S e p a r a t i o n o f G a s e o u s M i x t u r e s

U s i n g P o l y m e r M e m b r a n e s

WILLIAM J. KOROSDepartment of Chemical EngineeringThe University of TexasAustin, Texas

REY T. CHERNDepartment of Chemical EngineeringNorth Carolina State UniversityRaleigh, North Carolina

20.1 INTRODUCTION

20.1-1 General OverviewThe energy efficiency and simplicity of membrane separation devices make them extremely attractive forsolution of fluid-phase separation problems. The ability of ideal membrane processes to pass selectivelyone component in a mixture, while rejecting others in a continuous steady-state manner, defines the perfectseparation device. A substantial literature related to gas separation indicates, however, that numerous factorsmust be considered in achieving a commercially successful membrane-based process. Nevertheless, recentlymembranes have been shown to act as remarkably effective separating devices.112 By clever engineering,the productivities of these devices have been increased dramatically, and they are strongly competitivewith—if not superior to—more traditional chemical engineering separation approaches for several appli-cations involving gas treatment.

The historical development of membrane-based gas separation is traced briefly, and a discussion ofcurrent membrane types is presented along with a projection of requirements for the next generation ofmembrane materials. An overview of the fundamental principles governing the operation of gas separationmembranes also is presented. Finally, a review of the state of knowledge of membrane module constructionand operating configurations is presented in conjunction with a guide to the mathematical modeling of thesedevices. The coverage offered here should be useful to both the general reader interested in separationprocesses and to practicing engineers interested in understanding and evaluating membrane processes forpotential application in new situations. The present discussion does not treat the topic of liquid membranesthat have potential for gas separations, since this topic is treated in Chapter 19.

20.1-2 Historical Background

In 1831, Mitchell reported that india rubber membranes passed carbon dioxide substantially faster thanhydrogen under equivalent conditions.13 Mitchell's work marked the first known report of gas permselec-

C H A P T E R 2 0

tivity of a membrane. The understanding of mass diffusion as a process driven by a concentration gradientgave rise to Eq. (20.1-1), Fick's First Law for the diffusive flux N:14

N = -DVC (20.1-1)

where D is the diffusion coefficient, analogous to the thermal conductivity in Fourier's Law of heat con-duction, and C refers to the local penetrant concentration. For simple, one-dimensional diffusion througha flat membrane, Eq. (20.1-1) can be written as

(20.1-2)

In 1866, Graham made the next major step in understanding the permeation process.l5 He postulatedthat the permeation process in polymers involved a solution-diffusion mechanism by which the penetrantfirst was dissolved in the membrane and then transported through it by the same process as that occurringin the diffusion of liquids. He devised a membrane-testing device and demonstrated that atmospheric aircould be enriched from 21 to 41% oxygen using a natural rubber membrane. Moreover, he showed thatincreasing the thickness of a pinhole-free membrane reduces the rate of permeation of both componentsthrough the membrane, but does not affect its ability to act as a permselective separator for the twocomponents.15 Exner showed that the permeation rate of a penetrant through a soap film is proportional tothe product of the solubility and diffusivity of the penetrant in the film.16 von Wroblewski provided amathematical analysis of the process of permeation through polymer films that incorporated the observationsof these earlier workers.17 He defined a coefficient, the permeability, equal to the observed steady-stateflux divided by the driving pressure, Ap = p2 - p l t across the membrane normalized by the membranethickness /; that is,

(20.1-3)

As shown in Fig. 20.1-1, the upstream condition at x = 0 is distinguished by a subscript " 2 " and thedownstream condition at JC = / is distinguished by a subscript " 1 " in all cases in the following discussion.This convention ensures that the flux occurs in the positive x direction.

If the dissolved permeant concentration C obeys Henry's Law [Eq. (20.1-4)], there is a simple constantsolubility coefficient S relating C to the external penetrant pressure p ; that is,

(20.1-4)

Furthermore, if Fick's Law [Eq. (20.1-2)] with a constant diffusion coefficient applies to the diffusionprocess, von Wroblewski showed that the permeability P is equal to the product of the solubility anddiffusivity coefficients; that is,

FIGURE 20.1-1 Terminology and coordinate system convention for one-dimensional permeation througha membrane of thickness /.

U P S T R E A M

(Condi t ion"2" )

High Pressure

P2Flux

D O W N S T R E A M '

(Condit ion " I " ? *

Low P r e s s u r e *

Pi

(20.1-5)

An important parameter, referred to as the separation factor of the membrane for component A relative toB is defined by Eq. (20.1-6):l8

(20.1-6)

where the K1's and Y2's refer to the mole fractions of components A and B in the downstream (low-pressure)product and the upstream (high-pressure) feed streams, respectively. When the downstream pressure isnegligible compared to that upstream, one can substitute Eqs. (20.1-2) and (20.1-3) into Eq. (20.1-6) togive Eq. (20.1-7):18

(20.1-7)

The above ratio of permeabilities is referred to as the ideal separation factor and provides a useful measureof the intrinsic ability of the membrane to separate a given gas mixture of A and B into its components.

Shakespear demonstrated that the permeability of a gas is independent of the presence of other per-meating gases for rubbery polymers at low pressures.19 This result has been verified by Yi-Yan et al.20

The assumption of strict noninteraction between permeating components does not hold in general, however,for rubbery polymers at high pressures21 or for glassy polymer membranes even at relatively low penetrantpressures.22"29 While the deviations from such an assumption generally tend to be small, as low as a 15mm Hg partial pressure of water vapor has been reported to cause nearly a 60% reduction in flux of bothmembers of an H2-CH4 mixture.27 Similar but less dramatic results, in the range of 20% flux depression,also have been observed because of the presence of hydrocarbons in feed streams.22

Conversely, at higher relative humidities or partial pressures, Stern and coworkers have shown thatplasticization of rubbery polymers can produce significant increases in the permeability of mixture com-ponents.30 A recent report also suggests that methane solubility (and perhaps permeability) can be increasedowing to the presence of a second component such as carbon dioxide.31 One therefore might be surprisedto find Shakespear's observation supported in actual practice. Because of the current uncertainty in predictingthe exact magnitude of such interactive effects, however, a retreat to Shakespear's constant permeabilityassumption often is made. This issue is treated in more detail in a later section on fundamentals. Cusslerhas considered an even more subtle general situation in which coupling of the fluxes of the first componentto that of the second occurs.23 These effects, while obviously correct and significant for liquid systems,usually are neglected for gases in polymers.

Two serious limitations faced by pioneers in gas separation were the low selectivities and the ratherlow permeation fluxes observed for most membranes. The low-flux problem arose because membranes hadto be thick (at least 1 mil) to avoid pinholes, which destroyed selectivity as a result of almost indiscriminatepassage of all the feed components by Knudsen or viscous flow.

Discovery of the extraordinarily high permeability of silicone polymers (see Table 20.1-1 for compar-isons to other typical rubbery and glassy polymers) spurred a renewed interest in gas separation aimed atO2-N2 separation from air.33*34 Unfortunately, the O2-N2 selectivity of silicones is rather low. Moreover,even with silicone polymers 1 mil thick, very large membrane areas were required. Stern showed thatmembrane separations were not competitive with cryogenic processes using 1 mil silicone rubber membraneseven if the feed air was compressed considerably to reduce installed membrane cost.36

t

The development of casting techniques for ultrathin membranes comprised of 150 A silicone rubber-polycarbonate copolymers permitted formation of pinhole-free selective membranes with thicknesses ofaround 1000 A by laminating multiple layers.37 Such membranes offered flux increases of as much as 50-to 100-fold compared to their 1 mil silicone rubber counterparts. The membranes were supported typicallyin a plate-and-frame fashion on a porous substrate, so that accommodation of a large membrane area in asmall module was not feasible.

To overcome this problem, the so-called hollow-fiber and spiral-wound membrane configurations de-scribed below have been adopted in the gas separation field (as in the reverse osmosis and ultrafiltrationfields). Permeation area per unit of separator volume, for example, can be increased roughly 30-fold simplyby replacing plate-and-frame flat membranes with 200 /xm outside diameter (OD) fibers packed at a 50%void factor. The flat membrane configuration typically provides areas of about 300 ft2/ft3 of module volumeand the 200 pm diameter fibers give more than 10,000 ft2/ft3 of module volume.37 Clearly, even higherareas per unit volume can be achieved using smaller diameter fibers and higher packing densities. Studieshave been reported using low-flux polyester fibers of 36 /*m inside diameter (ID) fibers.2838 For the high-flux fiber currently in use, however, dimensions in the range of 100-600 /xm ID appear to be favored onthe basis of the information available in the open literature.39"43 Consideration of optimum fiber diameterchoice is dealt with in greater depth in the section on design case studies.

TABLE 20.1-1 Comparison of Permeabilities of Important Product Cases in Typical Rubbery andGlassy Polymers at 25°-30°C and 1 atm

Polymer Repeat Structure ^ H 2 ^CO 2 ^ O 2

Rubbery Polymers

Silicone rubber CH1 550 2700 500I

- S i - O -ICH3

Natural rubber - C H 2 - C = C H - C H 2 - 49 131 24ICH3

Polychloroprene - C H 2 - C = C H - C H - C H 2 - 20 22 4(Neoprene®) I

Cl

Glassy Polymers

Polyethyleneterephthalate)

(Mylar®) 0.6 0.10 0.03

Aromatic polyetherdiimide (Kapton®) 1.5 0.27 0.15

P o l y c a r b o n a t e 1 2 5.6 1.4(Lexan®)

* Units of permeability are Barrers. 1 Barrer = 10~10 (cm3(STP) •cmVicm^s-cm Hg).Source: Stannett et a!.35

Hollow-fiber technology as a means of producing large amounts of permeation area grew out of acoupled program dealing with gas separation, artificial kidney, and desalination work at the Dow ChemicalCompany in the 1960s.44 The first mention of hollow-fiber membranes appears to have occurred in a seriesof patents in 1966.45 The patents describe cylindrical modules with inlet feed on the side of the module asshown in Fig. 20.1-2. Small hollow-fiber bundles were sealed with an adhesive into header plates at oppositeends of the module in such a way that a large number of fibers could be included. Only the exterior of thefibers was epoxied at the two ends, so both open fiber ends communicated with the two collection chambersat the opposite ends of the module. A feed stream entering at the side moved axially down past the fiberbundles. The residual stream was removed from the exhaust port at the opposite end from the inlet port.The permeate diffused through the fiber walls and moved along the inside of the fiber bores to be removedfrom the collection chambers at the two ends of the module as shown in Fig. 20.1-2. The current Dowgas separation module undoubtedly has evolved considerably since this early design but it still is based ona hollow-fiber concept.

End Seal Unit* for Typical Small Hollow Fiber BundlesFIGURE 20.1-2 Early Dow hollow-fiber permeation device. Note that permeant is withdrawn from bothends.

A second hollow-fiber patent, issued in 1970 to the E. 1. Du Pont de Nemours & Co. for a reverseosmosis module, employed a U-shaped loop arrangement of the fiber bundle as shown in Fig. 20.1-3.**Several small changes in the design have occurred since then. Both ends of the fibers terminate in theheader plate separating the sample collection chamber from the main body of the permeator. The loopedend of the fiber bundle is held in an epoxy "deflector block/' A cylindrical flow screen confines the fiberbundle and forms an annular region between the outer shell and the sleeve for flow of rejected brine. Fluidfeed enters at the center through a perforated tube, where it then passes through numerous perforations inthe tube, and flows essentially radially outward. The nonpermeant is collected in the annular channelbetween the flow screen and flows to the brine header. Permeant diffuses through the fiber walls and istransferred down the length of the bore to the collection chamber. The crossflow effect, arising from theflow arrangement, causes movement perpendicular to the axis of the hollow fiber to minimize blocked flowpaths, thereby maximizing the use of the fiber surface. This basic module design also should be useful forgas separation applications based on high-flux membranes.

The Monsanto hollow-fiber module for gas separation appears to be a compromise between the twopreceding reverse osmosis module designs.47 As shown in Fig. 20.1-4, the hollow fibers are closed at oneend with an epoxy plug or similar device, and feed enters at the side at one end. The feed then flowsaxially along the fibers, and the nonpermeant exits at the opposite end from which the feed enters. Permeantdiffusing through the hollow-fiber wall into the bore moves countercurrently to the shell-side flow andultimately is collected in the chamber where all the open ends of the fibers terminate.

The so-called spiral-wound module currently used by Separex, Delta Engineering, and Envirogenicsdates back to 1968, when a reverse osmosis module was patented by Gulf General Atomics.48"50 Theessence of the spiral-wound concept is illustrated in Fig. 20.1-5. A sandwich consisting of a porous backingmaterial (e.g., Dacnon® felt) placed between the two halves of a folded continuous membrane is assembledwith a separator grid (e.g., polypropylene screen) on the top membrane half. The porous backing materialis wrapped around the perforated mandrel to provide an easy pathway for gas to the mandrel holes. Thenthe sandwich is sealed along its edges with a suitable epoxy at three sides. The fourth side terminates atthe central perforated mandrel. Finally, the assembly is wound spirally and loaded into a suitable cylindricalchamber such as that shown in Fig. 20.1-5. A feed stream enters at one end and moves through thepassageways provided by the polypropylene grid separator. The nonpermeant then exits at the opposite endof the module from where it entered. In the separator, permeant diffuses across the two membranes in thespirally wound sandwich and flows in the porous backing material inwardly toward the open end of thesandwich terminating at the perforated mandrel. The permeant then accumulates in the central collectiontube and is delivered as product. As a means of incorporating more area in a compact volume, multileavedcartridges can be used without requiring excessively long flow paths of permeant to the collection tube.51

Small FiberBundle N

Open Ends of Fibersto Permeant HeaderChamber

O v e r a l l V i e wPermeant

PermeantHeader Chamber

Permeant

Small Bundles ofHollow Fibers-^

PemeontHeaderChamber-

Feed

FIGURE 20.1-4 Sketch of Monsanto's Prism® hollow-fiber separator module.

Permeant gas outlet

Feed streamof mixed gases

Separators are 4" to 8" indiameter by 10' to 20' long

Hollow fibers

Fiber bundle plug

Non-permeant gas outlet

FIGURE 20.1-3 Sketch of a Permasep® hollow-fiber reverse osmosis module. Courtesy of E. I. Du PontCo.

Permeant

Non Permeontto CollectionChamber

Epoxy Tube Sheet

Flow ^Screen -

EpoxyDetectorBlock —

PorousSupportBlock

End Plate(Permeant)

End Plate(Feed) —

-HollowFibers-

O-Ring

Feed

NonPermeont

O-Ring Non PermeantCollectionChamber

•Feed Tube

Single Leaf Spiral Multileaf

Element Layout Element

FIGURE 20.1-5 Spiral-wound elements and assembly. The use of multileaf element avoids long pathwaysfor permeant through the porous backing material to minimize pressure buildup in the permeant channel.

20.1-3 Asymmetric Membranes

The development of asymmetric membranes marked another breakthrough in the drive to increase moduleproductivity. These membranes permitted the formulation of dry, nearly pore-free membranes with selectivelayers that were only 1000 A, rather than 1 mil, thereby increasing flux by a factor of more than 200.Coupling the higher permeation area density with the much smaller membrane resistances gives the pos-sibility of flux densities that are on the order of 10,000 times higher than those available in the early daysof gas separation in the 1960s,

Typical asymmetric membrane morphologies are shown schematically in Fig. 20.1-6. The dense skinon the outside of the membrane is supported by the porous substructure. The same general form can beobtained for flat and hollow-fiber asymmetric membranes. Although the technology of producing asym-metric structures is reasonably well developed, there is still considerable discussion about the detailedfundamental processes involved. The work of Loeb, Sourirajan, Resting, Strathmann, Cabasso, Smolders,and others has been important in establishing and interpreting protocols for the formation of asymmetricmembranes.52"62

Generally, it is agreed that two fundamentally different mechanisms of phase separation can occur, asshown in Fig. 20.1-7. The so-called binodal regions in the two-phase envelope mark metastable regimesin which a single phase can exist until a nucleus (homogeneous or heterogeneous) presents itself andinitiates a precipitation process.59 This process is similar in many respects to classical crystallization from

Membrane

Separator- Membrane

Porous Backing NonpermeantProduct

FeedNonpermeant

Feed

Permeant

Feed GasPermeant GasProduct

S p i r a l - w o u n d E lements and Assembly

Perforated Collection TubeEpoxy EdgeSeal-*)

Seporotor Grid.>-Epoxy Edge

Seal-MembranePorous Backing

^Membrane

Wrap

Thin MOOOA)Dense Skin —

Porous Support

^ ^ Porous Inside SkinFlat Film

Hollow FiberFIGURE 20.1-6 Schematic representation of an asymmetric membrane in flat-film and hollow-fiber form.The dark regions signify polymeric domains and the white regions signify nonpolymer-containing voidregions. The designations (a), (fc), and (c) refer to the regions shown in Fig. 20.1-7.

solution. The second regime is characterized by absolute instability, and systems lying in this so-calledspinodal region undergo spontaneous phase separation without the need for the presence of a nucleus. Theprocess is termed spinodal decomposition.63 The different properties of the two regimes are summarizedbelow based on the current literature.

Two types of membrane morphology can be envisioned to arise from phase separation due to nucleationbehavior [regions (a) and (b) in Fig. 20.1-7]. In some cases, precipitation conditions will create a localeffective concentration at a point in the coalescing membrane that falls in region (a) in Fig. 20.1-7. Thissituation produces a concentrated polymer solution, nucleating and growing as the dispersed phase in thislocal region of the developing membrane. In such cases, a latexlike suspension of polymer spheroids willform.59*64 Upon further coalescence, the spherical structures will tend to meld, leaving interstitial poresbetween the basically spherical structures such as those shown in Fig. 20.1 -6a. In such a case, the denseskin presumably corresponds to a more coalesced form of these small particles resulting from their moreintense contact with the external coagulating nonsolvent bath due to the absence of difftisional limitationsat the outside surface. Hoehn and coworkers suggest that the morphology in such cases may not in factcomprise a simple, well-defined surface skin supported by a highly open porous substructure. Instead, itis possible that a steady gradation exists with an open-cell support structure yielding gradually to anessentially pore-free surface region.64

On the contrary, in the second binodal region (b) in Fig. 20.1-7, where the local mixing point findsthe polymer-rich solution as the continuous phase, dispersed spheroids of nearly polymer-free fluid arenucleated. These domains then coalesce to produce a foam structure whose walls are composed of thesolidified dispersed polymer phase. To obtain an open-cell foam with low resistance to flow, defects clearlymust occur in the walls of the cells.59 Such a structure is shown in Fig. 20.1-66. The dense film on thesurface can be promoted by a brief exposure of the cast or spun nascent membrane to air to obtain a moreconcentrated region at the surface prior to immersion in the nonsolvent precipitation bath, which then setsthe dense layer in place and proceeds to nucleate the substructure as described above. This evaporationstep, however, is not required in all cases to produce acceptable skins.56'65'66

The third regime of precipitation occurs in the central area (c) of Fig. 20.1-7 and is more difficult toachieve. The tendency for nucleation and growth mechanisms to occur while one is attempting to establisha local mixing point in the spinodal region by diffusive exchange of solvent and nonsolvent is a practicalproblem that must be acknowledged.59 Nevertheless, it has been suggested that such processes can produceexcellent uniformity, highly open-cell foam support structures, which are the most suitable of the threeshown (see Fig. 20.1-6c) for asymmetric membranes.59*65

( a ) ( b ) ( O

( F i l m or F i b e r ) ( F i l m or F i b e r ) ( Fi lm or F iber )

50-IOOfitypicol

SOLVENT NON SOLVENTFIGURE 20.1-7 Ternary-phase diagram between polymer, solvent, and nonsolvent. The three regions (a),(fc), and (c) refer to the two-phase regimes for which precipitation of polymer occurs with the potential formembrane formation. If the local concentration conditions at a point in a precipitating membrane correspondto one of these domains, the resultant local morphology in the membrane at that point will resemble sketches(a), (b), or (c) in Fig. 20.1-6, respectively.

Whichever membrane morphology is desired, it is clear that the science of how to achieve the mor-phology trails the technology in the field. As a result, methodical trial-and-error optimization of solvent,nonsolvent, special additives, and spin dope conditions must be performed to produce desirable membranemorphology. Actual asymmetric membrane structures tend not to have all one type or the other of themorphologies shown in Fig. 20.1-6. Instead, depending on the conditions persisting at each point in themembrane at the instant when precipitation occurs, a complex graded structure with aspects of all the formsshown in Fig. 20.1-6 may be observed. Posttreatments by heating can help heal large pores in some cases,but the ideal situation is clearly to produce, by means of manipulation of spinning conditions, an open-cellsupport structure with an essentially pore-free skin.67 The use of selected additives such aspoly(vinylpyrrolidone) in the case of polysulfone spinning was found to be useful in producing good fiberskins by causing subtle alterations in the spin dope viscosity and phase relationship between polysulfoneand the solvent DMF.68

20.1-4 Actual Membrane Properties

The words * 'essentially pore free*' are extremely restrictive. Pores of even 10-50 A present at an areafraction of even 10 ppm can destroy the permselectivity of a membrane which must discriminate gasmolecules with characteristic dimensions of 3-5 A. A significant advance in technology occurred whenMonsanto introduced a process to posttreat asymmetric fibers with a minuscule amount of highly permeable"stop leak" material such as silicone rubber. This treatment eliminates most of the Knudsen and viscouscontributions to flow through the membrane and produces a high-flux membrane with selectivity approachingthat of true dense films.69 As demonstrated in the Monsanto patent on this matter, however, the coatingappears to be less than perfect, since dense-film selectivities typically are not achieved but may be ap-proached quite closely. Data from applications of this approach are shown in Table 20.1-2 for coated anduncoated fibers.70

A simple analysis, known as the resistance model, has been suggested as a framework for interpretingthe various flux-reducing impedances that gas molecules encounter in moving across a composite asym-metric membrane.69 The treatment is couched in terms of an electrical resistance analogue. The seriesresistances to flow arising from permeation through the elastomeric coating, permeation through the effectivedense selective layer, and ultimately through the open-cell foam support are taken into account. Whilehighly idealized, the model is useful for semiquantitative analysis of such composite membranes. A practicaldifficulty in application of this approach lies in a priori assignment of the effective layer thicknesses of theelastomeric and dense selective resistances. The Monsanto composite-membrane approach is marketedcommercially under the name Prism®, using an asymmetric polysulfone membrane treated with siliconerubber. The modules have proved effective and reliable in both H2 and CO2 separation applications.2*7

Cellulose acetate and modified cellulose acetates of various degrees of acetylation comprise a second

POLYMER

(C)SpinodolRegime

Regime with Polymer\as Dispersed Phase1—— -——^__^_

/One W/Phase V

'CRITICAL^POINT

M b ) \/ / Binodal \'/Regime with/Solution as .,'Dispersed/^PhaseyS

TABLE 20.1-2 Extent of Achievement of Dense-Film Ideal Separation Factors Using Coated High-Flux Asymmetric Polysulfone Fibers

Ideal Separation Factor

Membrane Type POJPHI PHJPCO

Dense 6 40Coated asymmetric 4.1 31Achievement of dense film

separation factor using coatedasymmetric film 68% 78%

Source: Henis and Tripodi.70

major commercial polymer used by a number of companies in the field. Dow, Separex, Delta Engineering,and Envirogenics are involved in either hollow-fiber (Dow) or spiral-wound module approaches (Separex,Delta, and Envirogenics) to membrane packaging using these polymers.4"6'71 Little detailed information isavailable concerning the performance of cellulose acetate (CA) and cellulose acetate-cellulose triacetate(CTA) blends in actual gas separation applications, but it appears to be roughly equivalent to polysulfoneon the basis of the available literature.9" Recent reports suggest a greater tendency toward plasticizationof cellulose acetate materials by CO2 than for polysulfone under equivalent temperature and CO2 partialpressure conditions.71 The detailed membrane formation and posttreatments for CA are proprietary. It isbelieved, however, that the posttreatments are similar to those employed by Gantzel and Merten72 andLonsdale.73 Gantzel and Merten used surfactants to reduce the interfacial tension between the pore wallsof the membrane and the water in the pores to permit evaporation of the water from the wet membranewithout having the pores collapse. Stage wise solvent exchange to alter gradually the interfacial tensionenvironment in the pores was used by Gantzel and Merten to produce a cellulose acetate membrane witha good ability to separate nitrogen and hydrogen at high flux rates of hydrogen.72*73

Du Pont, a leader in reverse osmosis technology built around a unique class of tailored aromaticpolyamides, was also an early leader in the gas separation field.27'28-7475 Molecularly engineered aromaticpolyimides were found by Du Pont to provide extraordinarily good flux and selectivity properties forhydrogen separations.27 Posttreatment processes for these membranes were not reported.

Many other national and international companies, some with extensive expertise in liquid separationsas well as others with primarily chemical and petrochemical histories, are either closely monitoring thefield or actively engaged in research aimed at tapping its exciting potential for growth. An interestingalternative approach to membrane formation has been the basis for reverse osmosis membranes marketedby Film Tech, UOP, and Albany International. These composite membranes are essentially the mirrorimages of the Monsanto composites.

In these alternative cases the membrane support is highly porous, and a thin, selective coating is formedon the porous support by interfacial polymerization.35*73'76 The patented interfacial polymerizationprocess involves the three steps illustrated in Fig. 20.1-8: (1) imbibing a low-molecular-weight prepolymeror a monomer of type A (e.g., trimesyl chloride) into the pores of a highly porous membrane support suchas polysulfone, (2) contacting only the outer film surface with monomer B (e.g., piperazine or an aromaticdiamine), and (3) follow with a final heat-curing step. As the thin layer of dense, high-polymer film (— 500-2500 A) forms, it restricts further invasion of monomer B, thereby limiting the coating thickness. Thetechnique tends to guarantee a pore-free membrane, because monomer B is convected through any poresand reacts with monomer A to seal the orifice. As noted above, this approach is the reverse of the Monsanto*4stop leak** technique since the coating in the interfacial polymerized case forms the actual separatinglayer, and the highly porous sublayer acts simply as a support.

The interfacial polymerization approach is clearly attractive, since a selective coating can be formedfrom a wide range of monomers displaying a tremendous spectrum of physical and chemical properties.Currently, no commercial gas separation membranes are available that use this technique. The durabilityof such composite membranes is reported to be quite good in reverse osmosis applications where they firstwere developed.77 Applications in gas separation service involve rather moderate sorption levels, so swellingstresses likely to dislodge such coatings should be low; however, in high-pressure CO2 service, somedifficulties may be encountered. Nevertheless, this interesting approach is likely to see more emphasis inthe future.

Membrane processes, like other unit operations, should be approached with a systematic design pro-cedure supported by a solid data base. Because of their novelty, the data base for membrane processes isstill much smaller than that for corresponding older unit operations such as distillation. The current lackof information often necessitates the estimation and use of constant values for component permeabilitiesalthough these coefficients are known to be functions of pressure and gas composition in many cases.28*29

Completed Thin FilmComposite Structure

FIGURE 20.1-8 Schematic representation of thin-film composite-type films pioneered by Cadotte forreverse osmosis application. Typical monomers might include for A, mesyl chloride; for B, piperazine or1,4 phenyldiamine.

As information and working experience with gas separation membranes broaden, analysis undoubtedly willmature also. The incorporation of pressure and composition dependency of permeabilities in permeatormodeling is somewhat analogous to the refinements achieved through the use of activity coefficients intraditional vapor-liquid and liquid-liquid operations. These effects can be treated either "phenomenolog-ically" (i.e., empirically), or more fundamentally in terms of physical explanations for the nonideality.

Perhaps the most important by-product benefit from fundamental understanding of the processes in-volved in membrane systems lies in the area of new membrane development. Analogous to solvent selectionin absorption and extraction processes, membrane selection lies at the heart of permselection processes.Therefore, discussions of the forms and interpretations of sorption, diffusion, and permeability coefficientsare offered in subsequent sections. First, however, to demonstrate the importance of these sections, anoverview of general design procedures and applications is given. The final topic to be discussed involvesthe detailed engineering and mathematical analysis required to arrive at an actual module design. Theimmediately following general overview section also provides a somewhat qualitative preview of thisinvolved topic.

20.2 GENERAL DESIGN PROCEDURES AND APPLICATION EXAMPLES

20.2-1 Procedures

The following phases of the design process typically are observed in the development of a suitable mem-brane-based gas separation system. The general elements are similar to those for other more traditionalseparation processes.

1. Prepare Flow Diagrams. A preliminary schematic of the proposed process option being consideredis prepared. As many variables as possible are specified on the diagram (temperatures, pressures, flows,etc.). Required outlet purities and key component recoveries are used to establish material balance con-straints where possible.

2. Acquire Basic Data. Because of the novelty of membrane-based gas separations, a scarcity ofimportant design data often is encountered. Some tabulations do exist, for example, Table 20.1-1 andTables 20.4-1 and 20.4-2, which are discussed later. In addition, membrane manufacturers can be of helpfor common systems. If one is considering unusual systems or novel membranes, some experimentaldetermination of permeabilities is likely to be necessary. Procedures and equipment for such measurementsare described in later sections.

3. Perform Detailed Design Calculations. This subject has been dealt with in varying degrees ofcomplexity by several authors. The first treatment of the problem was by Weller and Steiner in 1950.' A

Allow Monomer

or Polymer Ato sorb into

pores and coversur face

(1)Cross section of highly

porous sur face ofMembrane

Expose Membraneto Monomer B to

Crossl ink A ,thereby fo rming a

Sel f - l im i t ing Thin Film

(2)

(3)Heat to

complete cure

and rinse toremove excess

Unreacted A

ThinF i lm

s t a g e c u tFIGURE 20.2-1 Effect of flow pattern on degree of separation achievable in a single permeation stage.2

The figure refers to the separation of a mixture of 20.9 mol % O2 and 79.1 mol % N2 and shows theoxygen concentration (in mole fraction) in the permeated and unpermeated streams leaving the stage as afunction of stage-cut. Conditions: p2 = 380 cm Hg; px = 76 cm Hg; <x* = 5; r = 5; P02 - 5 x 1 0~8

[cm3 (STP) • cm]/cm3 • s • cm Hg). A: Countercument flow with no mixing. B: Crossflow with no mixing.C: Cocurrent flow with no mixing. D: Perfect mixing on both sides of membrane.

simple case dealt with by these authors assumes that both the permeant and the nonpermeant streams arewell mixed and a negligible recovery of feed occurs. Clearly, for practical modern modules, this assumptionis not valid; nevertheless, one can use the convenient results for this case even in real separators underconditions of low permeant recovery, since compositional changes are small in these cases.

Equation (20.2-1) is the expression for y,A, the permeant mole fraction of the fast gas (A) in an A-Bbinary mixture when the total upstream pressure is p2 and the downstream pressure is p,:

(20.2-1)

where \fr equals (aJB - \)(p2/p\) Y2A + (P2Zp1) + (aJB - 1), and a*B equals the ratio of permeabilitiesof component A to component B discussed in Eq. (20.1-7). The parameter Y2A, defined in Eq. (20.1-6),corresponds to the upstream (feed) gas mole fraction. Equation 20.2-1 shows the dependence of permeantcomposition on the ratio of upstream to downstream pressure. The assumption of perfect mixing can leadto substantial errors for higher product recoveries, which are typically of practical interest. More detailedtreatments of module operation require consideration of a variety of permeant-nonpermeant flow patterns.As an example, the effects of crossflow, countercument, and cocurrent operation are shown in Fig.20.2-1 for the O2-N2 separation using a hypothetical membrane with C*S2/N2

eQual to 5.2 The ratio ofupstream to downstream pressure is also equal to 5 in this example, which illustrates the substantialdifference in behavior at high stage-cut between the various modes of operation. The stage-cut is simplythe fraction of the feed that is collected as permeant.

4. Modify Preliminary Flow Diagrams. On the basis of the results of the single-module process, itmay be found that target product compositions and recoveries cannot be achieved without recycle strategies.

permeant

Vo2 i n

nonpermeant

A considerable literature exists dealing with the potential benefits and energy requirements associated withthese approaches. These techniques typically are applied in cases where high recoveries are desired. There-fore, the use of Eq. (20.2-1) to establish compositions for material balances is compromised somewhat,and rather tedious calculations are required. Examples of the applications of these techniques are summa-rized in the section entitled "Modeling and Design Considerations."

5. Perform Economic Evaluation of Chosen Designs. This part of the project is the same as for anyother separation operation. After all flows, compositions, and equipment ratings are known, capital, energy,and other operating costs can be assessed by a standard formula.

20.2-2 Application Examples

Applications of membrane-based gas separation technology tend to fall into three major categories:

1. Hydrogen separation from a wide variety of slower permeating supercritical components such asCO, CH4, and N2.3'7

2. Acid gas (CO2 and H2S) and water separations from natural gas.3"5*8"15

3. Oxygen or nitrogen enrichment of air. l5~17

The order of the various types of applications given above provides a qualitative ranking of the relativeease of performing the three types of separation. The extraordinarily small molecular size of H2 makes itextremely permeable and easily collected as a permeant compared to the other more bulky gases.18 Perhapssurprisingly, it is difficult to separate H2 from CO2 and H2S, although these latter gases are clearly muchlarger.

This observation can be understood from consideration of Eq. (20.1-5). Although H2 has a high dif-fusivity, because of its low condensibility, it has a very low solubility in membranes.19'20 Therefore, amore soluble, lower diffusivity gas such as CO2 may have a steady-state permeability comparable to thatof H2, since the product of solubility and diffusivity determines the permeability of a component throughthe membrane. The reasonably high solubilities of CO2, H2S, and H2O in membranes at low partialpressures, coupled with the relatively low solubility and diffusivity of the bulky methane molecule, havemade possible the second type of separations. The primary difficulties one encounters in this class ofsystems arise from possible loss in permselectivity of the dense selective layer and compaction of the open-cell support structure shown in Fig. 20.1-6 at high pressures due to plasticization by the permeatingcomponent.

By far, the most difficult of the three types of separation shown is the last one, involving O2 and N2.The potential market for O2-enriched air for medical and furnace applications is considerable. Moreover,N2-enriched air for blanketing of fuels and stored foods to provide nontoxic, nonresidual protection fromfire and oxygen-breathing pests is an interesting possibility. Unfortunately, currently available polymermembranes have only moderate selectivities to separate oxygen and nitrogen.21 One can understand thissituation by considering again Eq. (20.1-5). The size and shape (and hence difftisivity) of O2 and N2 arequite similar; moreover, the solubility of the pair in most membranes is similar. Since the factors enteringinto Eq. (20.1-5) are similar for the two components, the ratio of the permeabilities of the two componentstends to be similar, and hence the ideal separation factor [Eq. (20.1-7)] is low. Nevertheless, due to theimportance of the problem, processes have been designed that are able to produce economical supplies ofO2- and N2-enriched air for commercial applications. Recently, Monsanto announced plans to use theirPrism® modules, based on polysulfone hollow fibers, to provide N2 as a blanketing agent for fuels in tankershipments.17 Examples of all three of the above types of membrane application are reviewed in the followingsections.

HYDROGEN SEPARATION

The following discussion reviews an actual case involving an H2 recovery permeation unit in an operating100 x 106 gal/y low-pressure methanol plant owned by Monsanto at Texas City, Texas.6 The examplereemphasizes the fact that H2 and CO2 are not separated easily. In this particular case, however, the relativeinseparability of the pair turns out to be an advantage since both components must be split from N2 in apurge stream for recycle to the synthesis gas reactor as shown in Fig. 20.2-2. The methanol synthesis loopis based on reactions (I) and (II), which upon combination yield reaction (III), indicating a stoichiometricratio of three parts hydrogen to one part carbon dioxide entering the reactor loop:

Synthesis CO + 2H2 = MeOH (I)

Water gas shift CO2 + H2 ^ CO + H2O (II)

Combined CO2 + 3H2 = MeOH 4- H2O (III)

The detailed separator flow diagram with process conditions indicated is shown in Fig. 20.2-3. The

CO2 toSynloop

SyngosCompressors

MethonolReactor

ReformedGas

Synthesis LoopRecycle Stream Syngas

interchanger

Coo

Nonpermeontto Fuel Header

HeaterCoolingTowerCondenser

Prism Separators

MethanolScrubber

Methanol CrudeSeparatf Coo

Aqueous Methanolto DistillationCrude Methanolto Distillation

FIGURE 20.2-2 Schematic representation of oxo-alcohol process showing the two banks of 8 in. diameter,10 ft long Prism* separators.7

Nonpermeont Gas'to Fuel Header

Prism SeparatorsSteamHeater

Purge Gas

MethanolScrubber

Flow = 2700 SCFMPressure= 676psig

Hydrogen Permeantto Synloop

Flow = 1450 SCFMPressure = 380 psig

Aqueous Methanolto Distillation

FIGURE 20.2-3 Detailed flow, pressure, and composition diagram for the Prism® separator system shownin Fig. 20.2-2.7

0.6 GPMSCRUBBER

PUMP

ScrubbingWoter

Flow =4150 SCFMPressure = 682 psig

separator train involves two parallel banks of four 10 ft long, 8 in. diameter modules arranged in series.The modules contain polysulfone fibers coated with silicone rubber to prevent leaks. Although specificinformation about the 8 in. diameter modules is proprietary, if one assumes a standard 200 pm OD fiberand a 50% packing factor, roughly 80,000 ft2 of total membrane area can be estimated to be present in thecompact separator train to treat the feed gas required for the process.

Approximately 200 ppm residual methanol leaves the scrubber and enters the separator train. As indi-cated in Fig. 20.2-3, the major feed components consist of H2, CO2, CO, CH4, and N2 with a saturatedvapor pressure of water pesent from the scrubbing operation. The stream is preheated prior to entering theseparator train to prevent depression of the product gas permeation rate. This preheating prevents compli-cations arising from water condensation and other more subtle permeation effects discussed later in thefundamentals section. Then the feed is split and fed in parallel to the series of separators shown in Fig.20.2-3.

The permeant gas, consisting largely of H2 and CO2 for reasons noted earlier, is sent back to thesynthesis reactor, while the nonpermeant gas continues through the series of permeators. The permeantfrom each permeator is recycled to the synthesis reactor, and the nonpermeant from the last separator issent to the fuel header to be burned. As shown in Fig. 20.2-3, for a feed-side pressure of 682 psig and abore-side pressure of 380 psig, the purge gas is reconstituted to almost 80% H2 and depleted somewhat inCO2 because the permeabilities of H2 and CO2 are not identical.

The separators are reported to recover approximately half of the available H2 and CO2, which previouslyhad been sent to the ruet header. Reportedly, an impressive net 2.4% increased production rate of methanolcan be achieved based simply on elimination of this raw material waste. As noted by the Monsanto authors,the slightly slower permeation rate of CO2 relative to H2 requires the addition of a small amount of CO2

to the recycle stream to maintain the 3-to-l stoichiometry OfH2 to CO2 required by reaction (III). Accountingfor this supplement CO2 and a small debit for the fact that the entire purge stream can no longer providefuel value, an estimate of the net advantage of the permeator installation was reached by the Monsantoengineers. Even with the above debits, the permeator installation permitted a 13% reduction in incrementalcosts to produce each additional gallon of methanol from the purge stream components that had been burnedpreviously.

ENHANCED OIL RECOVERY, CARBON DIOXIDE RECLAMATIONEnhanced oil recovery (EOR) operations often involve injection of high-pressure (2000 psia) CO2 into areservoir. Subsequent removal of CO2 occurs along with oil and light gases (primarily methane) from wellsdrilled at a distance from the primary injection point (see Fig. 20.2-4). As shown in Fig. 20.2-5, takenfrom a recent experimental and modeling study by researchers at Shell, cooling of the gas streams passingthrough a separator occurs due to a Joule-Thompson-like effect.12 The 25°F drop in temperature resultswhen the nonideal CO2 is reduced in pressure as it permeates across the membrane. Removal of a substantialfraction of the CO2 also tends to increase the mole fraction of condensable components in the residual gas.This effect, producing a dew point above the operating temperature of the module, will cause undesirablecondensation of hydrocarbons if precautions are not taken. Preheating the feed is an adequate precaution

MembroneUnit

CH4 to User

Compressor Conditioning Units forH2S, H2O, Heovy Hydrocarbons

Removal

CO2,H2S, H2Oand Hydrocarbons

CrudeOil

TCO2 Injection

•; . . O I L v • •

. RESERVOIRV.

FIGURE 20.2-4 Schematic representation of enhanced oil recovery application of membranes forCO2-CH4 separation from gas recovery from a production well after injection of CO2.

DEW TEMP

FIGURE 20.2-5 Representation of the temperature and dew point change resulting from permseparationof a typical enhanced oil recovery gas which contains heavier hydrocarbons in addition to CH4.12

for streams containing low levels of heavier hydrocarbons; however, a condensation step shown in Fig.20.2-4 may be required in conjunction with preheating to mitigate this problem. Dehydration of the streamswith a glycol pretreatment step is sometimes used prior to the membrane unit.8

The gaseous products can be separated into a CO2-rich stream (95% CO2) used for reinjection and aCH4-HCh stream (98.5% CH4) used for pipeline gas. Alternatively, the stream can be conditioned to only90% CH4 and used as a field fuel. The study by researchers at Shell cited above considers the merits ofmembrane technology for these applications relative to other competitive technologies such as physical andchemical solvent scrubbing and cryogenic treatment.9 The Shell study was based on the permeability andselectivity properties of commercial asymmetric cellulose acetate membranes. The permeability and selec-tivity properties of the membranes were assumed to be independent of gas feed pressure and compositionas a first approximation. Considerable evidence indicates that at high CO2 partial pressures, this assumptionmay break down for pure CO2 feeds due to plasticization effects noted earlier in the background section.It has been reported, however, that the plasticization effects appear to be less severe in actual mixed-gassituations in the presence of substantial methane partial pressures.12

In view of the ambiguity of published data on this topic, the neglect of the plasticization effect by theShell group seems reasonable at the present time. The behaviors of polysulfone and cellulose acetate (inthe absence of the ill-defined plasticization issue) are similar to a first approximation. Therefore, the resultsof the study are reasonably representative of both types of existing membrane system. The study permitsinsights into the strengths and weaknesses of the current generation of membranes compared to chemicaland physical solvent treatment systems for these gas purification applications. The detailed feed and productconditions considered by Youn et al.12 are summarized in Tables 20.2-1 and 20.2-2. In addition, the processflow sheets for the membrane units are shown in Fig. 20.2-6. The flow diagram for case 4 is essentiallythe same as for case 2 except that the feed pressure is much lower, thereby necessitating more membranearea in case 4.

Cost data used by the Shell group are reported in Table 20.2-3. The data apply to the 1982-1983period. Clearly, some of the numbers are dependent on the module type employed; however, the valuesare generally adequate for illustrative purposes. This study indicates operating regimes in which membranesare clearly superior to other technologies. It also identifies regimes where membranes have problemscompeting with traditional technology due to insufficient selectivity and permeability of current membranematerials. This factor clearly emphasizes the need for the continued development of membrane materials.A point related to the costs of membrane area given below should be made. The prices in Table 20.2-3apply primarily to spiral-wound units, and even then may be a bit high. For more compact hollow-fibermodule configurations in which less steel shell and flanging are required to accommodate the same amountof membrane area, the indicated prices per square foot of membrane area may be somewhat high. Obviously,lower specific costs for new and replacement membrane areas will make the conclusions of the study insome cases even more decisive in favor of membranes. Moreover, it could swing the balance more in favorof membrane processes in other cases in Table 20.2-3.

A computer model of a spiral-wound permeator similar to the Separex design shown in Fig. 20.2-6was developed by the Shell group to predict performance of the module. Field tests of actual modules werefound to agree well with simulation results for conditions where concentration polarization and nonidealflow problems were not encountered. For commercially important flow rates, these conditions were foundto be always well satisfied, and the model performed well for all flow rates above 1000 SCFH to the 8 in.diameter spiral-wound modules containing about 1200 ft2 of area. A basis of 30 x 106 SCFD of feed gaswas taken in all the evaluations, and the system performances were reported on the basis of $/103 SCF oftreated feed gas. Credit was taken for heavy hydrocarbons that are retained in the residual gas by membraneprocesses and that typically are lost along with the CO2 in physical solvent systems. This benefit can besubstantial in some cases for these valuable components.

PERMEANT* CO2 95%

RESIDUAL 6ASMOLE FRACTION LIQ 0.1

GASEOUSFEED

TABLE 20.2-1 Description of Case Studies Considered in SHELL Evaluations

Case Number Description of Pertinent Variables

1 Feed gas containing 70% (molar) CO2/30% CH4 and other light hydrocarbonsat 900 psig

Product gases containing less than 1.5% CO2 (molar) at 850 psig as anonpermeant and a permeant of 95 % CO2 recompressed to 2000 psia suitablefor reinjection as a flood gas

2 Same feed conditions and permeant conditions as in case 1Nonpermeant stream may contain up to 10% CO2 and will be used directly as a

Meld fuel

3 Feed gas is 5% CO2 at 900 psigProduct gas contains less than 1.5% CO2 at 874 psia as a nonpermeant and the

low-pressure, CO2-rich stream is vented to a field heater

4 Feed gas containing 70% CO2 at 65 psiaProduct gases containing up to 10% CO2 at 50 psia as a nonpermeant to be

used directly as a field fuel with a permeant of 95 % CO2 at atmosphericpressure and subsequently compressed to 2000 psia; suitable for reinjectionas a flood gas

5 Same product stream property requirements as in case 4; however, the feed gascontains 30% CO2 at 65 psia

Although the details of the physical and chemical solvent systems were not published, it is likely thatthe physical solvent system was modeled after a material like N-methyl-2-pyrrolidone and the chemicalsolvent was modeled after the characteristics of tertiary amines.

The results of the study are presented in Table 20.2-4. The conclusions of the Shell researchers were:

The membrane processes are competitive for separation of gases containing high CO2 concentrationsinto residual gases containing substantial CO2, say 10% volume. Membrane processes appear tohave a greater sensitivity to the CO2 partial pressure ratio (inlet CO2 partial pressure/nonpermeantpartial pressure) compared to physical solvent processes. However, further optimization of themembrane processes would reduce this difference. Membrane processes are not competitive withthe chemical solvent processes for gases with low CO2 concentrations. This shows that the membraneapplications for CO2 recovery from flue gases are not viable with today's technology.

Clearly, more selective membranes with higher permeabilities could alter the last conclusion as the activeresearch programs in this area yield second-generation materials superior to cellulose acetate and polysul-fone. Applications in which membranes are used as "topping units" for high-CO2-content streams areextremely attractive even with current membrane materials. Another useful discussion of EOR applicationsof membranes has been presented by Schendel et al.8 These authors make comparisons with the Ryan-Holmes low-temperature distillation process. They found slight cost advantages associated with the mem-brane approach. More significant, however, was the important operating flexibility of membrane systems.They noted the following:

The real advantage with membrane use is flexibility and modular design. A reliable forecast ofultimate gas production is not required, and will not significantly affect the economics of the plant.With a pure distillation scheme, a plant must be built to accommodate forecasted gas production.If the plant is oversized, this will result in extra capital being spent for unused capacity; if the plantis undersized, inability to process gas may limit oil production.

Because of extremes in gas volume processed (turn-down ratio), the design basis in this caserepresents only half the anticipated peak volume. A second distillation plant will be required. Withmembranes, however, additional membrane capacity at the front end can be added as needed withoutadditional equipment required in the distillation section. Analyses of several associated gas forecastsindicate the exit gas from the first stage of membranes to be remarkably stable in composition andflow rate. This flexibility is not shown in a single case economic comparison.8

OXYGEN-NITROGEN SEPARATIONS

Significant advantages in burner efficiency in high-temperature flame applications are realized from evenmoderate increases in O2/N2 ratios. Surprisingly, this market and a corresponding one in N2-enriched air

TABLE 20.2-2 Detailed Feed and Product Stream Variables in SHELL Case Study Evaluations

End UseMole PercentPressure (psia)

PemneantNonpermeantPermeantNonpermeantCO2 FeedPermeantNonpermeantFeed (psia)Case Number

CO2 FloodCO2 FloodVentCO2 FloodCO2 Flood

PipelineField fuelPipelineField fuelField fuel

9595409595

1.510

1.51010

70705

7030

20002000

1520002000

8508408755050

900900900

6565

12345

-X- Cose 4 is similor to Cose 2 except the feed pressure is50 psig in Cose 4, so more membrane oreo is required.

FIGURE 20.2-6 System configurations used in Shell case studies of membrane applications in CO2-CH4

recovery.12

TABLE 20.2-3 Cost Data Used in SHELL Evaluation

Capital Costs to Include

1. Processing facilities2. Compressors (gas engine drivers)3. Initial membrane (or solvent charge for solvent stripping alternatives)4. Off-site facilities (roads, etc.)

Major Component Costs

1. Compressors(a) $1400/hp installed with intercoolers and separators(b) Overall fuel usage 10 SCF/hph

2. Membranes(a) $35/ft2 installed(b) $15/ft2 replacement cost(c) 3-year life expectancy anticipated

Operating Costs to Include

1. Capital charge: 25% per year

2. Fixed operating cost: 10% of capital per year

Utility and Product Schedules

1. Fuel gas: $5/106 Btu2. Electrical power: $0.07/kWh3. Carbon dioxide: $0.05/1O3 SCF uncompressed

Case 1

Cose 2

Cose 3

Case 4

• Vent

Case 5

TABLE 20.2-4 Summary of Results for SHELL Case Study

Treatment Cost($/103 SCFf

Compression(brake hp)

Capital Cost$ x 106Process Alternatives

CaseNumber"

1.501.001.000.97

1.400.900.66

0.170.180.25

1.601.601.601.20

<1.60>

0.811.801.50

8,2005,2005,2004,900

7,8004,0004,400

0100300

8,2009,900

11,0009,200

11,000

3,5006,2006,400

25142518

231215

455

2726342428

142036

1. Chemical solvent2. Physical solvent3. Membrane4. Membrane-chemical solvent

1. Chemical solvent2. Physical solvent3. Membrane

1. Chemical solvent2. Physical solvent3. Membrane

1. Chemical solvent2. Physical solvent after compression to 300 psia3. Membrane after compression to 300 psia4. Membrane after compression to 900 psia5. Cryogenic*"

1. Chemical solvent2. Physical solvent after compression to 300 psia3. Membrane after compression to 300 psia

1

2

3

4

5

"See Table 20.2-2 for description of details of feed and product stream characteristics.b Accounts for the fact that feed gas contains some heavy hydrocarbons which membranes retain as a small extra benefit."Process details not specified; standard cryogenic unit presumably considered.

TABLE 20.2-5 System Parameters to Make 107 SCF/day of 30% P-11 Membrane

Membrane area 78,000 ft2

Feed gas pressure 1 atm absolutePressure of permeant gas 0.35 atm absoluteTemperature 25 0CPower required to deliver permeant gas at 1 atm 0.15 kW-h/100 ft3

O2 required to make mixture 47.3 tonsPower required if O2 is supplied from low- 0.16 kW-h/100 ft3

temperature air separation plant(basis: 1.4 kW-h/100 ft3 pure O2)

Source: Ward etal.16

have not driven commercial development of membrane processes in the United States until Monsanto'srecent announcement of the N2 blanketing of tanker fuels.17 A program at General Electric in the 1960sdemonstrated the technical feasibility of such processes using flat, low-surface-area, plate-and-frame mem-branes composed of ultrathin silicone rubber-polycarbonate copolymers. This project, however, has beenterminated, and the technology currently is being used only to supply O2-enriched air for personal medicalapplications.15

The most probable reason for the slow development of the O2-N2 membrane systems is the strongcompetition encountered from existing, highly optimized cryogenic processes. For large-scale operations,cryogenic processes become progressively more economical, while each additional unit of capacity requiresan exactly corresponding additional unit of membrane area to perform the separation. Thus, membranesare most competitive in small- and intermediate-scale O2-N2 operations in which flexibility of operation isvaluable.

Table 20.2-5 presents the system parameters determined by Ward et al.l6 for producing 10 x 106 SCFDof 30% oxygen with single-stage 1000 A ultrathin silicone-polycarbonate copolymer membranes. In ad-dition to their thinness, these membranes had high permeabilities due to their silicone rubber component(57% on a mole basis) (see Fig. 20.2-7). The separation factor for the family of silicone-polycarbonatematerials shown in Fig. 20.2-8 increases as the fraction of flexibilizing silicone decreases. If one considersthe ratio of permeabilities at 0% silicone and at 57% silicone, it is clear that an approximately 100-foldincrease in permeation area is required to achieve the same oxygen productivity for pure polycarbonatemembranes as for the 57% copolymer. Thus, roughly 7.8 x [(? ft2 of membrane area with a 1000 Athick separating layer would be required to supply the same absolute amount of oxygen in the product gasfor the polycarbonate case as compared to 78,000 ft2 for the copolymer case.

The two cases are not entirely equivalent, since the higher selectivity of the polycarbonate fibers willreduce permeation of N2 relative to O2 by roughly a factor of 2 (see Fig. 20.2-8). If a large flow rate offeed air passes through the module, so that feed concentration depletion is not a serious problem, theWeller-Steiner expression in Eq. (20.2-1) can be used for calculating the oxygen composition in the limitof negligible feed recovery as suggested by Ward. The ratio of total downstream to total upstream pressure,P1Zp2, was equal to 0.35 in the example by Ward summarized in Table 20.2-5, and the mole fraction of

FIGURE 20.2-7 Oxygen permeability of a range of copolymersfrom pure polycarbonate to pure silicone rubber. The weight percentof silicone rubber in the copolymer is shown as the ordinate.l6

P Og

(Bar

rers

)

O2 in the feed air is equal to 0.21. Using the ideal separation factor for polycarbonate from Fig. 20.2-8with a value of p,//?2 = 0.35, a product gas composition of Y02 = 0.38 results rather than the Y02 = 0.30obtained with the copolymer membrane used by Ward. Clearly, since the oxygen production has beenassumed to be the same, the total product flow rate will amount to only (0.30/0.38) 10 x 106 SCFD or7.9 x 106 SCFD of 38% O2 product gas. This higher purity product is more valuable than the 30% productachievable with the silicone-polycarbonate membranes at the same value of p{/p2.

To compare equivalent product qualities, a material balance shows that 8.92 x 106 SCFD of standardair (21% O2) can be added to dilute the 38% stream to 30%. Alternatively, one could adjust the value ofthe pressure ratio (P1Zp2) to make the K02 calculated from Eq. (20.2-1) equal to 0.30. Since the primarydiscussion here relates to membrane area, the first approach is assumed to keep other parameters essentiallyconstant. Therefore, 16.83 x 106 SCFD of 30% air would result if the full 7.8 X 106 ft2 of membranearea were used. Therefore, to produce 10 x 106 SCFD of 30% air, one would require 7.8 x 106 (10/16.83) = 4.63 x 106 ft2 of membrane area. This area could be accommodated in roughly 450 low-pressure,8 in. diameter, 10 ft long modules. Given their compact size, this number of modules is not unreasonablylarge. Blowers, vacuum pumps, and compressors would be the only additional capital costs involved inthe system. As mentioned earlier, the membrane system also would provide easy turndown simply byeliminating whatever fraction of the module permeation capacity is not required at the time. The numberof modules required could be reduced greatly if the feed gas were compressed to a substantial pressure(say 5-10 atm). In such a case, more expensive module shells and compressor costs would need to bebalanced against the reduction in the membrane area requirements.

20.3 MEASUREMENT AND PHENOMENOLOGICAL DESCRIPTION OF GASSORPTION AND TRANSPORT IN POLYMERS

20.3-1 General Discussion

The detailed engineering design for gas permeators generally involves a rather complex computer simulationof the coupled momentum and mass transfer phenomena occurring in the module. Advantages of recycleand various flow options also must be evaluated to arrive at the best overall design. These considerations,introduced in the previous section, are dealt with in detail in the section entitled "Modeling and DesignConsiderations/' The key to success of the process, however, rests on the optimum choice of membraneproperties, just as solvent selection lies at the heart of solvent extraction processes. The present sectiontherefore focuses on basic polymer properties of importance to membrane selection. Emphasis is placedon factors affecting the sorption and transport properties of dense films because most preliminary screeningwork on novel membrane materials deals with such samples.

Temperature is an extremely important variable that directly affects physical properties of the membraneand hence its permeation and selectivity properties. As an example, if one considers the low-pressure limit,under which condition Eq. (20.1-5) applies, the magnitude of temperature effects can be illustrated for atypical group of gases. Permeabilities, ideal separation factors, diffiisivities, and solubility coefficients ofgases in natural rubber are plotted in Fig. 20.3-1 in semilogarithmic form as a function of 1/7*.l>2 Theslopes of the solubility and diffiisivity curves can be interpreted directly in terms of enthalpies of sorptionand activation energies of diffusion, respectively.1 The temperature dependence of the permeabilities andseparation factors is composed of contributions from both sorption enthalpies and activation energies, sothat their theoretical interpretation is more complex than that of the simple diffusion and sorption coeffi-cients.

The plots in Fig. 20.3-1 show clearly that the strongest effect of temperature is on the diffusioncoefficient. Changes of 200-300% occur over the temperature range from 25 to 500C, depending on thegas considered. The smallest molecule, H2, shows the smallest increase with increasing temperature. This

FIGURE 20.2-8 Ideal separation factor for O2-N2 versus percentsilicone rubber in the copolymer.16

FIGURE 20.3-1 Permeabilities, solubilities, diffusivities, and separation factors for CO2, H2, and CH4 innatural rubber over the temperature range from 25 to 5O0C.

trend often is observed; increases in temperature speed up the diffusion processes of the most bulkypenetrants the most. The solubility coefficients of the various gases change less than 30% even for CO2

over this same temperature range. The permeability—comprising the product of the solubility and mobilitycoefficients—tends to be dominated by the diffusivity and increases by roughly 120-160% between 25 and500C. The ideal separation factor, composed of a ratio of permeabilities, is moderated in its temperaturedependence because the temperature dependencies of the permeabilities of the various gases are rathersimilar.

The above trends often are observed even for glassy polymers at low pressures; however, the separationfactors tend to be much higher in glasses. Moreover, precipitous drops in separation factors can occur asone approaches the glass transition (softening point) of a glassy polymer. In such cases, marked deviationsfrom linear semilog behavior such as that shown in Fig. 20.3-1 occur.

Most separators tend to be operated over a relatively narrow range of temperatures; however, a wide rangeof feed pressures and compositions can be encountered. Therefore, it is appropriate to consider in moredetail the pressure or concentration dependence of the permeation, sorption, and diffusion coefficients thatcontrol module operation.

Ideal separationfactors

Permeabilities

Solubilitycoefficients

Diffusivities

P (B

arre

rs)

20.3-2 Concentration Dependence of Sorption and Diffusion Coefficients

Accurate engineering modeling of membrane-based gas permeators can be performed if the compositionand pressure dependence of the various component permeabilities are known at the temperature of interest.Permeabilities of gases and vapors have been reported to display behaviors represented by Figure20.3-2.3"6 For gases at low and intermediate pressures, behaviors shown in Fig. 20.3-la-c are most com-mon. Response (b) is characteristic of a simple plasticizing response.4 Interestingly, response (d) in thisfigure is simply a combination of responses (b) and (c). At higher pressures, even in plasticization-resistantmaterials, one can expect the response shown in Fig. 20.3-2c to evolve into a form such as the one shownin Fig. 20.3-2rf, since sorption levels will be high under these conditions. The entire response is apparentin Fig. 20.3-2*/ because of the high solubility of the penetrant in the polymer even at low partial pressures.

The magnitude of the pressure dependence of the various responses illustrated differs substantially.Assumption of a constant value for these coefficients in design calculations is tempting for responses (a)y

(c), and (</), where only about a 20-30% change occurs over the pressure range shown. In the case ofresponse (&), however, the strong dependence makes it ambiguous as to what average value is reasonableto use in modeling since large pressure differences typically exist across separating membranes. Even inthe less extreme cases, however, rational design would be aided by using the correct functional form forthe transport coefficients.

As noted earlier, when both the diffusion and solubility coefficients are constants, the simple formshown in Fig. 20.3-2a results. In all other cases, nonconstancy of either the sorption or diffusion coefficientscan cause nonconstancy of the observed permeability and selectivity. As illustrated, separation of the twocomponent contributions is straightforward if both equilibrium solubility and steady-state permeation dataare available.

Beginning with the definition of permeability in Eq. (20.1-3), one can proceed without the simplifyingassumptions in Eq. (20.1-5) that the diffusion and sorption coefficients are constants. In this case we find

(20.3-1)

where D(C) is the local concentration-dependent diffusion coefficient of the penetrant at an arbitrary point

'Polyethylene 'Polyethylene

P,

Bar

rers

'Polycarbonate Ethyl Cellulose

FIGURE 20.3-2 The pressure dependency of various penetrant-polymer systems: (a) at 30 0 C/ (b) at2O0C,4 (c) at 350C,6 and (d) at 400C5.

between the upstream and downstream surface and dC/dx is the local concentration gradient at this samepoint in the membrane. As before, N is the steady-state flux, and p2 and Px rc^er to the upstream anddownstream penetrant partial pressures, respectively. Although both D(C) and dC/dx may be positiondependent, their product is constant at each point in a flat membrane,$ since the steady-state permeabilityis a constant for fixed upstream and downstream conditions. Therefore, we see from integration of Eq.(20.3-1) with respect to x that

(20.3-2)

By the chain rule we find Eq. (20.3-3):

(20.3-3)

kinetic factor thermodynamic factor

Clearly, the observed permeability is a normalized integration of the product of a kinetic factor and athermodynamic factor across the entire membrane from upstream ("condition 2") to downstream ("con-dition 1"). The thermodynamic term dC/dp is determined by polymer-penetrant interactions. The kineticterm D(C) is determined by polymer-penetrant dynamics and requires localization of a sufficiently largetransient packet of volume contiguous to the penetrant to permit it to execute a so-called diffusive jump.

The ideal separation factor, equal to the ratio of the permeabilities of the two components, is alsointerpretable as a product of two factors: a "solubility selectivity*' and a "mobility selectivity.*' Thesetwo selectivity contributions, consisting of the ratios of the respective component solubilities and diffusivities,indicate the relative importance of thermodynamic and kinetic factors in the permselection process. Un-fortunately, optimization of product permeability and membrane selectivity is often difficult, and trade-offsin the two parameters may be necessary on economic grounds. A brief discussion of characterizationmethods and typical forms of sorption isotherms and local diffusion coefficients for gases and vapors inpolymers is presented below. This discussion serves as a background for rationalizing pressure dependenciesof permeabilities and selectivities.

SORPTION ISOTHERM FORMSAs shown in Fig. 20.3-3, a variety of isotherm shapes are observed for gases and vapors in polymers. Gassorption in rubbery polymers and low-concentration gas sorption in glassy polymers follow an apparentHenry's Law form represented by Fig. 20.3-3«. Simple homogeneous swelling of rubbery polymers bycompatible penetrants tends to produce isotherms like that shown in Fig. 2O.3-3&. Interestingly, rathercomplex polar and hydrogen-bonding penetrants, which tend to cluster together in nonpolar rubbery pol-ymers, also tend to exhibit isotherms like that shown in Fig. 20.3-3&. More complicated isotherms involvingan inflection, such as that shown in Fig. 20.3-3<tf, often are observed for vapor and even highly sorbinggases such as CO2 in glassy polymers under certain conditions.

The isotherm presented in Fig. 20.2-3c is observed commonly for gases up to moderate pressures (20-30 atm) in glassy polymers. It corresponds to the low-activity portion of the curve shown in Fig. 20.3-3d.The term dual-mode sorption applied to Fig. 20.3-3c derives from a specific physical model of the glassystate.6 The model suggests that two different environments exist in nonequilibrium glasses, resulting in twoidealized sorbed populations that exist at local equilibrium with each other because of rapid exchangebetween the two environments. This issue is pursued in greater depth in the section entitled "Fundamentalsof Sorption and Transport Processes in Polymers." For present purposes, such considerations are notnecessary, and a simple polynomial fit of C versus p to any of the data forms shown in Fig. 20.3-3 wouldsuffice to evaluate dC/dp for use in Eq. (20.3-3). Such an approach is termed phenomenological in that itsimply describes the phenomenon in question without considering its physical bases.

Although indirect techniques exist for generation of data such as shown in Fig. 20.3-3, the most reliableapproaches involve direct determination of the amount of penetrant sorbed into the polymer at a givenexternal pressure. At low pressures with highly sorbing vapors, gravimetric techniques involving weightgain monitoring by quartz spring or electrobalance are effective. For gases at high pressures, however,pressure decay during sorption monitored by accurate transducers with calibrated reservoir and receivingvolumes has proved to be the most effective method. Typical data collected using such a cell are shownin Fig. 20.3-4 for a variety of gases in polycarbonate.7 Design and operation of a pure gas cell (Fig. 20.3-5a) and a multicomponent cell (Fig. 20.3-5&), which requires a gas chromatograph, have been describedelsewhere in detail.89

^Curvature effects are neglected here since most screening studies of candidate membranes are conductedon flat dense films.

p , partial pressure of penetrant, atmFIGURE 20.3-3 Schematic representation of typical sorption isotherm forms.

DIFFUSION COEFFICIENT FORMSDetermination of concentration-dependent diffusion coefficient data usually is done indirectly. Typically,one determines -D(C) from the observed pressure dependence of the permeability in conjunction with theindependently determined dC/dp data discussed in the preceding section.6 When significant concentrationdependence is observed for the local diffusion coefficients, the form generally resembles one of the curvesshown in Fig. 20.3-6. Of course, for low-sorbing gases such as H2 and N2 in rubbery polymer, both Dand dCldp are essentially constant resulting in adherence to the simple situation indicated by Eq. (20.1-5).

Transport in hydrocarbon polymers exposed to organic vapors or hydrophilic polymers exposed to watervapor typically is characterized by diffusion coefficients that increase exponentially with the concentrationof plasticizing penetrant.10"13 Such a relationship is represented graphically in Fig. 20.3-6a. At relativelylow concentrations of a plasticizing penetrant, the linear relationship between D(C) and C shown in Fig.

Polycarbonate

Henry's Law BETC

t Co

ncen

tratio

n in

poly

mer

(c

c(ST

P)/c

c po

lymer

)

Dual Mode BET

FIGURE 20.3-4 Sorption isotherms for various gases in Lexan® polycarbonate at 350C.

Multicomponent Cell

(b)FIGURE 20.3-5 Sketches of (a) pure component and (b) multicomponent high-pressure sorption cells forcollection of data such as those shown in Figs. 20.3-3 and 20.3-4.

20.3-66 often is observed. Clustering of penetrant can reduce the effective diffusion coefficient, since insimple terms the size of the mobile penetrant effectively is increased.14 Such behavior is observed mostcommonly for the diffusion of hydrogen-bonding penetrants in relatively nonpolar environments. Sinceclustering becomes more pronounced at higher concentrations, the effective diffusion coefficient decreaseswith concentration, as shown in Fig. 20.3-6W. The monotonically increasing, albeit inflecting, response ofD(C) versus C presented in Fig. 20.3-6c is characteristic of diffusion coefficients for many penetrants atrelatively low concentrations in glassy polymers.6 This form of the relationship is consistent with the so-

Tronsducer B

Transducer A

Sample

Lead>Gosket -Grooves

Pure C o m p o n e n t Ce l l

Gasket

BodyNut

Tronsducer B

Transducer A

Tronsducer C

Tronsducer 0

LeadVGosket-

Somple

Grooves

To 60sChromatogroph Gos or

Vacuum

C, Local Penetrant Concentration in PolymerFIGURE 20.3-6 Schematic representation of typical forms for concentration-dependent diffusion coeffi-cients.

called dual-mode sorption and transport theory which was mentioned earlier in connection with the inter-pretation of Fig. 20.3-3. This theory is discussed in more detail in the section dealing with the propertiesof the glassy state.

Three types of laboratory apparatus are in common use for the measurement of gas permeation ratesthrough polymers to obtain data for analyses such as those discussed previously:15

Manometric cellsIsobaric cellsCarrier-gas cells

The manometric and isobaric cells are simple and differ primarily in the mode of sensing gas transmissionthrough the polymer. As shown in Fig. 20.3-1 a> the manometric approach involves monitoring gas per-meation into an accurately calibrated and thermostated, evacuated volume by recording the pressure-riserate in the volume. Several designs for this type of cell have been reported.31617 The most recent cellsgenerally rely on sensitive transducers such as the MKS-Baratron rather than a mercury McLeod gage,which was used in early designs.

The isobaric cell, shown in Fig. 20.3-76, generally operates with atmospheric pressure downstream.Gas permeation in this case is monitored by recording the change in position of a mercury or silicone oilplug or a soap bubble moving along a calibrated capillary. As with the manometric cell, several designshave been reported for the isobaric appartus. Stern and coworkers have developed the most advanced formof these cells.18

The so-called carrier-gas method is the most complicated approach to gas permeation monitoring.19

Either pure-component or multicomponent permeation rates through films can be monitored using thisdevice, shown in Fig. 20.3-8. A carrier gas such as helium, containing a desired partial pressure of thedesired component or components, flows past the upstream face of the membrane. A downstream sweepgas picks up the permeated components and routes them to a gas chromatograph for analysis of the fluxesof each penetrant. An excellent discussion of such a system has been offered by Pye et al.,3 and comparisonswere made with manometric cells for pure gas permeation to prove that the results for both cells areessentially identical if care is taken in operation.

As an example of analysis of permeation data to evaluate the concentration-dependent diffusion coeffi-

Effe

ctiv

e Co

ncen

tratio

n —

Depe

nden

t Di

ffusio

n Co

effic

ient

Dual mode

Clustering

FIGURE 20,3-7 (a) Manometric (variable downstream pressure) and {b) isobaric (variable downstreamvolume) permeation cells for determination of gas transport rates.

cients, consider a case in which the observed permeability continuously inflects upward (e.g., Fig. 20.3-2b) and the isotherm displays a BET III form (e.g., Fig. 20.3-36). The local value OfD(C) can be evaluatedreadily by differentiation of polynomial fits to both the permeation and sorption data. Equation (20.3-6) isderived by application of the Liebnitz rule for differentiation under an integral sign to Eq. (20.3-2). Forpresent purposes, the downstream pressure (p,) of the diffusing component in the derivation is assumed tobe negligible, since a vacuum or carrier gas generally is present in most testing situations. Thus, Eq. (20.3-2) becomes

(20.3-4)

Therefore, applying the Liebnitz rule

(20.3-5)

or

(20.3-6)

Using Eq. (20.3-6) one can determine D(C2) versus C2 for any chosen pressure condition for whichboth sorption and permeation data exist. If one applies Eq. (20.3-6) over the entire pressure range of interestto curves such as those shown in Fig. 20.3-2b and 2O.3-3a or 20.3-3b, a constantly upwardly inflectingD{C) versus C relationship similar to that shown in Fig. 20.3-6« will result.

One must be a bit cautious, however, about drawing sweeping conclusions from the general shape ofpermeation and sorption isotherms. If the slope of the sorption isotherm, dC/dp, increases more rapidly

Feed at TronstentStote

Film

Steady

Stotc

Downstreom Receiver

PressureTransducer

Time LogTime

Constont Pressure

Calibrated CapillaryReceiver Volume

MarkerPlug

Feed ot

To Vocuumotter RunComplete

Permeant

MorkerPositionHit)

TronsientStote

SteodyState

Time

GasChromatogroph

Corrier-Gas Feed System

Feed Stream Containing Penetrant at Some Portia!Pressure

Pick-up Gas Stream to Sweep Bottom Face ofMembrane

Penetrant-laden Pick-up Stream Leading to GCFIGURE 20.3-8 Carrier-gas permeation system for determination of gas transport rates. The equipmentis especially useful for work with multicomponent mixtures.

than the permeability increases, the effective diffusivity actually may be found to decrease with increasingvalues of C2. Such behavior is shown in Fig. 20.3-6c and is observed for hydrogen-bonding penetrantssuch as water and alcohols in nonpolar polymers like silicone rubber. The concentration dependence of apenetrant's diffusion coefficient therefore provides insight into the nature of polymer-penetrant interactions.

20.3-3 Partitioning Permeability into Thermodynamic and Kinetic Constituents

In cases where either or both of the coefficients appearing in Eq. (20.3-3) are not constants, it is useful toknow explicitly which of the two factors is primarily responsible for nonconstancy in the observed perme-ability. As noted above, this information cannot be known simply by measuring the steady-state perme-ability. Demonstration of the existence of a continuously upwardly inflecting exponential curve for theD(C) versus C response (Fig. 20.3-6) suggests that the membrane is being plasticized strongly by thepenetrant. This information would warn one to expect rather poor selectivity due to loss in ability of thepolymers to discriminate between penetrants of different sizes and shapes. On the other hand, concentrationdependence identified as "dual mode" in Fig. 20.3-6c is not associated with plasticization in general. Thisbehavior is observed for even low-sorbing gases such as N2, as well as for more strongly sorbing materialslike CO2 in glassy materials that maintain reasonable selectivity up to the point at which strong plasticizationis indicated by a sudden upturn in the diffusivity relationship.6

Unfortunately, except for a few gases in a few glassy polymers, high-pressure sorption and permeationdata are not available to pursue the concept of decoupling the thermodynamic and kinetic contributions tothe ideal separation factor. The technique, however, can be illustrated for the important case of CO2 andCH4, for which a fair number of data exist at pressures up to 20 atm. Carbon dioxide permeabilities at35 0C in a variety of glassy polymers at upstream pressures up to 20 atm (with a negligible downstreampressure) are shown in Fig. 20.3-9. Besides the dramatic range of permeabilities represented (more than a

C A R R I E R - G A S P E R M E A T I O N S Y S T E M

FeedGas

Heise GaugePressureRegulator

ToFlow Meter

PermeationCell

FlowControlValve

Pick-upGas N2

HeatExchanger

Feed Pressure (atm)FIGURE 20.3-9 Pressure dependence of the permeability of various polymers to CO2. The data weremeasured with a vacuum downstream except for the cellulose acetate (CA), which was estimated from avariety of sources.21"24

300-fold difference among polymers), the surprising difference in the reported response of cellulose acetateto increasing CO2 pressure compared to the other polymers is obvious.

The difference in the responses can be considered in terms of the composite nature of the permeabilitysuggested by Eq. (20.3-3). If D(C) in this equation is not a very strong function of concentration, thestrong reduction in dCldp due to the concave-shaped, dual-mode-type isotherms for such systems (Fig.20.3-3c) causes the observed permeability to decrease at high pressures. In the case of cellulose acetate,although the dual-mode isotherm shape still is observed,20 apparently the polymer exhibits a strong plas-ticization response (like Fig. 2O.3-6a rather than like Fig. 20.3-6c). This'sharp increase in penetrantdiffiisivity swamps the effect of the decreasing dCldp term, thereby causing the dramatic upswing inpermeability.

One may pursue the issue of the apparent special affinity of CO2 for cellulose acetate in an additionalfashion by considering the CO2-CH4 separation factor for the polymers presented in Fig. 20.3-9. Consid-ering Eq. (20.3-2) for component i for the case where the downstream partial pressure, pu is negligible,we see that

(20.3-7)

Multiplying the numerator and denominator of Eq. (20.3-7) by C21, we obtain the sorbed concentrationof component i in the film at the upstream partial pressure p2i:

(20.3-8)

PCO2

(Ba

rrer

s)Poly (phenylene oxide)

12.5XPolysulfoneCO2 Permeabilities

35 0 C

EstimatedCellulose Acetate

Polycarbonate

Polysulfone

Kapton

|i /26X Polysulfone

where D{ and S, are the average diffusivity and apparent solubility of component i defined by Eqs.(20.3-9) and (20.3-10)

(20.3-9)

(20.3-10)

Therefore, one may, express the ideal separation factor for the chosen upstream partial pressure, pA2

andpB2, as shown in Eqs. (20.3-11) and (20.3-12):

(20.3-11)

/mobility \ /solubility \( , . . ) ( , . ) (20.3-12)\selectivity/ \selectivity/

The ideal separation factors and the mobility and solubility contributions comprising this parameter forthe various polymers shown in Fig. 20.3-9 are presented in Table 20.3-1 for a case corresponding to a 600psia total feed pressure with 300 psia of CO2 upstream and very low downstream pressures of bothcomponents. The data for preparation of Table 20.3-1 were estimated from a number of sources, and theabsolute value of the entries for cellulose acetate may be in error up to 10-15%.2>2I~24 The data forselectivities reported in the table are higher than those normally reported for asymmetric polysulfone andcellulose acetate membranes since the dense-film forms of the samples tend to eliminate flow through poresthat are present in asymmetric membranes and decrease their selectivity (see Table 20.1-2).

It appears significant that the majority of the polymers at 20 atm CO2 pressure are selectively sorptivefor CO2 relative to CH4 by a factor of only 2-4. Cellulose acetate, on the other hand, appears to besubstantially more sorptive for CO2 relative to CH4.25 Conversely, the mobility selectivities of all thepolymers in Fig. 20.3-9 that do not show a plasticization response are more favorable than that of celluloseacetate. This observation assumes that plasticization of cellulose acetate causes no further loss in its abilityto distinguish between CO2 and CH4 compared to the pure component permeability ratios.

If this assumption is seriously in error, the actual mixed gas mobility selectivity of cellulose acetatemay be even lower than indicated by the diffusivity ratios in Table 20.3-1. Polymers such as celluloseacetate which are *'solubility selectors" may tend to display plasticization-type responses in the permeabilityversus pressure plots such as that shown in Fig. 20.3-26. More detailed sorption and diffusion data on asingle, well-characterized film sample for this interesting system are needed badly to investigate theseeffects further. Understanding the principles at play in the case of cellulose acetate may permit expansionof the ranks of such "solubility selecting" materials for possible use as thin-film composite membranes orin blending with other, more plasticization-resistant membrane materials.

The preceding analysis indicates the value of considering the separate solubility and mobility constituentcontributions to the permeability and selectivity of a given riiembrane. These data also suggest approachesfor modifying existing membrane materials at the two extremes of permeability shown in Fig. 20.3-9. Themose selective film (Kapton®) represented in Table 20.3-1 is also the least permeable, and the mostpermeable [poly(phenylene) oxide] is also the least selective: a rather unfortunate statement of Murphy'sLaw.

The interesting empirical correlation in Fig. 20.3-10 provides an impressive relationship between the

TABLE 20.3-1 Partitioning of the Ideal Separation Factor for CO2-CH4 into Its Kinetic andThermodynamic Contributions at 35 0C and 40 atm for a 50-50 Molar Feed Mixture

Polymer ^COI^CYU DcoJDctu 5CO2/5CH4

Poly(phenylene oxide) 15.1 6.88 2.2Polycarbonate 24.4 6.81 3.6Polysulfone 28.3 8.85 3.2Cellulose acetate 30.8 4.21 7.3Kapton® 63.6 15.38 4.1

Note: Assumes equal percent increase in CO2 and CH4 permeability due to any plasticization of celluloseacetate by CO2.

FIGURE 20.3-10 Ideal separation factors for CO2-CH4 with several polymers based on pure componentpermeability ratios. The solubility parameter of the polymer is a successful correlating parameter for theideal separation factor for the polymers shown here. !

solubility parameter of the membrane polymer and its ideal separation factor for CO2 relative to CH4.21"24

This plot suggests that if one were constrained to deal within the limits of the existing polymers in Fig.20.3-9, modifications should be carried out to increase the cohesive energy density of PPO (e.g., bysubstitution of a polar or hydrogen-bonding group on the phenylene ring) and to decrease the cohesiveenergy density of Kapton® [e.g., by introduction of structural irregularities, perhaps using a mixture ofaromatic diamines besides bis-4(aminophenyl) ether to make ordering of the imides more difficult, therebyto "open" the structure]. The logical conclusion of this concept indicates that it might be possible to openthe structure enough to allow almost unrestricted movement of the streamlined CO2 while still retardingthe bulky CH4 to a greater extent.

These concepts are largely derivative of the ideas of Hoehn of Du Pont, who developed high-perme-ability, high-selectivity membranes for hydrogen applications in the 1970s.3 A systematic study of theeffects of structural modifications on the solubility and mobility contributions to the observed permeabilitiesand selectivities of both the PPO and Kapton® films would be useful. Such an approach, based on the mostpermeable and least permeable candidate polymers, effectively would "surround" the problem and allowsystematic closure on the best membrane in terms of combined permeability and selectivity. Clearly, oneshould not be constrained to deal within the limits of the existing polymers shown in Fig. 20.3-9. The bestmembrane materials may not be the best engineering plastics, since the requirements are different for thetwo classes of materials. Stiff-chained, bulky, repeat-unit polymers with purposely introduced structuralirregularities are interesting candidates for future study.

A critical need exists for construction of a systematic, reliable data base for a wide number of gases ina wide number of polymers. Until this need is recognized and addressed in the same way that collectionof vapor-liquid equilibrium data is accepted, membrane development will be reduced largely to an "Edi-sonian" approach.

20.3-4 Transient Permeation Analyses to Check for Data Consistency

Most of the measurements to be performed in a membrane-testing program involve asymmetric membranesafter the first phase of work to screen candidate polymers. Nevertheless, it is wise to perform a benchmarkstudy using dense films of the polymer of interest. This approach permits an unambiguous determinationof the sorption and transport properties of the inherent polymer, unobscured by minuscule, but possiblysignificant, porous defects in the asymmetric structure. Moreover, if such data are available, drifts in thepermeability and selectivity of asymmetric membranes composed of the polymer can be understood better.By making comparisons between the asymmetric membrane results and those of the dense film, which arefree of time-dependent support effects, drifts due solely to support aging can be quantified.

Whichever of the methods depicted in Figs. 20.3-7 and 20.3-8 for monitoring permeation is used, atransient period of permeation typically is observed when films of more than a few microns are studied.

35 0 CAPPROXIMATE PERMEABILITYRATIOS FOR CO2/CH4

Kapton

PolysuHone CelluloseAcetate

Polycarbonate.

Poly (phenylene oxide)

Polystyrene

Upon analysis of this transient period, either as the zero-pressure intercept on the time axis for constantvolume systems (Fig. 20.3-7«) or as the corrected zero-moment of the detector response for carrier-gassystems (Fig. 20.3-8), one can derive a kinetic parameter 0, referred to as the "time lag".15*26'27

In most time-lag experiments, the initial downstream penetrant concentration, C1, is zero and theupstream concentration C2 is assumed to be established instantaneously at its equilibrium value. Although0 is an additional parameter not required to evaluate permeability and solubility data, it is wise, whenpossible, to verify that the time lags observed experimentally are consistent with the predictions of Fick'sLaw. To perform this test, one needs only to fit an empirical equation to the D(C) versus C data shownin Fig. 20.3-6 and to perform the integration indicated:2627

(20.3-13)

where / is the membrane thickness and D(u) and D(w) refer to the empirically determined form that bestdescribes the local diffusion coefficient data evaluated according to Eq. (20.3-6) and illustrated schematicallyin Fig. 20.3-6.

As an example, if the local diffusion coefficient varies exponentially with local sorbed concentration,for example, D-D0 exp (/4C), we find after integration27

(20.3.14)

If the sorbed concentration at the upstream face obeys Henry's Law as shown in Fig. 20.3-3a, then C2 =Sp2, and we can express the time lag directly in terms of pressure. If a more complex polynomial fit to thesorption isotherms shown in Fig. 2C.3-3a is necessary, it is clear that C2 versus p2 could still be substitutedinto Eq. (20.3-14) to obtain the pressure-explicit prediction of $ versus pressure for comparison to theexperimentally measured data.

The time-lag evaluation therefore provides a consistency check to verify that the data collected arebehaving in accordance with the standard Fickian transport model. Significant deviations (> 10-15%) maysignal either experimental problems in the data acquisition or long-term drifts in the polymer structure.Such long-term drifts could be associated with true glassy-state drifts or with a failure to remove traces ofcasting solvent. This latter problem could be verified and eliminated by replication of the measurementswith a more thoroughly heat-treated film. Failure to remove small traces of solvent residuals can lead to avariety of peculiar anomalies.28"30

For cases in which the diffusion coefficient is a constant, even for complex isotherm shapes,Eq. (20.3-14) reduces to a simple relationship:

(20.3-15)

In such cases, and only in such cases, it is correct to refer to the diffusion coefficient as

(20.3-16)

Unfortunately, the above equation often is used to calculate a parameter sometimes referred to as Dapp

(apparent diffusivity). This parameter does not have a simple physical meaning and is a complicated averageof the true local diffusion coefficient at the upstream and downstream conditions, as can be seen from theexpression for 6 in Eq. (20.3-13). This parameter tends to show less dependence on the upstream pressureor concentration than the true local diffusion coefficient does when evaluated at the upstream condition.

Consider a hypothetical plot of D(C) versus C, such as that shown by the solid line in Fig. 20.3-11.In a time-lag experiment with C, = 0 downstream and C2 fixed by the upstream pressure, the parameterDapp has a numerical value between the two limits of D(C2) and D(O) = D0. This is illustrated by thedashed line in Fig. 20.3-11, which is much less concentration dependent than the true D(C). The ambiguityarising from application of Eq. (20.3-16) to calculate a coefficient to characterize the local penetrant mobilityat a given upstream pressure or concentration becomes larger at high concentrations. The discrepanciesbetween the true mobility and the value of Dapp tend to disappear in the limit as results are extrapolated tothe zero-pressure limit. Unfortunately, this extrapolation does not permit one to analyze the high-pressurerange, where most gas separation operations are likely to occur, so that the use of Eq. (20.3-16) as afundamental measure of mobility is not desirable in general.

When the local diffusion coefficient evaluated from Eq. (20.3-6) is not too strongly concentrationdependent (10-20% variation over the range of interest), the error associated with the use of Eq.

Local Upstream Concentration, C2FIGURE 20.3-11 Demonstration of the marked difference in concentration dependence of the true localdiffusion coefficient (solid line) and the apparent diffusion coefficient (dashed line) for a hypotheticalexponentially varying case such as shown in Fig. 20.3-6a.

(20.3-16) is clearly not very serious. Several rather extensive examples of comparisons of measured andcalculated time lags for CO2 and other gases in glassy polymers have been reported recently. In most casesup to the 20 atm limit which have been investigated, Fick's Law appeared to be obeyed well.

20.4 FUNDAMENTALS OF SORPTION AND TRANSPORT PROCESSES IN POLYMERS

20.4-1 General Discussion

The following two subsections provide physical interpretations of the forms of sorption isotherms andconcentration-dependent diffusion coefficients observed for rubbery and glassy polymers, respectively.These sections are not required for simulation of module operations if a complete set of empirical pressure,temperature, and composition-dependent permeation data are available. A simple polynomial fit of perme-ability data as a function of all operating variables would suffice for design and simulation.

Generally, such detailed data are not available, and a theoretical framework is valuable to aid in thephysical interpretation of new data. Moreover, in some cases an appreciation of fundamentals can explainobservations that otherwise might be termed "anomalous" and cast doubt on the validity of a perfectlygood particular set of data. Examples of this sort of situation can be cited for the case of glassy polymersin which the following consistent, but surprising, observations were reported by two separate investigatorsregarding H2 permeation in the presence of a slower permeating gas (either CO or CH4):

There is some interaction between components of the binary mixture during permeation whicheffectively decreases the permeability of H2 relative to CO.1

The fast gas was slowed down by the slow gas and the slow gas was speeded up by the fast gas.2

Such behavior is not consistent with plasticization, since the slightly sorbing H2 would not be expectedto plasticize the polymer while the more condensable (and hence more strongly sorbing) CO or CH4 actsas an antiplasticizer. As is discussed in the section on glassy polymers, such behavior as described here isnot anomalous and can be shown to be consistent with inherent properties of glassy polymers under certainconditions.

The major emphasis of the following discussion is on glassy polymer membranes since the more rigidsize- and shape-selecting glassy materials tend to have substantially higher selectivities than do flexiblerubbers, which are essentially high-molecular-weight liquids. This effect can be seen clearly from com-parison of the ideal separation factor data in Tables 20.4-1, 20.4-2, and 20.4-3 for rubbery and glassypolymers.3 However, consistent with the preceding discussion of the two-part nature (solubility and mo-bility) of both permeability and selectivity, one might envision a rubbery polymer with sufficiently favorablesolubility for one of the components in the mixture to make it useful as a thin film coating on a compositemembrane. In such a case, plasticization of the separating membrane could be a less serious problem thanfor the materials whose permselection action relies on molecular sieving action based on penetrant size andshape. Therefore, treatment of transport in rubbers is reviewed prior to consideration of the more importantglassy polymer case.

Actual Local

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