Membrane Separation Processes

Transcription

1 Membrane Separation Processes Membrane separations represent a new type of unit operation. Te membrane acts as a semipermeable barrier and separation occurs by te membrane controlling te rate of movement of various molecules between two liquid pases, two gas pases, or a liquid and a gas pase. Te two fluid pases are usually miscible and te membrane barrier prevents actual, ordinary ydrodynamic flow. References: C.J. Geankoplis, Transport Processes and Unit Operations, 3rd ed., Prentice Hall, Englewood Cliffs, New Jersey, (Capter 13) W.L. McCabe, J.C. Smit, P. Harriott, "Unit Operations of Cemical Engineering", 5t ed., McGraw-Hill, New York, (Capter 26) 154

2 1. Classification of membrane processes Porous membrane Gas diffusion: Te rates of gas diffusion depend on te pore sizes and te molecular weigts. We may ave molecular, transition, and Knudsen diffusion regions depending on te relative sizes of pore and gas molecule. Microfiltration (MF): Tis refers to membranes tat ave pore diameters from 0.1 to 10 m. It is used to filter suspended particulates, bacteria or large colloids from solution. Ultrafiltration (UF): Tis refers to membranes aving pore diameters in te range A o. It can be used to filter dissolved macromolecules, suc as proteins and polymers, from solution. Reverse osmosis (RO): Te membrane pores are in te range of 5-20 A o in diameter, wic are witin te range of te termal motion of te polymer cains. Dialysis 155

3 Figure

4 Tigt (nonporous, or dense) membrane Here te permeants are sorbed into te membrane material under te influence of teir termodynamic potential and pass it as a result of a driving force exerted: Gradient of vapor pressure pervaporation (feed is liquid) vapor permeation (feed is vapor) Pressure gradient gas permeation (feed & permeant are gases) reverse osmosis (feed & permeant are liquids) Temperature gradient termoosmosis Concentration gradient dialysis (osmosis, liquid permeation) pertraction Gradient in electric potential electrodialysis (ion-selective membrane) 157

5 Membrane classification. 158

6 Types of membrane structures. 159

7 2. Dialysis (liquid permeation) In tis case te small solutes in one liquid pase diffuse troug a porous membrane to te second liquid pase were te permeants are diluted by means of a so-called sweeping solvent. Te driving force is a concentration gradient so te flux rates are low. If te boiling point of te permeants is muc lower tan tat of te sweeping liquid, te permeants can be separated by flasing from te sweeping liquid, te dialysis process is called pertraction. In practice dialysis is used to separate species tat differ appreciably in size, wic ave a large difference in diffusion rates. Applications include recovery of sodium ydroxide in cellulose processing, recovery of acids from metallurgical liquors, removal of products from a culture solution in fermentation, and reduction of alcool content of beer. 160

8 2.1 Series resistances in membrane processes In dialysis, te solute molecules must first be transported or diffuse troug te liquid film of te first liquid pase on one side of te solid membrane, troug te membrane itself, and ten troug te film of te second liquid pase. Tis is sown in Figure 2, were c1 is te bulk liquid pase concentration of te diffusing solute A in kg mol A/m 3, c1i is te concentration of A in te fluid just adjacent to te solid, and c1is is te concentration of A in te solid at te surface and is in equilibrium wit c1i. Te mass transfer coefficients are kc1 and kc2 in m/s. Te equilibrium distribution coefficient K is defined as: K c S c1is c2is ' (1) c c c L 1i 2i 161

9 Te flux equations troug eac pase are all equal to eac oter at steady state: D NA k c c AB c1 1 1i L c 1iS c 2iS k c2 c 2i c 2 Substituting Eq. (1) into Eq. (2), D K N k c c AB ' A c i c i c L p c c k c c i M 1i 2i c2 2i 2 (2) (3) D K p AB ' M (4) L were pm is te permeability in te solid in m/s, L is te tickness in m, and DAB is te diffusivity of A in te solid in m 2 /s. Instead of determining DAB and K in two separate experiments, it is more convenient to determine pm in one experiment. Te concentration differences can be obtained from Eq. (3): N c c A N c A N c A 1 1i c 1i 2i c 2i 2 kc1 pm kc2 (5) By adding tree equations, te internal concentrations drop out, te final equation is c c NA 1 2 (6) 1/ kc1 1/ pm 1/ kc2 Te denominator can be considered as te inverse of overall mass transfer coefficient. In some cases, te resistances in te two liquid films are quite small 162

10 compared to tat of te membrane resistance, wic controls te permeation rate. Example 1: Membrane diffusion and liquid film resistances A liquid containing dilute solute A at a concentration c1=0.030 kg mol/m 3 is flowing rapidly by a membrane of tickness L=3.0x10-5 m. Te distribution coefficient K =1.5 and DAB=7.0x10-11 m 2 /s in te membrane. Te solute diffuses troug te membrane and its concentration on te oter side is c2= kg mol/m 3. Te mass transfer coefficient kc1 is large and can be considered as infinite and kc2 =2.02x10-5 m/s. (a) Derive te equation to calculate te steady-state flux NA and make a sketc. (b) Calculate te flux and te concentrations at te membrane interfaces. Solution: For part (a) te sketc is sown in Fig. 3. Note tat te concentration on te left side is flat (kc1=) and c1 = c1i. Te derivation is te same as for Eq. (6) but 1/kc1 = 0 to give c c NA 1 2 (7) 1/ p 1/ k M c2 163

11 For part (b), 11 D K p AB ' ( 1. 5) 6 M L 5 m / s c c NA / p 1/ k 1/ / M c = kg mol / s m To calculate c2i, -8 5 NA = kc2 c2i c c2i Solving c2i = kg mol/m 3. c2is K' c2i kg mol / m 3 c1 K' c1 K' c kg mol / m 3 is i 164

12 3. Gas permeation 3.1 Series resistances in membrane processes Similar equations to dialysis can be written for gas permeation. Te equilibrium relation between te solid and gas pases is given by S cs c1is c2is H (8) pa pa1i pa2i were S is te solubility of A in m 3 (STP)/atm m 3 solid, and H is te equilibrium relation in kg mol/m 3 atm. Tis is similar to Henry s law. Te flux equations in eac pase are as follows: k N RT p p D A c1 AB A1 A1i L c 1iS c 2iS (9) DABH k pa i p c A i L RT p A2i p A2 Te permeability Pm in kg mol/s m atm is given by P D H D S m AB AB (10) Eliminating te interfacial concentrations as before, N A 1/(k c1 pa1 pa2 / RT) 1/(p / L) 1/(k (11) m c2 / RT) Note tat kg1= kc1/rt. An example of gas permeation in a membrane is use of a polymeric membrane as an oxygenator for a eart-lung macine. Pure O2 is on one side of a tin membrane and blood is on te oter side. Oxygen diffuses troug te membrane into te blood and CO2 diffuses in a reverse direction into te gas stream. 165

13 3.2 Types of membranes and permeabilities for gas separation Te permeation flux is inversely proportional to te tickness of te membrane. So if te membrane is tick (100 m), as used in te early stage to prevent any tiny oles wic reduced te separation, te flux is low. Some newer asymmetric membranes include a very tin but dense skin on one side of te membrane supported by a porous substructure. Te dense skin as a tickness of about 1000 A o and te porous support tickness is about m. Te flux is tousands of times iger tan te 100-mtick original membranes. Some typical materials of present membranes are a composite of polysulfone coated wit silicon rubber, cellulose acetate and modified cellulose acetate, aromatic polyamides or aromatic polyimides, and silicon-polycarbonate copolymer on a porous support. Experiments are necessary to determine te permeabilities of gases in membranes. Some typical data are listed in Table 1. In a given membrane te permeabilities of various gases may differ significantly. 166

14 For te effect of temperature T in K, te ln P A ' increases wit T following approximately a linear function of 1/T. However, operation at ig temperatures can often degrade te membranes. Wen a mixture of gases is present, te permeability of an individual component may be reduced by up to 10%. Hence, wen using a mixture of gases, experimental data sould be obtained to determine if tere is any interaction between te gases. Te presence of water vapor can also ave similar effects. 167

15 3.3 Types of equipment for gas permeation Flat membranes. Tese are mainly used to experimentally caracterize te permeability of te membrane. Te modules are easy to fabricate and use and te areas of te membranes are well defined. In some cases modules are stacked togeter like a multilayer sandwic or plate-and-frame filter press. Te major drawback of tis type is te very small membrane area per unit separator volume Spiral-wound membranes. Tis configuration increases markedly te membrane area per unit separator volume up to 328 m 2 / m 3 and decreases te pressure drop. Te assembly consists of a sandwic of four seets wrapped around a central core of a perforated collecting tube. Te four seets consists of a top seet of an open separator grid for te feed cannel, a membrane, a porous felt backing for te permeate cannel, and anoter membrane as sown in Fig. 4. Te spiral-wound element is 100 to 200 mm in diameter and is about 1 to 1.5 m long in te axial direction. Te flat seets before rolling are about 1 to 1.5 m by 2 to 2.5 m. Te space between te membranes (open grid for feed) is about 1 mm and te tickness of te porous backing (for permeate) is about 0.2 mm. 168

16 Te wole spiral-wound element is located inside a metal sell. Te feed gas enters at te left end of te sell, enters te feed cannel, and flows troug tis cannel in te axial direction of te spiral to te rigt end were te exit residue gas leaves. Te feed stream permeates perpendicularly troug te membrane. Tis permeate ten flows troug te permeate cannel toward te perforated collecting tube, were it leaves te apparatus at one end. 169

17 3.3.3 Hollow-fibre membranes. Te membranes are in te sape of very small diameter ollow fibres. Te inside diameter of te fibres is in te range of 100 to 500 m and te outside 200 to 1000 m wit te lengt up to 3 to 5 m. Te module resembles a sell-and-tube eat excanger. Tousands of fine tubes are bound togeter at eac end into a tube seet tat is surrounded by a metal sell aving a diameter of 0.1 to 0.2 m, so tat te membrane area per unit volume is up to m 2 / m 3. Te ig pressure feed enters into te sell side at one end and leaves at te oter end. Te ollow fibres are closed at one end of te tube bundles. Te permeate gas inside te fibres flow countercurrently to te sell-side flow and is collected in a camber were te open ends of te fibres terminate. 170

18 3.4 Types of flow in gas permeation Because of te very ig diffusion coefficient in gases, concentration gradients in te gas pase in te direction normal to te surface of te membrane are quite small. Hence, gas film resistance compared to te membrane resistance can be ignored. If te gas stream is flowing parallel to te membrane in plug flow, a concentration gradient occurs in tis direction. Hence, several cases can occur in te operation of a membrane module. Bot permeate and feed sides can be operated completely mixed or in plug flow. Countercurrent or cocurrent flow can be used wen bot sides are in plug flow. Tis is summarized in Figure

19 4. Complete-mixing model for gas separation 4.1 Basic equations used A detailed diagram is sown in Fig. 8 for complete mixing. Te overall material balance is qf q0 qp (12) were qf is te total feed flow rate in cm 3 (STP)/s; q0 is outlet reject flow rate in te same unit; and qp is outlet permeate flow rate, cm 3 (STP)/s. Te cut or fraction of feed permeated,, is given as: q p qf (13) Te rate of diffusion or permeation of species A (in a binary of A and B) is given below q q y A p p P A px plyp Am A ' m t 0 (14) were PA is te permeability of A in te membrane, cm 3 (STP) cm/(s cm 2 cm Hg); qa is te flow rate of 172

20 A in permeate, cm 3 (STP)/s; Am is membrane area, cm 2 ; t is membrane tickness, cm; p is te total pressure in te ig pressure (feed) side, cm Hg; pl is te total pressure in te low pressure or permeate side, cm Hg; x0 is te mole fraction of A in te reject side; and yp is te mole fraction of A in te permeate. Note tat px0 is te partial pressure of A in te reject gas pase. A similar equation can be written for component B: q q y B p( 1 p ) P B p x pl yp Am A ' ( 1 ) ( 1 ) m t 0 (15) Dividing Eq. (14) by (15) gives y p x0 ( pl / p ) yp (16) 1 y ( 1 x ) ( p / p )( 1 y ) p 0 l p Tis equation relates yp, te permeate composition, to x0, te reject composition, and te ideal separation factor is defined as ' P (17) PA B' Making an overall mass balance on component A qf xf q0x0 qpyp (18) Dividing by qf and solving for te exit compositions, xf yp xf x01 x0 or y 1 p (19) qf yp Am (20) PA'/ t px0 plyp 173

21 4.2 Solution of equations for te design of completemixing case For te design of a complete-mixing model, tere are seven variables, xf, x0, yp,,, pl/p, and Am, four of wic are independent variables. Let us consider two common cases. Case 1. xf, x0,, and pl/p are given and yp,, and Am are to be determined by solution of te equations. Eq. (16) can be rearranged as were a b a y by c 0 (21) p 1 2 p p p 1 x 0 1 p p x 0 p c p x l and te solution is l 0 b b ac yp 4 2a 2 l (22) (23) 174

22 Example 2. Design of membrane unit for complete mixing A membrane is to be used to separate a gaseous mixture of A and B wose feed flow rate is qf = 1x10 4 cm 3 (STP)/s and feed composition of A is xf = 0.50 mole fraction. Te desired composition of te reject is x0 = Te membrane tickness t = 2.54x10-3 cm, te pressure on te feed side is p = 80 cm Hg and on te permeate side is pl = 20 cm Hg. Te permeabilities are PA = 50x10-10 cm 3 (STP)/(s cm 3 cm Hg) and PB = 5x Assuming te complete-mixing model, calculate te permeate composition, yp, te fraction permeated,, and te membrane area, Am. Solution: P ' A PB' 5 10 a b c p p 1 x 0 1 p p x 0 l ( ) 1 10 ( 0. 25) p p x ( 0. 25) l l 175

23 2 2 CENG 5210 Advanced Separation Processes b b ac yp ( 9)( 10) 2a 2( 9) xf yp ( ) x Solving = qf yp Am P '/ t p x p y = A 0 l p 0.706( / = cm m 4 )( ) Case 2. xf,,, and pl/p are given and yp, x0, and Am are to be determined. Eq. (19) is substituted into Eq. (16) and te result in te form of 2 b b a c a1yp b1yp c1 0 and yp a1 is p a l pl pl pl 1 p p p p b c p p p p 1 x l l l l f p p p p x f x f 176

24 4.3 Minimum concentration of reject stream If all of te feed is permeated, ten = 1 and te feed composition xf = yp. For all values of < 1, te permeate concentration yp > xf. Rearranging Eq. (16) to give p y l p yp p x0 (24) 1 y y p wic means tat x0 is a monotonic increasing function wit yp. Wen yp is at its minimum value of xf, te reject composition ave its minimum as p x l f xf p x0m (25) 1 xf xf Hence, a feed of xf concentration cannot be stripped lower tan a value of x0m even wit an infinitely large membrane area for a complete mixed system. To strip beyond tis limiting value a cascade-type system or a single unit of plug flow sould be used. p 177

25 5. Cross-flow model for gas separation CENG 5210 Advanced Separation Processes A detailed flow diagram is sown in Figure 9. Te flow in te ig-pressure or reject stream is considered to be of plug flow. On te low-pressure side te permeate stream is pulled into vacuum, so te flow is perpendicular to te membrane. No mixing in bot sides is assumed. Tis cross-flow pattern is an approximation to te actual spiralwound membrane separator wit a ig-flux asymmetric membrane resting on a porous support. Te local permeation rate over a differential membrane area dam at any point in te stage is PA ' ydq px plydam (26) t 178

26 P ' ( 1 t CENG 5210 Advanced Separation Processes y)dq B p (1 x) pl(1 y) dam (27) were dq is te total flow rate permeating troug te area dam. Dividing Eq. (26) by (27) gives y x pl p y 1 y ( / ) (28) ( 1 x) ( pl / p )( 1 y) Tis relates te permeate composition y to te reject composition x at a point along te pat. It is similar to Eq. (16) for complete-mixing. Te solution to te tree equations (26) - (28) is R S 1 (1 x) u E / D u F u 1 x were f u 1 q q f u E / D f Di ; i x 1- x f u D i 2Ei F 0. 5 F f F u F (29) T D P P l E 2 DF 179

27 F 1 P 0.5 l 1 P R S 1 2D 1 (D 1) (2D 1) F / 2 1 T 1 D (E / F) F Te term uf is te value of u at i = if = xf/(1-xf). Te value of is te fraction permeated up to te value of x in Fig. 9. At te outlet were x = x0, =, te total fraction permeated. Te total membrane area required is if tq 1 (1 f x)di A m (30) ' P PB i0 1 P l 1 fi i 1 i P 1 fi were D i 2Ei F 0. 5 fi (Di F) values of in te integral can be obtained from Eq. (29). 180

28 Case 1. Te values of xf, x0,, and Pl/P are given and yp,, and Am, are to be determined. or can be calculated from directly from Eq. (29). Since all oter variables are known, yp can be calculated from Eq. (19). Te membrane area Am is calculated from Eq. (30) numerically. Case 2. xf,,, and Pl/P are given and yp, x0, and Am, are to be determined. Tis is trial and error. An initial value of x0 is assumed and substituted into Eq. (19) to calculate yp. 181

29 182 CENG 5210 Advanced Separation Processes

30 183 CENG 5210 Advanced Separation Processes

31 184 CENG 5210 Advanced Separation Processes

32 6. Countercurrent-flow model for gas separation A detailed flow diagram is sown in Figure 10. Making a total and a component balance for A over te volume element and te reject, q q0 q' (31) qx q0x0 q' y (32) Differentiating Eq. (32) d( qx) 0 d( q' y) (33) 185

33 A balance for component A on te ig- and lowpressure sides of te volume element gives qx ( q dq)( x dx) ydq (34) Simplifying to become ydq qdx xdq d( qx) (35) Te local flux out of te element wit area dam is PA ' ydq px plydam (36) t Combining Eqs. (33), (35), and (36) PA ' d(q' y) d(qx) ydq px plydam (37) Similarly, for component B, d[q'(1 PB ' y)] d[q(1 x)] t t p (1 x) pl(1 y) dam (38) Combining Eqs. (31) and (32) to eliminate q and multiplying dx, x y q0dx ( qdx) (39) y x0 Since d[ xq( 1 x)] xd[ q( 1 x)] q( 1 x) dx (40) ( 1 x) d( qx) qxd( 1 x ) we ave qdx (1 x)d(qx) xd[q(1 x)] (41) Substituting qdx from (41), d(qx) from (37), and d[q(1-x)] from (38) into Eq. (39) gives 186

34 CENG 5210 Advanced Separation Processes q0t dx y x (1 x) ( rx y) x[ r(1 x) (1 y)] pl PB ' dam y x0 were r p / p and P '/ P ' Similarly, we can obtain x y q0dy x x l A B. (42) ( q' dy) (43) 0 q0t dy x y (1 y) ( rx y) y[ r(1 x) (1 y)] pl PB ' dam x x0 (44) At te outlet of te residue stream of composition x0, te permeate y = yi, and x0 are related by Eq. (16), wic is given below as Eq. (45) yi x0 ( pl / p ) yi (45) 1 yi ( 1 x0 ) ( pl / p )( 1 yi ) Eqs. (42) and (44) are solved simultaneously by numerical metods starting at te ig-pressure outlet stream of composition x0. Te area Am can be arbitrarily set equal to zero at tis outlet and a negative area will be obtained wose sign must be reversed. 187

35 7. Effects of processing variables on gas separation by membranes 7.1 Effects of pressure ratio and separation factor on recovery By using te complete-mixing model (Eq. 16), te effects of pressure ratio, p/pl, and separation factor,, on permeate purity are plotted in Figure 11 for a fixed feed composition (30%). Above an of 20 or a pressure ratio of 6, te product purity is not greatly affected. 188

36 7.2 Effects of process flow patterns on separation and area Figure 12 sows te permeate concentration versus stage cut,, for a feed of air (x0 = for oxygen) wit = 10 and p/pl = 5. As expected, te countercurrent flow pattern gives te best separation, followed by cross-flow, cocurrent, and te completemixing pattern offers te lowest separation. All four patterns become identical at a value of 0 or 1. Te required membrane areas to acieve te same separation for all four types of flow are witin about 10% of eac oter. Te countercurrent flow again gives te lowest area required. 189