Theoretical Study on Membrane Extraction in Laminar Flow Circular-Tube Modules

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1 Tkng Journl of Scinc nd Enginring Vol. 11 No. 4 pp (8) 339 Thorticl Study on Mrn Extrction in Linr Flow Circulr-Tu Moduls Ji-Jn Guo nd Chii-Dong Ho* Dprtnt of Chicl nd Mtrils Enginring Tkng Univrsity Tsui Tiwn 51 R.O.C. Astrct Th odling qutions for th concntrtion distriution nd xtrction rt in concntric circulr rn xtrctor odul undr countrcurrnt-flow with vrious rrir loctions wr drivd thorticlly with th us of th ss lnc on ch suchnnl. Th nlyticl solution is otind y using th sprtd vril thod with n orthogonl xpnsion tchniqu xtndd in powr sris. Th xtrction rt nd ss trnsfr fficincy in this study r rprsntd grphiclly with th volutric flow rt nd prl-rrir loction s prtrs. Th iprovnts of xtrction rt nd ss trnsfr fficincy wr chivd y th suitl djustnt of th rrir loction nd undr th countrcurrnt-flow oprtion. Th influncs of oprtion nd dsign prtrs on th xtrction rt nd ss-trnsfr fficincy nhncnt r lso discussd. Ky Words: Mrn Extrction Orthogonl Expnsion Tchniqus Mss-Trnsfr Grtz Nur Mss Trnsfr Efficincy 1. Introduction Mrn-sd sprtion procsss hv n widly usd in concntrtion or purifiction procsss s rfrrd to th rn contctors [1] such s solvnt xtrction [4] gs sorption [57] ion xchng [89] nd rn distilltion [111]. Extrction-sd liquid ixtur sprtion procsss r conoiclly or ttrctiv thn distilltion du to lowrnrgy rquirnts. Disprsion-fr iiscil ixtur contct using icroporous rns is ing studid for liquid solutions or gsous ixtur quiliriu sprtion. A nw disprsion-fr icroporous rn-sd solvnt xtrction tchniqu hs n introducd. Th typs of icroporous rns usd in rn xtrction studis includ hydrophoic [11 14] nd hydrophilic [1517] nd coposit rns [18]. Convntionl solvnt xtrction procsss hv n pplid in dvics such s pckd coluns ixrsttrs tc. which sk to xiiz th intrfcil ss *Corrsponding uthor. E-il: cdho@il.tku.du.tw trnsfr contct r. Thr r ny disdvntgs such s flooding liittions on th indpndnt phs flow rt vritions intit ixing rquirnt for dnsity diffrnc nd inility to hndl prticults [ ] for convctionl solvnt xtrction pplictions. Mss Trnsfr of rn solvnt xtrction in th ss xchngrs cn nlogous to th ht trnsfr in ht xchngrs [1]. Th ss xchngrs usd in rn solvnt xtrction r diffrnt in dsign fro ordinry ht xchngrs ut in principl th only diffrnc is th rltiv dirction th two fluids ov. Th nuricl pproxition of concntrtion distriutions is dtrind y solving th first-ordr ordinry diffrntil qutions [34]. Thrfor instd of ordinry diffrntil qutions two prtil diffrntil qutions for solut concntrtion distriutions s wll s th outlt concntrtions r otind y solving ths qutions using orthogonl tchniqu nd vril sprtion thods [658]. Th purpos of this study is to dvlop th thticl forultion of countrcurrnt-flow circulrtus rn xtrctor. This work discusss th influ-

2 34 Ji-Jn Guo nd Chii-Dong Ho ncs of th suchnnl thicknss rtio on th ss trnsfr fficincy xtrction rt nd xtrction fficincy with th volutric flow rt nd th initil solut concntrtion in th rffint phs s prtrs. Th ffcts of th oprtion nd dsign prtrs on th xtrction rt nd ss-trnsfr fficincy r lso dlintd in this study.. Mss Trnsfr Modl Figur 1 shows concntric circulr rn xtrctor with insrting hydrophoic icroporous prl rrir to divid circulr tu into two suchnnls with thicknsss of R nd (1 )R rspctivly conducting doul-flow oprtion. Extrction nd rffint phss flow fd in diffrnt suchnnls whn th oprtion procds. Th volutric flow rt Q nd Q nd th initil concntrtion C nd C r for th rffint nd xtrction phs rspctivly. Th thticl forultions for th trnsport phnon of such dvics long to th ctgory of conjugtd Grtz prols nd cn solvd nlyticlly using th ignfunction xpnsion tchniqu with th orthogonlity conditions [658]. Th ssuptions r: () stdy stt fully-dvlopd linr flow in ch suchnnl; () ngligil xil diffusion s wll s ntrnc lngth nd nd ffcts; (c) th pplicility of locl throdynic quiliriu; (d) th rn is copltly xtrctionphs filld. Th vlocity distriutions nd th dinsionlss qutions of ss trnsfr for ch suchnnl y writtn in trs of th dinsionlss vrils s nd whr v( ) v1 v 1 v( ) 1 ln ln ln 1 v DL ( ) R ( ) 1 ( ) v DL ( ) R ( ) 1 ( ) Gz Gz C C DL DL (1) () (3) (4) Q Q r z v v ( R) R ( R) R L C C v R v R (5) Th oundry conditions rquird for solving Eqs. (3) nd (4) r Figur 1. Schtic digr of th concntric circulr rn xtrctor.

3 Thorticl Study on Mrn Extrction in Linr Flow Circulr-Tu Moduls 341 ( ) (1 ) ( ) RDc ( )[ H c ( ) H c ( )] D ( ) D ( ) ( ) D ( 1) (6) (7) (8) (9) (1) All th cofficints d n nd n cn xprssd in trs of ign-vlu s nd d Gz d3 Gz d n ( 4) dn [ d ] n n [( n1) n] (16) (11) whr is th prility of rn nd H c nd H c r distriution cofficints of solut twn two diffrnt phss such s nd ( ) H c H c intrfc solut concntrtion in phs intrfc solut concntrtion in phs intrfc solut concntrtion in phs intrfc solut concntrtion in phs Th nlyticl solution to this conjugtd prol y otind using n orthogonl xpnsion tchniqu in powr sris. Th vril sprtion lds to th following for ( ) S F ( ) G ( ) ( ) S F ( ) G ( ) (1) (13) Without loss of gnrlity w y ssu th ignfunctions F () nd F () to polynoils thn xprssd in th following fors [78]: n n 1 n F ( ) d d 1 (slctd) d n n 1 n F ( ) 1 (slctd) c c (14) (15) whr Gz 3W [1 ] 4Gz W 3 9 W1 (1 ) n Gz 3W W n n n W W n ( 3) (1 ) n ( 4) ] n [(1 ) ( n) 1(1 )[ ( 1) 1] W1 [ ] 1 1 ln 1 W [ ] 1 ln (17) Whn n th orthogonlity condition in this liquid-liquid rn xtrctor syst is 1Rv( ) DH c S S nf nf d LD Rv( ) DH c S S nf nf d LD (18) By following th s clcultion procdur prford in th prvious work [656] th cofficints for S nd S r s follows:

4 34 Ji-Jn Guo nd Chii-Dong Ho 4 n Gz D ( R) v ( ) q Sq Fq d q LD H cd F q( ) RF q( ) 1 Rv HcRD F q(1) LD DF (1) c[ DF (1) ] ( R) v ( ) Sq [ ] F ( ) Fq ( ) d q LD F F RDH cs F F 1 DF (1) 1 RDH c[ ] [ F ( )]; DF ( ) RD H nd q DF (1) (1) [ (1) (1) ] (1) c[ ] DF (1) ( R) v ( ) Sq [ ] F ( ) Fq ( ) d q LD 1 DF (1) ( R) v ( ) c D F ( ) LD q 1 R v( ) c q q( )[ ] ( ) q LD RD H 4Gz Fq d 4GzHcD S 4 Gz ; HcD (19) () RD H [ ] [ ] F ( ) d RD H S F F d nd q D (1) Th dinsionlss vrg concntrtions in th ntir rn xtrctor for oth strs wr otind s follows: 1 1 ( ) S S F ( ) 4Gz ( ) S S F (1) 4Gz 1 () (3) 3. Mss Trnsfr Efficincy in th Mrn Extrction Syst Th locl Shrwood nur in th rffint phs is dfind y Sh S F () q 1 D 1 1 4Gz k D S F ( ) F () (4) whr k is th locl ss trnsfr cofficint for rffint phs nd D q is th quivlnt ditr of suchnnl k D ( ) R ( ) ( ) So th vrg Shrwood nur cn otind s Sh Sh d (5) (6) Th totl xtrction rt M is dfind th totl ount of th solut trnsfr fro th rffint phs to xtrction phs dtrind y using Eqs. (7) s follows M Q ( C C ) Q ( C C ) (7) A nuricl xpl with so quipnt prtrs nd physicl proprtis of th glcil ctic cid thyl isoutyl kton nd th icroporous cllulos rn r givn s follows [1314]: D D D H H 4 6 c kg/ s; kg/ s; 4 c 1; c 1.9;.67; Rsults nd Discussions It ws found tht in Tl 1 n = 14 is good nough in convrgnc tst during th ign-vlu clcultion for =.5 Gz = 1 nd Gz = 1. Ths ign-functions in Eqs. (14) nd (15) rfrrd to nd suchnnls rspctivly r xpndd in trs of powr sris. Th ccurcy of th solution ws xind with th rsults for th xtndd powr. A trunctd sris of n = 14 ws slctd nd usd for th clcultion procdur. Tl shows th clcultion rsults for th fiv through svn ign-vlus nd thir ssocitd xpnsion cofficints s wll s th din-

5 Thorticl Study on Mrn Extrction in Linr Flow Circulr-Tu Moduls 343 Tl 1. Th convrgnc of powr sris in Eqs. (14) nd (15) with =5Gz = 1 nd Gz = 1 n Tl. Th dinsionlss outlt concntrtion in th quous phs for th ign-vlu nur nd xpnsion cofficints with nlyticl solution in countrcurrnt-flow dvic. n = 14 Gz = 1 nd Gz = S S 1 S S 3 S 4 S 5 S sionlss outlt concntrtion in th quous phs clcultd for Gz = 1 nd Gz = 1 which shows tht du to th convrgnc only th six ign-vlus ust considrd during th clcultion procdur. Following th thticl trtnt usd in prvious work [656] th dinsionlss concntrtion distriutions in oth suchnnls for countrcurrnt-flow dvic wr otind y govrning qution nd th corrsponding oundry conditions. Figur shows th vrg solut dinsionlss concntrtion distriution in whol rn contctor nd th thorticl qutions r xprssd y Eqs. () nd (3). Th vrg dinsionlss concntrtion distriution in xtrction phs incrss s th suchnnl thicknss rtio ovs wy fro.5 spcilly for <.5 (th thicknss of th suchnnl is lrgr thn tht of th suchnnl ). Figur 3 shows th dinsionlss outlt concntrtion of suchnnl ( ) with suchnnl thicknss rtio nd ss-trnsfr Grtz nur in th xtrction Figur. Avrg dinsionlss concntrtion distriution for countrcurrnt-flow dvic in th ntir rn xtrctor (Gz = 3 nd Gz = 3). phs (Gz ) s prtrs rspctivly. It is sn in Figur 3 tht th in countrcurrnt-flow dvic incrss with incrsing ss-trnsfr Grtz nur in th rffint phs (Gz ) du to th lrg ss-trnsfr cofficint of th fluid s th suchnnl thicknss rtio

6 344 Ji-Jn Guo nd Chii-Dong Ho Figur 3. Dinsiolss outlt concntrtion of th suchnnl with suchnnl tkicknss rtio nd Gz s prtrs ( ). ovs wy fro.5 spcilly for <.5. It ws lso found tht th dcrss with incrsing sstrnsfr Grtz nur in th xtrction phs owing to th dilut ffct. Th xtrction rt incrss with incrsing sstrnsfr Grtz nur s th suchnnl thicknss rtio ovs wy fro.5 s confird fro Figur 4. Th thorticl rsults of th vrg Shrwood nur in th rffint phs (Sh ) vrsus ss-trnsfr Grtz nur vritions in th rffint phs (Gz ) r indictd in Figur 5. Th lrgr th ss-trnsfr Grtz nur is oprtd th lrgr Sh is otind. Figurs 4 nd 5 lso show tht th xtrction rt nd ss-trnsfr fficincy incrs with suchnnl thicknss rtio oving wy fro.5 spcilly for < Conclusions Figur 4. Extrction rt of th suchnnl tkicknss rtio nd Gz s prtrs ( ). Mss trnsfr fficincy through linr countrcurrnt-flow rn xtrctor conductd with insrting prl rrir ws invstigtd nlyticlly. Th thorticl forultion through th circulr-tus ws studid y using th sprtion vril nd powr sris with n orthogonl xpnsion tchniqu. Thr r ny oprtion nd dsign prtrs such s th volutric flow rt fd concntrtion nd suchnnl thicknss rtio tht y ffct th dvic prfornc in th rn xtrctor. Th optil oprtion prtr for suchnnl thicknss rtio is oving wy fro =.5 in th circulr-tu with insrting prl rrir. It is lso found in Figurs 4 nd 5 th xtrction rt nd ss trnsfr fficincy incrs with incrsing ss Grtz nur in th xtrction phs nd in th rffint phs. A good pproxition ws otind using six ign-vlus s shown in Tl. Furthror th ovrll ss-trnsfr cofficint ws ndd in stiting whthr to us xprintl runs or sixprintl qutions to clcult th xtrction rt in th on-dinsionl odl. Th dvntg nd vlu of th

7 Thorticl Study on Mrn Extrction in Linr Flow Circulr-Tu Moduls 345 Figur 5. Th vrg Shrwood nur in th rffint phs of th suchnnl tkicknss rtio nd Gz s prtrs ( ). thorticl odl in this study li in th fct tht thy cn stit th xtrction rt dirctly without xprintl runs nd dvlop th two-dinsionl dinsionlss concntrtion profil qution in th whol rn xtrctor on oth xtrction nd rffint phs. Th thorticl rsults showd tht th lrgr volutric flow rt nd suchnnl thicknss rtio oving wy fro.5 cn nhnc th ctic cid xtrction rt nd ss-trnsfr fficincy in th prsnt liquid-liquid rn contctor. Acknowldgnt Th uthors thnk th Ntionl Scinc Council of th Rpulic of Chin for its finncil support. B conduit width Noncltur C solut concntrtion ol/ 3 D ordinry diffusion cofficint of ctic cid in wtr /s D ordinry diffusion cofficint of ctic cid in MIBK /s d n cofficint in th ignfunction F n cofficint in th ignfunction F F ignfunction ssocitd with ignvlu Gz ss Grtz nur H distriution cofficint k ss trnsfr cofficint of ctic cid /s k locl ss trnsfr cofficint of ctic cid /s L conduit lngth M xtrctiv rt dfind y Eq. (7) ol/s R insid ditr of th outr tu R Rynolds nur S xpnsion cofficint ssocitd with ignvlu Q volutric flow rt of conduit 3 /s Sh locl Shrwood nur Sh vrg Shrwood nur v vlocity distriution of fluid /s v vrg vlocity of fluid /s r trnsvrsl coordint z longitudinl coordint Grk Lttrs suchnnl thicknss rtio dfind y Eq. (5) trnsvrsl coordint dfind y Eq. (5) ign-vlu longitudinl coordint dfind y Eq. (5) dnsity of th fluid kg/ 3 dinsionlss concntrtion dfind y Eq. (5) Suprscripts nd Suscripts in th rffint phs in th xtrction phs t th inlt t th outlt Rfrncs [1] Muldr M. (Ed.) Bsic Principls of Mrn Tchnology Kluwr Acdic Pulishrs London (1997). [] Vjd M. Hvld I. nd Mck R. Mrnsd solvnt xtrction nd stripping of zinc in hollow-fir contctor oprting in circulting od

8 346 Ji-Jn Guo nd Chii-Dong Ho Dslintion Vol. 163 p. 19 (4). [3] Yh H. M. Chn C. H. nd Yuh T. Y. Influnc of chnnl-width rtio on solvnt xtrction through doul-pss prlll-plt rn odul J. Mrn Sci. Vol. 3 p. 13 (4). [4] Ortiz I. Brings E. Sn Roán M. F. nd Urtig A. M. Slctiv sprtion of zinc nd iron fro spnt pickling solutions y rn-sd solvnt xtrction: Procss viility Sp. Sci. Tch. Vol. 39 p. 441 (4). [5] Kur P. S. Hogndoorn J. A. Fron P. H. M. nd Vrstg G. F. Nw sorption liquids for th rovl of CO fro dilut gs strs using rn contctors Ch. Eng. Sci. Vol. 57 p (). [6] Wng W. P. Lin S. T. nd Ho C. D. An nlyticl study of linr co-currnt flow gs sorption through prlll-plt gs-liquid rn contctor J. Mr. Sci. Vol. 78 p. 181 (6). [7] L H. K. Jo H. D. Choi W. K. Prk H. H. Li C. W. nd L Y. T. Asorption of SO in hollow fir rn contctors using vrious quous sornts Dslintion Vol. p. 64 (6). [8] Gnusin N. P. Brzin N. P. Kononnko N. A. nd Dyoin O. A. Trnsport structurl prtrs to chrctriz ion xchng rns J. Mr. Sci. Vol. 43 p. 31 (4). [9] Tnk Y. Concntrtion polriztion in ion-xchng rn lctrodilysis: Th vnts rising in n unforcd flowing solution in dslting cll J. Mrn Sci. Vol. 44 p. 1 (4). [1] Ugrozov V. V. Elkin I. B. Nikulin V. N. nd Ktv L. I. Thorticl nd xprintl rsrch of liquid-gp rn distilltion procss in rn odul Dslintion Vol. 157 p. 35 (3). [11] Gln A. nd Hwng S. T. Hollow fir rn contctors J. Mrn Sci. Vol. 159 p. 61 (1999). [1] Prsd R. nd Sirkr K. K. Hollow firs solvnt xtrction: prforncs nd dsign J. Mrn Sci. Vol. 5 p. 153 (1999). [13] Yh H. M. nd Chn C. H. Rcycl ffct on solvnt xtrction through concurrnt-flow prlll-plt rn oduls J. Mrn Sci. Vol. 19 p. 35 (1). [14] Prsd R. nd K. K. Disprsion-fr solvnt xtrction with icroporous hollow-firs oduls AIChE J. Vol. 34 p. 177 (1988). [15] Yun C. Prsd R. nd Sirkr K. K. Mrn solvnt xtrction rovl of priority orgnic pollutnts fro quous wst str Ind. Eng. Ch. Rs. Vol. 31 p. 179 (199). [16] Jung R. S. Chn J. D. nd Hun H. C. Disprsionfr rn xtrction: cs studis of tl ion nd orgnic cid xtrction J. Mrn Sci. Vol. 165 p. 59 (). [17] Jung R. S. nd Hung H. C. Non-disprsiv xtrction sprtion of tls using hydrophilic icroporous nd ction xchng rns J. Mrn Sci. Vol. 156 p. 179 (1999). [18] Ding H. nd Cusslr E. L. Frctionl xtrction with hollow firs with hydrogl-filld wll AIChE J. Vol. 37 p. 855 (1991). [19] Prsd R. nd Sirkr K. K. Microporous rn solvnt xtrction Sp. Sci. Tch. Vol. p. 619 (1987). [] Prsd R. nd Sirkr K. K. Solvnt xtrction with icroporous hydrophilic nd coposit rn AIChE J. Vol. 33 p. 157 (1987). [1] Ho C. D. Yh H. M. nd Shu W. S. An nlyticl study of ht nd ss trnsfr through prlll-plt chnnl with rcycl Int. J. Ht Mss Trnsfr Vol. 41 p. 589 (1998). [] Ho C. D. Iprovnt in prfornc of doulflow linr countrcurrnt ss xchngrs J. Ch. Eng. Jpn. Vol. 33 p. 545 (). [3] Yh H. M. nd Hung C. M. Solvnt xtrction in ultupss prlll-flow ss xchngrs of icroporous hollow-fir oduls J. Mrn Sci. Vol. 13 p. 135 (1995). [4] Yh H. M. nd Chn Y. K. Corrction-fctor nlysis of rn xtrction in flt-plt oduls J. Chin. Inst. Ch. Engrs. Vol. 3 p. 453 (). [5] Nung R. J. Gill W. N. Anlysis of ht trnsfr in so countrcurrnt flows. Int. J. Ht Mss Trnsfr Vol. 8 p. 873 (1965). [6] Nung R. J. Gill W. N. An nlyticl study of linr countrflow doul-pip ht xchngrs AIChE J. Vol. 1 p. 79 (1966). [7] Ho C. D. Yh H. M. nd Ching S. C. A study of ss trnsfr fficincy in prlll-plt chnnl with xtrnl rfluxs Ch. Eng. J. Vol. 85 p. 7 (). [8] Ho C. D. nd Guo J. J. An nlyticl study of sprtion fficincy on th nrichnt of hvy wtr in doul-flow thrl-diffusion coluns with flow-rt frction vritions Ch. Eng. Coun. Vol. 19 p. 44 (5). Mnuscript Rcivd: Sp Accptd: Apr. 8 8