Membranes

CHAPTER 11MEMBRANES

J. S. Taylor, Ph.D., P.E.Alex Alexander Professor of Engineering

Civil and Environmental Engineering DepartmentUniversity of Central Florida

Orlando, Florida

Mark Wiesner, Ph.D.Professor of Engineering

Environmental Sciences and Engineering DepartmentRice UniversityHouston, Texas

Membranes represent an important new set of processes for drinking water treat-ment. Their tremendous potential results from universal treatment capabilities andcompetitive cost. There are very few drinking water contaminants that cannot beremoved economically by membrane processes, and several applications have beendescribed in textbooks on water treatment (Weber, 1972; Belfort, 1984; Nalco, 1988).However, membrane processes with the greatest immediate application to potablewater treatment are reverse osmosis (RO), nanofiltration (NF), electrodialysis(ED), ultrafiltration (UF), and microfiltration (MF).

Reverse osmosis is primarily used to remove salts from brackish water or seawa-ter, although RO is also capable of very high rejection of synthetic organic com-pounds (SOCs). Nanofiltration, the most recently developed membrane process, isused to soften fresh waters and remove disinfection by-product (DBP) precursors.Electrodialysis is used to demineralize brackish water and seawater and to softenfresh water. Ultrafiltration and microfiltration are used to remove turbidity,pathogens, and particles from fresh waters. In the broadest sense, a membranethecommon element of all these processescould be defined as any barrier to the flowof suspended, colloidal, or dissolved species in any solvent. The applicable sizeranges for membrane processes are shown in Figure 11.1.

Typically, the cost of membrane treatment increases as the size of the soluteremoved decreases. The ionic range in Figure 11.1 encompasses potable watersolutes such as sodium, chloride, total hardness, most total dissolved solids, andsmaller DBP precursors. The macromolecular range includes large and small col-loids, bacteria, viruses, and color. The fine particle range includes larger turbidity-producing particles, most total suspended solids, cysts, and larger bacteria. The

11.1

membrane processes normally used in the ionic range remove macromolecules andfine particles, but because of operational problems, they are not as cost effective asmembranes with larger pores.

Drinking water contaminants are presented as biological, inorganic, and organiccontaminants, as well as radionuclides, particulates, and other groupings. The abilityof membranes to remove these contaminants can be inferred from Table 11.1 andFigure 11.1, both of which show effective size ranges of contaminants that can bepartially or completely removed by each membrane process. If sieving or size exclu-sion is the mechanism of solute rejection, complete removal can be achieved by amembrane system free of defects. All membrane processes can reject contaminantssuch as turbidity or pathogens, but UF and MF are the most cost-effective processesfor control of large particles. Smaller contaminants are removed via size exclusion,charge repulsion, or diffusion mechanisms in membrane processes, leaving someresidual. Although such a residual may be below the detection level, it is present.

Contaminants larger than the maximum pore size of the membrane are com-pletely removed by sieving in a diffusion-controlled process. Contaminant rejectionby diffusion-controlled membrane processes increases as species charge and sizeincrease. Consequently, satisfactory removal of metals, total dissolved solids (TDS),biota, radionuclides, and disinfection by-product precursors can be attained. No com-mercially available membrane effectively removes dissolved and uncharged speciessuch as hydrogen sulfide (H2S) and small, uncharged organic contaminants. Otheraqueous contaminants should be treatable by membrane processes, although, onceagain, the cost of this treatment generally increases as the size of the removed con-taminant decreases. Many membrane manufacturers specify the molecular weight cut-off (MWC) values for membranes. The MWC represents a nominal molecular weightof a known species that would always be rejected in a fixed percentage, using a specificmembrane under specific test conditions. (However, MWC testing conditions varyamong manufacturers, which limits the use of MWC for membrane specification.)

Although many factors affect solute separation by these processes, a generalunderstanding of drinking water applications can be achieved by associating mini-

11.2 CHAPTER ELEVEN

FIGURE 11.1 Size ranges of membrane processes and contaminants.

mum size of solute rejection with membrane process and regulated contaminants(Taylor et al., 1989). One correct interpretation of Figure 11.1 is to assume that eachmembrane process has the capability of rejecting solutes larger than the size shownin the exclusion column. As shown in Table 11.1, regulated drinking water solutescan be simplified to the categories of pathogens, organic solutes, and inorganicsolutes. Pathogens can be subdivided into cysts, bacteria, and viruses. Organics canbe subdivided into DBPs and SOCs. Inorganic parameters are total dissolved solids,total hardness, and heavy metals, among others.

Electrodialysis and electrodialysis reversal (EDR) processes are capable ofremoving the smallest charged contaminant ions to 0.0001 m. Consequently, EDand EDR are limited to treatment of ionic contaminants and are ineffective forpathogen and organics removal in most cases. Contaminant rejection by RO and NFoccurs by both diffusion and sieving. They can remove all pathogens and manyorganic contaminants by sieving; by diffusion, they can achieve almost total removalof ionic contaminants. The RO and NF processes have the broadest span of treat-ment capabilities. Commercial UF membranes can achieve greater than 6-logremoval of all currently known pathogens from drinking water. Commercial MF

MEMBRANES 11.3

TABLE 11.1 Potable Water Contaminants Classified by Effective Membrane Size Range

Size range

Ionic Macromolecular/Colloidal Fine particle

BiologicalViruses XBacteria XHelemitis XAlgae XProtozoa XCysts XFungi X

InorganicsMetals XChlorides XFluoride XSulfate XNitrate XCyanide X

OrganicsPriority pollutants XSurfactants XNOM XTHM precursors XDPB precursors X

RadionuclidesParticulates

Turbidity XTSS X

OtherColor XTDS X

NOM, natural organic matter; THM, trihalomethane; TSS, total suspended solids; TDS, total dissolvedsolids.

membranes can achieve greater than 6-log removal of cysts. Consequently, theseprocesses effectively remove turbidity and microbiological contaminants, makingthem ideal for treating the majority of drinking water sources in the United States.

Both pressure-driven membranes (RO, NF, UF, and MF) and coagulation, sedi-mentation, and filtration (CSF) processes remove particles and pathogens from drink-ing water. A pressure-driven membrane process accomplishes this goal by presentinga static barrier that rejects any pathogen too large to pass through the membranespores. A CSF process removes pathogens through a dynamic process. Coagulationencourages formation of nuclei, which agglomerate during flocculation into large par-ticles that can be removed by sedimentation/filtration. Effective removal requires thatpathogens collide and remain with flocculated particles.Without effective coagulation,even large pathogens like cysts can pass through a CSF system.

Cysts, bacteria, and viruses can be grouped into ranges of 101 , 10.1 , and lessthan 0.1 . The nominal pore size of an MF membrane is less than those of cysts andbacteria, but this process alone cannot accomplish virus removal (Jacangelo et al.,1991; Taylor, Reiss, and Robert, 1999). Ultrafiltration has been shown to achievemore than 6-log removal of all pathogens. Reverse osmosis and nanofiltration havebeen shown to achieve 4-log pathogen removal (Taylor, Reiss, and Robert, 1999).Direct comparisons of conventional treatment (CSF) with membrane processes isdifficult due to lack of literature; however, many state regulatory requirements allow3-log removal of Giardia by CSF processes. No process is capable of absolutepathogen removal; however, the literature indicates a significant advantage formembrane processes over conventional CSF treatment for pathogen rejection.

Regulatory Environment for Membrane Processes

Existing regulations have been and will be modified to include more stringent con-trol of chemical and biological toxins. The Safe Drinking Water Act (SDWA)amendments that were modified in 1996 still require the United States Environ-mental Protection Agency (USEPA) to create new drinking water regulations. Theregulatory changes will continue to create a need for new drinking water technologyto meet these challenges.

The surface water treatment rule (SWTR) has been in effect since 1993 and wasdeveloped to reduce the potential for pathogenic contamination of drinking water.The SWTR requires that all surface waters and waters under the direct influence ofsurface waters achieve a minimum of a 3-log reduction of Giardia cysts and a 4-logreduction of enteric viruses. In addition, disinfection is required by the SWTR tomeet a CT (mg/L disinfectant disinfectant contact time) standard.The required CTis dependent on disinfectant used, pathogen, and water quality parameters. Theenhanced SWTR scheduled to be promulgated in 2000 will link the required logremoval of pathogens to the source water quality. The USEPA has stated that well-operated coagulation, sedimentation, and filtration systems are capable of 2.5-logremoval of Giardia and 3-log removal of viruses. However, pilot studies have shownthat some membrane processes can consistently achieve greater than 6- to 7-logpathogen removal (Jacangelo et al., 1992).The current proposal for the groundwaterdisinfection rule (GWDR), planned for finalization in 2000, requires most ground-water source utilities to maintain disinfectant residuals. Based on pore size alone,MF should be capable of removing bacteria and cysts, while UF, NF, and RO shouldremove all pathogenseven viruses. However, all of the membrane processes mustbe followed by disinfection to ensure distribution system water quality.

Contrary to the focus on chemical contamination during the 1980s, improvingmethods for detection of biological pathogens have shown that contamination by

11.4 CHAPTER ELEVEN

waterborne disease-causing agents may well be the more serious problem. Specificcontamination by Salmonella, Legionella, E. coli, and Cryptosporidium haverecently been documented in the United States, and indications are that many inci-dents of waterborne disease go unidentified and unreported. Consequently, the needto use the best treatment technology and ensure distribution system water qualityhas been emphasized in recent regulatory action. The Total Coliform Rule, in effectsince 1991, requires a maximum concentration of zero for total coliform, fecal coli-form, and E. coli. These species can be totally rejected by any pressure-driven mem-brane process, which provides the maximum protection by a treatment process. Inaddition, NF and RO can remove a significant amount of disinfectant demand,enhancing the stability of the residual in the distribution system. Membranes areamong the best options to meet existing and future drinking water regulationsregarding pathogens.

Inorganic compounds (IOCs), synthetic organic compounds (SOCs), and volatileorganic compounds (VOCs) are regulated by amendments to the SDWA. Fivephases of IOC, SOC, and VOC regulations are in place, and the final phases willeventually be enacted. The radionuclides rule, which covers radon gas, uranium,radium, and some alpha emitters, is expected to be finalized in 2000. Sulfate andarsenic rules are proposed, and the regulations are expected to be finalized by 2000and 2001, respectively.

The IOC, SOC, and VOC regulations involve hundreds of specific compounds,which have varying susceptibility to removal by membrane processes. Some gener-alizations can be made, though. No commercially available membrane process isbeing used for VOC removal at this time. Research has shown that membranes arefeasible for VOC removal, but this process has not been developed by suppliers.VOCs are uncharged, have low molecular weights (MWs), and pass through mem-branes with water. Like any dissolved gas, the VOC concentrations in the feed, per-meate, and concentrate streams are essentially identical in conventional membraneprocesses. However, gas separation membranes are used commercially and may beadapted to drinking water treatment in the future.

The EDR, MF, and UF processes by themselves generally are not capable of reject-ing SOC or IOC contaminants.The RO and NF processes can achieve significant SOCand IOC rejection because the exclusion limit of these membranes is so small thatmany SOCs cannot pass or are diffusion controlled (Duranceau,Taylor, and Mulford,1992). It would be incorrect to infer that all SOCs or IOCs can be rejected by RO orNF, but these processes have shown promise to remove such contaminants. The ROand NF processes rely primarily on both sieving and diffusion mechanisms to rejectSOCs and IOCs from drinking water. Rejection increases as the molecular weight andcharge of the contaminant increase.While EDR, RO, and NF remove arsenic and sul-fates, UF and MF do not; UF and MF could remove SOCs if powdered activated car-bon (PAC) were added prior to membrane treatment. EDR should be considered as aviable means of removing any charged solute from drinking water.

The lead and copper rule (LCR), finalized since 1991, is intended to control theconcentrations of these metals in drinking water. Corrosion in the distribution sys-tem emphasizes the importance of finished water chemistry. Corrosion is signifi-cantly affected by the sulfate, sodium, chloride, and bicarbonate ion concentrationsin the finished water.The UF and MF processes do not affect corrosion because theyremove no ions. The RO and NF processes reject sodium, sulfate, chloride, calcium,and bicarbonate ions, potentially producing a corrosive finished water in theabsence of buffering. However, if a base is added to the RO or NF permeate streamprior to aeration, the carbon dioxide will be converted to bicarbonate, and alkalinityrecovery will be accomplished. If CaO is used as the base, the finished water willcontain very little ion content except for calcium and bicarbonate. Generally, the

MEMBRANES 11.5

least corrosive water would be a stable water with from 1 to 3 meq/L of calcium andbicarbonate alkalinity, which is easily produced by alkalinity recovery, as discussedlater in the chapter.

The information collection rule (ICR) was put into effect in mid-1996. In additionto extensive water quality monitoring, it requires large utilities using surface waterwith total organic carbon (TOC) greater than 4 mg/L and groundwater with finishedwater greater than 2 mg/L to conduct bench or pilot studies using either granularactivated carbon (GAC) or membrane processes.The primary intent is to gain infor-mation on a national level on the ability of GAC and membrane processes toremove DBP precursors. The information collected under the ICR will be used toformulate future regulations such as the Enhanced Surface Water Treatment Rule(ESWTR) and the disinfection by-products rule (DBPR). The DBPR has twophases, with phase 1 finalized in 1998 and phase 2 to be finalized in 2002. The exist-ing DBP maximum contaminant level (MCL) of 100 g/L for THMs applies to util-ities serving more than 10,000 customers. Phase 1 of the DBPR will change the MCLto 80 g/L for THMs and 60 g/L for haloacetic acids (HAAs) and will apply to allutilities. If enacted, phase 2 of the DBPR will reduce the MCLs to 40 and 30 g/LTHMs and HAAs, respectively. Membrane processes can effectively control DBPformation by removing precursors in the form of natural organic matter, usuallymeasured as TOC. Not all TOC solutes are DBP precursors, but all organic DBPprecursors are TOC. By removing the precursors, a utility can maintain a free chlo-rine residual in the distribution system and reduce DBPs below the proposed phase2 MCLs.

Since EDR does not remove any uncharged species, and since the vast majorityof organic DBP precursors are uncharged, EDR is not effective for organic DBPcontrol. Pores of UF and MF membranes are too large to reject significant amountsof DBP precursors, but these processes can be used to control DBP and TOC if theyare preceded by coagulation. They replace conventional sedimentation and filtra-tion and are limited to the 50 to 75 percent TOC reductions achieved by coagulation(Taylor et al., 1986). The RO and NF processes can achieve more than 90 percentTOC removal. By rejecting disinfectant demand, these processes greatly reduce thedisinfectant dose, while achieving maximum distribution system integrity becausethe residual lasts longer. A final major advantage of membranes is the removal ofcontaminants without producing any oxidation by-products. All oxidants, includingchloramines, produce organic by-products that may be controlled by future regula-tions. In the not too distant future, TOC may be regulated, further encouraging useof membranes. A summary of membrane process applications and drinking waterregulations is shown in Table 11.2.

The growth of drinking water regulations for both chemical and biologicalspecies has created treatment applications that can be met by membrane processes.Membranes can be effectively used for total removal of pathogens, for highremovals of inorganic and organic contaminants, and for maintaining the highestpossible distribution system integrity. There are very few instances where mem-branes cannot be utilized to meet or exceed all drinking water regulations.

CLASSIFICATIONS AND CONFIGURATIONS OF MEMBRANE PROCESSES

Some membrane processes rely on pressure as the driving force to transport fluidacross the membranes.They can be classified by the types of materials they reject and

11.6 CHAPTER ELEVEN

the mechanisms by which rejection occurs.The progression of microfiltration to ultra-filtration to nanofiltration to reverse osmosis corresponds to a decreasing minimumsize of components rejected by membranes as well as increasing transmembranepressures required to transport fluid across the membranes and decreasing recover-ies. Although a continuum of mechanisms likely contributes to separation in thesepressure-driven processes, very clear differences in separation methods distinguishreverse osmosis from microfiltration.These mechanisms are discussed later in the text.

While pressure-driven processes like RO pass water through the membranes,electrodialysis involves the passage of the solute rather than the solvent through themembrane. As a consequence, both the mechanism of separation and the physicalcharacteristics of membranes in ED differ substantially from those in pressure-driven processes. The ED membranes are fundamentally porous sheets of ion-exchange resin with a relatively low permeability for water.

Membranes are classified by solute exclusion size, which is sometimes referred toas pore size. A reverse osmosis or hyperfiltration membrane rejects solutes as smallas 0.0001 m, which is in the ionic or molecular size range. A nanofiltration mem-brane rejects solutes as small as 0.001 m, which is also in the ionic and molecularsize range. Solute mass transport in these processes is diffusion controlled. Ultrafil-tration and microfiltration membranes have a minimum solute rejection size of 0.01and 0.10 m, respectively. These membranes reject colloidal particles, bacteria, andsuspended solids by size exclusion, and contaminant rejection is not diffusion con-trolled. Pressure drives the transport of water (the solvent) through these mem-branes. Electrodialysis relies on charge for solute separation and pulls ions throughED membranes, so it is unaffected by pore size.

Membranes can be classified by molecular weight cutoffs, solute and solvent per-meability, solute and solvent solubility in the membrane film, active film material,active film thickness, surface charge, and active film surface. The molecular weightcutoff is the degree of exclusion of a known solute, as determined for a given set oftest conditions in the laboratory. Typical known solutes used for determination ofmolecular weight cutoff are sodium chloride, magnesium sulfate, dextrose, and somedyes. Solute mass transport through a diffusion-controlled membrane is influenced

MEMBRANES 11.7

TABLE 11.2 Summary of Membrane Process Applications for Drinking Water Regulations

Membrane process

Rule EDR RO NF UF MF

SWTR/ESWTR no yes yes yes yesCR* no yes yes yes yesLCR yes yes yes no noIOC yes yes yes no noSOC no yes yes yes yes

(+PAC) (+PAC)Radionuclides yes yes yes no no

(no radon) (no radon) (no radon)DBPR no yes yes yes yes

(+ coagulation) (+ coagulation)GWDR no yes yes yes yes

(expected) (expected) (expected) (expected)Arsenic yes yes yes yes yes

(+ coagulation) (+ coagulation)Sulfates yes yes yes no no

* CR, Coliform Rule.

by solute type and aqueous environment, so attempts to characterize them benefitfrom the use of additional organic solutes such as aromatic and aliphatic compoundsof known molecular weight and structure.

Diffusion-controlled solute and solvent permeability are best described by masstransfer coefficients (MTC), although percent rejection is sometimes used todescribe solute mass transfer for a given environment. The solvent and solute masstransfer coefficients, like molecular weight cutoffs, are measured in the laboratorywith standardized test conditions and test cells. Continuous flow test cells that oper-ate at less than 1 percent recovery can be used to minimize concentration-polarization so that linearly determined mass transfer coefficients can be used tocharacterize membranes. Such test cells can also be used to determine the changes insolvent mass transfer coefficients over time for different films (membranes) todetermine a potential correlation between films and fouling.

Solute and solvent solubility in the membrane film are very important character-istics of diffusion-controlled membrane processes. Ideally the active film would haveno solubility for the contaminants or foulants and complete solubility for water.Thesolute mass transfer coefficient increases as the solubility of the contaminant in the film increases. Hence, the lower the contaminant solubility in the film, the lowerthe contaminant concentration in the permeate. If needed, the film material can bemodified to effect solubility by inclusion of functional groups, or a different filmmaterial can be substituted.

The thickness and chemical structure of the film are important membrane char-acteristics and are difficult to measure, although techniques do exist. Plasma etchinghas been used to measure film thickness. A plasma is introduced to initiate a chemi-cal reaction with the top layer of the film, producing gases. The rate of gas produc-tion during etching indicates surface morphology and thickness of a nonporous film.Electron spectroscopy and X-ray photoelectron spectrometry can be used to deter-mine the thickness of the top layer.

Membrane characterization also gives desirable information about the potentialof particular membranes to reject pesticides.This information could be used to mod-ify existing membranes or develop new membranes that would effectively rejectpesticides from drinking water sources.

Classification by Material

The development of a variety of membrane materials, both synthetic and modifiednatural polymers coupled with various manufactured forms, has played an integralpart in the development of industrial-scale membrane separation applications. Inany such process, several important membrane characteristics must be considered.Membrane selectivity, permeability, mechanical stability, chemical resistance, andthermal stability are among these critical factors, which are highly dependent uponthe type of material and the process control variables applied during manufacturing(Rautenbach and Albrecht, 1989).

Among the many raw materials used for membrane manufacturing, most basictypes involve various forms of modified natural cellulose acetate materials and avariety of synthetic materials. To name a few, these synthetic materials are primarilycomposed of polyamides, polysulfone, vinyl polymers, polyfuran, polybenzimida-zole, polycarbonate, polyolefins, and polyhydantoin. The diverse chemistries of thespecific polymers and the associated production kinetics yield the individualattributes that provide for the myriad of membrane selectivity and productivitycombinations (Rautenbach and Albrecht, 1989).

11.8 CHAPTER ELEVEN

Porous materials produced by precipitation from a homogeneous polymer solu-tion are termed phase inversion membranes. They incorporate both symmetrical(homogeneous) and asymmetrical structures. The basic production process consistsof five fundamental steps.A homogeneous polymer solution must first be produced.The polymer film is then cast, followed by partial evaporation of the solvent fromthe polymer film. Immersion of the polymer film in a precipitation solution thenallows the solvent to be exchanged for the precipitation agent. Imperfections in theprecipitated membrane film are restructured by treatment in a heated bath solution.Variations in environmental conditions for each of these steps can generate anassorted range of membrane structures that affect system performance. Typicalmembrane structural profiles can range from well-defined cavities in the shape offingers to pores arranged in a dense sponge structure (Figure 11.2). These configu-rations result from the membrane structure both at the membrane surface andwithin the support structure itself (Rautenbach and Albrecht, 1989).

Both symmetric and asymmetric membranes can be produced by the phaseinversion process. The difference between these two membrane classifications is theenvironmental conditions in which the membranes are produced and their resultingstructural profiles. In the production of symmetrical membranes, homogeneous con-ditions for material formation throughout the membrane matrix lead to a uniformpolymer structure. Conversely, structural properties vary throughout asymmetricmembranes. Production of an asymmetric membrane forms a dense surface layer ofsubmicron thickness that gives the membrane its selectivity properties. This activelayer is in turn supported by a porous support structure. The combination yieldsmembrane materials that are both selective and mechanically stable, with enhancedproductivity. Given the reduction in thickness of the active layer, hydraulic lossesacross the membrane are significantly less than those associated with symmetricmembranes of comparable thickness. Consequently, development of the asymmetricmembrane structure is an additional component integral to the commercial successof both RO and UF. An actual scanning electron microscope (SEM) image of oneasymmetric membrane is provided in Figure 11.3.

Another classification of phase inversion membranes is the composite mem-brane. In such a membrane, the materials composing the active surface are different

MEMBRANES 11.9

FIGURE 11.2 SEM photograph of two common membrane structures: (a) finger structure; (b)sponge structure. (Source: R. Rautenbach and R. Albrecht, Membrane Processes. Copyright 1989John Wiley & Sons. Reprinted by permission of John Wiley & Sons Limited.)

(a) (b)

from those of the support material. Thesemembranes are produced by lamination ofthe active surface layer onto the supportlayer (e.g., polysulphone). This class ofmembranes is generally regarded as animprovement in membrane material designin that a specific active surface layer can bematched with a support layer of optimumporosity. This combination enhances mem-brane productivity while retaining thedesired rejection properties offered by thedense active surface layer. Figure 11.4shows the characteristic layers in a compos-ite membrane. Interestingly, the supportlayer itself is an asymmetric membrane.

The active layer or membrane film is apolymer or combination of polymers form-ing a composite layer of varying thin filmsor a single thin-film layer. These polymersare generally in the form of straight chaincompounds such as cellulose acetate or aro-matic compounds such as a polyamide orpolyimide. Several different interactionsoccur between the polymers that form theactive layer of the membrane and, conse-quently, between the membrane and solutesthat pass through it. The three types of sec-ondary forces are dipole forces, dispersion

forces, and hydrogen bonding forces. Covalent and ionic forces are primary forces,with stronger effects than those of the secondary forces in the active membrane film. Average values of primary and secondary forces in membrane polymers are 400 kJ/mole for covalent and ionic forces, 40 kJ/mole for hydrogen bonding forces,20 kJ/mole for dipole forces, and 2 kJ/mole for dispersion forces. These membraneforces can interact with corresponding forces associated with solutes, possibly pro-moted by functional groups on pesticides.

Hyperfiltration (reverse osmosis at 800 to 1200 psi), reverse osmosis, and nanofil-tration membrane films have active layers of cellulose compounds, aliphatic or aro-matic polyamides, and thin-film composites. Cellulose triacetate is used as the activefilm for many desalination applications. Cellulose derivatives have good propertiesfor membranes, since their crystalline and hydrophilic properties enhance durabilityand their capacity to transport water. Cellulose membranes are subject to chemicaldegradation by hydrolysis and biological degradation by oxidation. They must beoperated at ambient temperatures from pH 4.0 to 6.5 with a biocide to avoid degra-dation.

Polyamide membranes are also very effective films. Aromatic polyamides aregenerally preferred over aliphatic polyamides because of their mechanical, thermal,chemical, and hydrolytic stability and their permaselective properties. The aliphaticpolyamides are porous and therefore not permaselective.They may be used for siev-ing applications such as ultrafiltration and microfiltration processes.

The development of the cross-linked fully aromatic polyamide thin-film compos-ite membrane in the late 1970s represented a major advance in membrane technol-ogy. Thin-film composites provided very thin active films that required much less

11.10 CHAPTER ELEVEN

FIGURE 11.3 Polyhydantoin asymmetricmembrane. (Source: R. Rautenbach and R.Albrecht, Membrane Processes. Copyright 1989 John Wiley & Sons. Reprinted by per-mission of John Wiley & Sons Limited.)

energy to induce fluid passage than previous materials, making them more econom-ical to use on a large scale. As previously mentioned, thin-film composites layerasymmetric films to form membranes with several different characteristics. Bothhydrophilic and hydrophobic films are laid in a composite film by cross-linking dif-ferent polymers. The thickness of the nonporous layer is typically less than 1 m.Cross-linking to the porous film provides needed support for the nonporous film.Removal of macromolecules and ionic species is achieved by a nonporous film in apressure-driven membrane process.

Classification by Geometry

Reverse osmosis and nanofiltration membranes are made from different materialsand in different configurations. Both the material and configuration of such a mem-brane affect its mass transport or performance. As the effects of materials and con-figurations on solute rejection by membranes is largely unknown, the followingparagraphs briefly discuss membrane materials and configurations.

RO/NF Configuration. The RO and NF membranes for drinking water treatmenthave either spiral wound (SW) or hollow fine fiber (HFF) configurations. The SWconfiguration is the most common for production of drinking water. The HFF con-figuration is used extensively for desalination of seawater in the Middle East. Thegeometry of an SW membrane is subject to fewer dead areas than that of an HFFmembrane, it can be cleaned more thoroughly, and it is less subject to fouling. Theratio of surface area to volume is higher for an HFF element than for an SW ele-ment. However, dominant fouling mechanisms in seawater may differ from those inbrackish waters.

An HFF membrane element consists of a tube that contains a bundle of HFFs, asshown in Figure 11.5. A group of HFFs folded in a U form are sealed into a tube tocreate a bundle.A 4-in DuPont B-10 membrane, for example, contains 650,000 HFF,

MEMBRANES 11.11

FIGURE 11.4 Composite membrane structure (PEC 1000 Toray). (Source: R. Rauten-bach and R. Albrecht, Membrane Processes. Copyright 1989 John Wiley & Sons.Reprinted by permission of John Wiley & Sons Limited.)

each approximately 4 ft (3.28 m) long with 1500 ft2 (139 m2) of surface area. Theinside and outside diameters of the fibers are 1.33E-4 ft (4.1E-5 m) and 2.94E-4 ft(11.0 E-5m), respectively. As the feed stream passes along the outside surface of thehollow fine fibers, the permeate or purified stream passes from the outside to theinside. The feed stream enters the hollow fine fiber element from a feed tube in the center of the element. The feed stream flows radially from the center feed tubeto the brine collection channel at the outside of the element.The highest feed streamvelocity occurs next to the feed stream tube, and the lowest velocity occurs at thebrine collection tube. The recovery from a hollow fine fiber element ranges from 10to 50 percent and is typically higher than that from an SW element. The radial feedstream velocity along the outside surface of the HFF varies from approximately 0.01to 0.001 ft/s (0.003 to 0.0003 m/s), which gives a Reynolds number ranging from 100to 500 for transport through the membrane.There are other sizes of hollow fine fiberelements but the feed stream velocities, recoveries, and Reynolds numbers are simi-lar to those of the described B-10 element.The feed flow is in the laminar region andis most likely to produce chemical or colloidal fouling near the brine collector.Also,fouling from the collection of filtered particles may occur near the feed tube. Thephysical configuration of the hollow fine fiber element is prone to fouling by partic-ulates removed by sieving, and the bundle of HFFs is difficult to clean.

Spiral wound elements are manufactured using flat-sheet membranes, asopposed to bundles of fibers, as shown in Figure 11.6.A typical SW element consistsof envelopes attached to a center tube that collects the permeate stream. Designs ofSW elements differ among manufacturers; however, the following description isapplicable to Filmtec, Desal, Hydranautics, and Fluid Systems SW membranes.

An envelope is formed by folding one flat sheet over a permeate stream spacer.The sheet itself consists of at least two layers, a nonporous active membrane film and


FIGURE 11.5 Diagram of a hollow fine fiber reverse osmosis membrane. (Source: Courtesy ofDuPont Permasep.)

a porous membrane support.The active layer is on the outside of the fold.The enve-lope is glued along three open sides and near the fold, completely enclosing the per-meate spacer. The glue line on the fold end is a short distance away from the fold,because the fold end is attached to the center collection tube. The glue line at thefold end stops the flow of the feed stream and allows the remaining pressure in thepermeate stream to drive it through the membrane into the center collection tube.Afeed stream spacer is attached to each envelope prior to establishing the fold-endglue line. Several envelopes and feed stream spacers are attached to the center col-lection tube and wrapped in a spiral around it. An epoxy shell or tape wraps areapplied around the envelopes, completing the SW element.

The feed stream enters the end of the SW element in the channel created by thefeed stream spacer. The feed stream can flow either in a path parallel to the centercollection tube or through the active membrane film and membrane supports into achannel created by the permeate stream spacers.The permeate stream follows a spi-ral path into the center collection tube and is taken away as product water in a drink-ing water application. As with hollow fine fiber membranes, the feed streambecomes progressively more concentrated as it passes to a succeeding element. A 4-in. Filmtec NF70 membrane contains four envelopes with approximately 90 ft2

(8.33 m2) of surface area in a sheet that measures 3 ft (0.91 m) 3.75 ft (1.14 m).Thetotal element is 3.33 ft (1.01 m) long, but the feed stream path along the active mem-brane film is approximately 3 ft (0.91 m).

The recovery in an SW element varies from approximately 5 to 20 percent. Themanufacturer-specified maximum feed and concentrate stream flows in a 4-in(1.57-cm) element are approximately 16 gpm (4.2E-3 m3/min) and 3 gpm (7.9E-4m3/min). Neglecting the effect of the feed stream spacer, the Reynolds number typi-cally ranges from 100 to 1000. The feed stream spacer creates additional turbulenceand increases the Reynolds number. The physical configuration of the SW elementproduces a more turbulent feed stream than that in an HFF element and leaves themembrane more easily accessible to cleaning agents. The highest and lowest feedstream velocities occur at the entrance and exits of the element, respectively. Thefeed flow is in the laminar region and is most likely to produce chemical or colloidalfouling in the last elements in series. Fouling from particle deposition occurs mainlyin the first elements in series.

MF-UF Configuration. The flow in microfiltration or ultrafiltration processes canrun from inside out or outside in, as shown in Figure 11.7. These processes typically

MEMBRANES 11.13

FIGURE 11.6 Diagram of a spiral wound reverse osmosis membrane. (Source: Courtesy ofDuPont Permasep.)

use hollow fibers larger in diameter than the HFFs previously described. Theinside and outside diameters of the HFF are 1.33E-4 ft (4.1E-5 m) and 2.94E-4 ft(11.0 E-5m), whereas the inner and outer diameters of an HF fiber are 3.08E-4 ft (1E-3M) and 6.16E-3 ft (2E-3), respectively. Some UF or MF membranes have beenproduced in SW configurations for industrial applications. In a conventional UF orMF process, the driving force to produce filtrate can work in two ways; positive pres-sure moves fluid through the fibers, usually at a rating lower than 35 psi, and negativepressure moves fluid through fibers under vacuum pressure. Combining the two dif-ferent flow regimes and the two driving forces allows four different configurations:

Inside-out flow with positive pressureOutside-in flow with positive pressureOutside-in flow with negative pressureInside-out flow with negative pressure

Both inside-out and outside-in flow patterns can be further characterized aseither dead-end or cross-flow operations. In a dead-end operation, the entire feedflow passes through the membrane. In one pass, the dead-end mode of operation isanalogous to conventional coarse filtration in that the retained particles accumulateand form a type of cake layer at the membrane surface. In a cross-flow operation,only a portion of the flow passes through the membranes, and only a portion of theretained solutes accumulate at the membrane surface. The remaining flow (reten-tate) is recycled on the feed side. The cross-flow regime also incorporates a tangen-tial flow that shears the cake and minimizes the accumulation of solids on themembrane surface. In all cases, a frequent backwash (every 15 min to 1 h or morefrequently) removes the cake formed on the membrane surface.

Classification by Driving Force

Membrane processes can be classified based on the driving forces that induce trans-port of materials across the membranes. Examples of driving forces and corre-sponding membrane processes are listed in Table 11.3.


FIGURE 11.7 Individual fiber flow pattern for (a) inside-out and (b) outside-in flow.

(b)

(a)

Although interest in industrial applications for pervaporation is growing,industrial-scale applications of membrane processes for environmental quality con-trol have so far been dominated by the pressure-driven processes such as RO and byelectrodialysis and electrodialysis reversal, which employ electrical potential as thedriving force.

Electrodialysis

Electrodialysis is a membrane process driven by electric potential for removingcharged species (ions) from an aqueous stream. Electrodialysis is an electrochemicalseparation process in which ions are transferred through ion exchange membranesby means of a direct current (DC) voltage. In a simple electrolytic cell, negativelycharged ions (anions) are drawn toward the positively charged electrode, or anode,and positively charged ions (cations) are drawn toward the negatively charged elec-trode, or cathode.

The ED process differs fundamentally from the pressure-driven membrane pro-cesses by transport mechanisms and effect. An electrochemical separation processremoves ions from a process stream, whereas a pressure-driven separation processremoves water from the process stream. Both membrane processes can remove ions,but electrochemical separation processes cannot remove pathogens, as pressure-driven processes can, giving them no role in disinfection. Electrochemical separationprocesses are often less costly than NF/RO, however, because they achieve higherrecoveries through lower salt rejection and mass transport advantages. A basic dia-gram of a batch electrodialysis process is shown in Figure 11.8.

ED Cell. The basic ED cell consists of alternating anion-permeable and cation-permeable membranes, which provide a basis for separation of ions under DC volt-age. Redox reactions occur during ED. Water and chlorine are oxidized at thecathode, and water is reduced at the anode:

H2O 4H+ + 4e + O2 2Cl Cl2 + 2e

H2O + 2e 2OH + H2 These by-products of the ED cell are removed as electrode waste products andtreated by aeration and neutralization (reduction), if necessary.

A simplified diagram of a complete cell for NaCl removal is shown in Figure 11.9.Sodium ions pass through the cation-transfer membrane, and chloride ions pass

MEMBRANES 11.15

TABLE 11.3 Categorization of Membrane Processes by Driving Force

Driving force Examples of membrane processes

Temperature gradient ThermoosmosisConcentration gradient Dialysis, pervaporation, osmosisPressure gradient RO, NF, UF, MF, piezodialysisElectrical potential Electrodialysis, electroosmosis

through the anion-transfer membrane. Thesodium and chloride ions are trapped in the brine channel by the alternating ion-exchange membranes, as only cations canpass the cation-permeable membranes andonly anions can pass the anion-permeablemembranes. The alternating ion-exchangemembranes produce a demineralizedstream and a concentrate stream, as shownin Figure 11.9. Water flows across thesemembranes, not through them, as it does inpressure-driven processes.

As shown in Figure 11.10, an ion-exchange membrane has a polymeric support structure with fixed sites and water-filled passages that reject common ions andpass counterions through the membrane. InFigure 11.10, a fixed, negatively charged,

sulfonated functional group and a fixed, positively charged, tertiary amine are shownin the anionic and cationic membranes, respectively.These membranes are (1) imper-meable to water, (2) electrically conductive, and (3) ion selective. The anion mem-brane is composed of a cast anion exchange resin with a fixed negative charge insheet form.The fixed negative charge assists cations in passing and keeps anions frompassing through the anion membrane. The cation membrane has a fixed positivecharge and utilizes the same mechanism to repel cations and pass anions.

A spacer is placed between the anion-exchange and cation-exchange membranesto form a basic cell pair, as shown in Figure 11.11. The cell pair consists of an anion-exchange membrane, a concentrating spacer, a cation-exchange membrane, and ademineralizing spacer.The spacers are assembled with cross straps to promote turbu-lence and reduce polarization at the membrane surfaces.Several hundred cell pairs aregrouped into a common arrangement known as a membrane stack or module, as shownin Figure 11.12. These streams either pass to succeeding cells for additional treatmentor are discharged from the ED cell as concentrate waste and demineralized product.


FIGURE 11.8 Diagram of an electrodialy-sis batch process under applied DC voltage.(Courtesy of Ionics, Inc.)

FIGURE 11.9 Simplified diagram of an electrodialytic cell. (Courtesy of Ionics, Inc.)

The concentrate waste stream does not contain the redox products in the electrodewaste streams, although these streams may be combined in some applications.

ED Processes. Electrodialysis processes must work within polarization and scalinglimitations like those in pressure-driven, diffusion-controlled membrane processes,because of ion concentrations at the membrane surfaces. However, polarizationproblems arise in ED processes due to the lack of ions at the surface. Ions arrive ata membrane surface by electrical transport, diffusion, and convection, and they aretransported through the membrane electrically. As ions are transported through themembrane, the demineralized streammembrane interface becomes depleted ofions, causing an exponential increase in electrical resistance and current density.Thisprocess continues until polarization occurs, disassociating water into protons andhydroxide ions. This point is identified as the limiting current density. These prob-

MEMBRANES 11.17

FIGURE 11.10 Ion exchange cast membrane sheets show-ing a fixed charge and mechanisms of mass transport in theelectrodialysis process. (Courtesy of Ionics, Inc.)

FIGURE 11.11 Basic electrodialysis cell pair. (Courtesy of Ionics, Inc.)

lems have been reduced in ED applications by reversing module polarity every 15 to20 min during plant applications. This process, known as electrodialysis reversal,has the advantages of (1) reducing scaling potential, (2) breaking up fresh scale,(3) reducing microbiological growth on membrane surfaces, (4) reducing membranecleaning frequency, and (5) cleaning electrodes with acid formed during anodicoperation.The EDR processes reportedly achieve slightly higher recoveries than NFor RO processes, which can become an economic advantage when removal of un-ionized solutes such as disinfection by-product formation potential (DBPFP) orpathogens is not an issue.

The rate of ion removal in an electrochemical separation process is controlled bythe feed water characteristics, design parameters, and equipment selection. Thewater quality and temperature of the feed water determine the system recovery andrate of mass transfer. Ion removal increases as temperature increases and as chargeincreases. System recovery is typically limited by precipitation of the least solublesalt, as in RO or NF systems. Design parameters include current, voltage, currentefficiency, polarization, and finished water quality. As current or current densityincreases, the removal of ions also increases. Voltage is a function of the current,temperature, and ionic water quality. Current efficiency is determined by the effi-ciency of salt transfer. A 100 percent efficient process would transfer 1-gram equiv-alent of salt for every 26.8 ampere-hours. Polarization is controlled by limiting theallowable current density to 70 percent of the limiting current density. Finishedwater quality standards are set by design, within limits of back-diffusion.A high con-centration gradient between the demineralized and concentrate streams leads to dif-fusion of ions from the concentrate to the demineralized stream. This effect, termedleakage, is controlled by limiting the concentration ratio of the concentrate streamto the demineralized stream to less than 150.

An example of a three-stage EDR process is shown in Figure 11.13. The systemrecovery from this process is 90 percent, and the overall TDS rejection from the feedstream is 75 percent. Contrary to an RO or an NF process, the product water is takenonly from the final stage, as ions are continually removed from the product streamuntil the desired TDS concentration is obtained. The feed stream to the EDR pro-cess is pretreated with acid and/or an inhibitor, as is an RO or an NF feed stream, toprevent scaling at the desired recovery. Recycling of the concentrate stream to thefeed stream is not shown in Figure 11.13 but is often used in an EDR process to (1) reduce equipment requirements for a given recovery, (2) reduce concentrate


FIGURE 11.12 ED or EDR module. (Courtesyof Ionics, Inc.)

stream discharge, (3) reduce pretreatment, and (4) increase the transfer of ions tothe concentrate stream.

MEMBRANE PROPERTIES AND REJECTIONCHARACTERISTICS

Characterization of membrane properties is desirable because of the potential ofrelating these characteristics to solute rejection and membrane fouling studies. Thisinformation could be used to modify existing membranes or develop new mem-branes that would effectively reject inorganic and organic solutes from drinkingwater sources without fouling the membranes.

Fundamental research for mass transfer, membrane fouling, and solute-solventinteractions has been conducted or is in progress using several different techniques.Currently, feasible techniques are capable of measuring membrane surface charge,pore size, thickness, roughness, surface energy, and surface atomic composition.These techniques are presented in Table 11.4. These seven have actually been con-ducted in membrane research; others are in the R&D stage.

Dissolved Solute-Membrane Interactions

Dissolved inorganic and organic solutes markedly influence electrokinetic proper-ties of RO and NF membranes through various solute-membrane interactions.Among such interactions are adsorption of inorganic and organic solutes on themembrane surface and/or within the membrane pores. These solute-membraneinteractions have a significant impact on membrane rejection and fouling behavior.In the following text, the effect of solution composition (i.e., dissolved solutes) onmembrane rejection and fouling is documented based on recent publications.

Influence of Dissolved Solutes on Electrokinetic Properties of Membranes

The effect of dissolved solutes on electrokinetic properties of RO and NF mem-branes has been investigated by the streaming potential technique, which estimates

MEMBRANES 11.19

FIGURE 11.13 Four-line, three-stage EDR process. (Courtesy of Ionics, Inc.)

charge on membrane surface and in membrane pores (AWWA committee report,1998). Streaming potential measurements by Childress and Elimelech (1996)demonstrated that typical commercial RO and NF membranes are amphoteric, andthe isoelectric point ranges from pH 3 to 5. These authors also reported that, abovethe isoelectric point, a membrane becomes more negatively charged with increasingpH. This pH dependence is attributed to deprotonation of membrane surface func-tional groups originated from manufacturing processes.

Membrane charge is also greatly influenced by divalent cations. Hong and Elim-elech (1997) showed that membrane surface charge becomes less negative withincreasing divalent cation concentration. The decrease in the negative charge of themembrane was attributed to charge neutralization and effective screening of themembrane surface charge by divalent cations. Specific adsorption of divalent cationsto membrane surface functional groups may also, in part, have been responsible forthe decrease in the negative charge of the membrane.

Dissolved organic solutes such as NOM readily adsorb to the membrane surfaceand/or pores, affecting the membrane charge. It has been observed that the mem-brane surface becomes more negatively charged in the presence of humic acids(Childress and Elimelech, 1996; Hong and Elimelech, 1997).The increase in the neg-ative charge is ascribed to adsorption of the humic acids to the membrane surface.The adsorbed humic substances mask inherent membrane charge and dominate thesurface charge of the membrane.

Impacts on Membrane Rejection

Charge repulsion is an important rejection mechanism of RO and NF membranes.Thus, changes in electrokinetic properties of the membrane due to solute-membraneinteractions have a significant influence on membrane rejection characteris-tics (Braghetta, 1995). Hong and Elimelech (1997) observed a decline in organic


TABLE 11.4 Techniques to Characterize Membrane Surfaces

Techniques Application on membrane research References

Streaming potential Charge on membrane surface to Elimelech, Chen,determine electrostatic interactions. and Waypa, 1994

Contact angle Surface energy to distinguish hydrophilic Oldani and and hydrophobic membranes Schock, 1989

Attenuated total reflectance-Fourier Kinetics study on membrane-solute- Ridgway and transform infrared spectroscopy solvent interface Flemming, 1996(ATR-FTIR)

Secondary ion mass spectrometry Chemical analysis for sorption and Spevack and (SIMS) fouling for clean and fouled membrane Deslandes, 1996

X-ray photoelectron spectroscopy Chemical analysis for sorption and Jucker and Clark,(XPS) fouling for clean and fouled membrane 1994

Scanning probe microscopy Topological information to characterize Fritsche, et al., 1992roughness and pore size for clean and fouled membrane

Scanning electron microscopy (SEM) High-resolution image to characterize Fritsche, et al., 1992roughness and pore size for clean and fouled membrane

removal by NF membranes with decreasing pH. This observation can be explainedby the reduced electrostatic repulsion between organic matter and membrane sur-faces due to the lower membrane surface charge at pH less than 4.

Impacts on Membrane Fouling. The degree of membrane fouling is determinedby interplay between several chemical and physical interactions. Electrostatic repul-sion, one of the critical interactions, is affected by solution composition (Song andElimelech, 1995; Zhu and Elimelech, 1997). A recent NF study by Hong and Eli-melech (1997) reported that NOM fouling increases with increasing electrolyte con-centration and decreasing solution pH. In particular, at fixed solution ionic strengthand pH, the presence of divalent cations markedly increases NOM fouling. Divalentcations substantially reduce the electrostatic repulsion between NOM and the mem-brane surface, resulting in a substantial increase in NOM deposition on the mem-brane. Jucker and Clark (1994) also recognized the effect of divalent cations onNOM adsorption to membrane surfaces.

Organic Solute Removal

The removal of disinfection by-product precursors or nonpurgeable dissolvedorganic carbon (NPDOC) by RO or NF has been studied extensively (Taylor et al.,1986; Taylor, Thompson, and Carswell, 1987; 1989a,b; Jones and Taylor, 1992).Nanofiltration membranes have been shown to control trihalomethane formationpotential (THMFP) in highly organic (>10 mg/L NPDOC) potable water sources(Taylor et al., 1986). These efforts have often been necessitated by inadequate effi-ciency of DBP removal using conventional coagulation and softening treatment pro-cesses.

An early investigation using diffusion-controlled membrane processes hadshown that membrane material would achieve the same solute rejection (McCartyand Aieta, 1983). In addition to membrane chemistry, characterization of raw waterorganic fractions was found to be an important consideration for appropriate mem-brane selection (Fouroozi, 1980; Conlon and Click, 1984; Taylor, 1989a,b; Tan andAmy, 1991). In research conducted by Jones and Taylor (1992), over 90 percent ofthe NPDOC was removed for both surface water and groundwater supplies bymembranes for which a manufacturer reported an MWC of 300 to 500 Daltons. TheTHMs and HAAs in the permeate averaged 15 and 4 g/L, respectively, and repre-sented more than a 90 percent DBPFP reduction. However, lower MWC mem-branes removed very little additional DBPFP.

Effective DBPFP removal has also been demonstrated for highly organic potablewater sources where limited removal of inorganic contaminants was desired.Research published by Taylor (1989a,b) and Spangenburg et al. (1997) have shownhigh DBP removal capability while simultaneously meeting treatment objectives forhardness or alkalinity concentrations in the treated permeate. It should also benoted that energy requirements for membranes offering comparable DBPFPremoval efficiency have been shown to vary as much as 50 percent. This has beendemonstrated in single-stage membrane pilot systems operated in parallel using dif-ferent film chemistries and membrane manufacturers (Tan and Amy, 1991).Research attention has also been focused upon the rejection of specific THMspecies using membranes. The relative percentage of brominated THMs increased in permeates from membrane processes with increasing MWC (Laine, Clark, andMalleviale, 1990). While NF was found to control brominated DBPs, advanced pre-treatment was necessary to sustain production when using the bromide spiked sur-

MEMBRANES 11.21

face water source. Many NF membranes do not remove bromides effectively; hence,higher ratios of brominated DBPs are formed as the Br:NOM ratio increases in thepermeate.

High DBPFP reduction has been demonstrated for groundwaters and surfacewaters alike. However, due to increased fouling potential, surface water is generallymore difficult to treat by membrane processes than highly organic groundwater.Consequently, advanced pretreatment is frequently required to counter significantmembrane production losses in these applications. Long-term investigation ofTHMFP control at the Flagler Beach, Florida, water treatment plant (a groundwa-ter site) and at the Punta Gorda, Florida, water treatment plant (a surface water site)provided for comparison of groundwater and surface water membrane treatment.Although consistent control of permeate THMFP was achieved, severe water fluxloss was experienced in the system treating surface water. Membrane cleanings wereconducted on 20 occasions in an attempt to sustain a water flux of 10 gsfd.The oper-ating system at the groundwater site required prefiltration and acidification in orderto sustain a flux of over 15 gsfd with only a semiannual cleaning frequency (Tayloret al., 1989a). In research reported by European investigators, NOM adsorption ontoa membrane surface has been verified by XPS analysis (Heimstra and Nederlof,1997). As a result, an alternative membrane was studied that offered similar organicremoval and sustained operation capability (three-month cleaning frequency).

The referenced DBP investigations are summarized in Table 11.5. In all of theseinvestigations, the removal of naturally occurring dissolved organic carbon(NPDOC) or DBPFP by membranes was found to be virtually independent of oper-ating condition (i.e., flux or recovery), suggesting that natural organics removal isgenerally sieve controlled. Similar findings using nanofiltration and reverse osmosisto remove trace-level pesticides are reported by Duranceau and Taylor (1990). If theDBPFPs are assumed to be uncharged NPDOC, which is likely, then the removal ofuncharged organics such as pesticides and naturally occurring dissolved organiccompounds may be sieving controlled. Removal of organic compounds by sievingmay be increased if they can be placed in a state of increased size or steric hindrance.Some NOM compounds are diffusion controlled and affected by variations in fluxand recovery. However, differences in permeate NOM concentrations due to diffu-sion-controlled variables (flux and recovery) are in the tenths of mg/L and unlikelyto have any effect on DBP MCL compliance.

Suppliers of drinking water are subject to stringent government regulations forpotable water quality regarding allowable pesticide and herbicide (i.e., SOCs) con-centrations. In particular, European standards require less than 0.1 g/L for any oneparticular pesticide or herbicide and no greater than 0.5 g/L for total pesticides andherbicides in drinking water. Many investigators have shown that RO and NF areeffective techniques for pesticide and herbicide removal. However, specific mecha-nisms underlying SOC rejection are largely unknown. Some general statements canbe made about SOC rejection in membranes. Rejection has been observed toincrease as SOC molecular weight and charge increased and membrane polarityincreased. In Table 11.6, results and significant findings from published accounts ofpesticide and SOC removal are summarized.

Pathogen Removal

The removal of Giardia by microfiltration and ultrafiltration has been well docu-mented in the literature (Jacangelo et al., 1991; Coffey, 1993). In these studies, aremoval higher than 4 logs was reported, with ultrafiltration (Figure 11.14) and


TABLE 11.5 Summary of DBP Precursor Studies with Membrane Processes

Feed water Treated Percent Water Membrane THMFP THMFP THMFP

Citation source Pretreatment technology (g/L) (g/L) removalTaylor, Thompson, and Carswell, 1987 Ground Antiscalant, NF 961 2832 97

prefiltration NF 961 3139 9697UF 961 326947 266

Amy, Alleman, and Cluff, 1990 Surface Prefiltration NF 157182 5584 4970Ground Prefiltration NF 176472 695 7898

Parker, 1991 Surface None MF 60630 40420 20Coagulation MF 7080 3040 4060

Tan & Amy, 1991 Ground Prefiltration NF 259 39 85

Duranceau, Taylor, and Mulford, 1992 Ground pH adjustment NF 120 6 95Prefiltration

Laine, Clarke, and Mallevialle, 1993 Surface Prefiltration UF 40460 NA


TABLE 11.6 Literature Summary for SOC and Pesticide Removal

Membrane SOC and pesticides Rejection (%) Significant findings Researchers

CA Sodium alkyl benzene 99.9 Flat-sheet application Ironside and sulphonate Sourirajan, 1967

CA DDT 99.9 Flat-sheet application Hindin,TDE 99.5 Bennett, and BHC 52.0 Narayanan,Lindane 79.0 1969

TFC Heptachlor 99.5 (1) Application of Chian, Bruce,(aromatic Lidane 99.5 TFC membrane and Fang, 1975polyamide) DDT 99.5 (2) Organic solutes

Aalathion 98.0 were rejected higher Parathion 98.0 in TFC membraneAtrazine 72.0 than in CA Captan 99.0 membrane

RO (Toray Acetic acid 1172 Pilot application Whittaker and PEC100, Benzene 099 Szaplonczay,UOP TFC Propylene oxide 2870 1985; Whit-4600, Ethylene di-chloride 093 taker and FimTec Formal-dehyde 895 Clark, 1985Ft30 Desal 24-D 8399 DSI) P-chlorobenzo 7799

tri-fluoride

TFC Nylon Alachlor 98.5 (1) Pilot application Miltner, Fronk,Amide CA 84.6 (2) TFC > PA > CA and Speth,

71.4 1987

TFC Ethylene dibromide 350 (1) Pilot application Fronk, 1987(EDB)

Alachlor 100 (2) TFC > PA > CAMetolachlor 100

NF (NF-70) Ethylene dibromide 0 (1) Pilot application Duranceau,Dibromochloropropane 28 (2) SOC rejections Taylor, and Heptachlor 100 were dependent on Mulford, 1992Methoxychlor 100 charge and MW.Chlordane 100Alachlor 100

NF (NF-70, Simazine 6694 (1) Pilot application Hofman et al.,PVD1, PZ, Atrazine 7899 (2) Pesticide removal 1993SU-610) Diuron 4592

Bentazone 97100DNOC 3898 Dinoseb 80100

NF (CA-50, Uncharged SOC (1) Flat-sheet and pilot Berg and BQ-01, Simazine 080 applications Gimbel, 1997Desal Atrazine 590 (2) Charged SOC 5-DK, Terbutylazine 1296 were rejected higher NTC-20, Diuron 590 in charged mem-NTC-60, Metazachlorine 2095 branes.PVD-1, Charged SOCNTR-7250) TCA 6195

Mecoprop 6090

microfiltration membranes having provided absolute removal of this protozoan cyst.In these cases, the level of removal was limited only by the concentration of theorganism in the feed water.A more recent study reported that at bench scale, all thetested membranes (three MF and three UF) except one MF membrane (for whichthe membrane seal ring was found to be defective) removed Cryptosporidium andGiardia below the detection limit (1 cyst/L; Jacangelo, Adham, and Laine, 1995).These results were confirmed at pilot scale. Removal effectiveness ranging from 6 to7 logs was limited only by the influent concentration of the Cryptosporidium andGiardia. Polymeric MF and UF membranes behave as significant barriers to proto-zoan cysts as long as the membranes and all system components remain intact. How-ever, no process should be regarded as an absolute barrier to all pathogens.

Coffey observed a 0.32 mean log removal for heterotrophic plate count (HPC) inan MF process. The permeate contained an average of 182 CFU/mL for a mean of1480 CFU/mL in the feed water. In the same study, no E. coli or Giardia muris werefound in the filtrate for a feed concentration of 9.8 105 to 2.67 106 and 2.75 104,respectively. The low HPC removal was due to regrowth on the permeate channel

MEMBRANES 11.25

TABLE 11.6 Literature Summary for SOC and Pesticide Removal (Continued)

Membrane SOC and pesticides Rejection (%) Significant findings Researchers

RO and Simazine 1495 (1) Flat-sheet Chen and NF (20 Atrazine 4199 application Taylor, 1997membranes) Cyanazine 3399 (2) PA > CA

Bentazone 099 (3) Inorganic and Diuron 1583 organic solutes didnt DNOC 995 affect pesticide Pirimicarb 4897 rejection.Metamitron 1298 Metribuzin 4597 MCPA 099 Mecoprop 7899Vinclozolin 6495

FIGURE 11.14 Removal of seeded microorganisms by UF of Mokelummeand delta waters.

and the low HPC in the feed stream. These results are consistent with the resultspublished by Yoo et al. (1995): an intact 0.2 m MF filtration process appears to pro-vide a significant barrier to Cryptosporidium and Giardia. A microfiltration pilot hasbeen used at the Fishing Creek water supply for Frederick, Maryland, removing allthe total coliform in the feed water, which ranged from 10 to 1000 per mL (Olivieriet al., 1991). At Manitowoc, Wisconsin, no total coliform, fecal coliform, or E. coliwere detected in the MF filtrate. The feed contained 0 to 140 total coliform, 0 to 10fecal coliform per mL, and 0 to 6 E. coli per mL (Kothari et al., 1997). For theSaratago Water Treatment Plant, a microfiltration process reached more than 6-logremoval of Giardia and Cryptosporidium (Yoo et al., 1995). Between 1.7 and 2.9 logremoval of MS2 virus in a California surface water with a 0.2-m pore size hollowfiber microfiltration membrane was observed.The range of MS2 virus number in thefeed water was from 1.3 106 to 3 107, and the filtrate was found to contain 2.2 104 to 3.4 105 MS2 viruses (Coffey, 1993). Total removal of the MS2 virus wasfound for these feed concentrations using a hollow fiber UF membrane with a 0.01-m nominal pore size (Jacangelo et al., 1991). Membrane processes, like any process,will eventually fail, and pathogen passage is more likely to be detected as feed con-centration increases. However, membrane processes offer greater bacteria and pro-tozoa removal than other water treatment processes intended for the removal ofsuspended or dissolved matter.

Membrane Integrity

Membrane integrity is an essential issue in implementation and regulatory approvalof membrane processes. The high efficacy of MF and UF processes for removal ofturbidity and pathogens can be compromised if the membranes or some systemcomponents are damaged. Monitoring membrane system integrity is important toavoid any water quality degradation. As shown in Table 11.7, different membraneintegrity tests are divided into direct and indirect monitoring methods. This sectionpresents only the direct monitoring methods.

Air-Pressure Testing. This five-step test is used by U.S. Filter-Memtec to detect acompromised module. First, isolate modules by closing all their inlets and outlets.Second, drain membrane lumens via the filtrate exhaust line. Third, pressurize thefiltrate side to 15 lb/in2 with the feed side open to ambient pressure. Fourth, turn offthe membrane test pressure to the filtrate side, and watch for any decay in filtratepressure. Fifth, exhaust the pressure to the filtrate exhaust line. Usually the pressureis monitored after 2 and 4 min.A pressure drop between the readings at 2 and 4 minexceeding 0.4 lb/in2 may indicate breaks in one or more fibers.

To take the broken fiber out of service, maintenance personnel remove the ele-ment end cap and insert a pin into the broken fiber, which is identified by escapingair bubbles. If no broken fiber is found, then an O-ring or seal is defective. The air-pressure test method cannot be used for air-permeable membranes.


TABLE 11.7 Different Membrane Integrity Tests

Indirect monitoring methods Direct monitoring methods

Particle counting Air-pressure testingParticle monitoring Bubble-point testingTurbidity monitoring Sonic sensors

Bubble-Point Testing. The bubble-point test is used to detect a compromisedAquasource UF module. The module is taken off line, and the water outside thefiber is drained. Air pressure of 2 bars (29.4 lb/in2) is applied on the external sideof the fibers. A low-concentration surfactant solution is applied at the surface ofthe module end to assist in identifying any air bubbles coming through damagedfibers (Adham, Jacangelo, and Laine, 1995). A pressure decay higher than 50 mbar(0.7 lb/in2) in 5 min indicates damage to one or more fibers.

Sonic Sensor Method. An in-line sonic sensor is also used to detect defects in anAquasource UF module.A sensor located on the module is monitored for hydraulicnoise in a certain frequency range, which indicates membrane integrity loss. Whenmembrane integrity is compromised, hydraulic noise increases due to a rise in tur-bulence in the module.

MASS TRANSPORT AND SEPARATION

For an isothermal process, the total driving force (Ftot,i) for the transport of compo-nent i across the membrane can be expressed as the sum of the concentration poten-tial, electrical potential, and a pressure gradient:

Ftot, i = + + p (11.1)

Where R = universal gas constantT = temperature

ci = concentration gradientci = bulk stream concentration

m = membrane film thickness = potential gradientVi = molar volume

p = pressure gradient

Different driving forces typically come into play in transporting solutes, colloids,larger particles, and water across the membrane. Summing flux values for individualcomponents of a raw water (e.g., Na+, Cl, and H2O) gives Ji, a weighted sum of aminimum number of driving forces Fk, affecting all of the components. This sum ismathematically described by the Onsager relationship (Onsager, 1931) as:

Ji = n

k = 1

LikFk (11.2)

Each phenomenological coefficient, Lik, relates the flux of component i to force Fk.When one driving force dominates mass transport across the membrane, Eq. 11.1can be simplified in conjunction with the Onsager relationship to obtain expressionsfor the transport of water or solutes in a pressure-driven or electrically driven mem-brane process. Thus, these two expressions are the basis for describing a variety ofmembrane processes. For example, in electrodialysis the last term in Eq. 11.1 is neg-ligible, and expressions can be derived for the transport of solute across the electro-dialysis membrane. This issue will be taken up in a later consideration of principlesof separation in electrodialysis. First, however, some simplifications allow descrip-tions of performance for pressure-driven membrane processes such as microfiltra-tion, ultrafiltration, nanofiltration, and reverse osmosis.

Vim

zim

cici

RTm

MEMBRANES 11.27

Mass Transport Considerations in Pressure-Driven Membrane Processes

If pressure is the only driving force, as in UF and MF, Eqs. 11.1 and 11.2 reduce to aDarcy-type expression for the flux of water across the membrane:

J = (11.3)

where p is the pressure drop across the membrane (the transmembrane pressuredrop or TMP), is the absolute viscosity (of the water), and Rm is the hydraulic resis-tance of the clean membrane with dimensions of reciprocal length. In this case, thereis a single phenomenological coefficient L11, which by comparison of Eqs. 11.2 and11.3, is seen to be equal to (Rm)1. This expression is similar in form to the Kedem-Katchalsky equation commonly derived from irreversible thermodynamics todescribe solute transport across reverse osmosis membranes. However, in this case,the flux of solute and the buildup of an osmotic pressure across the membrane mustbe accounted for. If the flux of permeate J is much greater than the flux of solute Js,then such a derivation leads to the following result:

J (p ) (11.4)where Lv is a phenomenological coefficient, Vw is the molar volume of water, is thereflection coefficient (derived as the ratio of two phenomenological coefficients),and is the difference in osmotic pressure across the membrane. Empirically, per-meate flux is calculated from Eq. 11.4 as a function of the transmembrane pressure,the osmotic pressure, and two empirical constants corresponding to (Lv/Vw) and .By analogy, Eq. 11.3 may be modified directly to account for the reduction in the nettransmembrane pressure due to the effects of osmotic pressure:

J = (11.5)

Thus, permeate flux across a clean membrane is not predicted to occur until thetransmembrane pressure p exceeds the difference in osmotic pressure across themembrane. The osmotic pressure of a solute is inversely proportional to its molecu-lar weight. Larger macromolecules, colloids, and particles produce very little osmoticpressure. As a result, the correction for osmotic pressure is negligible for pressure-driven processes such as MF or UF that reject only these larger species.

Osmotic pressure is one of many phenomena that may reduce permeate flux asthe result of the rejection of materials by the membrane. Reductions in permeateflux due to the accumulation of materials on, in, or near the membrane are referredto as membrane fouling. As water moves across the membrane, it draws solutes andparticles toward the membrane. If these materials do not pass through the mem-brane, they may begin to accumulate on or near its surface, leading to the formationof additional layers of material through which water must pass. Particles may formcakes on the membrane surface, and macromolecules may form gel layers. Virtuallyall species achieve higher concentrations near the membrane surface in a flowingconcentration boundary layer referred to as the concentration-polarization layer.Concentration-polarization is often a precursor to cake or gel formation. In addi-tion, materials may precipitate or adsorb on or in the membrane, leading to reduc-tions in permeate flux that may be difficult to reverse. Elevated concentrations near

(p k)Rm

LvVw

pRm


the membrane resulting from the rejection of and subsequent concentration-polarization of these materials tend to exacerbate precipitative or adsorptive mem-brane fouling.

Permeate flux decline can be described mathematically by generalizing Eq. 11.5to the case where resistance to permeate flux is produced by both the membraneand by materials accumulated near, on, and in the membrane. These layers areassumed to act in series to present additional resistance to permeation, designated asRc and Rcp, respectively. These components of resistance vary as a function of thecomposition of materials rejected and thickness of each layer. The resulting expres-sion for permeate flux is

J = (11.6)

where c is the thickness of the cake (or gel) layer, and k is the mass transport coef-ficient of the material in the concentration-polarization layer. The resistance termsare all functions of time and are related to the hydrodynamics of the membrane sys-tem and the feed water quality. Adsorption or precipitation of materials within themembrane matrix as well as compaction of the membrane may lead to an increase inthe membrane resistance Rm(t) over time. The resistance of the cake Rc can beexpressed as the product of the specific resistance of the material that forms thecake Rc and the cake thickness c. By the Kozeny equation, the specific resistance ofan incompressible cake composed of uniform particles can be calculated as:

Rc = (11.7)

where c is the porosity of the cake, and dp is the diameter of particles deposited.This expression predicts that resistance to permeation by a deposited cake shouldincrease as the particles composing the cake decrease in size. The resistance produced by RO and NF membranes is likely to be large in comparison with theresistance of deposited colloidal materials or cakes. However, gel layers of macro-molecular materials may produce significant resistance. Cake resistance may also be small in comparison with the resistance of a UF or MF membrane if the par-ticles deposited in the cake are large compared with the effective pore size of themembrane. For feed streams containing large particles, permeate flux may be rela-tively independent of the concentration of particles. The morphology of the cakeappears to be an important variable in particle filtration, and cake porosity appearsto vary as a function of the hydrodynamics of the membrane module as well as thesize distribution of the particles. By comparison with the resistance produced bycake or gel layers, resistance from the concentration-polarization layer is typicallysmall.

Equations 11.3 through 11.6 at first appear to predict that permeate fluxincreases indefinitely with increasing TMP. However, it is frequently observed thatas pressure increases, a maximum permeate flux is eventually attained and permeateflux becomes pressure-independent (Figure 11.15). This maximum is usually inter-preted as a mass transportlimited flux. Under conditions of mass transportlimitedflux, an increase in pressure that would otherwise increase the flow of permeateacross the membrane is instantaneously balanced by an increased accumulation ofpermeate-limiting materials near the membrane. In other words, increases in theresistance terms in the denominator of Eqs. 11.4 through 11.6 offset the increase inp in the numerator.

180(1 c)2

dp2c3

(p k)(Rm(t) + Rc(c(t), . . .) + Rcp(k,J))

MEMBRANES 11.29

For a given TMP or under conditions of mass transferlimited permeate flux, theaccumulation of materials near the membrane can be envisioned as a balancebetween advection of materials toward the membrane due to permeation and back-diffusion that occurs as a concentration gradient builds up near the membrane.Assuming, therefore, a constant permeation rate and concentration-polarizationlayer with axial distance, mass balance on the concentration-polarization layer yields

D = Jc (11.8)

where c is the concentration of the species subject to concentration-polarization, Dis the diffusivity of this species, and y is the distance with the boundary layer suchthat c = cmem at y = 0 and c = cbulk at y = cp. Integrating this expression over the thick-ness of the concentration-polarization layer cp results in the following expressionfor the concentration of solute at the membrane surface cmem:

cmem = cbulk exp J (11.9)For constant operating conditions, the exponential term in Eq. 11.9 can be taken asa constant, referred to as the polarization factor (PF). Thus, concentrations ofrejected materials at the membrane surface exceed the local bulk concentration bya factor of PF, sometimes estimated as an exponential function of the recovery r suchthat PF = exp(Kr). The semiempirical constant K typically takes on values of 0.6 to0.9 for commercially available RO modules.

When permeate flux is mass transferlimited, Eq. 11.9 can be rearranged todescribe the limiting permeate flux J as a function of the bulk concentration cbulk, thelimiting concentration at the membrane cmem, the diffusion coefficient for the solute,and the concentration-polarization layer thickness:

J = ln (11.10)cmemcbulk

Dcp

cpD

cy


FIGURE 11.15 Transition from pressure-dependentto mass transferlimited permeate flux.

The ratio of diffusivity to concentration-polarization layer thickness in this filmtheory model defines a mass transfer coefficient k:

k = (11.11)

The thickness of the concentration-polarization layer is a function of the hydrody-namics of the membrane module. For example, for a module with tangential flowacross the membrane surface, a higher cross-flow velocity tends to decrease thethickness of the concentration-polarization layer if Brownian diffusion is the onlymechanism of back-transport (D = DB). In this case, the mass transfer coefficient canbe calculated directly using correlations for the Sherwood number Sh of the form:

Sh = = A(Re) (Sc)

(11.12)

where Re =

Sc =

v = kinematic viscosityuave = average cross-flow velocity

dh = hydraulic diameter of the membrane element (e.g., diame-ter of the hollow fiber)

A, , , and = adjustable parametersThe Graetz-Leveque correlation, which is valid for laminar flow when the velocityfield is fully developed and the concentration boundary layer is not fully developed,is often used to estimate the mass transfer coefficient:

Sh = 1.86 (Re)0.33 (Sc)0.33 0.33

(11.13)

The Linton and Sherwood correlation can be used to calculate the mass transfercoefficient in turbulent flow, which may occur in tubular membranes:

Sh = 0.023 (Re)0.83 (Sc)0.33 (11.14)

Concentration-Polarization and Precipitative Fouling. As one consequence ofconcentration-polarization in RO and NF membranes, salts may more readily pre-cipitate as a scale on membranes. The average concentrations of scale-formingspecies rejected by NF or RO membranes in the bulk flow inevitably increase aswater permeating through the membrane is removed from the salt-bearing solution.Concentration-polarization further elevates rejected salt concentrations near themembrane and exacerbates the tendency to form a scale.

Consider a sparingly soluble salt s consisting of anion A with charge zA and cationB with charge zB in equilibrium with precipitated solid phase. For example, metalssuch as calcium, magnesium, or iron most commonly precipitate as hydroxide, car-bonate, or sulfate scales. In the absence of interactions with other salts, the activitiesof A and B, aA and aB, in equilibrium with the precipitated phase are related to the

dhL

vDB

uavedh

v

dhL

kdhDB

Dcp

MEMBRANES 11.31

solubility product Ksp for that precipitate. This relation can be expressed as a func-tion of the concentrations of A and B as follows:

Ksp = Ax[Ay]x By[Bx+]y (11.15)

where A,B are the free ion activity coefficients of A and B, [A] and [B] and x and yare, respectively, the molal concentrations in solution and the stoichiometric coeffi-cients for the precipitation reaction of A and B. For example, if calcium and sulfateare present in sufficient quantities to initiate precipitation of CaSO4, then at equilib-rium at a temperature of 20C, the product of the activities of calcium and sulfate insolution will be equal to the Ksp for CaSO4; approximately 1.9 104.The mean activ-ity coefficients can be estimated as function of ionic strength I as,

log A,B = 0.509zAzB I (11.16)

For dilute solutions typical of most natural waters, the activity coefficients areapproximately equal to 1. However, as the feed water concentration increases, theactivity coefficients may decrease sufficiently to make concentration a poor approx-imation of activity. The presence of other electrolytes may further decrease ionactivities through effects on ionic strength and ion pairing. The average (bulk) con-centration of the rejected salts (for example, the cation B) in the concentrate streamexiting a membrane module cr increases over the feed concentration cf as the recov-ery r and global rejection R increase:

cr = cf (11.17)

The salt may precipitate when the ratio of the product of ion activities in the con-centrate (the right-hand side of Eq. 11.17 after substituting [A]r and [B]r calculatedfrom the feed concentration) to the solubility product Ksp is greater than 1. How-ever, concentration-polarization further increases the ion product at the membranesurface since cmem = cbulk PF = cr PF.Thus, taking the case of x = y = 1 (calcium sul-fate, for example) the theoretical conditions to avoid scale formation are given by:

(PF)2 2

[B]f[A]f < Ksp (11.18)

Transport of Colloids and Particles. The preceding discussion clearly suggeststhat the diffusivity of contaminants in water plays an important role in determiningthe permeate flux. However, Brownian diffusion alone does not adequately describethe transport of particulate and colloidal species near the membrane. The transportof colloidal and particulate species is of greatest significance in MF and UF systems,which are designed to remove these species. In a flowing suspension, particles maycollide with one another, producing random rotary and translational motions that,on the average, result in a net particle migration from regions of high concentrationand shear (near the membrane) to regions of lower concentration and shear (Davis,1992). Building on the work of Eckstein and coworkers (Eckstein et al., 1977),Leighton and Acrivos (1987) proposed the following expression for the shear-induced diffusion coefficient. The equation was reported as valid up to particle vol-ume fractions (the concentration of particle volume per volume of water) of = 0.5:

Dsh = ap2 Dsh() (11.19)

1 r(1 R)

(1 r)

1 r(1 R)

(1 r)


where ap is the particle radius, is the shear rate, and Dsh is a dimensionless functionof estimated for suspensions of rigid spheres as:

Dsh = 0.332(1 + 0.5e8.8) (11.20)Brownian diffusion is more important for smaller species such as solutes and smallmacromolecules, while shear-induced diffusion is increasingly important for largerparticles. Contaminants encountered in water treatment typically span severalorders of magnitude in hydrodynamic size, requiring consideration of both Brown-ian and shear-induced diffusion in estimating concentration polarization and per-meate flux. The sum of Brownian and shear-induced diffusivity D can be rewrittenas (Sethi and Wiesner, 1997),

D = + rp2 Dsh() (11.21)

where wall is the shear stress at the membrane wall, o is the absolute viscosity of thewater at low-particle volume fractions, and () is the relative viscosity, which varieswith volume fraction. Simultaneous consideration of Brownian and shear-induceddiffusivity yields a minimum in particle back-transport for particles in the size rangeof several tenths of a micron and a corresponding minimum in permeate flux. Thesum of the Brownian and shear-induced diffusion coefficients exhibits a minimumfor particles approximately 101 m in size for flow conditions typical of hollow fiberor SW modules (Figure 11.16). Consequently, the relatively low mass transfer coef-ficients of species in this unfavorable size range are predicted to produce minimumpermeate flux, while species either smaller or larger than this intermediate size arepredicted to produce higher permeate fluxes. Until recently, only indirect experi-mental evidence supported this hypothesized minimum in back-transport as inter-preted from permeate flux data (Fane, 1984; Wiesner, Clark, and Mallevialle, 1989;Lahoussine-Turcaud et al., 1990). However, a recent report gave the first direct

wallo()

kT6orp

MEMBRANES 11.33

FIGURE 11.16 Brownian and shear-induced diffusivity as a function ofparticle size for condition typical of hollow fiber UF membranes.

experimental confirmation of a minimum back-transport based on measurements ofparticle residence time distributions (Chellam and Wiesner, 1997).

Diffusive transport is significant near the membrane where boundary layers maydevelop. Differential transport of smaller species in the bulk flow (outside theboundary layers) is generally negligible. However, in laminar cross-flow filtration,the transport of larger particles from the bulk

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