Dynamic simulation of multi-effect falling-film evaporator: Milk powder production plant

Transcription

1 Dynam smulatn f mult-effet fallng-flm evapratr: Mlk pwder prdutn plant Fateme Medhat Bjnurd, Mhammad Al Fanae *, Had Zhree Department f Chem. Eng., Faulty f Eng., Ferdws Unversty f Mashhad, I. R. Iran Abstrat: In ths paper, tw types f dynam mdels, lumped and dstrbuted, were develped fr an ndustral fureffet fallng-flm evapratr whh s used t nentratng whle mlk. The predtns f eah mdel are mpared t ndustral data. The results shwed that the predtns f dstrbuted mdel he better agreement wth ndustral data rather than lumped mdel. Althugh n predtns f sme varables, these mdels he the same perfrmanes. Key wrds: fallng-flm evapratr, dynam smulatn, lumped mdel, dstrbuted mdel Intrdutn Fallng-flm evapratrs are mmnly used as part f the pwder prdutn press t make whle mlk, skm mlk and whey pwder, n fat a very wde range f prduts. Despte ther mmn usage fallng-flm evapratrs are stll nt well understd. Thus a mprehensve study f dynams and ntrl f ths press s well mtvated [1]. Analytal mdels an be benefal n assstng engneers t better understand and ntrl the dynam behr f presses. Analytal an be mplex but the best f these mdels may nt be the ne whh desrbes all the phenmena f the press behr. The ultmate applatn f an analytal mdel largely determnes the methd f analyss f the system and mplexty f the fnal mdel [2]. In the begnnng, nterest n develpng analytal mdels fr multple effet evapratrs was fused n the pssblty f nrpratng pen lp smulatns fr nventnal ntrl purpses. Hwever, n the last deade, mst studes he emphaszed the develpment f state spae mdels t nrprate the use f mult-varable ntrllers and state estmatns [3]. One f the reent lumped mdels fr ndustral evapratn plant s Mranda and Smpsn's wrk. Mranda and Smpsn (2005) develped a lumped mdel based n energy and mass balanes f the evapratr system [3]. Ths mdel was mplemented n a tmat nentratn plant and nludes sem-empral equlbrum funtns. Reently, Stefanv and H (2004) develped a dstrbuted mdel f a multple-effet fallng-flm evapratr plant [4, 5]. The mdel desrbes the mprtant phenmena f evapratn, heatng and ndensatn fr dfferent hydrdynam regmes as well as the pressure dynams f the plant. Ths mdel presn was valdated usng steady-state real plant data but there s n real dynam data t mparng wth smulatn results. In the urrent wrk, lumped and dstrbuted mdels are develped fr fur-effet fallng flm evapratrs t nvestgate the perfrmane f eah mdel n predtns the dynam behr f plant. Exstene f real dynam data helps us t mpare the smulatn results f eah mdel and ths mparsn s benefal t understandng ther advantages and dsadvantages. Press desrptn The ndustral equpment, as shematally shwn n fgure (1) nludes a frward feed flw, fur-effet evapratr fr nentratng the whle mlk. It nssts f fur bdes n whh the whle mlk s nentrated and equpped wth therm mpressr that rases the pressure f a part f send effet vapr t that f frst ne wth lve steam. Send bdy s dvded n t tw parts. Eah effet nssts f ne pre heater. At the end f the frth effet there are a pre heater and ndenser t aumulate vapr and prdue vauum fr the plant. Other spefatns f the smulated ndustral plant are shwn n Fg.1. Mathematal mdel In eah tube mlk flws as fallng flm and utsde f the tube flm ndensatn urs. It s assumed that, n the energy balane equatns, there s n aumulatn f energy and that nly phase hange urs. Ths assumptn s reasnable beause temperature f feed enterng t eah evapratr s hgher than ts saturated temperature and after flashng n dstrbutr lqud feed aheves ts saturated temperature. Therefre heat t the fallng flm wll spend t phase hange. In prate there s a small aumulatn f energy due t the blng pnt rse, hwever, ths term an be negleted fr mlk. Table 1. Spefatns f the smulated ndustral evapratr effets Evapratr effets Number f Dameter f tubes Length f Dameter f * fanae@um.a.r

2 tubes Inner dameter (mm) Outer dameter tubes (m) effet (m) Frst effet Frst part f send effet Send part f send effet Thrd effet Furth effet Fgure 1. Press flw dagram f the ndustral evapratr plant Lumped mdel In ths setn the dfferental and algebra equatns whh are used n lumped mdel are desrbed brefly. These equatns are derved by usng materal and energy balanes fr fallng flm nsde and ndensng flm utsde the tubes. Materal balane f the fallng flm nsde the tube: dm GL GL W (1) G L, G L and W are nlet mass flw rate f mlk, utlet mass flw rate f mlk and mass flw rate f prdued vapr, respetvely. M s the mass f lqud flm nsde the tube and an be defned as M τ (2) G τ s the erage resdene tme and assumed nstant. It an be alulated as L τ (3) v z

3 L s the length f tube. The erage values f lqud flm velty (v z ) and lqud flm mass flw rate (G ) an be defned as: v α v + 1 ) v (4) z ( α 1 z 1 z G + ( 1 α G 2 L 2 L G α ) (5) α 1 and α 2 are tunng parameters between zer and ne. Materal balane f the fallng flm sld ntents: d( M ) G G (6) L L The erage values f sld mass fratn ( ) an be defned as: α + 1 ) (7) ( α 3 3 α 3 s a tunng parameter between zer and ne. Energy balane f the fallng flm nsde the tube: 0 Q W (8) L Frm the abve equatn, the mass f evaprated water an be alulated as: Q L W (9) s the latent heat f water and Q L s the rate f heat transferred t the fallng flm. Materal balane f the ndensate flm utsde the tube: dm G G + W (10) CL CL C In the same as the fallng flm, the mass f ndensate utsde the tube (M ) an be alulated as fllws: M τ G (11) L τ vz (12) v α v + 1 ) v (13) z ( α 4 z 4 G + ( 1 α 5 CL 5 z G α ) G (14) CL α 4 and α 5 are tunng parameters between zer and ne. Energy balane f the ndensate flm utsde the tube: Q L 0 QL WC C W (15) W s the mass flw rate f ndensate and Q L s the rate f heat transfer frm ndensate. Energy balane n the wall f the tube: It s assumed that there s n heat lss. In the urrent study the tube wall s made f stanless steel wth thkness f 2 mm. Thus, t s pssble t slve energy balane f the wall assumng that equlbrum s aheved nstantaneusly. Wth the abve nsderatn, all heat prdued by vapr ndensatn utsde the tube lead t evapratn f water nsde the tube. Therefre Q Q Q L L t (16) Q U A( T T) (17) t C 1 U (18) 1 d ln( d / d ) d h 2k d h Dstrbuted mdel w

4 In ths paper the dstrbuted mdel presented by Stefanv and H [4, 5] was used fr mlk pwder plant. Evapratrs f the urrent study he tubes nstead f plates. Thus sme small hanges are ntrdued n Stefanv and H's mdel. Als n the urrent study the flm thkness s used fr alulatng the flm velty. Materal balane f the fallng flm nsde the tube: W + v v W, W (19) z z t z z Materal balane f the fallng flm sld ntents: W vz + v z t z G (20) Energy balane f the fallng flm nsde the tube: 0 Q W (21) π d z h ( T T) w Q π d z h ( T T) W (22) w Materal balane f the ndensate flm utsde the tube: W + v v W, W (23) z z t z z Energy balane f the ndensate flm utsde the tube: 0 Q W (24) Q πd z h ( T T ) w π d z h ( T Tw ) W (25) Energy balane n the wall f the tube: In the same as lumped mdel we he 2k ( T T ) w w w h d ( Tw T) hd ( TC Tw ) (26) ln( d / d ) In addtn t the abve equatns, mdelng the evapratn plant requres ther algebra and dfferental equatns fr pressure dynams, flashng press, therm mpressr and ntrl valve. These equatns wll be explaned n the full paper versn. Numeral slutn f mdels Ordnary dfferental equatns (ODEs) n the lumped mdel are slved usng the varable tme step sze methd defned by the funtn de113s n MATLAB 7.1. T slve the dstrbuted mdel, the partal dervatves f latn (z dmensn) were apprxmated by bakward fnte dfferene methd usng equal spae grds n the length f the tube. The resulted set f rdnary dfferental equatns s slved by the funtn de113s n MATLAB 7.1. Results and dsussn In ths setn the dynam perfrmane f lumped and dstrbuted mdels are mpared t ndustral plant data. There are spef dffultes related t expermentatn n the ndustral plant, als the number f sensrs are restrted. Hwever, n ths study we were able t measure the requred varables n the evapratn plant suh as pressure f lve steam t the therm mpressr, feed vlume flw rate, prdut mass flw rate, shell sde temperature f eah effet,

5 and prdut densty. These varables rerded at 30 sends ntervals. Thus we an ntrdue hanges f nput varables t the mdels and als mpare dynam behr f the plant wth utput data f lumped and dstrbuted mdels. Fgures (17) t (20) shw the atual steam temperature f eah effet and utputs f lumped and dstrbuted mdels. These results are pretty ndent when the respnses f the tw mdels are mpared qualtatvely wth ndustral data, but n prese lk, predted results f dstrbuted mdels after send lad are slghtly better than lumped mdel. It an be due t mttng sme detals n alulatng ndensate and vapr prdutn n lumped mdel. Fgure (21) shws the densty f the utlet flw. Dynam behrs f the tw mdels are slghtly smlar and there are n sgnfant dfferenes between the tw mdels. In the ase f tme needed fr alulatng, wth a gven data pressng system, the tme f alulatns fr the dstrbuted mdel s twe as muh as that f alulatns fr lumped mdel. It s reasnable beause the equatns f the dstrbuted mdel are mplated and slvng them needs mre tme. Fgure 17. Steam temperature f the frst effet Fgure 18. Steam temperature f the send effet

6 Fgure 19. Steam temperature f the thrd effet Fgure 20. Steam temperature f the furth effet Fgure 21. Densty f utlet stream (prdut) Cnlusn

7 Lumped and dstrbuted mdels were develped fr mult-effet fallng-flm evapratn plant. Perfrmane f dstrbuted mdel n predtn temperature f eah effet s better than the lumped mdel. But results f these mdels n the ase f prdut densty he smlarty t dynam behr. Althugh the dstrbuted mdel needs mre tme than the lumped mdel fr alulatn, t s mre relable fr dynam smulatn and als the mult-varable ntrl analyss. Referenes 1. Wnhester, J. A. and Marsh, C., "Dynams and ntrl f fallng flm evapratrs wth mehanal vapr rempressn," Trans IChemE, 77, 357 (1999). 2. Russell, N. T., Bakker, H. H. C. and Chapln, R. I., "A mparsn f dynam mdels fr an evapratn press," Trans IChemE, 78, 1120 (2000). 3. Mranda, V. and Smpsn, R., "Mdelng and smulatn f an ndustral multple effet evapratr: tmat nentrate," J. Fd Eng., 66, 203 (2005). 4. Stefanv, Z. and H, K. A., "A dstrbuted parameter mdel f blak lqur fallng flm evapratrs. Part 1. Mdelng f sngle plate," Ind. Eng. Chem. Res., 42, 1925 (2003). 5. Stefanv, Z. and H, K. A., "A dstrbuted parameter mdel f blak lqur fallng flm evapratrs. Part 2. Mdelng f a multple effet evapratr plant," Ind. Eng. Chem. Res., 43, 8117 (2004).