. Quantitative analysis of such

aspects has not been investigated yet.

• The charge shielding phenomena has to be examined. The model requires

a proper estimation of the membrane charge density for any given set of

feed concentration and pH. A possible approximation technique is to fit

the rejection data for NaCl to the DSPM-DE model in order to determine

the effective charge density of the membrane [19], and use these data for

predicting the rejection of other electrolytes. However, it is questionable

wheter such approximation could properly describe the permeation trends

of partly charged amino acid solutions.

• Finally, the DSPM-DE approach requires iteration methods. In Chapter

VI we utilize the model for predicting the separation of an electrolyte

from neutral organic compounds that is conceptually similar to an amino

acid system. However, a complete rejection for the neutral compound was

considered that simplified the calculation procedure in that study. Assum-

ing incomplete rejection for zwitterions would require theutilization of

complex numerical methods.

Overall, further research is needed on the development of predictive transport

mechanism models describing amino acid permeation in orderto reduce the

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178

dependence of model parameters on experimental data fitting, since such de-

pendence defeats the purpose of having a predictive model.

In the second part of the thesis, we consider batch processes, and we demon-

strate the practical use of the NF modelling techniques described earlier in

Chapter I-IV.

Many papers in terms of batch process performances have beenpublished so far.

The classical mathematical treatment of batch filtration modelling is reviewed

in Chapter V and VI. Here, no further description is given in detail. In brief,

constant rejection coefficients are assumed, and concentration and dilution fac-

tors are used as a basis for calculations. In Chapter V we showthat under

conditions where the rejections of the solutes are stronglyvary depending on

their feed concentrations, and there is a considerably interdependence in their

permeation, the simulation based on the classical approachand the subsequent

optimization might lead to inaccurate results.

The general approach to batch system design proposed in thisthesis is illus-

trated in Fig. 10.

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17

9

C o m p u t a t i o n a l A l g o r i t h m

S y s t e m o f O D E s

E m p i r i c a l

T h e o r e t i c a l

M a t h e m a t i c a l P r o g r a m m i n gT e c h n i q u e s

T r a n s p o r t M e c h a n i s m M o d e l s

I r r e v e r s i b l e T h e r m o d y n a m i c s M o d e l s

E x p e r i m e n t a l D e s i g nw i t h m i n i m u m n u m b e r o f e x p e r i m e n t s

S I M U L A T I O NM E M B R A N E S E P A R A T I O N P E R F O R M A N C ER a n d J s t a t e f u n c t i o n s

O P T I M I Z A T I O N

Figure 10: Flow-chart of the general modelling approach.

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180

The main contribution of this thesis to the related field of discipline is the in-

troduction of a numerical simulation technique that has a modular structure and

accounts for variable solute rejection coefficients. We provide a mathematical

framework for modelling batch and semi-batch processes. Unlike most of the

approaches reported in literature, this framework hands separately the design

equations describing the engineering aspects of batch system design and the

models of mass transfer through the membrane. As graphically illustrated in

Fig. 10, the framework consists of three distinct stages. These are the stage of

the modelling of membrane separation behaviour, the simulation stage, and the

optimization stage.

Let us first consider the simulation stage. In Chapter VI we propose a sys-

tem of ordinary differential equations which can be used forpredictions. We

elaborate the common basis of the different operational modes, and deliver a

general model. Thus, all possible batch and semi-batch simulation tasks can be

described with the following initial-value problems:

dVf

dt(t) = Q− (1 − α)J(t)A

Vf (0) = V 0f

(37)

and, fori = 1, 2,

Vf (t)dcf,i

dt(t) = J(t)A[αcd,i(t) + cf,i(t)(Ri(t) − α)] +Q(cd,i(t) − cf,i(t))

cf,i(0) = c0f,i .

(38)

Many numerical software packages offer built-in functionsfor solving this sys-

tem of ordinary differential equations. In addition, we provide a practical com-

putational algorithm for an approximate solution of Eqs. (37) and (38). The

mathematical framework of the simulation stage is designedin a way, that the

estimation of flux and rejections can be carried out separately, using the most

convenient approach for the problem at hand. Generally speaking, this allows

us to handle an engineering problem (e. g. simulation of batch operation) in-

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181

dependently from a basic research-related problem (e. g. mass transfer through

membrane).

As illustrated in Fig. 10, the flux and rejection can be estimated using theoret-

ical or empirical approaches. Considering the empirical approach, we report

an experimental design in Chapter VI, that requires a minimum number of a-

prior experiments. As far as theoretical approaches considered, both irreversible

thermodynamics and transport mechanism models can be inserted in the math-

ematical framework without having to modify it. Thus, also the achievements

in the modelling of amino acid permeation, that was described in the previous

chapters of this thesis in detail, can be readily used for thesimulation of batch

processes.

The presented approach is very useful for analysing multi-step batch processes.

Its modular structure permits to easily describe batch processes involving dif-

ferent arrangements of the basic steps. In Chapter V we evaluate the optimum

operation of the classical multi-step process including pre-concentration, con-

centration mode and post-concentration steps consideringeconomical aspects

and technological demands.

Obviously, this concept is not restricted to NF applications, but valid for all

pressure-driven membrane filtration processes. The same approach was suc-

cessfully applied also for the modelling of a multi-step microfiltration process

for solvent exchange [20]. Moreover, an other important advantage of the pre-

sented numerical technique over the traditional algebraicdescription is that the

permeation of the individual components in a multi-solute system can be simul-

taneously evaluated. Such a technique was effectively employed to simulate

the fractionation of a biological multi-component system in an industrial-scale

multi-step ultrafiltration process [21].

For most of the traditional separation processes, there areeffective and reliable

calculation methodologies for process design. These methods allow the pre-

diction of the separation performance and the design of the separation equip-

ment. In an ideal case, such predictive models only utilize available physi-

cal and chemical properties of the separation mean and the components to be

separated. Although NF separation is generally consideredas proven technol-

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182

ogy, and widely used for industrial separations, there is still a real need for

model–assisted process design. In an attempt to achieve this objective, this the-

sis project reviews the permeation models that can be considered in order to

achieve this objective. We discuss their main pitfalls and their applicability to

predict amino acid permeation. We also investigate the major governing factors

affecting the transport of amino acids through NF membranes, and present a

quantitative prediction model. Finally, we provide a modelling approach for the

simulation of industrially relevant batch and semi-batch separation processes.

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