Membrane Technology Lecture1-42
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Transcript of 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
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
• 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
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
• 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
Feed
RejectPermeate
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
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
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
40 0C 80 0C 140 0C
Temp. Limits:
CA
PS, PA
Ceramic (130 0C)
0 7 14
Ceramic
PS, PA
CA
PH Limits:
Working Range
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
Chlorine (ppm) 1
10
Time of exposure
PS
PA
CA
Chlorine limits:
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
CA PA PS Ceramic
Water
Acid
Alkali
Butanol
Ethanol
Solvent Stability:
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
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)
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
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)
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
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.
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
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.
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
a). Addition of Precipitants:
• Precipitating agent: Mostly water , Air.
Polymer
Solvent Precipitate
AB
CTwo phase
region
Homogeneous region
• Porous membranes are obtained
Phase inversion diagram
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
b). Solvent evaporation:
• Solvent should be volatile.
• Allow solvent to evaporate (for pore formation).
Polymer
Solvent Non-solvent
Phase inversion diagram
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
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.
T1
T
Polymer + SolventSolvent rich
phase
Polymer rich phase
Polymer SolventPhase inversion diagram
• e.g.: Polypropylene membrane dissolved in N,N-bis-(2-hydroxyethyl)-tolylamine.
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
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
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
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.
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
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):
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
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.
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
1. Induced concentration gradient:
• At surface concentration is minimum.
• Under beneath concentration is higher.
A*A B
C
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
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
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.
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
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.
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
1. Sol-gel Process:
Alkoxide (metal salts, metal organics)
May be acidic, basic, aqueous media or in organic phaseHydrolysis
Condensation polymerization
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
• 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
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
• 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
Gel
Drying 50 0C Sintering
Ceramic layer
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
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
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
*
i
i
v V
v V
1 2 3* 1 2 3 1
1
......
n
iinn i
nmix
ii
c vc v c v c v c v
VC c
1 2 31 2 3 1
1
....
n
iinn i
nmix
ii
vv v v v
V
Mass average velocity:
Molar average velocity:
• Hypothetical velocities, it can’t be measured by instrument
Diffusion velocities of component ‘i’
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
* *
( )
( )
i ii
i i i
i ii
i ii
n v
N c v
J v V
J c v V
• Mass flux (Absolute) =
• Molar flux (Absolute) =
• Mass diffusion flux =
• Molar diffusion flux =
• Relation between absolute flux & diffusion flux:
1
*
1
n
i j iij
n
i j iij
n w n J
N x N J
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
1
1
1
1
1
( )
i i
i ii i i
n
jjj
i i i n
jj
ni
i i jnj
jj
n
i i jij
v v v v
v v v v
v
n J
n J n
n J w n
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
* *
* *
1*
1
*
1
1
*
1
( )
i i
i ii i i
n
jjj
i i i n
jj
ni
i i jnj
jj
n
i i jij
v v v v
c v c v v c v
c v
N J cc
cN J N
c
N J x N
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
Equation of continuity
ri (gm/cm3-s)
vi (cm/s)
ρi (gm/cm3)
z
x
y
∆y∆x
∆z
• 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
t
i iz i iz iz z zv x y v x y r x y z
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
( )( ) ( ) ( )
( )( ) ( ) ( )
( )
i iyi i ix i izi
iyi ix izi
ii i
vv vr
t x y z
nn nr
t x y z
n rt
• Dividing both sides by ∆x ∆y ∆z & taking ∆x 0, ∆y 0, ∆z 0
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
11 1
12 2
( )
( )
( )
( )1, (1)
( )2, (2)
( ), ( )
ii
ii ii i
i i
i ii i i i
ii i
nn n
MM rn
M Mt M M
c MN M RM
t
cN R
t
i n rt
i n rt
i n n r nt
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
1 2
1 1 1 21 2
1 21 2
( )( ) 0
( )
( )0
n
n nn
nn
n n nt
n n n v v v
v v v
v
vt
vt
• Adding above equations:
• This is known as equation of continuity
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
*
A A AB A
A A AB A
J D w
J c D x
• Fick’s law
• Valid only for binary system
• DAB = DBA
*
i i im i
i i im i
J D w
J c D x
• General equation of Fick’s law
Fick’s Law
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
*A A AB AJ c D x
*AB
A A A
DJ c
RT
, ,j
t
ii n T P
G
x
• Concentration difference – only driving force
• Chemical potential – main driving force
Chemical potential
This equation gives better result
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
ln
ln
d RTd P
RTd f
ˆln (1)
ˆln (2)i
i i
o oi
d RTd f
d RTd f
,
ˆln
ˆˆ
ˆln
ˆln
i
i
i
i
o ii o
ii i io
i
oi i
oi iT P
fd d RTd
f
fa x
f
d d RTd a
RTd a
Ideal gas
Real gas or Liquid
Mixture
Pure
• By (1) – (2)
• f = Fugacity
• a = Activity
• γ = Activity coefficient
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
*
*
ˆln
ln( )
ln
A A
A A
A A
AA
ABA A A
A
A A AB A
RT a
RT x
RT x
RTx
x
D RTJ c x
RT x
J c D x
γA=1, for ideal solution
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
• If pressure changes
*
*
*
ˆ, , ln
ˆ
ln
1
AA
T
o o oAA A A
A A A A
AA A
AAA
A ABA AAB A A
A
ABA AAB A A
ABA AAB A A
VP
T P T P RT a V P P
a x x
RT x V P
RT x V Px
c DJ D x c V P
x RT
DJ cD x c V P
RT
DJ cD x c V P
RT
For ideal gas,γA=1
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
1
P1
CB1
CA1
2
P2
CB2
CA2
X=δ
X=0
Semi permeable membrane
*
2 1 2 1
1 2 2 1
1 2 2 1
* 2 1 1 2
** 2 1 1 2
* 1 21 2
0
A ABAA AB A
A A ABAAB A
B B ABAAB A
B B ABAAB A
B B ABAA AB A
B B ABAA AB A
B B
A
dx D dPJ cD c V
dx RT dx
x x D P PcD c V
RT
cx cx D P PD c V
RT
c c D P PD c V
RT
c c D P PJ D c V
RT
c c D P PJ D c V
RT
c cP P
c
1 2
*1 2 1 2
B BA
RT c RT c RTV
P P
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
*
*
A AB AA A
A
B BA BB B
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
RT RT
Dc F
RT
DJ c F
RT
ZA = Charge
F = Faraday’s constant
µA* = Electro-Chemical
Potential
Ψ = Electrical Potential
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
• Temperature gradient Mass flux Sorret effect
• Concentration gradient Heat flux Dufour effect
• In Presence of Thermal Gradient:
*lnTAB
A A A A
TA
DJ c D T
RT
D
Thermal Diffusion Coefficient
• Thermal & Electrical effects are not significant
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
Theory of Irreversible Thermodynamics
11
22
33
nn
J X
J X
J X
J X
Flux
Forces
• Onsager 1931
• Works when system near to equilibrium
1, 1
1
1
1 2 31 11 12 13 1
1 2 32 21 22 23 2
n
ji
i j
n
ii
i
n
ii ikk
nn
nn
T J X
J X
J L X
J L X L X L X L X
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
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
• Lik (Phenomenological coefficient) determined by experiment.
• Theory of Irreversible T/D doesn’t say anything about Lik.
• Relation between Lik :
2
0ii
ii kk ik
ik ki
L
L L L
L L
• Curie principle : Flux Ji will depend on driving force xJ iff they have the same tensorial order or they differ by 2.
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
Force
Flux V T C
µ × × q × k DA
T
J × DAT DAB
J1 µ1’
J2 µ2’
µ1 ∆ µ1
µ2 ∆ µ2
∆x 0
x
0
iidx
x
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
1
0 0
0
1 1 2 2
1 11 1 12 2
2 21 1 22 2
[ ( )]
( )
n
i ii
x x
im i
xi
i i i
J
dx J dx
J dx Jx
J J
J L L
J L L
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
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.
1, 1
,
,
( )
ˆln
ˆln
ˆln
ln ln
1
nj i
ii i ji j ij
i i
i i
i T Pi i
ii T P i
ii
i i i i i
i ii
i i
v vx d x x
D
d RTd a
RT a
cRTd c
cd
cRTc
RT acRT
x x x x
x xx
d x
Concentration is the only driving force
(Assuming ideal mixture)
Dij = Binary diffusion coefficient
vi, vj = velocities
xi, xj = concentrations
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
• For two component mixture :2
1
1 11 1
2 1
1 212
2 12 1 1 21 2
12 12
2 11 1
12
1 2 112 1 1
1 1 21 12 1
( )
( )0
( )
(1 )
( )
( )
j
jj j
v vx x x
D
v vx x
D
x N x Nv vcx x
cD cD
x N x N
cD
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
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
• For three component mixture :
31
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
( ) ( )
j
jj j
i ik i
i ik k
v vd x x x
D
v v v vx x x x
D D
v v v vd x x x x x
D D
J L x
x R J
In Stefan-Maxwell Forces are given in terms of Flux.
In Theory of Irreversible T/D Flux is given in terms of Forces.
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
1
1
1
1
1
(1)
& ( ) (2)
( )1
n
i ji im ij
n
j iij
iim
ni j
j iij ij
ni j
j i
j ij
nim
j iij
N x N cD x
x N N
xcD
x xx v v
D
x xv v
D
cD x N N
By solving (1) & (2)
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
• 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
1
1
1 1
1
( )1
ni j
j i
j ij
nim
j iij
n nj ii j i j
j jij ij
n
j iij
x xv v
D
cD x N N
x x cv x x v
cD D
x N N
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
1 1
1
1 1
1 1
1
1 1
11
11
1
1
1 1
1 11
n nj j
ii ij jij ij
n
j iij
ii ii i
iim i
ii
iim i i
im i
im i
xNx x v
cD D
x N N
xNx x vcD D
cD x N N
x N x N
cD cD x N N
xcD cD
D D
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
1
1
1
1
1
1
( )1
1( )
( )1
ni j
j i
j ij
nim
j iij
ni j
j i
jij
n
j iij
nij ji
j
nij
j iij
x xv v
D
cD x N N
cx xv v
D c
x N N
x Nx N
c c
D x N N
2. If Dij’s are same
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
1 1
1
1 1
1
1
1 1
1 1
1 11
n nij ji
j j
nim ij
j iij
n n
j ii jj j
nim ij
j iij
n
jjim ij
im ij
x Nx N
c c
cD D x N N
x N N x
cD cD x N N
xcD cD
D D
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
3. Components 2, 3, 4, …, n are moving with same velocity.
i.e. v2 = v3 = … = vn = v & v1 ≠ v
1
1
11
1 1
111
1
111 1
111
( )1
( )1
( )
(1)
ni j
j i
j ij
nim
j iij
nj
j
j j
nm
j
j
nj
j j
n
j
j
x xv v
D
cD x N N
x xv v
D
cD x N N
xx v v
D
x N N
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
1 1 2 3 11 1 1 2 3 11
1 11 1 1 2 1 3 1 1
11 1 1 1
11 1
111 1
11 1
[ ... ]
[ ... ]
[ (1 ) (1 )]
(1 )( ) (2)
( )1
(1 )( )
(1
n
j nnj
n
nj
j j
im
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
D
cD cx x v v
1
1 1
) nj
jim j
xx
D D
(From 1 & 2)
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
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.
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
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.
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
Membrane modules:
1. Flat sheet membrane:
• Plate & frame module
Rectangular or Hexagonal shape, 30-40 plates required
• Spiral bound module
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
• Illustration of a spiral-wound module
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
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
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
• Flow directions inside the shell of a hollow-fibre module
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
• Flow pattern in a parallel-flow hollow-fibre module (fibre-side feed).
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
• Flow pattern in a radial-flow hollow-fibre module (shell-side feed).
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
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
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
• Osmotic pressure
' ''
' ''( )
i i
i i i
c RT
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
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
• Expression for work required to separate salt from water
Water(2) (pure)
Salt + Water(1)
Salt
'
'
'
(1)
( )
( )
(2)
(3)
dQds
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
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
'
,
',
',
'1 2
' '2 1
' '1 2
(4)
( ) (5)
( )
( )
T P
T P
T P
Tds dU PdV dw
G H Ts
U PV Ts
dG dU PdV Tds
dG dw
dG dw
G G w
G G w w
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
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
Transport Model
Support
Dense Layer
Z = 0
Z = LLow pressure
sideHigh pressure
side
CijC22
(C22)m
Feed
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
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
Film Theory ModelAssumptions:
• Turbulent flow
• All mass transfer resistance lies in a film near the surface
• Film is stagnantMembrane
Film
C21= Conc. At high pressure side
C21= Interphase Conc.
C23
(C23)m
(C22)m
Z = 0
Z = δ
C22
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
2c
t
0
2 2N R
0
22 2
22
*
1
22 2 1 2 21
0
0 .
,
( ) (1)
yx z
zz
ii i jj
z z z
NN N
x y z
NN Constt
z
as N x N J
xN x N N cD
z
• By equation of continuity
At steady state
Considering only z direction
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
22
21
2 1 2 23
221 1 2 2 23
2 1 2
2 23 21
1 22 23
21 0
22 23 1 2
21 23 21
22 23 1 2 1 2
21 23 21
, ( ) (2)
( )( )
ln( )
ln
ln( / )
z z z
z z
z z
zx z zx
z
z z
z z z z
also N N N x
xcD N N x x
zdx N N
dzx x cD
N Nx x z
cD
x x N N
x x cD
c c N N N N
c c c D ck
k
21
22 23 1 2
21 23
/
exp z z
D
c c N N
c c ck
From (1) & (2)
After integrating both sides
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
• (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
23
22
21
0
exp ( )v
c
JcA
c k
• 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
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
C21= Interphase Conc.
C23
(C23)m
(C22)m
C22
C21
• 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
21 23
2exp vc c J Sc
c c f u
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
22 23 23
22 22
21 23 23
21 21
22 23
21 23
22 23 21 22
22 21 23 21
2322
23 21
23
23 21
22
1
1
, exp
exp
1exp
1exp
obs
v
v
v
obs
v
obs
c c cR
c c
c c cR
c c
c c Jas
c c k
c c Jc c
c c c c k
c JcR
R c c k
c JRcR c kc
• Rejection:
What membrane actually does
We can observe this
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
1(1 ) exp
(1 )
(1 ) (1 )exp
1 1ln ln
vobs
obs
obs v
obs
obs v
obs
JRR
R R k
R JR
R R k
R JR
R R k
• 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
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
Solution Diffusion Model
C23
(C23)m
(C22)m
C22
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
111
11 1 1
1 11 1
2 22 2
(1)
ln
ln
ln. . (2)
(3)
&
ii i i
i ii
iii
x x
DN c
RT
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)
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
1
21
1 11 1
0 1
11
11 1 2 11
0
11 1
11 1 21
0
1
01 1
0
ln
ln
ln (4)
ln
l
x
x x
x
x x
x
x xcritical N
x
DN dx c RTd a v dP dx
RT
aDN x c RT v P P
RT a
ac DN RT v P P
xRT a
aRTP
v a
RT
1
1
10
1 11 11
1
11 1
n (5)
,
x x
x
av
a
c DN v v P
xRT
N A P
c v Dwhere A
xRT
From (2) & (3)
From (4) & (5)
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
2 22 lnd RTd a v dP
0
22
2 2 2
2 2
2
2 2 22
2 2 22
2
2 22
2
2 22 2 2
ln
ln ln
,
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
x dx
dcx dcN D D
dx dx
For ideal dilute solution
γ2 = 1 For ideal solution
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
23 222 2
22 232 2
22 231 2
22 23
1 2
22 232 2
22 22 23
2
2
( ) ( )
( ) ( )
( ) ( )&
( )
,
m m
m m
m m
c cN D
xc c
N Dx
c ck k
c c
k k k
kc kcN D
xD k
N c cx
N B c
D kwhere B
x
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
Kimura – Sourirajan Model• Kimura – Sourirajan Model also gives:
1
2
22 23
22 23
1
1
2
( )
( )
. ,
( )
,
0
s
N A P
N B c
f c c
i e bc
b c c
For pure wter
N A P
N P
N B c
The value of A & B different for SD Model & KM Model
N1
∆P
θ
A = Tanθ, we can find A
We can’t find B because we can’t measure C22
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
Kimura – Sourirajan analysis:
1 22 23
2 22 23
22 23 1 2
21 23
2
23
22
2. { ( )}
3. ( )
4. exp
Find 'k'
1 1ln ln (1
1. Find 'A' from pure water permeability data
)
1 1
obs v
obs
N A P b c c
N B c B c c
c c N N
c c ck
R JR
R R k
cNc
Rc
1 2
22
22 232
22 22
( )1 1
v v
N N
c
B c cN
J c J c
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
23
22
1 1
1
1 1
1
1
1 11 1 1 (2)
1ln ln From (1) & (2)
1ln ln
v
v
v
v
v v
obs v
obs v
obs vv
obs
cBR
J c
BR R
J
BR
J
RBJ
R B B
R R J J
R JB
R J k
R JJ B
R k
ln B
θ1ln obs
vobs
RJ
R
Jv
From Tanθ = 1/k
1ln obs
vobs
RJ
R
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
• K = a Qb
• Q1 K1, Q1 K1, Q1 K1, …..
a
θln k
ln Q
• Turbulent b = 0.8
• Laminar b = 0.33
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
Kedem – Katchelky model• Based on Theory of Irreversible Thermodynamics (1954)
• Its 3 Parameter Model
1
10 0
10
0
[ ( )]
[ ( )]
Ma
Biological memb
ss Transfer only in x direction (Assume)
[ ( )]
ranes very near to equilibriu
[ ( )]
mn
i ii
x x n
im ii
x n
m ix i xi
xn
ix i xi
J
dx J dx
J dx
J d
x
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
0
00
1 2
( )
( , ) (1)
ˆ, , ln
ˆln
&
xn
ixi
xn
ix i i i ix x xi
m w w s s
w ww w wp s
s pw w pp s
m
o o oii i i
ww w
s
dJ dx
dx
dJ dx
dx
J J w water s salt
J L L
J L L
J c J p
T P T P RT a V P P
RT a V P
RT
ˆln ssa V P
Js
Jw
∆μw, ∆c
∆μw, ∆p
x = ∆x x = 0
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
w
0
0 0
ˆ ˆln ln
ˆ ˆln ln (2)
ˆln ln ln ( For ideal solution =1)
ln(1 ) ln(1 ) ln(1 )
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
a x x
x x x
x x c x c xc
0
1 1( )
ˆln
s s sx x x
sw
c c cc c
ca
c
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
0
ln
0ln
ln 0
ln
ln
ˆln ln
ln ln
ˆln
ln
1 1
s s
s sx x x
s
s
s ss x x xs s
s s x
s x x
w sm w s w s ss
s ww sm w s
s
m v
a x
x x
x c
x c
c cca c
c c
c
J V J V P RT J J cc c
J JJ V J V P
c c
J P
DJ
From (2)
• JwVw = vol. flux of water
• JsVs= vol. flux of salt
• Vi = partial molar vol. of i
• Jv = vol. flux
• JD = Drift flux
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
ln
(3)
( )
1
v P PD
D DP D
PD DP
PDv P
P
P
PD
P
D P D
sw wD w
s
J L P L
J L P L
L L
LJ L P
L
L P
Lwhere
L
J L P L
and
JJ J V V
c c
• LP = Direct coefficient for Jv
• LD = Direct coefficient for JD
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
ln
ln
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
0
ln
ln
ww
s P D P s
v
P
v
P
vs P D v s
P
J V
J L P L L P c
JP
L
JP
L
JJ L L J c
L
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
2
ln
2
ln ln
ln
1
1
s v v P D s
D P s v s
s v sDiffusion part
Convective part
v P
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
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
Spiegler-Kedem Model (1965)• Its much better model
x=0x=∆x
Consider infinitesimal small strip is in thermodynamic equilibrium
1
0 0
[ ( )]
( )
1
( )
n
i ii
v v
s v s
x x
v v
v v
vv
v
J
dP dJ P For a small strip
dx dx
and
dJ W J c
dxFor wholemembrane
dP dJ dx P dx
dx dx
J x P P
PJ P
xdP d
Pdx dx
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
x=∆x x=0
C’sC”s
"
'
"
'
0
" '
1
1
1
1
1ln 1
1
1ln 1 ln 1
s
s
s
s
s v s
ss s v
ss s v s
c xs
s v s sc
c
s v sv sc
vs v s s v s
s
dJ W J c
dxdc
P c Jdx
dcP c J J
dx
dc dx
c J J P
xc J J
J P
J xc J J c J J
P
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
"
'
" "
' "
"
" "
' "
"
" '
"
'
"
'
1 1ln
1
1 1ln
1
1 1ln
1
1ln
1
ln
1
s v s v
s v s s
s v v s v
s v v s s
s v s
s s v
s s s
vs
ss s
s
s
s
s
c J J J x
c J J P
c J J c J x
c J J c P
J J c
c c J x
c c P
J xc
Pc c
c
c
c
c
"
'
1
1 1ln
1 1
1
v
s
v
s
s
s
J x
P
R J x
R P
cR
c
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
1 1ln
1ln
1
1exp
1
1
1
1
v s
v
v
R J PP
R P x
JR
R P
JRF
R P
R F FR
R F F
FR
F
• LP = Hydrodynamic permeability
• σ = Reflection coefficient
• P = Solute permeability
3 parameters of SK model
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
N1 = A (∆ P - ∆π)
N2 = B (∆ C)
2
1 1ln ln
1ln ln
,
0
10
1 10
1 1
obs v
obs
obs v
obs v
Y
m m
v
v
v v
v
v
v
R JR
R R k
R JB
R J k
To find Min or Max valueof Y
dY
dJ
JdY B
dJ B J k
J k
J k
J k
From slide 82 & 83
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
JVJV
Rob
• At JV = k, will have maximum or minimum value1
ln obs
obs
R
R
1ln obs
obs
R
R
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
Design of RO System
Low pressure side
High pressure side
C22
(C22)m
Permeate side
(C23)m
(C23)
(C23)avg
QP
Total permeate flow rate
Feed side
X = 0
X = L
Vx , C21 , (1-QF) , ∆
Vxf , C21f , QF
QF
22 23 1 2
21 23
1
22 23
2 22 23
223
1 2
exp 1
{ ( )} 2
( ) 3
4
P
F
Q
Q
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
cNc
N N
Recovery i.e. for 50% recovery ∆=0.50
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
X21
Vx
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
11 1 1
21 2 2
5
x x x
x xx x dx
x
x
x
AV CX A V dV C X dX N Sdx
AC V X V X N Sdx
d V X N SC
dx A
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
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
For Tubular module and axial flow Hollow module
2B
L
2
22 21 23
11 1
21 2
22 23
2 2 1
2 1
2
x
x
R F P
S RL
A R L R hWL S
andBWL A B
c c c
d V X N
dx chd V X N
dx chc c c
Q Q Q
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
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
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
111
221
1x
x
d V NX
dx ch
Nd V X
dx
0
21
21 21
21
21
21
21
0
.
1
1
1
x
x xf f
x
xf f
chV X Constt
V X V X
V X
V X
VX
XV
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
21
21 2221 22
21 21
2323
21
,
,
f
xf
f f
x
f xf
bcX
Pk
A PcB
A Pc
A Px X
chV
X XX X
X X
X VX V
X V
• Dimensionless parameters:
Dimensionless Osmotic Pressure
Dimensionless Mass Transfer Co-efficient
Solute Diffusivity Parameter
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
1 22 23
22 23
1
( )
(1
N A P b c c
b c cN A P
0
22
22
2221
21
1 22
2
22 23
)
1
1
1
1
&
(
ff
P
bcA P
P
cX bA P
P
X bcA P X
X P
N A P X
N B c
B c c
0
22
2 21 22
)
f
BcX
N BcX X
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
22 23,c c
as
0
21 23c c
1 2
0 expN N
0
22 22 1
21 21
2222
21
22 22
21
exp
1exp
1exp
ck
c cX N
c cX ck
A P XX
X ck
X X
X
1
221
x
xf
dV Nand
dx ch
A P Xd V V
X chd
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
22
22
22
22 22
21
1
1
1
1, exp
xf
xfxf
A P XdVV
dX ch
A P XA P dVV
chV dX ch
dVX
dX
X Xas
X
22X 21
22
X
X
V
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
221exp
X
1
exp
V V
1 ln 6
. 0 0, 1x xfBC x X V V V
11
.V If Turbulent Cond
1
1
V
1
1 1V
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
,as V
1 ln
dV
d
1 ln
1
1 ln 2
1 lndV
d 1 ln
2
d
1 lnand
1
V
ln
V
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
221
1
dVX
dXdV
dX
1
For any
V
dV
1 0
[ ,
1 ]
1
eV L
xe Re
xf F
F P F F
F F
dx
VV QA
X L L VV A Q
Q Q Q Q
Q Q
dVL
1
1
7
V
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
From (6) & (7)
1
1 1 1 2 1 2
1
ln
i iL e E u E u E w E w
w
1 ln
,u
23
1 0
2
, 0 & 0
1 1, ln
1
1
at inlet x
at outlet x L
E Exponential Function
If u w
Then L
Land X
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
x=0
x=L
1
21
dV
dX
2
1 1
V
dVdX
2
1
1 ln
V
L
d
1 ln
2
d
ln
2
1
dL
ln 1 ln 2
1
d ln 1 ln
2
21
dL
ln 1 ln 1
2
1
I
d
ln 1 ln 2
2
21
I
L
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
1
dI
ln 1 ln 2
1
d
ln d
1 ln
2 2
1 1
,
ln
Lets assume
w we d 1 ln
,
we dw
and
lnu
1 u
1 1u
ue e e d
1
12 2
1
1 1
u
w u
e e du
e dw e duI e
w u
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
• Exponential Integrals
1
2 2
1 1
2
1 2
1
2
2 1
1
,
u
u
w w
i
b c b
a a c
w w w
w
i i
w
i i
eE u du
u
eand E w dw
w
as f x dx f x dx f x dx
e dw e dw e dw
w w w
e dwE w E w
w
e dwE w E w
w
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
2 2
1 1
2
1 1 1 2
1
12 2
1 1
1
1 1 1 2 1 2
,
1
1
u u u
u
w u
i i
and
e du e du e du
u u u
e duE u E u
u
e dw e duL e
w u
L e E u E u E w E w
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
1 lnw 1 2, lnw 2
1
1 lnu
1
2
1 ln,u
2
,as
1
exp
V
For
1 0 . . 1at x i e V
1
1exp
1
1
For
2 . . 1at x L i e V
2
1exp
2
1
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
,As 1
exp
, 0 & 0,
V
For u w
1
1
V
2
1
1
1
V
V
dVand L dX
2
1
1
V
dVL
2
1
2
1
V
VL dV
V
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
2 2
1 1
2 1
1 1
1
1
ln ln
1ln
1ln 1 ln 1 1 1
1 1ln
1
V
V
VL dV dV
V V
L V V V
L V V
L
L
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
x22
Permeate side
x23
x23 = avg.QP
Total permeate flow rate
Feed side
X = 0
X = L
QF
Vx , x21
QR
23232323
21 21
'
'
2
23 2
1
2
23 2
1
2
22
1
,
, /
.
f f
P F xf
P
xf
X XX X
X 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
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
2'
23 22
1
'23
xf
xf
cX V A BcX Sdx
cX V A Bc
2
21
1
X Sdx
22
2122 22
2121 21
21
'23
f
f
xf
XXX X
XX XX
cX V A BcS
221
21211
21'23
ff
fxf
X XX d
X
x X
BcSXcX V A
2
21
1
X dX
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
23
21 f
X B c
X
S
c 'xfV A
2
21
1
23
21 f
xf
X dX
X BS
XV
'
xf
A PA
chV
2
21
1
23 '
1
X dX
cB hSX
A P A
2
21
1
23
X dX
X
2
21 '1
1
I
SX dX
A h
I
2
21
1
X dX
I
2
21
1
1dX X
V V
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
I
2
1 1
dV
V
1
V
dV
dX
1
dVdX
V
1
V
I
2
1 1
dV
V
11 1
V
I
2
1 1
dV
V
2
1
1
1
V
dVI dV
2
1
V
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
2
1
23
23
1
11 1
1
1
1
1
I V L
I L
I L
I L
X L
LX
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
1
1 1 1 2 1 2
23 1
1
1 ln1 ,
i iL e E u E u E w E w
LX u
1
1, lnw
1
'1
1
'
1
' '1
'
11, ln
!
1, ln!
0, 0,
ln , 0.56 .
ln
n n
n
n
in
i
uFor u E u u
n n
wand for w E w w
n n
If u w Then
E u u u Where Constt
and E w w w
• Design Equations:
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
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.
Org./aq.
aq. phase
Org. phase
Gas
aq. phase
Org. phase
Gas
Feed PhaseReceiving Phase
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
• 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
LM
LM
LM
Organic or Solid support
• Here the transfer occurs through the pores
Big dropsReceiving phase
Feed Phase
Liquid Membrane
LM
LM
LM
LM
LM
LM
LM
Feed
Receiving Phase
Fiber
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
• 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
A
B
LMFeed
1. Add additive to increase or decrease selectively of one of the components in liquid membrane
A
A
B
B
LM (aq.)A (Aromatic (org.))
NA
• Additive N-methylpyrolidone Its increase solubility of A several folds
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
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.
A
B
Aq.
Phenol
Org.
(Kerosene)
Cheaper
CAq.
Feed Side LM Receiving Side
NaOH
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
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
AB
B
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
A
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
(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
CA
CB
A
B
B
A
Feed Side LM Receiving Side
• Example: separation of metal ion
• Cu++ + 2HR CuR2 + 2H+
Carrier complex
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
(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
AC
C
AA
hυ
(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+
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
• 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
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
(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
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
• 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
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
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
LM
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.
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
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)
Water
Demulsification
O/W Emulsion
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
• 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
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
• Surfactants: SPAN80, ECA4360J
• Carrier species: LIX64N
• Commercial applications:
Phases
Applications
Phase I
(Feed)
Phase I I
(LM)
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
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
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.
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
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.
Sol.
Phenyl Hexane
Crown ether De-ionized Water
Polypropylene
0.3 40 30
(Hollow fiber)
Example of SLM
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
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
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
Disadvantages:
ELM:
1. Membrane breakage due to agitation, poor membrane formation, excessive internal drop size.
2. Requires emulsification.
SLM:
1. Solvent loss by evaporation or by pressure differences across the micro porous membrane.
2. Carrier loss can occur due to irreversible side reaction.
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
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
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
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
LM
A
AB
B
Feed Strip gas
A
A
CAo
X = 0
CAL
X = L
1
2
k
k
i
A B AB
C
t
0
2
1 22
( . )i A
AA A B AB
N R at S S
d CA D k C C k C
dx
B AB AD D D
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
2
1 22
2
1 22
2
2 12
0
0
, & '
&
AA A B AB
BB A B AB
ABAB AB A B
B B
x x L
AB AB
x x L
d CA D k C C k C
dx
d CB D k C C k C
dx
d CAB D k C k C C
dxAs B ABdon t leak throughthemembrane
dC dC
dx dx
dC dC
dx dx
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
Limiting cases:
1. Reaction equilibrium exists through out the membrane
2
2
1 2
0
00
2 1
00
0
.
( . )
,
0,
,
, &
AA
A
A
A A
LA A
LA A
A
LA A
A A
d CA D
dxdC
ConsttdxC c x c Linear conc profile
Putting
at x C C
x L C C
C CWe get c C c
L
C CC x C
L
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
As, we have linear conc. profile
00
1 2
1 2
2
1 2
1
1 2
2
.
0
.
0
( )11
&1
LAB ABx x LA A
A A AB
A B AB
T B AB
A B T B
TB
A
T TB
AA
AAB T
A
C CC CN D D
L LAt all pts in membrane
k C C k C
Total conc of B is
C C C
k C C k C C
k CC
k C k
C C kC k
k kC kCk
kCC C
kC
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
0
0 0
00
0
0
00
0
0
0
1 1
1 1
,
1 1
11 1
T
LT A T A
L LA A A A
A A AB
LLT A AA A
A A AB LA A
A
A C
LLT A AA A
A AB LA A
LA A
A
TL
A 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
N
kC C CC CD D
L L kC kC
C CD
L
kC
kC kC
A ABD D
After putting the values of CAB
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
• 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.
1 2
2
1 22
0
& (1)
A B AB
AA A B AB
k C C k C
d CD k C C k C
dx
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
1 2 2
1 1 1
1 1 2 2
1 2 202 1 2 1
1
sinh cosh
, ,
cosh,
sinh
&
A
B AB
LA
A
AB
B B KC k x k x
K K K
Where K k C K k C
K C K B kLB K C K B
kL
Kk
D
• Solving the above equation (1) by keeping CB & CAB constant we get
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
• Coupled transport:
1
122 2
, &
k
kCu HX CuX H
Cu m HX HX H h
MX2
HX
M2+
2H+
2H+
M2+
m1b
m2b
m1
m1
m2
m2
12 3
4
5
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
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
• Here we assume that the thickness of membrane is very small & so we consider linear concentration profile
1
1
1 200
1 1 200
2
1120 0 1 1 2
2 2
m
m
k
k
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
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
0 0
1121 1 2
11
11 1 1 1 1
11 1
1 1 11 1
2 2
1 11 2 2
1 1
2
1
0 20 1
, 0
0
0
eq b eq
b eqm
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
h h
m k HXDJ
h
% % % % % % % % % % % % % %
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
0
1
2
20 1
2
,.
( )
b
eqm
FluxAs Permeability
ConcJ
Pm
k HXDP
h
a P HX
Log [HX]
Log P
Tanθ= 2
2. Slow chemical reaction & no resistance in diffusion layer.
• Thus m1b = m1 but R0 – R0 ≠ 0
• Net transported = Net reacted0 00
11
1 11 1 1 1 10
i
m
J J R R
Dm k m HX h k m HX h
% % % % % % % % % % % % % %
θ
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
1 11 1 1 1 1 1
11 1
1 1 1 10 0
11 1 1
0 10
1 10
2
10
21 011 1 1
0
,
b
m m
bm
m
m
mb
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
2
arg ,
P HX
If HX L e Then P HX
Log [HX]
Log P
Tanθ1 = 2
Tanθ2 = 1
θ1
θ2
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
3. Slow reaction, resistance in the diffusion layer.
1 11
1
1 0
1 0
1 11
1 0
11 11
1 0
0
11
1 11 1 1 1 10
.
,
bm
a
m
i
b mm
a
a m b m
m a
i
m
m mJ D
D diffusivity of metal ion in aq phase
J J J
as J J
Dm mD m
D mD mm
D
and J J
Dm k m HX h k m HX h
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
11 11 11 11 1 1 1
0 1 0
11 11
1 1 1 1 1 1 1 10 0
11 1 1
11
111 1 1 1
0 0
11
m a m b m
m a
m a mb
m
b
m a m
m
D D mD mm k HX h k m HX h
D
D Dm k HX h k HX h k m HX h
D
k m HX hm
D Dk HX h k HX hD
km
2
1
221
1 1 1 10 0
2
1 1
02
20 11 1 1 1
0 0
b
m a m
m
bm
m a m
m
m HX
D DHX h k HX k h
D
k m HXDJ
D DHX h k HX k h
D
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
2
1 1
02
21 01 1 1 1
2
10
21 20 11 1 1 1
2
0
,
arg ,
b
a
m m
b a
mm
k m HXJ
HX h k HX k hD D
k HXJThus P
mk h k HX h HX
D D
If HX Small Then P HX
If HX L e Then P HX
Log [HX]
Log P
Tanθ1 = 2
Tanθ2 = 0
θ1
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
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
Anode
Cations
AnionsNormal tendency
Concentrated brines
Lean in brines
NaCl – Water solutionAEM AEMCEM CEM
(AEM) (CEM)
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
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.
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
• Production of H2SO4 and NaOH
+++++
++++++
++++++
+
Cathode
+
Anode
H+,OH-
BMCEM CEMAEM AEM
Na+ Na+
Na+
H+
OH-SO42-
SO42-
SO42-
Na2SO4
H2SO4 NaOH
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
+
CEM WaterBrine
Na+
Cl-
H+
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:
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
• 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.
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
• 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
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
Transport phenomena in electro dialysis:
• μi = Chemical potential in membrane phase
• μi’ = Chemical potential in solution phase
• i = anions/cations
• μi = μi’
CEM
Solution+
ln lni i iRT m RT Z ' ' '& ln ln
i
i i i
F
RT m RT Z
'
'
2 2' '.
,
. ( )
(1) : in 2 ( )
i
i i
sol Iin
R I
F
As
Conc of anions in the membrane
Case Salt dissociate ions like NaCl
CCo
M
Where,
mi = molar Conc.
Ψ = Electrical potential (EP) in membrane phase
F = Faraday’s constt.
MR = Charge on membrane
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
Nernst Plank ion flux equation:
ii i
diffusion part
dcJ D Z
dx
.
ii i
becoz of EP across the mem
D dFc
RT dx
I Z
.
i i
i
J F
Current carried out
by the particular ionTransport No
Total current
F Zt
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
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
1. Cations flow in a Cation Exchange Membrane (CEM):
CEM
Cathode
+
Anode
x = 0 x = δx = δ1x = 0
Cation
C’D,b
C’D,m
C’B,m
C’B,b
C’D,b
Dilute
Bulk
Solution
i
F Zt
i i
ii
J
I
ItJ
F Z
'
( )
i
t iFlux in Solution Feed
Z
''
i
FluxduetoEP
dcD
F dx
t iFlux in membrane
Z
i
dcD
F dx
0
t+ is large and D (dc/dx) is very small in membrane
Dilute side
Brine side
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
'
,As Flux in Solution Flux in membrane
t i
Z
'
'
i
t idcD
F dx Z
'
iF
t i
Zi
t i
F Z
''
' ',
' ',
'
''
0,
,
i
D b
D m
in membrane in solution
dcD
F dx
At x c c
At x c c
t t
dc iD
dx Z
'
,
',
'
'D m
D b
i
c
c
t tF
idc
Z
'
0
t tF
'0.95 & 0.5t t
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
' ', , 'D m D b
ic c
D Z '
' ', , 'D m D b
t tF
ic c
D Z
'
',
' ',
lim
0D m
D b
t tF
c
c D Zi
'
' ', , 'B m B b
F
t t
For brine side
ic c
D Z
'
i
t tF
t iJ
Z
F
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
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
2. Flow of anions through Cation Exchange Membrane (CEM)
CEM
Cathode
+
Anode
Anions
C’D,b
C’D,m
C’B,m
C’B,b
't t
3. Flow of cations through Anion Exchange Membrane (AEM)
Dilute side
Brine side
Cathode
+
Anode
Cations
C’D,b
C’D,m
C’B,m
C’B,b
Dilute side
Brine side
++++++
'
'0.04 & 0.5
in membranein solution
t t
t t
AEM
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
4. Flow of anions through Anion Exchange Membrane
Cathode
+
Anode
Anions
C’D,b
C’D,m
C’B,m
C’B,b
Dilute side
Brine side
++++++
AEM
't t
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
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
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
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
Feed
Mem
brane
• There should not be any pin hole in the membrane
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
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.
A B
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
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
ii i
dcJ D Non fician
dx
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
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
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
Permeability of gases:
x = 0 x = δ
Cli
Chi
PhiPli
Low pressure side
High pressure side
0
.
.
'
li
hi
hi
li
ii i
c
i i i
c
c
i i i
c
i
i i hi li
hi hi hi
li li li
dcJ D
dx
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
c k P
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
,
,
. ,
,
hi
li
hi
li
hi li i
i i i hi li
i ii hi li
i i i
ii hi li
c
i i i
c
i
ii hi li
c
i i
ci
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
D dc
Where Dc c
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
'
,
,
,
hi hi hi
li li li
hi li i
ii i
hi li
ii hi hi li li
i
i hi hi li li
ii hi li
i hi hi li lii
hi li
c k Pif Henry s law is applicable
c k P
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
P P
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
• As temperature increases the permeability is also increased & reverse behavior is also observed
• Cohen & Turnbull (Fujita) Free – volume theory
Pi Pi
PhiT
Pl Ph
Ph >> Pl
Henry’s law is applicable
*
02*
expf
f f s s
h
f
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
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
*
2
*
2* *
*
*
:
1
(2)
3
.
,
1 2
(1)
,
(2)
,
h
o
h
o
h
o
h
c
f
P vs P
If k
P then P
If k
P then P
If k
P then P Constt
Calculate T from following equation
T
TT V
If T T
As T then P
If T T
As T then P
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
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
Feed
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
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
2. Chemical inertness and physically stable
3. Absence of pinholes or other mechanical defects.
• Separation factor:
,
1,
1,
AA B
B
A
A
A B
A B
PSelectivity
P
Where P Permeability of A
and P Permeability of A
If then A comes as permeate
If then B comes as permeate
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
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
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
2. Cross flow pattern
• Driving force is different every where
3. Co – current flow
4. Counter current flow
• Highest efficiency
Feed
Compositions are different every where
Un permeated stream
Permeate stream
Compositions are different every where
Un permeated stream
Permeate stream
Feed
Permeate stream
Feed Un permeated stream
Cross flow pattern
Co – current flowCounter current flow
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
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
Pl
Ph
,
,
1
, 1
oA
oA
ol oA
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
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
1 1 1 2
3
4
, ,
1 ,
15
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
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
From
y P x P y
and from
y P x P y
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
5 & 6 ,
1
&
(4),
1
1 71
h l
oA
loA oA
h
lih iA oh oA ol oA
h
oh l oliA oA oA
ih h ih
liA oA
h
h l
liA
h
Adding we get
P P
y
Px y
P
from
PL x L y L y
P
L P Lx y y
L P L
Px y
P
P PP
xP
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
7
7
ol
oA
ol
oA
If is known
Find from and A can be calculated as
LAP
If A is known
LFind from
AP
and from can be calculated
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
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
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
Concentration polymerization:
• Membrane is semi permeable
• Solute is retained at membrane surface
• Gel formation on membrane surface takes place
Gel layer
Work as RO
∆P
JV
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
JV
Time (hr)5 hr 20 hr
• ∆P = fixed
• Due to membrane fouling
Concentration polarization
Membrane fouling
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
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
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
Membrane transport model:
*
*
* *
*
*
:
:
m Pw
p
w
psm s
s
ps p
p s
pm s
s
Permeability
v L P
LP
For other solvents
Lv P
L LP
L
Lv P
• ηw = Viscosity of water
• LP* = Standard permeability
• α = Standard permeability coefficient
Phone – poulene membrane
Solvent
LP* = 10-12
α
Methanol 1.0
Acetone 1.0
n – Heptane 0.7
Toluene 0.9
Dioxane 0.05
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
• Concentration polarization less than the limiting flux
22 23
21 23
23
21
23
22
ln
22ln
exp ,
1
1
1
v
obs
v P
s v sDiffusion part
Convective part
s
c c J
c c k
cR and
c
cR
c
From Kedem Katchelky Model
J L P
J W J c
c c
JV
Robs
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
1 1
1 1ln ln
1ln
1
m
v
obs v
obs
m v
v
obs obs
P
R J
R JR
R R k
P J
J k
T R
JV
Tobs
JV
Robs
JV
1 - Robs
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
Pore Flow Model & Hindrance Transport Model for Ultra filtration:
rP
Z = δ Z = δ
CP Cf
JV (m/s)
V = Vavg
0
1
. .
1
ss c s d
s
s
P
s sz z
f P
sd c s s
sd c s P
dCN k VC k D
dzdC
D diffusion transport in bulkdz
i e free from hindrance
r
r
C CPartition coefficient
C C
from
dCk D k VC N
dzdC
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
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
0
0
0
0
0
1ln
ln
ln
1 1
1ln
s z
s z
s z
s z
C
s
c s P dC
C
c s P Cc d
c s Pz c
c s P dz
c P P c
c f P d
v
P P
f f
c
dC Vdz
k C C k D
Vk C C z
k k D
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 C
k
P c v
c f P d
C k J
k C C k D
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
,1
1ln
1 1
1ln
1 1
1ln
1ln 1
1, . .
1 1ln
1
c
c v
d
c v
d
c v
d
vd
dm m
d
v
m
Let k
R k J
R k D
R k J
R k D
R k J
R k D
RJ
R k D
k DLet P i e P
k D
R J
R P
R
1
exp v
m
J
R P
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
1exp
1
1 1, exp
1
v
m
v
m
JRF
R P
R F FR
F JR where F
F P
• Same as Spiegler – Kedem model
• But here reflection coefficient σ and permeability are depends on thickness and hindrance factor
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
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
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
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
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
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
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
"
"
'
'
'
"
1 1
A
BA B
A
B
A B
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
h
Swelling
Dry
ϕ”ϕ’
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
Anisotropic swelling occurs in case of pervaporation
' "
' "
' "
. ,
,
V
V
V
V
dJ D
dxFraction of penetrant within the membrane
J Dh
if D Constt sp
p pJ Ds
h
p pJ P
h
Where P Permeability
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
'
"
0
' "
' ' " "
' ' ' " " "
0 exp
0 0
0 exp
0exp exp
0exp exp
, &
h
V
V
V
D D g
D at
J dx D g d
DJ g g
gh
DJ g s p g s p
gh
where s p s p
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
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:
' ',
' ',
P A A
P B B
F
C A w
C B w
( F – V )
" ",A BV w w
,
,
, ,& .
.
v A
v B
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
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
' ' ' ' " ", , , ,
" ", ,
' ' ' ', ,
", , ,
' ' ' ', , ,
' ' " "
' ', , , ,
,
',
1 & 1
, &
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
v B
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
HVT
F C
By heat balance i.e. the amount of heat the liquid has lost = Heat gained in vaporization
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
0
,
500
0.3
, 150
if component B is water then
VT
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
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
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
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
Q’out, C’out
Q”in, C”in
Q’in, C’in
Q”out, C”out
' ' ' ' " " " "
' "
' ' ' "
:
,
:
.
in in out out out out in in
oo
in out
o
in in in out
m
Lost by feed side Gained by dialysate
Q C Q C Q C Q C
Dialysates
MD M Over all mass transfer
C C
Extraction ratio
D ME
Q Q C C
Actual removal
Max amt that can remove
Feed side
Dialysate side
Counter current
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
2 1C1S
C1m
C2mC2S
km
C1b
k’k”
l
dAC”
Q’, C’
C’ + dC’
2
1 2
' "0
' "0
' ' " "
' "' "
' "' "
,
1 1 1 1
1 1
1 1
smim m
sm sms s m
m
o
o
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
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
' "0
' "
' "
' " ' "
' " ' "
' "
1 1
1 1
1 1
,
,
1 1
out
in
C M o
C
o
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
C CM
Q Q
For counter current
C C C C C C
For co current
C C C C C C
d CQ Q
0' "
1 1
o
d M
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
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
0' "
0' "
0
0
0ln
' '
" "
1 1
,
1 1
ln
ln
out
in
C
C
out in outo
in
oin out
out
in
o
in out
in out
d Ck dA
C Q Q
Integrating both sides
d Ck A
C Q Q
C C Ck A
C MC C
M k AC
C
M C k A
Q QHere flow rates are assumed
Q Q
0'T
to be same throughout
k AN
Q
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
'
"
',
1 exp 1
1
1 exp 1
1 exp 1
o
T
T
T
QZ
Q
Once M known
DFind E
Q
N ZE For co current
Z
N ZE For counter current
Z N Z
Z=0.25
Z=0.5
Z=1
Z=0.25
Z=0.5
Z=1
Counter current Co – current
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
Variations of dialysis:
• In spite of normal membranes, charged membranes are used
1. Donnan dialysis
CEM
Cu++
Feed
Conc. H2SO4
Stripping side
2' '
" "
24
7 6
10 1
10 10
Cu H
Cu H
a aRatio of activities
a a
2. Ion exchange dialysis
Cu++
2H+
Feed
CuSO4, H2SO4H+
Cu++4SO
H+
4SO Weak type anion exchange
i.e. only H+ not other cation can pass
Prevents cation to pass through
Weak type AEM
H2SO4
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
• 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
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
1. Gas absorption & stripping:
Micro porous hydrophobic membrane
gas Liq (aq.)
Immobilized face
Pg Paq
Pores
• 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
Pores
• 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.
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
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
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
2. Membrane based Solvent Extraction:
Micro porous hydrophobic membrane
Org Liq (aq.)
Immobilized face
Porg Paq
Pores
• 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
Pores
• In this case pore (membrane) will be occupied by water
• Porg > Paq
• Porg – Paq = ∆Pr < Breakthrough press.
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
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
Pw1
Pw2
Low osmotic
solution (aq)
High osmotic
solution (aq)
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India
3. Membrane distillation:
• Here temperature is driving force
Pw1
Pw2
Hot solution
(more salt)
Cold solution
(less salt)
Department of Chemical Engineering Indian Institute of Technology-Delhi, New Delhi 110 016, India