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CHAPTER 31 Fundamentals of Momentum, Heat and Mass Transfer-2.pdf

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Chapter 31 Mass-Transfer Equipment In earlier chapters, the theory currently used to explain the mechanism of convective mass transfer between phases was introduced, and correlations for the interphase convective mass-transfer coefficients were listed. In this chapter, we will develop methods for applying the transport equations to the design of commercial mass-transfer equipment. It is important to realize that design procedures are not rest
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  Chapter 31 Mass-Transfer Equipment I n earlier chapters, the theory currently used to explain the mechanism of convectivemass transfer between phases was introduced, and correlations for the interphaseconvective mass-transfer coefficients were listed. In this chapter, we will developmethods for applying the transport equations to the design of commercial mass-transferequipment. It is important to realize that design procedures are not restricted to thedesign of new equipment, for they may also be applied in analyzing existing equipmentfor possible improvement in performance.The presentation or development of mass transfer from the defining equations tothe final design equations, which is presented in this chapter, is completely analogousto our earlier treatment of energy transfer. Convective mass-transfer coefficients aredefined in Chapter 28. These definitions and the methods of analysis are similar tothose presented in Chapter 19 for convective heat-transfer coefficients. An overalldriving force and an overall transfer coefficient expressed in terms of the individualcoefficients were developed to explain the transfer mechanisms of both mass- andenergy-transport processes. By integrating the appropriate energy-transfer relation inChapter 23, we were able to evaluate the area of a heat exchanger. Accordingly, weshould expect to find similar mass-transfer relations that can be integrated to yield thetotal transfer contact area within a mass exchanger. 31.1 TYPES OF MASS-TRANSFER EQUIPMENT A substantial number of industrial operations in which the compositions of solutions and/ or mixtures are changed involve interphase mass transfer. Typical examples of suchoperations could include (1) the transfer of a solute from the gas phase into a liquid phase,as encountered in absorption, dehumidification, and distillation; (2) the transfer of a solutefrom the liquid phase into a gas phase, as encountered in desorption or stripping andhumidification; (3) the transfer of a solute from one liquid phase into a second immiscibleliquid phase (such as the transfer from an aqueous phase to a hydrocarbon phase), asencountered in liquid–liquid extraction; (4) the transfer of a solute from a solid into a fluidphaseasencounteredindryingandleaching;and(5)thetransferofasolutefromafluidontothe surface of a solid as encountered in adsorption and ion exchange.Mass-transferoperationsarecommonlyencounteredintowersortanksthataredesign-ed to provideintimate contact of the two phases. This equipment may be classified into oneof the four general types according to the method used to produce the interphase contact.Many varieties and combinations of these types exist or are possible; we will restrict ourdiscussion to the major classifications.  Bubbletowers consistoflargeopenchambersthroughwhichtheliquidphaseflowsandintowhichthegasisdispersedintotheliquidphaseintheformoffinebubbles.Thesmallgas 603  bubbles provide the desired contact area. Mass transfer takes place both during the bubbleformation and as the bubbles rise up through the liquid. The rising bubbles create mixingaction within the liquid phase, thus reducing the liquid-phase resistance to mass transfer.Bubbletowersareusedwithsystemsinwhichtheliquid phasenormallycontrolstherateof masstransfer;forexample,itisusedfortheabsorptionofrelativelyinsolublegases,asintheairoxidationofwater.Figure31.1illustratesthecontacttimeandthedirectionofphaseflowinabubbletower.Asonewouldexpect,thecontacttime,aswellasthecontactarea,playsanimportant role in determining the amount of mass transferred between the two phases. Thebasic mass-transfer mechanism involved in bubble towers is also encountered in  batchbubbletanksorponds wherethegasisdispersedatthebottomofthetanks.Suchequipmentis commonly encountered in biological oxidation and in wastewater-treatment operations.Exactly opposite in principle to the bubble tower is the  spray tower.  In the spray tower,the gas phase flows up through a large open chamber and the liquid phase is introduced byspray nozzles or other atomizing devices. The liquid, introduced as fine droplets, fallscountercurrent totherising gasstream.Thespraynozzle isdesigned tosubdividethe liquidinto a large number of small drops; for a given liquid flow rate, smaller drops provide agreater interphase contact area across which mass is transferred. However, as alsoencountered in bubble towers, care in design must be exercised to avoid producing dropsso fine that they become entrained in the exiting, countercurrent stream. Figure 31.2illustrates the contact time and the direction of phase flow in the spray tower. Resistance totransferwithinthegasphaseisreducedbytheswirlingmotionofthefallingliquiddroplets. Gas in Z  Liquid outLiquid inGas out Figure 31.1  Bubble tower. Gas inGas in Z  Liquid outLiquid in Figure 31.2  Spray tower. Gas inGas out Z  Liquid outLiquid in Figure 31.3  Countercurrent packed tower. 604  Chapter 31 Mass-Transfer Equipment  Spray towers are used for the mass transfer of highly soluble gases where the gas-phaseresistance normally controls the rate of mass transfer. Packed towers  are the third general type of mass-transfer equipment, which involves acontinuous countercurrent contact of two immiscible phases. These towers are verticalcolumnsthathavebeenfilledwithpackingasillustratedinFigure31.3.Avarietyofpackingmaterialsisused,rangingfromspeciallydesignedceramicandplasticpacking,asillustratedinFigure31.4,tocrushedrock.Thechiefpurposeofthepackingistoprovidealargecontactareabetweenthetwoimmisciblephases.Theliquidisdistributedoverthepackingandflowsdown the packing surface as thin films or subdivided streams. The gas generally flowsupward,countercurrenttothefallingliquid.Bothphasesarewellagitated.Thus,thistypeof equipment may be used for gas–liquid systems in which either of the phase resistancescontrols or in which both resistances are important.Special types of packed towers are used to cool water so that it can be recirculated as aheat-transfer medium. These structures are made of wood-slat decks, having louverconstruction so that air can flow across each deck. The water is sprayed above the topdeckandthentricklesdownthroughthevariousdeckstoabottomcollectionbasin.Coolingtowers may be classified as natural draft when sufficient natural wind is available to carryaway the humid air or as forced or induced draft when a fan is used. In the forced-drafttowers,airispulledintolouversatthebottom ofthestructureandthenflowsupthroughthedecks countercurrent to the water flow.  Bubble-plate and sieve-platetowers arecommonlyusedinindustry.Theyrepresentthecombined transfer mechanisms observed in the spray and the bubble towers. At each plate,bubbles of gas are formed at the bottom of a liquid pool by forcing the gas through smallholes drilled in the plate or under slotted caps immersed in the liquid. Interphase masstransfer occurs during the bubble formation, and as the bubbles rise up through the agitatedliquid pool. Additional masstransfer takes place above the liquid pool because of spraycarryover produced by the active mixing of the liquid and gas on the plate. Such plates arearrangedoneabovetheotherinacylindricalshellasschematicallyillustratedinFigure31.5.Theliquidflowsdownward,crossingfirsttheupperplateandthentheplatebelow.Thevaporrisesthrougheachplate.AsFigure31.5illustrates,thecontactofthetwophasesisstepwise.Such towers cannot be designed by equations that are obtained by integrating over acontinuous area of interphase contact. Instead, they are designed by stagewise calculationsthataredevelopedandusedindesigncoursesofstagewiseoperations.Weshallnotconsiderthedesignofplatetowersinthisbook;ourdiscussionswillbelimitedtocontinuous-contactequipment. 31.2 GAS–LIQUID MASS-TRANSFER OPERATIONS IN WELL-MIXED TANKS Aeration is a common gas–liquid contacting operation where compressed air is intro-duced to the bottom of a tank of liquid water through small-orifice dispersers, such as Raschig ringLessing ringPall ringBerl saddle Figure 31.4  Common industrialtower packing.31.2 Gas–Liquid Mass-Transfer Operations In Well-Mixed Tanks  605  perforated pipes, porous sparger tubes, or porous plates. These dispersers produce smallbubbles of gas that rise through the liquid. Often, rotating impellers break up the bubbleswarms and disperse the bubbles throughout the liquid volume. Gas–liquid mass-transferprocesses induced by aeration include  absorption  and  stripping.  In gas absorption, asolute in the aeration gas is transferred from the gas to the liquid. Often, the solute is theoxygen gas in air, which is sparingly soluble in water. The absorption of oxygen intowater underlies many processes important to biochemical engineering. In liquid strip-ping, the volatile dissolved solute is transferred from the liquid to the aeration gas.Stripping underlies many wastewater-treatment processes important to environmentalengineering.The gas–liquid contacting pattern in aeration processes is gas dispersed, meaning thatthe gas is dispersed within a continuous liquid phase. Consequently, the material balancesfor solute mass transfer are based on the liquid phase. Recall from Section 29.2 that theinterphasemass-transferfluxforsolute  A acrossthegas-andliquid-phasefilms,basedontheoverall liquid phase driving force, is  N   A  ¼  K   L  ( c   A    c  A ) (29-11)and the transfer rate for solute  A  is W   A  ¼  K   L   A i V V  ( c   A    c  A )  ¼  K   L  a : V  ( c   A    c  A ) (30-27)with c   A  ¼  p  A  H  where  P  A  is the partial pressure of solute  A  in the bulk gas phase. Recall from Section 30.5that the interphase mass-transfer area per unit volume is hard to measure, and so capacitycoefficients, e.g.,  K   L  a , are used.Well-mixed gas–liquid contacting processes can be either continuous or batch withrespect to the liquid phase. A continuous process is shown in Figure 31.6. For a batch Gas outLiquid outLiquid inGas inGasSieve plateBubble plate Figure 31.5  Plate towers. 606  Chapter 31 Mass-Transfer Equipment
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