Membrane_separations.pptx

Membrane Separations
-Brajendra shukla
IET, BU( Deptt. Of Biotechnology)

Membrane separations used in DSP

Membrane separations: Introduction
• Membranes are semi-permeable barrier used for
– Particle-liquid separation
– Particle-solute separation
– Solute-solvent separation
– Solute-solute separation
• Applications
– Product concentration
– Product sterilization
– Solute fractionation
– Solute removal from solutions (desalination, demineralization)
– Purification
– Clarification

Factors utilized in membrane separations
• Solute size
• Electrostatic charge
• Other non-covalent interactions
• Diffusivity
• Solute shape

Transport of material through a membrane
Diffusion driven
separation
Pressure driven separation
(convective transport) Membrane module
Retentate
Permeate
Membrane
Membrane module
Retentate
Permeate
Membrane
Sweep
Feed
Feed

Dead-ended or
conventional
filtration
Cross-flow filtration

Membrane materials
• Organic polymers
– Polysulfone (PS)
– Polyethersulfone (PES)
– Cellulose acetate (CA)
– Regenerated cellulose
– Polyamides (PA)
– Polyvinylidedefluoride
(PVDF)
– Polyacrylonitrile (PAN)
• Inorganic materials
– Glass
– Metals
– Ceramics
– Layers of chemicals
– Pyrolyzed carbon

Membrane preparation by casting
• Precipitation from vapour phase
– This is achieved by penetration of the precipitant through a polymeric
film from the vapour phase, which is saturated with the solvent used.
• Precipitation by evaporation
– The polymer is dissolved in a mixture of more volatile and less volatile
solvents. As the more volatile component evaporates, the polymer
precipitates to form the membrane.
• Immersion precipitation
– This involves immersion of the cast film in a bath of non-solvent for
coagulation of the membrane material.
• Thermal precipitation
– The polymer is precipitated from solution by a cooling step.

Other membrane making procedures
• Stretching:
– Involves stretching a polymer film
at normal or elevated temperature
in order to produce pores of
desired size.
• Sintering:
– Powdered material is sintered by
compression with/without heating
to give microporous membranes.
• Slip casting:
– Most inorganic membranes are
prepared using this method.
– The method involves coating
repeated layers of uniform particles
with decreasing sizes on porous
support.

Other membrane making procedures
• Leaching:
– Some inorganic membranes are
prepared by leaching technique.
– Isotropic glass membranes are
prepared by a combination of
phase separation and acid leaching.
• Track etching:
– A homogeneous polymer film is
exposed to laser beams or beams
of collimated charged particles.
– This breaks specific chemical bonds
in the polymer matrix.
– The film is then placed in an
etching bath to remove the
damaged sections thus giving rise
to monodisperse pores

Membranes: Structural classification
Isotropic
Anisotropic

Porous membranes
Isoporous membrane Microporous symmetric Microporous asymmetric

Basic forms of
membranes
• Flat sheet membrane
• Tubular membrane
• Hollow fibre membrane

Factors influencing the performance of a
membrane
• Mechanical strength
– Tensile strength, bursting pressure
• Chemical resistance
– pH range, solvent compatibility
• Permeability to different species
– Pure water permeability, sieving coefficient
• Average porosity and Pore size distribution
• Sieving properties
– Nominal molecular weight cut-off
• Electrical properties
– Membrane zeta potential

Driving force in membrane separation
• Transmembrane (hydrostatic) pressure (TMP)
• Concentration or electrochemical gradient
• Osmotic pressure
• Electrical field
• Partial pressure
• pH gradient

Membrane processes that
separate primarily based on
size (pressure driven)
1 to 50 psi
10 to 100 psi
200 to 600 psi

Membrane processes that separate based
on principles other than size
• Pervaporation
– Separates a volatile or
low-boiling-point liquid
from a non-volatile
liquid
– The driving force is a
vacuum on the
gaseous side of the
membrane
– Tool for separation of
liquid mixtures,
especially dehydration
of liquid hydrocarbons

Applications of pervaporation
• Dehydration of ethanol–water azeotrope
• Removal of water from organic solvents
• Removal of organics from water

Membrane processes that separate based
on principles other than size
• Electrodialysis (ED)
• Electrochemical process used to separate charged particles from an
aqueous solution or from other neutral solutes
• A stack of membranes is used, half of them passing positively charged
particles and rejecting negatively charged ones; the other half doing
the opposite.
• An electrical potential is imposed across the membranes and a
solution with charged particles is pumped through the system.
• Positively charged particles migrate toward the negative electrode, but
are stopped by a positive-particle-rejecting membrane
• Negatively charged particles migrate in the opposite direction with
similar results

Flux
• Throughput of material
through a membrane
• Flux depends on
– Applied driving force
– Resistance offered by
membrane
• Fouling
– Increase in membrane
resistance during a process
– The decline in flux through a
membrane with time in a
constant force membrane
process is due to fouling
Flux
Time
Decline in flux due to fouling in a
constant driving force membrane
separation
Pressure
Time
Fouling in constant flux
membrane separation

Membrane element and module
Membrane element refers to the basic form of the
membrane:
• Flat sheet
• Hollow fibre
• Tubular
Membrane module refers to the device which houses
the membrane element:
• Stirred cell module
• Flat sheet tangential flow (TF) module
• Tubular membrane module
• Spiral wound membrane module
• Hollow fibre membrane module

Membrane
modules
Stirred cell unit Arrangement flat sheet TF module
Small scale flat sheet TF module
Pilot plant scale flat sheet TF module

Stirred cell
Membrane
Stirrer bar
Permeate/filtrate
Nitrogen/compressed air
Magnetic stirrer
Feed
Pressure gauge
Permeate
collection
chamber
•Research and small-scale manufacturing
•Used for microfiltration and ultrafiltration
•Excellently suited for process development work

Flat sheet tangential flow module
Feed Retentate
Permeate
Permeate
Membranes
•Similar plate and frame filter press
•Alternate layers of membranes, support
screens and distribution chambers
•Used for microfiltration and ultrafiltration

Spiral flow membrane module
•Flat sheet membranes are fused to form an envelop
•Membrane envelop is spirally wound along with a feed
spacer
•Filtrate is collected within the envelope and piped out

Tubular membrane module
Feed
Retentate
Permeate (flows radially)
•Cylindrical geometry; wall acts as the membrane
•Tubes are generally greater than 3 mm in diameter
•Shell and tube type arrangement is preferred
•Flow behaviour is easy to characterise

Tubular membranes are used for all types of pressure
driven separations
Tubular modules are widely used where it is advantageous
to have a turbulent flow regime
Advantages
1. Low fouling and hence relatively easy cleaning
2. Easy handling of suspended solids & viscous fluids
3. Ability to replace or plug a damaged membrane.
Disadvantages
1. High capital cost
2. Low packing density
3. High pumping costs
4. High dead volume
Tubular membrane module

Section of tubular module Large scale tubular module

Hollow fibre membrane module
•Similar to tubular membrane module
•Tubes or fibres are 0.25 - 2.5 mm in diameter
•Fibres are prepared by spinning and are potted within the module
•Straight through or U configuration possible
•Typically several fibres per module

Plate and
frame
Spiral wound Tubular Hollow fiber
Packing
density
30 – 500 200 – 800 30 – 200 500 – 9000
Resistance to
fouling
Good Moderate Very good Poor
Ease of
cleaning
Good Fair Excellent Poor
Relative cost High Low High Low
Main
Applications
D, RO, PV, UF,
MF
D, RO, GP, UF,
MF
RO, UF D, RO, GP, UF
Comparison of different membrane modules

Type
Fluid flow
regime
Membrane
area/module
volume
Mass
transfer
coefficient
Hold-up
volume
Special remarks
TF flat
sheet
Laminar-
turbulent
Low
Low to
moderate
Moderate
Can be dismantled
and cleaned easily
Spiral
wound
Laminar Moderate Low Low
High pressures
cannot be used
Hollow
fibre
Laminar-
turbulent
High
Low to
moderate
Low
Susceptible to fibre
blocking
Tubular Turbulent Low
Moderate to
high
Moderate
to high
Flow easy to
characterize
Excellently suited
for basic
membrane studies.
Operating characteristics of membrane modules

Flow patterns
in membrane
modules

Membrane characterization
The performance of a membrane process depends on the
properties of the membrane:
• Mechanical strength
• Tensile strength, bursting pressure
• Chemical resistance
• pH range, compatibility with solvents
• Permeability to different species
• Pure water permeability, gas permeability
• Average porosity and pore size distribution
• Sieving properties
• Nominal molecular weight cut-off
• Electrical properties
• Membrane zeta potential

Ultrafiltration
General Industrial Uses:
Concentration of macromolecules
Purification of solvent by removal of solutes
Fractionation of macromolecules
Clarification
Retention of catalysts
Analysis of complex solutions for specific solutes
Bioprocess Applications:
Fractionation of biological macromolecules e.g. proteins, DNA
Concentration of polymer solutions
Removal of LMW solutes from protein solutions
Removal of cells and cell debris from fermentation broth
Virus removal from therapeutic products
Harvesting of biomass e.g., cells and sub-cellular products
Membrane bioreactors
Effluent treatment

Ultrafiltration membranes
•Pores: 10 to 1000 Angstroms
•Generally anisotropic (skin layer 0.2 to 10 micron thick)
•Properties of an ideal ultrafiltration membrane:
•High hydraulic permeability to solvent
•Sharp “retention cut-off” properties: The membrane must be
capable of retaining completely nearly all the solutes above some
specified value, known as the molecular cut-off (MWCO)
•Good mechanical durability
•Good chemical and thermal stability
•Excellent manufacturing reproducibility and ease of manufacture

Sharp and diffuse cut-off membranes

Ultrafiltration: Pore flow model
p
p
m
v
l
P
d
J


32
2


Jv = Permeate flux
m =Membrane porosity
dp = Average pore diameter
P =Transmembrane pressure
 =Viscosity
Lp =Average pore length
f
o
i
P
P
P
P -
+


2
Membrane
Retentate
Feed
Permeate/filtrate
Pi
Po
Pf
Hagen-Poiseuille’s law for permeate flux
of pure solvent
Pi and Po inlet and outlet pressures on
the feed side
Pf is the pressure on the filtrate side
The pressure drop for a
Cross flow membrane module

Ultrafiltration: Flux equations
Pore flow model: UF of solvent
p
p
m
v
l
P
d
J


32
2


Resistance model: UF of solvent
m
v
R
P
J


Osmotic pressure model: UF of solution
cp
m
v
R
R
P
J
+

-



g
cp
m
v
R
R
R
P
J
+
+

-



Rm = membrane hydraulic
resistance
Rcp = resistance due to concentration polarization
Rg = gel layer resistance
Rm = membrane hydraulic resistance

Concentration polarization
Membrane
Bulk feed
db = Thickness ofconcentration polarization layer
Cb
Cw
Cp
Permeate

Concentration polarization model UF
of solution








-
-

p
b
p
w
v
C
C
C
C
k
J ln
0
v v p
dC
J C J C D
dx
- + 
Material balance in a control volume
within the concentration polarization
layer at steady state
Upon integration with boundary conditions
C= Cw at x=0 and C=Cb at x=δb we get
concentration polarization equation for
partially rejected solutes
For total solute rejection i.e, Cp = 0 ln w
v
b
C
J k
C
 
  
 
When Cw is equal to the gelation concentration, there
will be no further increase in the value of Cw
Hence we write gel polarization equation as lim ln g
b
C
J k
C
 
  
 

Effect of transmembrane pressure
on permeate flux
Permeate
flux
Transmembrane pressure
Pressure
dependent
Pressure
independent
?
Limiting
flux
At constant TMP the
permeate flux decreases
as the feed concentration
increases
When Cw = Cg the
permeate flux is
independent of the TMP

Problem
A protein solution (conc, 4.4 g/l) is being ultrafiltered using a spiral
wound membrane module which totally retains the protein.
At a certain transmembrane pressure the permeate flux is
1.3x10-5 m/s. The diffusivity of the protein is 9.5 x 10-11 m2/s while
the wall concentration at this operating pressure is estimated to be
10 g/l.
Predict the thickness of the boundary layer.
If the permeate flux is increased to 2.6 x 10-5 m/s while maintaining
the same hydrodynamic conditions within the membrane module,
what is the new wall concentration?

Where there is total retention we can use the equation
This equation can be written as
The mass transfer coefficient is given by
Therefore
When Jv is increased to 2.6 x 10-5 m/s and k remains the same, the wall
concentration can be obtained from the concentration polarization equation for
totally retained solute
ln w
v
b
C
J k
C
 
  
 
5
5
1.3 10
1.584 10 /
10
ln
ln
4.4
v
w
b
J
k m s
C
C
-
-

   
   
 
   
 
b
D
k
d

11
6
5
9.5 10
5.99 10
1.584 10
b m m
d
-
-
-

  

6
5
2.6 10
exp 4.4 exp / 22.727 /
1.584 10
w b
Jv
C C g l g l
k
-
-
 

 
   
 
 

   

Effect of feed concentration on
permeate flux
TMP
Jv
Cb
Jlim
ln Cb
Cs or Cg
k
For a given feed concentration,
the limiting flux increases with
increases in mass transfer
coefficient
Permeate flux decreases as the feed
concentration is increased

Mass transfer coefficient (k)
Affects back-diffusion of accumulated solute
Measure of the hydrodynamic conditions within the module
k = (D/db)
Mass transfer coefficient can be measured experimentally
•Plot of limiting flux versus log of feed concentration
•Plot of sieving parameter versus (Jv/k)
Mass transfer coefficient can be estimated using heat-mass
transfer analogy
•Dimensionless equations: Sherwood number as function of Reynolds
number and Schmidt number

Schmidt number = Momentum transfer/Mass transfer
kd
Sh
D
 
  
 
Reynolds number = Inertial forces/Viscous forces
Sherwood number = Total mass transfer/Diffusive mass transfer
Re
du du
 
 
 
 
   
   
v
Sc
D D


 
 
 
   
   
Mass transfer correlations
Peclet number = Convective mass transfer / Diffusive mass transfer h
d
Pe
D

Grashof number = Gravitational forces/ Viscous forces
3 2
2
'
L B g t
Gr




Froude number = Interial forces/ Gravitational forces
2
v
Fr
gL


Mass transfer correlations
Fully developed laminar flow (i.e. Re < 1000) in tubular
membrane 0.33
0.33 0.33
1.62 Re
t
d
Sh Sc
l
 
  
 
Turbulent flow (i.e. Re > 2000) in tubular
membrane 33
.
0
8
.
0
Re
023
.
0 Sc
Sh 
Graetz-Leveque
Dittus-Boelter
Fully developed laminar
flow
33
.
0
67
.
0
33
.
0
816
.
0 -
 t
L
D
k  Porter
Shear rate at the wall  = 8 ul / d for tubes
 = 6 ul / b for rectangular channels (b = channel depth)

Problem: Shear-Induced Diffusivity
Shear-induced diffusivity is 3 x 10-7 cm2/s.
Hydrodynamic diffusivity is 2 x10-9 cm2/s.
Shear-induced diffusivity is about 150 times larger.
6 A A
RT
D
R N


2
s w
D a


Compare hydrodynamic and shear-induced diffusivity values for
a 1-mm particle at a shear rate of 1,000 s-1. Assume the value of
α to be 0.03 for ultra filtration processes

0.8 0.33
0.023 Re
Sh Sc

Problem:
Calculate the mass transfer coefficient for ultrafiltration of milk at
50oC employing tubular membrane system with the following
configurations:
Pore diameter of 1.25 cm; Length = 240 cm;
Number of channels = 18;
superficial velocity = 200 cm/sec;
Pressure drop over length = 2 kg/cm2.
The physical properties of milk are as follows:
Density = 1.03 g/ml;
viscosity 0.008 g/cm/sec;
Diffusivity = 7.0 x 10-7 cm2/sec.
The bulk protein concentration is 3.1% and the gel protein
concentration is 22%. Assume turbulent regime for the process and
make use of Dittus-Boelter correlation

3
1.25( ) 200( / sec) 1.03( / )
Re
0.008( / / sec)
du du cm cm g cm
g cm

 
   
 
  
   
   
= 32188
3 7 2
0.008( / / sec)
1.03( / ) 7 10 ( / sec)
v g cm
Sc
D D g cm cm

 -
 
 
  
   
 
   
= 11096
For calculating Sherwood number in turbulent flow regime (i.e. Re >
2000) in tubular membrane, Dittus-Boelter correlation can be used
0.8 0.33 0.8 0.33
0.023 Re 0.023 (32188) (11096)
Sh Sc
   
= 2008

kd
Sh
D
 
  
 
Now for calculating mass transfer coefficient k we will make use of the
Sherwood number
7 2
2 2 2
2008 7 10 ( / sec)
1.25( )
0.0011( / / sec) 60 10 ( / / )
DSh cm
k
d cm
cm cm litre m hr
-
-
 
 
  
To calculate the flux for the process
2 2
22
ln 60 10 ln 79.3654 / /
3.1
g
b
C
J k litre m hr
C
-
   
   
   
 
 

Calculate the mass transfer coefficient for ultrafiltration of milk at
50oC employing tubular membrane system with the following
configurations:
Pore diameter of 1.25 mm; Length = 240 cm;
Number of channels = 18;
superficial velocity = 200 cm/sec;
Pressure drop over length of tube = 2 kg/cm2
Shear rate at wall = 7272.0 /sec
The physical properties of milk are as follows:
Density = 1.03 g/ml;
viscosity 0.008 g/cm/sec;
Diffusivity = 7.0 x 10-7 cm2/sec.
The bulk protein concentration is 3.1% and the gel protein
concentration is 22%. Assume turbulent regime for the process and
make use of Dittus-Boelter correlation

Effect of hydrodynamic parameters
on permeate flux
Crossflow velocity
Permeate
flux
Mass
transfer
coefficient
Reynolds number
Turbulent
Laminar

Enhancement of permeate flux
• By increasing the cross-flow rate
• By creating pulsatile flow
• By pressure pulsing
• By creating oscillatory flow
• By flow obstruction using baffles
• By generating Dean vortices
• By generating Taylor vortex
• By gas-sparging into the feed

Dean vortices
• Dean vortices are helicoidal flows created by
centrifugal forces in curved channels
– Coiled or helically twisted tubular membranes
• Enhance solute back transfer away from the
membrane
• Effective for enhancing permeate flux by
depolarization of the solute layer on the
membrane

Dean vortices
• Dean vortices are secondary
tangential flows that create a
self-cleaning flow mechanism
when induced within a cross-
flow filtering system
• The general principle of this
technology
– to design, develop and use these
tangential flows to sweep
around a curve to “clean” the
membrane, leading to enhanced
filter performance and longer
membrane life

Taylor Vortex
• Specialised type of Couette flow
• When the angular velocity of the
inner cylinder is increased above a
certain threshold
• Couette flow becomes unstable
and a secondary steady state
characterized by axisymmetric
toroidal vortices
Plasma collection from donors in
transfusion centers by microfiltration

Plasma cell filter for
plasma collection
from donors with a
rotating cylindrical
membrane
DYNAMIC FILTRATION
Biodruckfilter (sulzer AG, Winterthur,
Switzerland) http://www.sulzer.com.
Rotary biofiltration device (Membrex
Inc.) and merged into GE Osmonic
(www.gewater.com)

Rotating Disk Modules MSD system (Westfalia
Separator, Aalen, Germany)
Multishaft systems with overlapping
rotating membranes
The MSD system features 31-cm-
diameter ceramic membranes on eight
parallel shafts located on a cylinder for
a membrane area of 80 m2
All disks rotate at the same speed and
are enclosed in a cylindrical housing
The membrane shear rate is unsteady
and reaches a maximum in the
overlapping regions

Rotating disk dynamic filtration system (Pall Corp., Massachusetts, USA)
www.pall.com
Dyno (Bokela GmbH, Karlsruhe, Germany) www.bokela.com
Optifilter CR (Metso Paper, Raisio, Finland) www.metso.com/
Multi-disk system (SpinTek, Huntington, CA, USA) www.spintek.com
MSD system (Westfalia Separator, Aalen, Germany) www.westfalia-
separator.com
Rotostream (Canzler, Dueren, Germany) http://www.sms-vt.com/index.php
Multishaft disk (MSD) system (Hitachi Ltd.) www.hitachi.com
Self Cleaning Filtration, (novoflow, Oberndorf, Germany)
http://www.novoflow.com/en/home
Rotating Disk Modules

Flux Enhancement by Pulsatile Flows
• Another method for enhancing permeate flux
and mass transfer without using very high
fluid velocity
• Consists of superposing flow and pressure
pulsations at the membrane inlet with a
piston-in-cylinder system or special pumps
such as modified roller pumps
Pulsatile blood flow to enhance gas transfer in
membrane blood oxygenators

Retrofiltration
• Technique for reducing membrane fouling by
pressurizing the permeate above retentate
pressure in order to inject permeate into
retentate and clean the pores
– Backwashing
– Backpulsing

Vibratory shear-enhanced processing
Schematic of the vibratory
shear-enhanced processor
(VSEP) pilot series L with a
single membrane oscillating
around its vertical axis
Vibratory shear-enhance processing
(VSEP) (New Logic Research, Inc.)
www.vsep.com
PallSep Vibrating Membrane Filter
(Pall Corporation)
http://www.pall.com

Solute transmission through UF
membranes
Amount of solute going through an UF membrane can be
quantified in terms of the membrane intrinsic rejection coefficient
(Ri) or intrinsic sieving coefficient (Si):
i
w
p
i S
C
C
R -

-
 1
1
Cw is difficult to determine and hence it is more practical to use the
apparent rejection coefficient (Ra) or the apparent sieving
coefficient (Sa):
a
b
p
a S
C
C
R -

-
 1
1

Factors influencing the retention of a
solute by membrane
• Primary variable
– Solute diameter to pore diameter ratio
• Also depends on
– Solute shape
– Solute charge
– Solute compressibility
– Solute-membrane interactions
– Operating conditions
The amount of solute going through the membrane can be quantified in terms of
intrinsic rejection coefficient (Ri) and intrinsic sieving coefficient (Si)

Rejection coefficient:
Older theory  new theory
 
 2
2 
 -

a
R
1

a
R
for  < 1
for   1
 = (di / dp)=solute-pore diameter ratio
In other words, Ra is
constant for a solute-
membrane system.
It is now recognised that rejection coefficients depend on
operating and environmental parameters such as
•pH
•Ionic strength
•System hydrodynamics
•Permeate flux
 1 p
i
w
C
R
C
 -
1 p
a
b
C
R
C
 -

Sieving coefficients
w
p
i
C
C
S 
Intrinsic sieving coefficient
•Depends on solute-membrane system
•Depends on physicochemical parameters
such as pH and ionic strength
•Depends on permeate flux
Apparent sieving coefficient
•Depends on solute-membrane system
•Depends on physicochemical parameters
such as pH and ionic strength
•Depends on permeate flux
•Depends on system hydrodynamics
b
p
a
C
C
S 

Effect of permeate flux on intrinsic
sieving coefficient
1
exp
exp
-








+













eff
m
v
eff
m
v
i
D
J
S
S
D
J
S
S
S
d
d
Intrinsic
sieving
coefficient
Permeate flux (log scale)
Asymptotic
intrinsic sieving
coefficient
S͚

Effect of permeate flux and mass transfer
coefficient on apparent sieving coefficient
  







+
+
















-
-








+







k
J
D
J
S
S
D
J
S
S
k
J
D
J
S
S
S
v
eff
m
v
eff
m
v
v
eff
m
v
a
d
d
d
exp
exp
1
1
exp
Permeate flux (log scale)
Apparent
sieving
coefficient
Mass transfer coefficient
Apparent
sieving
coefficient

Determination of intrinsic sieving
coefficient and mass transfer coefficient






+








-









- k
J
S
S
S
S v
i
i
a
a
1
ln
1
ln








- a
a
S
S
1
ln






k
Jv








- i
i
S
S
1
ln

Problem
The intrinsic and apparent rejection coefficients for a
solute in an ultrafiltration process were found to be
0.95 and 0.63 respectively at a permeate flux value of
6 x 10-3 cm/s.
What is the solute mass transfer coefficient?

Solution:






+








-









- k
J
S
S
S
S v
i
i
a
a
1
ln
1
ln
Sa = 1-Ra = 1-0.63 = 0.37
Si = 1-Ri = 1-0.95 = 0.05
ln ln
1 1
v
a i
a i
J
k
S S
S S

   
-
   
- -
   
3
3
6 10
/
0.37 0.05
ln ln
1 0.37 1 0.05
2.486 10 /
k cm s
cm s
-
-


   
-
   
- -
   
 

Solute fractionation
For fractionation of a binary mixture of solutes, it is desirable to
achieve maximum transmission of the solute desirable in the
permeate and minimum transmission of the solute desirable in the
retentate.
 
 
2
1
2
1
1
1
a
a
a
a
R
R
S
S
-
-



Enhancement of fractionation
• pH optimization
• Feed concentration optimization
• Salt concentration optimization
• Membrane surface pre-treatment
• Optimization of permeate flux and system hydrodynamics
Selectivity parameter

Problem
A feed solution (10 g/l) of dextran (MW=505 kDa) is ultrafiltered through a 25 kDa
MWCO Membrane. The pure water flux values and the dextran UF permeate flux
values at different TMP are given below
The osmotic pressure is given by the following correlation
where Δπ is in dynes/cm2 and Cw is in %w/v.
Calculate the membrane resistance and the mass transfer coefficient for dextran
assuming that Rg and Rcp are negligible
ΔP (kPa) Pure water flux
(m/s)
Jv (m/s)
30 9.71x10-6 6.24x10-6
40 1.23 x 10-5 7.08x10-6
50 1.57x10-5 7.63x10-6
60 1.87x10-5 8.02x10-6
0.35
log 2.48 1.22( )
w
C

  +

y = 3E-07x + 4E-07
0.00E+00
2.00E-06
4.00E-06
6.00E-06
8.00E-06
1.00E-05
1.20E-05
1.40E-05
1.60E-05
1.80E-05
2.00E-05
0 20 40 60 80
Plot of Pure water flux vs transmembrane pressure
Pure water flux (m/s)
Linear (Pure water flux (m/s) )
Solution
The MWCO of the membrane is 25 kDa while the MW of dextran is
505 kDa. Hence we can safely assume that dextran is totally
retained. Pure water ultrafiltration is governed by
m
v
R
P
J


Rm = 3.33 x 109 Pa.s/m

v
m cp g
P
J
R R R

 - 

+ +
We also know that
v
m
P
J
R

 - 

Since Rcp and Rg are negligible the equation becomes
Using the above equation we can calculate the osmotic pressure for
every value of transmembrane pressure
ΔP
(kPa)
Pure
water flux
(m/s)
Jv
(m/s)
Δπ
(kPa)
Δπ
(dynes/c
m2)
Cw
(%w/v)
Cw
(g/l)
K
(m/s)
30 9.71x10-6 6.24x10-6 9.22 92208 7.63 76.31 3.07x10-6
40 1.23 x 10-5 7.08x10-6 16.42 164236 10.04 100.43 3.7x10-6
50 1.57x10-5 7.63x10-6 24.59 245921 11.99 119.94 3.07x10-6
60 1.87x10-5 8.02x10-6 33.29 332934 13.61 136.08 3.07x10-6

The correlation for osmotic pressure given in the problem can be
rearranged to
 
2.857
log10 2.48
1.22
w
C

 -
 
  
 
Using the above equation the wall concentration at different TMP
can be calculated
The mass transfer coefficient in an UF process with total solute
retention is given by
ln w
v
b
C
J k
C
 
  
 
Rearranging the equation we get
ln
v
w
b
J
k
C
C

 
 
 

Microfiltration
• Microfiltration separates
micron-sized particles from
fluids
• The modules used for
microfiltration are similar to
those used in ultrafiltration
• Microfiltration membranes are
microporous and retain
particles by a purely sieving
mechanism
Microfiltration can be operated either in
dead-ended (normal flow) mode or cross-
flow mode
Typical permeate flux values are higher than ultrafiltration
processes even though the processes are operated at much lower
TMP

Applications of microfiltration
• Cell harvesting from bioreactors
• Virus removal for solutions
• Clarification of fruit juice and beverages
• Removal of cells from fermentation media
• Water purification
• Air filtration
• Sterilization

The permeate flux in microfiltration
)
( C
M
v
R
R
P
J
+



Jv = Permeate flux
P = Pressure difference across the
membrane
RM = Membrane resistance
RC = Cake resistance
 = Liquid medium viscosity
The cake resistance
M
S
C
A
V
r
R 
r = Specific cake resistance
VS = Volume of cake
AM = Area of membrane
For micron sized particles, r is given by













 -
 2
3
1
1
180
s
d
r

  = Porosity of cake
ds = Mean particle diameter

Problem: Microfiltration of bacteria
Bacterial cells having 0.8 micron average diameter are
being microfiltered in the cross-flow mode using a
membrane having an area of 100 cm2.
The steady state cake layer formed on the membrane has
a thickness of 10 microns and a porosity value of 0.35. If
the viscosity of the filtrate obtained is 1.4 cP, predict the
volumetric premeate flux at a transmembrane pressure
of 50 kPa.
When pure water of viscosity 1 cP was filtered through
the same transmembrane pressure, the permeate flux
obtained was 10-4 m/s

v
M
P
J
R



For pure water filtration the flux is written as
11
3 4
50000
5 10 /
(1 10 ) (1 10 )
M
v
P
R m
J

-
- -

   
  
The specific cake resistance of the bacterial cell cake can be calculated
from
The cake resistance Rc can be calculated from
15 2
3 2 3 7 2
1 1 1 0.35 1
180 180 4.264 10 /
0.35 (8 10 )
s
r m
d

 -
   
- -
   
   
   
   

    
 
15 5 10
4.264 10 1 10 4.264 10 /
S
C c
M
V
R r r m
A
d -
       
Solution

The permeate flux can be calculated from
3 10 11
50000
( ) 1.4 10 (4.264 10 5 10 )
v
M C
P
J
R R
 -

 
+    + 
= 6.58 x 10-5 m/s

Dialysis
• The mode of transport in
dialysis is diffusion
• Separation occurs
because
– Small molecules diffuse
more rapidly than larger
ones
– Also due to the degree to
which the membrane
restricts transport of
molecules usually
increases with solute size
Membrane
Bulk concentration
on downstream side
(C2)
Boundary layers
Concentration profile in dialysis
Bulk concentration
on upstream side (C1)

The rate of mass transport or solute flux (N) is directly proportional
to the difference in concentration (C) at the membrane surfaces
d
C
SD
N eff


S is a dimensionless solute partition coefficient
Deff is the effective diffusivity of the solute within the
membrane
d is the membrane thickness
Deff and d can be combined and termed the membrane mass
transfer coefficient (KM) for a given membrane-solute system
M
M
R
C
C
K
N




Dialysis

2
1
1
1
1
1
K
K
K
K M
O
+
+

KO = the overall mass transfer coefficient
K1 and K2 are the mass transfer
coefficients on the upstream and
downstream sides
 
2
1 C
C
K
N O -

In terms of mass transfer coefficient
C1 and C2 are the upstream (feed) and
downstream (dialysate) concentrations
2
1 R
R
R
R M
O +
+

The membrane resistance alone seldom governs the overall mass
transport. The liquid boundary layers on either side of the
membrane also contribute to resistance to transport
RO = the overall resistance
R1 = the resistance on the upstream surface
R2 = the resistance on the downstream
surface

Hollow fiber dialyser
C1
C2
C3
C4
Co-current flow Counter-current
flow
C1
C3
C2
C4
Feed
Dialyzing solution
(sweep stream)
Dialysate
Product
Feed
Dialyzing solution
(sweep stream)
Dialysate
Product

Co-current and counter-current dialysis








-
-
-
-
-


4
2
3
1
4
2
3
1
ln
)
(
)
(
C
C
C
C
C
C
C
C
Clm
Log-mean concentration difference (∆Clm)
Co-current Counter-current








-
-
-
-
-


3
2
4
1
3
2
4
1
ln
)
(
)
(
C
C
C
C
C
C
C
C
Clm
Length of membrane
Conc.
Feed side
Dialysate
Conc.
Length of membrane
Feed side
Dialysate









-
-
-
-
-


4
2
3
1
4
2
3
1
ln
)
(
)
(
C
C
C
C
C
C
C
C
Clm
Co-current flow
Co-current operation is preferred when
liquid flow causes significant pressure
drop between inlet and outlet side
Generally in co-current mode membrane
utilization is incomplete









-
-
-
-
-


3
2
4
1
3
2
4
1
ln
)
(
)
(
C
C
C
C
C
C
C
C
Clm
Counter-current flow
Counter current mode ensures uniform
gradient and hence uniform solute flux
Counter current dialysis is most commonly
used as it ensures full membrane utilization

Co-current flow Counter-current flow
C1
C3
C3
C4
C1








-
-
-
-
-


4
2
3
1
4
2
3
1
ln
)
(
)
(
C
C
C
C
C
C
C
C
Clm








-
-
-
-
-


3
2
4
1
3
2
4
1
ln
)
(
)
(
C
C
C
C
C
C
C
C
Clm
Dialysis modes
C4

Applications of dialysis
• Removal of acid or alkali from products
• Removal of alcohol from beer (to make alcohol free
beer)
• Removal of salts and low molecular weight
compounds from solutions of macromolecules
• Concentration of macromolecules
• Dialysis provides a tool for controlling the chemical
species within a reactor
• Purification of biotechnological products
• Haemodialysis

The figure below shows a completely mixed dialyser unit. Plasma
having a glutamine concentration of 2 kg/m3 is pumped into the
dialyser at a rate of 5x10-6 m3/s and water at a flow rate of 9 x 10-6
m3/s is used as the dialysing fluid. If the membrane mass transfer
coefficient is 2 x 10-4 m/s and the membrane area is 0.05 m2,
calculate the steady state concentrations of glutamine in the product
and dialysate streams.
Problem

Solution
The overall material balance for glutamine gives ------- (a)
The glutamine concentration flux per unit area can be obtained using equation
The amount of glutamine in of the dialysate should be equal to the product of
the concentration flux and area:
The amount of glutamine in the dialysate = Q2C4, therefore
------- (b)
Solving the two equations simultaneously, we get:
C2 = 1.027 kg/m3
C4 = 0.541 kg/m3
2 4
( )
c m m
J K C K C C
   -
2 4
* * * ( )
c m m
J A K A C K A C C
   -
2 4 2 4
Q C K *A(C C )
m
 -
1 1 l 2 2 4
Q C Q C Q C
 +

Packed bed adsorption has several major
limitations
• High pressure drop
• Increase in pressure drop
during operation
• Column blinding by
proteins
• Dependence on
intraparticle diffusion for
the transport of proteins
to their binding sites
• High process times (due
to iv)
• High flow rates cannot be
used
• High recovery liquid
volume
• Radial and axial dispersion
resulting from the use of
polydisperse media
• Problems associated with
scale-up

Advantages of membrane adsorbers
• Low process time
• Low recovery liquid volume
• Possibility of using higher flow rates
• Lower pressure drop
• Less column blinding
• Ease of scale-up
• Fewer problems associated with validation (if
a disposable membrane is used)

Comparison of solute transport in particulate
packed bed and membrane adsorbers

Different types separation chemistries are
used in membrane adsorption
• Affinity binding
• Ion-exchange interaction
• Reverse phase and hydrophobic interaction
Size exclusion based separation using membrane
beds has not yet been feasible

Membrane adsorption
• Membrane adsorption processes are carried
out in two different modes
– Pulse
– Step
• Based on the membrane geometry, three
types of membrane adsorbers are used:
– Flat sheet
– Radial flow
– Hollow fibre

Operation of flat sheet membrane adsorber

Operation of hollow fibre membrane
adsorber

δm
θC θD
Diffusion and convection times in
membrane adsorption
Re
s pore
pore
u d
v
 
  
 
Reynolds number of the fluid flowing through
the membrane pores
us = superficial velocity (m/s)
dpore = average pore diameter (m)
v = kinematic viscosity (m2/s)
ε = porosity (-)
2
m
c
s
u
d 
 
2
4
pore
d
d
D
 
Time taken for solute to diffuse
from central line to the pore wall
Residence time of solute moving
along central line through a pore
dpore

An adsorptive membrane has a thickness of 2 mm
and a diameter of 5 cm. The porosity of the
membrane is 0.75 and the tortuosity is 1.5. The
pore diameter was estimated to be 2 x 10-6 m.
If we are to use this membrane for adsorption of a
DNA fragment (diffusivity = 9.5 x 10-12 m2/s) from an
aqueous solution, what is the maximum solution
flow rate that can be used? Assume that the flow
through the pores is laminar
Problem: Membrane adsorption of DNA

Area of the membrane = 1.964 x 10-3 m2
The superficial velocity is given by
The convection time can be obtained from
Diffusion time can be calculated using
For total capture of DNA θC > θD . Therefore
The solution flow rate should be lower than 2.098 x 10-5 m3/s.
3
3 2
( / )
/
1.964 10 ( )
s
Q Q m s
u m s
A m
-
 

3 3 6
2 10 ( ) 1.5 0.75 1.964 10 2.2095 10
2 2
m
c
s
m
s
u Q Q
d 

- - -
     
  
2 6 2
12
(2 10 )
0.1053
4 4 9.5 10
pore
d
d
s
D

-
-

  
 
6
2.2095 x10
0.1053
Q
-

Solution

ChromaSorb™ Membrane Adsorber (Millipore)
Single-use, flow-through anion exchanger designed for the removal of
trace impurities including host cell protein (HCP), DNA, endotoxins and
viruses from monoclonal antibody or other protein feedstocks.

Sartobind™ Membrane Adsorber (Sartorius)

Schematic representation of membrane adsorber
and the operations of one purification cycle

Liquid membrane technology
• Liquid membrane extraction
involves
– the transport of solutes
across thin layers of liquid
interposed between two
otherwise miscible liquids
• There are two types of
liquid membrane processes:
– Emulsion liquid membrane
(ELM) processes
– Supported liquid membrane
(SLM) processes

Liquid surfactant membrane process

Schematic diagram of the membrane
emulsification process

Limitations
1. Film diffusion
2. Pore diffusion
3. Binding kinetics
Limitations
1. Film diffusion
3. Binding kinetics

Reverse Osmosis
Introduction
Reverse Osmosis
Reverse Osmosis Equipment

Introduction
• In RO, the goal is usually to remove a solute
from solution by passing the solvent through
the membrane and leaving the solute in a
concentrated retentate (reject) stream
• Note that this is a continuous process, unlike
filtration; purified water is produced
continuously

Advantages
• low energy consumption
• high removal of solute in one stage
• no components added (such as absorbing gas
or extracting liquid)
• no phase change
• low capital costs
• easy, modular, installation

Disadvantages
• Membrane life (hopefully 3-5 years)
• Fouling
• Pretreatment costs (removal of suspended solids, fouling
materials)
• Relatively low concentration of solutes
• In order to understand and to predict membrane performance
it is necessary to have transport equations that describe the
transport of solvent and solute through the membrane
• In all membrane processes, we are looking at relationships
between forces (driving forces) and fluxes;
– [Class: you name some examples of these relationships that you
already know.]

Osmotic Pressure
• Thermodynamic property of a solution which represents how
different a solution is compared to a pure solvent in terms of
the pressure required to bring the solution up to the same
chemical potential (ie., in equilibrium with) pure solvent
– what this means, practically, is that osmotic pressure acts against the
pressure driving force for transport across a membrane.
• This osmotic pressure can be 'looked up' in a book - a
thermodynamic property.
• A reasonable approximation of osmotic pressure is the Van't
Hoff Eqn
where n is the kmol of solute per
Vm m3 of pure solvent, which is the
same as the molar concentration, ci

Osmotic pressure
cRT
 
2 3
1 2 3
( ......)
RT AC A C A C
  + + +
For concentrated solutions of
uncharged solutes correlations
involving series of virial coefficients
are used
van’t Hoff equation
The osmotic pressure difference across a
membrane is given by
1 2
  
 -

Summary of the transport equations
Solvent flux )
( 

-

 P
A
N W
W
)
( P
A
N W
W 

Pure water flux
Solute Flux )
(
)
( 2
2 c
c
A
c
c
L
K
D
N b
S
b
M
S
S
S -

-

Concentration Polarization
)
(
)
(
ln
2
1
2
c
c
c
c
k
c
N
N
c
N
J b
S
W
T
V
-
-

+


Material Balance on Solute
S
W
S
N
N
N
c
c
+

2

Membrane_separations.pptx

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