Membrane Science and Membrane Separation Processes

ChE 413

Department of Chemical Engineering & Chemical Technology Imperial College, London

South Kensington London SW7 2AZ

Contents . Membranes and membrane processes 1.1 Membranes '

Definition of Membrane Classification of Membrane

1.2 Membrane Processes Gas permeation Pervaporation Reverse osmosis and ultrafiltration Microfiltration Dialysis Electrodialysis Liquid membrane process Membrane-based gas absorption and stripping Membrane reactors Electrochemical membrane process for gas separation

2. Membrane preparation techniques Sintering Stretching Track-etching Phase inversion

Membrane preparation via immersion precipitation Flat sheet membrane Hollow fibre membranes Annular hollow fibre membranes

Coating Dip-coating Interfacial polymerization

3. Membrane transport 3.1 RONF transport 3.2 Gas Transport in Membranes

Transport in homogeneous membranes Transport in porous membranes Transport in asymmetric and composite membranes

4. Membrane modules and module calculation .. 4.1. Module types

~ l a t g and frame module Spiral-wound module Tubular module Hollow fibre module

4.2. Module calculation Membrane gas separation

Perfect mixing. Cross flow pattern. Cocurrent flow pattern. Countercurrent flow pattern. One side mixing.

Special Topic: Membrane based gas absorption or stripping Introduction Mass transfer through hollow fibre membranes

Nonwetted mode -f

Wetted mode Permea-sorption modes Mass transfer in hollow fibre lumen Mass transfer across membrane Mass transfer in shell side of a module Effect of chemical reaction

Design equations Some specific applications studied

Dissolved oxygen removal Removal of COz from a breathing gas mixture Elimination of H2S

Notation References

1. Membranes and Membrane Processes

l .l Membranes

Definition of Membrane Students joining the membrane course certainly have a question of "What is membrane? in their mind. The possible definition is (Hwang and Kammermeyer, 1 975):

A region of discontinuity interposed between two phases

Based on the above definitions, the membranes can be gas, liquid or solid, or combination of these phases.

Feed Retentate

~ e r n d a n e Permeate

Figure 1.1-1 A membrane process

The above illustration (Figure 1.1-1) tells us that a membrane is placed in a vessel so that two compartments, i.e. upper and lower compartments, are established. As a feed stream of a fluid mixture containing constituents of A and B flows along the membrane in the upper compartment, one of the constituents permeates selectively and is enriched in the permeate stream.

Classification of Membrane Membranes for industrial separation processes may be classified according the their nature, structure, application and mechanism. Figure 1.1-2 summarizes these classifications.

Figure 1.1-2 Classification of Membrane ('

a. Nature of membrane , . Synthetic

1.2 Membrane Processes

+

Membrane processes have recently become an accepted unit operation for a variety of separations in industries. The processes are driven by pressure, concentration, or electric field across the membrane and can be differentiated according to type of driving force, molecular size, or type of operations. The common industrial membrane processes are briefly described below.

Porous

Gas permeation Gas mixtures can be separated by either porous or dense membranes. In general gas transport through membranes is based on Knudsen-difision,

b. Structure of membrane

Nonporous

b. Gas-gas

c. Application of membrane

Gas-liquid Liquid-liquid Gas-solid

b. b.

Liquid-solid

Adsorptive Difisive Osmotic Ion-selective Non-selective

,l .' b.

d. Mechanism of membrane '

--b.

b.

solution-diffusion or molecular sieving. Figure 1.2-1 illustrates these three different gas transport 'mechanisms.

Upstream Upstream

Transient gap opening in matrix

-- /,Cjk' - ~ x i I

'\ Downstream Downstream /I Downstream

Knudsen flow Molecular sieving Solution-Diffi.sion separation is based separation is based separation is based on on the inverse on the difhsion and both solubility and square root ratio of sor~tion mobility factors in all the molecular characteristics. cases. Difhsivity favors weights A & B. condensable molecule.

Figure 1.2- 1 Gas transport mechanism G

Apart from the commercial process for H2 recovery from synthesis gas, gas separation is of interest in the following:

0 2 enriched air for combustion and medical applications N2 enrichment for Wafer-Fab, metallurgy and Inerting CO2 for enhanced oil recovery CH4 from biogas Helium recovery from natural gas

Pervaporation Pervaporation (Figure 1.2-2) is a separation process where a liquid mixture is in direct contact with one side of membrane and where the permeate stream is removed in vapour state from the other side of the membrane. Because of the presence of the membrane, the liquid-vapour equilibrium is perturbed as shown in Figure 2-3. Application of pervaporation includes:

Separation of:

azeotropic mixtures

mixture of closed boiling point component Seat-sensitive products

Figure 1.2-2 A pervaporation process

0.0 0.2 0.4 0.6 0.8 1 .O

Molar fraction water in liquid

Figure 1.2-3 Perturbation of liquid-vapour equilibrium by membranes

Reverse osmosis and ~ltr~afiltration Reverse osmosis processes allow selective passage of a particular species (solvent), while other species, i.e. solutes are retained partially or completely. Solute separation, f and solvent permeability, A are the membrane characteristics and are dependent on the membrane material and structure of the membrane layer.

Mechanical pressure

p> An

solutiop . F '

A: Osmosis ' B: Osmotic equilibrium C: Reverse osmosis

Figure 1.2-4 Phenomenon of osmosis

As illustrated in Figure 1.2-4, osmosis is a natural phenomenon where water passes (see Figure 1.2-4a) through a membrane from a side with lower solute concentration to a higher solute concentration until the osmotic equilibrium is reached (Figure 1.2-4b). To reverse the water flow, a mechanical pressure (Figure 1.2-4c) is applied, providing the pressure difference greater than the osmotic pressure difference; as a result, separation of water from a solution becomes possible. This phenomenon is referred as reverse osmosis.

Applications of reverse osmosis process include: seawater desalination waste water treatment and ultrapure water production

Ultrafiltration is a process based on the same principle as that of reverse osmosis. The main difference is that the ultrafiltration membranes have a larger pore size. At present, the pressure difference applied in reverse osmosis is up to 80 bar. If the membrane retains only macromolecules or particles with an insignificant osmotic pressure, the necessary operating pressure can be

much lower (2-10 bar). In this case, the process is termed as ultrafiltration. This is no sharp distihtion between ultrafiltration annd reverse osmosis, and the two merge into each o,her like ultrafiltration and microfiltration as shown below (Figure 1.2-5):

I

Filtration

I, MF

. . UF

, R 0

Figure 1.2-5 Relation between the membrane process and.the membrane pore size

Microfiltration When pressure-driven flow through a membrane or other filter medium is used to separate micron-sized particles from --fluid, the process is called microfiltration.

There are two types of microfiltration configurations: Dead-endfiltration and cross-Jlowfiltration illustrated below:

Figure 1.2-6 Schematic diagram of filtration processes, A-Deadend filtration and B-crossflow

Feed

a 00 "8 o&$$J 00 + + + + +

Permeate

A Cake thickness

A

A

Feed O o "P,eC$$oeBC#%

Retentate - - Flux

Cake thickness

B b

Dead-endJiltration is only suitable for dealing with suspensions with a very low solid content, while'cross-flow Jiltration can be used for much higher concentration as the deposits on the membrane are swept away by membrane- parallel flow.

Dialysis Dialysis is basically a diffusion process and it describes the separation of substances in solution by means of their unequal difhsion rate through porous membranes, therefore, the dialysis is achieved by imposing a concentration gradient across the membrane. Typical application for this process is the artificial kidney shown in Figure 1.2-7.

Figure 1.2-7 Typical hollow fibre hemodialyzer

Electrodialysis Electrodialysis is a process where solute ion move across membranes by application of an electrical field. Although electrodialysis was started as a modification of the ordinary dialysis by adding a couple of electrodes, the two processes are distinctly different in many ways.

Ordinary dialysis

Based on concentration gradient

Use of normal membranes

Flow direction: high con. -+low con.

Con. gradient diminish as results of mass transfer

Electrodialysis

Based on external electrical field

Use of ion-exchange membranes

Flow direction: high con. a low con.

Desired degree of separation is achievable

Figure 1.2-8 shows the application of electrodialysis in caustic soda industry .' t ' t C ' z Cation exchange

membrane t"'

Figure 1.2-8 Electrodialysis for caustic soda industry

Liquid membrane process In liquid membrane processes, liquids such-'as hydrophobic solvents form selective barriers between the aqueous feed solution and aqueous absorption phase. The membranes are either fixed to a porous base or they are in the form of double emulsions which offer the advantage that large membrane specific surface areas (1000-3000 m2/m3). Figure 1.2-9 gives theageneral picture of the emulsion membrane:

Figure 1.2-9 Emulsion liquid membrane

An example of removal of phenol from water is shown as follow:

The wastewater containing phenol is external, continuous phase;

The encapsulated droplets containing NaOH in water make up internal phase;

The liquid phase between the internal and external phases is the membrane;

The phenol permeates through the membrane and reacts with NaOH to form Sodium phenolate which is insoluble in membrane phase and trapped in the internal phase.

Surfactant Liquid Membrane n

Hydrophobic-Hydroph~hc Phenol React~on

(Non-Permeable)

Aqueous Feed Outs~de

Figure 1.2- 10 Removal of phenol from water

Membrane-based gas absorption and stripping Unlike the conventional membrane process that the membrane is the selective layer towards the fluids to be separated, the membranes used in absorption or stripping processes act only as somewhat a "packing material" as shown in . . .

Figure 1.2- 1 1

The advantages and disadvantages of using membranes in gas absorption are:

Provide larger surface area per unit volume compared to the conventional a6sorption processes such as packed columns.

There is no flow ciinstraint such as flooding and loading point usually existed in the conventional absorption processes.

Membranes supply new mass transfer resistance, that of membrane, which is not presented in packed columns.

C02+CH4

Absorbent out 7

Absorbent in

Figure 1.2-1 1 Schematic diagram of membrane based gas absorption

Membrane reactors The term membrane reactor describes a number of different types of reactor configurations, which contains a membrane. The main feature of the reactor is to remove the reaction product out of the reactor with the membrane so that equilibrium of the reversible reaction is shifted and the reaction continues to proceed to the right toward completion. Figures 1.2-12 and 1.2-13 show a dehydrogenation reaction in a membrane reactor.

Figure 1.2- 12 Schematic diagram of a membrane reactor

80

70 h 5 E 0 '" 60 2 E

U" 50

40

0.0 1 .O 2.0 3.0

Space time (sec) I .

Figure 1.2-13 Comparison of conversion achieved in the rnemhrane rea.ctnr and the cnnventional nacked bed reactor

Electrochemical membrane process for gas separation The separation of gases in this process is achieved with application of external electrical field. Figure 1.2-14 illustrates an electrochemical membrane, which can be used for separation of COz.

I l Porous Polyamide Immobilized with Potassium Carbonate Nickel Screen

- / +

\ \ Ploypropylene Hydrophobic Nickel Screen

Membrane

Figure 1.2-1 4 Electrochemical Membrane

Figure 1.2-15 shows the concentration profile of COz in the electrochemical membrane.

Gas-catholyle Elecl.nde ir~terface

02 t 2Hz0 t 4e- - 40H- 4 OH-?' . - 01 t .?H20 t 4e- C& t OH- - HCO; HCO; - CQ t OH- HCO; t OH- - c(h" + HLI C&'-+ t1z0 - NCO; + OH-

( Chemical reaction at cathode ) ( Chemical reaction .at anode )

Figure 1.2- 15 Concentration profile

2; Membrane Preparation

A number of different techniques are available in preparing synthetic membranes. Some of these techniques can be used to prepare organic as well as inorganic membranes and are shown in Table 2-1.

Table 2- 1 Membrane Preparation Techniques

Membrane Preparation Processes

Phase Inversion

Phase SeparatiodLeaching

Sol/Gel Techniques

Sintering

Types of Membranes Prepared

Gas, reverse osmosis, ultrafiltration, microfiltration, and dialysis membranes. Na20-B203-rich phase SiOz-rich phase (glass/cerarnics) Metal alkoxides hydrolyzed, polymerized (alurnina, titania, zirconia) 0.1-20 microns pore size (fibrous mats, fi

Controlled Stretching

Extrusion/Activation Controlled Pyrolysis

Track-Etching

Thin-Film Deposition

Anodic Oxidation/Etching

Coating

0.1-5 microns pore o or et ex@ and celgard? Silicone rubber, NAFIOP Base organic membranes pyrolyzed to form silica or carbon molecular sieve membranes Radioactive source exposure, then etch with acids, (0.5-1 nrn, NUCLEOPORE@ Sputtering plating, vapour deposition (transition metals alloys, i.e. AYAg, CuIZr, Ni/Pd) Oxidation from one face; etching by strong acid of metal Composite membranes

Sintering

Porous membranes can be obtained from both organic and inorganic material using the sintering technique. This method involves pressing a powder of particles of a given size and then sintering at elevated temperatures. The temperature required for sintering depends on the material used. During the sintering, the interface between the contacting particles disappears as shown in Figure 2- 1.

heat - Figure 2- 1 Sintering Process

Materials suitable for making membranes usi& iintering method are:

-E polyethylene

Polymer powder polytetrafluorothylene polypropylene

Metals -< stainless steel tungsten

ceramics -c aluminium oxide

zirconium oxide

Graphite (carbon)

Glass (silicates)

The pore size of the resulting membranes is determined by the particle size and particle distribution in the powder. The narrower the particle size distribution the narrower the pore size distribution in the resulting membrane.

The polymeric membranes made from sintering method usually have low porosity(lO%), but for metals membranes, it's porosity is quite high, sometimes upto 80%. The structure of a typical sintered membrane under the scanning electron microscope is shown in Figure 2-2.

Figure 2-2. SEM of sintered membranes

Stretching

In this method, an extruded film made from partially crystalline polymeric materials is stretched perpendicular to the direction of the extrusion, so that the crystalline regions are parallel to the extrusion direction. When a mechanical stress is applied, small ruptures occur and a porous structure is obtained with pore sizes of about 0.1 to 20 pm. The structure of a typical stretched membrane under the scanning electron microscope is shown in Figure 2-3.

The stretched membranes can be prepared using semi-crystalline polymeric materials such as polytetrajluoroethylene, polypropylene and polyethylene. The porosity of these type of membranes are high and upto 90%.

Figure 2-3 SEM of stretched membranes

The materials used to prepare the stretched membranes are usually hydrophobic type, therefore, this type of membranes has been used as stable interface in gas absorption processes.

The track-etching process can produce a microporous membrane with very uniform, almost perfectly round cylindrical pores. The entire process is schematically shown in Figure 2-4.

Radiation source

I X C7 1

Figure 2-4 Track-etching process

In this method, a membrane film is subject to high energy particle radiation applied perpendicular to the film. The particles damage the polymer matrix and create tracks. The film is then immersed in an acid or alkaline bath and the polymeric material is etched away along these tracks to form uniform pores with pore size from 0.02 to 10 structure of a typical etched membrane under the scanning electron microscope is shown in Figure 2-5.

Figure 2-5 SEM of etched membranes

Phase inversion

Phase inversion is a process where a polymer is transferred in a controlled manner from a liquid to a solid state. The following techniques are often used in preparation of phase inversion membranes:

l) Precipitation by solvent evaporation In this method, a polymer is dissolved in a solvent to form a polymer solution which is then cast on a suitable support. After the casting procedure, the solvent in the polymer solution is evaporated in an inert atmosphere so that a dense homogeneous membrane can be formed.

2) Precipitation from the vapour phase This method is used for preparation of porous membranes. The cast film, consisting of a polymer and a solvent, is placed in a vapour atmosphere where the vapour phase consists of a nonsolvent saturated with the solvent. The high concentration of the solvent in the vapour phase prevents the evaporation of solvent from the cast film. The membrane formation

occurs due to the diffusion of the nonsolvent into the cast film resulting in formation of membranes with porous structure.

3) Precipitation by controlled evaporation In this method, the polymer is dissolved in a mixture of solvent and nonsolvent. Since the solvent is more volatile than the nonsolvent, the composition shifts during evaporation to a higher nonsolvent and polymer content. This leads eventually to the polymer precipitation resulting in the formation of asymmetric membrane.

( 4) Thermalprecipitation

A solution of polymer in a mixed or single solvent is cooled to enable phase separation to occur. Evaporation of the solvent often allows the formation of a skinned (or asymmetric) membrane. - , .

5) Immersionprecipitation Most membranes currently available in market are prepared by immersion precipitation. A polymer solution is first cast on a suitable support and then immersed in a coagulation b&th containing a nonsolvent. The precipitation occurs due to the exchange of solvent and nonsolvent. The membranes prepared via this process are usually have an asymmetric structure.

Membrane preparation via immersion precipitation

Flat sheet membrane The preparation of flat sheet membranes on small scale is shown blow:

I Polymer solution I 7'7 Casting knife

Flat sheet membrane

n-woven support layer

Coagulation bath

Firmre 2-6 Schematic diarzram of flat sheet membrane au~aratus

The polymer solution, i.e. casting solution, is cast directly on a support layer by a casting knife. The cast film is then immerse in a nonsolvent bath where exchange occurs between the solvent and nonsolvent and the polymer eventually precipitates. Although, choice of solvent and nonsolvent is very important for the resulting membranes, water is still often used as nonsolvent. Other preparation parameters such as polymer concentration, evaporation time, humidity, temperature and the composition of the casting solution (additive) are also responsible for the ultimate membrane performances. The relation between these parameters and membrane structures will be discussed later.

Hollow fibre membranes The alternative geometry of the membranes prepared is the tubular f o m Based on the difference of their dimensions, the following types may be distinguished:

hollow fibre membranes(diameter: 0.5m.m) capillary membranes(diameter: 0.5-5' mm) tubular membranes(diarneter: > 5 mm)

The dimension of the tubular membranes are so large that they have to be supported, while the hollow fibres and capillaries are self-supporting. The following diagram shows the preparation of the hollow fibres and tubular membranes:

Figure 2-7 Schematic diagram of a hollow fibre spinning apparatus

Annular hollow fibre membranes Concentric annular hollow fibre membranes can be prepared using a triple-orifice spinneret.

Figure 2-8 Schematic diagram of an annul? hollow fibre spinning apparatus r .

Coating Coating is a very important technique for preparation of composite membranes. Methods of dip-coating, interfacial polymerisation and plasma polymerisation are usually used for coating a ultrathin layer on a porous support.

Dip-coating Dip-coating is a very simple and useful technique for preparation of composite ( membranes with a very thin but dense top layer. Membranes prepared by this method are used in reverse osmosis, pervaporation and gas separation. The schematic diagram of this technique is shown below:

1. Coating solution tank 1 2. Holloe fibre 3. Drying column 1 4. Coating solution tank 2 5. Drying column 2 6. Mass flow controller

, 7. Moter guide

Figure 2-9 Coating apparatus F A

It can be seen that a hollow fibre is immersed in a coating bath (coating solution tank 1) containing a polymer or monomer solution with it's concentration less than 1%. When the hollow fibre is removed from the coating bath, a thin layer of the solution adheres to it. The coated membrane is then put into a drying column (drying column 1) where the solvent of the coating solution evaporates and the crosslinking takes place which leads to the thin layer becoming fixed onto the porous sublayer. The coating process can be repeated so that the coating thickness cn be controlled. Figure 2-9 shows a two-step coating apparatus.

Interfacial polymerisation Interfacial polymerisation provides another method for depositing a thin layer upon a porous support. In this case, a polymerisation reaction takes place between two very reactive monomers at interface of two immiscible solvents. This is shown schematically below:

The support layer (Fig. 1) in immersed in an aqueous solution(Fig. 2) containing a reactive monomer. The film is then immersed in a second bath containing a water immiscible solvent where another monomer is dissolved(Fig. 3). These two reactive monomer react each other to form a dehse polymeric top layerpig. 4).

Heat treatment is often required to compiete the interfacial reaction and to crosslink the water-soluble monomer. The thickness of the top layer formed by this method is within the 50 nm range.

3. Membrane Transport '

3.1 ROIUF transport

The transport equations developed below are based on the analysis of experimental R 0 data involving single-solute aqueous solution systems, all levels of solute separations, and isothermal operating conditions.

Mechanical pressure

Mem rane t f

Dilute so6tion Co3centrated solution

A: Osmosis B: Osmotic equilibrium C: Rverse osmosis

Figure 3- 1 Phenomenon of osmosis

Based on the diagram in Figure 3-1, the solvent flux, Jg through membrane pores can be written as:

where: A = proportionality constant

- pressure at feed side Ph -

~ ( ~ 4 3 ) = pressure at permeate side

7c(~42) = osmotic pressure at feed side

n(m3) = osmotic pressure at permeate side

When the feed liquid is pure water, both n(~p2) and n(-3) are zero, eq.(3-1) reduces to:

As solvent (water) flow through the membrane, transport of solute by diffusion through the membrane phase would inevitably take place. This is illustrated in (, Figure 3-2.

Figure 3-2 Concentration profiles of a solute in boundary layers and in membrane phase

The rate of solute transfer, JA, will depend on the concentration gradient of solute ( in the membrane and can written as:

where: DAM is the diffusivity of solute in the membrane phase, 6 is membrane thickness, C ~ 2 is concentration of solute in membrane phase at feed side,

GM43 is concentration of solute in membrane phase at permeate side.

CMA2 and CMA3 are in equilibrium with CA2 and CA3 (see above Figure), therefore:

' U 4 2 = KACA2 (3-4)

'ha3 = KACA3 (3-5)

where KA is equilibrium constant. Substituting eqs.(3-4) and (3-5) into eq.(3-3), we obtain:

DMKA J A = T x ( ' A 2 - C A , ) (3-6)

is called solute transport parameter and its dimension is m/s. S

Furthermore,

c~~ = 'IxA1 (3-7) ' A 2 = ' Z X A 2 (3-8) ' A 3 = C3x.43 (3-9)

Cl and X A ~ , C2 and X A ~ and C3 and Xk3 are total molar concentration and mole fraction of solute in feed, concentrated boundary layer and permeate sides respectively. Substituting eqs.(3-8) and (3-9) into eq.(3-6), we have:

Since:

Eq.(3-10) can also be written as:

When a complete separation of a solution takes place by a reverse osmosis process, only solvent of the solution goes through the membrane and is enriched in the permeate side. The solute is left behind on the feed side of the membrane. The concentration of the solute at liquid-membrane interface increases and the

solute diffuse back to the bulk of the liquid. This phenomenon is called concentration polarization.

At steady state, the concentration gradient of the solute between liquid-membrane interface and the bulk of the liquid is established and is illustrated in Figure 3-3.

Figure 3-3 Solute concentration profiles ,- - . .

Based on the film theory, the flux of solute diffused back to the bulk, JP:

Therefore, the flux of solute in the boundary layer should be equal to the summation of the flux of the solute permeated through the membrane and the flux of the solute back to the bulk: (

where:

Rearranging eq.(3 -5):

where:

D A B k=- 6

Assuming that the total molar concentration in bulk liquid, boundary layer and permeate side are the same, i.e.:

c, = c, = c, Eq.(3-16) becomes:

Thus, Basic transport equations in reverse osmosis process:

J B = (ph -P(xA,) - ( T ( X ~ ~ ) - Z ( X ~ ~ ) ) )

(pWP/S)= J B = A X (P, - p(,,,) 1 J B = ~ x [ ~ ) ( c x d X, , 2 A2 - ~ , X A , )

JB = kC,(l- xA3)ln

The above set of four equations constitutes the basic transport equations for reverse osmosis systems. From any single set of primary R 0 data and operating conditions of the experiments, one can calculate the coefficients, A, DAMKA/S, k and X A ~ applicable to the system, using the above transport equations.

D K Calculation of A, + and k J % O ~ experimental data

The experimental set-up for reverse osmosis experiments is shown in Figure 3-4:

Figure 3-4 Illustrations of R 0 experiments .fir , -

m1

V Retentate

As can be seen in Figure 3-4, the following data are usually obtained from the RO:

l

Pure water permeation rate (PR) Product rate

f Solute separation

b

With given operating conditions such as pressure and temperature and feed conditions such as molality of feed, together with the above mentioned R 0 data, the transport parameters, A, (DAMKAA) and k can be calculated.

m3 V PWP or PR

From the product rate, (PR), the water flux can be'calculated:

and from solute separatiop, f, the molality of the permeate solution can be obtained:

m, = ( I - f ) x m , where:

m1 is molality of feed, (moles of solute/1000 gram of water)

m3 is molality of permeate solution, (moles of solute/1000 gram of water)

MB is molecular weight of water, gram

MA is molecular weight of solute, gram

S is membrane area, m2

With given osmotic pressure data, the mole fraction of solute in the boundary layer, X A ~ can be calculated using following equation:

Example 1 ,. - .

A fruit juice with a solute content of 0.5 molal is concentrated using a membrane module at 25 OC. The permeation rate (PR) andit's solute content are found to be 12.0 h o V h and 0.04 molal, respectively. The feed pressure is operated (gauge) at 3830 kPa, while the permeate pressure (gauge) is maintained at 0.0 kPa. The total membrane area of the module is 1.3 m2 and the pure water permeability, A, for the membrane module is 1.7 x 1 0 - ~ km01 @a-'

(a) Calculate the water permeation flux, JB, and the solute separation, $

(b) Calculate the solute concentration of the fruit juice at the membrane interface and indicate whether the concentration polarization is significant?

The osmotic pressure data given in the following table may be useful:

Solute(mola1ity) Osmotic pressure

(@a)

0.2 .g17

0 0

0.1 462

0.3 1372

0.4 1820

0.5 2282

0.6 2744

Solution 1 (a)

Calculate solute separation:

Calculation of water flux from (PR) data:

!OM) IOW - (PR) X 12x A

18.01 - %+0.04 J , = - = 2 . 5 6 ~ 10-~ kmolls m2 S X 3600 1.3 X 3600

The osmotic pressure at boundary layer:

J B ' T ( ~ A . 2 ) = P h - P ( ~ A 3 ) + Y x A 3 ) -7 r

The corresponding molality in boundary layer, m2(from table 1)

The polarization factor:

A concentration difference of 9.8% between the interface and the bulk solution would not have much effect on the water flux, therefore, the concentration polarization is not significant in this process.

3.2 Gas Transport in Membranes

The phenomenon of gas permeation through a polymeric membrane has been known for a long time. The first recorded experiment on the transport of a gas through a membrane is attributed to Graham in 1829, who used a wet pig bladder inflated to the bursting point to observe the gas permeation (Phil. Mag., 32(1866)401).

Figure 3-5 Gas permeation through a membrane

1 Pure gas

Figure 3-5 illustrates a simple experiment where a membrane is placed in a vessel and two compartments, i.e. upper and lower compartments, is established. With a pure gas pressurising in the upper compartment, a permeation flux could be obtained in the lower compartment. The relation between the permeation. flux and the operating conditions can be described by:

where J is permeation flux, cm3 /S cm2 ; ph is feed side pressure, cmHg; p1 is permeate side pressure, cmHg; P is permeability, Barrer ( I O - ' ~ C ~ ~ ( S T P ) cm cm-* sec" c m ~ ~ - ' ) ; 6 is membrane thickness, cm.

Ph > P1

Membrane

The permeability value, P from the above experiment is dependent on the nature of the membrane material and the operating conditions used. A number of phenomenological and physiochernical models (see Figure 3-6) have been

Permeation flux, J- v :, - * . '

P h P

PI

developed for gas transpoa, each of which is specific for particular types of penetrant-membrane systems over limited ranges of pressure and temperature.

Transport in homogeneous membranes 1. Solution/diffusion model( for rubbery polymer) 2. Dual sorption model(for glassy polymer) 3. Free Volume Theory

Transport in porous membranes 3. Pore model

Transport in asymmetric and composite membranes 4. Resistance model

Figure 3-6 Gas transport through different membranes

Transport in homogeneous membranes F .

Solution/dzffusion model Several approaches have been used over the years to describe the penetration of rubber membranes by low-molecular-weight species. Common to most theories is the solution/diffusion model. From Fick's first law of diffusion, i.e:

the flux or permeation rate per unit area of membrane can be illustrated in Figure 3-7.

Penetrant g a s P

Figure 3-7 Permeation flux through a dense membrane

As can be seen, the concentration of the gas molecular in the membrane is assumed to obey Henry's law i.e.:

Substituting eq.(3-19) to eq.(3- 18) and then integrating, we have:

where is the membrane thickness and ph and p) are gas pressures at the interfaces.

A mean permeability coefficient can be defined as:

p = 1 Ph J D S ~ ~ =

JS (3-21)

Ph -?'l p, Ph - PI.:

If the diffusion and solubility coefficients are independent of pressure, then

The product SD is the permeability coefficient. In many cases, D depends on C and S depends onp. As product of D and S, P is not a fundamental property, being dependent on both diffusivity and solubility characteristic.

As illustrated by Stem (), P may be dependent on the operating conditions such as feed concentration and operating pressure and its can be classified into the following three categories:

(Henry's law obeyed)

(2) z B -=- ; D = D(c), C = s(p)p (Henry's law not obeyed)

tr: d -=- a a (D z); D = D(C, r); C = ~ ( p ) p (Henry's law not obeyed)

The temperature dependence of D and S obeys relationship similar to the Arrhenius equation:

where, Do and So is preexponential factors, &.is activation energy of difhsion

(J/rnol) and MS is the enthalpy of solution ( k o l ) . Combining eqs.(3-.23) and (3- 24); we have:

ED is usually positive, MS is sometimes negative if the sorption process is ( endothermic. Therefore, Ep may be either positive or negative.

Dual sorption model When temperature is lower than the glass transition temperature of a polymer, the polymer is at the glassy state and may have microvoids. Nonlinear sorption isotherm in the glassy polymer is usually observed for many different types of gases. This behaviour can be explained by dual sorption theory which postulates that the difisive flux of a penetrant is the sum of two contributions: one is contributed by the concentration gradient of the dissolved mode; the other is due to the concentration gradient of the additional mode in the microvoids of the glassy polymer.

The solubility isotherm resulting from dual-mode sorption is given by:

. . -

The first term represents the Henry's law sorption of normally diffusible species, . .- . .

while the second term represents sorption in "hole" characterized by affinity and. saturation constants, b and CL. When p is small, the above eq.(3-26) i s . approximated by: ?. . . +.

.- - -

and when p <S large, eq.(3-26) is approximated by:

Thus, the dual sorption model predicts that the isothermal plot of C vs p will' '

consist of a low-pressure linear region and a Vgh-pressure linear region which are connected by a nonlinear region. Some exper'imental results for typical examples of dual sorption are illustrated in Figure 3-8.

a- ,.

. . . . . : . . : < . j

Figure 3-8 CO;! sorption data in a polymeric membrane

Figure 3-9 shows experimental data reflecting dual-mode sorption character and outlines a procedure for det;rmining the pertinent sorption parameters.

(a)

LeNWUIR ROT

. c".C-c,P

U .G!?? P (m01 - I*bp P(W)

t 1 cU&-sa?Trn MO#L: kO,Ci.b

C.C"+CD

C. - I+bD L 4

ko .MNRY'S LAW CONSTANT. CC.*s (STP) cc. paymcr-otm.

C; HOLE SATLRATlON CmSTANT. Cc- gas(STP' cc. pdwer

Based on the dual sorption:model, the gas transport equations through the glassy poIymer can be developed with the following assumptions:

1. Two modes of sorption, Henry's law sorption and Langmuir sorption, take place simultaneously.

2. Between the above two modes of sorption, local equilibrium is maintained in the membrane.

3. The gas molecules sorbed by the Langmuir mode are partially immobilized.

4. All gas molecules sorbed by the Henry mode are mobile.

The total flux through the glassy polymer can be written as:

Since: C D = k, P

Substituting eqs.(3-20) and (3-21) into eq.(3-19), we have:

Integrating of eq.(3-22) from high pressure pz to low pressure p,, we obtain:

p, is the feed gas pressure obtained as a gauge pressure, whilep, is the pressure at permeate side and usually is at atmosphere, i.e.(gauge pressure=O), therefore, eq.(3-23) can be rewritten as:

whei-e:

Eq.(3-24) indicates that the permeability coefficient, P decreases with the feed pressure. K is a ratio characteristic of the relative amounts of gas sorbed in two modes, and F is a measure of the degree of immobilization. For total immobilization, F=O and eq.( 3-24) reduce to P = DDkD ; at the other extreme of the complete mobility, F=I and the permeability is very pressure dependent. i Free Volume Theory The free volume theory of transport postulates that movement of molecules depends on the free volume available as well as the availability of energy sufficient to overcome polymer-polymer attractive forces.

Above the glass transition temperature, i.e. in the rubbery state, the mobility of the chain segments is increased and 'frozen' microvoids no longer exist. A number of physical parameters change at the glass transition temperature and one of these is the density or specific volume shown in Figure 3- 10.

specific volume

Figure 3-1 0 Specific volume of a polymer as a fhnction of temperature. .' -

The free volume Vf is defined as the volume generated by thermal expansion of the initially closed-packed molecules at 0 K:

where:

VT is the observed volume a temperature T and

V, is the volume occupied by the molecules at 0 K.

The fraction of fiee volume can, therefore be written as:

The observed or specific volume at a particular temperature can be obtained from the polymer density, whereas the volume occupied at 0 K can be estimated from group contribution.

At condition of T>>Tg, thqfree volume increases linearly with temperature and can be ex~ressed as:

According to. Fujita et a1.(56(1960)424, Trans. Faraday Soc), the thermodynamic diffusion coefficient is dependent on the fractional free volume according to the relationship:

where, Af and B are related to the size and shape of the penetiant molecule and must be determined empirically.

For the case of non-interacting systems such as polymers with permanent gases, 02, NZ and He, the polymer morphology is'not influenced by the presence of these gases. This means that there is no extra contribution towards the free volume and eq.(3-28) predicts a straight line when l n D ~ is plotted against the

reciprocal of the fractional free volume, (v-l assuming that Af and B are independent of the polymer type.

In the case of interacting systems (i.e. organic vapours), the free volume is not only a function of temperature, i.e. vf = f(g, but also the concentration of (

penetrant as well, i.e. vf = f(d$. Under these conditions, the free volume will increase with increased penetrant concentration and based on the additive rule, the following equation can be written:

where: ~$0, T ) is the free volume of the polymer at temperature T in the absence of penetrant.

4 is the volume fraction of penetrant.

P(T) is a constant characterising the extent to which the penetrant contributes to the free volume.

Based on eq;(3-28), the diffusion coefficient at zero penetrant concentration, D, is given by:

Combining eq.(3-28) and (3-30), we have:

DT In- = B - B

Do vr(O,T) v, ( U ) , - ,.. .

Substitution of eq.(3-29) into eq.(3-3 l), we obtain:

The relationship between the measured diffusion coefficient and the thermodynamic diffusion coefficient is given by:

d l n a D - DT[-] dln4

Because gases exhibit a relatively low solubility in polymer, the term, (d In aid In 4 ) is + 1, therefore, D % Dr.

Pore model for gas transpo~t in porous membrane First, let's consider that the'surface of porous membrane is composed of a bundle of capillary tubes with a Gaussian normal distribution of pore size represented by the function:

N, .,R.)=- exp [ -- :[R,'J] - (3-34) 4%

where:

R = pore radius, m a = average pore radius, m N(R) = normal pore size distribution function, l/m Nt = total number of pores on a given membrane surface

c = standard deviation of the pore size distribution, m

When gas flow through a single capillary, two distinct phases may be assumed. One is the layer of adsorbed gas molecules which are at the gas-pore wall interface and under strong interaction force from the pore wall, while the other is the gas molecules that are free from the influence of the pore wall. The former is considered to be a condensed phase and the latter is in a gas phase and under no restriction from the pore wall. Both phases flowing through the single capillary tube are illustrated in Figure 3-1 1.

Interfacial fluid in

Bulk fluid in gas phase

Figure 3- 1 1 Mechanisms of gas permeate through membrane pores

For the free gas flowing in the single pore, three flow mechanisms, i.e. viscous flow, slip flow and Knudsen flow, can be observed depending on the size of the

pore relative to the mean tree path of the permeating gas molecules. The mean free path is defined as:

where: R = Gas constant T = Temperature, K d = Collision diameter of gas molecules, m N = Avogadro number P = @h +pl)/2, mean pressure across the membrane, Pa

For Knudsen flow, qk:

For slip flow, q,l:

where:

For vicous flow, g,:

when R 0.05 2 (3-36)

when 0.05R < R < 5 0 a (3-37)

when R > 50A

The total transport of the free gas through all the pores is given by:

As Gaussian normal distribytion of pore size given by eq.(3-34) is assumed, the summation in eq.(3-39) can be replaced by integration to give following expression:

where:

and

For the condensed gas flowing through the membrane, Gilliland et al. (AIChE, 4(1958)90) derived an expression for surface flow based on two-dimensional force balance on an adsorbed film as given by:

where: Ap is the cross-sectional area of pores for a given membrane, m2

S, is the specific surface area of the solid over which the

adsorbed gas modecules are mobile, m2

CR is the coefficient of resistance, kg/(m2s)

z is the tortuosity facter

LP is the pore length, m

PP is the apparent density of the membrane, kg/m3

x is amount of adsorbed gas per unit weight of the membrane, kmol/kg

Eq.(3-42) can be recast to fit the terminology of the present approach to include pore size distribution with following expreesions:

Surface flow: Qs

where: 6=zLp

In view of eqs(3-43) and (3-44), eq.(3-42) becomes:

If the adsorption isotherms follow Henry's law form, i.e.:

Substitute eq.(3-46) into eq.(3-45):

Let:

Eq.(3-47) becomes:

r -

The total gas flow through the membrane is the summation of the free gas flow and condensed flow (surface flow):

N, Q, =Q,+Q, =-(G,I,+G,I, I G , I ~ ~ , - ~ , ) + A ; ~ ~ ( P ~ - ~ , ) (3-48) 6 15

Furthermore, the permeability, AG, is defined as:

where S is membrane area. Substituting eq.(3-48) into (3-49), we have:

where:

Eq.(3-50) has a fundamental physicochemical basis. From any set of experimen$. Ap vs AG, the average pore radius, K, on the membrane, it standard deviation,

and the quantities-A] .and A2 can be obtained by regression analysis. .. .

. 1 :

Resistance model for gas transport in composite membranes . .

The composite membrane is defined as a membrane that consists of sever4 barrier layers of distinct nature stacked together. Unlike asymmetric membranes,' the composite membrane has a clear discontinuity at the boundary of two neighboring barrier layers, either in the chemical structure or in the morphology of the material of which the barrier layer consists.

The permeation rate, Qi for a component i through a homogeneous membrane can be written as:

Based on Ohm's law:

the permeation rate, Qi can be analogous to the current, the driving force, Ap to the electrical potential, and the remaining in eq.(3-5 1) would be resistance which can be written as:

Therefore, eq.(3-5 1) becomes

The eq.(3-53) always validkas long as the gas permeation rate is related to the pressure difference in a linear fashion.

The resistances in composite membranes are usually connected in following different ways:

1. Series 2. Parallel 3. Two resistance arms

1. Two resistances connected in series

Imagine two layers with resistances RI and R2 (Figure 3-12) combined in series, I on the top of 2. Denoting two different perrneants by subscripts a and b, the overall resistance R for each permeant is:

Gas a and b

R1

R2

(')a = (4 )a + ('2 )a - Component a

( N b = (4 )b + (4 )b - Component b

Figure 3-12 Resistances in series

Defining the ratio of the resistances for perrneants a and b as:

where i = I and 2. The ratio of the overall resistance for permeants a and b, designated as a, becomes:

(R), - a1 ('1 )a + a 2 ('2 k - a, + a2 [('2 )a '('1 I a=- - - (')a . (',)a+('2)a 1 + [('2 )a '('1 )a I

'4' - 0 When a, = - ('1 )a

Eq.(3-53) becomes:

Eq.(3-55) indicates that the selectivity of the composite membrane is controlled by a barrier layer whose resistance is far greater than the other.

The above derivation indicates ( especially from eq.(3-54)) that both barriers will equally control the selectivity when the resiktances from both layers are nearly equal. Therefore, even when an extremely selective top surface layer is prepared, the overall selectivity could be lowered if the support layer is thick and its pore size is relatively small.

2. Two resistances connected in parallel The gas flow through a membrane with a structure described below is used as an example for the analysis of resistances connected in parallel.

Pathway 1 Pathway 2

R3

sulfone membrane

Figure 3- 13 Resistances in parallel

It can be seen fiom the Figure 3-13 that the gas flows through both network of the polymer cell and the void space (pore or defects) between the polymer cell. The resistance to the flow through the polymer network is R2, while the resistance to the flow through the void space is RJ, both of which are connected in parallel. Therefore, the overall resistance for gas a can be written as:

For gas b:

Since:

F

The overall selectivity, a:

When R3/R2 = 0,

indicating that the overall selectivity is controlled by the membrane component with a small resistance. The gas transport of a membrane with the above

mentioned structure is mostly through the void space (sometimes called defects), therefore the selectivity is ;ery low. When the surface defects of the membrane are extremely low, i.e. the area of the void space is much reduced, the resistance of R3 is increased dramatically based on eq.(3-52). This would result in a better selectivity as it is governed by the network component of the membrane.

3. Parallel combination of two resistances

Imagine a homogeneous film of relatively high permeability laminated on the top of the membrane used in previous case. The structure of such a membrane is described by in Figure 3- 14.

Pathway 1 Pathway 2

Asymmetric polysulfone membrane

Defects

Figure 3- 14 Resistances in parallel combination

It can be seen from the Figure 3-14 that it is assumed that the gas flow is strictly vertical to the surface of the membrane. In other word, the gas flow through portion of the homogeneous film that covers the polymer network should pass through the polymer network, and gas flow through the portion of the homogeneous film that covers the void space should pass through the void space, No mixing is allowed between these two flows. The overall resistance for the gas a and b is:

For gas b:

Comparing two arms of the parallel resistances, Rl+R2 and R ' ~ +R3, the former arm will govern the overall resistance if

In the arm R1 +R2, R2 will govern the resistance of this series resistance if

From the above comparison, it is quite obvious that R2 which corresponds to the resistance of the polymer network in polymer cell; can govern the overall resistance if eqs.(3-61) and (3-62) are satisfied simulta~eously. This means that the defects between the polymer cell can be stopped by the lamination of the top layer. Eq.(3-61) can also be satisfied when the area occupied by the void space is very small.

4. Membrane Modules and Module Calculation

4.1. Module types

There are several types of membrane modules currently available in industries, and four of the basic ones are described below:

1. Plate and frame module, 2. Spiral-wound module, 3. Tubular module and 4. Hollow fibre module.

l. Plate and frame module This type of module appeared in the earliest stage of industrial membrane applications. The structure is simple and the membrane replacement is easy. As illustrated in Figure 4-1, spacer-membrane-support plates are stacked alternately. The feed flows in the module, inwards and outwards, enabling the entire membrane surface to be covered by the feed stream. The membrane permeate is collected from each support plate. The space6 surface is made uneven in order to promote turbulence of the feed of fluid and to minimise concentration polarization.

Feed + 2 Figure 4- 1 Plat and frame membrane module

2. Spiral-wound module , The basic structure of this module is illustrated in Figure 4-2. A permeate spacer is sandwiched between two membranes. Three edges of the membranes are sealed with epoxy resin to form a membrane envelope, the open end being connected to a central tube with holes. The membrane leaf so produced is wound spirally around the central tube together with a feed spacer.

Feed spacer

I Permeate Permeate crpacer

Membrane . . . , .

Figure 4-2 An envelope of a spiral-wound module

In order to make the leaf length shorter, several membrane leaves are wound simultaneously as illustrated in Figure 4-3.

Permeate spacer

Membrane

Feed spacer

Figure 4-3 Multiple envelopes of a spiral-wound module

Usually two to six leaves p e used for a module of 4-in. diameter, and 4 to 30 leaves in a module of 8-in. diameter. A polypropylene or polyethylene, 0.2 to 2.0 mm thick is used for feed spacer, while polyester cloth, 0.2 to 1.0 mm thick is used for permeate spacer.

3. Tubular module In this type of module, a number of membranes of tubular shape are encased in a shell. Figure 4-4 shows the structure of the tubular module.

Figure 4-4 Tubular module

The membranes are formed in the internal wall of the support tube. The feed liquid flows inside the tube, and permeate flows from the inside to the outside of the membrane tube and is collected at the permeate outlet. The main features of the tubular module are:

1. The module can be operated with simple pre-treatment of feed liquid. 2. Membrane contamination can be minimized by high feed flow rate. 3. Contaminated membrane surfaces can be easily washed.

4. Membrane replacement is easy. 5. The membrane areahodule space ratio is small. 6 . Energy consumption per amount of liquid treated is high.

4. Hollow fibre module The development of hollow fibre membranes represented an important advance in membrane fabrication technology. The main advantage of the hollow fibre is that large areas can be packed in to small volume. Hollow fibre modules reach packing densities as high as several thousand m21m3, while the flat and spiral wound modules only permit packing densities less than a few hundred, rn2/m3. Figure 4-5 shows a typical hollow fibre module used in gas separation.

Figure 4-5 A hollow fibre module for gas separation

The key design data of the hollow fibre module currently used in industries are given in Table 4- 1.

Table 4- 1 Monsanto hollow-fibre module

Shell diameter D = 0 . 1 m; 0.2 m Module length L=3000 mm Maximum feed pressure 148 bar Maximum trans-membrane pressure difference 115 bar Feed side pressure loss 0.3 bar Packing density ca. 8000 m * m-'

4.2. Module calculation

Membrane gas separation In membrane gas separation, five different flow patterns, as shown in Figure 4- 1, may be existed in a single stage membrane module. They are:

a. Perfect mixing. b. Cross flow pattern. c. Cocurrent flow pattern.: -

d. Countercurrent flow pattern. e. One side mixing.

Figure 4-1 Different flow patterns in membrane modules - a) perfect mixing, b) cross flow pattern, c) cocurrent flow pattern, d) countercurrent flow pattern, e) one side mixing.

These five different models was developed based on the following assumptions:

1. All components in the feed stream are permeable,

2. the permeability of each gas component is the same as that , . of pure gas and is independent of pressure,

3. negligible pressure drop of feed and permeate streams occurs along the flow path, and

4. diffusion along the flow path is insignificant compared to bulk flow.

a. Perfect mixing In the case of perfect mixing (Figure 4-1 a), it is assumed that the rate of mixing

on the high pressure side of the permeator is 5b.;apid, as compared with the flow

rate, that the gas stream has the same composition as the unpermeated stream at all points along the membrane. The same assumption is made for the low pressure

side. The permeation of gases through the membrane is further assumed to be the rate controlling step. Therefore, for a multicomponent gas mixture, the mass conservation over the overall membrane surface area At may be written for each component as: (

The material balance equations for each component are:

where 4 is the fraction of feed allowed to permeate, usually called the "stage cut",

defined as L/ Lf

Rearranging the above equations leads to the following expression

r . -

Eqns (4-5) and (4-6) with eqns (4-3) and (44)'have been solved by the iteration technique:

1 . A value is assumed for y l ,

2. The membrane area may be calculated from eq.(4-5),

3. y2 to yn are calculated from eq.(4-6) n n

4. yi is determined and steps 1 to 3 are repeated until Cyi =l i=l i=l

5. XI to xn are calculated from eq.(4-2).

In the case of cross flow with no mixing, the gas on the high pressure side of the stage is assumed to flow parallel to the membrane with plug flow, while the

permeated gas on the low pressure side flows perpendicular to the membrane as shown in Figure 4- l b.

For a multi-component gas mixture, mass conservation over the differential membrane area dA' leads to:

An additional assumption is made for the low pressure side of the stage that the permeated stream is swept away by convection from the outgoing membrane surface, and transport by molecular diffusion in this direction is negligible. Therefore, the mole fraction y/ of the permeated stream can be approximated as:

Rearranging eqns (4-7 and (4-S), a system of-ordinary differential equations can be obtained for each component:

With the following condition:

the system of differential eqns (4-9) and (4-10) with eqns. (41 1) and (4-12) have been solved by a standard Runge Kutta method with the initial conditions xi'= Xf L, =Lf and A ' =O to find:

. ~

3. Cocurrentflow For the cocurrent flow case, as illustrated in Figure 4-lC, the permeate and unpermeate streams flow in the same direction. Plug flow has been assumed on both sides of the membrane. . . .

For a multi-component gas mixture, mass conservation over the differential. membrane area dA ' gives:

In addition, at any point in the system downstream from the inlet, it is possible to write the overall material balance:

where L, and L, are the local molar flow rates of uppermeate and permeate streams respectively. The corresponding material balances for each component are then:

Rearranging eqn. (4-13) yields the same equations as for the cross flow case eqns.. (4-9) and (4- 10):

Substituting eqn. (4- 14) into eqn. (4-1 5) yields:

+xi, L',, = Lj

/ :

Eqn.(4-17) is obtained by application of 1'Hopital' rule as L,'+L~ Again, the system of differential eqns.(4-9) and (4-10) with eqns.(4-16) and (4-17) is formulated and has been integrated by a fourth order Runge Kutta method with initial conditions ofxi'=% L,'=L~ A'=o, to find:

4. Countercurrent flow

Countercurrent flow in a single permeation stage is shown in Figure 4-ID. From an analytical point of view, this case is similar to the case of cocurrent flow with the exception that the permeate and uppermeate streams flow in opposite directions along the membrane.

As for cocurrent flow, mass conservation over the differential membrane area dA for a multi-component gas mixture yields eqn.(4- 13):

and therefore eqns.(4-9) and (4-10) are still valid. The overall material balance for this case is

with material balances for each component:

Substituting eqn. (4-1 8) into eqn. (4- 19) we obtain:

with the condition that:

The system of differential eqns.(4-9) and (4-10) with eqns.(4-20) and (4-20) has been integrated with initial conditions of

x.=X. L =L A=O ' X, - (l - @ ) X ,

I I , U f; I yi = yi = to find: 4

at L',, = L, - $Ll

Numerical integration of this system of equations is iterative with an initial guess of X, in order to find a satisfactory result for xi = xi at L, = L/ - 4LJ.

5. One side mixing

In this type of case, as shown in Figure 4-lE, it is assumed that the gas stream at the high pressure side is in plug flow, while the gas stream on the low pressure side is maintained perfectly mixed which means that the mole fraction of permeated gas is uniform at all points along the membrane. For a multi- component gas mixture, mass conservation over a differential membrane area gives:

Rearranging eqn. (4-22) yields:

with the condition that:

Initial conditions for the system of differential eqns (4-23) and (4-24) with eqn.(4- ( 25) are given by xi'=& L.'=L~ A '=o, to find:

Again, the numerical integration of the system of differential eqns.(4-23) and (4- 24) with eqn.(4-25) is iterative with an initial guess of y i to obtain the satisfactory relation:

X, - (l - 4)x, y . = when xi = xi

4

5. Special Topic: Membrane based gas absorption or stripping

5.1. INTRODUCTION . Microporous hollow fibre membrane modules employed in gas absorption or stripping processes have attracted considerable attention in the past and was first studied by Qi and Cussler [1,2] and Cooney and Jackson [3]. The hollow fibre membrane used by them acts as a fixed interface and keeps the gas and liquid phases separated while mass transfer of gases takes place through the membrane. Depending on the membrane material, the physico-chemical properties of the liquid and the operating pressures employed, the pores of the membrane can be filled with either gas or liquid, which will result in great differences in the mass transfer resistance of the membrane employed [4].

Compared with conventional absorption or stripping processes such as bubble columns and packed beds, there are several advantages of using microporous hollow fibre modules for gas absorption or stripping. These include larger interfacial area per unit volume, independent control of gas and liquid flow rates without any flooding, loading, foaming, etc., and known gas-liquid interfacial area. These advantages have led.30 a number of investigations on the use of the membrane modules for gas absorption and stripping [5-101. In most studies, however, emphasis has been focused on nonwetted operating mode, shown in Figure la, whereby the membrane pores are filled with gases. The primary reason for such an operating mode is quite obvious, since the usual physical absorption processes used in industry are limited by the mass transfer rates in the liquid phase. The overall mass transfer coefficients in these cases are between 10" and lo4 m/s [l l]. Adding the mass transfer resistance of the nonwetted membrane, which is several order of magnitudes smaller than

(

that of liquid, will result in a negligible effect on the overall mass transfer coefficient. Due to the considerably larger interfacial area, the overall mass transfer per unit volume, Kra for the membrane module, is therefore, much higher than that of conventional columns. Thus, the membrane based gas absorption or stripping offers a promising alternative.

In principle, a membrane process may replace a conventional gas absorption process. However, the success of the membrane processes over the conventional absorption processes will largely depend on the types of gas- liquid systems and of hollow fibre membranes used. For example, as mentioned above, for a liquid film resistance controlled system such as CO2- HzO, the use of a microporous hydrophobic membrane will give a negligible

mass transfer resistapce to the overall mass transfer provided that the hydrophobic membrarie remains 'non-wet', i.e. the membrane pores a e filled with gases [5,10]. In addition to the characteristics of membranes, operating conditions such as solution pressure will also play a major role in the overall membrane absorption performance [4,12]. As illustrated by Poddar et al. [l 21 and Malek et al. [13], the operating pressure at the liquid phase should always be kept higher than that at the gas phase in order to prevent bubble formation resulting in loss of gas components and operating stability. However, it has been observed that maintenance of a high pressure at the liquid phase for long- term operation could lead to wetting of the microporous membrane by the liquid absorbent as shown in Figure l b [13]. As a result, the gas transfer rate was found to be greatly reduced due to this wetting of the hydrophobic membrane. It was indicated by Kreulen et al. [l41 that the performance of a hydrophobic membrane module at the wetted condition is inferior compared to the conventional processes for gas absorption.

Figure 1. Microporous hollow fibre membrane module operated under (a) nonwetted mode; (b) wetted mode; (c) partially wetted mode.

In order to prevent the membrane from getting wet, the liquid pressure should always be operated lo6er than the wetting pressure of the membrane employed [l 5- 1 71. For a microporops hydrophobic hollow membrane module where liquid is fed into the fihre lumen, because of the small size of the fibre diameter, pressure drop of the liquid in the fibre lumen will inevitably be increased with the liquid velocity and length of the fibre used according to the Hagen-Poiseuille law. In this case, the membrane module may be partially wetted due to the pressure gradient along the fibre lumen as shown in Figure lc. Such a phenomena has been observed by Tai [l81 who found that water droplets are formed at the outer surface of the hollow fibre membrane, especially near the inlet of the membrane module. The overall mass transfer coefficients obtained by Tai [l 81 at different liquid velocities for the system of 02-H20 system exhibit a maximum value which may suggest that the membrane module is partially wetted fiom the inlet of the module due to a high liquid pressure in the fibre lumen. The partially wetted membrane module may result in a reduction of the overall mass transfer coefficient compared with the nonwetted mode, hence giving a maximum value of the overall mass transfer coefficient as a function of the water velocity.

Microporous hydrophobic membranes were also studied for gas film controlled systems such as NHn in H~SOP, SO2 in NaOH and H2S (low concentration) in NaOH by Qi and Cussler [2] and by Kreulen et al. [19]. The KAg values measured by them are in the range of 0.0035 to 0.0073 d s , which are considerably lower than the kA,values of 0.01-0.1--m/s measured in the conventional gas absorbers [20]. Therefore, it is not surprising that membrane resistance controls the absorption of all these gases in the membrane modules used by Qi and Cussler [2]. The membrane resistance, l/kAM, may be reduced if hydrophobic asymmetric membranes are employed for the gas absorption with the systems mentioned above. Li et al. [21] studied the removal of H2S from a gas mixture using a concentrated alkaline solution in an asymmetric polysulfone hollow fibre membrane module. The experimentally evaluated membrane's coefficient, kAM for the polysulfone is in the range of 0.0125 to 0.025 mls, which are better than the value of 0.0073 obtained from symmetric microporous polypropylene membranes [2].

Gas absorption can also be carried out using dense membrane modules. Li and Teo [22] investigated experimentally the CO2 absorption using an ultrathin skinned hollow fibre membrane module originally developed for gas separations [23]. This module consists of a bundle of hollow fibres having a dense skin layer at the outer edge of the fibre as shown in Figure 2. The existence of the dense skin layer in the hollow fibre membrane inevitably

increases the mass transfer resistances for gases. However, it may have two advantages. First, op&ating pressures at gas phase side can be more flexible and higher than liquid side may also be operated as long as no bubble formation is observed in the liquid. Second, the dense skin layer of the fibre eliminates the possibility of filling the membrane pores with the liquid, and thus, prevents the dramatic reduction of gas transfer rate.

olyethersulfone Hollow Fibres

Figure 2. Ultrathin skinned membrane module for gas absorption

In this article, we have attempted a broad coverage of both scientific and engineering aspects of the membrane based gas absorption or stripping. The basic principles, design of the process, and its significance to current chemical industries are the subjects of the review. In contrast to many other reviews, which are mainly written principally for specialists in their own field, the present article is intended to provide a comprehensive reading material in the area of membrane based gas absorption or stripping to readers who have no extensive background in the areas of membranes and gas absorption. Therefore, in certain sections, the materials provided are somewhat course notes. In the following sections, mass transfer of gases through various hollow fibre membranes is presented first, followed by discussions on design equations and potential application of hollow fibre modules in some specific

areas of gas absorption or stripping.

In a hollow fibre membrane module, gas absorption is a three-step process. It involves transfer of a gas component from gas phase to a membrane, through the membrane and then into liquid phase. Depending on membrane characteristics, physico-chemical properties of the absorbing liquid and operating conditions employed, three possible transfer modes, i.e. 1. Nonwetted, 2. Wetted, and 3. Permea-sorption modes are possible at any point of a hollow fibre membrane. Theoretical treatment of local point mass transfer under these three transfer modes as illustrated in Figure 3 are presented in detail below.

2.1 Nonwetted mode Nonwetted transfer mode is often achievable in hollow fibre modules where the hollow fibre membrane employed is microporous and hydrophobic. As shown Figure 3a, an aqueous solution which does not wet the membrane flows on one side of the membrane, while a gas mixture containing gas A flows on the other side of the membrane at a less than that at aqueous phase. The membrane pores are remained gas-filled so long as the pressure difference between the gas phase and the solution phase is less than the wetting pressure, p, of the membrane. Local rate of the gas A transfer, NA through the membrane at steady state can, therefore, be expressed as

where kAg, kAMg and kAr are the individual mass transfer coefficients in gas film, membrane and liquid film, respectively and AM, the surface area of membrane. The pAi and CAi are the partial pressure and concentration of A at

interface, respectively, while and CA,e are the equilibrium partial pressure and concentration of A in gas and liquid phase, respectively and they may be related by Henry's law:

Microporous membrane Gas/liquid interface \

Lquid

Gas liquid inte ace Liqup filled pores ff

1 , Microporous m&branc Lquid

Ultrathin skinncd layer li id hIterface \ Y

PA - 1

Gas

Figure 3. Concentration profiles in (a) nonwetted microporous membrane; (b) wetted microporous membrane; (c) ultrathin skinned dense membrane.

Because the mass transfer of the gas A through the gas film, the membrane and the liquid film are in sGries, the overall mass transfer coefficient, Ka, or KAl in eqs. (4) and (5) can be expressed, respectively, as

1 1 --p 1 HA - +- +- KA, k ~ , k m , kA1

and

2.2 Wetted mode When pressure difference between gas phase and aqueous solution phase is greater than wetting pressure p, of a microporous hydrophobic membrane, wetting of the membrane becomes possible. As shown ~i~urci '3b, the aqueous solution is filled up in the pores of the membrane and eqs. (1) to (3) may be modified as

Rearranging eqs. (9) to (11) together with eqs. (4) to (6), the overall mass transfer coefficient based on the gas phase coefficient, KAg or based on the ( liquid phase, KAI for the completely wetted membranes can be expressed as

1 1 HA HA -=- +- +- K,, k,, M , kA/

1 1 1 1 -=-+-+- K,! HAkAg , kA1

2.3 Permea-sorption modes

Permea-sorption mode is only achievable in hollow fibre modules where a nonporous hollow fibrk membrane is employed. As a resuli, operating pressilre at gas phase can be greater than that at aqueous solution phase. As shown Figure 3c, the gas transfer takes place through two combined operations, i.e. permeation and absorption, and the local rate of the gas A transfer, NA, through the membrane at steady state can, therefore, be expressed as . . . .

where, PA is the permeability of gas A and 6 is the membrane thickness. Rearranging eqs. (14) to (16) together with eqs (4) to (6), the overall mass transfer coefficient based on the gas phase coefficient, KAg;0r based on the liquid phase, KAI for the permea-sorption mode can be expressed as

1 1 -=- S l +-+- K,, H A k A g P, kAI

Hollow fibre modules can also be employed for gas stripping. The operation is identical compared to the gas absorption with exception that gas species are transferred from the liquid to the gas phase. Therefore, the above equations derived for gas absorption are still useful for gas stripping so long as the sign is reversed.

2.4 Mass transfer in hollow fibre lumen When an aqueous solution is fed into hollow fibre lumens of a module, the pressure drop of the liquid in the fibre lumens will inevitably be increased with the liquid velocity and length of the fibre used according to the Hagen- Poiseuille law. If microporous membrane modules were employed, three different operating modes, i.e. nonwetted, wetted or partially wetted modes, shown in Figures l a- l c in a hollow fibre module, can be realized depending on

characteristics of the hollow fibre module and operating conditions.

For nonwetted operating mode, the concentration profiles of the gas A in the aqueous liquid can be described by the differential steady state material balance equations as below:

with boundary conditions:

C* I z=O = CAI

The flux equation at membrane-liquid interface is

where,

For liquid film controlled processes such as 02-H20 and COt-H20 systems, resistances of membrane, I/kAMg and gas film, l/kAg are negligible if the module can be operated under entire nonwetted and eq. (20c) can, therefore be reduced as

Therefore, analytical Solutions for the gas absorption can be derived using the methods given by Leveque and Greatz [24,25]. The Graetz solution is an infinite series solution, which is obtained by solving eq.(19) using the method of separation of variables. This series solution is given as

Sh = 0.5GzB where:

and p, = 4(j-1)+8/3; j = 1,2,3,4 ,...... (21b)

B, = (-1)'" X 2.84606p;"' (2 1 c)

The Leveque solution, on the other hand, is more restricted since it was derived based on the assumption that concentration gradients in the liquid are limited to a thin layer near the fibre wall. This assumption also means that aC, / & can be taken as constant along the fibre length. One important consequence of this assumption is that the model is only applicable for Gz numbers exceeding 400; that is, for short fibres or large liquid flow rates. The Leveque equation is given as

It is clear from the derivation of the analytical solutions of Graetz and Leveque that these two models are only applicable to nonwetted mode of operation, i.e. negligible of resistance of membrane, l/kAMg and gas film, l/kA,.

When the microporous hollow fibre membrane is totally wetted, the general conservation equations remain the same, except that the interface concentration and the fibre wall concentration are generally not the same and are related by eq. (23) assuming that gas phase mass transfer resistance in the shell side is negligible.

This problem cannot be solved analytically. Malek et al. [l31 introduced an orthogonal collocation technique to obtain the concentration profiles of the gas in liquid in the hollow fibre lumen down the length of the module leading to a calculation of mass transfer coefficient.

As it was mentioned in the preceding section, in actual hydrophobic hollow fibre modules, it is likely that the membrane module is partially wetted. The extent of wetting of the hollow fibre module is as yet an unknown function of the operating conditions. Aqueous solution such as water may not penetrate through the hydrophobic hollow fibres due to the presence of a finite wetting pressure, p,, acting along the direction opposite to that of penetration. The penetration of water through the hollow fibres, i.e. wetting of the fibres, however, becomes possible if the hydraulic pressure drop across the fibre wall exceeds the wetting pressure. Therefore, the wetting phenomena of a hollow fibre module can be related to the hollow fibre wetting pressure, p,, described by the Laplace equation, i.e. p, = -2ycose;/r,. The fibre wall is considered to be wetted for portions of the fibre length where the hydraulic pressure drop across the fibre wall exceeds the wetting pressure (Figure lc). The shell side pressure can generally be taken as atmospheric pressure, while the tube side gauge pressure can be calculated using the ~ a ~ e n - ~ o i s e u i l l e equation as follows:

where, z is the length of fibre measured from the inlet. Based on eq.(24), the pressure profile in the fibre lumen can be calculated. As shown in Figure 4 [13], the pressure in the fibre lumen is dependent on both the liquid velocity and length of the fibre. Hence, the partially wetted model solves for mass transfer using the wetted hollow fibre model where the wall pressure drop is larger than the wetting pressure, p , and switches to the non-wetted model otherwise. Again, an orthogonal collocation technique can be employed to obtain the concentration profiles of the gas in the hollow fibre lumen down the length of a module leading to a calculation of the overall mass transfer coefficient.

a Length of the fibre, z, m

Figure 4. Pressure drop in hollow fibre lumen, fibre length, L= 500 mm, fibre ID, di= 0.56 mm

2.5 Mass transfer across membrane When a dense membrane is employed in g@ absorption, the solution-diffusion mechanism describes the gas transport through the membrane and the mass transfer coefficient can be calculated by the expression:

where PA is the permeability of gas A and 6 is the membrane thickness. The permeability values, PA is independent of the hydrodynamics of the fluid flow, but sometimes varies with gas phase operating pressures depending on the characteristic of a membrane [26].

If a microporous membrane is employed, because of the small pore size, the convection can be neglected and the film model describing molecular diffusion can be employed for calculation of the mass transfer coefficient:

where E and G are the porosity and the thickness of the membrane, respectively. T is the tortuosity which corrects the membrane pore geometry.

DA refers gas A diffusion coeficient in either gas filled pores or liquid absorbent filied porei'depending on the operating modes, i.e. nonwetted or wetted modes.

For the nonwetted mode, two types of diffusion can be distinguished, i.e. the continuum diffusion determined by the interactions of the different molecular, and the Knudsen diffusion when the interactions of molecular with the walls of the pores becomes important. In general, the Knudsen diffusion is important only in small gas filled pores. In liquid filled pores, because of high density, the interaction of liquid molecular with the walls of porous structure usually can be neglected. In the intermediate region in which both types of diffusion play a role, the difTusion coefficient can be related between the continuum and the Knudsen diffusion coefficients and is expressed by

When the ratio of the membrane pore radius r, to the mean free pass of the gas, h, rdh is much less than 1, Knudsen flow becomes dominate. The transfer coefficient, kAM can be obtained froh Knudsen flux expression as

2.6 Mass transfer in shell side of a module Hollow fibres in the shell of a module are usually packed randomly, which (5 complicates the mass transfer in the shell side of the module. As shown by Costello et al. [g], shell side flow is likely to be characterized by regions of low local packing, through which a disproportionately high amount of flow passes, and regions of high local packing which are, by comparison, starved of flow. For an uniform packing in a triangular array, concentration profiles of- the gas A in an aqueous solution flowing in the shell side of a module can be described by considering a series of identical sectors as defined in Figure 5. The differential material balance equation for gas A at steady state condition is

where U, is the local velocity and CA is the concentration of gas A in the aqueous solution, wdch is hnction of I, r and 8. A finite difference solution to the equation of this form developed by Miyatake and Iwashita [27] can be adopted to calculate the change of concentration profiles of the gas A in the shell side down the length of the module leading to a calculation of the mass transfer coefficient so long as assumptions of steady state operation, insignificant axial diffusion, constant liquid properties and constant concentration of gas A at interface are valid.

Figure 5. Analytical system and coordinates

For randomly packed hollow fibre modules, shell side mass transfer coefficient has been obtained empirically. Several correlations describing the mass transfer coefficient at outside of hollow fibres are listed in Table 1. The correlation given by Yang and Cussler [5 ] was developed using the experimental data of deaeration obtained from two hydrophobic hollow fibre modules with different packing fractions. The correlation developed by Prasad

and Sirkar [28] includes the packing fraction, 4 as a para~eter in the correlation and shows' a smaller variation with the Reynolds number. The correlation proposed by Costello et al. [g] also includes the packing fraction, 4, but the factor of dJL was iliminated as their experimental results indicate that the length of the fibre has no effect on the mass transfer coefficient. The corrlations given by Ahmed and Semmens [6] eliminates both packing fraction and the factor of dJL as their experimental data obtained from oxygenation experiments indicates independence of both the factors to the mass transfer coefficient. The shell side mass transfer has also studied by Li et al. [10,22] who employed both microporous hydrophobic and ultrathin skinned hollow fibre modules for CO2 absorption. Their experimental data plotted in Figure 6 together with the correlations given in Table 1 indicate that data from the ultrathin skinned hollow fibre module fits well with the correlation of Costello et al., but deviate fiom the correlations given by Yang and Cussler, and Prasad and Sirkar. For the microporous hydrophobic membrane module, the opposite results were obtained, i.e. the data fits correlations of Yang ahd Cussler, and Prasad and Sirkar fairly well, but deviate from Costello et al. From the comparisons between the experimental data and the correlations in Figure 6, it may suggest that these correlations may be correct at a particular operating condition and can be selectively employed.for design purpose. The different correlations developed may represent different degrees of back mixing in the different module geometries.

Table 1 Shell side mass transfer correlations

de=(4xflow area)/(total fibre circumference)

Range of Reynolds number

O<Re<500

500 < R, < 15000

Reference

Yang and Cussler (1986)

Prasad and Sirkar(1988)

Ahrned and Semmens(l992)

Costello et al(1993)

Correlations

S,+ = 1-25

Sh = S . 8(1- (

~h = 0.0 104 ~ ~ 0 . 8 0 6 033

S,.

Sh = (0.53 - 0.581)~eO~'~ S?'

C

m 0 0

E 9) Hydrophobic module L V1 10 100

d -I

Y U

i

Reynolds number. (vLd,/v) I

L

V Ewpe~rnental data -.m- Yang 6 Cussler, 1986 - Costello et al., 1992

Figure 6 . Sherwood number versus Reynolds number for the experimental data obtained for CO2-H20 system.

P] a . . e . Praaad & Sirkar, l988

a E 3

2.7 Effect of chemical reaction Chemical reaction is often employed in gas absorption processes to enhance the mass transfer rate of gases to be.'rimoved. The reaction can be instantaneous, fast, or slow and can be irreversible or reversible. The enhanced gas transfer rate is due to the enhancement of mass transfer coefficient and an increased driving force. Figures 7 and 8 illustrate mass transfer with various chemical reactions for a nonwetted transfer mode.

2.7.1 Instantaneous reaction For an instantaneous reaction, gas A reacts with an aqueous solution containing a solute B as follow:

A + b B + R (30)

As the reaction takes place within the liquid film with a reaction zone flattens to a plane shown in Figure 7a, the rate of gas A transfer can, therefore be evaluated with the Hatta approach as below:

DHCBH,

DA, b + P A

N A = 1 1 H ,

Reaction zone flattens e. zero thickness

gas-liquid interface and reaction plane

membrane / liquid film

Figure 7. Mass transfer with chemical reaction, (a) Instantaneous reaction; (b) Instantaneous reaction with high CB

gas-liquid interface mehbrant: /

gas-liquid interface .. -

membrane /

Figure 8. Mass transfer with chemical reaction, (a) Fast second order reaction; (b) Pseudo first order reaction.

If the resistances in gag phase and in membrane are negligible, i.e. p~ = pili, eq. (3 1) is simplified as

When concentration of reactant B in liquid becomes very high, i.e., C, is high, the reaction zone is expected to shift to the gas-liquid interface as shown in Figure 7b and k A r + ~ , eq. (3 1) reduces to

where

2.7.2 Fast reaction if . - For a fast second order reaction of A + bB + R , the rate of gas A transfer can be written as

Eq. (35) is written with an assumption that concentration of gas A in the liquid is negligible, which is admissible as for fast reaction, the reaction still takes (' place within the liquid film illustrated in Figure 8a. In eq.(35), E is the enhancement factor due to the chemical reaction, which can be evaluated from the classical solution of gas absorption accompanied by a second-order chemical reaction [l l , 291:

where

D C H ..Ei = l + B' B A

bDAl PAI

where k is the reaction rate constant. At high concentration of CB as shown in Figure 8b, the fast second order reaction approaches to the Pseudo-first order [l l] and E+MH. Under such a condition, the overall mass transfer coefficient can be evaluated by

As can be seen from eq. (39), the overall mass transfer coefficient, K; is

independent of the liquid velocity if high concentration of CB is employed for the mass transfer.

3. DESIGN EQUATIONS

The design equations for membrane based gas absorption closely follow the conventional gas absorption processes. Depending on the membrane characteristics and arrangement of gas and liquid flow, the gas-liquid interface can be either at the hollow fibre lumen or at outer surface of the hollow' fibre. In the following sections, the design equations are derived for a hollow fibre module containing n hollow fibres of internal diameter (ID), d,, external diameter (OD), do and hollow fibre length, L. As shown in Figure 9, the flow streams of a gas mixture, containing gas A and inert gases, and an aqueous solution are in countercurrent flow. Assuming that the gas-liquid interface is at outer surface of the hollow fibre, i.e. nonwetted operation, the differential mass transfer equation for the gas A absorbed can be written as

where Y ' is the local mole ratio of gas A and inert gases in the gas phase at the hollow fibre length, z, KAg, the overall mass transfer coefficient based on the

gas phase and G,, the inert gas flow rate.

I f%zins gas A and inert B)

.( Gas oui -.

Figure 9. Membrane based gas absorption, Countercurrent operation

The local partial pressure of gas A at the bulk of gas phase, and partial pressure of gas A in equilibrium with the liquid phase, are given by the following:

(

where, y' represents local mole fraction of gas A. Substituting eqs.(41) and (42) into eq.(40), we obtain:

When the aqueous selution is in excess, or an instantaneous or fast reacticn takes place between the reactant B and the dissolved gas A in liquid, concentration of the gas A in the liquid approaches to zero resulting in Y,' =O. Therefore eq. (43) is reduced, after integration, to

If the concentration of gas A in the gas mixture is dilute, i.e. y' =Y 'and ye' =Y , eq. (43) can be simplified as

For dilute concentrations, the material balance of the gas A from inlet of the module to any point of the module is

9 '.

where L, is the inert liquid flow rate. If the entering aqueous solution is free from the gas A, then xi, = 0 and

For the dilute solution, the Henry's law holds:

where

Substituting eqs. (47) and (48) into eq. (49, upon rearrangement, the

following expression may be obtained: *'

Again, at a condition that the absorbing liquid is in excess, or an instantaneous or fast reaction takes place between the reactant B and the dissolved gas A in liquid, eq. (50) reduces to

, - .

Finally, the design equation can be written as

where HTU is the height of transfer unit defined as

HTU = Gm K A g n d o P

In eq.(52), the number of transfer unit, NTU is defined as

or for dilute gas A in the gas mixture,

The above design equations were derived for nonwetted operation with gas flowing in hollow fibre lumen and liquid flowing in shell side. For any other operating modes or for gas stripping processes, the design equations can be easily derived with exactly the same manner shown above.

4. SOME SPECIFIC APPLICATIONS STUDIED

Membrane based gas absorption or stripping may be applied to any gas-liquid systems treated by conventional processes. For liquid film controlled systems, the membrane resistance of nonwetted membranes is usually negligible. Considering much higher interfacial area, membrane modules offer a promising alternative. For gas film controlled systems, the membranes provide resistance to the overall mass transfer. However, as the mass transfer capacity of absorbers is most important, the high interfacial area provided by membranes may compensate the reduced mass transfer and give still higher capacity of the membrane based gas absorbirs: In the following sections, three potential applications for hollow fibre modules used as either absorbers or scrubbers are discussed based on our laboratory data.

4.1. Dissolved oxygen removal Production of ultrapure water is one of the key support services for semiconductor, pharmaceutical, biotechnology, power and specialized chemical industries. Removal of dissolved oxygen from water is an important step in this production process and can be achieved by either physical or chemical methods. Conventional physical methods such as thermal degassing, vacuum degassing or nitrogen bubble deaeration have inherent drawbacks in terms of both operating costs and bulky construction. Also, with these physical methods, it is difficult to reduce the dissolved oxygen concentration from parts per million (ppm) levels down to a few parts per billion levels (ppb) [29-311 which is often required in the semiconductor industry for wafer cleaning. The conventional chemical methods such as addition of hydrazine or sodium sulfite, although, provide an alternative to the physical methods, are undesirable because of the toxicity of the hydrazine material and because the addition of the sodium sulfite will result in an increase of the solid content of the water.

Tai et al. [32] studied the removal of the dissolved oxygen from water using membrane modules. The modules used by them are made of a hydrophobic microporous membrane. Water containing saturated oxygen was fed into the fibre lumen, while the p ih ied nitrogen acting as purge gas was introduced into the shell side. Therefore the removal of dissolved oxygen from water is achieved by fast mass transfer rather than selective permeation. The experimental results obtained by them indicate that the hydrophobic membrane modules were capable of reducing the dissolved oxygen content in water to a level of around 8-ppb.

During the course of their study, Tai [l81 observed that water droplets were formed at the outer surface of the hollow fibre membrane, especially near the ( inlet of the membrane module and overall mass transfer coefficients obtained at different liquid velocities exhibit a maximum value which cannot be explained by existing mass transfer models. Conventionally, for the membrane modules operated under nonwetted mode, increase of the..water flow will generally increase the overall mass transfer coefficients for the 02-H20 system. The existence of a maximum value of the overall mass transfer coefficient was explained by Malek et al. [l31 that the membrane module is partially wetted from the inlet of the module due to high liquid pressure in the fibre lumen. The partially wetted membradkibdules may result in a reduction of the overall mass transfer coefficient compared with the nonwetted mode, hence giving a maximum value of the overall mass transfer coefficient. Figure 10 shows the theoretical results together with the experimental data given by Malek et al. [13]. It can be seen that the observed experimental data shows a maximum value of the mass transfer coefficient at Graetz number around 350. The experimental data agrees exceptionally well with the theoretical results at lower Graetz number region, i.e. non-wetted mode. As Graetz number increases, the partial wetting of the module becomes inevitable resulting in a decrease in the mass transfer coefficient. Overall, the experimental data is in fairly good agreement with the simulation results obtained at p,=1.5 bars. When the partial wetting of the fibre takes place in the module, the experimental results deviate from the theoretical results; however, the general trends are sufficiently clear to merit a meaningful comparison between the simulation and experimental results. It was also observed that after a week operation, the DO concentration in the product stream was slightly increased for the water flow range studied. Nevertheless, the maximum overall mass transfer coefficient calculated from the measured DO data was always obtained.

I ' Non-wetted mode

pw=2.0 pw= \ .S

(BOB):

pw=l . l

Wetted mode

i . . . . ' , l

Graetr Number, Gz

Figure 10. Comparison between experimental data and theoretical calculations, @experimental data.

4.2. Removal of CO2 from a breathing gas mixture It is important that in closed or semi-closed habitable environments such as submersibles and space capsules, carbon dioxide, produced fiom normal physiological activities, must be continuous3y.removed. If no means of carbon dioxide removal exists, the concentration of carbon dioxide in the environment will, inevitably, be increased, which will result in toxic effects to humans. The extent of toxicity induced depends on both the time of the exposure and the partial pressure of carbon dioxide. In both commercial and military diving circles, the threshold limit of CO2 concentration at range between 0.5% and 1% is widely accepted for long-term exposure [33]. Therefore, facilities for removal of carbon dioxide are essential for these closed or semi-closed environments.

In the case of individual underwater breathing systems, normally used in diving applications, the carbon dioxide is mainly removed by methods which involve absorption in solids or liquids. Because the chemical activity of these caustic absorbents, the treated breathing gas becomes very warm for breathing. Also, there is the probability of the dust inhalation, resulting fiom their attrition, which can have physiological effects on human lungs.

One of the alternative methods for removal of CO2 from life support systems is its selective removal by permeation through a membrane material. Membranes have the advantage of long life, are maintenance fiee and their cost are now comparable with other systems. Sarich [34] has investigated a

possibility of using a membrane process for a self contained breathing system, employing a siliconk rubber membrane as the permeation barrier. This membrane material gives preferential permeation for carbon dioxide and may be used to remove the waste product of carbon dioxide in the breathing system. Li et al. also studied the problem of carbon dioxide removal from life support systems using microporous hydrophobic [l01 and dense [35] membrane modules. Their experimental results indicate that it is feasible to remove CO;! fiom a breathing gas mixture using the microporous hydrophobic membrane modules. The design of the module may follow the correlation of

0.967 o 33 Sh = 1.164(~e d, I L) S, developed during the course of their study.

4.3; Elimination of H2S Natural gas, refinery gas and coal gas, commonly employed for industrial and domestic heating as well as for chemical processing contain hydrogen sulphide (H2S) as one of their major impurities. Hydrogen sulphide is a highly toxic and corrosive gas and is one of the major sources for the environ&ntal problem of acid rain. In addition, hydrogen sulphide is often released from the anaerobic decomposition of wastes resulting in an extremely unpleasant odour. Therefore, in order to utilize these fuel gases for chemical processing or energy generation, and to control or to eliminate- the odour emission, the H2S concentration in the gas stream must be reduced to a very low level; less than 0.01 15 g/m3 is required for some specific applications [36].

Li et al. [21] investigated both experimentally and theoretically the removal of H2S from a waste streams using membrane modules prepared from either asymmetric polysulfone or polyethersulfone hollow fibre membranes [37,23]. An aqueous solution containing 10% of NaOH used as absorbent was circulated through the shell side of the module, while a gas mixture containing 16 to 24 ppm of H2S was fed into the fibre lumen. The experimental results obtained by them reveal that rate of H2S removal is solely controlled by the membrane resistance. The polysulfone asymmetric hollow fibre membrane yielded a greater H2S depletion than that of the polyethersulfone as the former has a more porous external ultrathin layer. The experimentally evaluated membrane's coefficient, kAM for the polysulfone is better than that of literature value for conventional microporous polypropylene membranes, while for the polyethersulfone, the kAM value is much inferior.

Despite the introduction of an additional membrane resistance, the absorption of H2S using the membrane module eliminates problems associated with flooding, loading and maldistribution commonly encountered in the

conventional absorption systems. Thus, these hollow fibre membrane modules studied by Li et al. ate particularly suitable for purification purpose such as removal of a trace amount of H2S from various contaminated gas streams.

NOTATION

A -Area, m2 b -Stoichiometric coefficient C -Concentration in liquid, m01 m" d -Hollow fibre diameter, m 4 -Equivalent diameter, m 4 -Pore diameter, m D -Diffusivity, m2 S-'

DAB -Continuum diffusion coefficient, m2 S-'

DAK -Knudsen diffusion coefficient, m2 S-'

E -Enhancement factor G, -Inert gas flow rate, m01 S-'

Gz - u m d i 2 / ( ~ ~ ) ; Graetz number H -Henry's constant, atm m3 mol" k -Reaction rate constant in eqs.(33) and (34) k -Mass transfer coefficient in liquid Lphase, mls or in gas phase, m01 S- 1 -2 m atm-' K -Overall mass transfer coefficient in liquid phase, m/s or in gas phase, m01 S-'mm2 atm-' L -Module length, m L, -Flow rate of aqueous solution, m01 S-'

m -Henry's constant, defined in eq.(44) M -Molecular weight MH -Hatta number defined in eq. (33) n -Number of hollow fibres in a module N -Rate of mass transfer, molls P -Pressure, atm p, -Wetting pressure, atm p[ -Gauge pressure in fibre lumen at a given length of the fibre, atm

P -Permeability coefficient, m01 m S-' atm-' r -Radial coordinate, m

r~ -Pore radius, m R -Fibre inner radius, m Re -Reynolds number R0 -Fibre outer radius, m

Sh -kd/D; Sherwood number U, -Average velocity in fibre, rnfs X -Mole fraction of gas A in aqueous solution Y -Mole fraction of g& A Y -y/(I -y), mole ratio z -Axial coordinate, m Z -Module length given in Table 1

Symbols E -porosity 6 -membrane thickness, m T -tortuosity

P -liquid viscosity h -Mean free path

4) -packing fraction

Subscript

out

f T

-Gas A -Reactant B .in aqueous solution Y - -

-Gas phase -Equilibrium -Gas-liquid interface -Hollow fibre ID -Module inlet -Liquid phase -Membrane -Hollow fibre OD -Module outlet -Feed -Total

Superscript

3 -Local value

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