CHAPTER 9:

MEMBRANE SEPARATION

PROCESS

Sem 2 2011/2012 ERT 313 BIOSEPARATION ENGINEERING

MOHAMAD FAHRURRAZI TOMPANG

Course details

Credit hours/Units : 4

Contact hours : 3 hr (L), 3 hr (P) and 1 hr (T) per week

Evaluations

Final Exam – 50%

Midterm Tests – 20%

Course works – 30%

Laboratories – 10%

Assignments – 10%

PBL – 10%

CARRY MARKS – 50%

Course details

Course Outcome (COs) will be covered:

CO3 – Ability to apply principles, analyze mechanical-

physical separation process and develop design of

membrane unit (C4, P3, A3)

Course works (Overall evaluations)

Assignments – 2

Quizzes – 2

Midterm test – 1

Class participations – Max. of 3 points

Important reminder

Attendance should not less than 80%, or else you will be barred from taking final examination.

Plagiarism and copying other students’ work is strictly prohibited especially in doing assignments and lab reports, or else both parties will get zero.

Cheating in quizzes and examinations is also prohibited, or else both parties will get zero.

Therefore, study hard and smart. Take note of the important chapters or things that will be highlighted throughout lectures.

Week 10 (16 - 20 Apr 2012)

Reading assignment:

1. Chapter 26, Unit Operations of Chemical Engineering. McCabe, Smith, Harriot (Main)

2. Chapter 4, Bioseparations Science and Engineering. Harrison, Todd, Rudge, Petrides

Membrane Separation Process C-9

WHAT IS A MEMBRANE?

Membranes are materials which

have voids in them, letting some

molecules pass more

conveniently than some other

molecules.

A semi-permeable membrane

is a VERY THIN film that allows

some types of matter to pass

through while leaving others

behind

Membrane Separations

Introduction

Membranes enable filtration to be extended to separation of colloids, cells and molecules by microfiltration, ultrafiltration or reverse osmosis

A membrane – considered as a permselective barrier between two phases (refer figure 4.1)

Mass transport of a component across the membrane occurs due to the presence of a driving force (Figure 4.2)

Separation mainly determined by the membrane morphology: porous membrane and non-porous membrane (Figure 4.3)

Figure 4.1: Classification of particles by size and applicable filtration separation process

Figure 4.2: Schematic representation of a two-phase system separated by a membrane

Figure 4.3: Schematic drawing of a porous and non-porous membrane

Porous membrane Microfiltration/ ultrafiltration

Nonporous membrane Gas separation/ pervaporation

Type of Driving Force for Membrane Separation

Membrane process can be distinguished according to the type of

driving force ensuring the transport through the membrane (T 4.1)

Table 4.1: Membrane processes grouped according to their driving force

Driving force Type of membrane

Hydrostatic pressure, ∆p Microfiltration

Ultrafiltration

Hyperfiltration (reverse

osmosis)

Electric field ∆ψ Electrodialysis

Concentration ∆C Dialysis

continued

Importance to the installation of membrane system are:

average flux

degree of fouling

cleaning possibilities

membrane lifetime and costs

ease with which membranes can be replaced

containment and/or sterility

automation

capital investment

Type of Membrane Process

Reverse Osmosis (RO)

Ultrafitration (UF)

Microfiltration (MF) – Cross-flow

Dialysis

Reverse Osmosis (RO)

Reverse osmosis uses membranes that are permeable to water but not to salts and most larger, MW species.

Also known as hyperfiltration refers to the fact that applied pressures must exceed the osmotic pressure of the feed before water is forced through the membrane.

The normal osmotic flow of water is thus reversed by the applied pressure.

Have a nonporous skin layer that allows water transport through microvoids, or spaces, between polymer chains.

Salt transport is impeded because the ions cannot find “free” water for solvation within the membrane

Other solvents, particularly alcohols, may pass through RO membranes.

Ultrafiltration (UF)

The membranes used for ultrafiltration (UF) are finely microporous and in many eases they are asymmetric.

Water transport is by viscous flow through the pores, driven by a moderate applied pressure

Small solutes may also pass through the membranes, but macrosolutes colloids, and some charged species are retained.

Cross flow Microfiltration (MF)

Microfiltration is an extension of UF, but the membranes have a larger pore size.

Macrosolutes are passed, but large colloids and micron-sized particles such as cells are retained.

Transport of solvent and solute through the membranes occurs by convective flow through the micropores. This convective transport is pressure-driven.

Dialysis

Membranes that are very finely microporous (less microporous than UF membranes) are used in dialysis.

Often have the nonporous characteristics of RO membranes and the finely micro-porous characteristics of UF membranes

Separates solute mixtures on the basis of molecular size and, possible, molecular conformation and net charge. T

The driving force is concentration difference.

For the removal of ionic species, it is more common to use electrodialysis (ED). ED uses ion-exchange membranes and a voltage gradient as the driving force

Basic Principle of Membrane

Separation

The basic principle of membrane

separation is illustrated in

Figure 4.4

the feed is pumped along a membrane which act as

a selective barrier to the different components

some components can freely permeate through the membrane while others will be retained

in this way the feed is separated into two streams: the retained enriched phase, and the permeated stream containing small components

Figure 4.4: Basic principle of a membrane separator

or Retentate

or Filtrate

Advantages & Disadvantages of

Membrane Separation

Advantages Disadvantages

Separation can be carried out

under mild conditions

Energy consumption –

generally low

Separation can be carried out

continuously

No additives – required

Scale-up can easily be

accomplished

Membrane properties are

variable and can be adjusted

Little resistance to high/low

pH values and temperatures

Cleaning and sterilization

difficult

Fouling, causing severe

problems

Figure 4.5 Overview of various type of resistance towards mass transfer transport across membrane in pressure driven processes

Membrane Structure

Membrane may be formed in a no. of ways, the manner of

fabrication determining key characteristics such as the

throughput and the separation capacity of the membrane

The basic structure of a membrane is shown in Fig. 4.6 where

the relative dimensions of the elements comprising the total

membrane are shown

It is clear that the active membrane surface is very thin in

comparison to the overall depth of the support structure

This latter structure – vital for comparing the necessary

strength to the membrane so that it can withstand the –

pressure of operation

continued 22

continued

Figure 4.6: Cross-section of typical membrane structure showing presence of significant depth of porous support structure

continued

Microfilration

(MF)

Depth filters with pores evenly distributed

across surface.

Particles retained within filter structure tend to

block membrane and are hard to recover

Ultrafiltration

(UF)

Asymmetric structure with dense separating

surface on a much coarser “finger-like” sub-

structure

Act as surface filters

Reverse Osmosis

(RO)

Asymmetric structure but support is “sponge-

like” with pore diameter increasing away from

membrane surface

Mechanically strong membrane

Note:

membrane can be generally classified into two categories: symmetric (or homogeneous) and asymmetric membranes

in homogeneous membranes, the diameter of pores are almost constant over the entire cross section of the membrane. Consequently, the entire membrane thickness acts as a selective barrier

this differs from asymmetric membranes, where only a thin top layer determines the selective barrier

these differences are clearly shown in Fig. 4.7

Figure 4.7: Comparison between symmetric and

asymmetric membranes: (a) asymmetric (b) symmetrical

Comparison Between Symmetric and

Asymmetric Membranes

Isotropic, symmetric

membranes

Anisotropic, assymmetric

membranes

Have defined pores that typically

follow a tortuous path

The pore diameters in such a

membrane will be slightly larger than

the particle that they retain

A relatively rough surfaces may

capture (and become plugged by)

deformable materials such as cells or

cell debris that are swept across its

surface

Typically used in systems where

filtration is carried out in a dead-end

mode

Anisotropic membranes with a pore-

limiting skin are smooth and allow

particles or molecules that are larger

than the pores to freely moves across

the surface without getting caught

Has only a small capacity when used

in a dead-end mode, since particles

quickly plug the pores in the filter

structure

continued

Membrane selectivity – mainly the result of the sieve action of the pores, but to some extent it is also caused by hydrophilic/hydrophobic interactions and membrane charge

Since the pores of a membrane are not uniform in size the selectivity shows a certain variation

The smaller the pore size distribution, the better the selectivity

The membrane selectivity – often expresses in terms of molecular weight cut off (MWCO) ‘cut-off ’ – values – relate the pore dimensions of the membrane to the size of the macromolecular solutes in solution

Figure 4.8: Molecular weight cut off for (a) ideal membrane, (b)

broad pore size distribution (c ) narrow pore size distribution

continued

Definition of MWCO: MW of globular proteins/ (macro)molecular solutes that are 90% rejected by the membrane in an ideal UF membrane, all the molecules below the MWCO- value will be permeated while all the other molecules will be retained (refer to Fig.4.8, curve a)

QA: Examine fig. 4.8 carefully, which curves represent membranes with a broad pore size distribution, and which represents a narrow pore distribution?

Selection of a membrane will represent a compromise between the “tightness” of cut-off, the flux characteristics and the cost

Pop Quiz

Question: Complete the following statements :

1) In membrane separations the [ ] stream contains relatively small components

2) Membrane selectivity is often expressed in terms of [ ] cut off

3) For [ ] membranes only a thin top layer determines the selective barrier

4) A membrane with a sharp molecular weight cut off will have a [ ] pore size distribution

Answer:

1) In membrane separations the [ permeated] stream contains relatively small components

2) Membrane selectivity is often expressed in terms of [ molecular weight] cut off

3) For [asymmetrical] membranes only a thin top layer determines the selective barrier

4) A membrane with a sharp molecular weight cut off will have a [narrow] pore size distribution

4.3.2 Membrane Module Designs

A variety of module designs exist for mounting the membrane in Table 4.2: Typical Characteristics of Membrane Modules

Plate and

Frame

Spiral wound Tubular Hollow-Fiber

Packing

density, m2/m3

30 to 500 200 to 800 30-200 500 to 9,000

Resistance to

fouling

Good Moderate Very good Poor

Ease of

cleaning

Good Fair Excellent Poor

Relative cost High Low High Low

Main

application

D,

RO,PV,UF,MF

D,RO,GP,UF,MF RO,UF D,RO,GP,UF

Note: D, dialysis; RO, reverse osmosis; GP, gas permeation; PV, pervaporation; UF, ultrafiltration; MF,

microfiltration

continued

Figure 4.9: A plate-and-frame membrane

Plate-and-frame

(Fig. 4.9)

Similar to a filter press in that each filter is a flat sheet

Mainly used for UF or RO

Easy disassembly for cleaning or membrane replacement

High initially investment

continued Figure 4.10: Example of a tubular membrane system (by courtesy of Koch Membrane Systems)

Tubular system

(Fig. 4.10)

Membrane manufactured in form of a smaller dia. tube (1-2cm)

supported by a rigid outer shell

Mainly used in MF and UF

Fouling can be reduced by use of appropriate flow management

Low surface area/volume ratio makes costs high

continued

Figure 4.11: Conventional capillary module (by courtesy of Pall Corporation)

Capillary system

(Fig. 4.11)

Separating surface on inside of membrane capillary

Filtrates permeate through membrane and leaves system from

the outer shell

Mainly used in UF

High surface area/volume ratio keeps costs down

Mechanically weak, low burst pressure

continued

Figure 4.12: Example of a hollow-fiber membrane (by courtesy of Dupont)

Hollow fibre system

(Fig. 4.12)

Fibres have small dia. (~100nm)

Outer skin is membrane

Fouling can be severe. Use restricted to relatively clean

solutions

High surface area/volume ratio keeps costs low

continued

Figure 4.13: A spiral-wound module (by courtesy of Koch Membrane Systems)

Spiral wound module

(Fig. 4.13)

Membrane sandwiched between porous support and spacer

screen and wound in a spiral-type configuration

High surface area/volume ratio and relatively low

investment costs

continued

Dynamic or rotating

membranes (Fig. 4.14)

A more recent development of two co-axial cylinders of

which the inner rotates within a fixed outer membrane

Both cylinder walls can be used for filtration

Inner cylinder rotates at 2-3000rpm to create a

hydrodynamic regime known as “Taylor” vortices in the

annulus.

These vortices enable higher flux rates and better

transmission as a result of improved local mixing

continued

Figure 4.14: A rotary membrane unit (by courtesy of Pall corporation)

continued

Figure 4.15 (continued)

Membrane materials

Common membrane materials and their properties are listed in Table 4.3

Commercial MF membranes can be based on hydrophilic or hydrophobic polymers

Recent advances include mineral or ceramic membranes composed of a porous calcinated carbon support with several superposed layers of metallic oxide, such as zirconia, to form a very thin microporous membrane

UF membranes – mainly made of polysulphone, cellulose nitrate or acetate, nitrocellulose or acrylic

RO membranes – mainly cellulosic in nature though polyether/polyamide and other materials have been used

Table 4.3: Common membrane materials (Costa, C.A. and Cabral, J.S., 1991)

Material Application pH range Approximate max.

Temperature (0C)

Cellulose acetate MF,UF,RO 3.5-10 75

Mixed cellulose esters MF,UF,RO 4-8.5 120

Polysulfonate MF,UF,RO 1-14 130

Polyester MF,UF NA 150

Polyamide MF,UF,RO 2-12 NA

Nylon MF NA NA

PIFE MF 1-14 140

Dynel UF 2-12 60

Polymide UF NA NA

Acryclic copolymer MF NA 88

Polypropylene MF 1-14 130

Polycarbonate MF,UF NA NA

Polybinylidene difluoride MF NA 145

Ceramic MF,UF 1-13 140

4.3.4 Fluid management

Figure 4.16:Comparison of (a) dead-end filtration and (b) cross-flow filtration

Comparison between dead-end and cross-flow membrane filtrations

Dead-end membrane filtration Cross-flow filtration

The fluid passes normal to and through

the face of the membrane

And the particles or molecules retained

by the membrane are held at its surface

Requires only the energy necessary to

force the fluid through the filter

the fluid to be filtered is pumped across

the membrane parallel to its surface

only the small fraction of fluid actually

passing through the membrane flows

normal to the filter

by maintaining a high velocity across the

membrane, the retained material is swept

off the membrane surface

preferred - when significant quantities of

material will be retained by the

membrane, when the retentate is soluble

or when the solid retentate is

compressible

continued

the following equations describing dispersion along a concentration gradient in a flowing system

the relevant dimensionless groups are:

where Sh = Sherwood number, Sc = Schmidt number Re = Reynolds number, D = diffusity (m2/s) d = hydraulic diameter (m), k = mass transfer coefficient (m/s) ν = kinematic viscosity (m2/s) and v = velocity (m/s)

DkdSh

DvSc

Hvd

HQ

v

d

1

4;Re

continued

H = constant, a function of the geometry of the conduit; it is π/4 for a circular conduit and 1 for a square conduit

Turbulent flow

Turbulent flow past the membrane (in the range

2500< Re<10,000)

An equation variously attributed to Dittus-Boelter and Desalius is:

Solving for k:

33.088.0Re023.0 ScSh

52.012.0

88.067.0

023.0d

VDk

E 4.1

E 4.2

continued 47

continued

Laminar flow flow regimes up to a Re no. about 2200, an equation

modified from Leveque’s heat-transfer formulation shows that for practical situations:

the mass transfer coefficient k = the rate constant for movement of solute along the concentration gradient. Solving for k:

33.0

Re62.1

L

dScSh

33.02

62.1

Ld

VDk

E 4.3

E 4.4

continued 48

4.4 Complication from fouling

fouling is a major problem in all membrane operations

it causes significant problems in measuring and interpreting pore size in both MF and UF membranes

It has an effect on RO membranes as well, quite distinct from the effects in UF and MF

fouling is an irreversible process; it cannot be rectified by changing processing conditions such as flow or pressure

it can be reversed only by cleaning or replacing the membrane

it is often an adsorption involving significant binding energy

continued 49

4.4.1 Effects on pore dimension

MF and UF membranes contain ‘pores’ and for most membranes, they are not all of the same size

fouling affects pores differently Belfort illustrated three cases affecting MF

membranes A fourth case primarily affecting UF is added as

shown in Figure 4.17

continued 50

continued

Figure 4.17: Fouling effects on pore dimensions: Case A =

adsorption; Case B = plugging smallest pores; Case C =gel/cake

formation; Case D = plugging larger pores

continued

Cases Details

Case A Adsorption causes all pores to become smaller, and may result in the smallest pores

plugging

In the case of a protein probe present in dilute solution, this fouling error would cause

the test to understate the size of pores and

Could truncate the distribution on the low pore-size end of the spectrum

Case B Show pore plugging.

Any adsorption, means that particles may plug pores

In example shown, smaller pores would be expected to suffer disproportionately

Case C Represents the deposition of a material that supersedes the porous structure of the

membrane

Fouling is reversible to the extent that the layer nearest the membrane is probably

adsorbed onto it

Throughout the layer, the binding may or may not be irreversible

At the surface, quite a degree of dynamic reversibility remains

One may assume that in all cases, the effect is to shift the effective pore size

downwards

Case D Peculiar to membranes with small pores filtering particles much larger than pores

4.4.2 Effects on flux

Fouling effects flux dramatically

The pure-water flux through a virgin UF membrane is commonly 10-fold greater than the water flux after the membrane has been exposed to protein

Flow will be laminar through a cylindrical pore because of its size

continued

when reviewing the four cases of pore narrowing;

Case A Narrowing of all pores and plugging of some of the

smallest, will have a greater impact

Because loss of some pore dimension

Case B Which smaller pores are plugged and larger ones are

unaffected will have least impact on flux

Case C Is a guess, as the porosity of a cake layer on the

membrane can be anything

Case D Results in a dramatic loss of throughput, because that

form of plugging takes out the most productive pores

4.4.3 Overall effect on retention

continued 54

passage of material through a pore obviously depends on how much is flowing and what that pore will pass

big pores pass large quantities but their retention is different from smaller pores

as a membrane fouls, the retention characteristics worked out for the virgin membrane will change, often dramatically

fouling processes that plug only the very smallest pores have little effect on retention

fouling by almost any other mechanism raises retention; either it substitutes a cake layer on top of the membrane, or it narrows pores, or it selectively plugs larger ones

Improving fluxes

Destruction of gel layer is only one way of enhancing flux, a further approach is to prevent fouling

Method for improving flux fall into four categories: operating conditions change feed properties membrane selection slowing flux decline

continued

Parameter Details

Operating

conditions

Increasing the mass transfer coefficient, kd, by

using a higher velocity, smaller channel width

or reducing viscosity

Feed

properties

Changing pH may reduce fouling

Membrane-

related

methods

Alter membrane surface charge to minimize

blinding

Use of corrugated membranes to enhance

shear

Slowing flux

decline

Reduce fouling load by pre-filtration

Use of pulsed flow or electric fields

Back flushing

Application of membrane separations

Membrane

technology

Typical application

Microfiltration Sterilization of drugs

clarification and biological stabilization of

beverages

purification of antibiotics

separation of mammalian cells from a liquid

Ultrafiltration Preconcentration of milk before making cheese

clarification of fruit juice

recovery of vaccines and antibiotics from

fermentation broth

color removal from Kraft black liquor in

paper-making

Reverse

osmosis

Water purification

small molecules

4.6.1 Reverse-Osmosis Membrane Processes

continued 58

A. 1.Introduction useful for separation of different species, a membrane must allow passage of certain molecules and exclude or greatly restrict passage of others. In osmosis, a spontaneous transport of solvent occurs from a dilute solute or salt solution to a concentrated solute or salt solution across a semipermeable membrane which allows passage of the solvent but impedes passage of the salt solutes. In Fig, 4.18a, the solvent water normally flows through the semipermeable membrane to the salt solution. The levels of both liquids are the same as shown. The solvent flow - reduced by exerting a pressure on the salt-solution side and membrane, as shown in Fig. 4.18b, until at a certain pressure, called the osmotic pressure π of the salt solution, equilibrium is reached and the amount of the solvent passing in opposite directions is equal

continued

continued 59

The chemical potentials of the solvent on both sides or the membrane are equal.

The properties of the solution determine only the value of the osmotic pressure, not the membrane, provided that it is truly semipermeable.

To reverse the flow of the water so that it flows from the salt solution to the fresh solvent, as in Fig. 4.18c, the pressure is increased above the osmotic pressure on the solution side.

This phenomenon, called reverse osmosis is used in a number of processes. An important commercial use is in the desalination of seawater or brackish water to produce fresh water.

Unlike distillation and freezing processes used to remove solvents, reverse osmosis can operate at ambient temperature without phase change.

continued 60

continued

Figure 4.18: Osmosis and reverse osmosis: (a) osmosis, (b) osmotic equilibrium (c) reverse osmosis

OSMOSIS •Pure water flows from a dilute solution

through a semipermeable membrane

(water permeation only) to a higher

concentrated solution

•Rise in volume to equilibrate the pressure

(osmotic pressure)

•If pressure greater than the osmotic

pressure is applied to the high

concentration the direction of water flow

through the membrane can be reversed.

REVERSE OSMOSIS

Osmotic pressure- P required to equalize the solvent activities if pure solvent is

on one side of membrane

continued

This process is quite useful for the processing of thermally and chemically unstable products.

Applications include concentration of fruit juices and milk, recovery of protein and sugar from cheese whey, and concentration of enzymes.

2. Osmotic pressure of solutions.

Experimental data show that the osmotic pressure π of a solution is proportional to the concentration of the solute and temperature T. Van’t Hoff originally showed that the relationship is similar to that for pressure of an ideal gas

For example, for dilute water solutions,

RTV

n

m

E 4.5

continued

where n = the number of kg mol of solute

Vm = the volume of pure solvent water in m3 associated with n kg mol of solute,

R = the gas law constant 82.057 x 10-3 m3.atm/kgmolK

T = temperature in K

If a solute exists as two or more ions in solution, n represents the total number of ions

For more concentrated solutions. Eq. (4.5) is modified using the osmotic coefficient φ which is the ratio of the actual osmotic pressure π to the ideal π calculated from the equation.

For very dilute solutions, φ has a value of unity and usually decreases as concentration increases

in Table 4.4 some experimental values of π are given for NaCl solutions, sucrose solutions, and seawater solutions

Example 1: Calculation of Osmotic Pressure of Salt Solution

Calculate the osmotic pressure of a solution containing 0.10 g mol NaCI/1000 g H2O at 250C

Osmotic Pressure of Various Aqueous Solutions at 250C

Types of Membranes for Reverse Osmosis

One of the more important membranes for RO is the cellulose acetate membrane.

The asymmetric membrane is made as a composite film in which a thin, dense layer about 0.1- 10 μm thick of extremely fine pores is supported upon a much thicker (50- 125 μ m) layer of microporous sponge with little resistance to permeation.

The thin, dense layer has the ability to block the passage of quite small solute molecules.

In desalination the membrane rejects the salt solute and allows the solvent water to pass through.

Solutes which are most effectively excluded by the cellulose acetate membrane are the salts NaCl, NaBr, CaCl2 and Na2SO4 ; sucrose; and tetralkvl ammonium salts.

main limitations of the cellulose acetate membrane

can only be used in aqueous solutions and

it must be used below about 600C

continued

Another important membrane useful for seawater, wastewater. nickel-plating rinse solutions, and other solutes is the synthetic aromatic polyamide membrane “Permasep,” made in the form of very fine, hollow fibers

When used industrially this type of membrane withstands

continued operation at pH values of 10 to 11

Many other anisotropic membranes have also been synthesized from synthetic polymers, some of which can be used in organic solvents, at higher temperatures, and at high or low pH

continued

cellulose

acetates

susceptible to biological attack and acidic or

basic hydrolysis back to cellulose

necessary to chlorinate the feed water and

control the pH (4.5 to 7.5)

polymamides Not susceptible to biological attack and resist

hydrolysis in the pH range of 4 to 11

Polyamides Attacked by chlorine

Flux Equations for Reverse Osmosis

Basic models for membrane processes

Two basic types of mass-transport mechanisms which can take place in membranes.

In the first basic type, using tight membranes, which are capable of retaining solutes of about 10 Å in size or less, diffusion-type transport mainly occurs.

Both the solute and the solvent migrate by molecular or Fickian diffusion in the polymer, driven by concentration gradients set

up in the membrane by the applied pressure difference. In the second basic type, using loose, microporous membranes

which retain particles larger than 10 Å, a sieve-type mechanism occurs, where the solvent moves through the micropores in essentially viscous flow and the solute molecules small enough to pass through the pores are carried by convection with the solvent.

2. Diffusion-type model

continued 70

For the diffusion of the solvent through the membrane, as shown in Fig. 4.19

where Nw = the solvent (water) flux in kg/sm2 Pw = the solvent membrane permeability, kg solvent/s. m atm Lm = the membrane thickness, m: Aw = the solvent permeability constant, kg solvent/sm2 atm ΔP = P1 – P2, (hydrostatic pressure difference with P1 pressure

exerted on feed and P2 on product solution), atm and Δπ = π1 – π2 (osmotic pressure of feed solution - osmotic

pressure of product solution), atm.

PAPL

PN w

m

ww

m

ww

L

PA

E 4.6

E 4.7

continued

continued 71

Figure 4.19: Concentrations and fluxes in reverse-osmosis process

continued

continued 72

Note that subscript 1 is the feed or up stream side of the membrane

and 2 the product or downstream side of the membrane.

For the diffusion of the solute through the membrane, an approximation for the flux of the solute is

2121 ccAccL

KDN s

m

sss

m

sss

L

KDA

E 4.8

E 4.9

continued

continued 73

where

Ns = the solute (salt) flux in kg solute/sm2

Ds = the diffusivity of solute in membrane, m2/s

Ks = cm/c (distribution coefficient), conc. of solute in membrane/conc. of solute in solution;

As = is the solute permeability constant, m/s

c1 = the solute concentration in upstream or feed (concentrate) solution, kg solute/m3 and

c2 = the solute concentration in downstream or product (permeate) solution, kg solute/m3

The distribution coefficient Ks is approximately constant over the membrane.

continued

continued 74

Making a material balance at steady state for the solute, the solute diffusing through the membrane must equal the amount of solute leaving in the downstream or product (permeate) solution:

where cw2 = the conc. of solvent in stream 2 (permeate), kg solvent/m3

If the stream 2 is dilute in solute, cw2 is approximately the density of the solvent.

In reverse osmosis, the solute rejection R is defined as the ratio concentration difference across the membrane divided by the bulk conc. on the feed or concentrate side (fraction of solute remaining in the feed stream):

2

2

w

ws

c

cNN E 4.10

1

2

1

21 1c

c

c

ccR

E 4.11

continued

continued 75

This can be related to the flux equations as follows, by first substituting Eqns. (4.6) and (4.8) into (4.10) to eliminate Nw and Ns in Eq. (4.10). Then, solving for c2/c1 and substituting this result into Eq. (4.11),

where B is in atm-1

PB

PBR

1

22 ws

w

wss

w

cA

A

cKD

PB

E 4.12

E 4.13

C. Application, Equipment and Models for RO

continued 76

1. Effects of Operating Variables Operating pressures in reverse osmosis range from about 1035

up to 10350 kPa (150 up to 1500 psi).

Comparison of Eq. (4.6) for solvent flux with Eq. (4.8) for solute flux shows that the solvent flux Nw depends only on the net pressure difference, while the solute flux Ns depends only on the concentration difference.

Hence, as the feed pressure is increased, solvent or water flow through the membrane increases and the solute flow remains approximately constant, giving lower solute concentration in the product solution.

continued

continued 77

At a constant applied pressure, increasing the feed solute concentration increases the product solute concentration.

This is caused by the increase in the feed osmotic pressure, since as more solvent is extracted from the feed solution (as water recovery increases), the solute concentration becomes higher and the water flux decreases.

Also, the amount of solute present in the product solution increases because of the higher feed concentration.

If a reverse-osmosis unit has a large membrane area (as in a commercial unit), and the path between the feed inlet and outlet is long, the outlet feed concentration can be considerably higher than the inlet feed c1

Then the salt flux will be greater at the outlet feed as compared to the inlet.

Example: Prediction of Performance in a Reverse-Osmosis Unit

continued 78

A reverse-osmosis membrane to be used at 25°C for a NaCl feed solution containing 2.5 g NaCl/L (2.5 kg NaCl/m3, ρ = 999 kg/m3 has a water permeability constant Aw = 4.81 x 10-4

kg/sm2atm and a solute (NaCl) permeability constant As = 4.42 x 10-7 m/s. Calculate the water flux and solute flux through the membrane using ΔP = 27.20 atm and the solute rejection R. Also calculate c2 of the product solution.

2. Concentration Polarization in RO Diffusion Model

continued 79

In desalination, localized concentrations of solute build up at the point where the solvent leaves the solution and enters the membrane. The solute accumulates in a relatively stable boundary layer (Fig. 4.20) next to the membrane.

Concentration polarization, β,

defined as the ratio of the salt concentration at the membrane surface to the salt concentration in the bulk feed stream c1

causes the water flux to decrease, since the osmotic pressure π1 increases as the boundary layer concentration increases and the overall driving force (ΔP - π) decreases.

Also, the solute flux increases, since the solute concentration increases at the boundary. Hence, often the ΔP must be increased to compensate, which results in higher power costs

continued

continued 80

The effect of the concentration polarization β can be included approximately by modifying the value of Δπ in Eqs. (4.6) and (4.12) as follows:

assumed that the osmotic pressure π1 is directly proportional to the concentration, which is approximately correct. Also Eqn. (4.8) can be modified as

usual concentration polarization ratio is 1.2 to 2.0 - the concentration in the boundary layer is 1.2—2.0 times c1 in the bulk feed solution. This ratio is often difficult to predict.

21 E 4.20

21 ccAN ss E 4.21

continued

continued 81

In desalination of seawater using values of about 1000 psia = ΔP, π1, can be large. Increasing this, π1 by a factor of 1.2- 20 can appreciably reduce the solvent flux.

The boundary layer - reduced by increasing the turbulence by using higher feed- solution velocities.

However, this extra flow results in a smaller ratio of product solution to feed. Also, screens can be put in the path to induce turbulence.

Equations for predicting the mass-transfer coefficient to the surface and, hence, the concentration polarization, are given for specific geometries such as flow past plates, inside tubes, outside tubes, and so on

3. Types of Equipment for RO

continued 82

plate-and-

frame

In the plate-and-frame-type unit thin plastic support

plates with thin grooves are covered on both sides with

membranes as in a filter press.

Pressurized feed solution flows between the closely

spaced membranes .

Solvent permeate through the membrane and flows in

the grooves to an outlet.

Hollow-fiber High packing density and containing fibers of cellulose

acetates or aromatic polyamides

Is used for the desalinization of brackish water

containing less than 0.5 wt% dissolved salts if fouling is

not serious

In the hollow-fiber type, fibers of 100-200 μm

diameter with walls about 25 μm thick are arranged in a

bundle similar to a heal exchanger

continued

tubular membranes in the term of tubes are inserted

inside porous-tube casings which serve as a

pressure vessel.

These tubes are then arranged in bundles like

a heat exchanger.

spiral-

wound

In the spiral-wound type, a planar membrane

is used and a flat, porous support material is

sandwiched between the membranes.

Then, the membranes, support, and a mesh

feed-side spacer are wrapped in a spiral around

a tube.