Adsorption. (CHE 512) M.P. Dudukovic Chemical Reaction Engineering Laboratory (CREL), Washington University, St. Louis, MO

Transcription

1 dsrptn (CHE 5) M.P. Dudukvc Chmcal Ractn Engnrng Labratry (CREL), Washngtn Unvrsty, St. Lus, MO

2 bruary 8, 005 ChE 5 CHPTER 3 DSORPTION BSIC NOTION dsrptn s a prcss by whch a chmcal cmpnnt (spcs) frm a flud phas (gas r lqud) s rmvd by attachmnt t a sld phas. Th spcs bng adsrbd s ftn calld th adsrbat, whn t rsds n th sld, and th sld s calld th adsrbnt. Evry adsrptn at gvn cndtns f tmpratur, prssur and cmpstn f th flud phas can b charactrzd by ts qulbrum stat and by ts dynamcs cnsstng f th kntcs f th adsrptn-dsrptn prcss. Cnsdr fr xampl spcs n a flud phas (f) that s adsrbd n sld sts (S ) by a smpl mchansm ndcatd by quatn () blw: k + () k a ( f ) S ( s) S () s d If w assum that all sld sts ar dntcal n thr affnty fr spcs, and ar all qually accssbl t th flud cntanng, thn a sngl adsrptn rat cnstant k a, and a sngl dsrptn rat cnstant, k d, ar suffcnt t dscrb th adsrptn-dsrptn mchansm f quatn (). Th rat f adsrptn can nw b wrttn as: ( )( S ) ra = ka a) and th rat f dsrptn as ( S ) rd = kd (b)

3 t qulbrum th tw rats ar qual r a = r d (3a) whch ylds th qulbrum cnstant (n apprprat unts): K k a = = k d ( S ) ( S )( ) q (3b) Nt that th ttal numbr f actv sts (actually cncntratn f actv sts) avalabl fr adsrptn f s cnstant and qual t ( S. Thus, ttal sts ar mad up f thr unccupd sts ( S ) r sts cntanng th adsrbat ( ) ) S as xprssd by quatn (4): ( S ) ( S ) + ( S ) = (4) Smultanus slutn f quatns (3b) and (4) ylds th fllwng xprssns fr th fractn f th sts cvrd by th adsrbat, θ, and fr th fractn f fr sts, ( ) θ at qulbrum ( S ) ( S ) ( ) ( ) K θ = = (5a) + K = q ( S ) ( S ) = + K ( ) θ (5b) q It s nfrmatv t plt th fractn f th surfac sts cvrd by th adsrbat as a functn f flud phas cncntratn f, ( ) wth whch th sld s qulbratd.

4 θ ½ /K () IGURE : Langmur Isthrm Ths plt f quatn (5a) s th s calld Langmur sthrm,.. th plt f th adsrbat cncntratn n qulbrum at cnstant tmpratur cndtns wth th surrundng flud. Th plt rvals that at th flud phas cncntratn f th adsrbng spcs qual t th rcprcal f th adsrptn qulbrum cnstant (xprssd n apprprat unts) th qulbrum fractnal cvrag f th adsrbnt s xactly n half. s th flud cncntratn f s ncrasd ndfntly (whch f curs has practcal lmtatns) th qulbrum surfac cvrag f th adsrbnt by th adsrbat tnds t unty. Hw fast ths apprach t unty ccurs dpnds n th valu f th qulbrum cnstant K. r an rrvrsbl adsrptn plt n gur s a Hvsds stp functn at ( ) =, θ = H (( ) ) K and θ = at all cncntratns f.. th 0. Lt us xamn nw th ffct f tmpratur n th adsrptn prcss. Th tru thrmdynamc cnstant, K, fr th abv cnsdrd adsrptn prcss s unt-lss and gvn n trms f actvts: K = a S = G RT a S a (6) r spcs that ar prfrntally adsrbd n th slds sts (and w clarly spak f chmsrptn hr) th Gbbs fr nrgy fr adsrptn s ngatv as th prcss prcds spntanusly (.. G < 0 ). Ths mans 3

5 G = H T S < 0 (7) Hwvr, as th mlculs f gt adsrbd, thy ls a dgr f frdm (as thr mtn n th surfac f th sld s cnstrand n tw dmnsns cmpard t thr dmnsnal mtn n th flud phas) and thrfr thr s a dcras n ntrpy du t adsrptn,.. S < 0. Nw fr th lft hand sd f quatn (7) t b ngatv, as t shuld, n must hav H < 0. Th nthalpy chang du t adsrptn ( H = H H ~ S ~ ) s ngatv,.. hat s vlvd (rlasd) du t adsrptn. Ths s an accrd wth ur cmmn xprncs as adsrptn s a prcss akn t cndnsatn (.g. vapr mlculs cndns n a surfac) whch als s accmpand wth hat rlas. Oftn n talks abut th hat f adsrptn dfnd by q a H = (8) W rcall th Van t Hffs quatn s: d ln K dt H = (9a) RT r d ln K dt H = (9b) RT Snc H < 0, K dcrass wth ncrasd tmpratur, and th fractnal cvrag f th surfac wth th adsrbat, θ, dcrass at gvn cncntratn f wth ncrasd tmpratur. (Thr ar fw xcptns t ths gnral rat). 4

6 W stll nd t cnsdr th rats f adsrptn and th apprprat unts fr varus cnstants. In a lqud stat w can xprss th actvts n trms f th prduct f th actvty cffcnt and cncntratn α = γ C Thn j j j ( ) () K = γ S S = K γ S S γ K (0) ()γ Th unts f K γ ar ths f cncntratn, say (ml/l) r M, and th unts f cncntratn f n th flud s thn masurd n (ml/l) r M. K thn ar M -. Th In gass, t s ftn mr cnvnnt t us th partal prssur f P ( atm), as a masur f gas phas cncntratn f th adsrbng spcs. Thn, basd n dal gas quatn n gts ( atm ) = K ( RT ) = K K ( atm ) K p γ () Th qulbrum cnstant ( atm ) (5b) whl K p s thn usd n th adsrptn sthrm f quatn (5a) and,. P rplacs th cncntratn f ( ) Th nt rat f adsrptn s th dffrnc btwn th rat f adsrptn and dsrptn whch can b wrttn wth th hlp f (a), (b) : r ad ( S ) ( )( ) k ( S ) θ θ d 0 = k () a Strctly spakng basd n th cncpts ntrducs s far w wuld xpct t masur th rat n ( s) mls adsrbd by sld pr unt surfac ara f sld sts and unt tm,.. ml ( dm) r nt us f dm s ndd snc L = ( dm) 3 and cncntratns ar masurd n ( ml L) masur f (S ) 0 n mls pr unt surfac f th sld.. ( dm) and dsrptn rat cnstants shuld hav th fllwng unts: ( ). Th. Th natural ( ) 3 k a ( dm ml s) and ( s ) ml n whch cas th adsrptn k d. 5

7 ~ n Hwvr, n practc th nt rat f adsrptn s mst frquntly xprssd as ( ml g sld s) whch cas th capacty f th sld absrbnt fr th adsrbat s xprssd as ( ) ( ml g sld ) Th adsrptn and dsrptn rat cnstants rman unchangd. If, hwvr, n rplacs th cncntratn f n quatn (), (), wth partal prssur f P ( atm) ndd adsrptn cnstant K bcm ( s ) a p atm. r ad S 0,, thn th unts f th. On shuld nt that by subtractng th nt rat f adsrptn at qulbrum (whch s zr) frm quatn () n can rprsnt th rat f adsrptn as bng drvn by th fractnal surfac cvrag dpartur frm qulbrum,.. r ad = [ k a () S 0 ()+ k d S ]θ θ () 0 ( ) (3) whr ( ) ( ) K θ = (5a) + K On shuld nt that th abv smplfd dvlpmnt assums a chmsrptn prcss,.. a prcss rqurng bnd frmatn btwn and S whch has an actvatn nrgy. It s assumd that nly mcr mlcular cvrag ccurs. Ths dvlpmnt als gnrs pssbl ffct f mass transfr rats va bundary layr dffusn n th rat f adsrptn. It ds nt cnsdr prus slds and th ffct f pr dffusn n th adsrptn prcss. It ds, hwvr, prsnt a vry basc ntn f adsrptn. ddtnal varus typs f dsscatv, dual st, cmpttv and nhbtry adsrptn mchansms wll b dscussd n th appndx. In catalytc prcsss ftn t s assumd that adsrptn s rapd and qulbratd whl th rat lmtng stp s th surfac ractn that cnvrts S t a nw spcs. Th rat f that rat lmtng stp s thn prprtnal t th qulbrum surfac fractnal cvrag, θ. 6

8 Instad f dscussng htrgnus catalyzd ractns, that always nvlv adsrptn as an mprtant stp, w fcus hr n rmval f cmpnnts frm a gas r lqud stram by adsrptn whch s a frquntly usd unt prcss n nvrnmntal ngnrng. PCKED DSORBTION COLUMNS ND BREKTHROUGH CURVES Whn w ar ntrstd n rmvng a partcular cmpnnt frm a flud phas by adsrptn, w mst frquntly us packd (fxd) bds f sld adsrbnt. Ths s dn bcaus such an arrangmnt prvds th largst pssbl mass f slds pr unt vlum f th flud and th flw pattrn f th flud s th clsst t plug flw. Bth f ths ar cnducv t achvng a hgh vlumtrc prductvty and thrughput rats. Cnsdr a cylndrcal clumn packd wth adsrbnt as shwn n gur Q C f Q C f IGURE : Typcal Packd Bd dsrbr Th clumn has a damtr D and lngth H. Cnstant vlumtrc flw rat f flud Q f pumpd thrugh th clumn. Th packng n th clumn s unfrm and has an quvalnt damtr f Intally thr s n adsrbat n th packng n th clumn. t tm t = 0 w swtch at th nlt frm a flw f pur carrr flud t a flw (at th sam flw rat Q f ) f a stram that cntans ( ml L) C n th fd. Th clumn s kpt sthrmal. t th xt w mntr cntnuusly th cncntratn f, C, n th fflunt.. w btan th brak thrugh curv. d p. gnral brak thrugh curv wll hav th shap ndcatd n gur 3. 7

9 C C C C dt IGURE 3: Schmatc f a Brakthrugh Curv W ar ntrstd n undrstandng and quantfyng th faturs f ths curv. mass balanc n th adsrbng spcs fr th whl clumn rqurs: Ttal accumulatn f = Ttal nput f Ttal utput f (4) Ttal accumulatn f n clumn = munt f n th clumn at nfnt tm munt f n th clumn at tm 0 = ε b VC M + ( ε b )Vρ p W 0 (5) whr ε b = bd vdag 8

10 V(L)= clumn vlum ( π D 4) H ( ml L) C = mlar cncntratn f n th fd ( kg ml ) M = mlcular wght f p ( kg L) ρ = dnsty f frsh sld adsrbnt ( kg kg sld ) w = saturatn capacty f frsh adsrbnt fr.. hw many kg pr kg frsh srbnt can n pck up at qulbrum at C. Ttal = Input f Q f C M dt (6a) Ttal = Output f Q f C M dt (6b) whr Q f ( Ls) = vlumtrc flw rat thrugh th clumn ( ml L) C = xt cncntratn f as a functn f tm t () s = tm n stram (snc C ntrducd) Equatn (4) nw bcms ε b VC + ε ( b)v ρ p w = Q f ( C C )dt (7) M Ths can b rwrttn as: ε b V Q f + ε ( b)v ρ p w = C dt (8) Q f C M C 9

11 Th rght hand sd f quatn (8) rprsnts th dashd ara n gur 3. Hnc, a brakthrugh xprmnt, n a mdl fr bass, prvds drct nfrmatn n th adsrptn saturatn capacty f th sld. Th frst trm n th lft hand sd s th man rsdnc tm f th flwng flud xtrnal t th packng. It tlls us hw lng t taks t rplnsh th vlum f th flud n th clumn wth ncmng flw rat. It als tlls us hw lng n th avrag a flud lmnt stays n th flud phas f th clumn. Th scnd trm n th lft hand sd s th rat f th capacty f th sld adsrbnt n th bd fr adsrbat t th carryng capacty f th nlt flw fr. It tlls us hw lng a tm th nlt flw rat must b sustand t prvd nugh t saturat th whl bd. In a way t s a masur f th avrag rsdnc tm f th adsrbat n th adsrbnt. Equatn (8) and th abv dscussn mak t clar that frm a brakthrugh xprmnt n can calculat th adsrbnt saturatn capacty w cncntratn M ( ml g sld) whch crrspnds t flud phas C. By rpatng th brakthrugh xprmnts at dffrnt lvls f C n can fnd th adsrptn sthrm f w M vs C. W rcgnz nw that th ara rprsntd by ( C C ) dt s drctly prprtnal t th saturatn capacty f th bd. Nxt w xamn th shap f th curv. Lt us call th dmnsnlss -curv, r brakthrugh curv, fr th adsrbat. C = t b C ls cnsdr = C C0 as a stp rspns, brakthrugh curv, f a nn-adsrbng nrt spcs. Thn th fllwng stuatns dpctd n gur 4 may ars. 0

12 tm, t tm, t a) b) tm, t tm, t c) d) IGURE 4: Schmatc f Brakthrugh Curvs f Inrt (Nnadsrbng) and dsrbng Spcs In gur 4a, th brakthrugh,, f an nrt (nnadsrbng) spcs s shwn tgthr wth th brakthrugh f th adsrbat. Th sharp stp-ws rs f th curv ndcats that th flw n th clumn s plug flw, (pstn flw) as all th flud lmnts that ntr tgthr flw tgthr untl th xt. Th ara ( ) dt = t f s th man rsdnc tm f th flud. Th fact that s als a sharp rsng stp ndcats that all adsrptn-dsrptn prcsss ar nstantanus n th tm scal f flw. Th ara s gvn by quatn (8). In gur 4b, th fact that s f sgmdal S shap ndcats th rspns f a flw prfl thr than plug flw, and pnts t pssblts f flw maldstrbutn. Snc s th sam n shap as, but just translatd n tm, ndcats that th rat prcsss nvlvd n adsrptn-dsrptn ar

13 stll nstantanus n th tm scal f flw. Th ara ( )dt quals th sum f th tw trms n th lft f quatn (8) whl th ara (8). (- )dt quals th frst trm n th lft f quatn In gur 4c, th sharp stp-lk rs f ndcats a prfct plug flw pattrn n th clumn. Th fact that s nw f sgmdal S-shap s ndcatv f th prsnc f substantal rsstancs n th adsrptn-dsrptn prcss. In thr wrds, th kntcs, dffusn and thr factrs affctng th adsrptn must b dscrbd t prdct th shap f th S-curv. gur 4d cmpars tw brakthrughs, and f spcs and, rspctvly. Th sld adsrbnt has th sam adsrptn capacty fr bth and.g. ( ) dt = ( ) dt. Snc s a sharp rsng stp-ws curv ths ndcats that th flw n th clumn s plug flw and all th stps nvlvd n adsrptn f, ar ssntally nstantanus n th tm scal cnsdrd. Clarly, majr rsstancs ar prsnt n adsrptn f whch rsults n th sgmdal curv. In adsrptn th gal ftn s t rmv a cmpnnt frm th flud phas and, hnc, whn that cmpnnt braks thrugh at an undsrd lvl, th flw must b stppd and swtchd t anthr adsrptn clumn. Clarly thn n gur 4d th adsrbnt usd s xcllnt fr rmval f but ds nt yld a gd brakthrugh curv fr adsrptn. Thus runs f small adsrptn clumns culd rapdly dtrmn th sutablty f varus adsrbnts fr rmval f dffrnt adsrbats. stp brakthrugh curv wth a lng brakthrugh tm s sught. Oftn adsrptn clumns ar usd n prdc pratn. Th adsrptn stp s fllwd by th dsrptn stp n whch th adsrbat s rlasd n a nw flud phas frquntly n cncntratd

14 frm. r xampl, adsrptn at lw tmpratur can b fllwd by dsrptn at lvatd tmpratur upn hatng th clumn. In gas phas hgh prssur adsrptn can b fllwd by lw prssur dsrptn. Ths swng prssur adsrptn prcss s usd xtnsvly n ndustral applcatns. On shuld als nt that th thry f adsrptn clumns s ntmatly td t th thry f chrmatgraphy. r xampl, f w dfn d E = and dt d E = (9) dt Thn E and E rprsnt th mpuls rspns f th clumn t a dlta functn (nstantanus) unt njctn f nrt I and spcs. E E IGURE 5: Impuls Rspnss fr gur 4b Impuls rspnss drvd frm brakthrugh curvs f gur 4b ar shwn n gur 5. Th cntrd f ths can b shwn t b t E () t ε b V dt = Q f (0a) te ()dt t = ε V b Q f ( + ε b)vρ p w Q f C M (0b) 3

15 Ths s prcsly th prncpl usd n chrmatgraphc clumns t sparat cmpnnts that hav dffrnt adsrptn qulbrum cnstants ( w M C ). W xamn nw ngnrng mdls fr th brakthrugh curv. ENGINEERING MODELS OR BREKTHROUGH CURVES Th task s t hav a rbust nt vrly cmplx mdl fr prdctn f th brakthrugh tm and th sgmdal shap f th brakthrugh curv and th ablty t calculat th mdl paramtrs bth by fttng xprmntal brakthrugh curvs and t prdct thn th thry. It s mprtant that th mdl has th ablty t assss th ffct f th chang n scal f th clumn, r wth pratng cndtns, n th shap f th brakthrugh curv. r many systms, ncludng adsrbrs, t s pssbl t rprsnt th dmsnabl mpuls rspns t a unt dlta functn nput n th nlt n trms f th ncmplt gamma functn E (θ) = θ ( σ D ) xp( θ /σ D ) Γ( σ D ) whr θ = t /t wth t bng gvn by quatn (0b) and θ D = σ t () whr σ = (t t ) E (t)dt (3) whr σ s drvd frm a mdl f adsrptn, flw, transprt n th bd. () r dtals s Lnk and Dudukvc (98). Th us f such a rprsntatn n dscrbng th prfrmanc f a cyclc md f pratn s dscrbd fr hat rgnratrs by Dudukvc and Ramachandran (985, 99). Th analgy t adsrbrs shuld b slf vdnt. 4

16 Rfrncs:. Dudukvc, M.P. and P.. Ramachandran, Hat Rgnratrs: Dsgn and Evaluatn, Hat Transfr Dsgn and Mthds (J.M. McKn, d.), Marcl Dkkr, 99 pp Dudukvc, M.P. and P.. Ramachandran, Quck Dsgn and Evaluatn f Hat Rgnratrs, Chmcal Engnrng, Jun 0, 985, pp Lnk,. and M.P. Dudukvc, Rprsntatn f Brakthrugh Curvs fr xd-bd dsrbrs and Ractrs Usng Mmnts f th Impuls Rspns, Th Chm. Eng. Jurnal 3, 3-36 (98). 5

17 REERENCE MTERILS ( Hat Rgnratrs: Dsgn and Evaluatn (Cvr pag) < Hat Rgnratrs: Dsgn and Evaluatn (rtcl) < Dsgn%0and%0Eval uatn.pdf> Quck Dsgn and Evaluatn f Hat Rgnratrs < n%0f% 0Hat%0Rgnratrs.pdf> Sulfur Dxd dsrptn n Mtal Oxds < n%0m tal%0oxds.pdf> Rprsntatn f Brakthrugh Curvs fr xd-bd dsrbrs <