Ghasem D. Najafpour. Biochemical Engineering and Biotechnology

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decrease is due to particle deposition resulting from incomplete removal by the cross-flow

liquid, then (16.5.1) may be written as:

(16.6.1)

where R

now represents the resistance of the cake, which if all filtered particles remain in

the cake, may be written as:

(16.6.2)

where r is the specific resistance of the deposit, V is the total volume filtered, V

the volume

of particles deposited, C

the bulk concentration of particles in the feed (particle volume/feed

volume) and A

the membrane area. The specific resistance can be related to the properties

for spherical particles by the Carman relation as:

(16.6.3)

where e is the void volume of the cake and d

the mean particle diameter.

Combining (16.6.1) and (16.6.2) gives:

(16.6.4)

RrVCA

⫽⫽

⫹

mmbm

()

⌬

⫽

⫺

180

rVC

⫽⫽

⫽

⫹

()

⌬

364 BIOCHEMICAL ENGINEERING AND BIOTECHNOLOGY

(c)

(b)

(a)

Time

Membrane permeation rate

FIG. 16.13. Time dependence of membrane permeation rate during cross-flow filtration: (a) low cross-flow velocity,

(b) increased cross-flow velocity, (c) back flushing at the bottom of each ‘saw-tooth’.

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Solution of (16.6.4) for V at constant pressure gives:

(16.6.5)

yielding a straight line on plotting t/V versus V.

The early stages of cross-flow microfiltration often follow such a pattern. However, the

growth of the cake is limited by the cross-flow of the process liquid. There are several ways

of accounting for the control of cake growth. A useful method is to rewrite (16.6.1) as:

(16.6.6)

where R

is the resistance that would be caused by deposition of all particles and R

is the

resistance removed by cross-flow. Assuming the removal of solute by cross-flow to be con-

stant and equal to the convective particle transport at steady-state (⫽ J

), then,

(16.6.7)

where J

can be obtained experimentally or from the film-model (16.7.5).

In several cases, a steady rate of filtration in never achieved. In such cases it is possible to

describe the time dependence of filtration by introducing an efficiency factor b representing

the fraction of filtered particles remaining in the filter cake rather than being swept along

by the bulk flow. Equation 16.7.4 then becomes

(16.6.8)

where 0 ⬍b⬍ 1. The layers deposited on the membrane during cross-flow microfiltration are

sometimes considered to constitute dynamically formed membranes with their own rejec-

tion and permeation characteristics.

Film and gel-polarisation models are developed for ultrafiltration. These models are also

widely applied to cross-flow microfiltration.

16.7 ULTRAFILTRATION

Ultrafiltration is one of the most widely used of the pressure-driven membrane separa-

tion processes. The solute retained or rejected by ultrafiltration membranes are those with

rVC

⫽

RVAJtrC

mmmssb

⫽

⫹⫺

(( ))

⌬

RRR

⫽⫽

⫹⫺

m m sd sr

()

⌬

Cr V

⫽⫹

||⌬

⌬2

MEMBRANE SEPARATION PROCESSES 365

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molecular weights of 1000 or greater, depending mostly on the MWCO of the membrane

chosen. The process liquid, dissolved salts and low molecular weight organic molecules

(molecular weight 500–1000) generally pass through the membrane. The pressure difference

applied across the membrane is usually in the range 0.1–0.7 MN/m

(MPa) and membrane

permeation rates are typically 0.01–0.2 m

h. In industry, ultrafiltration is always operated

in the cross-flow mode.

4,8,11,18

The separation of process liquid and solute that takes place at the membrane during

ultrafiltration gives rise to an increase in solute concentration close to the membrane sur-

face (Figure 16.14). This is termed ‘concentration polarisation’ and takes place within the

boundary film generated by the applied cross-flow. With a greater concentration at the

membrane, there will be a tendency for solute to diffuse back into the bulk feed according

Fick’s law. At steady-state, the rate of back-diffusion will be equal to the rate of removal of

solute at the membrane, minus the rate of solute leakage through the membrane:

(16.7.1)

Here solute concentration C and C

(in permeate) are expressed as mass fractions, D is the

diffusion coefficient of the solute and y is the distance from the membrane. Rearranging

and integrating from C⫽ C

when y ⫽ l the thickness of the film, to C ⫽ C

, the concentra-

tion of solute at the membrane wall, when y⫽0, gives:

(16.7.2)

(16.7.3)

⫺

⫽ exp

⫺

⫽

ÚÚ

JC C D

()-

⫽⫺

366 BIOCHEMICAL ENGINEERING AND BIOTECHNOLOGY

Membrane

Permeate

Solute build-up

Solute concentration (C)

Distance from membrane (y)

-D

IG. 16.14. Concentration polarisation at a membrane surface.

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If it is further assumed that the membrane completely rejects the solute, that is, R ⫽ 1 and

⫽ 0, then:

(16.7.4)

where the ratio C

is known as the polarisation modulus. Note that it has been assumed

that l is independent of J and that D is constant over the whole range of C at the interface.

The film thickness is usually incorporated in an overall mass transfer coefficient h

, where

⫽D/l, giving:

(16.7.5)

The mass transfer coefficient is usually obtained from correlations for flow in non-porous

ducts.

Process patterns diagnostic of gel-polarisation type behaviour are shown in Figure

16.15. The dependence of membrane permeation rate on the applied pressure is shown

in Figure 16.15a. There is an initial pressure-dependence region followed by a pressure-

independent region. The convergence of plots of the membrane permeation rate against C

(Figure 16.15b) is a test of (16.7.5).

The basic features of the flux-pressure profiles (Figure 16.15a) are:

(1) at low |⌬P| the slope is similar to that for pure solvent flow;

(2) as |⌬P| increases, the slope declines and approaches zero at high pressure.

16.8 REVERSE OSMOSIS

A classic demonstration of osmosis is to stretch a parchment membrane over the mouth of

a tube, fill the tube with a sugar solution, and then hold it in a beaker of water. The level of

solution in the tube rises gradually until it reaches a steady level. The static head developed

would be equivalent to the osmotic pressure of the solution if the parchment were a perfect

semipermeable membrane, such a membrane having the property of allowing the solvent to

pass through but preventing the solute from passing through. The pure solvent has a higher

chemical potential than the solvent in the solution and so diffuses through until the difference

is cancelled out by the pressure head. If an additional pressure is applied to the liquid column

on the solution side of the membrane then it is possible to force water back through the mem-

brane. This pressure driven transport of water from solution through membrane is known as

‘reverse osmosis’. Note that it is not quite the reverse of osmosis because, for all real mem-

branes, there is always a certain transport of the solute along its chemical potential gradient,

and this is not reversed. This phenomenon of reverse osmosis has been extensively developed

⫽ ln

⫽ exp

MEMBRANE SEPARATION PROCESSES 367

Ch016.qxd 10/27/2006 10:52 AM Page 367

as an industrial process for the concentration of low molecular weight solutes and especially

for the desalination, or more generally demineralisation, of water.

3,4,11,15

Typically, a membrane that rejects 93% of Na

⫹

or Cl

⫺

will reject 98% of Ca

2⫹

or SO

2⫺

when rejections are measured on solutions of a single salt. With mixtures of salts in solution,

368 BIOCHEMICAL ENGINEERING AND BIOTECHNOLOGY

(a)

(b)

High cross-flow

velocity

Low cross-flow

velocity

In C

(c)

Turbulent

Slope 0.8

Slope 0.33

Laminar

In u

In J

|ΔP|

FIG. 16.15. Dependence of membrane permeation rate J on (a) applied pressure difference, (b) feed solute

concentration C

and (c) cross-flow velocity (u) for ultrafiltration.

Ch016.qxd 10/27/2006 10:52 AM Page 368

the rejection of a single ion is influenced by its relative proportion in the mixture. Thus for 0.1

kg/m

⫺

in the presence of 1kg/m

2⫺

there would be only 50–70% rejection compared

with 93% for solutions of a single salt. The rejection of organic molecules depends on mole-

cular weight. The molecular weights less than 100 are usually not rejected, those with mole-

cular weights of about 150 have about the same rejection as NaCl, and those with molecular

weights greater than 300 are effectively entirely rejected.

16.9 MEMBRANE MODULES

Industrial membrane plants often require hundreds of thousands of square metres of mem-

brane to perform the separation required on a useful scale. Before a membrane separation

can be used industrially, therefore, methods of economically and efficiently packaging large

areas of membrane are required. These packages are called membrane modules. The areas of

membrane contained in these basic modules are in the range 1–20 m

. The modules may be

connected together in series or in parallel to form a plant of the required performance. The

four most common types of membrane module are tubular, spiral, wound and hollow fibre.

Despite the importance of membrane module technology, many researchers are astonish-

ingly uninformed about module design issues. In part this is because module technology has

been developed within companies, and many developments are only found in patents, which

are ignored by many academics. An overview of the principal module types are given below,

followed by a summary of the factors governing selection of particular types for different

membrane processes. Cost is always important, but perhaps the most important issues are

membrane fouling and concentration polarisation. This is particularly true for reverse osmo-

sis and ultrafiltration systems, but concentration polarisation issues also affect the design of

gas separation and pervaporation modules.

9,18

16.9.1 Tubular Modules

Tubular modules are widely used where it is advantageous to have a turbulent flow regime;

for example, in the concentration of high solids content feeds. The membrane is cast on the

inside of a porous support tube which is often housed in a perforated stainless steel pipe

(Figure 16.16). Individual modules contain a cluster of tubes in series held within a stain-

less steel permeate shroud. The tubes are generally 10–25mm in diameter and 1–6 m in

length. The feed is pumped through the tubes at Reynolds numbers greater than 10,000.

Tubular modules are easily cleaned and a good deal of operating data exist for them. Their

main disadvantages are the relatively low membrane surface area contained in a module of

given overall dimensions and their high volumetric hold-up.

16.9.2 Flat-Sheet Modules

Flat-sheet modules are similar in some ways to conventional filter presses. An example

is shown in Figure 16.17. This consists of a series of annular membrane discs of outer

diameter 0.3 m placed on either side of polysulphone support plates which also provide

MEMBRANE SEPARATION PROCESSES 369

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370 BIOCHEMICAL ENGINEERING AND BIOTECHNOLOGY

FIG. 16.16. Tubular membrane module.

Concentrate

Permeate

Faed

Spacer

Permeate

Membrane

Support plate

FIG. 16.17. Schematic diagram of a flat-sheet module.

channels through which permeate can be withdrawn. The sandwiches of membrane and

support plate are separated from one another by spacer plates which have central and

peripheral holes, through which the feed liquor is directed over the surface of the mem-

branes, the flow is laminar. A single module contains 19 m

of membrane area. Permeate is

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collected from each membrane pair so that damaged membranes can be easily identified,

though replacement of membranes requires dismantling the whole stack.

16.9.3 Spiral-Wound Modules

Spiral-wound modules consist of several flat membranes separated by turbulence-promoting

mesh separators and formed into a Swiss roll (Figure 16.18). The edges of the membranes

are sealed to each other and to a central perforated tube. This produces a cylindrical mod-

ule which can be installed within a pressure tube. The process feed enters at one end of the

pressure tube and encounters a number of narrow, parallel feed channels formed between

adjacent sheets of membrane. Permeate spirals roward the perforated central tube for col-

lection. A standard size spiral-wound module has a diameter of about 0.1m, a length of

about 0.9 m and contains about 5 m

of membrane area. Up to six such modules may be

installed in series in a single pressure tube. These modules make better use of space than

tubular or flat sheet types, but they are rather prone to fouling and difficult to clean.

16.9.4 Hollow-Fibre Modules (Figure 16.19)

Hollow fibre modules consist of bundles of fine fibres, 0.1–2.0 mm in diameter, sealed in a

tube. For reverse osmosis desalination applications, the feed flow is usually around the outside

of the unsupported fibres with permeation radially inward, as the fibers cannot withstand high

pressure differences in the opposite direction. This gives very compact units capable of high

pressure operation. However, the flow channels are less than 0.1 mm wide and are therefore

readily fouled yet difficult to clean. The flow is usually reversed for biotechnological appli-

cations so that the feed passes down the centre of the fibres giving better controlled laminar

flow and easier cleaning. However, this limits the operating pressure to less than 0.2 MN/m

(MPa), that is, to microfiltration and ultrafiltration applications. A single ultrafiltration module

will typically contain up to 3000 fibres and be 1m long. Reverse osmosis modules will

contain larger numbers of finer fibres. This is a very effective means of incorporating a

large membrane surface area in a small volume.

MEMBRANE SEPARATION PROCESSES 371

Permeate collection holes

Anti-telescoping device

Concentrate

Permeate out

Permeate flow (after passage

through membrane into permeate

collection material)

Covering

Feed channel spacer

Membrane

Feed flow across

feed channel spacer

Feedsolution

Permeate

collection material

FIG. 16.18. Schematic diagram of spiral-wound module.

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Membrane modules can be configured in various ways to produce a plant of the required

separation capability. A simple batch recirculation system has already been described in cross-

flow filtration. Such an arrangement is most suitable for small-scale batch operation, but

larger scale plants will operate as ‘feed and bleed’ or ‘continuous single pass’ operation

(Figure 16.20).

(a) Feed and bleed. Such a system is shown in Figure 16.20a. The start up is similar to a batch

system in that the retentate is initially totally recycled. When the final required solute con-

centration is reached within the loop, a fraction of the loop is continuously bled off. Feed

into the loop is controlled at a rate equal to the permeate plus concentrate flow rates. The

main advantage is that the final connection is then continuously available as feed is

pumped into the loop. The main disadvantage is that the loop is operating continuously

at a concentration equivalent to the final concentration in the batch system and the flux

is therefore lower than the average flux in the batch mode, with a correspondingly higher

membrane area required.

Large-scale plants usually use multiple stages operated in series to overcome the

low-flux disadvantage of the feed and bleed operation and yet to maintain its continu-

ous nature (Figure 16.20b). Only the final stage is operating at the highest concentra-

tion and lowest flux, while the other stages are operating at lower concentrations with

higher flux. Thus, the total membrane area is less than that required for a single stage

operation. Usually a minimum of three stages is required, and seven to ten stages are

quite common. The residence time, volume hold-up and tankage required are much less

than for the same duty in batch operation. Feed and bleed systems also require less fre-

quent sterilisation than batch processes in biotechnological applications, allowing

longer effective operating times.

372 BIOCHEMICAL ENGINEERING AND BIOTECHNOLOGY

FIG. 16.19. Hollow-fibre module and, inset, a single fibre.

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(b) Continuous single pass. In such a system the concentration of the feed stream increases

gradually along the length of several stages of membrane modules arranged in series

(Figure 16.20c). The feed only reaches its final concentration at the last stage. There is

no recycle and the system has a low residence time. However, such systems must either

be applied on a very large scale or have only a low velocities to control concentration

polarisation. The smallest possible single-pass system will have a single module in the

final stage, with a typical feed flow rate of about 0.1 m

/min. Such systems are used in

large-scale reverse osmosis desalination plants but are unlikely to be used in biotech-

nological applications.

16.10 MODULE SELECTION

The choice of the most suitable membrane module type for a particular membrane separa-

tion must balance several factors. The principal module design parameters that enter into

the decision are summarised in Table 16.3.

MEMBRANE SEPARATION PROCESSES 373

Feed

tank

Feed

tank

Recycle

loop

Membrane

Permeate

Stage 1

Stage 2

Stage 3

Permeate

Feed

Stage 1

Stage 2 Stage 3

Stage 4

Retentate

(a)

(b)

(c)

FIG. 16.20. Schematic flow diagrams of (a) single-stage ‘feed and bleed’, (b) multiple-stage ‘feed and bleed’ and

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