Modeling of the permeation process in the cross flow ultrafiltration of protein solution

There are four classical models that are typically used to describe fouling: complete pore blockage, internal pore blockage or pore constriction, standard blockage, intermediate pore blo

MODELING OF THE PERMEATION PROCESS IN THE CROSS-FLOW ULTRAFILTRATION OF PROTEIN SOLUTION

TUAN-ANH NGUYEN

IN THE PARTIAL FULFILLMENT OF THE REQUIREMENT FOR THE DEGREE OF DOCTOR OF ENGINEERING (CHEMICAL ENGINEERING)

THE GRADUATE SCHOOL OF SCIENCE AND ENGINEERING

TOKYO INSTITUTE OF TECHNOLOGY

AUGUST 2013

ACKNOWLEDGEMENTS

I would like to express my deep gratitude to my supervisor, Assoc Prof YOSHIKAWA Shiro, for giving me the opportunity to work in a modern technique of separation The constant guidance and encouragement are also indispensable to me for completing my research

I wish to express my appreciation to Prof KURODA Chiaki, Prof OHTAGUCHI Kazuhisa, Prof ITO Akira, Prof SEKIGUCHI Hidetoshi, Assoc Prof OOKAWARA Shinichi for their time and effort in evaluating my work I have benefited from their constructive comments on my report

I want to express my sincere appreciation to the Chemical Engineering Department of Tokyo Institute of Technology, Japan and to the Faculty of Chemical Engineering of Ho Chi Minh University of Technology, Vietnam: for all the best things that they have offered me during

my study and research

I would also like to acknowledge JICA project for giving me the chance to improve my knowledge in the doctoral degree and the financial support

I also would like to thank all my lab-mate and my friends in Japan; for sharing with me their ideas and experience They are always available whenever I have trouble

Finally, I would like to dedicate my thesis to my family, with love and gratitude

TABLE OF CONTENTS

TABLE OF CONTENTS i

LIST OF TABLES v

LIST OF FIGURES vi

LIST OF NOTATIONS viii

Chapter 1 Introduction 1

1.1 Whey protein production and utilization 1

1.2 Concentrating Whey—Early Efforts 3

1.3 Concentrating Whey—Modern Techniques 4

1.4 Filtration theory 6

1.4.1 Darcy’s law 6

1.4.2 Classical fouling model 8

1.5 Cross-flow versus dead-end configuration 9

1.6 Classical filtration model for cross-flow filtration 10

1.7 Combination model 10

1.8 Objective of the study 12

Reference 13

Chapter 2 Filtration laws and the applicability to cross-flow filtration of protein solution 15

2.1 Introduction 15

2.2 Filtration theory 16

2.2.1 Darcy’s Law 16

2.2.2 Classical membrane fouling model 19

2.2.3 Compressible cake layer 23

2.3 Modification of filtration model to cross-flow operation system 24

2.3.1 Classical fouling model 25

2.3.2 Compressible cake 27

2.4 Experiments 28

2.4.1 Materials 28

2.4.2 Membrane 28

2.4.3 Cross-flow UF apparatus 29

2.4.4 Cross-flow membrane module 30

2.5 Results and discussion 30

2.5.1 Complete blocking law 30

2.5.2 Intermediate blocking law 32

2.5.3 Cake filtration model 33

2.5.4 Compressible cake model 34

2.6 Conclusions 36

Reference 37

Chapter 3 Combination model for permeate flux in cross-flow ultrafiltration of protein solution 39

3.1 Introduction 39

3.1.1 Combine pore blockage and cake filtration 41

3.1.2 Combined pore blockage and compressible cake layer model in sequent 44

3.2 A new combined model which consider pore blockage and compressive cake layer simultaneously 45

3.2.1 Model 46

3.2.2 Boundary and initial condition 47

3.2.3 Numerical scheme 48

3.3 Experiments 51

3.4.1 Pure water flux 52

3.4.2 Suspension permeation results 52

3.4.3 Comparison of the model with the experimental results 54

3.4.4 Effect of operating conditions 56

3.5 Conclusion 58

Reference 59

Chapter 4 Estimation of steady state permeate flux in cross-flow ultrafiltration of protein solution 60

4.1 Introduction 60

4.2 Correlation and dimensional analysis 61

4.3 Steady state estimation 62

4.4 4 Results and discussions 63

4.4.1 Comparison with experimental data 63

4.4.2 Effect of operating condition to removal rate or steady state permeate flux 65

4.4.3 Pore blockage coefficient α: 69

4.4.4 Calculation of the permeation process 73

4.5 Conclusions 73

Reference 74

Chapter 5 Application in design and optimization problem 76

5.1 Introduction 76

5.2 System configuration and model calculation 77

5.2.1 System configuration 77

5.2.2 Modeling of module performance 78

5.3 Estimate costs 81

5.3.1 Operating costs 81

5.3.2 Capital cost 83

5.4 Formulizations of the problem 86

5.4.1 Fix parameters: 86

5.4.2 Design variable: 86

5.4.3 Objective function 87

5.4.4 Constraints 87

5.5 Cyclic coordinate method for optimization 88

5.6 Case study 89

5.7 Results and discussion 90

5.7.1 Effect of recirculation flow rate on the total cost 90

5.7.2 Effect of module inlet pressure operation 91

5.7.3 Effect of module height 92

5.7.4 Effect of module width 93

5.7.5 Optimum design 94

5.8 Conclusions 95

Reference 96

Chapter 6 Conclusions and recommendations 98

6.1 Summary 98

6.2 Conclusions 98

6.3 Recommendations 100

LIST OF TABLES

Table 1.1 Typical chemical composition (g/L) of sweet and acid whey [2] 2

Table 1.2 Typical and species retained by MF, UF and RO membrane [7] 5

Table 3.1 Experimental conditions 51

Table 5.1 System parameter representing the ―baseline design configuration‖ 89

Table 5.2 Optimum design of membrane module 94

LIST OF FIGURES

Figure 1.1 Schematic of cheese making process and image of coagulation

(http://uktv.co.uk/food/item/aid/640812 access on 2013/06/03) 1

Figure 1.2 Liquid whey processing [1] 3

Figure 1.3 Dead-end mode and cross-flow mode of filtration [25] 10

Figure 2.1 Fouling mechanisms of porous membrane [18] 19

Figure 2.2 Relation between volume fraction and yield shear stress [12] 28

Figure 2.3 Schematic diagram of experimental apparatus 29

Figure 2.4 Cross sectional drawing of the flat membrane module 30

Figure 2.5 Fitting results using complete blockage model 31

Figure 2.6 Fitting results using intermediate blockage model 32

Figure 2.7 Fitting results using cake filtration model 33

Figure 2.8 Fitting results using compressible cake filtration model 35

Figure 2.9 Magnification in the initial period of filtration process 35

Figure 2.10 Magnification at the initial period using conventional cake layer model 36

Figure 3.1 Schematic of the developing blockage region 42

Figure 3.2 Schematic diagram of permeation process 45

Figure 3.3 Numerical Scheme 50

Figure 3.4 Effect of trans-membrane pressure to pure water permeate flux 52

Figure 3.5 Experimental results 53

Figure 3.6 Experimental results at the initial period 54

Figure 3.7 Comparison between calculation and experiment 55

Figure 3.8 Magnification at the very initial period 55

Figure 3.9 Effect of ΔP to fitting parameters 57

Figure 3.10 Effect of feed flow rate to fitting parameters 58

Figure 4.1 Comparison between model calculation and experimental data 64

Figure 4.2 Relation between mass Stanton number and dimensionless group 66

Figure 4.3 Steady state permeate flux versus cross-flow velocity 68

Figure 4.4 Relation between protein blocked fraction and dimensionless group 71

Figure 4.5 Comparison between predicted and calculate pore blockage parameter α 72

Figure 4.6 Comparison between calculations based on correlation equation and experimental

results 73

Figure 5.1 Schematic of membrane system operational configuration 78

Figure 5.2 Time value of money and cash flow [8] 82

Figure 5.3 An illustration of the cyclic coordinate method 89

Figure 5.4 Effect of recirculation flow rate on the total cost of plant 90

Figure 5.5 Effect of inlet pressure on the total cost of plant 91

Figure 5.6 Effect of module height on the total cost of plant 92

Figure 5.7 Effect of module width on the total cost of plant 93

Figure 5.8 Behavior of cost per unit flow rate design in optimum condition with plant capacity 94

f’R’ : growing cake factor (m/kg)

J: filtrated flux per unit membrane (m/s)

t: top of the cake layer

y: compressive yield stress

0: initial

∞: infinite

Chapter 1 Introduction 1.1 Whey protein production and utilization

Whey is the liquid resulting from the coagulation of milk and is generated from cheese manufacture [1] Figure 1.1 shows the simplified schematic diagram of cheese making process and the image of cheese curding Sweet whey, with a pH of at least 5.6, originates from rennet-coagulated cheese production such as Cheddar Acid whey, with a pH no higher than 5.1, comes from the manufacture of acid-coagulated cheeses such as cottage cheese While both whey types contain approximately the same amounts of whey proteins and lactose, the main difference is found in the calcium and lactic acid contents Compositional ranges of each are shown in Table 1.1

Figure 1.1 Schematic of cheese making process and image of coagulation

(http://uktv.co.uk/food/item/aid/640812 access on 2013/06/03)

Milk

Whey

Cultural, Additive Pasteurization

Curding

Cheese

Coagulant

Draining

In general, about 9 liters of whey is generated for every kilogram of cheese manufactured, and a large cheese making plant can generate over 1 million liters of whey daily ([2]) Due to the large amount and its low concentration, whey has been viewed until recently as one of the major disposal problems of the dairy industry Whey not used for humans was fed to pigs or other livestock, spread to the field as fertilizer, or simply thrown out However, whey is a potent pollutant with a high biological oxygen demand (BOD) of 35-45 kg/l; 4,000 l of whey, the output

of a small creamery, has the polluting strength of the sewage of 1,900 people [3] Therefore, whey constitutes a major ecological burden as well as severe odor problem if disposed as a waste material or spraying onto field The high BOD of whey also leads to an over load of waste treatment facilities and make this approach seldom practiced

Table 1.1 Typical chemical composition (g/L) of sweet and acid whey [2]

Beside the environmental effect, nowadays whey is evolving into a sought-after product because of the lactose, minerals, and proteins it contains as well as the functional properties it imparts to food A number of products are obtained from whey processing, as shown in Figure 1.2

Figure 1.2 Liquid whey processing [1]

1.2 Concentrating Whey—Early Efforts

The health benefits of whey led to the development of processes to isolate the solids by concentration and drying The initial industrial attempts were based on heat process: concentration and drying

The multiple-effect evaporator, which boils water in a sequence of tanks with successively lower pressures, is the conventional method for whey concentration Since the boiling point of water decreases as pressure decreases, the vapor boiled off in one vessel is used to heat the next and an external heat source is needed for the first vessel only and thus this method can reduce the high energy cost for concentration However, concentrated whey is a supersaturated lactose solution and, under certain conditions of temperature and concentration, the lactose can sometimes crystallize before the whey leaves the evaporator At concentrations above a dry material content of 65%, the product can become so viscous that it no longer flows

Roller drying is a process in which whey is dried on the surface of a hot drum and removed

by a scraper Although it is the cheapest drying technique, it may cause undesirable heat damage

for most functional applications of whey products In addition, it is difficult to remove the dried whey from the drum surface and filler such as wheat need to be mixed before drying

Spray drying is the most common technique for drying whey In this process, the lactose, which is amorphous and hygroscopic, is cooled and crystallized to nonhygroscopic α-lactose monohydrate The concentrated whey is then dispersed by a rotary wheel or nozzle atomizer into

a drying chamber through a hot-air stream, producing a powder with 10–14% moisture The evaporation keeps the temperature down and preventing denaturation [4] The wet powder is dried to 3–5% moisture in a vibrating fluid bed [5]

1.3 Concentrating Whey—Modern Techniques

Until the 1970s whey protein was available only in the heat-denatured form, a insoluble, gritty, yellowish-brown powder that found limited use ([6]) Membrane filtration then arrived, which allowed for the separation and fractionation of whey proteins at ambient temperature and therefore retaining their solubility A membrane is a barrier which separates two phases and restricts the transport of various chemical species in a rather specific manner The driving forces arise from a gradient of chemical potential or electrical potential The permeability

water-of the species depends on the membrane/solute/solvent interaction The permeate flows through the membrane while passage of the retentate is blocked In membrane filtration, the mobility of the species is primarily determined by the molecular size and the structure of membrane material The dividing line between permeate and retentate is also expressed as the molecular weight cut off (MWCO) Based on the pore size and species retained, membrane filtration usually classified

as reverse osmosis (RO), nanofiltration (NF), ultrafiltration (UF) and microfiltration (MF) as shown in Table 1.1

Table 1.2 Typical and species retained by MF, UF and RO membrane [7]

The principle of membrane filtration was developed for water desalinization in the 1950s and applied to food processing starting in 1965

Whey processors employ these types of membrane filtration and electrodialysis (ED) and combination of these processes All are followed by spray drying to obtain a dry (<5% moisture) product to create whey protein powders with different protein contents

In UF, whey retentate consists of protein, fat, and insoluble salts while the permeation consists of lactose, soluble minerals, and much of the water Diafiltration (DF), the addition of water to the retentate followed by a second UF, has been developed for the removal of salts and lactose [8]

MF allows for selective separation of microbial flora, the different whey proteins, and other components [9]

ED is another method for demineralizing whey In this electrochemical process (the other membrane filtration techniques used for whey are pressure-driven processes), direct current is passed through whey inside chambers with ion-permeable walls

NF, sometimes called ultra-osmosis, and is also suitable for desalting and demineralizing whey The method also selectively separates lactose [10] An operating pressure between 1.5 and

3 MPa is sufficient to increase the total solids of whey from 5 to 40% while removing 40% of the minerals [11]

In RO, whey is pumped at high pressure (between 2.7 and 10 MPa) through membranes to remove minerals [8] The MWCO is only 150 Da, which may result in membrane-fouling problems [12] Two-thirds of the water in whey can be removed by RO, leaving a concentrate that can be dried or shipped more efficiently [13]

1.4 Filtration theory

In the simplest of terms, filtration is a unit operation that is designed to separate suspended particles from a fluid media by passing the solution through a porous membrane or medium As the fluid or suspension is forced through the voids or pores of the filter medium, the solid particles are retained on the medium's surface or, in some cases, on the walls of the pores, while the fluid, which is referred to as the filtrate, passes through In some cases, the solid retained on the surface builds up to form a cake and then also becomes filter media Therefore, the fundamental of the filtration is the fluid flow porous media and many authors have contributed in this field

1.4.1 Darcy’s law

Most discussion of flow through porous media begin with Darcy’s law, i.e a differential representation of Darcy’s observation of flow through beds of sand [14]

k dP v

 m c

P J

where J is the permeate flux, V is the total volume of permeate, A is the membrane area, Rm

is the membrane resistance (which can increase with time due to membrane fouling and

compaction), and Rc is the cake resistance (which can increase due to cake build up and compression)

1.4.1.1 Membrane resistance

For a membrane whose pores are assumed to consist of cylindrical capillaries of uniform radius perpendicular to the face of the membrane, the membrane resistance is obtained from Poiseuille flow as [15]

1.4.1.2 Cake resistance

When a cake is incompressible, its porosity and resistance are independent of the imposed differential pressure The specific cake resistance per unit thickness may then be estimated by the Carman- Kozeny equation [16] :

 2 23

where α0 is a constant related primarily to the size and shape of the particles forming the

cake, and s is the cake compressibility which varies from zero for an incompressible cake to a

value near unity for a highly compressible cake

Although useful in practice, equation (1.5) represents an oversimplification of the behavior

of compressible filter cake More rigorous analyses of cake compression have been attempted by many authors with equivalent forms such as in [18-23] The present of Landman, et al [23] is used in this study and will be discussed in 2.2.3

1.4.2 Classical fouling model

The critical problem in filtration is the flux declination due to the increase of resistance caused by fouling Fouling of a membrane can occur by deposition of particles inside or on top

of the membrane There are four classical models that are typically used to describe fouling: complete pore blockage, internal pore blockage (or pore constriction, standard blockage), intermediate pore blockage (or partial pore blockage), and cake filtration

In the complete pore blockage model, the flux is shut off by protein aggregates depositing

on the membrane surface, and filtrate can only pass through the unblocked pore area

The pore constriction model accounts for fouling that occurs in the internal structure of the membrane In the pore constriction model, membranes are assumed to have straight through cylindrical pores The membrane pore radius is reduced by the uniform adsorption of protein to the internal membrane surface

The partial pore blocking or intermediate pore blockage mode is similar to the complete pore blockage model and accounts for the possibility that particles can land on top of other deposited particles

The cake filtration model assumes that a uniform cake layer forms over the entire membrane

surface, and this fouling layer is permeable to fluid flow with resistance Rc The rate of change of

cake layer resistance Rc is directly proportional to the convective transport of protein aggregates

to the membrane surface

The laws of filtration proposed for these classical fouling mechanism is summarized by Hermans and Bredée [24]:

2 2

d t dt k



The exponent n characterizes the filtration model, with n=0 for cake filtration, n=1 for intermediate blocking, n=3/2 for pore constriction (also called standard blocking), and n=2 for

complete pore blocking

1.5 Cross-flow versus dead-end configuration

The filtration process usually operate in two types of configuration: dead-end mode and cross-flow mode

In dead-end mode the flow direction is perpendicular to the membrane surface The retained particles build up with time as a cake layer or build up in the void space of the membrane In both case, the particles build up results in an increased resistance to filtration (known as membrane fouling) and the permeate flux will decrease in constant pressure mode or the pressure need to increase in constant flux mode Therefore, the dead end filtration process must be stopped periodically in order to remove the deposited particle or replace the filter medium As such, dead-end filtration basically is batch process

The cross-flow configuration has been increasingly used as an attractive alternative to end configuration In this operation mode, the flow direction is made to be tangential to the surface of the membrane The imposed trans-membrane pressure drop causes a cross-flow of the permeate flux through the membrane to occur The permeate flux carries particle to the membrane and the retained also forms a cake layer, which blocks the void spaces of the membrane However, unlike dead-end mode, this cake layer does not build up indefinitely The shear stress exerted by the tangential flow removes the deposited particles and makes the cake layer approach the equilibrium state Therefore, relatively high fluxes may be maintained over prolonged time period The comparison between two operational modes is shown in Figure 1.3

dead-Figure 1.3 Dead-end mode and cross-flow mode of filtration [25]

1.6 Classical filtration model for cross-flow filtration

In cross-flow operation mode, due to the existence of the tangential flow, the material will

be transport back to the bulk stream Therefore the transport back flux should be presented in the model The mathematical form of the classical fouling in cross-flow filtration is first summarized



The exponent n characterizes the fouling mechanism, with n=0 for cake filtration, n=1 for intermediate blocking, and n=2 for complete pore blocking The pore constriction fouling is identical to dead-end filtration mode and hence, does not include here

1.7 Combination model

The flux decline during protein filtration can be efficiently analyzed using one of these simple models such as in [27], [28], [29], [30] More extensive studies of protein fouling have often reported a transition in fouling mechanism during the course of the filtration For example, Tracey and Davis [31] examined the total resistance of membrane versus time in filtration of bovine serum albumin solution and found that the data in the initial period is consistent with pore blockage mechanism while the cake model is appropriate in the long times Therefore, a single

simple model may not be enough to give good estimation for permeate flux in many cases of filtration processes, especially in protein system There are several combination of classical fouling mechanisms have been proposed in order to describe the flux declination Ho and Zydney [32] used the combined model which includes pore blockage and filtration cake model for protein fouling in protein filtration The membrane resistance is increased by the initial fouling due to pore blockage and subsequent fouling due to the growth of protein cake layer deposit over these blocked regions Furthermore, Duclos-Orsello, et al [33] proposed more complicated model which includes three mechanisms: pore constriction, pore blockage and cake filtration model Bolton, et al [34] proposed five new models that combined two mechanisms from different individual effect of membrane fouling Pore blockage and cake filtration model have also been applied with some modification for describing the cross-flow filtration process For example, Mondal and De [35] considered sequential intermediate pore blocking and cake formation in cross-flow membrane filtration of oily-water emulsion Daniel, et al [36] integrated pore blockage and cake filtration model for cross-flow filtration of waste simulant water with back-pulsing Mattaraj, et al [37] combined pore blockage, osmotic pressure and cake filtration model for cross-flow nanofiltration of natural organic matter and inorganic salts Although there are significant contribution to describe the permeate flux, the fundamental of cross-flow ultrafiltration of protein solution still need to be considered The growth of filtration cake in these combination models was considered as the conventional cake layer, in which the resistance of cake was assumed to be directly proportional to the weight of solid deposit However, Iritani, et al [38] and [39] reported that in the UF of a whey suspension, the protein cake layer was often compressible In the study of Karasu, et al [40], a combination of compressive yield stress model and pore blockage mechanism in sequence was considered In the initial period, the pore blockage mechanism is dominant and thus, the combined pore blockage and cake filtration is used In the later period, the compressible cake layer model for dead-end filtration process was adapted and modified to the cross-flow system The removal rate of the cake was introduced to the model and the volume fraction of the surface element was determined based on the rheology of the suspension and the shear stress exerted by the feed flow However, the physical meaning and the time when the transition occurs are difficult to explain

1.8 Objective of the study

Filtration has a long history in the chemical engineering field both from the standpoint of the production of high value products, as well as a technology extensively used in pollution control and prevention In this process, one of the critical problems is the declination of permeate flux caused by fouling The mechanism of membrane fouling and cake formation has not yet fully understood Therefore, the goals of this study are: (1) to contribute an understanding of the importance physical phenomena governing the filtrate flux in cross-flow filtration of whey solution, and (2) to use this physical understanding to develop mathematical model which are capable of explaining experimental observation as well as provide a basic for the design and optimization of the filtration process

In order to accomplish these objectives, several related studies were conducted First, several models and characteristic of permeate flux and physical structure of the membrane and fouling were extensively reviewed and examine for the applicability From these knowledge, a simple model which incorporated simultaneously pore blockage and compressive cake layer mechanisms for the permeate flux were developed

From the model, the steady-state permeate flux, which is an important parameter in flow filtration operation, were estimated based on the equilibrium Dimensional analysis was conducted in order to correlate steady-state permeate flux and pore blockage parameter to the operating conditions The results give full prediction of filtration process and therefore useful for the design and operation problem The results also suggest for the mechanism of particle transport in cross-flow ultrafiltration of whey

cross-Next, the proposed model was applied to a simple optimization design problem base on economic analysis and energy consumption The analysis contributes a basic strategy for the optimization in design and operating an ultrafiltration plant

Finally is the general summary, conclusion and some suggest for further study in cross-flow ultrafiltration of protein whey solution

The thesis itself is organized in six chapters according to the outline mentioned above Although there are many aspect of cross-flow ultrafiltration of whey solution has not been concerned, a logical way from the building model to application in the design and optimization

of the process was investigated The study tries to contribute a viewpoint to the knowledge of cross-flow ultrafiltration, especially in whey protein solution system

[12] L.L Muller, W.J Harper, Effects on membrane processing of pretreatments of whey, J Agric Food Chem., 27 (1979) 662-664

[13] C Roger, Whey: Ready for Takeoff?, U.S Dairy Markets & Outlook, 7 (2001) 1-4

[14] H Darcy, Les Fontaines Publiques de la Ville de Dijon, Dalmont, Paris 1856

[15] R Davis, D Grant, Theory for Deadend Microfiltration, in: W.S.W Ho, K Sirkar (Eds.) Membrane Handbook, Springer US, 1992, pp 461-479

[16] P.C Carman, Fundamental Principles Of Industrial Filtration, Trans Inst Chem Eng., 16 (1938) 168–187

[17] M.C Porter, What, when, and why of membranes MF, UF, and RO, Journal Name: AIChE Symp Ser.; (United States); Journal Volume: 73:171, (1977) Medium: X; Size: Pages: 83-103 [18] M.S Willis, I Tosun, A rigorous cake filtration theory, Chem Eng Sci., 35 (1980) 2427-

2438

[19] I Tosun, Formulation of cake filtration, Chem Eng Sci., 41 (1986) 2563-2568

[20] W R.J., A Numerical Integration of the Differential Equations Describing the Formation and Flow in Compressible Filter Cakes, Transactions of The Institution of Chemical Engineers,

56 (1978) 258-265

[22] K Stamatakis, C Tien, Cake formation and growth in cake filtration, Chem Eng Sci., 46 (1991) 1917-1933

[23] K.A Landman, C Sirakoff, L.R White, Dewatering of flocculated suspensions by pressure filtration, Physics of Fluids A: Fluid Dynamics, 3 (1991) 1495-1509

[24] P.H Hermans, H.L Bredée, Zur Kenntnis der Filtrationsgesetze, Recl Trav Chim Bas, 54 (1935) 680-700

Pays-[25] M Cheryan, Ultrafiltration and Microfiltration Handbook, CRC Press, USA, 1998

[26] R.W Field, D Wu, J.A Howell, B.B Gupta, Critical flux concept for microfiltration fouling, J Membr Sci., 100 (1995) 259-272

[27] W.R Bowen, Q Gan, Properties of microfiltration membranes: Flux loss during constant pressure permeation of bovine serum albumin, Biotechnol Bioeng., 38 (1991) 688-696

[28] M Hlavacek, F Bouchet, Constant flowrate blocking laws and an example of their application to dead-end microfiltration of protein solutions, J Membr Sci., 82 (1993) 285-295 [29] S.T Kelly, A.L Zydney, Effects of intermolecular thiol–disulfide interchange reactions on bsa fouling during microfiltration, Biotechnol Bioeng., 44 (1994) 972-982

[30] J Hermia, Constant pressure blocking filtration laws - Application to power-law Newtonian fluids, Trans Inst Chem Eng, 60 (1982) 183 - 187

non-[31] E.M Tracey, R.H Davis, Protein fouling of track-etched polycarbonate microfiltration membranes, J Colloid Interface Sci., 167 (1994) 104-116

[32] C.-C Ho, A.L Zydney, A combined pore blockage and cake filtration model for protein fouling during microfiltration, J Colloid Interface Sci., 232 (2000) 389-399

[33] C Duclos-Orsello, W Li, C.-C Ho, A three mechanism model to describe fouling of microfiltration membranes, J Membr Sci., 280 (2006) 856-866

[34] G Bolton, D LaCasse, R Kuriyel, Combined models of membrane fouling: Development and application to microfiltration and ultrafiltration of biological fluids, J Membr Sci., 277 (2006) 75-84

[35] S Mondal, S De, A fouling model for steady state crossflow membrane filtration considering sequential intermediate pore blocking and cake formation, Sep Purif Technol., 75 (2010) 222-228

[36] R.C Daniel, J.M Billing, R.L Russell, R.W Shimskey, H.D Smith, R.A Peterson, Integrated pore blockage-cake filtration model for crossflow filtration, Chem Eng Res Des., 89 (2011) 1094-1103

[37] S Mattaraj, C Jarusutthirak, C Charoensuk, R Jiraratananon, A combined pore blockage, osmotic pressure, and cake filtration model for crossflow nanofiltration of natural organic matter and inorganic salts, Desalination, 274 (2011) 182-191

[38] E Iritani, K Hattori, T Murase, Analysis of dead-end ultrafiltration based on ultracentrifugation method, J Membr Sci., 81 (1993) 1-13

[39] E Iritani, S Nakatsuka, H Aoki, T Murase, Effect of Solution Environment on Unstirred Dead-End Ultrafiltration Characteristics of Proteinaceous Solutions, J Chem Eng Jpn., 24 (1991) 177-183

[40] K Karasu, S Yoshikawa, S Ookawara, K Ogawa, S.E Kentish, G.W Stevens, A combined model for the prediction of the permeation flux during the cross-flow ultrafiltration of

a whey suspension, J Membr Sci., 361 (2010) 71-77

Chapter 2 Filtration laws and the applicability to cross-flow filtration of

protein solution 2.1 Introduction

The ultrafiltration (UF) process has been utilized widely in the dairy and biotechnology industry such as the separation and concentration of protein whey solution, recovery of vaccines and antibiotic in fermentation broth In such processes, the critical problem is the decrease of filtration flux due to the increase of resistance caused by fouling Therefore, the behavior of permeated flux and fouling in the filtration process has received attention in significant numbers

of studies

One of the classical work is the laws of filtration proposed by Hermans and Bredée [1], which consist of a set of power-law relationships between the rate of filtration and its time derivative corresponding to supposedly different particle retention mechanisms operating in filtration These classical fouling models may be generally classified into four types: pore blockage, intermediate blockage, pore constriction and cake filtration The flux decline during protein filtration can be efficiently analyzed using one of these simple models proposed by [2], [3], [4], [5]

However, the classical laws of filtration, which is first proposed by Hermans and Bredée [1] and later summarized in the work of Hermia [6], is only applicable for dead-end filtration system Different from dead-end mode, in cross-flow filtration mode, the existence of tangential flow makes the cake formation and membrane fouling limited Therefore, some modification should

be made to the filtration laws for the application in cross-flow system One of the classical works

is the paper of Field, et al [7], in which the incorporation of cross-flow removal mechanisms into classical filtration laws is introduced Three mathematical expressions were proposed in cross-flow mode corresponding to three membrane fouling mechanisms in dead-end filtration Although these equations seem to be useful for analyzing permeate flux decline with time, there

is only few study using them to describe the data of cross-flow filtration and to discuss the mechanism of fouling [8]

In addition, the growth of filtration cake in classical model was considered as the

to the weight of solid deposit However, Iritani, et al [9], [10] reported that in the UF of a whey suspension, the protein cake layer was often compressible In such a compressible cake layer, an increase of the filtration pressure or the permeate flux results in a more compact cake Iritani, et

al [9] clarified the internal structures of the filter cake formed in protein ultrafiltration using ultracentrifugation experiments The experimental results were analyzed based on the compressible resistance model It was revealed that a compressible cake resistance model could accurately describe the UF behavior of whey systems For example, Landman, et al [11] developed a model including compressional rheology of flocculated suspension The model was applied to estimation of the filtration process in dead-end mode for a wide range

In the work of Karasu et al [12, 13], it suggested that the combination of conventional pore blockage and cake filtration is not suitable to analyze cross-flow filtration of protein suspension

at long-term operation, some points should be further clarified The pore blockage and cake filtration model used in this work is adapted from the dead-end mode of filtration and thus missing the back flux term Although in the very early stage of operation, the filtration model in dead-end mode could expand to cross-flow mode, the applicability of cake filtration model for long-term operation should be checked again

Due to the existence of several mechanisms to analyze the filtration data and the reasons mentioned above, the purpose of this part is to examine the applicable of each model to describe the filtration data of the cross-flow ultrafiltration of whey protein solution for developing an appropriate model For this purpose, the deriving of the mathematical model for the four classical mechanisms as well as the compressive cake layer model was reviewed in both dead-end model and the modification to cross-flow mode operation After that, the mathematical models were applied to describe the experimental data and some conclusion was made from the comparison This part also proposes a modification procedure to significantly reduce the calculation task in fitting the experimental data

2.2 Filtration theory

2.2.1 Darcy’s Law

Most discussion of fluid flow through porous media begin with Darcy’s law [14]

k dP v

dy



where ν is the filtration velocity, k is the permeability, µ is the fluid viscosity, and dP/dy is

the pressure gradient

In membrane literature, the equivalent form of Darcy formula in term of resistance in series

is also frequently used:

where J is the permeate flux, V is the total volume of permeate, A is the membrane area, Rm

is the membrane resistance (which can increase with time due to membrane fouling and

compaction), and Rc is the cake resistance (which can increase due to cake build up and compression)

channels, the hydraulic diameter is related to the bed porosity (εc) and the mean specific surface

of the solid in the cake (Sc) as follows:

where K is the Kozeny constant which is a function of the shape and size distribution of the

cross-sectional areas of the capillaries and accounts for the tortuosity of the fluid path where the effective pore length is larger than the apparent bed length

Many cake materials, such as flocculated clays and microbial cells, are highly compressible, exhibiting a decrease in void volume and an increase in the specific resistance as the differential pressure is increased The effects of cake compressibility are often estimated by assuming that the specific cake resistance is a power-law function of the imposed pressure drop [17]:

 0

s c

where α0 is a constant related primarily to the size and shape of the particles forming the

cake, and s is the cake compressibility which varies from zero for an incompressible cake to a

value near unity for a highly compressible cake

Although useful in practice, equation (2.8) represents an oversimplification of the behavior

of compressible filter cake For example, it assumes that the cake compression depends on the pressure drop across both the membrane and the cake layer and not that across just the cake Also, the porosity and specific cake resistance vary throughout the cake height A more thorough analysis of cake compression is proposed by many authors with equivalent forms The present of Landmann [11] is used in this study and will be discussed in 2.2.3

2.2.2 Classical membrane fouling model

Fouling of a membrane can occur by deposition of particles inside or on top of the membrane There are four classical models that are typically used to describe fouling as described in Figure 2.1: complete pore blockage, internal pore blockage (or pore constriction, standard blockage), intermediate pore blockage (or partial pore blockage), and cake filtration The mathematical expressions of the classical fouling models are discussed below

Figure 2.1 Fouling mechanisms of porous membrane [18]

2.2.2.1 Complete pore blocking

In the complete pore blockage model, the flux is shut off by protein aggregates depositing

on the membrane surface, and filtrate can only pass through the unblocked pore area and decrease with time Thus, the rate of pore blockage is assumed to be proportional to filtrate flow

rate (Qopen) and bulk concentration (Cb) The mathematical expression is:

open

open b 0 open

open 0 0

dA

dt A

In which A0 is the total membrane area, Aopen is the area of the clean membrane, J0 is the

permeate flux through clean membrane, α is the pore blockage parameter

Solving the system of equations, it can be obtained

From the equation, the filtrate flow rate decreases exponentially with time

2.2.2.2 Internal pore blocking

The pore constriction model accounts for fouling that occurs in the internal structure of the membrane In the pore constriction model, membranes are assumed to have straight through cylindrical pores The membrane pore radius is reduced by the uniform adsorption of protein to the internal membrane surface The membrane area does not vary with time, only membrane resistance change From equation (2.3) it can be obtained that the membrane resistance is inversely proportional to the square of pore area

pore

b 2 pore

0 2 pore,0

dA

dt A

Apore and Apore,0 are the area and initial area of the pore,

α is the blockage parameter,

Q is the permeate flow rate,

J and J0 are the permeate flux and initial permeate flux

A A

KJ t



in which 0 0 b

pore,0 pore,0

kJ A C K

2.2.2.3 Partial pore blocking

The partial pore blocking or intermediate pore blockage mode is similar to the complete pore blockage model and accounts for the possibility that particles can land on top of other deposited particles In this case, the rate of pore blockage is assumed to be proportional to the ratio of the unblocked area to the total area

The cake filtration model assumes that a uniform protein cake layer forms over the entire

membrane surface, and this fouling layer is permeable to fluid flow with resistance Rc The rate

of change of cake layer resistance Rc is directly proportional to the convective transport of solute

to the membrane surface (Jf'Cb), where f' is the fraction of solute that will deposit on the membrane, and R' is the specific protein layer resistance

 

0

c m

b m

c m

d R R

R f JC kJ dt

21

21

2.2.2.5 Summary of classical membrane fouling

Those equations of classical fouling mechanisms can be group together to give a unified equation:

complete pore blocking

In the differential form

0 3

n n n



In constant pressure dead-end filtration mode, the general governing equation is usually

expressed in term of total volume filtrated V as [6]

2 2

n

d t dt k

2.2.3 Compressible cake layer

In practice many materials give rise to compressible filter cakes A compressible cake is one whose cake resistance increases with applied pressure difference Change in cake resistance is due mainly to the effect on the cake voidage In compressible cake system, Landman, et al [11] proposed a compressive yield stress model for dead-end operation mode and the detail is discussed below

When the solidity of the solution reaches a certain point, an irreversible network will form

The network has a compressive yield stress Py which is a function of volume fraction:

where p, q are constant The values depend on the properties of the suspension

The dynamic compression of the network

where Dϕ/Dt is the material derivative of the local volume fraction, that is, the rate of

change of volume fraction as we follow a particular element of the network through the

separation process being modeled, κ(ϕ) is a rate constant called the dynamic compressibility, Ps

is the local particle pressure or local pressure of the solid phase

If, however, we accept the hypothesis that the hydrodynamic drainage of water from

between the network structure is the rate-determining step in the consolidation process, κ(ϕ) in this situation is a very large parameter If once Ps exceeds Py(ϕ), collapse rapidly readjusts the network local volume fraction until Py(ϕ) at that volume fraction exactly matches Ps In this large

dynamic compressibility limit, we do not need the κ(ϕ) parameter and may replace equation

(2.25) by

 

From the particle and fluid force balance in the suspension, the equations for a dimensional model of pressure filtration are

one- 

s f

2

r P

where Pf is the local pressure of the fluid phase, r(ϕ) is the hindered settling factor r(ϕ)

accounts for the hydrodynamic interaction among local particles The following power law

equation for r(ϕ) was proposed by Landman and White [19]

P dV

dz R V

2.3 Modification of filtration model to cross-flow operation system

In cross-flow operation mode, due to the existence of the tangential flow, the material will

be transport back to the bulk stream The mechanism might be caused by concentration polarization, shear induced diffusion, surface transport or inertial lift Therefore some modification should be made in order to describe the decline flux in cross-flow mode The detail

of classical fouling model and compressible cake layer model will be discussed as follows

2.3.1 Classical fouling model

2.3.1.1 Complete blocking mechanism

Similar to dead-end mode, it is assumed that each particle reaching the membrane participates in blocking by means of pore sealing A term representing a removal rate of particles from the pore mouths should be added in The velocity through the unblocked pores is unaffected, thus the fractional reduction in flux is equal to the fractional reduction in open area, i.e

open

A J

In which Jb is the back flux

Solving this first order differential system, it can be obtained

0 open

The permeate flux becomes

 0 bexp 0  b

2.3.1.2 Cake filtration laws

Cake filtration model [4] assumed that the accumulation of the particles on the membrane

was proportional to the difference between permeate flux J and back transport velocity of the particles Jb

m 0

d R R

R f J J C k J J dt

open 0 0

2.3.1.5 Summary

Similar to the unifying equation for dead-end operation mode, Eq (2.22), it can be generate

a unifying equation for cross-flow filtration



The exponent n characterizes the filtration model, with n=0 for cake filtration, n=1 for intermediate blocking, and n=2 for complete pore blocking

2.3.2 Compressible cake

The application of the model described above to cross-flow UF was also attempted by Karasu, et al [12] In the cross-flow UF model, it is assumed that some of the particles in the fouling layer are continuously removed by the shear stress exerted by the feed liquid flow The fouling layer is expected to be so thin that the change in the thickness of the layer does not affect the shear stress It is, therefore, assumed that the shear stress on the top of the layer is constant throughout the filtration process and that the volume of particles removed by this shear stress per unit time and unit membrane area is also constant

In UF processes, it is considered that a concentration polarization exists between the fouling layer and the feed liquid and it causes an increase of the resistance to permeation In the cross-flow UF, however, since the thickness of the concentration polarization layer gets much thinner than the height of the channel on the membrane due to the shear stress exerted by the feed flow and the small diffusion coefficient of the proteins, it can be assumed that the concentration polarization layer does not affect the shear stress on the top of the fouling layer and the resistance to permeation

It is assumed that the surface of the cake layer can be removed by the shear stress even if the

volume fraction is higher than ϕgel when the shear stress is greater than the yield stress On the other hand, the surface of the cake layer is immobile and is not removed by the shear stress when the shear stress is lower than the yield shear stress Based on these considerations, the volume fraction at the top surface of the cake layer in cross-flow UF is predicted to be equal to the volume fraction at which the yield shear stress is the same as the shear stress exerted by the feed flow This shear stress on the surface of the cake layer is calculated as the product of the viscosity of the feed liquid and the velocity gradient at the wall of the channel of the membrane module, measured by an electrochemical method [20] The volume fraction at the top surface of

the cake layer, ϕt, is estimated from the shear stress by means of the relationship as shown in Figure 2.2

Figure 2.2 Relation between volume fraction and yield shear stress [12]

In addition, material balance from time t to t+Δti is expressed as follows,

1

0 0

2.4.2 Membrane

A regenerated cellulose membrane (MILLIPORE) was used in all experiments with diameter 90mm and molecular weight cut off (MWCO) of 5000 As the smallest molecular weight among the protein components of WPC is α-lactalbumin at 14200g/mol, it can be considered that all proteins were fully rejected by the membrane

The temperature of the feed liquid was kept constant by circulate the coolant through a copper coil, which was installed in the reservoir The feed flow rate and the trans-membrane

pressure (ΔP) were adjusted with the valves installed in the retentate line and the by-pass The

concentration of the feed liquid was assumed to be constant because the volume of the feed liquid was about 100 times larger than that of the permeate liquid removed during the experiment

Figure 2.3 Schematic diagram of experimental apparatus