SEPARATION PROCESS
`PRINCIPLES
`
`J. D. Seader
`
`/ Ernest J. Henley
`
`GE-1010.001
`
`GE-1010.001
`
`

`
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`Copyright © 1998 John Wiley & Sons, Inc. All rights reserved.
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`
`ISBN 0-471-58626-9
`
`Printed in the United States of America
`
`10987654321
`
`About the Authors
`
`J. D. Seader is Professor of Chemical Engineering at the University of Utah. He received
`B.S. and M.S. degrees from the University of California at Berkeley and a Ph.D. from the
`University of Wisconsin. From 1952 to 1959, Seader designed processes for Chevron
`Research, and from 1959 to 1965, he conducted rocket engine reseach for Rocketdyne.
`Before joining the faculty at the University of Utah, he was a professor at the University
`of Idaho. Combined, he has authored or coauthored 102 technical articles, six books, and
`four patents, and also coauthored the section on distillation in the 6th and 7th editions of
`Perry’s Chemical Engineers’ Handbook. Seader has been a trustee of CACHE for 26 years,
`serving as an executive officer from 1980 to 1984. For 20 years, he directed the use and
`distribution of Monsanto’s FLOWTRAN process simulation computer program for various
`universities. Seader also served as a director of AIChE from 1983 to 1985. In 1983, he
`
`presented the 35th Annual Institute Lecture of AIChE, and in 1988, received the Computing
`in Chemical Engineering Award of the CAST Division of AIChE.
`
`Ernest J. Henley is Professor of Chemical Engineering at the University of Houston. He
`received his B.S. degree from the University of Delaware and his Dr. Eng. Sci. from
`Columbia University, where he served as a professor from 1953 to 1959. Henley also has
`held professorships at the Stevens Institute of Technology, the University of Brazil, Stanford
`University, Cambridge University, and the City University of New York. He has authored
`or coauthored 72 technical articles and 12 books, the most recent one being Probabilistic
`
`Risk Management for Scientists and Engineers. For 17 years, he was a trustee of CACHE,
`serving as President from 1975 to 1976 and directing the efforts that produced the seven-
`volume set of “Computer Programs for Chemical Engineering Education” and the five-
`volume set, “AIChE Modular Instruction.” An active consultant, Henley holds nine patents
`and serves on the Board of Directors of Maxxim Medical, Inc., Procedyne, Inc., Lasermed-
`ics, Inc., and Nanodyne, Inc.
`
`GE-1010.002
`
`

`
`722 Chapter 14 Membrane Separations
`
`SOLUTION
`
`where cm3 (STP)/cm2-s) refers to the volumetric transmembrane flux of the diffusing species
`in terms of standard conditions of 0°C and 1 atm, cm refers to the membrane thickness, and
`cmHg refers to the transmembrane partial pressure driving force for the diffusing species.
`The barrer unit is named for R. M. Barrer, who published an early article [10] on the nature
`of diffusion in a membrane, followed later by a widely referenced monograph on diffusion in
`and through solids [11].
`If the transmembrane partial pressure driving forces for H2 and CO, respectively, are 240
`psi and 80 psi, calculate the transmembrane fluxes in kmol/(m2~s). Compare the hydrogen flux
`to that for hydrogen in the commercial application discussed at the beginning of this chapter.
`
`At 0°C and 1 atm, 1 kmol of gas occupies 2.242 X 106 cm3. Also, 2 pm thickness =2 X 10‘‘‘
`cm and 1 cmHg AP = 0.1934 psi. Therefore, using (14-1):
`-10
`
`4
`)(240/o.1934)(10 ) 2 0.554 kmol
`NHZ Z (200,000)(10
`(2.242 x 106)(2 x 104)
`m2—s
`
`: (700)(10"°)(80/O.1934)(10") =
`(2.242 X 106)(2 x 10-4)
`
`kmol
`000065 m2—s
`
`NCO
`
`In the application discussed at the beginning of this chapter, the flux of Hz for the polymer
`membrane is
`
`1685.1 1/2.205
`)
`X
`(
`(16,000)(0.3048)2(3600)
`
`=0.000143
`
`kmol
`,
`m -s
`
`Thus, the flux of H2 through the ultramicroporous glass membrane is more than 1,000 times
`higher than the flux through the dense polymer membrane. Large differences in molar fluxes
`through different membranes are common.
`I
`
`14.2 MEMBRANE MODULES
`
`The asymmetric and thin-film composite polymer membrane materials described in the
`previous section are available in one or more of the three shapes shown in Figure 14.4a,
`b, and c. Flat sheets have typical dimensions of 1 m by 1 m by 200 um thick, with a dense
`skin or thin, dense layer 500 to 5,000 A in thickness. Tubular membranes are typically 0.5
`to 5.0 cm in diameter and up to 6 in in length. The thin, dense layer ia on either the inside,
`as shown in Figure 14.4b, or the outside surface of the tube. The porous supporting part
`of the tube is fiberglass, perforated metal, or other suitable porous material. Very small~
`diameter hollow fibers, first reported by Mahon [12,13] in the 1960s, are typically 42 um
`i.d. by 85 um o.d. by 1.2 m long with a 0.1 to 1.0 um-thick dense skin. Hollow fibers,
`shown in Figure 14.4c, provide a large membrane surface area per unit volume. A honey-
`comb monolithic element for inorganic oxide membranes is shown in Figure 14.4.d. Ele-
`ments of both hexagonal and circular cross-section are available [14]. The circular flow
`channels are typically 0.3 to 0.6 cm in diameter, with a 20 to 40 mm-thick membrane layer.
`The hexagonal element in Figure 14.4d has 19 channels and is 0.85 in long. Both the bulk
`support and the thin membrane layer are porous, but the pores of the latter can be very
`small, down to 40 A.
`'
`The membrane shapes of Figure 14.4 are incorporated into compact commercial modules
`and cartridges, some of which are shown in Figure 14.5. Flat sheets used in plate-and-
`frame modules are circular, square, or rectangular in cross-section. The sheets are separated
`by support plates that channel the permeate. In Figure 14.5a, a feed of brackish water
`flows across the surface of each membrane sheet in the stack. Pure water is the permeate
`product, whereas the retentate is a concentrated brine solution.
`Flat sheets are also fabricated into spiral—wound modules shown in Figure 14.5b. A
`laminate, consisting of two membrane sheets separated by spacers for the flow of the feed
`and permeate, is wound around a central perforated collection tube to form a module that
`
`Active layer
`
`Porous support
`‘We’
`
`la)
`
`Fiber bore
`
`14.2 Membrane Modules
`
`723
`
`porous Support
`tube
`
`Membrane
`
`Porous
`support
`
`Permeate
`
`(d)
`
`Figure 14.4 Common membrane shapes: (a) flat asymmetric or thin-composite
`sheet; (b) tubular; (c) hollow fiber; (d) monolithic,
`
`inserte: into a pressure Vessel. The feed flows axially in the channels created between
`' e mgm ranes by the porous spacers. Permeate passes through the membrane, traveling
`inwar
`in a spiral. path to the central collection tube. From there, the permeate flows in
`either axial direction through and out of the central tube. A typical spiral~wound module
`;s 0.1] to 0.3 I1’1.1I1 diameter. and 3 in long.
`such modules are often placed in series. The
`our- eaf modification in Figure 14.50 minimizes the pressure drop of the permeate because
`the permeate travel is less for the same membrane area.
`The hollow-fiber module shown in Figure 14.5d, for a gas permeation application, resem-
`bles a shell—and-tube heat exchanger. The pressurized feed enters the shell side at one
`end, While. flowing over the fibers toward the other end, permeate passes through the
`fiber walls into the central fiber channels. Typically the fibers are sealed at one end and
`embedded into a tube sheet with epoxy resin at the other end. A commercial module
`might be 1m long and 0.1 to 0.25 m in diameter and contain more than one million
`hollow fibers.
`
`EA tlubular module is shown in Figure 14.5e. This module also resembles a shell—ancl-
`tu e eat exchanger, but the feed flows through the tubes. Permeate passes through the
`wall of the tubes into the shell side of the module. Tubular modules contain up to 30 tubes
`Télhel monolithic module in Figure 14.5f contains from 1 to 37 monolithic elements in a
`11110 u e housing. The feed flows through the circular channels and permeate passes through
`t e membrane and porous support and into the open region between elements.
`Table 14.4 is.a comparison of the characteristics of four of the modules shown in Figure
`14;_5.hTl}i)e packing density is the membrane surface area per unit volume of module, for
`Iw ic
`t e hollow-fiber membrane modules are clearly superior. Although the plate-and-
`rarne module has a high cost and a moderate packing density, it finds use in all membrane
`applications except gas permeation. It is the only module widely used for pervaporation.
`The spiral-wound module is very popular for most applications because of its low cost and
`reasonable resistance to fouling. Tubular modules are only used for small applications or
`
`GE-1010.003
`
`

`
`724 Chapter 14 Membrane Separations
`
`Product
`water
`
`Membrane
` . support plate
`membrane
`Spacer
`
`Porous feed-
`spacer membrane
`
`mm.
`
`Porous permeate-
`spacer membrane
`
`A 7
`3:
`U
`
`'
`
`———>- Reject
`V —> permeate
`
`Fiber bundle
`end seal
`
`‘i’ Permeate
`
`Rete ntate
`-—>
`>
`
`:
`
`Hollow, thin-walled
`plastic tube
`
`14.3 Transport in Membranes
`
`725
`
`Table 14.4 Typical Characteristics of Membrane Modules
`
`Plate and Frame
`
`Spiral—Wound
`
`Tubular
`
`Hollow-Fiber
`
`500 to 9,000
`30 to 200
`200 to 800
`30 to 500
`Packing density, m2/m3
`Poor
`Very good
`Moderate
`Good
`Resistance to fouling
`Poor
`Excellent
`Fair
`Good
`Ease of cleaning
`Low
`High
`Low
`High
`Relative cost
`
`Main applications D, RO, GP, UF D, RO, PV, UF, MF D, R0, GP, UF, MF R0, UF
`
`
`
`Note. D, dialysis; RO, reverse osmosis; GP, gas permeation; PV, pervaporation; UF, ultrafiltration; MF, microfiltration.
`
`when a high resistance to fouling and/or ease of cleaning are essential. Hollow-fiber
`modules, with a very high packing density and low cost, are popular where fouling does
`not occur and cleaning is not necessary.
`
`14.3 TRANSPORT IN MEMBRANES
`
`For a given application, the calculation of the required membrane surface area is based
`on laboratory data for the selected membrane. Although permeation can occur by one or
`more of the mechanisms discussed in this section, these mechanisms are all consistent with
`(14-1) in either its permeance form or its permeability form, with the latter being applied
`more widely. However, because both the driving force and the permeability or permeancc
`depend markedly on the mechanism of transport, it is important to understand the nature
`of transport in membranes, which is the subject of this section. Applications to dialysis,
`reverse osmosis, gas permeation, and pervaporation are presented in subsequent sections.
`Membranes can be macroporous, microporous, or dense (nonporous). Only microporous
`or dense membranes are permselective. However, macroporous membranes are widely
`used to support thin microporous and dense membranes when significant pressure differ-
`ences across the membrane are necessary to achieve a reasonable throughput. The theoreti-
`cal basis for transport through microporous membranes is more highly developed than
`that for dense membranes, so porous~membrane transport is discussed first.
`
`Mechanisms for the transport of liquid and gas molecules through a porous membrane
`are depicted in Figure 14.6a, b, and c. If the pore diameter is large compared to the molecular
`diameter, and a pressure difference exists across the membrane, bulk or convective flow
`through the pores occurs, as shown in Figure 14.6a. Such a flow is generally undesirable
`
`Porous Membranes
`
`Permeats
`
`Module
`housing
`Multichannel
`element
`
`Retentate out
`
`(el
`
`(f)
`_
`'
`Figure 14.5 Common membrane modules: (a) plate-and frame, (b) SP1T211'W0l1I1d« (3) four lea
`spiral-wound, (d) hollow—fiber, (e) tubular, (f) H10T1011th1°-
`
`f
`
`(C)
`
`Figure 14.6 Mechanisms of transport in membranes. (Flow is downward.)
`(a) Bulk flow through pores; (b) diffusion through pores; (c) restricted
`diffusion through pores; (d) solution-diffusion through dense membranes.
`
`GE-1010.004
`
`

`
`726 Chapter 14 Membrane Separations
`
`Bulk Flow
`
`because it is not permselective and, therefore, no separation between components of the
`feed occurs. If fugacity, activity, chemical potential, concentration, or partial pressure
`differences exist across the membrane for the various components, but the pressure is the
`same on both sides of the membrane, permselective diffusion of the components through
`the pores will take place, effecting a separation as shown in Figure 14.6b. If the pores are
`of the order of molecular size for at least some of the components in the feed mixture,
`the diffusion of those components will be restricted (hindered) as shown in Figure 14.6c,
`resulting in an enhanced separation. Molecules of size larger than the pores will be pre-
`vented altogether from diffusing through the pores. This special case is highly desirable
`and is referred to as sieving. Another special case exists for gas diffusion where the pore
`size and/or pressure (typically a vacuum) is such that the mean free path of the molecules
`is greater than the pore diameter, resulting in so—called Knudsen diffusion, which is depen~
`dent on molecular weight.
`
`Consider the bulk flow of a fluid, due to a pressure difference, through an idealized straight,
`cylindrical pore. If the flow is in the laminar regime (NR, = Dvp/p. < 2,100), which is
`almost always the case for flow in small-diameter pores, the flow velocity, v, is given
`by the Hagen~Poiseuille law [15] as being directly proportional to the transmembrane
`pressure drop:
`
`D2
`1’ = 32p.L (Po ~ PL)
`
`A
`
`<14-2)
`
`where D is the pore diameter, u, is the viscosity of the fluid, and L is the length of the
`pore. This law assumes that a parabolic velocity profile exists across the pore radius for
`the entire length of the pore, that the fluid is Newtonian, and if a gas, that the mean free
`path of the molecules is small compared to the pore diameter. If the membrane contains
`n such pores per unit cross~section of membrane surface area normal to flow, the porosity
`(void fraction) of the membrane is
`
`e = n*n'D2/4
`
`(14-3)
`
`Then the superficial fluid bulk-flow flux (mass velocity), N, through the membrane is
`n1'rpD4
`128]J.lM
`
`epD2
`
`N "
`
`(Po
`
`PL) "
`
`(Po
`
`PL)
`
`(14-4)
`
`where [M is the membrane thickness and p and pt are fluid properties.
`In real porous membranes, pores may not be cylindrical and straight, making it necessary
`to modify (14-4). One procedure is that due to Carman and Kozeny, as extended by Ergun
`[16], where the pore diameter in (14-2) is replaced, as a rough approximation, by the
`hydraulic diameter:
`
`Volume available for flow
`L1,, = 4 ——————-————
`Total pore surface area
`
`4 Total pore volume
`Membrane volume
`
`(Total pore surface area
`
`Membrane volume
`
`where the membrane volume includes the volume of the pores. The specific surface area,
`a,,, which is the pore surface area per unit volume of membrane, is
`
`an = a/(1 — e)
`
`(14-6)
`
`GE-1010.005
`
`

`
`764 Chapter 14 Membrane Separations
`_
`
`SOLUTION
`
`‘
`V
`-
`The followmg Independent equations apply IO 21
`ances:
`
`11 parts of this example. Component material bal
`.
`V
`
`_
`
`"Ir: nil? + nip’ Z: H’M
`
`Dalton’s law ofpartial pressures: Pk = pa, + pM,.
`
`k = F. R, P
`
`Partial pressure—mole relations:pHk = P/fink/(fin, ‘l’ ”M,,)>
`
`k = Fa R P
`
`(1,2)
`
`(3»4a5)
`
`(6,733)
`
`10%-mean Partial‘
`-
`-
`-
`'
`'
`—
`’
`S l
`t
`,
`-diffusion transport rates are obtained using (_14 32), assumlni‘-Z» 3
`presOs11i11~éV;riving force based on the exiting permeate partial‘pres:u:1e:tosr:;:ie downstream side
`of the membrane because of the assumption of perfect mixing 0
`-
`
`,
`
`,
`A
`
`r *
`
`fl,-P = ?MiAM
`
`PI’: _ pi’?
`___.—_. ,
`1n(Pz, ‘ pip)
`Pzk “ Pip
`
`I
`;= H, M
`
`14.7 Pervaporation
`
`765
`
`Part
`—..—._j—_j___._.:____
`(1)
`(2)
`(3)
`
`495
`55
`3,370
`
`425
`75
`3,370
`
`450
`50
`2,528
`
`424.2
`18.2
`70.8
`36 8
`.
`
`450
`S0
`329
`171
`19.18
`0.82
`
`369.6
`25.9
`55.4
`491
`.
`
`425
`75
`265
`235
`18.69
`1.31
`
`338.4
`11.5
`111.6
`38 5
`.
`
`450
`50
`372
`128
`19.34
`0.66
`
`V
`
`Fixed:
`nnp, lbmol/H
`nM., lbmol/h
`A,;, a2
`Calculated, in lbmol/h:
`
`IIM
`Cafculated, in psia:
`pap
`pMr
`pHR
`pMR
`pH’,
`pMP
`
`Thus, we have a system of 10 equations in the following 18 variables:
`
`From the above results, the following are computed:
`
`VIM,
`R
`
`nm
`VIM
`
`,.
`
`PF
`
`PR
`
`PP
`
`PH, PH,
`PH,,
`PM;
`PMR PW
`
`«
`
`Mol% H2 in permeate
`% H2 recovery in permeate
`
`(=1)
`95.3
`90
`
`(b1)
`95.9
`85.7
`
`(b2)
`93.5
`87.0
`
`(b3)
`96.7
`75.2
`
`Part
`
`Thus, eight variables must be fixed. For all parts of this example, the following five variables
`are fixed:
`
`,
`
`_
`RV!“ and PMM given above
`PF = 500 psia PR = 500 psia pp = 20 psia
`
`For each part’ three additional Variables must be fixed.
`(21)
`
`,
`
`mm = 0.9(s0o) = 450 lbmol/h
`
`nM,_. = 0.1(500) = 50 183101/h
`nu, = 0-9(450) = 4051bm°1/h
`
`Solving Equations (1)—(10) above, using a PC Pfogram Such 55 Mathcadv We Obtain
`
`AM = 3,370 ftz
`W, = 20,01bmo]/h nHR = 45.0lbmo1/h nmk = 30.01bm01/h
`1’
`_
`I7H,.. = 450 Psia
`PM,.— = 50 psia
`PHI: 2 300 psla
`PMR __. 200 psia PH? = 19_()5 psia
`pMP = 0.94 psia
`(b) Calculations are made in a similar manner using Equations (1)*(10)- R€Su1tS for parts (1).
`(2), and (3) are:
`
`,
`
`From these resuhs, we see that when the feed rate is increased by 10% (part b1), the
`hydrogen recovery drops about 5%, but the permeate purity is maintained. When the feed
`composition is reduced from 90% to 85% hydrogen (part b2), the hydrogen recovery
`decreases by about 3% and the permeate purity decreases by about 2%. With 25% of the
`membrane area inoperative (part b3), the hydrogen recovery decreases by about 17%, but
`the permeate purity is about 1% higher. Overall, percentage changes in hydrogen recovery
`and purity are less than the percentage changes in feed flow rate, feed composition, and
`membrane area, thus tending to confirm the insensitivity of gas permeation separators to
`changes in operating conditions.
`I
`
`14.7 PERVAPORATION
`As shown in Figure 14.22, pervaporation (PV) differs from dialysis, reverse osmosis, and
`gas permeation in that the phase state on one side of the membrane is different from that on
`the other side. The feed to the membrane module is a liquid mixture (eg, an alcohol—water
`azeotrope) at a pressure, P1, that is usually ambient or elevated high enough to maintain
`a liquid phase as the feed is depleted of species A and B to produce the product retentate.
`A composite membrane is used that IS. selective for species A, but species B usually ‘has
`some finite permeability. The dense, thin membrane film 1S in contact with the liquid side.
`The retentate is enriched in species B. Generally, a sweep fluid is not used on the other
`side of the membrane, but a pressure, P), is maintained at or below the dew point of the
`permeate, making it vapor. Often, P2 is a vacuum. Vaporization may occur near the
`downstream face of the membrane, such that the membrane can be considered to operate
`with two zones, a liquid-phase zone and a vapor—phase zone, as shown in Figure 14.22.
`
`GE-1010.006
`
`

`
`766 Chapter 14 Membrane Separations
`
`Asymmetric or
`thin~film
`composite
`membrane
`
`.
`
`Liquid feed i
`Pressure: P1
`
`Vapor
`i Pfifmeafe
`pressure, P,
`
`Liquid
`retentate
`
`P1 > P2
`
`Figure 14.22 Pervaporation.
`
`Alternatively, the vapor phase may only exist on the permeate side of the membrane. The
`Vapor permeate is enriched in species A. Overall permeabilities of species A and B
`depend upon their solubilities in and diffusion rates through the membrane. Generally,
`the solubilities cause the membrane to swell.
`The term pervaporation is a combination of the two words, permselective and evapora-
`tion. It was first reported in 1917 by Kober [43], who studied several experimental techniques
`for removing water from albumin/toluene solutions. Although the economic potential of
`PV was shown by Binning et al.
`[44] in 1961, commercial applicationswere delayed
`until the mid-1970s, when adequate membrane materials first became available. Major
`commercial applications now include (1) dehydration of ethanol; (2) dehydration of other
`organic alcohols, ketones, and esters; and (3) removal of organics from water. The separa-
`tion of organic mixtures is receiving much attention.
`Pervaporation is best applied when the feed solution is dilute in the main permeant
`because sensible heat of the feed mixture provides the enthalpy of vaporization of the
`permeant. If the feed is rich in the main permeant, a number of membrane stages may
`be needed, with a small amount of permeant produced per stage and reheating of the
`retentate between stages. Even when only one membrane stage is sufficient, the feed may
`be heated before entering the membrane module.
`Many pervaporation separation schemes have been proposed [6], with three of the more
`important ones shown in Figure 14.23. A hybrid process for integrating distillation with
`pervaporation to produce 99.5 wt% ethanol from a feed of 60 wt% ethanol is shown in
`Figure 14.23a. The feed is sent to a distillation column operating at near—ambient pressure,
`where a bottoms product of nearly pure water and an ethanol—rich distillate of 95 wt% is
`produced. The distillate purity is limited because of the 95.6 wt% ethanol in water azeotrop6-
`The distillate is sent to a pervaporation step where a permeate of 25 wt% alcohol and 3
`retentate of 99.5 wt% ethanol is produced. The permeate Vapor is condensed under vacuum
`and recycled to the distillation column. The vacuum is sustained with a vacuum pump-
`The dramatic difference in separability of the pervaporation membrane as compared to
`vapor—liquid equilibrium for distillation is shown in Figure 14.24, taken from Wesslein Gt
`
`147 Pfirvaporation
`
`Ethanol product
`Vacuum pump
`
`9’
`
`Phase
`Separator
`
`Permeate
`recycle
`
`Water—saturated
`dichloroethylene
`feed
`
`Preheater
`
`Wastewater
`feed
`
`Water—rich
`liquid
`
`Purified DCE
`
`vacuum pump
`
`Three—phase
`separator
`
`Recycle DCE—rich
`permeate
`
`Wastewater
`TO treatment
`
`Nearly pure water
`
`Pervaporation
`
`Vacuum pump
`
`Three-phase
`separator
`
`VOC-rich liquid
`
`(0)
`
`Figure 14.23 Pervaporation processes. (a) Hybrid process for removal of water from
`ethanol. (b) Dehydration of dichloroeth l
`.
`R
`1
`f
`'
`'
`Pounds (VOCS) from wastewater.
`y me (C)
`emova O volame Orgamc com-
`
`al. [45]. For pervaporation, the compositions refer to a liquid feed (abscissa) and a Vapor
`permeate (ordinate) at 60°C for a polyvinylalcohol (PVA) membrane and a vacuum of 15
`t
`. F
`'
`~
`-
`-
`-
`-
`.
`.
`‘Err
`tin: membrane, there is no limitation on ethanol purity and the separation index
`i very ig
`or feeds containing more than 90 wt% ethanol.
`A pervaporation process for dehydrating dichloroethylene (DCE) is shown in Figure
`14.23b.
`'
`'
`~
`-
`»
`.
`90°C at $171:t1r1I(1]lE.il:1(Z:j feCC:,tWh1]:l\'1/V is DCE saturated with water (0.2 wt%), is preheated to
`.
`sen o a
`A membrane system, which produces a retentate of almost
`P‘-We DCE (<10 PP111 H20) and a permeate vapor of 50 wt% DCE under vacuum Followin
`condensation, the two resulting liquid phases are separated with the DCE‘riCh pha g
`7
`‘
`se
`recycled back to the membrane system and the water—rich phase sent to an air stripper,
`stea
`t '
`d
`'
`‘
`~
`~
`.
`m 3 Upper, 3 SOFPUOH llnlt, Or hydrophobic pervaporation membrane system for resid-
`ual DCE removal.
`
`GE-1010.007
`
`

`
`768 Chapter 14 Membrane Separations
`1.0
`
`Vapor—|iquid equilibrium
`
`9 oo
`
`.° or
`
`.0 4>
`
`Vapor composition for
`permeate pressure =15 mm Hg
`
`
`
`
`
`Weightfractionalcoholinvapor
`
`0.8
`0,6
`o_4
`02
`Weight fraction alcohol in liquid
`
`1.0
`
`F‘
`14.24 Comparison of cthanol~water separabilities.
`[lggldfrl M. Wesslein et al., J. Membrane Sci., 51, 169 (1990).]
`
`-
`f
`11
`al of VOCS (e.g., toluene and trichloroethylene)
`f Pervapfn-atlton(l:/nti)e:v1::>(dr:tidnev::Ili1l)1‘ollow-fiber modules of silicone rubber, as shown
`tom was ewa er
`_
`.
`VOC
`(1 th
`rmeate,
`in Figure 14.23c. The retentate is almost pure water (<5 131313 of h
`5) 3;‘ aneespsetem and
`after condensation, is (1) a water-rich phase that is recycled to t e mem r
`y
`.
`(2) a nearly pure VOC phase. I
`_
`_
`_
`f
`A pervaporation module typically operates adiabatically with the enthalpy o Vap0r1Za
`1
`.
`.
`.
`{on supplied by sensible enthalpy of the feed. Consider the pervaporation of a binary
`_
`_
`-
`tl uid s ecific
`liquid mixture of components A and B. Assume constant pure eomponqnT iqm enfhalpy
`heats and ignore heat of mixing. For an enthalpy datum temperaturefo
`or
`t‘
`_ as
`’
`.
`'
`‘
`~'
`d heats 0 vaporiza ion, giv
`balance, in terms of mass flow rates, in, liquid sensible heats, an
`
`_
`
`(I71,»\FCpA + mBFCPB)(TF _ T0)
`= [(mA, - mA,,)Cr>,, + (map ‘ mBP)CPB]<TR ‘ T0)
`‘i’ (W1/’*pC'I’,\ + mBpCPB)( TP — TO) + mAPAHXlp
`
`(14.73)
`
`+ mBPAH§‘P
`
`-
`w ere
`enthalpies of vapori7ation are evaluated at Tp. After collection of terms, (1443)
`h
`reduces to
`
`(W5/XFCFA + mBFCPB)(TF _ TR) : (mAPCPA + mBPCPB)(TP W TR)
`+ (mAPAHY£P + mg,,AHt£“’)
`
`meate vacuum
`'
`'
`t
`C PCY14 74)
`The temperature of the permeate, T1) , is the permeate dew pom 3
`the
`_
`upstream of the condenser. The retentate temperature is computed from (
`—
`in
`.
`.
`..
`.
`-
`'
`‘
`fPV,
`h
`use
`Membrane selection 1S critical in the commercial .Elppl11-lCa$:.(())Il1‘:)i1iC me:/lbigne materials
`presence of organic Compounds. For water peIlI3Ii1*:i1itdOi]sLoff]en uied for the dehydration 0f
`are preferred. For example, a three-layer mem
`'
`_
`1 eS_
`ethanol with water being the main permeating species. The support layer 1S porous pop;
`1
`.’
`.
`.
`mbrane. The I13
`‘
`'
`1f
`ter, which is cast on a microporous polyacrylonitrile or polysu 0116 me
`
`tth
`
`14.7 Pervaporation 769
`
`layer, which provides the separation, is dense PVA of 0.1 pm in thickness. This composite
`combines chemical and thermal stability with adequate permeability. Hydrophobic mem-
`branes, such as silicone rubber and Teflon, are preferred when organics are the permeat-
`ing species.
`
`Commercial membrane modules for PV are almost exclusively of the plate-and-frame
`type because of the ease of using gasketing materials that are resistant to organic solvents
`and the ease of providing heat exchange for evaporation and high-temperature operation.
`However, considerable interest is evident in the use of hollow-fiber modules for the removal
`of VOCs from wastewater. Because feeds are generally clean and operation is at low
`pressure, membrane fouling and damage can be minimal, resulting in useful membrane
`lives of 2-4 years.
`
`Various models for the transport of a permeant through a membrane by pervaporation
`have been proposed, based on the solution—diffusion model. They all assume equilibrium
`between the upstream liquid and the upstream membrane surface, and between the down-
`stream vapor and the other side of the membrane. Transport through the membrane
`follows Fick’s law with a concentration gradient of the permeant in the membrane as the
`driving force. However, because of the phase change and nonideal-solution effects in the
`liquid feed, simple equations like (14-55) for dialysis and (14-32) for gas permeation do
`not apply to pervaporation.
`A particularly convenient PV model is that of Wijmans and Baker [46]. They express
`the driving force for permeation in terms of a partial vapor pressure difference. Because
`pressures on the both sides of the membrane are low, the gas phase follows the ideal gas
`law. Therefore, at the upstream membrane surface (1), permeant activity for component
`1' is expressed as
`
`a?” =f§"/f§°’ =70?"/Pf“)
`
`(14-75>
`
`where P?‘ is the vapor pressure at the feed temperature. The liquid on the upstream side
`of the membrane is generally nonideal. Thus, from Table 2.2:
`
`Combining (14-75) and (14-76):
`
`af“ : «,§‘>x§‘>
`
`pf“ = «y§‘>x§”P§<1>
`
`On the downstream vapor side of the membrane (2), the partial pressure is
`
`p 52> = y§”P§3>
`
`Thus, the driving force can be expressed as (yf1)x§1)Pf(1) - y,l2)P§,2))
`
`The corresponding permeant flux, after dropping unnecessary superscripts, is
`
`PM/,
`Ni : E ('YiXiP? ‘ MPP)
`
`N; = FA/[l_("/,'X,'I3"2. “ )/(Pp)
`
`(14-76)
`
`(14-77)
`
`(14-73)
`
`(14-79)
`
`where y, and x,» refer to the feed-side liquid, Pi is the vapor pressure at the feed-side
`temperature, y,- is the mole fraction in the permeant vapor, and P12 is the total permeant
`pressure.
`
`Unlike gas permeation where PM‘ depends mainly on the permeant, the polymer, and
`temperature, the permeability for pervaporation depends additionally on the concentrations
`of permeants in the polymer, which can be large enough to cause polymer swelling and
`
`GE-1010.008
`
`

`
`770 Chapter 14 Membrane Separations
`.
`.
`-
`-
`'
`'
`b k— lculate and correlate the
`cross-diffusion effects. For a binary system it isfbesttto ::au<1>:1e and permeate pressure.
`permeant flux with feed composition at a given ee
`emp
`~
`.
`'
`‘
`be a strong function of feed concentra-
`Because of these nonideal effects, the selectivity can
`of selectivity 111 some cases, as illustrate
`.
`tion and permeate pressure, causing inversion
`in the following example.
`_
`-
`-
`h
`t" n of liquid
`Wesslein et al. [45] present the following experimental tdateaoffogOto5 f}(3:I:a§;TI-iégte pressure
`mixtures of ethanol (1) and water (2) at 3 feed tempera “I
`of 76 mmHg using a commercial polyvinylalcohol membrane:
`
`WW” ethanol
`Feed
`Permeate
`
`Total Permeation Flux
`kgl111241
`
`38
`17.0
`26.8
`36.4
`49.0
`60.2
`68.8
`75.8
`
`10.0
`16.5
`21.5
`23.0
`22.5
`17.5
`13.0
`9.0
`
`2.48
`2.43
`2.18
`1.73
`1-46
`0-92
`0.58
`0.40
`
`l and water, respectively.
`_
`At 60°C, vapor pressures are 352 and 49 mmHg for ethano
`Liquid-phase activity coefficients at 60 C for the ethanol (1)—water (2) system are gwen
`by the van Laar equations:
`
`1n 'y1 = 1.6276[
`In 1/2 = 0.9232 [
`
`1.6276x1 + 0.9232x2
`
`0.9232x2
`1.6276x.
`
`1.6276261 + 0.92328
`
`T
`T
`
`Calculate values of permeance for water and ethanol from (14-80).
`
`SOLUTION
`
`For the first row of data the mole fractions in the feed mixture (X2) and the permeate 07)’
`.
`’
`‘
`1
`,
`using molecular weights of 46.07 and 18.02 for ethanol and water, respective y are
`
`0.088/46.07
`_
`X‘ " 0.088 + (1.0 — 0.088)
`46.06
`18.02
`
`= 0.0364
`
`x2 = 1.0 — 0.0364 ~ 0.9636
`
`_ 0.10/46.07
`V1” 0.10 + 0.90
`46.07
`18.02
`
`= 0.0416
`
`y, = 1.0 - 0.0416 = 0.9584
`
`The activity coefficients for the feed mixture are
`
`‘/1 = exp {1‘6276[1.6276(0.0364) + O.9232(0.9636)
`232
`1.6276(0.0364)
`1.6276(0.0364) + 0.9232(0.9636)
`
`12 = “P 0'9
`
`= 4_1s2
`T} _ L004
`
`Summary
`
`771
`
`From the given total mass flux, the component molar fluxes are
`
`kmol
`___ (2.48)(0.10) =
`0.00538 h _ m,
`N, ———46'07
`kmol
`_ (2.48)(0.90) _
`NZ — ———18.0Q — 0.1239h _ m,
`
`From (14-80), the permeance values are
`
`_
`
`P =
`"2
`
`kmol
`0.00538
`(4.182)(0.0364)(352) — (0.0416)(76) ‘ 0000107 h — m2 — mmHg
`kmol
`0.1239
`_ _
`__m_i_
`(2.004)(1.0 — 0.0364)(149) — (1.0 - 0.0416)(76)
`0 001739 11 — ml — mmHg
`
`Results for the other feed conditions are computed in a similar manner:
`
`wt% Ethanol
`Feed
`Permeate
`
`Activity Coefficient
`in Feed
`Ethanol
`
`Water
`
`Permeance,
`kmollh-m2-InmHg
`Ethanol
`Water
`
`8.8
`17.0
`26.8
`36.4
`49.0
`60.2
`68.8
`75.8
`
`'
`
`10.0
`16.5
`21.5
`23.0
`22.5
`17.5
`13.0
`9.0
`
`4.182
`3.489
`2.823
`2.309
`1.802
`1.477
`1.292
`1.177
`
`1.004
`1.014
`1.038
`1.077
`1.158
`1.272
`1.399
`1.539
`
`1.07 X 10‘4
`1.02 X 10"‘
`8.69 X 10’5
`6.14 X l0'5
`4.31 X 10‘5
`1.87 X 10'5
`7.93 X l0‘5
`3.47 X 106
`
`1.74 X 10”3
`1.62 X 10‘3
`1.43 X 10’3
`1.17 X 1O‘3
`1.10 X 10‘3
`8.61 X 10“‘
`6.98 X 1074
`6.75 X 10"‘
`
`The PVA membrane is hydrophilic. Thus, as the concentration of ethanol in the feed
`liquid increases, the sorption of feed liquid by the membrane decreases, resulting in a
`reduction of polymer swelling. The preceding results show that as swelling is reduced, the
`permeance of ethanol decreases more rapidly than that of water, thus increasing the
`selectivity for water. For example, the selectivity for water can be defined as
`
`at
`
`: (100 “ W1)P/(W1)P
`“ (100 — W1)p/(1411);:
`
`where wl = weight fraction of ethanol. For the cases of 8.8 and 75.8 wt% ethanol in the
`feed, the selectivities for water are, respectively,