6. ELUTRIATION OF PARTICLES FROM FLUIDIZED BEDS

Transcription

1 6. ELUTRIATION OF PARTICLES FROM FLUIDIZED BEDS Elutratn s the prcess n whch fne partcles are carred ut f a fludzed bed due t the flud flw rate passng thrugh the bed. Typcally, fne partcles are elutrated ut f a bed when the superfcal velcty thrugh the bed exceeds the termnal velcty f the fnes n the bed. Hwever, elutratn can als ccur at slwer velctes. Fne partcles are present n fludzed beds frm several surces: Feed streams Mechancal attrtn r breakage f larger partcles Temperature stress crackng Sze reductn due t chemcal reactns, shrnkage, etc. When fnes elutratn s a sgnfcant prblem and mdfcatns t the bed desgn cannt ad n reducng the prblem, fnes can ften be recvered such as wth cyclnes r hydrcyclnes. Leva (Chem. Engr. Prg., 47, 39, 1951) measured the rate f elutratn (ttal mass per tme) frm a bed f partcles wth a bmdal sze dstrbutn. He fund that (1) When the clumn heght abve the bed s small, the elutratn rate s hgh. But f the heght exceeds a certan mnmum sze then the rate s a cnstant mnmum value (Fgure 6-1). Ths ccurs because small partcles that are expelled frm the tp f the bed have hgh velctes and they requre greater dstance t slw dwn and turn arund t return t the bed. (2) The elutratn prcess causes a decrease n partcle cncentratn. The cncentratns may be emprcally mdeled by an Arrhenus type expressn as C Mt = C e (6-1) where C = cncentratn at tme, t; C s the ntal cncentratn; and M s an emprcal cnstant. 6-1

2 Fludzed Bed Free Space Abve the Bed Elutratn Rate Ar flw Free Space Heght Abve the Bed Fgure 6-1. Elutratn Rate (ttal mass/tme) vs the free space heght abve the bed. A fludzed bed behaves smlar t a mxture f lquds wth dfferent vlatltes. In the lqud-lqud mxture, the mre vlatle materal leaves the mxture at the lwer blng temperature. By analgy wth blng f lqud mxtures, fner partcles have a lwer blng temperature than larger partcles. The blng temperature s analgus t the fludzatn velcty. The hgher the velcty, the greater the rate at whch the lw blers wll leave the bed. The free space heght abve the bed serves as a cndenser, t cl and slw dwn the elutrated partcles and return them t the mxture. The greater the blng rate, the greater capacty that s needed f the cndenser, hence the greater free space heght. Nt all elutratn bad. Smetmes elutratn can be helpful. Fr example, elutratn may be used t remve dusts r very fne partcles frm carser partcles. 6.1 Defntn f Terms G s Lets defne sme terms that we can use t descrbe the elutratn prcess. The flux f slds carred ut f the tp f the clumn s called entranment, G s [kg/m 2 /s] The bulk densty f the slds n the extng gas stream s called the hldup. ρ [kg/m 3 ] H f Ar flw rate Q = AV Lean Phase Dense Phase We nte that the entranment s related t the hldup and the superfcal velcty by G s = ρ V (6-2) Fgure 6-2. Fludzed bed wth flux rate G s. Free Bard Heght, H f, s defned t be the measure f the free space abve the bundary between the dense phase and the lean phase (Fgure 6-3). 6-2

3 Fr desgn, we need t knw the rate f entranment and the sze dstrbutn f the entraned partcles n relatn t the sze f the partcles n the bed. A fludzed bed usually has tw regns r phases: dense bubblng phase and lean dspersed phase (Fgure 6-2). Only fnes are entraned n ths regn H f TDH Bth fnes and carse partcles are entraned n ths regn Dense Phase Ar flw rate Q = AV Bulk densty, ρ Fgure 6-3. Bth fnes and carse partcle are entraned n the Transprt Dsengagement Heght (TDH) regn. Abve the TDH nly fnes are entraned. The Transprt Dsengagement Heght (TDH) s the heght abve the dense-phase/leanphase bundary abve whch entranment and bulk densty d nt change apprecably. TDH depends upn the superfcal velcty and the partcle prpertes. The TDH s the heght at whch the knetc energes f partcles due t the cllsns n the bed has been expended aganst gravty ptental, and the carse partcles whse termnal velctes are greater than the superfcal velcty are able t fall back dwn t the bed. The fne partcles, whse termnal velctes are less than the superfcal velcty, cntnue t be entraned ut f the clumn. When H f > TDH then the hldup and entranment rates are clse t ther mnmums. Usually H f = TDH s the mst ecnmcal desgn heght fr the fludzed bed. If H f < TDH then carse partcles wll be carred ut f the clumn. 6-3

4 6.2 Estmatn f TDH fr Geldart A Partcles. Fr beds f fne partcles (Geldart A classfcatn, see Fludzatn ntes 5) there are several methds dscussed n lterature. Kun and Levenspel gve a gd revew f ths lterature. In these ntes yu are nly gven a bref ntrductn. METHOD 1. Zenz and Wel (AICHE J. 4, 472, 1958) prpsed a crrelatn between dmensnless TDH and the vessel dameter. Fr catalyst pellets n 2 t 15 mcrn sze range, n a lg-lg plt, the relatn between the dmensnless TDH and the vessel dameter are nearly lnear (see Kun and Levenspel Fgure 5 page 173) as ndcated n Fgure 6-4. V TDH/dt d t Fgure 6-4. Dmensnless TDH/d t vs vessel dameter, d t. We can mdel the data n the chart n the frm f Lg( TDH / dt ) = mlg( dt ) + Lg( b) (6-1) where d t s the vessel dameter. Takng data pnts frm the chart and plttng them we can curve ft t fnd the parameters m and b: m.115v.587 = b = 4. 64V (6-2) (6-3) Fnally, we take the abve equatns and try t cmpress the chart by plttng the 2 dmensnless TDH/d t versus the Frude Number, Fr = V / dt / g t get the plt shwn n Fgure 6-5. (HANDOUT 6.1) 6-4

5 TDH/dt y = x R 2 = V2/dt/g Fgure 6-5. Dmensnless TDH/d t versus Frude Number. If we take the lnear ft n Fgure 6-5 t represent the materal behavr, then we can relate 2 TDH V = (6-4) d d g t t r, upn rearrangement, we get V 2 = cnstant =.432 (6-5) TDH g The cnstant n Eq.(6-5) s lkely t be materal specfc. Furnl et.al. (Can. J. Chem. Engr., 51, 41, 1973) ndependently determned, fr a fludzed bed f fne catalyst partcles, d p =58 mcrns, the TDH fr ths materal t be gven by V 2 =.1 (6-6) TDH g 6-5

6 6.3 Entranment Rate frm Tall Vessels There are several methds fr estmatng entranment rates. Fllwng the wrk by Zenz et.al. (AICHE J., 4, 472, 1958; and Fludzatn III, Grace & Matsen, eds., Plenum, N.Y. 198) we assume that the flux rate f sld sze d p s prprtnal t ts mass fractn, x, G = s x G s (6-7) where Gs s the flux rate frm an magnary bed f all partcles f sze dp. Ths apprach extends the analgy between fludzed beds and blng f a lqud mxture (dscussed n the ntrductn t Sectn 6). Rault s Law fr an deal flud mxture (R.E. Balzhser, M.R. Samuels, and J.D. Elassen, Chemcal Engneerng Thermdynamcs, Prentce Hall, Englewd Clffs, New Jersey, 1972) equates the partal pressure f cmpnent n the vapr phase t the mle fractn n the lqud phase tmes the pure flud vapr pressure. P = x P (6-8) hence, the flux rates are analgus t the vapr pressures. The prcedure t determne the flux rate frm a bed wth knwn partcle sze dstrbutn s as fllws: 1. Dvde the sze dstrbutn nt narrw ntervals and fnd whch ntervals have termnal velctes greater than the superfcal velcty (these are the partcles that are entraned, because H f < TDH). 2. Fnd G s fr each sze range. 3. The ttal entranment s gven by G s = xgs (6-9) In terms f a cntnuus sze dstrbutn, P(d p ), the ttal entranment rate s gven by G G P( d ) dd (ntegratn ver all partcles entraned) (6-1) s = s p p T apply ths prcedure, a crrelatn such as shwn n Fgure 6-6 s requred t fnd. G s 6-6

7 1 1 1 Fnes remved frm larger partcle beds 1 ( u u ) gd p t Geldart A beds wth mst partcles entranable gd 5 u 2 p G s ρ g u Fgure 6-6. Data taken frm Kun & Levenspel, Fludzatn Engneerng, 2ed, Butterwrth, Bstn, 1991 (fgure 6 page 175). Frm ths plt the value f G s may be determned fr Geldart A partcles and fr fnes remved frm larger partcle beds. Fr Geldart class B, C, r D partcles (the larger partcles) ther predctve mdels are avalable. Recmmended references: Kun and Levenspel (J. Chem. Eng. Japan, 2, 84, 1969) Lews et. al. (Chem. Eng. Prg. Sympsum Seres, 58 (38), 65, 1962) Wen and Chen (AICHE J., 28, 117, 1982) Kun and Levenspel (Fludzatn Engneerng, 2ed, Butterwrth, Bstn, 1991). 6-7