Membrane Technology Lecture1-42

Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India

MEMBRANE SCIENCE AND TECHNOLOGY

BYProf. S. K. Gupta

Presentation on

• Membrane: Its allows some selected components to pass through it and hence aids in separations.

• Membranes physical phase: solid, Liquid & gas.

• Membrane Types: Homogeneous, Heterogeneous, Symmetric & Asymmetric Membranes.

• Advantages: 1. Can work at room temp.

2. Less energy required. (Open Pan evaporator = 600 KWH/1000 kg water

5-7 effect evaporator = 37-53 KWH/1000 kg water

Reverse Osmosis membrane = 5-20 KWH/1000 kg water)

3. No phase change (except Pervaporation).

Introduction

• Disadvantages:

1. Purity is not achieved or if achieved it will be costly.

2. Completely dry products is not obtained. (Pressure Swing Adsorption is used after membrane separation.)

3. Fouling of membrane takes place.

4. Concentration polarization takes place.

Low Concentration of Salt

High concentration of Salt

Negligible Concentration of Salt

RejectPermeate

Membrane Materials:

1. Polymeric: Used up to 70 0C Temp. range.

• Cellulose Acetate (CA).

• Polysulfane (PS).

• Polyamide (PA).

• Polycarbonate.

• Polyacrylonitrile.

2. Inorganic: Used at high temp. also about 100 0C.

• Alumina.

• Zirconia.

• Stainless Steel.

• Carbon Composite.

• Silica.

Membrane Materials

40 0C 80 0C 140 0C

Temp. Limits:

PS, PA

Ceramic (130 0C)

0 7 14

Ceramic

PS, PA

PH Limits:

Working Range

Chlorine (ppm) 1

Time of exposure

Chlorine limits:

CA PA PS Ceramic

Alkali

Butanol

Ethanol

Solvent Stability:

1. Manufacturing technique: Pressing & Sintering of polymers.• Membrane material: Ceramic (Powder form), Metal, Polymer powder.• Pore size: 1-20 µm.• Application: Micro filtration (Asymmetric Membrane). • Irregular Pore size. Porosity 10 % to 40 % .

Methods of Preparation

…………………………….............…………………………………

………………………………………

:::::::::::::::::::::::::::::::::::::::::::::::::::::::::

Pressurizing (also heating just below the MP of Powder)

Plates100-500 µm

• Fine Powder.

• Binding Material may be used.

• Also Lubricant is used.

Pressurizing (also heating just below the MP of Powder)

2. Manufacturing technique: Stretching of polymer sheet.

• Membrane material: Polymer sheet.

• Pore size: 0.5-10 µm.

• Application: Micro filtration, Burn dressing, Artificial blood vessel.

• Irregular pore size. Porosity 60 % to 70 % .

Stretch very slowly (Bonds are broken)

3. Manufacturing technique: Track Etched.

• Membrane material: Polymer sheet.

• Pore Size: 0.2-10 µm.

• Application: Micro filtration, Burn dressing, Artificial blood vessel.

• Uniform pore size .Nuclear source

Polymer sheet

• First step: The bonds become weak from where radiations pass.

• Second step: Etching bath to wash out the weak bonds & create pores.

4. Manufacturing technique: Inversion technique.

• Membrane material: Any Polymer.

• Pore Size: 0.01-5 µm.

• Application: Micro filtration (MF), Ultra Filtration (UF), Reverse Osmosis (RO).

• Uniform pore size .

In first step:

Polymer + Solvent = Homogeneous solution (10 - 30 %wt Polymer)

Glass support

Homogeneous solution

In second step:

It can be done in 3 ways.

a). Addition of Precipitants:

• Precipitating agent: Mostly water , Air.

Polymer

Solvent Precipitate

CTwo phase

region

Homogeneous region

• Porous membranes are obtained

Phase inversion diagram

b). Solvent evaporation:

• Solvent should be volatile.

• Allow solvent to evaporate (for pore formation).

Polymer

Solvent Non-solvent

Phase inversion diagram

c). Thermally induced phase inversion:

• Lower the temperature of homogeneous solution.

• We get 2 separate phases.

• From top remove solvent rich phase & polymer (membrane) remains on glass plate.

Polymer + SolventSolvent rich

Polymer rich phase

Polymer SolventPhase inversion diagram

• e.g.: Polypropylene membrane dissolved in N,N-bis-(2-hydroxyethyl)-tolylamine.

Preparation of asymmetric membrane

1. Asymmetric membrane:

0.2 µm Membrane thickness which provides resistance 0.2 mm

Porous material

2. Composite membranes: (Most recent technique)

a). Coating on micro porous membrane.

b). Interfacial polymerization.

Polymer solution with cross linking agent

For polymer support

3. Integral asymmetric membrane:

• Polymer + Solvent = Homogeneous solution (10 - 30 %wt Polymer).

• Homogeneous solution put above glass plate & add precipitating agent.

• The film is quenched in non solvent or in precipitating agent.

• Annealing.

100-500 µm Skin layer formed.

Types of Asymmetric membrane:

1. Finger structure:

• Good for ultra filtration.

2. Sponge structure (kept in wet condition):

• Good for RO.

3. Sponge structure (can be kept in dry condition):

Factors that leads to different Asymmetric membrane:

1. The polymer & its concentration.

2. Solvent.

3. Precipitants.

4. Form of precipitants (vapor or liquid).

5. Temp. of precipitants.

• High precipitation rate leads to Finger type.

• Slow precipitation rate leads to sponge type.

1. Induced concentration gradient:

• At surface concentration is minimum.

• Under beneath concentration is higher.

Polymer

Solvent Precipitants

2. Surface super saturation:

• Initially mass transfer takes place at upper Thin layer but beneath homogeneous solution.

• The thin layer impart resistance and hence reduce mass transfer.

NSNSSolvent

P + SThin layer

Inorganic membraneAdvantages of inorganic membrane:

1. Higher thermal stability.

1. Can be steam stabilized.

2. Allows higher pressure.

3. Resistance to chemical corrosion.

4. Resistance to microbial degradation.

5. Ability regenerate thermally.

Disadvantages:

1. Expensive (much more than polymer membrane).

2. Only micro filtration & Ultra filtration membranes are available.

• Micro porous = 5 nm to 50 µm.

• Nano porous & Ultra porous < 2 nm.

Manufacturing techniquesManufacturing techniques:

1. Sol-gel process.

2. Chemical Vapor Deposition (CVD) modified membrane.

3. Leached hollow glass fibers.

4. Anodic oxidation.

Preparation of support:

• Ceramic powder, Inorganic binding lubricant & water.

• Paste is extruded in desired shape drying Sintering.

1. Sol-gel Process:

Alkoxide (metal salts, metal organics)

May be acidic, basic, aqueous media or in organic phaseHydrolysis

Condensation polymerization

• Acidic & Aqueous media:

• Solvation of Metal ion:

MZ+ + n H2O M(OH2)nZ+ Solution of Metal ion

M(OH2)nZ+ M(OH)(OH2)n-1

(Z-1)+ + H+

Monomer

• Hydrolysis:

2 M(OH)(OH2)n-1(Z-1)+ M2(OH)2(OH2)2n-4

2(Z-1)+ + 2 H2O

• Basic & Organic media:

M(OH) + (OH)- MO- + H2O

MO- + n ROH M(OR)n + -OH

M(OR)n + H2O M(OR)n-1OH + ROH

M(OR)n + M(OR)n-1OH M2O(OR)2n-2 + 2 ROH

• Colloidal solution (destabilized by evaporation)

Glass support

Drying 50 0C Sintering

Ceramic layer

Fluxes

• Multi component diffusing mixture:

1, 2, 3,......………., n Components 1 2 3, , ,........, nv v v v

1 2 3, , ,..........., n Velocities

Mass concentration (g/cm3)

• These are not densities.

Molar concentration (gmol/cm3)1 2 3, , ,.........., nc c c c

ρmix = ρ1 + ρ2 + ρ3 + …… + ρn = Density of the mixture

Cmix = c1 + c2 + c3 + …… + cn

1 2 3* 1 2 3 1

......

iinn i

c vc v c v c v c v

1 2 31 2 3 1

iinn i

vv v v v

Mass average velocity:

Molar average velocity:

• Hypothetical velocities, it can’t be measured by instrument

Diffusion velocities of component ‘i’

J c v V

• Mass flux (Absolute) =

• Molar flux (Absolute) =

• Mass diffusion flux =

• Molar diffusion flux =

• Relation between absolute flux & diffusion flux:

i j iij

n w n J

N x N J

i ii i i

i i i n

i i jnj

i i jij

v v v v

n J w n

i ii i i

i i i n

i i jnj

i i jij

v v v v

c v c v v c v

N J cc

cN J N

N J x N

Equation of continuity

ri (gm/cm3-s)

vi (cm/s)

ρi (gm/cm3)

∆y∆x

• Conservation of mass:

Accumulation = Inflow – Outflow + Generation

( )ii ix i ix i iy i iyx x x y y y

x y zv y z v y z v x z v x z

i iz i iz iz z zv x y v x y r x y z

( )( ) ( ) ( )

i iyi i ix i izi

iyi ix izi

t x y z

• Dividing both sides by ∆x ∆y ∆z & taking ∆x 0, ∆y 0, ∆z 0

( )1, (1)

( )2, (2)

( ), ( )

ii ii i

i ii i i i

M Mt M M

c MN M RM

i n rt

i n n r nt

1 1 1 21 2

1 21 2

( )( ) 0

n n nt

n n n v v v

• Adding above equations:

• This is known as equation of continuity

A A AB A

J c D x

• Fick’s law

• Valid only for binary system

• DAB = DBA

i i im i

J c D x

• General equation of Fick’s law

Fick’s Law

*A A AB AJ c D x

ii n T P

• Concentration difference – only driving force

• Chemical potential – main driving force

Chemical potential

This equation gives better result

d RTd P

ˆln (1)

ˆln (2)i

d RTd f

o ii o

ii i io

oi iT P

fd d RTd

d d RTd a

Ideal gas

Real gas or Liquid

Mixture

• By (1) – (2)

• f = Fugacity

• a = Activity

• γ = Activity coefficient

ABA A A

A A AB A

D RTJ c x

J c D x

γA=1, for ideal solution

• If pressure changes

ˆ, , ln

o o oAA A A

A A A A

A ABA AAB A A

ABA AAB A A

T P T P RT a V P P

RT x V P

RT x V Px

c DJ D x c V P

DJ cD x c V P

For ideal gas,γA=1

Semi permeable membrane

2 1 2 1

1 2 2 1

* 2 1 1 2

** 2 1 1 2

* 1 21 2

A ABAA AB A

A A ABAAB A

B B ABAAB A

B B ABAA AB A

dx D dPJ cD c V

dx RT dx

x x D P PcD c V

cx cx D P PD c V

c c D P PD c V

c c D P PJ D c V

c cP P

*1 2 1 2

RT c RT c RTV

A AB AA A

B BA BB B

c D dxRT dPJ V

RT x dx dx

c D dxRT dPJ V

RT x dx dx

Dilute Solution: A Solvent : xA 1;

B Solute : xB 0.

In this case pressure is not a deciding factor in flux calculation.

• In Presence of Electric Field

AB ABA A A A A

ABA A A

ABA A A A A A

D DJ c c F

DJ c F

ZA = Charge

F = Faraday’s constant

µA* = Electro-Chemical

Potential

Ψ = Electrical Potential

• Temperature gradient Mass flux Sorret effect

• Concentration gradient Heat flux Dufour effect

• In Presence of Thermal Gradient:

*lnTAB

A A A A

DJ c D T

Thermal Diffusion Coefficient

• Thermal & Electrical effects are not significant

Theory of Irreversible Thermodynamics

Forces

• Onsager 1931

• Works when system near to equilibrium

1 2 31 11 12 13 1

1 2 32 21 22 23 2

ii ikk

J L X L X L X L X

Ф = Rate of dissipation of Free energy

σ = Rate of change of Entropy

Lik= Phenomenological Coefficient

• Lik (Phenomenological coefficient) determined by experiment.

• Theory of Irreversible T/D doesn’t say anything about Lik.

• Relation between Lik :

ii kk ik

• Curie principle : Flux Ji will depend on driving force xJ iff they have the same tensorial order or they differ by 2.

Flux V T C

µ × × q × k DA

J × DAT DAB

J1 µ1’

J2 µ2’

µ1 ∆ µ1

µ2 ∆ µ2

∆x 0

1 1 2 2

1 11 1 12 2

2 21 1 22 2

[ ( )]

dx J dx

J dx Jx

Stefan Maxwell equation• Forces are given in terms of Flux, where as in Theory of

Irreversible T/D Flux is given in terms of Forces.

ii i ji j ij

i T Pi i

ii T P i

i i i i i

v vx d x x

d RTd a

cRTd c

RT acRT

x x x x

Concentration is the only driving force

(Assuming ideal mixture)

Dij = Binary diffusion coefficient

vi, vj = velocities

xi, xj = concentrations

• For two component mixture :2

1 11 1

2 12 1 1 21 2

2 11 1

1 2 112 1 1

1 1 21 12 1

v vx x x

v vx x

x N x Nv vcx x

x N x N

cD x x N N N

N x N N cD x

Bulk flow term Diffusion term

Fick’s law of diffusion including mass flux diffusion

• For three component mixture :

1 1 11 1

2 1 3 1

1 2 1 312 13

2 1 3 1

1 1 1 2 1 312 13

( ) ( )0

( ) ( )

i ik i

i ik k

v vd x x x

v v v vx x x x

v v v vd x x x x x

In Stefan-Maxwell Forces are given in terms of Flux.

In Theory of Irreversible T/D Flux is given in terms of Forces.

& ( ) (2)

i ji im ij

j iij ij

N x N cD x

x xx v v

x xv v

cD x N N

By solving (1) & (2)

• Examples:

1. Components 2, 3, …, n are in trace amount in nearly pure component 1.

i.e. x2, x3, …, xn << 1 or x1 ≈ 1 & N2, N3, …, Nn << N1

n nj ii j i j

j jij ij

x xv v

cD x N N

x x cv x x v

n nj j

ii ij jij ij

ii ii i

iim i i

xNx x v

xNx x vcD D

cD x N N

x N x N

cD cD x N N

xcD cD

nij ji

x xv v

cD x N N

cx xv v

x Nx N

D x N N

2. If Dij’s are same

n nij ji

nim ij

j ii jj j

nim ij

jjim ij

x Nx N

cD D x N N

x N N x

cD cD x N N

xcD cD

3. Components 2, 3, 4, …, n are moving with same velocity.

i.e. v2 = v3 = … = vn = v & v1 ≠ v

x xv v

cD x N N

x xv v

cD x N N

xx v v

1 1 2 3 11 1 1 2 3 11

1 11 1 1 2 1 3 1 1

11 1 1 1

[ ... ]

[ (1 ) (1 )]

(1 )( ) (2)

(1 )( )

x N N x c v c v c v c v c v

c x x v x x v x x v x x v x v

c x v x vx x

cx x v v

xx v v

cD cx x v v

(From 1 & 2)

Reverse OsmosisApplications:

1. Water purification ( Potable water or drinking water) : Municipalities, restaurants, hotels, homes, offshore oil rigs.

2. Ultra pure water : Semiconductor industries, hem-dialysis, drug formulation, boiler feed water.

3. Concentrate or dewatering applications in food industry : Milk concentration (whey), concentration of juices (coffee), de-alchoholizing of wines & beers.

4. Pollution control of waste water from industry : Textile industry, pulp & paper industry, metal industry.

Membrane materials:

1. Cellulosic :

• Cellulose acetate & Cellulose tri-acetate.

• Magged, relatively chlorine insensitive, & inexpensive.

• Don’t have high fluxes and restricted to narrow PH range.

2. Non-cellulosic :

• Polyamide, polyacrylonitrile, polyvinyl alcohol, polysulfone.

• Not magged, relatively chlorine sensitive, & expensive.

• Higher fluxes and can be used for wide PH range.

• Very little compaction Lower membrane life.

Membrane modules:

1. Flat sheet membrane:

• Plate & frame module

Rectangular or Hexagonal shape, 30-40 plates required

• Spiral bound module

• Illustration of a spiral-wound module

2. Tubular membrane:

• Tubular module

I D > 1/2˝ , 20 ft long

• Hollow fiber membrane

Axial flow hollow fiber module

Radial flow hollow fiber module

• Flow directions inside the shell of a hollow-fibre module

• Flow pattern in a parallel-flow hollow-fibre module (fibre-side feed).

• Flow pattern in a radial-flow hollow-fibre module (shell-side feed).

Parameters

Modules

Packing density (ft2/ft3)

Water flux at 600 psi (gal/ft2-d)

Salt rejection

Water output

Per unit vol.

(1gal/ft3-d)

Flow channel

size (inch)

Ease of cleaning

Tubular 30-50 10 Good 300-500 0.5-1 Very good

Spiral-bound

250 10 Good 2500 0.1 Fair

Hollow fiber (axial)

1000 5 Good 5000 0.254 Fair

Hollow fiber

(radial)

5000 1-3 Good 5000-15000 0.002 Poor

Plate & frame

35 10 Good 350 0.01 Good

Comparison of RO Modules

• Osmotic pressure

' ''( )

RT c c

Where υi = Von’t Hoff factor

= No. of ions present in a molecule of salt

e.g. For NaCl, υi = 2

BaCl2, υi = 3

• Expression for work required to separate salt from water

Water(2) (pure)

Salt + Water(1)

TdU dQ dw a

dw PdV dw b

dQ dU PdV dw

Tds dU PdV dw

( + for work on the system

- for work by the system)

From (a) & (2)

From (1) & (2)

• Combined statement of 1st & 2nd Law of Thermodynamics (T/D)

• Equal sign for reversible process & inequality sign for irreversible process

' '2 1

' '1 2

( ) (5)

Tds dU PdV dw

G H Ts

U PV Ts

dG dU PdV Tds

G G w w

From (3)

From (4) & (5)

Integrating both sides

= Work done on the system for required change

= Useful work obtained from the system

Transport Model

Support

Dense Layer

Z = LLow pressure

sideHigh pressure

CijC22

(C22)m

Permeate (C23)m

(C23)C23

Main ResistanceThis resistance can

be neglected

Asymmetric Membrane

• i = Component

• i = 1 Solvent

• i = 2 Solute

• j = Location

• j = 1 Bulk feed phase

• j = 2 Interface between membrane & feed

• j = 3 Bulk permeate phase

Film Theory ModelAssumptions:

• Turbulent flow

• All mass transfer resistance lies in a film near the surface

• Film is stagnantMembrane

C21= Conc. At high pressure side

C21= Interphase Conc.

(C23)m

(C22)m

Z = δ

2 2N R

22 2 1 2 21

( ) (1)

ii i jj

NN Constt

as N x N J

xN x N N cD

• By equation of continuity

At steady state

Considering only z direction

2 1 2 23

221 1 2 2 23

2 23 21

1 22 23

22 23 1 2

21 23 21

22 23 1 2 1 2

21 23 21

, ( ) (2)

( )( )

ln( / )

zx z zx

z z z z

also N N N x

xcD N N x x

zdx N N

dzx x cD

N Nx x z

x x N N

x x cD

c c N N N N

c c c D ck

22 23 1 2

exp z z

c c N N

c c ck

From (1) & (2)

After integrating both sides

• (N1z + N2z) / c = [gmol / (area-time)] / [gmol / vol.]

= vol. / (area-time)

(N1z + N2z) / c = Jv

• If membrane is perfect & doesn’t allow any permeate, then

exp ( )v

• Equation (A) is not valid for laminar flow assumption

• From (A) we can say higher flux will result in higher concentration polarization

• For laminar flow also (A) can be used but result will not be fully correct

• C22/C21 should be as less as possible because if any opening in membrane all salt concentration will goes to other side

C21= Interphase Conc.

(C23)m

(C22)m

• In this region we assume liquid is stagnant

• If we take some velocity then it doesn’t improve result that’s why we take former assumption that simplify the problem

• 30,000 ppm ∆P > 30 atm

• 20,000 ppm ∆P > 20 atm

• Then we will design on 30,000 ppm ∆P > 30 atm basis

• (k)permeable & (k)nonpermeable values differ only 10%, so we can use same correlation for both

• J = f / 2 = [k (Sc)2/3] / u

• So, k = (f / 2) u Sc2/3

2/322 23

2exp vc c J Sc

c c f u

22 23 23

21 23 23

22 23 21 22

22 21 23 21

c c cR

c c Jas

c c Jc c

c c c c k

R c c k

c JRcR c kc

• Rejection:

What membrane actually does

We can observe this

1(1 ) exp

(1 ) (1 )exp

1 1ln ln

• Model based on Mechamstic (Role model)

N1 = A ( ∆P - ∆∏i )

• Model based on theory of Irreversible T/D

N2 = B ∆C

• As we increase no. of parameters model predicts better but at the cost of complex problem, 3 parameters problem gives good result

Solution Diffusion Model

(C23)m

(C22)m

x = 0x = ∆x

2 1• Homogeneous membrane i.e. no big pore i.e. there is only diffusion takes place in the membrane

• ∆P = P1 – P2

• ∆C = C22 – C23

11 1 1

1 11 1

2 22 2

ln. . (2)

ii i i

d RTd a v dP

d d a dPRT v

dx dx dx

d d a dPi e RT v

dx dx dxD

N cRTD d

N cRT dxD d

N cRT dx

From (1)

1 11 1

11 1 2 11

11 1 21

ln (4)

x xcritical N

DN dx c RTd a v dP dx

aDN x c RT v P P

ac DN RT v P P

1 11 11

c DN v v P

c v Dwhere A

From (2) & (3)

From (4) & (5)

2 22 lnd RTd a v dP

2 2 22

2 22 2 2

d d aRT

dx dxd x d x

RT RTdx dx

d dxRT

dx x dx

c D das N

RT dxc D dxRT

NRT x dx

D dxcx

dcx dcN D D

For ideal dilute solution

γ2 = 1 For ideal solution

23 222 2

22 232 2

22 231 2

22 232 2

22 22 23

( ) ( )

( ) ( )&

c cN D

c ck k

kc kcN D

N c cx

D kwhere B

Kimura – Sourirajan Model• Kimura – Sourirajan Model also gives:

i e bc

For pure wter

The value of A & B different for SD Model & KM Model

A = Tanθ, we can find A

We can’t find B because we can’t measure C22

Kimura – Sourirajan analysis:

1 22 23

2 22 23

22 23 1 2

2. { ( )}

3. ( )

4. exp

Find 'k'

1 1ln ln (1

1. Find 'A' from pure water permeability data

N A P b c c

N B c B c c

c c N N

c c ck

22 232

( )1 1

B c cN

J c J c

1 11 1 1 (2)

1ln ln From (1) & (2)

1ln ln

obs vv

R R J J

R JJ B

θ1ln obs

From Tanθ = 1/k

1ln obs

• K = a Qb

• Q1 K1, Q1 K1, Q1 K1, …..

θln k

• Turbulent b = 0.8

• Laminar b = 0.33

Kedem – Katchelky model• Based on Theory of Irreversible Thermodynamics (1954)

• Its 3 Parameter Model

[ ( )]

Biological memb

ss Transfer only in x direction (Assume)

[ ( )]

ranes very near to equilibriu

[ ( )]

m ix i xi

ix i xi

dx J dx

( , ) (1)

ˆ, , ln

ix i i i ix x xi

m w w s s

w ww w wp s

s pw w pp s

o o oii i i

J J w water s salt

J c J p

T P T P RT a V P P

RT a V P

ˆln ssa V P

∆μw, ∆c

∆μw, ∆p

x = ∆x x = 0

ˆ ˆln ln

ˆ ˆln ln (2)

ˆln ln ln ( For ideal solution =1)

ln(1 ) ln(1 ) ln(1 )

w sm w w s s

w sm w w s s w s

w w w w

s s sx x x

s s s sx x x x x x

J RT a V P J RT a V P

RT J a J a J V J V P

x x c x c xc

1 1( )

s s sx x x

c c cc c

ˆln ln

s sx x x

s ss x x xs s

w sm w s w s ss

s ww sm w s

c cca c

J V J V P RT J J cc c

J JJ V J V P

From (2)

• JwVw = vol. flux of water

• JsVs= vol. flux of salt

• Vi = partial molar vol. of i

• Jv = vol. flux

• JD = Drift flux

v P PD

D DP D

sw wD w

J L P L

LJ L P

Lwhere

J L P L

JJ J V V

• LP = Direct coefficient for Jv

• LD = Direct coefficient for JD

ws D w s

P D v s

w sv w s

J J J V c

L P L J c

J J V J V

s P D P s

vs P D v s

J L P L L P c

JJ L L J c

s v v P D s

D P s v s

s v sDiffusion part

Convective part

J J J L L c

L L c J c

J W J c

and J L P

• LP = Hydrodynamic permeability

• W = Solute permeability

• σ = Reflection coefficient

• For totally perfect membrane, σ = 1, i.e. completely reflect

• For totally imperfect membrane, σ = 0, i.e. completely passes

Three parameters of K-K Model

Spiegler-Kedem Model (1965)• Its much better model

x=0x=∆x

Consider infinitesimal small strip is in thermodynamic equilibrium

[ ( )]

dP dJ P For a small strip

dJ W J c

dxFor wholemembrane

dP dJ dx P dx

J x P P

Pdx dx

x=∆x x=0

C’sC”s

1ln 1 ln 1

ss s v

ss s v s

s v s sc

s v sv sc

vs v s s v s

dJ W J c

P c Jdx

dcP c J J

c J J P

xc J J

J xc J J c J J

s v s v

s v s s

s v v s v

s v v s s

c J J J x

c J J P

c J J c J x

c J J c P

c c J x

R J PP

R F FR

• LP = Hydrodynamic permeability

• σ = Reflection coefficient

• P = Solute permeability

3 parameters of SK model

N1 = A (∆ P - ∆π)

N2 = B (∆ C)

1 1ln ln

1ln ln

To find Min or Max valueof Y

dJ B J k

From slide 82 & 83

• At JV = k, will have maximum or minimum value1

ln obs

1ln obs

Design of RO System

Low pressure side

High pressure side

(C22)m

Permeate side

(C23)m

(C23)avg

Total permeate flow rate

Feed side

Vx , C21 , (1-QF) , ∆

Vxf , C21f , QF

22 23 1 2

2 22 23

{ ( )} 2

c c N N

c c ck

N A P A P b c

A P b c c

N B c B c c

Recovery i.e. for 50% recovery ∆=0.50

Vx + d Vx

X21 + d X21

• S = surface area per unit length of the membrane

• AVx C X11 It is coming

• A = Cross Sectional area feed channel

11 11 11 1

11 11 1

11 1 1

21 2 2

x xx x dx

AV CX A V dV C X dX N Sdx

AC V X V X N Sdx

d V X N SC

d V X N S NC

dx A h

d V X N S Nand C

dx A h

(S/A*L/L=S/A=Surface/Vol. of the module=1/h)

For Solvent :

For Solute

For Tubular module and axial flow Hollow module

22 21 23

A R L R hWL S

andBWL A B

d V X N

dx chd V X N

dx chc c c

For nearly perfect membrane (∆P and k also constant)

[ Pressure drop due to friction is very small as compared to the applied ∆P so we can assume ∆P as constant. As k α Q0.8 For Turbulent flow and k α Q0.3 For Laminar flow Thus for smaller recovery say 20% we assume k as constant If we have analytical solution for 20% and the recovery given in problem is 80% then divide the model in 3 or more parts to keep k constant]

For Plate & Frame and Spiral wound module

x23x22 x21

x = 0Vxf , x21f

• At x = 0, Vx = Vxf

x21 = x21f

• For dilute solution, nearly 100 % salt rejecting membrane C22 – C23 ≈ C22

• N1 > > N2

d V NX

Nd V X

x xf f

chV X Constt

V X V X

21 2221 22

A Px X

X XX X

X VX V

• Dimensionless parameters:

Dimensionless Osmotic Pressure

Dimensionless Mass Transfer Co-efficient

Solute Diffusivity Parameter

1 22 23

N A P b c c

b c cN A P

cX bA P

X bcA P X

N A P X

2 21 22

N BcX X

22 23,c c

21 23c c

0 expN N

22 22 1

c cX N

c cX ck

A P XX

dV Nand

A P Xd V V

1, exp

A P XdVV

A P XA P dVV

chV dX ch

22X 21

221exp

1 ln 6

. 0 0, 1x xfBC x X V V V

.V If Turbulent Cond

1 ln 2

1 lndV

d 1 ln

1 lnand

For any

F P F F

X L L VV A Q

Q Q Q Q

From (6) & (7)

1 1 1 2 1 2

i iL e E u E u E w E w

, 0 & 0

1 1, ln

at inlet x

at outlet x L

E Exponential Function

If u w

Then L

Land X

ln 1 ln 2

d ln 1 ln

ln 1 ln 1

ln 1 ln 2

Lets assume

w we d 1 ln

ue e e d

e e du

e dw e duI e

• Exponential Integrals

eE u du

eand E w dw

as f x dx f x dx f x dx

e dw e dw e dw

e dwE w E w

1 1 1 2

1 1 1 2 1 2

e du e du e du

e duE u E u

e dw e duL e

L e E u E u E w E w

1 lnw 1 2, lnw 2

1 ln,u

1 0 . . 1at x i e V

2 . . 1at x L i e V

, 0 & 0,

For u w

dVand L dX

1ln 1 ln 1 1 1

VL dV dV

L V V V

Permeate side

x23 = avg.QP

Total permeate flow rate

Feed side

Vx , x21

23232323

P F xf

X XX X

Q Q V A

A Areaof Feed Channel S surfacearea length

cX Q N Sdx Total amt of Salt in Permeate

cX V A N Sdx

Bc Sdx

Vxf , x21f

cX V A BcX Sdx

cX V A Bc

2122 22

2121 21

cX V A BcS

X XX d

BcSXcX V A

c 'xfV A

cB hSX

dVI dV

1 1 1 2 1 2

1 ln1 ,

i iL e E u E u E w E w

1, lnw

11, ln

1, ln!

ln , 0.56 .

uFor u E u u

wand for w E w w

If u w Then

E u u u Where Constt

and E w w w

• Design Equations:

Liquid Membrane

• It is used in place of polymer membrane.

• As diffusivity is more in liquid than solid.

• Additives are added to increase/decrease the solubility of any one species.

• It is of two types:

1. SLM Supportive Liquid Membrane

2. ELM Emulsion Liquid Membrane

Org./aq.

aq. phase

Org. phase

aq. phase

Org. phase

Feed PhaseReceiving Phase

• Formation method :

1. Take a micro porous membrane and put liquid membrane material in its pores.

2. Surfactants are used It is a sort of double emulsion process

3. Hollow fiber liquid membrane

Organic or Solid support

• Here the transfer occurs through the pores

Big dropsReceiving phase

Feed Phase

Liquid Membrane

Receiving Phase

• Separation mechanism in Liquid membrane

SA Solubility rate of A

SB Solubility rate of B

• Selectivity, i i A A

ijj j B B

D S D SB

D S D S

LMFeed

1. Add additive to increase or decrease selectively of one of the components in liquid membrane

LM (aq.)A (Aromatic (org.))

• Additive N-methylpyrolidone Its increase solubility of A several folds

2. Permeation with solute trapping mechanism

A + C D ( Instantaneous reaction)

Phenol + NaOH Sodium Phenolate ( Instantaneous reaction)

• Thus Conc. of Phenol at receiving side becomes zero ( as Phenol is trapped as Sodium Phenolate) Thus Conc. difference increases & thats why mass transfer rate increases.

Phenol

(Kerosene)

Cheaper

Feed Side LM Receiving Side

3. Carrier Mediated Transport:

(a) Facilitated Transport

• If solubility of A in LM is very small & still we have to remove A from feed.

• Carrier B should be very mobile i.e. higher molecular carrier & it should combine with A easily.

• We use external energy to maintain both interfaces conditions.

• A + B AB

LMFeed Side Receiving Side

• A + B AB

• As AB is formed so AB conc. is high here

Carrier B should not leak out

from LM

• AB A + B

• Conc. of B is maximum here

(b) Coupled Transport

• In this case one component transport from feed side to permeate side & second component from receiving side to feed side simultaneously.

• A + CB CA + B

• C Carrier complex

Feed Side LM Receiving Side

• Example: separation of metal ion

• Cu++ + 2HR CuR2 + 2H+

Carrier complex

(c) Photo Facilitation

• If reverse reaction is not possible or very-very small.

• Carrier complex is very stable.

• If carrier complex is photo sensitive then we use light energy.

• AC + hυ A + C

(d) Electro facilitation

• AC AC+ + e- A + C+ + e-

• At cathode: A + C+ AC+ & AC+ + e- AC

• At anode: AC AC+ + e- & AC+ A + C+

• Property of carrier:

• It should be soluble in LM.

• It Should form complex which is soluble in LM.

• It should be insoluble in both external phases.

• It should form complex easily.

• Complex should be moderately stable.

• Should be high mobility.• Commercially it is (LM) used for metal ions separation.

• Carrier species for metal extraction:

1. Acidic:

(a) Hydroximes

• Commercial carriers: LIX63, LIX65N, LIX64N, LIX70

• LIX 63: CH3-(CH2)3-CH(C2H5)-CH(OH)-C(NOH)-CH(C2H5)-(CH2)3-CH3

(b) B-diketones

• Acetyl acetone, Benzyl acetone.

(2) Basic:

• D2EHPA (Di-2-Ethylphosphoric Acid)

(3) Neutral:

• TBP (Tri-n-butylphosphane)

• Grown ethers It is basically monocyclic polyether

• Method of preparation (Emulsion Liquid Membrane):

1. Emulsification

2. Emulsion – external phase contacting

3. Settling

4. Demulsification

e.g.: De – aromatization of Kerosene

1. Emulsification:

EmulsionFeed Kerosene

Aqueous surfactant

Micro drops of kerosene

Aqueous phaseOil – Water (O/W) Emulsion

2. Gas oil – external phase:

• Here should not more mixing because that results to breaking of drops and eventually lost separation.

Gas oil

O/W Emulsion

Receiving phase O/W EmulsionGas oil

Double EmulsionFeed

3. Settling:

Gas oil + aromatics

O/W Emulsion

Separate them

• Aromatic compounds transferred from feed to gas oil.

• Separate the 2 phases Now O/W Emulsion needs to be Demulsified.

• Strong surfactant difficulty in Demulsification.

• Weak surfactant possibility of breakage of drops.

4. Demulsification: No. of techniques are used.

a. Electrostatic demulsification

b. Heat treatment

c. Phase dilution

d. Shear forces

e. Adsorption of Kerosene

Kerosene (Oil)

Demulsification

O/W Emulsion

• Important parameters: Membrane stability, Large interfacial area, Mass transfer coefficient.

• All important parameters are depend on different parameters: Concentration of surfactant, Micro drop hold up, Temperature, Treatment ratio, RPM, Internal reagent concentration.

Parameters Stability Mass transfer Interfacial area

Conc. of surfactant + + + + + +

Micro drop hold up + + + + + +

Temperature + + + + + + +

Treatment ratio + + + + + +

RPM + + + + + + + +

Internal reagent conc. + + + + +

• + Low, + + Moderate, + + + High

• Surfactants: SPAN80, ECA4360J

• Carrier species: LIX64N

• Commercial applications:

Phases

Applications

Phase I

(Feed)

Phase I I

Phase I I I

(Receiving Ph.)

Copper extraction

Aq. phase containing metal ions

Kerosene, SPAN80, ECA4360 J, LIX64N

0.5 mol/l H2SO4

Phenol separation

Aq. phase 1000 ppm Phenol

Kerosene, ECA4360J, Liq. Paraffin

NaOH solution

Hydrocarbon separation

n – Heptane solution Aq. solution of non ionic surfactant + up to 10 % N –

methyl pyrolidone

Dodecane

Ammonia separation

0.1 mol/l NH3 Paraffin oil, SPAN80, ECA4360J

0.2 % wt H2SO4

SLM (Supported Liquid Membrane):

• We use a micro porous support.

• LM should be compatible with support.

• Support material should not react with LM or with feed phase or receiving phase.

• LM should wet the micro porous membrane completely.

• Cellulose triacetate can be used as a for aqueous LM i.e. for hydrophilic LM.

• Poly propylene can be used as a support for organic LM i.e. hydrophobic LM.

• ∆P α 1/Rpore

• If some pore are too small then some pore may remain W/O LM. Smaller pore size also reduce the vapor pressure of LM.

• Porosity should be high as much as possible.

• Tortuosity should be small else fluxes will reduce

• Thickness should also be small.

Permeable species

Solvent (LM)

Carrier Stripping phase

Polymer support

Pore size (μm)

Porosity

Thickness (Module)

Uranium in ground water

n-Dodecane

Cynex-272 [Bis-(2,4,4)-

trimethyl pentyl

phosphoric acid]

HEDPA (1-hydroxyetha

ne-1,1-diphosphori

c acid)

Polypropylene

0.02 38 25

(Flat sheet)

″ ″ Bis-(2-ethylhexyl)pho

sphoric acid

″ ″ ″ ″ ″

SO2 in flue gas

Water NaHSO4 Helium ″ ″ ″ ″

Cu++ in plating bath

Kerosene Phenyl alkyl Ketone

dil. H2SO4 Teflon 5 60 12.5

(Flat sheet)

K+, Li+, Na+, Sr+ in aq.

Phenyl Hexane

Crown ether De-ionized Water

Polypropylene

0.3 40 30

(Hollow fiber)

Example of SLM

Advantages:

• Offers large interfacial area. ELM 3000 m2/m3, SLM 10,000 m2/m3

• Scalable.

• Very high selectivity and fluxes.

• The strip solution volume may be made smaller than the feed so that the solution can be concentrated simultaneously.

• Both extraction and stripping are carried out simultaneously.

Extraction Scrubber Stripper

RaffinateFeed

Impurities

are removedScrubbing

solution

Strip liq.

Stripping solution

Solvent

Liq. – Liq. ExtractionRaffinate Feed

Strip. Liq.Stripping solution

Solvent

Liquid membrane

Disadvantages:

1. Membrane breakage due to agitation, poor membrane formation, excessive internal drop size.

2. Requires emulsification.

1. Solvent loss by evaporation or by pressure differences across the micro porous membrane.

2. Carrier loss can occur due to irreversible side reaction.

Gas separation using facilitated transport in LM:

1. O2/N2 Cobalt – salen as a carrier.

2. CO2 Bicarbonate as a carrier.

3. H2S 1. Bicarbonate as a carrier.

2. Ion exchange membrane (cation exchange membrane), Organic diamine cations as carriers.

4. Ethylene – Propylene separation Ag+ is used as carrier ethylene selectivity is 1000 time than propylene

Mathematical modeling

• Facilitated transport (ward 1970):

Assumptions:

1. Limited solubility of A.

2. CAo (at x = 0) & CA

L (at x = L) are known.

3. All the reactions are 1st order with respect to A, B & AB

4. B & AB don’t leak through the membrane

• CT (known) = CB + CAB

Feed Strip gas

A B AB

( . )i A

AA A B AB

N R at S S

d CA D k C C k C

B AB AD D D

AA A B AB

BB A B AB

ABAB AB A B

d CA D k C C k C

d CB D k C C k C

d CAB D k C k C C

dxAs B ABdon t leak throughthemembrane

Limiting cases:

1. Reaction equilibrium exists through out the membrane

d CA D

ConsttdxC c x c Linear conc profile

Putting

at x C C

x L C C

C CWe get c C c

C CC x C

As, we have linear conc. profile

LAB ABx x LA A

A A AB

A B AB

T B AB

A B T B

C CC CN D D

L LAt all pts in membrane

k C C k C

Total conc of B is

k C C k C C

C C kC k

k kC kCk

LT A T A

L LA A A A

A A AB

LLT A AA A

A A AB LA A

LLT A AA A

A AB LA A

C kC C kCC C kC kC

N D DL L

kC C CC CN D D

L L kC kC

NAs Enhancement factor

kC C CC CD D

L L kC kC

A ABD D

After putting the values of CAB

• Thus from above expressions we can say that:

• More the conc. Of ‘B’ more is the transfer of species ‘A’ i.e. more is the enhancement.

• After a particular conc. Of ‘B’ any further addition doesn’t increase the mass transfer of ‘A’. This is due to change in viscosity. Because diffusivity is a function of viscosity.

2. Slow chemical reaction

Approximation: As the reaction rates are small CB & CAB are constant.

A B AB

AA A B AB

k C C k C

d CD k C C k C

1 1 2 2

1 2 202 1 2 1

sinh cosh

B B KC k x k x

Where K k C K k C

K C K B kLB K C K B

• Solving the above equation (1) by keeping CB & CAB constant we get

• Coupled transport:

kCu HX CuX H

Cu m HX HX H h

δa1 δa2δ0

1. Boundary layer resistance

2. Reaction between metal ions and carrier complex

3. Diffusion of metal ion complex

4. Reverse reaction takes place

5. Transfer to bulk phase of receiving side

• Here we assume that the thickness of membrane is very small & so we consider linear concentration profile

1 1 200

1120 0 1 1 2

DJ m m

DJ m m m

Cu HX CuX H

From kinetic data

R R k Cu HX H k CuX HX H

% % % % % % % % % % % % % %

Cases:

1. Fast interfacial reaction no resistance in the diffusion layer.

• Thus R0 – R0 = 0 and m1b = m1

1121 1 2

11 1 1 1 1

1 1 11 1

1 11 2 2

0 20 1

eq b eq

As R R

k Cu HX H k CuX HX H

k m HX h k m HX h

HXk hm m

k h HX

m k HX m k HXm

m k HXDJ

% % % % % % % % % % % % % %

FluxAs Permeability

k HXDP

a P HX

Log [HX]

Tanθ= 2

2. Slow chemical reaction & no resistance in diffusion layer.

• Thus m1b = m1 but R0 – R0 ≠ 0

• Net transported = Net reacted0 00

1 11 1 1 1 10

J J R R

Dm k m HX h k m HX h

% % % % % % % % % % % % % %

1 11 1 1 1 1 1

1 1 1 10 0

11 1 1

21 011 1 1

k m HX h k m HX hm

D Dk HX h k HX h

k m HX hDJ

Dk HX h

k HXDJThus P

DmHX h k m h

If HX Small Then

If HX L e Then P HX

Log [HX]

Tanθ1 = 2

Tanθ2 = 1

3. Slow reaction, resistance in the diffusion layer.

1 11 1 1 1 10

a m b m

m mJ D

D diffusivity of metal ion in aq phase

as J J

Dm mD m

D mD mm

and J J

Dm k m HX h k m HX h

11 11 11 11 1 1 1

1 1 1 1 1 1 1 10 0

11 1 1

111 1 1 1

m a m b m

m a mb

D D mD mm k HX h k m HX h

D Dm k HX h k HX h k m HX h

k m HX hm

D Dk HX h k HX hD

1 1 1 10 0

20 11 1 1 1

D DHX h k HX k h

k m HXDJ

D DHX h k HX k h

21 01 1 1 1

21 20 11 1 1 1

k m HXJ

HX h k HX k hD D

k HXJThus P

mk h k HX h HX

If HX Small Then P HX

If HX L e Then P HX

Log [HX]

Tanθ1 = 2

Tanθ2 = 0

Electro dialysis

• Electrically charge membranes are used to remove electrically charge species.

• Minimum two pairs are used.

• Basically this process is used where salts are present.++++++

1 Pair

Anion Exchange membrane

cation Exchange membrane

+ + ++ +

Cathode

It collects cations i.e. it is negatively charged

It collects anions i.e. it is positively charged

Cations

AnionsNormal tendency

Concentrated brines

Lean in brines

NaCl – Water solutionAEM AEMCEM CEM

(AEM) (CEM)

Applications:

1. Production of potable water i.e. Desalination.

2. Waste water treatment.

3. Removal of salts & acids from pharmaceutical solution. Also used them for food processing.

4. Removal of tartaric acid from wine.

5. Production of salt from sea water.

6. Water splitting using Bipolar membrane.

7. Membrane cell process for caustic soda production.

Bipolar membrane (BM)

H2O H2O

H+,OH-

Bipolar membranes:

• Made in one step. Consists of two layers, one is CEM & other is AEM.

• If it form by joining CEM & AEM then it will not work, because it will require very high potential to keep them altogether.

• Production of H2SO4 and NaOH

++++++

Cathode

H+,OH-

BMCEM CEMAEM AEM

Na+ Na+

OH-SO42-

Na2SO4

H2SO4 NaOH

CEM WaterBrine

OH-Na+

Dilute brine Conc. Caustic Soda (Na+ + OH- NaOH)

• We use high Electric Potential & hence water splits

• CEM are PEM:

1. Nefion per fluoro sulphonic acid

2. Flemion per fluoro carbon

3. Nefion + Teflon + Flemion

• Membrane cell process for caustic soda production:

• Ion Exchange Membrane (IEM) Properties:

1. High selectivity for opposite charged ions and high permeability.

2. Low electrical resistance.

3. High mechanical strength and stability.

• Types of IEM:

1. Heterogeneous membrane

2. Homogeneous membrane

• Procedures to produce Heterogeneous membrane:

1. Dry modeling

2. Polymer solution + ion exchange powder Cast the film Evaporate

3. Partially polymerized film + ion exchange powder Complete polymerization.

• Procedures to produce Homogeneous membrane:

1. Polymerization of mixture of reactants that can undergo condensation polymerization. One of reactants must contain a moety (charged group), can made up of anionic or cationic.

2. Introduction of anionic or cationic moety into a polymer by technique such as graft polymerization. Dissolve in solvent Cast the film And evaporate the film.

• Moety:

1. -SO32-, -CO2

-, -PO32-, -HPO2, -ASO3

2-, SeO3- for CEM

2. -NR3+, -R3N2

+, -R3P+, -R2S+ for AEM

Transport phenomena in electro dialysis:

• μi = Chemical potential in membrane phase

• μi’ = Chemical potential in solution phase

• i = anions/cations

• μi = μi’

Solution+

ln lni i iRT m RT Z ' ' '& ln ln

RT m RT Z

2 2' '.

(1) : in 2 ( )

sol Iin

Conc of anions in the membrane

Case Salt dissociate ions like NaCl

Where,

mi = molar Conc.

Ψ = Electrical potential (EP) in membrane phase

F = Faraday’s constt.

MR = Charge on membrane

Nernst Plank ion flux equation:

diffusion part

dcJ D Z

becoz of EP across the mem

Current carried out

by the particular ionTransport No

Total current

i iJ F Z

I i iJ

F Z i iJAEM CEM

Ideally t+ = 0 t+ = 1

Ideally t- = 1 t- = 0

Really t+ = 0.04 t+ = 0.95

Really t- = 0.94 t- = 0.05

This should be as

low as possible

1. Cations flow in a Cation Exchange Membrane (CEM):

Cathode

x = 0 x = δx = δ1x = 0

Cation

C’D,b

C’D,m

C’B,m

C’B,b

C’D,b

Dilute

Solution

t iFlux in Solution Feed

FluxduetoEP

t iFlux in membrane

t+ is large and D (dc/dx) is very small in membrane

Dilute side

Brine side

,As Flux in Solution Flux in membrane

t idcD

F dx Z

in membrane in solution

At x c c

'0.95 & 0.5t t

' ', , 'D m D b

c D Zi

' ', , 'B m B b

For brine side

For limiting current

• If Electric Potential (EP) increases then ‘i’ increases & thus (t+ - t+

’) will increase gradually & a point will reach the C’D,m = 0 & if ‘i’ further increases then water will start splitting & electro dialysis will not take place.

• Normally we use 75 % of ‘ilim’

• Diffusion is negligible & most of transport is due to EP

In each pair of AEM & CEM, we need to find the local fluxes, then integrate these fluxes

2. Flow of anions through Cation Exchange Membrane (CEM)

Cathode

Anions

C’D,b

C’D,m

C’B,m

C’B,b

3. Flow of cations through Anion Exchange Membrane (AEM)

Dilute side

Brine side

Cathode

Cations

C’D,b

C’D,m

C’B,m

C’B,b

Dilute side

Brine side

++++++

'0.04 & 0.5

in membranein solution

4. Flow of anions through Anion Exchange Membrane

Cathode

Anions

C’D,b

C’D,m

C’B,m

C’B,b

Dilute side

Brine side

++++++

Gas separation• Monsanto Composite Hollow Fibre

• Different producers of membrane: Dow, DuPont, Air product, Union carbide.

• Conditions for application:

1. Feed stream in the range of 4.2 × 103 to 57 × 106 m3/day

2. Moderate concentration of more permeable gas in the feed i.e. 10 to 85 %

3. Moderate high pressure i.e. 18 to 137 atm

4. Moderate temperature i.e. 0 to 65 0C

5. Acceptability of moderate recovery i.e. less than 97 to 98 %.

• Applications:

1. H2 recovery from purge gases.

2. CO2 separation e.g. Tertiary oil recovery.

3. Air separation: (a) N2 enriched (b) O2 enriched air

4. SO2 removed from smelter gas

5. H2S & water removal from natural gas.

6. NH3 removal from recycle stream in Ammonia synthesis.

7. Olefin / Paraffin separation in hydrocarbon processing

8. Pollution control: (a) Hydrocarbons (b) Chlorofloro carbons

9. Dehydration of natural gas convention: Glycol dehydration process Benzene, Toluene

Low Pressure Side

High Pressure Side

Reject

• There should not be any pin hole in the membrane

Transport Mechanism:

1. Knudson diffusion

• lA + lB > rP, lA & lB are mean free path, rP = Pore radius

• Permeation α 1/√MW

• Air + CO2 CO2 has less permeation

2. Molecular sieving

• Pore radius < 7 Å

3. Solution – Diffusion Mechanism

• Diffusion coefficient can not assumed to be constant and are function of concentration in membrane, position and may also be of time.

Solution – Diffusion Mechanism:

• If T < Tg polymer becomes crystalline

1. Type I diffusion

• If T > TC (Critical temperature), T > Tg (Glass transition temperature)

(a) Henry’s law is obeyed

(b) Diffusion coefficients are constant

2. Type II diffusion

• T < TC , T > Tg

• All simple gases with low critical temperature as compare to ambient temperature. E.g. Diffusion of C4 in natural rubber

(a) Henry’s law is obeyed

(b) Concentration dependent diffusion coefficient

dcJ D Non fician

3. Type III diffusion

• T ≤ TC, T < Tg

• E.g. Organic vapor of C5 – C8 in Polyethylene

(a) Henry’s law is not obeyed

(b) Concentration dependent diffusion coefficient

4. Type IV diffusion

• T > TC or T < Tg

• Unexplainable situation

• E.g. Organic vapors in ethylene cellulose

(a) Henry’s law is not obeyed

(b) Diffusion coefficients are concentration and time dependent

Permeability of gases:

x = 0 x = δ

PhiPli

Low pressure side

High pressure side

i i hi li

hi hi hi

li li li

J dx D dc

J D dc if flux is constt

If D constt

J D c c

c k Pif Henry s law is applicable

hi li i

i i i hi li

i ii hi li

ii hi li

Let k k k

J D k P P

D kJ P P

P k D Permeability

PJ P P

As J D dc

if D is not constt then

J D c c

Where Dc c

hi hi hi

li li li

hi li i

ii hi hi li li

i hi hi li li

ii hi li

i hi hi li lii

c k Pif Henry s law is applicable

if k k k

Then P D k

if k k

Then J D k P k P

DJ k P k P

PAs J P P

D k P k PP

• As temperature increases the permeability is also increased & reverse behavior is also observed

• Cohen & Turnbull (Fujita) Free – volume theory

Ph >> Pl

Henry’s law is applicable

f f s s

D ARTV

V V V T T P P

P C T k PV

• Vf = Total free volume available

• Vf* = At std. state (no gas inside polymer)

• V = Volume occupied by gas

• K0 = Solubility using Henry’s law

• γ = Conc. Coefficient

• α = Thermal expansion coefficient

• β = Compressibility coefficient

P vs P

P then P

P then P Constt

Calculate T from following equation

If T T

As T then P

If T T

As T then P

Engineering consideration in gas permeability:

• Gas permeation unit: Stage cut (θ), Temperature (T), Permeability (Pi), Flow pattern

• Stage cut (ϕ): Amount of feed that is allowed to permeate through membrane

Un permeate stream

Permeate stream

Membrane

Low pressure side

high pressure side

• Membrane properties:

1. A high permeability towards a specific component to be separated from a gas mixture and high selectivity for this component relative to other components in mixture.

• Pi = ki Di

• Separation will be if

(a) ki’s are different and Di’s are same

(b) Di’s are different and ki’s are same

(c) Ki’s as well as Di’s are different most desirable condition

2. Chemical inertness and physically stable

3. Absence of pinholes or other mechanical defects.

• Separation factor:

PSelectivity

Where P Permeability of A

and P Permeability of A

If then A comes as permeate

If then B comes as permeate

Michaels (1966)

1. A membrane is selectively permeable towards that component of gaseous mixture that has highest critical temperature, the smallest molecular diameter or both.

2. Selectivity of membrane invariably decreases with increasing temperature (fluxes increases with temperature).

3. Stiff chain polymer membranes although less permeable gases than flexible chain polymer of similar chemical constituent, are more selective towards smaller molecules relative to longer ones.

Flow patterns:

1. Fully mixed flow pattern

• Least efficiency

• Driving is force same every where Feed

Composition is same due to mixing

Un permeated stream

Permeate stream

Composition is same every where

2. Cross flow pattern

• Driving force is different every where

3. Co – current flow

4. Counter current flow

• Highest efficiency

Compositions are different every where

Un permeated stream

Permeate stream

Compositions are different every where

Un permeated stream

Permeate stream

Feed Un permeated stream

Cross flow pattern

Co – current flowCounter current flow

For fully mixed flow (solved by Weller (1950)):

• A – B two component system

• POA Permeability of ‘A’, POB Permeability of ‘B’

• ϕ = Stage cut

• A = Area of the membrane

Lol, yoA, yoB

Loh, xoA, xoBLil, yiA, yiB

oAA h oA l oA

oAol oA A h oA l oA

ol oB ol oA

If known find A y

If A known find y

Amount of A out L y

PJ P x P y

APL y AJ P x P y

As L y L y

1 1 1 2

11 1 1 6

oBol oA h oA l oA

ih oh ol

ih iA oh oA ol oA

ol ol oA

ih oBoA

oA h oA l oA

APL y P x P y

L L L overall mass balance

L x L x L y

L L PAL PP

y P x P y

and from

y P x P y

5 & 6 ,

loA oA

lih iA oh oA ol oA

oh l oliA oA oA

ih h ih

liA oA

Adding we get

PL x L y L y

L P Lx y y

If is known

Find from and A can be calculated as

If A is known

LFind from

and from can be calculated

UltrafiltrationApplications:

1. Metal finishing: Electro paint, Oil/Water emulsions, Spray paint

2. Dairy: Whey protein, Protein in milk

3. Pharmaceutical: Recovery of enzymes, vaccines, plasma proteins, antibiotics, pyrogens, membrane reactions

4. Food: separation of potato starch, egg white, gelatins, juice classification

5. Textile: Removal of dyes, sizing chemicals

6. Pulp & paper: Removal of lignin compounds

7. Chemicals: Waste polymer, waste latex

8. Leather working: Tannery waste

9. Sewage treatment

10. Water (treatment) purification: Removal of bacteria, pretreatment for RO

Concentration polymerization:

• Membrane is semi permeable

• Solute is retained at membrane surface

• Gel formation on membrane surface takes place

Gel layer

Work as RO

Limiting flux

Membrane fouling:

• If module is operated at high fluxes, some of the particles go inside the membrane and the membrane gets permanently damaged

Commercial membrane:

• Polyamide, polysulfone: phase inversion technique

• Limited PH range

• Temperature 80 0C to 90 0C

Time (hr)5 hr 20 hr

• ∆P = fixed

• Due to membrane fouling

Concentration polarization

Membrane fouling

Carbosep membranes:

• Tubular membranes made of micro porous carbon

• MW: 20,000

• PH: 0 to 14

• T: Can be used till 120 0C

• Pressure: 20 atm

Micro porous carbon

Coating from inside of 20 μm Zirconium oxide

Membrane transport model:

Permeability

For other solvents

• ηw = Viscosity of water

• LP* = Standard permeability

• α = Standard permeability coefficient

Phone – poulene membrane

Solvent

LP* = 10-12

Methanol 1.0

Acetone 1.0

n – Heptane 0.7

Toluene 0.9

Dioxane 0.05

• Concentration polarization less than the limiting flux

s v sDiffusion part

Convective part

cR and

From Kedem Katchelky Model

J W J c

1 1ln ln

obs obs

1 - Robs

Pore Flow Model & Hindrance Transport Model for Ultra filtration:

Z = δ Z = δ

JV (m/s)

V = Vavg

ss c s d

s sz z

sd c s s

sd c s P

dCN k VC k D

D diffusion transport in bulkdz

i e free from hindrance

C CPartition coefficient

dCk D k VC N

k D k VC VCdz

Ns = Flux of individual component i.e. solute moving inside a pore

D∞ = Diffusion coefficient in free solution

kc & kd are convective & diffusive transport correction facto i.e. hindrance factor

c s P dC

c s P Cc d

c s Pz c

c s P dz

c P P c

c f P d

dC Vdz

k C C k D

Vk C C z

k C C k V

k C C k D

k C C k V

k C C k D

J V where porosity in membrane

C CR R

c f P d

k C C k D

1, . .

k DLet P i e P

1 1, exp

R F FR

F JR where F

• Same as Spiegler – Kedem model

• But here reflection coefficient σ and permeability are depends on thickness and hindrance factor

Pervaporation

• Pervaporation = Permeation + Evaporation

• Vacuum is applied on permeate side and the permeate is removed in vapor form

• Partial pressure on permeate side should be as low as possible

Liquid

Vacuum

Pervaporation

(Permeate)

Liquid

Carrier gas + Pervaporation

Liquid Permeate

Carrier gas (N2, He etc. ) to reduce mole fraction i.e. ultimately partial pressure

Condense

Pervaporation

Mole fraction of water in liquid form

Mole fraction of w

ater in vapor form

Water – Dioxane mixture

Advantages:

1. No additive is required

2. Low energy demands, because only permeating component needs to be evaporated

3. Closed loop operations are possible, as small volume of permeate needs to be recycled

4. Lower capital cost as compared to distillation

Membrane:

1. Polyvinyl Alcohol (PVA) Hydrophilic membrane Water >> MeOH > EtOH >> Other organic components absorbing power

2. Silicone composite Hydrophobic (Organophilic) MeOH > EtOH > Aldehydes > Ketones >> Water

3. Modified Cellulose Esters Use for separation of two organic compounds Aromatics > Paraffins Olefins > Paraffins

Diens > Olefins n – Paraffins > Branched Paraffins Low MW Paraffins > High MW Paraffins

Potential Applications:

1. Mixtures that are difficult to separate by conventional techniques such as azeotropic mixtures

2. Separation of heat sensitive products such as in food industries

3. Elimination of traces of impurities

4. Enrichment of organic pollutants for quantitative defection

5. Drying of natural gas obtained from offshore

wFeedw

w Pervaporatew

should be Or

• Mass transport within membrane and membrane selections:

1. Solvation of permeating molecules on a liquid side of the membrane

2. Diffusion of these molecules through the membrane

3. Evaporation from vapor side of the membrane

Anisotropic swelling: Nonlinear expression for solubility as well for diffusion coefficient

Liq. Vapor

Swelling

ϕ”ϕ’

Anisotropic swelling occurs in case of pervaporation

dxFraction of penetrant within the membrane

if D Constt sp

p pJ Ds

p pJ P

Where P Permeability

' ' " "

' ' ' " " "

0exp exp

J dx D g d

DJ g g

DJ g s p g s p

where s p s p

1. Downstream pressure is determining parameter in fixing the flux, where the upstream pressure has very little effect

2. When temperature is raised, the fluxes increased following Arrhenius like relationship

3. Because both solubility and diffusivity are functions of concentration of both component of the binary mixture , a complex transport occurs. In general the flux decreases when the mixture becomes poorer in A, where A is more rapidly permeating species and loses its swelling properties, simultaneously selectivity increases.

Calculation of temperature drop:

( F – V )

" ",A BV w w

, ,& .

v A v B

H Heat of vaporisation of A

H Heat of vaporisation of B

H H assume constt

but it changes with temp

' ' ' ' " ", , , ,

" ", ,

' ' ' ', ,

", , ,

' ' ' ', , ,

' ' " "

' ', , , ,

P A A P B B v A A v B B

v A A v B B

P A A P B B

v B v A v B A

P B P A P B A

B A B A

v A v B P A P B

F C w C w T V H w H w

H w H wVT

F C w C w

H H H wVT

F C C C w

w w w w

Let H H C C

By heat balance i.e. the amount of heat the liquid has lost = Heat gained in vaporization

if component B is water then

Fif Stage cut

then T C

• Thus, we have to put a heat exchanger say after ∆T=20 0C i.e. we need inter stage heater

Dialysis

• It is a membrane process in which compounds having different molecular weight are separated through membrane

• Driving force is concentration gradient

• Fluxes are very small

• Advantages (used when):

1. Concentration polarization phenomena is high

2. The external forces are damaging to the fluid being treated

• Applications:

1. Homodialysis: Artificial kidney

2. Alchohol reduction in beer

Q’out, C’out

Q”in, C”in

Q’in, C’in

Q”out, C”out

' ' ' ' " " " "

' ' ' "

in in out out out out in in

in out

in in in out

Lost by feed side Gained by dialysate

Q C Q C Q C Q C

Dialysates

MD M Over all mass transfer

Extraction ratio

Q Q C C

Actual removal

Max amt that can remove

Feed side

Dialysate side

Counter current

2 1C1S

C2mC2S

k’k”

dAC”

Q’, C’

C’ + dC’

' ' " "

' "' "

1 1 1 1

smim m

sm sms s m

DN C C

lkD kD

C C where kl l

k k k k

dM k C C dA

Q dC Q dC

dC dC d MQ Q

d C C d MQ Q

' " ' "

in out

oin out

in out in out out in

in out in in out out

d C d MQ Q

C C MQ Q

For counter current

C C C C C C

For co current

C C C C C C

d CQ Q

k CdAQ Q

Q’out, C’out

Q”in, C”in

Q’in, C’in

Q”out, C”out

Feed side

Dialysate side

Co – current

out in outo

oin out

in out

d Ck dA

Integrating both sides

d Ck A

C C Ck A

C MC C

M k AC

M C k A

Q QHere flow rates are assumed

to be same throughout

1 exp 1

Once M known

DFind E

N ZE For co current

N ZE For counter current

Z=0.25

Counter current Co – current

Variations of dialysis:

• In spite of normal membranes, charged membranes are used

1. Donnan dialysis

Conc. H2SO4

Stripping side

a aRatio of activities

2. Ion exchange dialysis

CuSO4, H2SO4H+

Cu++4SO

4SO Weak type anion exchange

i.e. only H+ not other cation can pass

Prevents cation to pass through

Weak type AEM

• New applications of micro porous membranes:

1. Gas absorption and stripping

2. Membrane based solvent extraction

3. Membrane distillation

• Conventional process:

1. Packed column

2. Fluidized bed columns

3. Bubble column

4. Trickle bed reactors

5. Spray tower

6. Venturi scrubbers

• Problem associated with conventional process:

1. Flooding, 2. Weeping, 3. Priming, 4. Foaming, 5. Entrainment, 6. Dumping

New applications

1. Gas absorption & stripping:

Micro porous hydrophobic membrane

gas Liq (aq.)

Immobilized face

Pg Paq

• In this case water (aq.) will not go in membrane pore

• To avoid bubble formation through liq Paq > Pg

• But if Paq be too large then it break through gas phase Paq – Pg = ∆Pr < (2r cos θ) / rP

Micro porous hydrophilic membrane

gas Liq (aq.)

Immobilized face

Pg Paq

• In this case pore (membrane) will be occupied by water

• To liquid can’t breakthrough the gas Pg > Paq

• To gas can’t bubble through liquid Pg – Paq = ∆Pr < Breakthrough press.

Advantages:

1. The gas and liquid flow rates can be varied independently [i.e. there is no problem of weeping, flooding etc.]

2. The gas/liquid interfacial area is known (a priority), since membrane area is known

3. All membrane surface area is available for contacting even at very low flow rates

4. Scale up is easier

5. Offer very high surface area

6. No moving parts required

2. Membrane based Solvent Extraction:

Micro porous hydrophobic membrane

Org Liq (aq.)

Immobilized face

Porg Paq

• In this case organic compound not water (aq.) inside membrane pore

• Paq > Porg

• Paq – Porg = ∆Pr < Break through pressure

Micro porous hydrophilic membrane

Org Liq (aq.)

Immobilized face

Porg Paq

• In this case pore (membrane) will be occupied by water

• Porg > Paq

• Porg – Paq = ∆Pr < Breakthrough press.

Gas membrane:

• Pores are filled with membraneLiq1(aq) Liq2(aq)

Hydrophobic

Osmotic distillation:

• Driving force = Osmotic pressure (This is finally related to concentration)

• Pw1 > Pw2

Hydrophobic

Low osmotic

solution (aq)

High osmotic

solution (aq)

3. Membrane distillation:

• Here temperature is driving force

Hot solution

(more salt)

Cold solution

(less salt)

Membrane Technology Lecture1-42

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