Air-lift pumps characteristics under two-phase ow conditionsSadek Z. Kassaba, Hamdy. A. Kandila, Hassan A. Wardaa, Wael H. Ahmedb,*aMechanical Engineering Department, Faculty of Engineering, Alexandria University Alexandria, EgyptbNuclear Safety Solution Ltd., AMEC, 700 University Avenue, Toronto, Ontario, Canada M5G 1X6arti cle i nfoArticle history:Received 31 March 2008Received in revised form 22 September2008Accepted 23 September 2008Available online xxxxKeywords:Air-lift pumpsTwo-phase owVertical pipeabstractAir-liftpumpsarendingincreasingusewherepumpreliabilityandlowmaintenancearerequired,where corrosive, abrasive, or radioactive uids in nuclear applications must be handled and when a com-pressed air is readily available as a source of a renewable energy for water pumping applications. Theobjective of the present study is to evaluate the performance of a pump under predetermined operatingconditions and to optimize the related parameters. For this purpose, an air-lift pump was designed andtested. Experiments wereperformed for nine submergence ratios,and three risers of differentlengthswith differentair injectionpressures. Moreover, thepump wastestedunderdifferenttwo-phaseowpatterns. A theoretical model is proposed in this study taking into account the ow patterns at the bestefciency range where the pump is operated. The present results showed that the pump capacity and ef-ciency are functions of the air mass ow rate, submergence ratio, and riser pipe length. The best efciencyrange of the air-lift pumps operation was found to be in the slug and slug-churn ow regimes. The pro-posed model has been compared with experimental data and the most cited models available. The pro-posed model is in good agreement with experimental results and found to predict the liquid volumetricux for different ow patterns including bubbly, slug and churn ow patterns. 2008 Elsevier Inc. All rights reserved.1. IntroductionThe great focus towards the renewable energy for water pump-ing applications brought the attention to revisit the analysis of theair-lift pumps operated in two-phase ow. As the pneumatic trans-mission wind pumps operate on the principle of compressed air byusing a small industrial air compressor to drive an air-lift pump orpneumatic displacement pumps. The main advantage of this meth-od is that there is no mechanical transmission fromthe windmill tothe pump, which avoids water hammer and other related dynamicproblems. The pump can operate slowly even while the windmill isrunning rapidlywithnodynamicproblem.Other advantagesareitssimplicityandlowmaintenance. However, thistechnologyisstill under development and will require intensive eld testing be-fore it can be commercialized.Air-lift pump is a device for raising liquids or mixtures of liquidsandsolidsthroughaverticalpipe, partiallysubmergedintheli-quid, bymeansofcompressedairintroducedintothepipenearthe lower end. The air then returns up in a discharge pipe carryingthe liquid with it. The pump works by aerating the liquid in thedischarge pipe. The added air lowers the specic gravity of the uidmixture. Since it is lighter than the surrounding liquid, it is pushedupwards.The principles of air-lift pumping were understood since about1882, but practical use of air-lift did not appear until around thebeginning of the twentieth century (Bergeles 1949). In comparisonwith other pumps, the particular merit of the air-lift pump is themechanical simplicity. Moreover, they can be used in a corrosiveenvironment, and are easy to use in irregularly shaped wells whereother deep well pumps do not t. Thus, theoretically, the mainte-nance of this kind of pumps has a lower cost and higher reliability.There is a wide use of the air-lift pumps in many applications suchas in under water explorations or for rising of coarse particle sus-pensions (Stenning and Martin 1968), dredging of riverestuariesandharbors, andsludge extractioninsewage treatment plant(Storch 1975).The present study is concerned with the applications of air-liftpumps in pumping liquids. In this case, the ow in the pump riseris a two-phase ow. The ow of the two phases in the riser of anair-lift pump is a direct application of the upward ow in verticalround tubes. The common owpatterns for vertical upwardow arechanging asthemassquantity isincreased (Taitel etal.1980).Sharma and Sachdeva (1976) studied the factors that affect theperformanceofbigdiameterair-liftpumpsoperatinginshallowdepths. Theyrelatedthepumpperformancetothetypeofowpatternintheriser. Inaddition, DeCachardandDelhaye(1996)showedexperimentallythat the dominant owpatterninthepractical operating range of a small diameter air-lift pump is slug0142-727X/$ - see front matter 2008 Elsevier Inc. All rights reserved.doi:10.1016/j.ijheatuidow.2008.09.002*Corresponding author. Tel.: +1 6135846814; fax: +1 6135849497.E-mail addresses: wael.ahmed@amec.ca, wael.ahmed@gmail.com (W.H. Ahmed).International Journal of Heat and Fluid Flow xxx (2008) xxxxxxContentslistsavailableatScienceDirectInternational Journal of Heat and Fluid Flowj our nal homepage: www. el sevi er . com/ l ocat e/ i j hf fARTICLE IN PRESSPlease cite this article in press as: Kassab, S.Z. et al., Air-lift pumps characteristics under two-phase ow conditions, Int. J. Heat Fluid Flow(2008), doi:10.1016/j.ijheatuidow.2008.09.002ow. A few studies are available on the effect of the liquid proper-ties such as surface tension and viscosity and pipe geometry on theair-lift pump performance. For example, Khalil and Mansour(1990) carried out experimental work to study the effect of intro-ducingasurfactantinthepumpedliquid. Theyprovedthattheuseof asurfactant insmall concentrationalwaysincreasesthecapacity and efciency of the pump. Further, they found that thepumpperformanceisafunctionofthevolumetricair-owrate,submergenceratio(Hs/L)asshowninFig. 1, air-supplypressureand surfactant concentration. Iguchi and Terauchi (2001) studiedthe effect of the pipe-wall wettability on the transition among bub-bly and slug ow regimes in airwater two-phase ow in a verticalpipe. They changed the advancing contact angle of an acrylic pipebycoatingits inner wall byahydrophilic substanceor liquidparafn. Somedifferenceswereobservedbetweenpipewallsofdifferent wettability. Flow pattern maps were developed for differ-ent pipe-wall wettability. Also, Furukawa and Fukano (2001) inves-tigatedexperimentallytheeffectsof theliquidviscosityontheowpatternsof upwardairliquidtwo-phaseowinaverticalpipe. They used three different liquids including water and glycolsolutions. They proposed ow pattern maps for each liquid viscos-ity. It was found that ow pattern transitions strongly depend ontheliquidviscosity. Recently, Hitoshietal. (2003)foundexperi-mentally that the gas-injection point has a big effect on dischargedwater. They concluded that, as gas-injection point increases above45 pipe diameters, the discharged water decreases.Although the geometry of the pump is very simple, the theoret-ical study of its performance is very complicated. The efforts to ex-plainandstudyits performance startedveryearlyinthelastcentury. Amongtheearlyclassical theoriesof theair-liftpump,are those proposed by Harris, Lorenz, Gibson, and Swindin, as men-tionedbyStapanoff(1929). Harrisconsideredtheforceofbuoy-ancyof the air bubbles as the motive force of the pump. Heanalyzed the motion of the bubble, and obtained the relation be-tween the size of the bubble, slip (relative velocity of the air bubblewithrespect tothewater), andtheheadproduced. Lorenz, indeveloping his theory, wrote Bernoullis equation for a differentialhead corresponding to a given ow in the discharge pipe, introduc-ing variable pressure, density of mixture, and integrating betweenthe head limits and thus he obtained the relation between the vari-ables involved. Stapanoff (1929) used the thermodynamics theoryin studying the effect of the submergence, the diameter of the riserpipe, airtowaterratio, climate, andintroducingcompressedairabovethesurfaceof thewaterinthewell, ontheefciencyofthe air-lift pump. He found that treating the air-lift pump thermo-dynamically has a denite advantage in explaining many points ofits operation.Morethanthreedecadeslater, atheoreticaltreatmentoftheair-lift pump, based on the theory of slug ow, was presented byNicklin(1963). He studied the effects of different parametersincluding; diameter, length, pressure at the top of riser tube, sub-mergenceratio, andwatervolumetricowrate, ontheair-lift-pump efciency. He found that, by neglecting the entrance effectsand assuming slug ow in the riser tube, the performance of theair-liftpumpmaybeobtainedbasedontwo-phaseslugowre-gime. He used a denition of the efciency of the pump as the workdone in lifting the liquid, divided by the work done by the air as itexpandsisothermally. ThetheorypresentedbyNicklinwasex-tended by Reinemann et al. (1986) taking into account the effectNomenclatureA pipe cross-sectional area, m2b wetted perimeter of pipeD pipe diameter, mf friction factorg gravitational acceleration, m/s2Hsstatic depth of water, mHdstatic liftK friction parameterL pipe length, mLspipe suction length, mP pressure, N/m2Q volume ow rate (discharge), m3/sSrSr = Hs/L, submergence ratios slip ratioU supercial velocity, m/sV velocity, m/sW weight, Nq density, kg/m3g efciency,%s wall shear stress, N/m2e pipe roughnessReReynolds numberSubscripts1 entering injection zone2 leaving injection zonea atmosphericgs gas as a single phaseg gasL liquidls liquid as a single phaseS solid8 10 1191312316615147541HsLLs2Fig. 1. A schematic diagram of the experimental setup. 1.Riser, 2. Down comer, 3.Overhead collecting tank, 4. Scale, 5. Drain, 6.Water feeding tank, 7. Over ow pipe,8. Compressor, 9. Regulator, 10. Pressure gage, 11. Thermometer, 12. Air-jacket, 13.Below meter, 14. Feeding water line, 15. Control valve, 16. Float.2 S.Z. Kassab et al. / International Journal of Heat and Fluid Flow xxx (2008) xxxxxxARTICLE IN PRESSPlease cite this article in press as: Kassab, S.Z. et al., Air-lift pumps characteristics under two-phase ow conditions, Int. J. Heat Fluid Flow(2008), doi:10.1016/j.ijheatuidow.2008.09.002of surface tension on the bubble velocity. Another analytical studyof air-lift pump performance was presented by Stenning and Mar-tin(1968). Theyusedthecontinuityandmomentumequations,assuming one-dimensional ow in the pump riser, and used the re-sults of two-phase ow research to solve the governing equations.They found that one-dimensional-ow theory forms a good basisfor the performance analysis of air-lift pumps. Also, Clark and Da-bolt (1986) introduced a general design equation for air-lift pumpsoperating in slug owregime by integrating the differentialmomentumequationover thewholepumplength. Themodelwasvalidated bytheoperation curvesplotted fromtheir experi-mental results. They indicated also that the analysis presented byNicklin(1963)wasaccurateonlyinthedesignof shortpumps,since there is no provision for variation in gas density over the tubelength. In addition, they concluded that, the frictional pressure lossbecomes signicant for small riser diameter of about 10 mm.Thepresent studyreviewedthepreviousmodels, dealt withthe air-lift pump performance when operating in two-phase owregime. A modied version of these models is developed. The re-sults of the proposed modied model are then compared with theexperimental measurements of Kassabet al. (2007) andotheravailable models. In order to study the performance of the air-liftpumpunderdifferentowpatternstheair-owraterangewasextendedinthepresent studytocover different owpatternsincluding bubbly, slug, churnand annular owconditions. Inaddition, pipeswithdifferentlengthswereusedtostudytheef-fectof theriser-pipelength, atthesamesubmergenceratio, onthe pumpperformance. Experiments were performedfor ninesubmergenceratios, andthreelengthsofthepiperiserwithdif-ferent air injectionpressures. Moreover, the different owre-gimes and the transition of the ow patterns were observed andrecordedandtheresultsarediscussedtakingowpatternsintoconsideration.2. Experimental setupThe experimental setup used in the present study is schemati-cally shown in Fig. 1. It consists of a vertical transparent pipe (1),of 3.75 m length and 25.4 mm inner diameter, and a down-comer(2) of 30 mm inner diameter. The riser pipe is divided into threesectionstoallowstudyingtheeffect of changingthelengthofthe riser pipe. The upper end of the riser is connected to an over-head-collecting tank (3) where the air escapes to atmosphere andwaterowrateismeasuredaccordingtothewaterlevel inthetankusingacalibratedscale(4). Theoverheadtankisdesignedtoabsorbthewatersurfaceuctuationsanddampfreevorticesandthusprovidesaccurateowratemeasurements. Watermaybe directed through a pipe (5) to the drain. The movable water sup-plytank (6)iskeptataconstant waterhead byoverowing thewater through a pipe (7). The tank may also be moved up or downto change the submergence ratio. All pipes and tanks are made oftransparent material for visibility of the ow structure.Airissuppliedtotheairinjectionsystemfromacentral aircompressor station. The station consists of a 55 kW Ingersoll Randscrew compressor (8) delivering 8.2 m3of free air per minute at amaximumpressureof 8 bar, throughamassrefrigerationdryerandltrationsystem, andanairreservoirof3 m3capacity. Air-ows from the air reservoir through a 25.4 mm diameter pipelinetoanon/offvalve, thentoapressure-reducingvalve(regulator)(9), where the pressure is reduced to the desired working pressure(1 1042.7 105Pa)tocovertherequiredexperimentalrange.Air is then injected into the riser ata constant pressure that canbemeasuredbythepressuregage(10). Amercurythermometer(11) is used for measuring the upstream air temperature. Then aconstant air mass owrate passes throughanair jacket (12)aroundtheverticalpipeusinganairinjector. Thevolumeofairis measured using a calibrated below-meter (13). The air injectorconsists of 56 small holes of 3 mm diameter uniformly distributedaround the pipe perimeter in seven rows and eight columns to in-sureuniformfeedoftheairintothepipeatthemixingsection,which is 20 cm above the lower end of the pipe.Varioussubmergenceratios(from0.2to0.75) wereinvesti-gated in the present study. This range of submergence ratios wasobtained in increments approximately 0.1, that covers most indus-trial applications where the air-lift pump is used. For each submer-genceratio, theair-owratewasvariedandthecorrespondingow rate of water was measured. In order to obtain specied andplaned measurements, a specic operating procedure was followedfor each run.3. Results and discussion3.1. Water ow rateThe results of lifting water in the riser tube of an air-lift pump,at various values of air mass ow rates corresponding to differentvaluesofairinjectionpressuresarepresented. Fig. 2showsthewater ow rate as a function of the air-ow rate at a submergenceratio of 0.4. Using ow visualization, Fig. 3, and the experimentalresults, it was noticed that for low values of air mass ow rate from0 to 1 kg/h depends onthe submergence ratio, nowater is lifteddue to the buoyant force exerted by the air bubbles is not enoughto raise any water. The total quantity of air penetrates the watercolumn without lifting any water. Fig. 3a shows that the ow re-gimeistotallybubblyforverysmall valuesof air-owrate. Asthe air mass ow rate is increased, a train of air slugs starts to de-velop in the pipe. It consists of some small slugs of lengths from 10to 15 cm distributed along the pipe length. The biggest bubble islocated at the upper part of the pipe while the smallest one is lo-catedatthelowerpartofthepipe. Thetrainofairslugsmovesslowlyupwardsleavingthepipewithoutanybubblesforafewseconds. The distribution is then repeated after a few seconds. Thisis because the air takes a few seconds to accumulate in the lowerend of the pipe. It was observed that the air pressure at injectionpointuctuatesby1or2 kPaaroundameanvalue. Thisisdueto the accumulation of air to form a slug that is strong enough topenetratethewater columnandmoveupwards. Whentheairmass ow rate is increased slightly over 0.229 kg/h, the water owstarts, andtheowpicture, Fig. 3b, issimilartothecaseofthepenetrating column except that, the slugs become taller. The0 4 8 12 16 20Air mass flow rate (kg/hr)0100020003000Water mass flow rate (kg/hr)a b c, d e,f g,hBubbly flowBubbly-SlugSlug flowSlug-Churn flowAnnular flowSubmergence ratio = 0.4Fig. 2. Variation of air mass ow rate with water mass ow rate at submergenceratio = 0.4 (ag represent the sequence of photos presented in Fig. 3).S.Z. Kassab et al. / International Journal of Heat and Fluid Flow xxx (2008) xxxxxx 3ARTICLE IN PRESSPlease cite this article in press as: Kassab, S.Z. et al., Air-lift pumps characteristics under two-phase ow conditions, Int. J. Heat Fluid Flow(2008), doi:10.1016/j.ijheatuidow.2008.09.002structureoftheslugowinthepipecanbedescribedbyase-quence of a big air slug followed by a water slug that contains somesmall air bubbles and then smaller air and water slugs. The cycle isthen repeated as shown in Figs. 3cd. This observation agrees withthe experimental work by Sekoguchi et al. (1981). This sequence ofslugformationmaybeduetothetimetakentochargeenoughquantity of air capable of lifting a certain amount of water. This ex-plains the oscillation of the air injection pressure. The oscillationand the instability of the pump were studied by Hjalmars (1973).He found that, for a large air-lift pump, when the static lift was in-creased to about 30-40 pipe diameters, the instability of the air-liftpump starts. However, when the value of the static lift reached acritical value, instability sets in with a periodic and increasing var-iation of water discharge around its stationary value. The reason oftheseoscillationswasalsodiscussedbySekoguchi etal. (1981).Theyreferredthisbehaviortothecompressibilityof thegasinthe gasliquid two-phase mixture and reversal of water ow fromthetwo-phasemixingsectiontotheheadtank. Inthepresentstudy a very small variation was observed, and hence the instabil-ity effects were neglected.The reason for the transition from bubbly to slug ow is that, asthe gas ow is increased, the bubbles get closer together and colli-sion occurs. Therefore, some of the collisions lead to coalescence ofbubblesandeventuallytotheformationofslugs. Forasubmer-gence ratio of 0.75, the lifting of water becomes noticeable at a va-lue of air-ow rate of approximately 1 kg/h. Any slight increase inthe airow rate beyond that value causes the water ow rate to in-crease rapidly. It is noted that in the region where the water massow rate is increasing (from 403 to 642 kg/h), the ow regime ismostlyslug-churnow. Inaddition, themaximumowrateofwater (642 kg/h) occurs when the ow pattern is slug-churn ow.As can be seen in Fig. 2, the water mass ow rate increases asthe air mass ow rate increased, until it reaches a maximum value.It was noticed that, in the region in which the water ow rate in-creases, the ow pattern changed from slug to slug-churn ow asshown in Fig. 3ef. This can be explained as follows: as the gas slugrises through the liquid, the direction of gas velocity inside the slugisupwards, whilethewater velocitydirectioninthethinlmaround theair slugis usually downwards, so theow is countercurrent. At some critical value of air mass ow rate the gas velocitywill suddenly disrupt the liquid lm (the lm will ood) and there-fore the slug ow will break down to give churn ow with pulsat-ing,highly unstable pattern,as suggested by Nicklin (1963). Itisnotedthattheregionoftheslug-churnowisthemainregionwhere the pump should be operating. The quantity of lifted waterremains almost constant for a small range of air-ow rates (from5.3 kg/h to 6.2 kg/h). Physically, the maximum water ow rate isreached when the frictional pressure drop caused by further addi-tion of air exceeds the buoyancy effect of the additional air, as wasexplained by Reinemann et al. (1986). Further increase in the air-ow causes a slight decrease in the water ow rate to a value of(51 kg/h), and the ow regime changes from slug-churn to annularowtypeasshowninFig. 3g. Thistransitionisbecausethegasvelocity becomeshighenoughtosupporttheliquidasalmonthetubewall, andalsobecausethepressuredropexceedsthebuoyancy effect.Fig. 3h shows the annular ow pattern and also how water isliftedthroughthepiperiser. Asmall amountof wateristrans-ported as a liquid lm on the tube walls, while another part formssmall droplets of water injected in the pipe core upward. Measure-ments were performed at different values of submergence ratios,and the results are shown in Fig. 4. It is clear that the performancecurves of the air-lift pump are shifted upward while the submer-genceratioisincreased. All theperformancecurvesatdifferentFig. 3. Photos present the sequence of the ow patterns: (a) Bubbly, (b) bubbly to slug, (c and d) slug, (e and f) slug-churn, (g and h) annular.0 4 8 12 16 20Air mass flow rate(kg/hr)050010001500200025003000Water mass flow rate (kg/hr) Sr=0.2Sr=0.227Sr=0.3Sr=0.4Sr=0.484Sr=0.57Sr=0.67Sr=0.75Fitting LinesFig. 4. Variation of water mass ow rate with air mass ow rate at different valuesof submergence ratio.4 S.Z. Kassab et al. / International Journal of Heat and Fluid Flow xxx (2008) xxxxxxARTICLE IN PRESSPlease cite this article in press as: Kassab, S.Z. et al., Air-lift pumps characteristics under two-phase ow conditions, Int. J. Heat Fluid Flow(2008), doi:10.1016/j.ijheatuidow.2008.09.002valuesofsubmergenceratiohavesimilartrend. Also, duringtheexperiments, it was noticed that the ow pattern changes by thesame sequence as indicated earlier (for the 0.4 submergence-ratiocase). In addition, Fig. 4 shows that, for a xed value of air massowrate, thewaterowrateincreaseswiththeincreaseofthesubmergence ratio.3.2. The pump efciencyThe denition of the air-lift pumps efciency is given by Nicklin(1963) asg qgQLL HsPaQaLnpinPawhere QLis the water discharge, Qa is the volumetric ow rate of air,Pin the injection pressure of air, q is the liquid density and Pa is theatmospheric pressure.Pumpefciencyversusairmassowrate, forasubmergenceratioof0.4, isshowninFig. 5a. Astheairmassowrateisin-creased, theefciencyincreasesrapidlyfrom0toreachamaxi-mumvalueof 32.4%at anair mass owequals 1.5 kg/h, andthen, it tends to decrease as the air mass ow rate is increased.Theefciencycurvesatdifferentvaluesofsubmergenceratioare presented in Fig. 5b. They have similar trend as theone pre-sented in Fig. 5a for submergence ratio of 0.4. In addition the bestefciencyrangeisintherst regionof theperformancecurve,which is a slug ow region. The maximum efciency increased to44% when the submergence ratio is increased to 0.75 as presentedin Fig. 5b. Comparing the water mass ow rate results presented inFig. 4 with the efciency results presented in Fig. 5, it is importantto notice that, the maximum efciency does not occur at the max-imum water mass ow rate for all values of submergence ratio.3.3. Effect of riser lengthThe effect of riser length was also studied in the present study.This was done by xing the submergence ratio and varying the sta-tic lift by changing the riser length. Experiments were performedfor submergenceratiovaluesof 0.4, 0.484, 0.5, 0.57, 0.67, and0.74, anddifferent total pipe lengths of; 175 cm, 275 cm, and375 cm. Theperformancecurvesof thepumparepresentedforeach case in Fig. 6. While the effect of the variation of the static lifton pump efciency for submergence ratio equal to 0.57, is showninFig. 7. Itisclearfromtheseguresthat, foranyriserlength,there is a slight effect of the total pipe length on the performancepattern, intheslugowregion. However, themaximumwatermassowratedecreaseswhenthestaticlift isdecreased, andtheperformancecurveshiftsdownbyasmall amount for theremainingregions. Moreover, forsubmergenceratioslowerthan0.3, it was noticed that, there was no water lifted if the static liftisincreasedto82.5 cm(32pipediameters). Thisisbecauseairwasnot abletocarrythewatercolumntoadistanceequal tothe static lift, and air penetrates the water column without liftinganaccountablemassof water. TheresultspresentedinFigs. 6and 7 show that not only the submergence ratio affects the air-liftpump performance but also the magnitude of the riser length.3.4. Flow pattern mapFig. 8a shows the distribution of the test data on the ow pat-tern map proposed by Taitel et al. (1980). It can be seen that theregions occupied by the experimental data points agree with theobservations. Some experimental measurements fromthehighefciency range (g > 20%) at different submergence ratios aremapped on the ow-pattern map as shown in Fig. 8b. The best ef-ciencyrangewheretheefciencyexceeds20%liestotallyintheslug or slug-churn owregions. This may explain why most analyt-ical studies were based on the slug or slug-churn ow patterns.4. Modeling the air-lift pump performanceTheproblemconsideredisthepredictionof theliquidmassowrateasafunctionoftheairmassowrate. Thegeometricparameters (L, Hs, Ls, and D), the pressure conditions (Pa, Pin), andthe uid properties are given as input data to the theoretical modelequations. Where L is the riser-pipe length, Hs is the static head ofwater, Ls is the length of the suction part of the pipe, D is the pipediameter, Paistheatmosphericpressure, andPinistheinjectionpressuretotheriserpipe. Asthebasicperformancedataoftheair-lift pump is computed, secondary results such as the efciencymay easily be determined.4.1. Clark and Dabolt modelThe general design equation for air-lift pumps operating in theslug ow regime that was developed by Clark and Dabolt (1986) istakenasapreliminaryinvestigationmodel of thepumpperfor-mance. A computer program was developed for the equations de-rivedbyClarkandDabolt(1986), usingthemomentumbalance.Derivation is based on the assumption that the two-phase ow re-mains within the slug ow mode and the ow is one-dimensional.0 4 8 12 16 20Air mass flow rate (kg/hr)Air mass flow rate (kg/hr)02040Efficency (%)Efficency (%)Spline smoothingSubmergence ratio= 0.40 4 8 12 16 20103050Submergence ratio (Sr)Sr=0.74Sr=0.67Sr=0.57Sr=0.4Sr=0.277abFig. 5. Variationofpumpefciencywithairmassowrateat:(a)submergenceratio = 0.4 (b) different values of submergence ratio.S.Z. Kassab et al. / International Journal of Heat and Fluid Flow xxx (2008) xxxxxx 5ARTICLE IN PRESSPlease cite this article in press as: Kassab, S.Z. et al., Air-lift pumps characteristics under two-phase ow conditions, Int. J. Heat Fluid Flow(2008), doi:10.1016/j.ijheatuidow.2008.09.002Thetheoretical predictionsusingClarkandDaboltmodel to-gether withthe corresponding experimental results of Kassabetal. (2001)arepresentedinFig. 9forasubmergenceratioof0.4. The agreement between these two results is quite reasonableup to an air mass ow rate of 3.4 kg/h. The theoretical model doesnotpredicttheexperimentaldataforairmassowrateshigherthan 3.4 kg/h. The results obtained for different submergence ra-tios(not shown), werealsocomparedwiththosepredictedbythe model proposed by Clark and Dabolt (1986). The comparisonshowed that the model is suitable only for the rst region of pumpperformance, wheretheowregimeisslug. Fromthepreviouscomparisonandinorder toextendtheoperatingrangeof theair-lift pump, it is essential to develop a model which is more gen-eral than that proposed by Clark and Dabolt (1986).4.2. A modied model for the performance of the air-lift pumpsAs discussed earlier in the literature review, the direct approachtostudytheair-liftpumpperformanceemploysthemomentumequation and the continuity equation, assuming one-dimensionalow. This assumption is valid for the practical operating range ofthe air-lift pumps as concluded by Clark and Dabolt (1986). Con-0 4 8 12 16 2001000200030000 4 8 12 16 2001000200030000 4 8 12 16 2001000200030000 4 8 12 16 2001000200030000 4 8 12 16 20 Air mass flow rate (kg/hr) Air mass flow rate (kg/hr) Air mass flow rate (kg/hr)Air mass flow rate (kg/hr) Air mass flow rate (kg/hr)Air mass flow rate (kg/hr) 0100020003000 water mass flow rate (kg/hr) water mass flow rate (kg/hr) water mass flow rate (kg/hr) water mass flow rate (kg/hr) water mass flow rate (kg/hr) water mass flow rate (kg/hr)0 4 8 12 16 200100020003000abcfedSubmergence ratio= 0.5Static lift= 187.5 cmStatic lift= 137.5 cmStatic lift= 87.5 cmSubmergence ratio= 0.4Static lift=225 cmStatic lift=165 cmStatic lift=105 cmSubmergence ratio=0.57Static lift =161.25 cmStatic lift =118.25 cmStatic lift =75.25 cmSubmergence Ratio=0.484Static Lift=193.5 cmStatic Lift=142 cmSubmergence ratio=0.67Static lift= 123.75 cmStatic lift=90.75 cmSubmergence ratio=0.74Static lift =97.5 cmStatic lift =71.5 cmFig. 6. Effect of static lift on the air-lift pump performance at various values of submergence ratio.6 S.Z. Kassab et al. / International Journal of Heat and Fluid Flow xxx (2008) xxxxxxARTICLE IN PRESSPlease cite this article in press as: Kassab, S.Z. et al., Air-lift pumps characteristics under two-phase ow conditions, Int. J. Heat Fluid Flow(2008), doi:10.1016/j.ijheatuidow.2008.09.002sider a vertical pipe partly full of liquid, and let the base of the pipehave a reference height of zero as shown in Fig. 10. Since the tube islled to a static head of Hs, then the static pressure, Po, at the baseof the pipe is given by Bernoullis equation as follows:Po PaqLgHs12qLV211where qL is the liquid density, Pa is the atmospheric pressure and V1is the water velocity at the inlet section.Neglecting the density changes of the air, the continuity equa-tion can be written as follows:AV2 QgQL QgAV12where V2is the mixture velocityof air andwater leavingtheinjector.Dividing all terms of Eq. (2) by QL = AV1, givesV2 V11 QgQL_ _3Neglecting the air mass ow rate compared to the liquid mass owrate, the continuity equation can be written as follows:q2AV2 qLAV14So,q2 qLV1V25Substituting Eq. (3) in Eq. (5), we obtainq2 qL1 QgQL_ _ 6Themomentumequationappliedtotheinjectorasacontrolvol-ume, neglecting the wall friction, is given byP2 PoqLV1V2V1 7From Eq. (3) in (7), thenP2 PoqLV1QgA8Hence, combining (1) and (8), givesP2 PaqLgHs12qLV21qLV1QgA9Neglecting momentumchanges causedbythe owadjustmentafter the mixer, the momentum equation for the upper portion ofthepumpcanbewrittenas suggestedbyStenningandMartin(1968) in the form:P2Pa sLbA WA10where s is the average wall shear stress, b is the wetted perimeter ofthe pipe, and W is the total weight of the gas and liquid in the pipe.An expression for the average shear stress, s, was suggested byGrifth and Wallis (1961) as follows:s f qLQLA_ _21 QgQL 11where fis the friction factor assuming that the water alone owsthrough the pipe.The weight of the uid in the pipe equals the totalweight of liquid plus gas, which can be obtained as follows:W LqLALqgAg 120 4 8 12 16 20Air mass flow rate (kg/hr)103050Efficency (%)Submergence Ratio=0.57Static Lift=161.25 cmStatic Lift=118.25 cmStatic Lift=75.25 cmFig. 7. Variation of the pump efciency with the static lift at submergenceratio = 0.7.0.0 0.1 1.0 10.0 100.00.0 0.1 1.0 10.0 100.0Gas superfitial velocity(m/s)Liquid superfitial velocity (m/s)Present observation Slug flow Slug-Churn flowAnnular flowSlugSlug or ChurnAnnularGas superfitial velocity(m/s)0.000.010.101.0010.000.000.010.101.0010.00Liquid superfitial velocity (m/s)Present observation Slug flow Slug-Churn flowSlugSlug or ChurnAnnularFig. 8. Comparison between the results of the present study and Taitel et al. (1980)ow-pattern map: (a) distribution of the experimental data (b) distribution of thebest efciency points.S.Z. Kassab et al. / International Journal of Heat and Fluid Flow xxx (2008) xxxxxx 7ARTICLE IN PRESSPlease cite this article in press as: Kassab, S.Z. et al., Air-lift pumps characteristics under two-phase ow conditions, Int. J. Heat Fluid Flow(2008), doi:10.1016/j.ijheatuidow.2008.09.002where AL is the area for the liquid phase, and Ag is the area for thegas phase.A ALAg13Qg AgVg14QL AlVL AV115Substituting (13)(15) in (12) and neglecting the density of gas withrespect to the liquid density, we obtain:W LqLA1 QgsQL_ _ 16where s is the slip ratio which equals:s VgVL17where Vgand VLare the actual velocities of gas and liquid,respectively.Substituting from Eqs. (11) and (16) in Eq. (10), we get:P2 Pa4fLDqLV211 QgQL_ _qLL1 QgsQL_ _ 18This equation was obtained by Stenning and Martin (1968) and itcan be written as followsHsL 11 QgsQL_ _ V212gLK 1 K 2QgQL_ _19where K is the friction factor which is given byK 4fLD20Stenning and Martin (1968) used the above equations in theiranalytical model but theyxedthevaluesof theslipratio(s),andthefrictionfactor (K). Physically, theslipratiochangesasthewatermassowrateandairmassowratechanges. Also,the friction factor changes with changing the ow conditions.In the present work, the slip ratio is considered as a function ofthe water and air mass ow rates as expressed by Grifth and Wal-lis (1961) for slug ow in the form:s 1:2 0:2QgQL0:35 gD_V121Also, thefrictionfactorisobtainedusingColebrookequationaslistedbyHaaland(1983), wherethefrictionfactor, f, maybeob-tained by solving the following equation:1f_ 2:0loge=D3:7 2:51Re f__ _22where e is the pipe roughness and Re is the Reynolds number.Finally, the pump efciency is calculated in thepresent studyusing the denition given by Nicklin (1963) as follows:g qgQLL HsPaQalnpinPa23where QL is the water discharge, Qa is the volumetric ow rate of air,Pinis the injectionpressure of air, and Pais the atmosphericpressure.The modied model is obtained by inserting Eqs. (21) and (22)inEq. (19). Usingthismodied model, acomputerprogram wasdevelopedinordertoinvestigatetheair-liftpumpperformanceover an extended range of the pump operation. A calculation pro-cedure to obtain the results using the proposed model as follows:(1) ThegeometricalparametersofL, D, piperoughness e, andthe water density q and viscosity l, are known. Then for aknownair inlet pressuretheinlet air mass owrate isassigned.(2) Select a static head Hs for a certain submergence ratio.(3) Assume a value of water mass ow rate.(4) Compute the coefcient of the friction f from Colebrook Eq.(22), also calculate the slip ratio s from Eq. (21).(5) Calculate the value of friction factor K from Eq. (20).(6) Calculate the value of the left hand side and the right handside of Eq. (19).(7) Repeat steps 36 until the total difference between the lefthand side and the right hand side of (19) becomes less than0.001.5. Comparison with the experimental dataIn order to evaluate the validity of the results obtained using theproposedmodel acomparisonwiththeexperimental resultsof12 8 4 0Air mass flow rate (kg/hr)050010001500Water mass flow rate (kg/hr) Submergence Ratio = o.4Clark &Dabolt (1986)Experimental dataslug flowFig. 9. Comparison between the results of Clark and Dabolt (1986) and theexperimental results of Kassab et al. (2001).(1)(2)WaterAir AirHsLDischFree SurfaceAir JacketFig. 10. Model for analysis of airlift pump.8 S.Z. Kassab et al. / International Journal of Heat and Fluid Flow xxx (2008) xxxxxxARTICLE IN PRESSPlease cite this article in press as: Kassab, S.Z. et al., Air-lift pumps characteristics under two-phase ow conditions, Int. J. Heat Fluid Flow(2008), doi:10.1016/j.ijheatuidow.2008.09.002Kassab et al. (2001) was performed. This comparison is shown inFig. 11a for a submergence ratio of 0.484. It is clear from this gurethat the agreement between the results of the proposed model andthe experimental data is good over a range of air mass ow ratesupto8.3 kg/hwhilethereisalargedeviationfortheremainderofthepumpperformancecurve. Thisisduetothetransitiontothe annular ow regime that is not taken into account in the pres-ent model.More comparisons between the results of the proposed modeland the experimental results obtained by Kassab et al. (2001), forsome other submergence ratios, are shown in Figs. 11bd. In gen-eral, good agreement is obtained for all presented submergence ra-tios. Inaddition, comparingtheresultspresentedinFig. 9withthoseinFig. 11, onenoticesthat theagreementof thepresentmodied model with the experimental data is better than that ofClark and Dabolt (1986).Theaveragedeviationbasedonrootmeansquarevaluesbe-tween the results of the present model and the experimental re-sultsisabout 15%, whichisacceptableif themodel isusedtoinvestigatetheperformanceinpractical applications. It appearsthat the one-dimensional theory forms a good basis for the perfor-mance analysis of air-lift pumps.The inuence of the riser pipe length on the airlift performancewas also studied using the modied model. Fig. 12 shows the effectof the riser pipe length on the air-lift pump performance in boththeoretical andexperimental results. Itisnotedthat, themodelproposed in the present study senses well the change of riser pipelength.The efciency of the air-lift pump is computed using the pres-entmodel basedonthedenitionpresentedbyNicklin(1963).TheobtainedresultsarepresentedinFig. 13andarecomparedwith the experimental results of Kassab et al. (2001). Good agree-ment between the theoretical and experimental results is achieved.0 4 8 12 16 20Air mass flow rate (kg/hr)Air mass flow rate (kg/hr)050010001500050010001500Submergence ratio=0.484experimental dataProposed modelAnnular flow regime(a) Submergence ratio = 0.484 12 8 4 0Air mass flow rate (kg/hr)12 8 4 0Air mass flow rate (kg/hr)12 8 4 0water mass flow rate (kg/hr)water mass flow rate (kg/hr)Submergence ratio=0.57Theortical modleExperimental data(b) Submergence ratio = 0.57water mass flow rate (kg/hr)0100020003000water mass flow rate (kg/hr)0100020003000Submergence ratio=0.67Theoritecal modelExperimental data(c) Submergence ratio = 0.67 Submergence ratio=0.74Theortical modelExperimental data(d) Submergence ratio = 0.74Fig. 11. Comparisons between the proposed model and the experimental results of Kassab et al. (2001).0 4 8 12Air mass flow rate(Kg/hr)050010001500Water mass flow rate (Kg/hr) Submergence ratio=0.484Theortical model (L=3.75m)Theortical model (L=2.75m)Experimental data (L=3.75m)Experimental data (L=2.75m)Fig. 12. Effect of the riser pipe length on the airlift-pump performance.S.Z. Kassab et al. / International Journal of Heat and Fluid Flow xxx (2008) xxxxxx 9ARTICLE IN PRESSPlease cite this article in press as: Kassab, S.Z. et al., Air-lift pumps characteristics under two-phase ow conditions, Int. J. Heat Fluid Flow(2008), doi:10.1016/j.ijheatuidow.2008.09.0025.1. Comparison with other modelsFig. 14 shows a comparison between the results of the proposedmodel and the corresponding results obtained using Clark and Da-bolt(1986)aswell asStenningandMartin(1968)models. Itisclearfromthecomparisonthattheproposedmodelgivesbetteragreement with the experimental data than especially in the bestefciency range while it is over predicting the experimental datain the annular owpattern region. The range of model applicabilityis taken as acceptable error between the experimental data and themodel predictions. Inthepresent experimental range(airmassow rate between 0 and 12 kg/h), the model found to be predictthewater mass owratewithin15%basedontheroot meansquare. This difference found to increase as the owpatternchanges to annular ow. Also, the proposed model tends to predictthe point where the pump starts to operate much better than theother two models.6. Uncertainty analysisThe uncertainty analysis was performed according to the multi-variate Taylor Series method and summarized in Table 1UR oRoX1UX1_ _2oRoX2UX2_ _2 oRoXJUXJ_ _2_ _1=224whereUXistheuncertaintyinthemeasuredvariableX. Also, theuncertainty for a measuring instrument is calculated from:UX e2o e2c_25where eo is the interpolation error, ec is the instrument erroreo 12Re solution 26Forexampletheproceduresofcalculatingtheuncertaintyofthemeasured variable are as follows:7. Concluding remarksThefollowingconcludingremarkscanbededucedfromthepresent study: As the submerged ratio increases, the maximumefciency of thepump increases at the same air-ow rate. The air-lift pump lifted maximum amount of liquid if operatedin the slug or slug-churn regimes. The maximum efciency does not occur at the maximum watermass ow rate. Thebestefciencypointsalwayslocatedintheslugorslug-churn ow patterns. For the same submergence ratio, varying the length of the riserpipe affects the air-lift pump performance. The one-dimensional model proposed in the present study canpredict theair-lift pumpperformanceandit canbeusedinthe design of air-lift pumps for different ow patterns includingbubbly, slug and churn ow patterns. Theproposedmodelgivesagoodagreementwiththeexperi-mental resultswithinthepractical rangeof operationof theair-lift pumps.ReferencesBergeles, A.E., 1949. Flow of gasliquid mixture. Chem. Eng., 104106.Clark, N.N., Dabolt, R.J., 1986. A general design equation for air-lift pumps operatingin slug ow. AICHE J. 32, 5664.DeCachard, F., Delhaye, J.M., 1996. A slug-churn ow model for small diameter airlift pumps. Int. J. Multiphase Flow 22, 627649.Furukawa, T., Fukano, T., 2001. Effects of liquidviscosityonowpatterns invertical upward gasliquid two-phase ow. Int. J. Multiphase Flow 27,11091126.Grifth, P., Wallis, G.B., 1961. Two-phase slug ow. J. Heat Transfer, Trans. ASME 83,307320.Haaland, S.E., 1983. Simple and explicit formulas for the friction factor in turbulentow. J. Fluids Eng. 103, 8990.Hitoshi, F., Satoshi, O., Hirohiko, T., 2003. Operationperformanceofasmall air-lift pumpfor conveyingsolidparticles. J. EnergyResour. Technol. 125, 1725.Hjalmars, S., 1973. The origin of instability in air lift pumps. J. Appl. Mech. Trans.ASME 95, 399404.Iguchi, M., Terauchi, Y., 2001. Boundaries among bubbly and slug ow regimes inairwater two-phase ows in vertical pipe of poor wettability. Int. J. MultiphaseFlow 27, 729735.Kassab, S.Z., Kandil, H.A., Warda, H.A., Ahmed, W.H., 2001. Performance of an air liftpumpoperatingintwo-phaseow. In: Proceedingsof ICFDP7:TheSeventhInternational Congress on Fluid Dynamics & Propulsion, December 1820, 2001,Cairo, Egypt, Paper No. ICFDP7-2001004.0 4 8 12Air mass flow rate (kg/hr)02040Submergence ratio=0.48Experime t n al dataTheoretical model % Fig. 13. Comparisonbetweenthecalculatedefciencyandthatobtainedexperi-mentally by Kassab et al. (2001).2 1 8 4 0Air mass flow rate (kg/hr)050010001500Water mass flow rate (kg/hr)Submergence Ratio= 0.4Experiment al dataClar k&Dabolt(1986)Stenning&Mar tin(1968)Propose d modelFig. 14. Comparison between the results of various models and the experimentalresults of Kassab et al. (2001).Table 1Uncertainty of the measured variablesQuantity Percentage uncertainty (%)Air mass ow rate 2.5Water mass ow rate 4Pressure 3Temperature 2.510 S.Z. Kassab et al. / International Journal of Heat and Fluid Flow xxx (2008) xxxxxxARTICLE IN PRESSPlease cite this article in press as: Kassab, S.Z. et al., Air-lift pumps characteristics under two-phase ow conditions, Int. J. Heat Fluid Flow(2008), doi:10.1016/j.ijheatuidow.2008.09.002Kassab, S.Z., Kandil, H.A., Warda, H.A., Ahmed, W.H., 2007. Experimental andanalytical investigations of airlift pumps operating in three-phase ow. Chem.Eng. J. 131, 273281.Khalil, M.F., Mansour, H., 1990. Improvement of the performance of an air lift pumpbymeansof surfactants, PresentedattheSixthInternational SymposiumofHeat and Mass Transfer, Miami, FL, USA.Nicklin, D.J., 1963. The air lift pump theory and optimization. Trans. Inst. Chem. Eng.41, 2939.Reinemann, D.J., Patrlange, J.Y., Timmons, M.B., 1986. Theory of small diameter airlift pump. Int. J. Multiphase Flow 16, 337355.Sekoguchi, K., Matsumura, K., Fukano, T., 1981. Characteristics of ow uctuation innatural circulation air lift pum. 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