CHAPTER 9: MEMBRANE SEPARATION PROCESS

Transcription

1 CHAPTER 9: MEMBRANE SEPARATION PROCESS MOHAMAD FAHRURRAZI TOMPANG Sem /2012 ERT 313 BIOSEPARATION ENGINEERING

2 Course details Credit hours/units : 4 Contact hours : 3 hr (L), 3 hr (P) and 1 hr (T) per week Evaluations Final Exam 50% Midterm Tests 20% Course works 30% Laboratories 10% Assignments 10% PBL 10% CARRY MARKS 50%

3 Course details Course Outcome (COs) will be covered: CO3 Ability to apply principles, analyze mechanicalphysical separation process and develop design of membrane unit (C4, P3, A3) Course works (Overall evaluations) Assignments 2 Quizzes 2 Midterm test 1 Class participations Max. of 3 points

4 Important reminder Attendance should not less than 80%, or else you will be barred from taking final examination. Plagiarism and copying other students work is strictly prohibited especially in doing assignments and lab reports, or else both parties will get zero. Cheating in quizzes and examinations is also prohibited, or else both parties will get zero. Therefore, study hard and smart. Take note of the important chapters or things that will be highlighted throughout lectures.

5 C-9 Membrane Separation Process Week 10 (16-20 Apr 2012) Reading assignment: 1. Chapter 26, Unit Operations of Chemical Engineering. McCabe, Smith, Harriot (Main) 2. Chapter 4, Bioseparations Science and Engineering. Harrison, Todd, Rudge, Petrides

6 WHAT IS A MEMBRANE? Membranes are materials which have voids in them, letting some molecules pass more conveniently than some other molecules. A semi-permeable membrane is a VERY THIN film that allows some types of matter to pass through while leaving others behind

7 Membrane Separations Introduction Membranes enable filtration to be extended to separation of colloids, cells and molecules by microfiltration, ultrafiltration or reverse osmosis A membrane considered as a permselective barrier between two phases (refer figure 4.1) Mass transport of a component across the membrane occurs due to the presence of a driving force (Figure 4.2) Separation mainly determined by the membrane morphology: porous membrane and non-porous membrane (Figure 4.3)

8 Figure 4.1: Classification of particles by size and applicable filtration separation process

9 Figure 4.2: Schematic representation of a two-phase system separated by a membrane

10 Figure 4.3: Schematic drawing of a porous and non-porous membrane Porous membrane Microfiltration/ ultrafiltration Nonporous membrane Gas separation/ pervaporation

11 Type of Driving Force for Membrane Separation Membrane process can be distinguished according to the type of driving force ensuring the transport through the membrane (T 4.1) Driving force Hydrostatic pressure, p Electric field ψ Concentration C Type of membrane Microfiltration Ultrafiltration Hyperfiltration (reverse osmosis) Electrodialysis Dialysis Table 4.1: Membrane processes grouped according to their driving force

12 continued Importance to the installation of membrane system are: average flux degree of fouling cleaning possibilities membrane lifetime and costs ease with which membranes can be replaced containment and/or sterility automation capital investment

13 Type of Membrane Process Reverse Osmosis (RO) Ultrafitration (UF) Microfiltration (MF) Cross-flow Dialysis

14 Reverse Osmosis (RO) Reverse osmosis uses membranes that are permeable to water but not to salts and most larger, MW species. Also known as hyperfiltration refers to the fact that applied pressures must exceed the osmotic pressure of the feed before water is forced through the membrane. The normal osmotic flow of water is thus reversed by the applied pressure. Have a nonporous skin layer that allows water transport through microvoids, or spaces, between polymer chains. Salt transport is impeded because the ions cannot find free water for solvation within the membrane Other solvents, particularly alcohols, may pass through RO membranes.

15 Ultrafiltration (UF) The membranes used for ultrafiltration (UF) are finely microporous and in many eases they are asymmetric. Water transport is by viscous flow through the pores, driven by a moderate applied pressure Small solutes may also pass through the membranes, but macrosolutes colloids, and some charged species are retained.

16 Cross flow Microfiltration (MF) Microfiltration is an extension of UF, but the membranes have a larger pore size. Macrosolutes are passed, but large colloids and micron-sized particles such as cells are retained. Transport of solvent and solute through the membranes occurs by convective flow through the micropores. This convective transport is pressure-driven.

17 Dialysis Membranes that are very finely microporous (less microporous than UF membranes) are used in dialysis. Often have the nonporous characteristics of RO membranes and the finely micro-porous characteristics of UF membranes Separates solute mixtures on the basis of molecular size and, possible, molecular conformation and net charge. T The driving force is concentration difference. For the removal of ionic species, it is more common to use electrodialysis (ED). ED uses ion-exchange membranes and a voltage gradient as the driving force

18 Basic Principle of Membrane Separation The basic principle of membrane separation is illustrated in Figure 4.4 the feed is pumped along a membrane which act as a selective barrier to the different components some components can freely permeate through the membrane while others will be retained in this way the feed is separated into two streams: the retained enriched phase, and the permeated stream containing small components or Filtrate or Retentate Figure 4.4: Basic principle of a membrane separator

19 Advantages & Disadvantages of Membrane Separation Advantages Separation can be carried out under mild conditions Energy consumption generally low Separation can be carried out continuously No additives required Scale-up can easily be accomplished Membrane properties are variable and can be adjusted Disadvantages Little resistance to high/low ph values and temperatures Cleaning and sterilization difficult Fouling, causing severe problems

20 Figure 4.5 Overview of various type of resistance towards mass transfer transport across membrane in pressure driven processes

21 Membrane Structure Membrane may be formed in a no. of ways, the manner of fabrication determining key characteristics such as the throughput and the separation capacity of the membrane The basic structure of a membrane is shown in Fig. 4.6 where the relative dimensions of the elements comprising the total membrane are shown It is clear that the active membrane surface is very thin in comparison to the overall depth of the support structure This latter structure vital for comparing the necessary strength to the membrane so that it can withstand the pressure of operation

22 continued Figure 4.6: Cross-section of typical membrane structure showing presence of significant depth of porous support structure contin ued 22

23 continued Microfilration (MF) Ultrafiltration (UF) Reverse Osmosis (RO) Depth filters with pores evenly distributed across surface. Particles retained within filter structure tend to block membrane and are hard to recover Asymmetric structure with dense separating surface on a much coarser finger-like substructure Act as surface filters Asymmetric structure but support is spongelike with pore diameter increasing away from membrane surface Mechanically strong membrane

24 Note: membrane can be generally classified into two categories: symmetric (or homogeneous) and asymmetric membranes in homogeneous membranes, the diameter of pores are almost constant over the entire cross section of the membrane. Consequently, the entire membrane thickness acts as a selective barrier this differs from asymmetric membranes, where only a thin top layer determines the selective barrier these differences are clearly shown in Fig. 4.7

25 Figure 4.7: Comparison between symmetric and asymmetric membranes: (a) asymmetric (b) symmetrical

26 Comparison Between Symmetric and Asymmetric Membranes Isotropic, symmetric membranes Have defined pores that typically follow a tortuous path The pore diameters in such a membrane will be slightly larger than the particle that they retain A relatively rough surfaces may capture (and become plugged by) deformable materials such as cells or cell debris that are swept across its surface Typically used in systems where filtration is carried out in a dead-end mode Anisotropic, assymmetric membranes Anisotropic membranes with a porelimiting skin are smooth and allow particles or molecules that are larger than the pores to freely moves across the surface without getting caught Has only a small capacity when used in a dead-end mode, since particles quickly plug the pores in the filter structure

27 continued Membrane selectivity mainly the result of the sieve action of the pores, but to some extent it is also caused by hydrophilic/hydrophobic interactions and membrane charge Since the pores of a membrane are not uniform in size the selectivity shows a certain variation The smaller the pore size distribution, the better the selectivity The membrane selectivity often expresses in terms of molecular weight cut off (MWCO) cut-off values relate the pore dimensions of the membrane to the size of the macromolecular solutes in solution

28 Figure 4.8: Molecular weight cut off for (a) ideal membrane, (b) broad pore size distribution (c ) narrow pore size distribution continued

29 Definition of MWCO: MW of globular proteins/ (macro)molecular solutes that are 90% rejected by the membrane in an ideal UF membrane, all the molecules below the MWCO- value will be permeated while all the other molecules will be retained (refer to Fig.4.8, curve a) QA: Examine fig. 4.8 carefully, which curves represent membranes with a broad pore size distribution, and which represents a narrow pore distribution? Selection of a membrane will represent a compromise between the tightness of cut-off, the flux characteristics and the cost

30 Pop Quiz Question: Complete the following statements : 1) In membrane separations the [ ] stream contains relatively small components 2) Membrane selectivity is often expressed in terms of [ ] cut off 3) For [ ] membranes only a thin top layer determines the selective barrier 4) A membrane with a sharp molecular weight cut off will have a [ ] pore size distribution

31 Answer: 1) In membrane separations the [ permeated] stream contains relatively small components 2) Membrane selectivity is often expressed in terms of [ molecular weight] cut off 3) For [asymmetrical] membranes only a thin top layer determines the selective barrier 4) A membrane with a sharp molecular weight cut off will have a [narrow] pore size distribution

32 4.3.2 Membrane Module Designs A variety of module designs exist for mounting the membrane in Table 4.2: Typical Characteristics of Membrane Modules Packing density, m 2 /m 3 Resistance to fouling Ease of cleaning Plate and Frame Spiral wound Tubular Hollow-Fiber 30 to to to 9,000 Good Moderate Very good Poor Good Fair Excellent Poor Relative cost High Low High Low Main application D, RO,PV,UF,MF D,RO,GP,UF,MF RO,UF D,RO,GP,UF Note: D, dialysis; RO, reverse osmosis; GP, gas permeation; PV, pervaporation; UF, ultrafiltration; MF, microfiltration

33 continued Plate-and-frame (Fig. 4.9) Similar to a filter press in that each filter is a flat sheet Mainly used for UF or RO Easy disassembly for cleaning or membrane replacement High initially investment Figure 4.9: A plate-and-frame membrane

34 Figure 4.10: Example of a tubular membrane system (by courtesy of Koch Membrane continued Systems) Tubular system (Fig. 4.10) Membrane manufactured in form of a smaller dia. tube (1-2cm) supported by a rigid outer shell Mainly used in MF and UF Fouling can be reduced by use of appropriate flow management Low surface area/volume ratio makes costs high

35 continued Capillary system (Fig. 4.11) Separating surface on inside of membrane capillary Filtrates permeate through membrane and leaves system from the outer shell Mainly used in UF High surface area/volume ratio keeps costs down Mechanically weak, low burst pressure Figure 4.11: Conventional capillary module (by courtesy of Pall Corporation)

36 continued Hollow fibre system (Fig. 4.12) Fibres have small dia. (~100nm) Outer skin is membrane Fouling can be severe. Use restricted to relatively clean solutions High surface area/volume ratio keeps costs low Figure 4.12: Example of a hollow-fiber membrane (by courtesy of Dupont)

37 continued Spiral wound module (Fig. 4.13) Membrane sandwiched between porous support and spacer screen and wound in a spiral-type configuration High surface area/volume ratio and relatively low investment costs Figure 4.13: A spiral-wound module (by courtesy of Koch Membrane Systems)

38 continued Dynamic or rotating membranes (Fig. 4.14) A more recent development of two co-axial cylinders of which the inner rotates within a fixed outer membrane Both cylinder walls can be used for filtration Inner cylinder rotates at rpm to create a hydrodynamic regime known as Taylor vortices in the annulus. These vortices enable higher flux rates and better transmission as a result of improved local mixing

39 continued Figure 4.14: A rotary membrane unit (by courtesy of Pall corporation)

40 continued Figure 4.15 (continued)

41 Membrane materials Common membrane materials and their properties are listed in Table 4.3 Commercial MF membranes can be based on hydrophilic or hydrophobic polymers Recent advances include mineral or ceramic membranes composed of a porous calcinated carbon support with several superposed layers of metallic oxide, such as zirconia, to form a very thin microporous membrane UF membranes mainly made of polysulphone, cellulose nitrate or acetate, nitrocellulose or acrylic RO membranes mainly cellulosic in nature though polyether/polyamide and other materials have been used

42 Table 4.3: Common membrane materials (Costa, C.A. and Cabral, J.S., 1991) Material Application ph range Approximate max. Temperature ( 0 C) Cellulose acetate MF,UF,RO Mixed cellulose esters MF,UF,RO Polysulfonate MF,UF,RO Polyester MF,UF NA 150 Polyamide MF,UF,RO 2-12 NA Nylon MF NA NA PIFE MF Dynel UF Polymide UF NA NA Acryclic copolymer MF NA 88 Polypropylene MF Polycarbonate MF,UF NA NA Polybinylidene difluoride MF NA 145 Ceramic MF,UF

43 4.3.4 Fluid management Figure 4.16:Comparison of (a) dead-end filtration and (b) cross-flow filtration

44 Comparison between dead-end and cross-flow membrane filtrations Dead-end membrane filtration The fluid passes normal to and through the face of the membrane And the particles or molecules retained by the membrane are held at its surface Requires only the energy necessary to force the fluid through the filter Cross-flow filtration the fluid to be filtered is pumped across the membrane parallel to its surface only the small fraction of fluid actually passing through the membrane flows normal to the filter by maintaining a high velocity across the membrane, the retained material is swept off the membrane surface preferred - when significant quantities of material will be retained by the membrane, when the retentate is soluble or when the solid retentate is compressible

45 continued the following equations describing dispersion along a concentration gradient in a flowing system the relevant dimensionless groups are: d Re HQ ; H v vd 4 Sc v D Sh kd D 1 where Sh = Sherwood number, Sc = Schmidt number Re = Reynolds number, D = diffusity (m 2 /s) d = hydraulic diameter (m), k = mass transfer coefficient (m/s) ν = kinematic viscosity (m 2 /s) and v = velocity (m/s)

46 continued H = constant, a function of the geometry of the conduit; it is π/4 for a circular conduit and 1 for a square conduit Turbulent flow Turbulent flow past the membrane (in the range 2500< Re<10,000) An equation variously attributed to Dittus-Boelter and Desalius is: 0.88 Sh 0.023Re Sc 0.33 E 4.1 Solving for k: k D d V E 4.2

47 continued Laminar flow flow regimes up to a Re no. about 2200, an equation modified from Leveque s heat-transfer formulation shows that for practical situations: d Sh 1.62 Re Sc L the mass transfer coefficient k = the rate constant for movement of solute along the concentration gradient. Solving for k: VD.62 k Ld E E 4.3 contin ued 47

48 4.4 Complication from fouling fouling is a major problem in all membrane operations it causes significant problems in measuring and interpreting pore size in both MF and UF membranes It has an effect on RO membranes as well, quite distinct from the effects in UF and MF fouling is an irreversible process; it cannot be rectified by changing processing conditions such as flow or pressure it can be reversed only by cleaning or replacing the membrane it is often an adsorption involving significant binding energy contin ued 48

49 4.4.1 Effects on pore dimension MF and UF membranes contain pores and for most membranes, they are not all of the same size fouling affects pores differently Belfort illustrated three cases affecting MF membranes A fourth case primarily affecting UF is added as shown in Figure 4.17 contin ued 49

50 continued Figure 4.17: Fouling effects on pore dimensions: Case A = adsorption; Case B = plugging smallest pores; Case C =gel/cake formation; Case D = plugging larger pores contin ued 50

51 continued Cases Case A Case B Case C Case D Details Adsorption causes all pores to become smaller, and may result in the smallest pores plugging In the case of a protein probe present in dilute solution, this fouling error would cause the test to understate the size of pores and Could truncate the distribution on the low pore-size end of the spectrum Show pore plugging. Any adsorption, means that particles may plug pores In example shown, smaller pores would be expected to suffer disproportionately Represents the deposition of a material that supersedes the porous structure of the membrane Fouling is reversible to the extent that the layer nearest the membrane is probably adsorbed onto it Throughout the layer, the binding may or may not be irreversible At the surface, quite a degree of dynamic reversibility remains One may assume that in all cases, the effect is to shift the effective pore size downwards Peculiar to membranes with small pores filtering particles much larger than pores

52 4.4.2 Effects on flux Fouling effects flux dramatically The pure-water flux through a virgin UF membrane is commonly 10-fold greater than the water flux after the membrane has been exposed to protein Flow will be laminar through a cylindrical pore because of its size

53 continued when reviewing the four cases of pore narrowing; Case A Narrowing of all pores and plugging of some of the smallest, will have a greater impact Because loss of some pore dimension Case B Case C Case D Which smaller pores are plugged and larger ones are unaffected will have least impact on flux Is a guess, as the porosity of a cake layer on the membrane can be anything Results in a dramatic loss of throughput, because that form of plugging takes out the most productive pores

54 4.4.3 Overall effect on retention continued 54 passage of material through a pore obviously depends on how much is flowing and what that pore will pass big pores pass large quantities but their retention is different from smaller pores as a membrane fouls, the retention characteristics worked out for the virgin membrane will change, often dramatically fouling processes that plug only the very smallest pores have little effect on retention fouling by almost any other mechanism raises retention; either it substitutes a cake layer on top of the membrane, or it narrows pores, or it selectively plugs larger ones

55 Improving fluxes Destruction of gel layer is only one way of enhancing flux, a further approach is to prevent fouling Method for improving flux fall into four categories: operating conditions change feed properties membrane selection slowing flux decline

56 continued Parameter Operating conditions Feed properties Membranerelated methods Slowing flux decline Details Increasing the mass transfer coefficient, k d, by using a higher velocity, smaller channel width or reducing viscosity Changing ph may reduce fouling Alter membrane surface charge to minimize blinding Use of corrugated membranes to enhance shear Reduce fouling load by pre-filtration Use of pulsed flow or electric fields Back flushing

57 Application of membrane separations Membrane technology Microfiltration Ultrafiltration Reverse osmosis Typical application Sterilization of drugs clarification and biological stabilization of beverages purification of antibiotics separation of mammalian cells from a liquid Preconcentration of milk before making cheese clarification of fruit juice recovery of vaccines and antibiotics from fermentation broth color removal from Kraft black liquor in paper-making Water purification small molecules

58 4.6.1 Reverse-Osmosis Membrane Processes continued 58 A. 1.Introduction useful for separation of different species, a membrane must allow passage of certain molecules and exclude or greatly restrict passage of others. In osmosis, a spontaneous transport of solvent occurs from a dilute solute or salt solution to a concentrated solute or salt solution across a semipermeable membrane which allows passage of the solvent but impedes passage of the salt solutes. In Fig, 4.18a, the solvent water normally flows through the semipermeable membrane to the salt solution. The levels of both liquids are the same as shown. The solvent flow - reduced by exerting a pressure on the salt-solution side and membrane, as shown in Fig. 4.18b, until at a certain pressure, called the osmotic pressure π of the salt solution, equilibrium is reached and the amount of the solvent passing in opposite directions is equal

59 continued continued 59 The chemical potentials of the solvent on both sides or the membrane are equal. The properties of the solution determine only the value of the osmotic pressure, not the membrane, provided that it is truly semipermeable. To reverse the flow of the water so that it flows from the salt solution to the fresh solvent, as in Fig. 4.18c, the pressure is increased above the osmotic pressure on the solution side. This phenomenon, called reverse osmosis is used in a number of processes. An important commercial use is in the desalination of seawater or brackish water to produce fresh water. Unlike distillation and freezing processes used to remove solvents, reverse osmosis can operate at ambient temperature without phase change.

60 continued Figure 4.18: Osmosis and reverse osmosis: (a) osmosis, (b) osmotic equilibrium (c) reverse osmosis contin ued 60

61 OSMOSIS Pure water flows from a dilute solution through a semipermeable membrane (water permeation only) to a higher concentrated solution Rise in volume to equilibrate the pressure (osmotic pressure) REVERSE OSMOSIS If pressure greater than the osmotic pressure is applied to the high concentration the direction of water flow through the membrane can be reversed. Osmotic pressure- P required to equalize the solvent activities if pure solvent is on one side of membrane

62 continued This process is quite useful for the processing of thermally and chemically unstable products. Applications include concentration of fruit juices and milk, recovery of protein and sugar from cheese whey, and concentration of enzymes. 2. Osmotic pressure of solutions. Experimental data show that the osmotic pressure π of a solution is proportional to the concentration of the solute and temperature T. Van t Hoff originally showed that the relationship is similar to that for pressure of an ideal gas n For example, for dilute water solutions, RT E 4.5 V m

63 continued where n = the number of kg mol of solute V m = the volume of pure solvent water in m 3 associated with n kg mol of solute, R = the gas law constant x 10-3 m 3.atm/kgmolK T = temperature in K If a solute exists as two or more ions in solution, n represents the total number of ions For more concentrated solutions. Eq. (4.5) is modified using the osmotic coefficient φ which is the ratio of the actual osmotic pressure π to the ideal π calculated from the equation. For very dilute solutions, φ has a value of unity and usually decreases as concentration increases in Table 4.4 some experimental values of π are given for NaCl solutions, sucrose solutions, and seawater solutions

64 Example 1: Calculation of Osmotic Pressure of Salt Solution Calculate the osmotic pressure of a solution containing 0.10 g mol NaCI/1000 g H 2 O at 25 0 C

65 Osmotic Pressure of Various Aqueous Solutions at 25 0 C

66 Types of Membranes for Reverse Osmosis One of the more important membranes for RO is the cellulose acetate membrane. The asymmetric membrane is made as a composite film in which a thin, dense layer about μm thick of extremely fine pores is supported upon a much thicker ( μ m) layer of microporous sponge with little resistance to permeation. The thin, dense layer has the ability to block the passage of quite small solute molecules. In desalination the membrane rejects the salt solute and allows the solvent water to pass through. Solutes which are most effectively excluded by the cellulose acetate membrane are the salts NaCl, NaBr, CaCl 2 and Na 2 SO 4 ; sucrose; and tetralkvl ammonium salts. main limitations of the cellulose acetate membrane can only be used in aqueous solutions and it must be used below about 60 0 C

67 continued Another important membrane useful for seawater, wastewater. nickel-plating rinse solutions, and other solutes is the synthetic aromatic polyamide membrane Permasep, made in the form of very fine, hollow fibers When used industrially this type of membrane withstands continued operation at ph values of 10 to 11 Many other anisotropic membranes have also been synthesized from synthetic polymers, some of which can be used in organic solvents, at higher temperatures, and at high or low ph

68 continued cellulose acetates polymamides Polyamides susceptible to biological attack and acidic or basic hydrolysis back to cellulose necessary to chlorinate the feed water and control the ph (4.5 to 7.5) Not susceptible to biological attack and resist hydrolysis in the ph range of 4 to 11 Attacked by chlorine

69 Flux Equations for Reverse Osmosis Basic models for membrane processes Two basic types of mass-transport mechanisms which can take place in membranes. In the first basic type, using tight membranes, which are capable of retaining solutes of about 10 Å in size or less, diffusion-type transport mainly occurs. Both the solute and the solvent migrate by molecular or Fickian diffusion in the polymer, driven by concentration gradients set up in the membrane by the applied pressure difference. In the second basic type, using loose, microporous membranes which retain particles larger than 10 Å, a sieve-type mechanism occurs, where the solvent moves through the micropores in essentially viscous flow and the solute molecules small enough to pass through the pores are carried by convection with the solvent.

70 2. Diffusion-type model continued 70 For the diffusion of the solvent through the membrane, as shown in Fig N P A P where N w = the solvent (water) flux in kg/sm 2 w P L w m A w P w = the solvent membrane permeability, kg solvent/s. m atm L m = the membrane thickness, m: A w = the solvent permeability constant, kg solvent/sm 2 atm ΔP = P 1 P 2, (hydrostatic pressure difference with P 1 pressure exerted on feed and P 2 on product solution), atm and Δπ = π 1 π 2 (osmotic pressure of feed solution - osmotic pressure of product solution), atm. P L w m w E 4.6 E 4.7

71 continued continued 71 Figure 4.19: Concentrations and fluxes in reverseosmosis process

72 continued continued 72 Note that subscript 1 is the feed or up stream side of the membrane and 2 the product or downstream side of the membrane. For the diffusion of the solute through the membrane, an approximation for the flux of the solute is N s DsK L m s c c A c A s 1 2 s 1 c2 DsK L m s E 4.8 E 4.9

73 continued continued 73 where N s = the solute (salt) flux in kg solute/sm 2 D s = the diffusivity of solute in membrane, m 2 /s K s = c m /c (distribution coefficient), conc. of solute in membrane/conc. of solute in solution; A s = is the solute permeability constant, m/s c 1 = the solute concentration in upstream or feed (concentrate) solution, kg solute/m 3 and c 2 = the solute concentration in downstream or product (permeate) solution, kg solute/m 3 The distribution coefficient K s is approximately constant over the membrane.

74 continued continued 74 Making a material balance at steady state for the solute, the solute diffusing through the membrane must equal the amount of solute leaving in the downstream or product (permeate) solution: N c w 2 Ns E 4.10 cw2 where c w2 = the conc. of solvent in stream 2 (permeate), kg solvent/m 3 If the stream 2 is dilute in solute, c w2 is approximately the density of the solvent. In reverse osmosis, the solute rejection R is defined as the ratio concentration difference across the membrane divided by the bulk conc. on the feed or concentrate side (fraction of solute remaining in the feed stream): E 4.11 R c 1 c2 c2 1 c c 1 1

75 continued continued 75 This can be related to the flux equations as follows, by first substituting Eqns. (4.6) and (4.8) into (4.10) to eliminate N w and N s in Eq. (4.10). Then, solving for c 2 /c 1 and substituting this result into Eq. (4.11), BP E 4.12 R 1 B B P D K s w s c P A A c w w2 s w2 E 4.13 where B is in atm -1

76 C. Application, Equipment and Models for RO continued Effects of Operating Variables Operating pressures in reverse osmosis range from about 1035 up to kpa (150 up to 1500 psi). Comparison of Eq. (4.6) for solvent flux with Eq. (4.8) for solute flux shows that the solvent flux N w depends only on the net pressure difference, while the solute flux N s depends only on the concentration difference. Hence, as the feed pressure is increased, solvent or water flow through the membrane increases and the solute flow remains approximately constant, giving lower solute concentration in the product solution.

77 continued continued 77 At a constant applied pressure, increasing the feed solute concentration increases the product solute concentration. This is caused by the increase in the feed osmotic pressure, since as more solvent is extracted from the feed solution (as water recovery increases), the solute concentration becomes higher and the water flux decreases. Also, the amount of solute present in the product solution increases because of the higher feed concentration. If a reverse-osmosis unit has a large membrane area (as in a commercial unit), and the path between the feed inlet and outlet is long, the outlet feed concentration can be considerably higher than the inlet feed c 1 Then the salt flux will be greater at the outlet feed as compared to the inlet.

78 Example: Prediction of Performance in a Reverse-Osmosis Unit continued 78 A reverse-osmosis membrane to be used at 25 C for a NaCl feed solution containing 2.5 g NaCl/L (2.5 kg NaCl/m 3, ρ = 999 kg/m 3 has a water permeability constant A w = 4.81 x 10-4 kg/sm 2 atm and a solute (NaCl) permeability constant A s = 4.42 x 10-7 m/s. Calculate the water flux and solute flux through the membrane using ΔP = atm and the solute rejection R. Also calculate c 2 of the product solution.

79 2. Concentration Polarization in RO Diffusion Model continued 79 In desalination, localized concentrations of solute build up at the point where the solvent leaves the solution and enters the membrane. The solute accumulates in a relatively stable boundary layer (Fig. 4.20) next to the membrane. Concentration polarization, β, defined as the ratio of the salt concentration at the membrane surface to the salt concentration in the bulk feed stream c 1 causes the water flux to decrease, since the osmotic pressure π 1 increases as the boundary layer concentration increases and the overall driving force (ΔP - π) decreases. Also, the solute flux increases, since the solute concentration increases at the boundary. Hence, often the ΔP must be increased to compensate, which results in higher power costs

80 continued continued 80 The effect of the concentration polarization β can be included approximately by modifying the value of Δπ in Eqs. (4.6) and (4.12) as follows: E assumed that the osmotic pressure π 1 is directly proportional to the concentration, which is approximately correct. Also Eqn. (4.8) can be modified as E 4.21 N s A s c 1 c 2 usual concentration polarization ratio is 1.2 to the concentration in the boundary layer is times c 1 in the bulk feed solution. This ratio is often difficult to predict.

81 continued continued 81 In desalination of seawater using values of about 1000 psia = ΔP, π 1, can be large. Increasing this, π 1 by a factor of can appreciably reduce the solvent flux. The boundary layer - reduced by increasing the turbulence by using higher feed- solution velocities. However, this extra flow results in a smaller ratio of product solution to feed. Also, screens can be put in the path to induce turbulence. Equations for predicting the mass-transfer coefficient to the surface and, hence, the concentration polarization, are given for specific geometries such as flow past plates, inside tubes, outside tubes, and so on

82 3. Types of Equipment for RO continued 82 plate-andframe Hollow-fiber In the plate-and-frame-type unit thin plastic support plates with thin grooves are covered on both sides with membranes as in a filter press. Pressurized feed solution flows between the closely spaced membranes. Solvent permeate through the membrane and flows in the grooves to an outlet. High packing density and containing fibers of cellulose acetates or aromatic polyamides Is used for the desalinization of brackish water containing less than 0.5 wt% dissolved salts if fouling is not serious In the hollow-fiber type, fibers of μm diameter with walls about 25 μm thick are arranged in a bundle similar to a heal exchanger

83 continued tubular spiralwound membranes in the term of tubes are inserted inside porous-tube casings which serve as a pressure vessel. These tubes are then arranged in bundles like a heat exchanger. In the spiral-wound type, a planar membrane is used and a flat, porous support material is sandwiched between the membranes. Then, the membranes, support, and a mesh feed-side spacer are wrapped in a spiral around a tube.