Nonequilibrium models for a multi component reactive distillation column

Transcription

1 onequlbrum models for a mul componen reacve dsllaon column D. ROUZIEAU, M. PREVOST, M. MEYER IP/E..S.I.G.C LGC Equpe Séparaon Gaz Lqude 8 Chemn de la Loge, 3078 Toulouse Cedex 4, France Absrac A nonequlbrum model for mul componen separaon processes, ncludng lqud or/and gaze reacons, was developed n hs paper. Ths model nclude he fne mass ransfer rae descrbe by Maxwell Sephan equaons. I s assumed ha he bulk of boh he vapour and lqud are perfecly mxed and ha he ressance o mass and hea ransfer are locaed n wo flms a he lqud/vapour nerface (flm heory). There are no resrcve hypoheses as o he naure and he localsaon of he chemcal reacons. Ths models was solved numercally o smulae numerous example n he ProSm smulaor. So we can do he comparson beween he equlbrum sage models (EQ), n whch he hermodynamc equlbrum s consdered beween he wo phase, and he nonequlbrum model (EQ). Wh reasonable value of Murphee effcences he smulaon usng EQ model s almos equvalen o he EQ model. I seems o be dffcul o esmae effcences for mul componen reacve mxure, bu some EQ model requremens are equally delcae o predc, lke he flm hckness for he mass and hea ransfer. An oher smulaon show ha he model should use he Maxwell Sephan formulaon for mass ransfer even f Fck formulaon gve a good predcon. Inroducon Reacve dsllaon s a un operaon of grea ndusral neres. I can reduce capal and producon coss by combnng wo uns no once, and hs uns can mproved he selecvy, he hea negraon, he converson, ec... Smulaon and desgn of mul componen reacve dsllaon usually s carred ou usng he equlbrum sage model. The lmaon of convenonal equlbrum sage effcency calculaons s dscussed by Lee & Dudukovc (998), Baur & al. (2000), Taylor & Krshna (993), and Wesselngh (997). Ths auhor assume ha he generalsed nonequlbrum model should be preferred for he smulaon of a column for reacve dsllaon o he equlbrum model, because he accurae predcon of ndvdual Murphee ray effcences (or HEPT for packng) s very dffcul n he case of smulaneous mul componen separaon and reacons. The non equlbrum model seems o be beer because he model akes no accoun he echnque characerscs of he column (ype of plae, of packng...), so more near realy. Bu he non equlbrum model needs model requremens whch can be as dffcul o fnd as an effcency. In hs paper, we descrbe our non equlbrum model n he frs par, and defne he model requremens. The second objecve of hs sudy s o compare he convenonal equlbrum model, ncludng a predced ray effcency, and he non equlbrum model. Fnally, he radonal Fck approach for he mass ransfer s compared o he Maxwell Sephan approach.

2 2 onequlbrum model heory A shemac represenaon of he non equlbrum model (EQ) s shown n Fg.. Ths EQ sage may represen a ray or secon of packng. I s assumed ha he bulk of boh he vapour and lqud are perfecly mxed and ha he ressance o mass and hea ransfer are locaed n wo flms a he lqud/vapour nerface (flm heory, Krshna & Sandard, 976 ; Krshna, 977). V j Inerface L j- Sage j Q Vj Q Lj V j+ ev el L j Fgure : The nonequlbrum model Sage equaons The sage equaons are he radonal equaon of he mass balances and energy balances n he bulk phase for each sage (see Taylor & Krshna (993)). Ths equaons ake accoun reacons, and here are no resrcve hypoheses as o he naure and he localsaon of he chemcal reacons. The bulk varables ( composons, molar fluxes, emperaures, energy fluxes) are dfferen of he nerface varables. The emperaure of he vapor and he lqud phases are no assumed o be equal. The enre column s aken o conss of a sequence of such sages. We consder an sage column where sage can be a oal or paral condenser and sage a reboler. The modellng leads o a sysem of dfferenal and algebrac equaons, whch are solved afer dscresaon usng ewon s mehod. Mass and hea ransfer A novel model s used o compue hea and mass ransfer hrough he dffuson layer consdered n he flm heory. Indeed, he flud s consdered as an n componen reacve non deal mxure. The balance equaons for smulaneous hea and mass ransfer are wren n seady sae, akng accoun he reacons. The radonal model use he Fck Formulaon : x = c D m x + x 0 z e z Unforunaely, hs descrpon s lmed a wo componens mxures because does no ake he neracons beween he dfferen componens no accoun; moreover he non dealy for he drvng force s no consdered. So, for mass ransfer, he Maxwell Sephan dffuson law s used, n a novel formulaon. eher he dffuson coeffcens, nor he molar flux due o he reacon, are consdered o be consan. The complee formulaon for n non deal componens s : n j= δ j + x ln γ x j hn flms ressances for mass and hea ransfer T,P x = z n ( x j x j ) j= c D j 0 z e

3 o assumpon s made on he ype or he number of reacons, hus hey can be conrolled by knecs or equlbrum. So, n addon, he mass ransfer rae change due o he chemcal reacon. For he hea ransfer, he Dufour and Sore effecs are negleced and he dffuson hea rae s evaluaed by Fourer's law. These seady sae dfferenal equaons are solved by a DAE negraor whch allow conservng he n Maxwell Sephan formulaon. The complee model can used as well as he Maxwell Sephan formulaon as he Fck Formulaon. Ths allow dfferen smulaons wh he wo law o compare (see resul paragraph 3). Inerface equaon The nerface equaons lnk he wo phases. We assume physcal equlbrum a he vapor lqud nerface for each componen. Moreover, he mass and energy ransfer rae hrough he nerface should be connuous. Model requremens The complee model needs more requremens because of he more complee descrpon of he equpmen. For physcal chemcal properes, he model s lnked o he Prophy hermodynamc lbrary and negraed no he ProSm smulaor. The properes (hermal conducvy, denses, vscosy, surface enson, ec...) s calculaed by hs lbrary. Moreover, for he EQ model, he column equpmen mus be descrbed. : he column dameer, plae or packng characerscs. On he oher hand, for he EQ model, only he number of sages and wo physcal properes ( vapor lqud equlbrum and enhalpes) are needed. The drawback of hs model s he evaluaon of he effcences for he plae or he HEPT for he packng column n he case of mul componen reacve mxure. The EQ model nclude also some delcae conceps; ndeed for hs model we should evaluaed he vapor and lqud flm hckness (el and ev, see Fg. ), and he nerfacal area. The dfference model requremens beween wo models s shown n Fg. 2. Mul componen reacve column smulaon needs eed : Physcal Properes (enhalpes, equlbrum) umber of sage Evaluaed : Effcences (dffcul) HEPT (dffcul) EQ Model EQ Model eed : Physcal Properes (numerous) Column desgn Evaluaed : Flm hckness (dffcul) Inerfacal area (good correlaon) Smulaon resuls Comparason (See resuls) Smulaon resuls Fgure 2 : Model requremens for EQ model and EQ model

4 Plae number Smulaons resuls We wll dscuss wo examples o show he non equlbrum smulaon column n pracce : - Reacve dsllaon plae column wh Acec Acd Waer Acec Anhydrde non deal mxure; hs example perm he comparson beween EQ and EQ model. - Exracve dsllaon packng column wh aceone Mehanol Waer non deal mxure; hs example show he dfference beween Maxwell Sephan and Fck formulaon for he mass ransfer. Comparson EQ and EQ model Example parameers The example s a reacve dsllaon where he Acec Anhydrde reac wh Waer o oban 2 moles of Acec Acd. The reacon rae s gven by Marek (956). The column has 5 seve rays wh a feed a 6. The specfcaons feed and operaor condons are he same han Hgler & al. (999). The bnary neracons parameers (Wlson model) are gven by Hgler & al. (999). Smulaons The frs smulaon s he EQ model where he vapor flm hckness s fxed a 0-4 meers and he lqud flm hckness s fxed a 0-5 meers. The correlaon o calculae he nerfacal area s he Zuderweg Mehod. To compare wh EQ model, hs model smulaon was performed usng he Murphee ray effcences : - EQ smulaon wh Murphee effcences are assumed o be.0 - EQ smulaon wh Murphee effcences are predced by correlaon (MacFarland, 972) - EQ smulaon wh Murphee effcences are calculaed from he resuls of he non equlbrum model The correlaon of MacFarland predc effcences rangng from 0.69 o 0.72 for Acec Anhydrde, from 0.67 o0.83 for Waer and from 0.69 o 0.99 for Acec Acd. So, as here are one effcency for a plae, we choose 0.7 for he smulaon. The Murphee effcences calculaed from he resuls of he non equlbrum model are shown n Fg. 3; rangng from 0.54 o.4. Acd Aceque Waer Acec Anhydrde 4 0,5 0,6 0,7 0,8 0,9,,2 Murphee Effcences Fg.3 : Murphee effcences calculaed from he resuls of he non equlbrum model. Ths ndcaes ha he convenonal predcon of Murphee effcences from an emprcal correlaon may no be relable for mulcomponen reacve mxure n hs case. The Acec Acd molar fracon profle s shown n Fg. 4 for he dfferen smulaons (he concluson s he same for he oher consuens). The EQ model profle wh good predcon effcences (here 0.7 by Macarland) s almos smlar. In hs case, he predcon of EQ model s equvalen o he EQ model. An oher smulaon s effeced wh hgher flm hckness. The vapor flm hckness s fxed a 0-3 meers and he lqud flm hckness s fxed a 0-4 meers. Ths mples grea mass ransfer

5 rae. The gradens of he concenraons n he ressance flm are very mporan. The correlaon of MacFarland predc effcences rangng from 0.69 o 0.7 for Acec Anhydrde, from 0.70 o0.78 for Waer and from 0.73 o 0.9 for Acec Acd. The Murphee effcences calculaed from he resuls of he non equlbrum model are rangng from.39 o 0.73 (wh average value 0.2). So, an EQ model smulaon s effeced wh Murphee effcences a 0.2. The resuls are shown n Fg. 5. In hs case he predcon of MacFarland s so far of he EQ model. The EQ model profle wh predcon effcences a 0.2 s almos smlar. In he case wh grea mass ransfer seems o be dffcul o predced he effcences o smulae wh EQ model; he radonal correlaon can no be predced he real effcences of he plaes Plae number EQ Model Eff = EQ Model Eff = 0,7 (Mac Farland) EQ Model el =0-5 ev = 0-4 Plae number EQ Model el = 0-4 ev = 0-5 EQ Model Eff = EQ Model Eff = 0,7 (Mac Farland) EQ Model Eff = 0, , 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 Lqud molar fracon Fgure 4 : Lqud Acec Acd profle Smulaon 5 0 0, 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 Lqud molar fracon Fgure 5 : Lqud Acec Acd profle Smulaon 2 However, he resuls of smulaon 2 wh el = 0-4 and ev = 0-3 are very dfferen from he expermenal resuls of Marvek (956) and smulaon resuls of Hgler & al. (999). The frs smulaon s beer and seems correc; so, hs example shows ha he hckness of he ressance flm s a sensve parameer. Moreover, wh good predcon of Murphee effcences, he predcon of he EQ model smulaon s almos equvalen o he non equlbrum model smulaon. Descrpon wh Fck Formulaon and Maxwell Sephan Formulaon Example parameers Ths example s an exracve dsllaon of an Aceone - Mehanol mxure usng Waer as he solven. The column s a wo hegh random packng column and 0.5 meers for dameers. The flow shee and he feed almenaon are shown n Fg.6. Smulaons Two smulaons are effeced wh he EQ model : wh he Fck formulaon and wh Maxwell Sephan formulaon for he mass ransfer n he hn flms. Vapor flm hckness s fxed a 0-4 meers and he lqud flm hckness s fxed a 0-5 meers. The nerfacal area for he packng s calculaed by Onda correlaon. Feed (mol/s) : Aceone 0.00 Mehanol 0.00 Waer T = Feed 2 (mol/s) : Aceone Mehanol Waer 0.00 T = DL=22.22'mol/s R=0 2 M of random packng Fgure 6 : Spécfcaons for exracve dsllaon

6 Maxwell Sephan bnares dffuson coeffcens D j s calculaed by Fuller correlaon for he vapor and by Wlke-Chang and Vgnes correlaon for he lqud. Dffuson coeffcens of componen n mxure m D m for he Fck formulaon s predced by Blanc's law for he vapor and evaluaed Perkns and Geankopls for he lqud. The wo smulaons resuls are shown n Fgure 7. We can noce a dfference beween he wo laws. Ths s due o he drawback of he Fck law : - he neracons beween Aceone Waer and Mehanol does no ake no accoun - he non dealy of mxure (here UIQUAC daa fom Taylor R. 993) s no consdered wh Fck formulaon Moreover, he dffuson coeffcens are dfferen beween he wo formulaon of mass ransfer. 2,8, Fck Formulaon Maxwell Sephan Formulaon Hegh of Packng (m),4,2 0,8 0,6 Waer Mehanol Aceone 0,4 0, , 0,2 0,3 0,4 0,5 0,6 0,7 0,8 Molar Fracon Fgure 7 : Lqud phase composon profles wh Fck formulaon and Maxwell Sephan formulaon However, he radonal Fck formulaon s correc o predc he composon profle; ndeed he dfference wh Maxwell Sephan s no very mporan. The real Fck formulaon nconvenen s he predcon of he dffuson coeffcens D m whch are more absracs ha Maxwell Sephan bnares dffuson coeffcens D j. 4 concluson We have developed a non equlbrum model for mul componen reacve separaon echnques. Ths model was solved numercally and hen ncluded n he ProSm envronmen. The orgnaly of hs model s he Maxwell Sephan formulaon whch s solved n hs complee formulaon. The non equlbrum model was esed and compared wh he classcal equlbrum model. We can fnd he same resuls wh he EQ model, bu s dffcul o esmae Murphee effcences for a mul componen reacve mxure. EQ model smulaon s effeced wh Fck law and Maxwell Sephan law for he mass ransfer. The classcal Fck formulaon can predc concenraon profle bu hs law s no enough general for non deal mul componen mxure. We are acually developng an expermenal plo sudy n order o deermne he more effcen model.

7 omenclaure c Molar concenraon consuen (mol/m 3 ) c Toal concenraon oal (mol/m 3 ) D Dffuson coeffcen of componen n mxure m (m 2 /s) D m j n x z γ Maxwell Sephan dffuson coeffcen bnares -j (m 2 /s) Molar flux consuen (mol/m 2 /s) Molar flux molar oal (mol/m 2 /s) umber of consuens Molar fracon consuen Space reference (m) Acvy coeffcen consuen Acknowledgemen We are graeful for research suppor provded by ProSm S.A. (France). Helpful dscussons wh Dr Sere Pereygan (ProSm Techncal Manager) are acknowledged. REFERECES - Baur R., Hgler A.P., Taylor R., Krshna R., Comparson of equlbrum sage and nonequlbrum sage models for reacve dsllaon, Chemcal Engneerng Journal, Journal 76, 33-47, Hgler A., Krshna R., Taylor R., onequlbrum cell model for mulcoponen (reacve) separaon processes, AIChE J,Vol.45,, Krshna R., A generalzed flm model for mass ransfer n non deal flud mxure, Chem. Eng. Sc., 32, , Krshna R., Sandar G., A mulcomponen flm model ncorporang an exac marx mehod of soluon o he Maxwell Sephan equaon, AIChE J., 22, , Lee Jn-Ho, Dudukovc M.P., A comparson of he equlbrum and non equlbrum models for a mulcomponen reacve dsllaon, Compuers and Chemcal Engneerng 23, 59-72, MacFarland S. A., '' Predc dsllaon effcency'', Hydrcarbon Processng, -4, July Marek J., Recfcaon wh a chemcal reacon : II Plan recfcaon of a waer-acec acd-acec anhydrde mxure, Coll. Czech. Chem. Commun, 2, 56, Taylor R. & Krshna R., Mulcomponen Mass Transfer, Wley Seres n Chemcal Engneerng, (ew York), Wesselngh J.A., on-equlbrum modellng of dsllaon, Dsllaon and Absopon, Vol., -2, 997