Educational Workshop Fabrication of Polymer Membranes · Title: Microsoft PowerPoint - Educational...
Transcript of Educational Workshop Fabrication of Polymer Membranes · Title: Microsoft PowerPoint - Educational...
Fabrication of Polymer Membranes
Volker Abetz
University of Hamburg, Institute of Physical ChemistryMartin-Luther-King-Platz 6, 20146 Hamburg, Germany
Helmholtz-Zentrum Geesthacht, Institute of Polymer Research Max-Planck-Straße 1, 21502 Geesthacht, Germany
Acknowledgement: Torsten Brinkmann, Md. Mushfequr Rahman, Ulrich A. Handge
1Copyright © 2018 by Volker Abetz
Content
1. Introduction
2. Membrane Geometries and Membrane Production
3. Membrane Modules
4. Development of a Membrane Process
2Copyright © 2018 by Volker Abetz
Membranes forLiquid and Gas Phase Separations
H2O CO2 / N2 O2 / N2
CH4 / CO2
Copyright © 2018 by Volker Abetz
Largest Market for Membranes: Hemodialysis
Scheme of hemodialysis
Dialysis - Application:
Hemodialysis
Commercial dialyzerFresenius FMC-Magazin 2013http://www.fmc-ag.com
4Copyright © 2018 by Volker Abetz
Biogas Production
Source: http://www.ewe-biogas.de/
Co-fermentation mediaFeed vessel
Agriculture
Animalfeed
Manure
Hygienisation 70°C
Bio reactors37-39°C
Post fermentation Cooling CoolingH
2S R
em
ova
l
Ad
so
rpti
on
Conditioning unitCH4 enriched gas
Post condit-ioning
Connection to gas grid
Off-gasCondensateCond-
ensate
Com-pres-sion
Com-pres-sion
Gasstations
HouseholdsIndustry and decentralised energy production
Manure Manure storage
Gas grid
Decentralised energy production
Decentralised energy production
GP conditioning unit CH4 enriched gas
Post condit-ioning
Vacuumpump
Compres-sion Connection
to gas grid
Gas permeation
Heat supply
5Copyright © 2018 by Volker Abetz
Membrane Markets
HD = HemodialysisRO = Reverse OsmosisUF = UltrafiltrationMF = MicrofiltrationED = ElectrodialysisPV = PervaporationGS = Gas Separation
To give an impression where the big membrane business is located !!
6Copyright © 2018 by Volker Abetz
Membrane
ModuleRetainedComponent
PermeatingComponent
Feed Retentate
Permeate
Compressor:Driving force
Vacuum pump:Driving force
Heat exchanger:Processtemperature
Membrane Process (Gas Permeation)
Copyright © 2018 by Volker Abetz
Membrane
Module rejected component
permeating component
Feed Retentate
Permeate
Membrane Process:Principle of Separation
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Porous membrane Ultra- and microfiltration Gas separation
Solution-diffusion membrane Gas and vapour permeation Pervaporation Reverse osmosis Nanofiltration
Membranes for Separation Processes
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Membrane Processes - Classification
Driving force Separation mechanism
PhysicalState
Permeating particle / molecular size
Pressure difference
Difference in chemical potential
Sieving mech. (top layer filtrat.)
Sorption+Diffusion
Liquid / Liquid
Partial pressure/Difference in fugacity
Sorption+Diffusion+Volatility
Sorption+Diffusion
Liquid / Gas
Gas / Gas
Gas /Gas
Difference in concentration / activity difference
Sorption+Diffusion Liquid / Liquid
Electric potential difference
Electrophoreticmobility
Liquid / Liquid
Microfiltration
Ultrafiltration
Nanofiltration
Rev osmosis
Pervaporation
Vapor perm.
Gas perm.
Dialysis
Diffusion dial.
Bipolar electrodialysis
Electrodial.
1 nm 0,1 µm 10 µm
10Copyright © 2018 by Volker Abetz
Membrane Processes - Classification
Microfiltration/Ultrafiltration:
Nanofiltration:
Reverse osmosis:
Dialysis:
Electrodialysis:
Pervaporation:
Retention of drops and particles, such as extraction ofproteins from whey
Retention of components with M>300 kg/mol
Retention of dissolved substances in water, eg seawater desalination
Difference in concentration-driven permeation,e.g. hemodialysis
Separation of ions by alternation of anion and cation selectivemembranes, the driving force is the electric potential
Liquid feed, evaporation of the passing material stream in the permeate, the driving force is the difference in activity
Pre
ssur
edr
ivin
gfo
rce
por
ous
me
mb
rane
den
sem
em
bra
ne
11Copyright © 2018 by Volker Abetz
Gas permeation/Vapor permeation:
Contactors:
Membrane reactors:
Separation of gas and vapor mixtures, the driving forceis the difference of pressure or fugacity
The porous membrane is the mass transfer area for absorption, extraction desorption or distillation processes
Combination of reaction and separation in a basic operation, depending on the reaction conditions using porous or dense membranes
den
sem
em
bra
nep
orou
sm
em
bra
neMembrane Processes - Classification
12Copyright © 2018 by Volker Abetz
VOC recoveryPoly(dimethyl siloxane) PDMS
Poly(octyl methyl siloxane) POMSPolymers of Intrinsic Microporosity PIM
Polyacetylenes: Si; Ge; C Teflon AF ® : 2400; 1600
CO2 separationPoly(ether-block-ester) PolyActive™Poly(ether-block-amide) PEBAX®
Cellulose acetate / triacetateEthyl cellulosePDMS Polymers of Intrinsic Microporosity PIM
DehydrationPoly(vinyl alcohol)
TYLOSE ®
Cellulose acetate / triacetate
H2 separationPolyimidesPIMPPOPEI
O2/N2 SeparationCellulose Acetate
PDMSPIMPPO
NanofiltrationModified PDMS
PIM
Food storageEthyl cellulose
Catalytic membranesPDMSPIM
PEBAXTORLON®
Active and inactive additives to matrix materialsSiO2, TiO2, Pd nanoclusters, carbon (active and nano), PEG, amino compounds, active carriers etc.
13
Gas Separation MembranesState-of-the-art membrane materials
Copyright © 2018 by Volker Abetz
M. Ulbricht, Polymer 2006, 47, 2217.
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UF/MF membranesState-of-the-art membrane materials
Cellulose acetate
Polysulfone/ Polyethersulfone
Polyvinylidenfluoride
Polyamide
Track-etched
Cellulose nitrate
Polyethylene
Polytetrafluoroethylene
Polypropylene
Polyethylene terephthalatePolycarbonate
Cellulose, regenerated
Polyacrylonitrile
Ceramic membranes(Al2O3, TiO2, ZrO2, SiO2, SiC)
PolycarbonatePolyesterPolyimide
UF MF
Mesoporousmainly anisotropic
Macroporousisotropic
Copyright © 2018 by Volker Abetz
Content
1. Introduction
2. Membrane Geometries and Membrane Production
3. Membrane Modules
4. Development of a Membrane Process
15Copyright © 2018 by Volker Abetz
16
Molecular Weight Cut-off
Log MW
Rej
ectio
n
Copyright © 2018 by Volker Abetz
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UF / MFState-of-the-art membrane preparation metohds
Symmetric MF Membranes
Casting + leaching / evaporation Film-stretching
Asymmetric MF Membranes
Sintering / Slip casting
Phase inversion
Track-etchingAnodising process
K. Scott, Handbook of Industrial Membranes, 2. ed., Ed. 2, Elsevier Science & Technology Books, Oxon (UK) 1999, 118.
Copyright © 2018 by Volker Abetz
Membrane Preparation
Processing Via Sintering
I: Filling of mould III: Sintering under pressure
II: Precompression IV: Pressureless sintering EP 2 982 492
Ia Ib
II III IV
18Copyright © 2018 by Volker Abetz
Sintered Membranes
• Commercial Examples
• Ultra-high molecular weight polyethylene (UHMWPE) membranes
• UHMWPE: Excellent mechanical properties
• Processing requires special techniques
• Poly(tetrafluoroethylene) (PTFE) membranes
• PTFE: High chemical and thermal stability
• High hydrophobicity
• Applications: Filter membranes, dust filters,
• pressure compensation units
Figure sources: MICRODYN-NADIR GmbH (Wiesbaden); Berghof Products (Eningen)
SEPRODYN®
Screw-in filter
19Copyright © 2018 by Volker Abetz
20
Making microporous membranes by this uniaxial stretching method include three different stages:
1) Extrusion: To melt and extrude the polymer into uniaxially oriented films. It is crucial to achieve thestacked lamellar morphology after extrusion and rolling process because only stacked lamellae are ableto form open pores during the process of streching.
2) Annealing: The extruded films are annealed for to the perfection of the crystalline phase.
3) Stretching: In the last stage, the films are deformed along the machine direction to generate pores.
Paste extrusion Rolling Uniaxial stretching at RT
Fine powderwith lubricant
Paste extrusion(10-20 cm/ min)
Thin sheet Multiple rolling to reduce the thickness
5 mm 1 mm
Direction of rolling
Direction of stretching
Uniaxial Stretching Method
http://www.che.vt.edu/Faculty/Wilkes/GLW/jays_page/glw-webpage-jay.htm
Copyright © 2018 by Volker Abetz
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MD = Machine direction TD= Transverse direction
TEM micrograph (a) shows a uniaxially oriented high density polyethylene (HDPE) film melt extruded andcrystallized under directional flow. A stacked lamellar morphology is observed with the lamellae orientedalong the transverse direction. After a further annealing treatment, the melt extruded HDPE film wasdeformed along the machine direction. During the deformation process, the stacked lamellae tend toseparate to form microporous membranes, as shown in TEM micrograph (b).
http://www.che.vt.edu/Faculty/Wilkes/GLW/jays_page/glw-webpage-jay.htm
Uniaxial Stretching Method
Copyright © 2018 by Volker Abetz
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Free radical emulsion or suspension polymerization
Properties
• Tm (1. melting) = 342 °C
• Tm (2.,3… melting) = 327 °C
• below Tm insoluble in all organic solents
• enormous melt viscosity (1010 Pa·s @ 380 °C)
extended chain crystals
folded chain crystals
Biaxially Stretched MembranePoly(tetrafluoro ethylene) (PTFE)
Goretex® membrane
3 µm
Copyright © 2018 by Volker Abetz
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Etching bath
Membrane withporous structure
Radiation source
Polymer film
Two basic irradiation methods
1. fragments from the fission of heavy nuclei ( e.g. Cf or U)
2. heavy ion beams from accelerators
E. Drioli, L. Giorno, Comprehensive Membrane Science and Engineering, 1. ed., Elsevier, UK 2010, 98.S.K. Chakarvarti, Radiation Measurements 2009, 44, 1085.P. Apel, Radiation Measurements 2001, 34, 559.
Etching
• alkali solution (e.g. NaOH, KOH)
Pore-size and pore-shape
• uniform cylindrical, conical, tunnel-like, or cigar-like
• controllable due to e.g.
• target material
• the nature and energy of incident particles
• etch conditions (T, etchant, pre-etch storage)
Track Etched Membranes
A polymer film is bombarded with heavy ions and the radiation damaged areas are removed using an etching bath.
Copyright © 2018 by Volker Abetz
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• symmetric membranes
• very narrow pore size distribution
• pores diameter ranging from few nm to mm
• prevention of surface roughness effects
• various materials
• used in microbiology or particle analysis
• pore size < membrane thickness• pore blocking• cake layer formation
P. Apel, Radiation Measurements 2001, 34, 559.
Polyethylene terephthalatecigar-like pores
non-parallel pore channelsPolycarbonate Polypropylene
slightly conical parallel pores
Polyethylene terephthalate“bow-tie” pores
1 µm
1 µm1 µm
1 µm
Track Etched Membranes
Copyright © 2018 by Volker Abetz
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Common materials
Polyethylene terephthalate
• good stability in acids and organic solvents
• biologically inert
• mechanically strong
• high etch rate achievable (UV-sensibilisation)
• wide range of pore sizes
• relatively hydrophilic
Polycarbonate
• higher sensitivity smaller pore sizes (10 nm)
• lower resistance to organic solvents
• lower wettability
Track Etched Membranes
Copyright © 2018 by Volker Abetz
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10 µm
© Satorius
Most common: non-solvent induced
H. Matsuyama,K. Ohga,T. Maki, M. Tearamoto, S. Nakatsuka, Journal of Applied Polymer Science 2002, 89, 3951.
precipitation bath
Alternative: thermally induced
Phase Inversion Process
Cellulosic membrane
Copyright © 2018 by Volker Abetz
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limited pH-stability
not autoclavable (dry)
lack of tolerance to free chlorine
to aggressive cleaning chemicals
to temperature above 30 °C
susceptibility to biological degradation
gradual decline in flux over lifetime due to compaction
most-hydrophilic industrial-grade membrane material
low unspecific adsorption
high flux
high service life
inexpensive
easy to manufacture
low impact on environment (waste)
Properties
Cellulosic Membrane
CelluloseCellulose Triacetate
Copyright © 2018 by Volker Abetz
HZG Membrane Casting Machine
30 cm
Coating knife
Immersion bath
Solvent Evaporation
Nonwoven
Polymer solution
Casting of the polymer solution onto a substrate, e.g. nonwoven, on rolls up to 30cm width
S. Rangou, K. Buhr et al., J. Membr. Sci. 2014, 451, 266-275.
28Copyright © 2018 by Volker Abetz
M. Radjabian, et al., Polymer 2014, 55, 2986-2997. K. Sankhala, et al., Adv. Mat. Int. 2017, 4, 1600991
Outside-in Membranes Inside-out Membranes
Isoporous Hollow Fiber Membranes
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HZG Membrane Production Facility
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Asymmetric Membranes withFinger Pore Substructure from NIPS
12% cellulose acetate (CA)in dimethylacetamide (DMAc)
12% polyamide (PA) in dimethylsulfoxide (DMSO)
12% polysulfone (PSU) in dimethylformamide (DMF)
Filtration rate (m/s)
Retention g-globulin
Retention bovin serum albumin (BSA)
Porosity (%)
12% CA in DMAc
3.5 x 10-5 99 98 80
12% PA in DMSO
2.1 x 10-5 97 72 82
12% PSU in DMF
1.9 x 10-5 96 80 83
H. Strathmann, Introduction to Membrane Science and Technology, Wiley-VCH, Weinheim 2011
31Copyright © 2018 by Volker Abetz
Commercial Polymer MembranesMade by Phase Inversion
Membrane Material Membrane Structure Membrane ProcessCellulose Acetate (CA) Asymmetric EP, MF, UF, ROCellulose mixed esters Asymmetric and symmetric MF, DPolyacrylonitrile (PAN) Asymmetric UFPolyamide (aromatic and aliphatic) (PA)
Symmetric and asymmetric MF, UF, RO, MC
Polyimidie (PI) Symmetric and asymmetric UF, RO, GSPolypropylene (PP) Symmetric MF, MD, MCPolyethersulfone (PESU) Symmetric and asymmetric UF, MF, GS, DPolysulfone (PSU) Symmetric and asymmetric UF, MF, GS, DSulfonated polysulfone (SPSU)
Symmetric and asymmetric UF, RO, NF
Polyvinylidenefluiride (PVDF)
Symmetric and asymmetric UF
D: dialysisEP: electrophoresisGS: gas separationMC: membrane contactorMD: membrane distillation
MF: microfiltrationNF: nanofiltrationRO: reverse osmosisUF: ultrafiltration
H. Strathmann, Introduction to Membrane Science and Technology, Wiley-VCH, Weinheim 2011
32Copyright © 2018 by Volker Abetz
Membrane Formation by„Phase Inversion“
V. Abetz, Macromol. Rapid Commun. 2015, 36, 10.
33Copyright © 2018 by Volker Abetz
W.A. Philipp, M. A. Hillmyer, E. Cussler, Macromolecules, 2010, 43, 7763.
Composite Membranes with Block Copolymers
Alignment of cylindrical structure of PS-b-PLA at the surface
selective non-selectivesolvent
34Copyright © 2018 by Volker Abetz
K.-V. Peinemann, V. Abetz, P.F.W. Simon, Nature Materials 2007, 6, 992-996.A. Jung, S. Rangou, C. Abetz, V. Filiz, V. Abetz, Macromol. Mater. Eng. 2012, 729(8), 790-798.
Membrane Formation by„Phase Inversion“
N
N
35Copyright © 2018 by Volker Abetz
Upscaling of Integral AsymmetricBlock Copolymer Membranes
Porosity: 8%
Track etching membrane
36Copyright © 2018 by Volker Abetz
Self-Assembly in Solvents of Different Quality
M. Radjabian et al., ACS Applied Materials & Interfaces 2017, 9, 31224.
37Copyright © 2018 by Volker Abetz
Pore Sizes (ca. 15 -100 nm)
Pore size ≈ 25 nm
Molecular weight (PS-b-P4VP)
4-V
inyl
pyr
idin
con
ten
t
≈ 55 nm
≈ 40 nm
≈ 45 nm
≈ 35 nm
S. Rangou et al., J. Membr. Sci. 2014, 451, 266-275.
: : molecular weight
Molecular weight and composition control pore size
PS-b-P4VP Membranes with Different Pore Sizes (ca. 15 -100 nm)
38Copyright © 2018 by Volker Abetz
0.0 0.2 0.4 0.6 0.8 1.010
20
30
40
50
60
29 nm25 nm
21 nm
XPS75P4VP25100
PS83.7P4VP16.3100 / PS75P4VP25
100
Me
an p
ore
dia
met
er (
nm)
Tailoring Pore Size by Blending
M. Radjabian, V. Abetz, Advanced Materials 2015, 27, 352-355.
39Copyright © 2018 by Volker Abetz
Double Stimuli Responsive Membranes
polydopamine coating pNIPAM-NH2
T > LCST
T < LCST
pH <
0.4 µm 0.4 µm
Modification of pH-responsive PS-b-P4VP membranes with a temperature sensitive polymer (pNIPAM-NH2)=> Double stimuli-responsive membrane
J. I. Clodt , V. Filiz et al., Adv. Funct. Mater. 2013, 23, 731-738.
pH >
40Copyright © 2018 by Volker Abetz
Temperature- and pH dependent water flux
Membrane after polydopamine coating and further reaction with pNIPAM-NH2
0
200
400
600
800
1000
1200
1400
3.2 3.4 3.6 3.8 4 4.2 4.4 4.6 4.8 5 5.2
pH
Wat
er f
lux
[Lh
-1m
-2b
ar-1
]
T=45°C
T=40°C
T=35°C
T=30°C
T=25°C
J. I. Clodt , V. Filiz et al., Adv. Funct. Mater. 2013, 23, 731-738.
Double Stimuli Responsive Membranes
41Copyright © 2018 by Volker Abetz
Multilayer Thin Film Composite Membrane
Non-woven (d 100 µm)
Porous support layer (d 50 µm)
δ 300 nm (3 layers)Composite separation layers (d 0.3 µm)
Gutter layer
Protection layer
Separation layer
42Copyright © 2018 by Volker Abetz
Thin Film Composite Membrane Preparation
Porous supporting membrane
Casting solution
Composite membrane
43Copyright © 2018 by Volker Abetz
Casting Solution
Oven (100°C)
Composite membrane
PAN porous membrane
Production of Thin Film Composite Membrane
44Copyright © 2018 by Volker Abetz
Polyimides PEG containing polymers
Thermally rearranged polymers Polymers of intrinsic microporosity
Polyacetylenes Perfluorinated amorphous polymers
Gas Phase Separation Membrane Material ToolboxSelective Layer Polymers
45
A. Tena et al., Sci. Adv., 2016, 2, e1501859.; A. Tena et al., Macromolecules 2017, 50, 5839.
Copyright © 2018 by Volker Abetz
Semicrystalline Polymeric Membrane
Polyether based block copolymers
A - Amorphous soft segmentsB - Crystalline hard segments
A
B
Polyamide Polyether
Poly(ethylene glycol) terephthalate (PEGT) Polybutylene terephthalate (PBT)
PolyActive™
PEBAX®
46Copyright © 2018 by Volker Abetz
Polymers for Gas Separation Membranes
Polymer P(CO2)* CO2/N2 CO2/CH4 CO2/H2
Polysulphone 4.92 24.6 23.4 -
Cellulose Acetate 5.96 25.8 29.1 0.4
Polycarbonate 7.5 25 23.4 0.62
Matrimid 8.9 35.6 40.5 0.37
Ethyl Cellulose 14.7 22.4 10.4 1.9
Polyimide 44 35.2 30.3 -
Poly(phenylene oxide) 56.8 19.9 25.8 0.67
Poly(4-methyl pentene-1) 69.5 11.8 - 0.68
Poly(phenylene oxide) brominated 78 30 15.6 -
PEBAX 82.1 55.5 15.6 9.9
Polyactive 115 45.6 17 10.2
Poly(vinyl trimethyl silane) 190 23.8 14.6 0.95
Poly(dimethyl siloxane) 3489 9.9 3.5 4.9
Teflon AF 3900 5 6.5 1.2
Highlighted polymers are used in CO2/x separation processes* Permeability in Barrer: 1Barrer = 1*10-10 cm3(STP) cm cm-2 s-1 cmHg-1
47Copyright © 2018 by Volker Abetz
CO2 Supply to Algae Bioreactors
Co-operation between SSC Strategic Science Consult GmbH and HZG
Photo synthesis: algae fassade house
CO2 from heating flue gas: Increase of content from 9 to 40% required
Gas permeation unit equipped with CO2 selective membrane
Fluegas
Fluegas
CO2 richpermeate
CO2 leanRetentate Membrane
module
T. Wolff et al., Greenhouse Gas Sci. Technol. 2015, 15, 505.
48Copyright © 2018 by Volker Abetz
Content
1. Introduction
2. Membrane Geometries and Membrane Production
3. Membrane Modules
4. Development of a Membrane Process
49Copyright © 2018 by Volker Abetz
Requirements for Membrane Modules
• high packing density(AM/VM)
• low polarization effects, especially in RO, PV, VP, GP
• low pressure losses
• good cleaning possibilities (flushability, removal of solids), especially in UF / MF
• uniform flow over (no dead spots)
• high solids loading (UF / MF)
• mechanical, thermal and chemical stability
• cost-effective membrane change
• cost-effective manufacturing
50Copyright © 2018 by Volker Abetz
Basic Types of Membrane Modules
3-End Module 2-End Module
4-End Module, external flushing4-End Module, internal flushing
Feed Retentate(Concentrate)
Permeate
Feed(liquid)
Permeate(liquid)
Feed
Permeate
Retentate Feed Retentate
Permeate
all systems(here shown for GP / VP) UF/MF temporary
Sweepgas
GP/VP
Sweep gas
GP/VP
51Copyright © 2018 by Volker Abetz
Classification of Membrane Modules
Flat sheet membranes Tubular membranes
Disk module
Envelope type/Cushion module
Spiral wound module
Tubular module
Capillary module
Hollow fiber module
Packing densitycost-effective manufacturing
Modul flushabilitySolids loading capacity
52Copyright © 2018 by Volker Abetz
amafilter Ultrafiltration Plant
Envelope membrane modules
53Copyright © 2018 by Volker Abetz
Seawater desalinationplant in Ashkelon, Israel
R. Borsani, S. Rebagliati, Desalination 2005, 182, 29-37.
Reverse Osmosis
54Copyright © 2018 by Volker Abetz
Content
1. Introduction
2. Membrane Geometries and Membrane Production
3. Membrane Modules
4. Development of a Membrane Process
55Copyright © 2018 by Volker Abetz
Membrane: mass and heat transport locally taking place
Module: change of concentration, pressure and temperature profiles along the process line
Module interconnection: arrangement of membrane modules in series and parallel circuits, required additional equipment such as heat exchangers, condensers, compressors and pumps
Overall process: optimal transfer concentrations in relation to the total process, determination of returns, total optimization with respect toenergy consumption and economy
Levels of Membrane Process
56Copyright © 2018 by Volker Abetz
Membrane Process Development
Lab. scale investigations
Permeation behaviour
Pilot scale membraneproduction
Pilot plants
Module design Process simulation/design Comp. pilot plant/simulation
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2
Membrane area Az [m2]
n-C
4H
10 M
ole
fra
ctio
n y
R,C
4 [-
]
Lines: SimulationSymbols: Experiment
hm44.46V
hm34.20V
hm29.05V
3(STP)F
3(STP)F
3(STP)F
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2
Membrane area Az [m2]
n-C
4H
10 M
ole
fra
ctio
n y
R,C
4 [-
]
Lines: SimulationSymbols: Experiment
hm44.46V
hm34.20V
hm29.05V
3(STP)F
3(STP)F
3(STP)F
57Copyright © 2018 by Volker Abetz