18 MW H2S 34 MW CO2. operate regenerator top without boiling aq. amine solution.

Transcription

1 HSRemoval-EergyBalacemcd Eergy balace s the tool for fdg temperature, heat duty (heat trasferred) emperature, tur, affects partal pressure ad varous thermodyamc propertes, cludg heat capacty, heat of reacto (ethalpy), etropy, ad free eergy Whe there s o phase chage ad o reacto (eg, heat exchager, heatg, coolg, etc), we have sesble heat va heat capacty ΔH=C P Δ Whe there s phase chage (eg, absorpto, desorpto, vaporzato, codesato, etc), we have latet heat ΔH=(ΔH phasechage )(# mole udergog phase chage) Whe there s reacto (eg, ozato, Claus reactos, etc), we have heat of reacto ΔH=(ΔH rx ) (# moles reacto) Oxdato of H S For fast reacto, we model the reactor as adabatc Istructors: Nam Su Wag here are chemcal speces Assg ID umbers to ames Chemcal compoets compoet stream compoet j stream ( total CH4 CH6 CO HO HS MDEA SO SO S O N ) ( ) ( total methae ethae cdoxde water sulfde ame sdoxde stroxde sulfur oxyge troge ) ( ( dummy feed sweet amer amerwarm amel amelwarm offgas ar furace claus ) ( talze storage space for mole umber ad pressure hermophyscal data compoet, stream MDEA (-methyldethaolame) = CH N-(CH CH OH) = C 5 H NO MW MDEA 96 MW HO 8 MW HS 4 MW CO 44 molco MW CO gm molho MW HO gm molhs MW HS gm bolg pot & freezg pot bp MDEA 47 C mp MDEA C bp HO C mp HO C operate absorber ths rage bp HS 6 C mp HS 8 C operate regeerator top wthout bolg aq ame soluto bp S 4446 C mp S 5 C operate Claus reactor above dew pot Assg ar propertes to gas for whch data s uavalable; assg water propertes to lqud for whch data s uavalable Heat capacty for MDEA s roughly half of that of water o a per gram bass or ~7J/mole MDEA at 4 C: ref: Fg of Chu & L, Joural of Chemcal & Egeerg Data, 44, 96-4, joule C PHO gm K C PHO = 7566 joule molho K C PHO 7566 J/mole

2 C PMDEA 7 J/mole HSRemoval-EergyBalacemcd ΔH vapho 466 J/mole at C ΔH vapmdea ΔH vapho get ΔH vaps ΔH vaps = 75 5 J/mole at 5 C (surce: NIS) hermodyamc data (for gaseous state) heat capacty from SVA's Appedx C, able C; stadard heats of formato ΔH f98 from SVA Appedx C, able C4 std 985 K R 84 J/mole K template A B C D E ΔH of98 ΔG of98 template CH4 CH6 CO HO HS MDEA SO SO S O N MDEA MDEA MDEA MDEA MDEA MDEA MDEA CH4 CH6 CO HO HS MDEA SO SO S O N get Note: C P data for gaseous MDEA s mssg (ad ot used ths worksheet, so t does ot matter for ow) ΔH ad C P data for S comes from NIS ( NIS gves stadard heat of formato based o the stadard state of sold S havg ΔH of98 =, so that ΔH of98 =+85 J/mol for lqud S ad ΔH of98 =+777 J/mol for gaseous S hs s also cosstet wth the ΔH of98 values for SO ad SO gve by SVA (whch does ot explctly ote that ther values are also based o sold S havg ΔH of98 =) SVA's coveto s to set ΔG of98 = for elemets at the referece coos, whch meas ΔS of98 = for elemets at referece coo of =98K I cotrast, NIS gves ΔS of98 = for elemets at =K, accordace wth the rd law of thermodyamcs Whe data comes from dfferet sources, we eed recocle ot just the physcal uts, but the referece coos ΔH of98ssold (referece) ΔH of98slqud 85 ΔH of98sgas 777 J/mol ΔS of98ssold 54 ΔS of98slqud 685 ΔS of98sgas 6789 J/mol K Based o NIS's refererece of ΔS= at =K ΔG of98ssold ΔH of98ssold std ΔS of98ssold ΔH of98ssold std ΔS of98ssold = 9557 Based o SVA's refererece of ΔS= at = std =98K hs value s etered the above table ΔS of98ssold ΔS of98ssold 54 ΔS of98ssold = J/mol K ΔS of98slqud ΔS of98slqud 54 ΔS of98slqud = 4796 ΔS ΔS 54 ΔS = 5 775

3 ΔS HSRemoval-EergyBalacemcd of98sgas ΔS of98sgas 54 ΔS of98sgas = 5775 ΔG of98sgas ΔH of98s std ΔS of98sgas ΔG of98sgas = 6689 J/mol eter ths value the above tab C P data from NIS has a slghtly dfferet format from those from SVA C PS ( 784) he followg puts C P data SVA's format 6574 ( 5585) ( 668) C PS R 84 ( 66 ) 698 ( 678 ) 5 ( 9) he E term s cluded the NIS database, but ot SVA he followg shows that t s best to keep the term 84 ( 66 ) 698 ( 678 ) 5 ( 9) R = ( 66 ) Check: NIS gves for troge 698 C PN ( ) ( 85978) ( ) C PN std = 94 compare 5 R = 999 Correct for gas costat R ad multplers ( 678 ) 5 ( 7) R = 44 Add E-term for NIS data A A R B B R C C R 6 D D R 5 E E R 9 heat capacty at costat pressure: C P (, ) A B C D E where C P s J/mole K ad s K ( 6657) Beg a good egeer meas beg able to do quck estmate If I do ot have access to a computer, for back-of-evelop calculato, I would smply set all gas speces to have the same property as ar (deal gas, desty, molar heat capacty, etc) For example, settg C P to be 5 R (a value for ar at ambet) does ot chage the overall cocluso much Chage the followg to be a real assgmet equato ad see for yourself C P (, ) 5 R ucommet to use just oe costat value at for all speces for all temperatures Itegral of C P from std =985K to, case we eed to speed up computato B IC P (, ) A std C std std D std 4 4 std 4 E

4 4 HSRemoval-EergyBalacemcd Absorber Heat of absorpto of CO ad that of H S depeds o wt% MDEA ad loadg (mole CO absorbed/mole MDEA) he reported values are roughly the rage of 4~6 Btu/lb (Bull et al, ref?) Heat of absorpto of CO = ~5 BU/lb Heat of absorpto of H S = ~5 BU/lb 5 BU lb 5 BU lb = = 57 4 joule molco joule molhs ΔH absorbco 5 4 J/mole ΔH absorbhs 4 4 J/mole Gve top & feed, calculate temperature dfferece Sce the feed gas s avalable at 7 F= C ad the sweeteed gas s to be delvered at 7 F, we wll start at 7 F for the rch ame stream MDEA, amel HO, amel HS, amel CO, amel MDEA, amer HO, amer HS, amer CO, amer feed sweet amel 75 5 ethalpy balace HS, amer ΔH absorbhs CO, amer ΔH absorbco MDEA, amer C PMEDA HO, amer C PHO HS, amer ΔH absorbhs CO, amer ΔH absorbco Δ absorber MDEA, amer C PMDEA HO, amer C Δ absorber = 84 PHO amer amel Δ absorber amer = 9784 If a lessor amout of ame s eeded, the absorber top-to-bottom temperature dfferece may be order of ~ C Lookg ahead: Gve Hery's costats ad ketcs of hydrato (f reacto s rate lmtg) or mass trasfer coeffcet (f mass trasfer s rate lmtg), fd tme eeded to acheve a gve degree of approach toward equlbrum he tme aspect (the dyamc, ketcs) helps determe the physcal sze of the absorber ad desorber ut; equlbrum calculato aloe does ot yeld tme or sze Δ

5 5 HSRemoval-EergyBalacemcd Heat Exchager -- Coutercurret emperature the rch ame stream s rased ad temperature the lea ame stream s lowered by roughly the same degree, because both streams are domated by water+ame, wth a relatvely small amout of H S ad CO See the commet o temperature the Regeerator-dstllato secto Estmate bolg pot of lea ame soluto at the bottom of the regeerator (more refed estmato wll be based o pressure temperature relatoshp (Atoe equato) for H O ad MDEA ad regeerator colum pressure) MDEA, amel amel HO, amel bp bp MDEA bp HO 75 MDEA, amel HO, amel MDEA, amel HO, amel ame soluto returg from the bottom of the regeerator s at the bolg pot amelwarm amel bp amelwarm = 948 O the other had, we wat the top of the regeerator to be just a lttle below bolg amerwarm 9 75 amerwarm = 65 Δ htxr amerwarm amer Δ htxr = 6666 amelhtxr amelwarm Δ htxr amelhtxr = 644 We wat ths temperature to be lower Q htxr MDEA, amer C PMDEA HO, amer C PHO Δ htxr Heat duty of the (lea ame + rch ame) heat exchager Q htxr = J here s o chage composto amerwarm < amer > < amelwarm > < amel> amelhtxr from the (rch ame + lear ame) heat exchager does ot qute match amel that we wat to feed to the top of the absorber hus, we wll eed to stall a cooler to cool the lea ame stream from amelhtxr to amel Δ cooler amel amelhtxr Δ cooler = 64 Q cooler MDEA, amel C PMDEA HO, amel C PHO Δ cooler Heat duty of lear ame stream cooler Q cooler = 46 5 J (egatve umber for coolg)

6 6 HSRemoval-EergyBalacemcd Regeerator -- dstllato at bottom =~5 C=98K, top =below C (hgh eough to drve off acd gas wthout bolg the aqueous ame solvet, whch s mostly water based o mole fracto ad deftely above freezg of water at C); pck =~9 C as a frst approxmato (I my materal balace worksheet, I metoed passg ~5 C, whch was ot used materal balace) Overall ethalpy balace Maly the temperature dfferece the ame soluto ad the heat of desorpto, whch s smlar magtude but egatve sg to the heat of absorpto the absorber ΔH flow MDEA, amel C PMDEA HO, amel C PHO amelwarm ΔH = amerwarm flow 96 5 ΔH desorpto HS, amerwarm ΔH absorbhs CO, amerwarm ΔH absorbco ΔH desorpto = 86 4 Q regeerator ΔH flow ΔH desorpto Q regeerator = 46 5 Furthermore, boler ad codeser heat dutes deped heavly o the reflux rato Assume a smple L/V rato of ~ as a rough estmate Q boler ΔH vapho HO, amel = Q boler 5 6 J Q codeser Q regeerator Q boler Q codeser = 8 6 J

7 7 HSRemoval-EergyBalacemcd Claus Reactor Claus Reacto : H S + O SO + H O + heat Claus Reacto H S + SO S (g) + H O + heat Overall (Reacto + X Reacto ): 6 H S + O 6 S (g) + 6 H O Re-wrte the above reactos Claus Reacto : / H S + / O / SO + / H O + heat Claus Reacto / H S + / SO S (g) + / H O + heat Overall (Reacto + Reacto ): H S + / O S (g) + H O Possble udesrable sde Reacto : SO + / O SO (fd a coo to mmze ths later) Reacto 4 (=X Reacto - X Reacto ) to evaluate the equlbrum amout of SO : H S + SO 4 SO + H O Reacto stochometry ν compoet, 4 Reacto Reacto Reacto ν ν ν HS, HS, HS, ν O, ν SO, ν O, ν SO, ν, ν ν S ν SO, HO, HO, ν ν ν total, total, total, 6 Reacto 4 ν HS, 4 ν SO, 4 ν SO, 4 4 ν HO, 4 ν total, 4 rx 4 rx rx umber of reactos stadard heat of reacto ΔH rx98 at =98K s the sum of stadard heat of formato compoet ΔH rx98rx = rx ΔH of98 ν, stadard Gbbs eergy of reacto ΔG rx98 at =98K s the sum of stadard Gbbs eergy of formato compoet ΔG rx98rx = rx ΔG of98 ν, stadard etropy of reacto ΔS rx98 ΔH rx98rx ΔG rx98rx ΔS rx98rx std Check (& recocle wth lterature data) Data from Shreve's Chemcal Process Idustres ΔH =-79kJ/mole Reacto # (cosumg / mole of H S & producg / mole of H S) agrees wth my value

8 8 HSRemoval-EergyBalacemcd ΔH =-476 kj/mole Reacto # (cosumg / mole of H S to produce mole of S lqud state) ΔH =( ) kj/mole=+77 kj/mole Reacto # corrected for gas state (cosumg / mole of H S to produce mole of S gaseous state) agrees wth my value Data from Abed et al, Chemcal Egeerg Research Bullet, 4, -4 () ΔH =-86 kj/mole Reacto # (cosumg / mole of H S) agrees wth my value ΔH =+57 kj/mole Reacto # (cosumg / mole of H S to produce / mole of S? state -- state of S s uclear) ΔH =-6 kj/mole Reacto # (cosumg / mole of H S to produce /8 mole of S 8? state -- state of S s uclear) hs s gettg closer to my value of -467 kj/mole S Wkpeda's urelable formato s legedary; t reports uder "Claus process" the followg values: H S + O SO + H O ΔH = -447 kj/mol rx=-69 kj/mol SO produced) whch s ~4X of my value of -77 kj/ mole SO produced!!! If you use the Wkpeda values, your calculatos wll be garbage-, garbage-out!! H S + SO S + H O ΔH = -656 kj/mol rx=-885 kj/mol lqud? S produced, whch s ~8X of my value!! From the egatve ΔH value, I assume the reported value s for lqud S My values for gaseous S Note the large postve value of ΔH rx98 for Reacto & cosequetly a large postve value of ΔG rx98 for Reacto # hs meas there wll be o gaseous S at ay temperature ΔH rx98rx ΔG rx98rx ΔS rx98rx he above gves the reacto volvg gaseous S Claus Reacto (producg gas S) / H S + / SO + heat S (g) + / H O Corrected for lqud: S (g) S (l) + heat Addg the above two reactos gves lqud S as the reacto product Claus Reacto (producg lqud S) / H S + / SO S (l) + / H O + heat he followg lsts my values for lqud S Note that Reacto # s edothermc for gaseous S, but exothermc for lqud S Whle all reactos are exothermc, Reacto # releases about 4X more heat ΔH rx98 ΔH rx98 ΔH of98s ΔH of98slqud ΔH rx98 = ΔS rx98 ΔS rx98 ΔS of98sgas ΔS of98slqud ΔS rx98 = ΔG rx98 ΔH rx98 std ΔS rx98 ΔG rx98 = 95 4 stadard heat of reacto ΔH rx, stadard etropy of reacto ΔS rx, stadard Gbbs eergy of reacto ΔG rx, ad equlbrum costat K at

9 ΔH o (, rx) ΔH rx98rx ν, rx std 9 HSRemoval-EergyBalacemcd C P ( τ, ) dτ ΔS o (, rx) ΔS rx98rx ν, rx std ΔG o (, rx) ΔH o (, rx ) ΔS o (, rx) C P ( τ, ) τ dτ

10 HSRemoval-EergyBalacemcd Equlbrum -- Back-Of-Evelop Verso -- costat Cp for all temperatures ad for all chemcal speces If I do ot have access to a computer my back-of-evelop calculato, I would assg a detcal temperature-varat heat capacty for all speces hs approxmato greatly smplfes calculatos whle keepg the geeral bahavor tact Cp 5 R Just a costat value for all chemcal speces!! ΔG orough (, rx) ΔH rx98rx ν, rx Cp std ΔS rx98rx ν, rx Cp l std l( K) ΔG o R K(, rx) exp ΔG orough (, rx) R Effect of temperature o Equlbrum ΔH s a weak fucto of temperature It s the ΔS term that cotrbutes heavly to ΔG's depedece o temperature Although the ΔG values at two dfferet temperatures are of the same order of magtude, the equlbrum costats Ks (except for Reacto #) are may orders of magtude dfferet because ΔG gets hugely magfed by the expoetal fucto Exame the values at two dfferet temperatures: 5 5 K Reacto Reacto Reacto Reacto 4 ΔH o (, ) = 7 5 ΔH o (, ) = ΔH o (, ) = ΔH o (, 4) = 75 5 ΔH o ( 5, ) = 79 5 ΔH o ( 5, ) = 45 4 ΔH o ( 5, ) = 76 5 ΔH o ( 5, 4) = 8 5 ΔG o (, ) = ΔG o (, ) = 78 ΔG o (, ) = 55 5 ΔG o (, 4) = ΔG o ( 5, ) = ΔG o ( 5, ) = 87 4 ΔG o ( 5, ) = 4 5 ΔG o ( 5, 4) = 4 5 K(, ) = 6 7 K(, ) = 89 K(, ) = 48 K(, 4) = 69 K( 5, ) = K( 5, ) = K( 5, ) = 7 K( 5, 4) = 7 4 See the full treatmet below for commets o the above values -- the same commets apply here as the geeral treds rema uchaged Claus reactor bass: offgas O, ar HS, offgas CO, offgas O, ar = 7 HS, offgas HO, offgas 79 N, ar = 4 O, ar N, ar ar total, ar = 79 total, ar Assume complete combusto the furace at =flame temperature ε O, ar = ν O, materal balace for the furace total, offgas ε 75 extet of Claus Reacto to completely cosume O furace < offgas > < ar > ν ε Ethalpy Balace furace to fd flame temperature (dfferece back-of-evelop form)

11 offgas 5 75 ar 98 HSRemoval-EergyBalacemcd ε ΔH rx98 furace std offgas Cp std offgas, ε ΔH rx98 furace = 87 K a farly decet approxmato ar Cp std ar, offgas Cp std offgas,, furace Cp Equlbrum extet of Reacto (ε ) ad composto as a fucto of temperature claus ε furace ν ε y ε claus ε claus ε total P 5 Pa compoet ν, K ε, P y ε P P = ν total, K P S P P HS P furace Cp furace std, ar Cp std ar, P HO P P SO P y S y HO y HS y SO Note that the above defto of K apples for gaseous S Both deftos of K(,) ad K (ε,p) clude the S (lqud) term that s ormally excluded from the equlbrum costat However ths cluso does ot affect the calculato of ε, sce both sdes cota the same extra factor ad they cacel each other ε 5 tal guess Gve K ε, P K(, ) ε (, P) Fd ε P 5 5 claus ε claus, P = 44 claus 4 ε claus, P = 75 bp S bp S = 776 K claus 4, 45 4 P P 8 Claus Catalytc Step (Reacto ) Extet of Reacto (mole) ε claus, P 6 4

12 HSRemoval-EergyBalacemcd claus emperature (K) 8 Claus Catalytc Step (Reacto ) Composto (mole) claus ε claus, P claus ε claus, P claus ε claus, P 6 HS SO 4 S HS SO Elemetal S claus emperature (K) Eve wth the back-of-evelop calculato, the geeral tred of equlbrum wth temperature s preset, but the actual values are just a bt off hs s because a small devato ΔG s magfed by the expoetal fucto Lkewse, for extet of reacto ad equlbrum composto versus

13 HSRemoval-EergyBalacemcd Equlbrum -- Rgorous Verso Back to the more rgorouks varable heat capacty verso l( K) ΔG o R K(, rx) exp ΔG o (, rx) R Effect of temperature o Equlbrum ΔH s a weak fucto of temperature It s the ΔS term that cotrbutes heavly to ΔG's depedece o temperature Although ΔG values at two dfferet temperatures are of the same order of magtude, the equlbrum costats Ks (except for Reacto #) are may orders of magtude dfferet because ΔG gets hugely magfed by the expoetal Exame the values at two dfferet temperatures: 5 5 K Reacto Reacto Reacto Reacto 4 ΔH o (, ) = 7 5 ΔH o (, ) = ΔH o (, ) = ΔH o (, 4) = 75 5 ΔH o ( 5, ) = 79 5 ΔH o ( 5, ) = 45 4 ΔH o ( 5, ) = 76 5 ΔH o ( 5, 4) = 8 5 ΔG o (, ) = ΔG o (, ) = 78 ΔG o (, ) = 55 5 ΔG o (, 4) = ΔG o ( 5, ) = ΔG o ( 5, ) = 87 4 ΔG o ( 5, ) = 4 5 ΔG o ( 5, 4) = 4 5 K(, ) = K(, ) = 9 K(, ) = 744 K(, 4) = 49 K( 5, ) = 56 6 K( 5, ) = 876 K( 5, ) = 4 K( 5, 4) = 77 A examato of the equlbrum costats reveals that Reacto goes to completo rreversbly, ad ether all H S or all oxyge, whchever s lmtg, wll be completely cosumed If oxyge s ot the lmtg reactat Reacto, the equlbrum costat for Reacto shows that Reacto wll cosume all excess oxyge I the absece of oxyge, we rearrage the two reactos that cosume oxyge (Reacto & Reacto ) to yeld Reacto 4 that cacels oxyge he equlbrum costat for Reacto 4 dcates that SO s overwhelmgly favored over SO, whch s what we wat hus, t s mportat ot to feed excess oxyge he equlbrum costat of Reacto shows that temperature has a sgfcat effect o the equlbrum composto Assume we provde stochometrc amout of oxyge ( the form of ar) eeded to react wth H S he amout of H S to be reacted s based o equlbrum at the last Claus step, whch practce s equvalet to ~95% coverso of H S to elemetal S I other type of reactos, we ormally provde extra oxyge (perhaps 5% excess) to push for complete combusto of the fuel However, ths problem, we wat to avod geeratg excess SO wth excess O, because SO s ot the desred fal product I the fal desg, we should clude a cotroller for feedg O to the furace based o the H S measuremet Claus reactor bass: O, ar N, ar total, ar HS, offgas 79 O, ar ar CO, offgas O, ar N, ar total, ar 5 = 7 = 4 = 79 HS, offgas 75 HO, offgas Assume complete combusto the furace at =flame temperature 5 total, offgas offgas

14 ε O, ar = ν O, materal balace for the furace 4 HSRemoval-EergyBalacemcd ε 75 extet of Claus Reacto to completely cosume O furace < offgas > < ar > ν ε Ethalpy Balace furace to fd flame temperature (tegral form for varable C P, as opposed to the dfferece form for costat C P ) offgas 5 75 ar 98 furace 5 provde tal guess Gve Reacto ε ΔH rx98 +, offgas std offgas C P (, ) d, ar std ar C P (, ) d, furace furace std C P (, ) d furace Fd furace furace = 7654 K he above shows a relatvely low flame temperature reached from just Reacto # Lookg ahead, we see that ths low temperature may affect both Reacto # & Reacto # Whe temperature s too low, Reacto # (whch s bascally combusto of very lea fuel mxture of H S) may ot be self-sustaed ad may requre a catalyst he flame temperature would have bee hgher (by 8~K) f there were o CO or water the feed to the Claus reactor or f oxyge-erched ar or pure oxyge stead of ar were fed to the Claus reactor At ths pot, CO (whch s ~4X of the umber of moles of troge ad ~X of that of water) acts as a major heat sk hus, the level of CO the feed to the Claus process depeds o the outcome of a more careful desg of the absorber-regeerator, ad we may eed to add a flash step pror to the Claus steps to remove some CO ad to cocetrate H S Or, we may eed to pre-heat the off gas ad or ar to susta combusto If we assume Reacto # ca proceed to ts equlbrum level the furace the absece of a catalyst, we ca solve both the equlbrum equato ad the eergy balace equato smultaeously to calculate both the adabatc reacto temperature ad the extet of Reacto # (ε ) the furace; there wll be some S formed due to a ozero ε ad ths adabatc temperature wll be a a bt (~5C) hgher tha the temperature calculated above based o ε =) We ow clude Reacto # such that we covert 95% of H S to elemetal S 95 HS, offgas ε ε = 7 extet of Reacto # for 95% coverso of H S ν S, claus < furace > ν ε claus 5 provde tal guess Gve Reacto & Reacto ε ΔH rx98 ε ΔH rx98 +, offgas std C P (, ) d, ar std C P (, ) d, claus claus C P (, ) d

15 5 HSRemoval-EergyBalacemcd offgas ar std claus Fd claus claus = 799 K Cotug oto Reacto drectly over a catalyst bed wll rase the adabatc temperature by 9K Note that we dd ot cosder equlbrum for ths calculato; we smply set the extet of reacto ε to correspod to 95% coverso As we wll see the ext secto whe we cosder equlbrum, percet coverso that s possble depeds o temperature, ad ths 95% coverso s ot possble at 79K Claus Reactor ethalpy balace We the cool dow the furace exhaust to as low as possble to favor equlbrum coverso but ~ C above the dew pot of S subsequet reactors (dew pot at ~ C) to avod codesg S o the catalyst ad deactvatg the catalyst Amout of heat to be removed to cool the Claus reacto product to C hs represets the et amout of heat f there are a seres of codesers ad reheaters for multple catalytc Claus reactors seres claus 75 claus = 485 ε = 7 Q ε ΔH rx98 ε ΔH rx98 +, offgas std offgas C P (, ) d, ar std ar C P (, ) d, claus claus std C P (, ) d Q = 99 4 J Equlbrum extet of Reacto (ε ) ad composto as a fucto of temperature claus ε furace ν ε y ε claus ε claus ε total P 5 Pa compoet ν, K ε, P y ε P P = ν total, K P S P P HS P P HO P P SO P y S y HO y HS y SO Note that the above defto of K apples for gaseous S Both deftos of K(,) ad K (ε,p) clude the S (lqud) term that s ormally excluded from the equlbrum costat However ths cluso does ot affect the calculato of ε, sce both sdes cota the same extra factor ad they cacel each other ε 5 tal guess Gve K ε, P K(, ) ε (, P) Fd ε P 5 5 claus ε claus, P = claus 6 ε claus, P = 7 ε=7 correspods to 95% coverso of H S at =6K bp S bp S = 776 K claus 4, 45 4 Claus Catalytc Step (Reacto ) P P

16 8 6 HSRemoval-EergyBalacemcd Extet of Reacto (mole) ε claus, P claus emperature (K) 8 Claus Catalytc Step (Reacto ) Composto (mole) claus ε claus, P claus ε claus, P claus ε claus, P 6 HS SO 4 S HS SO Elemetal S claus emperature (K)

17 7 HSRemoval-EergyBalacemcd Reacto -- Dyamc Smulato of Isothermal Reactor wth Abed Rate Expresso Reacto rate parameters (from Abed et al, Chemcal Egeerg Research Bullet, 4, -4, ) reacto rate "costat" for forward ad reverse reactos; the forward ad reverse pre-expoetal reacto rate costats (e, k & k ) may both be multpled by a factor to accout for dfferet actvtes (say, due to catalyst deactvato or packg desty) k 576 mole/s-m E 494 J/mol actvato eergy for forward reacto k 56 mole/s-m E 89 J/mol actvato eergy for reverse reacto k ( ) k exp E R k ( ) k exp reacto rate expresso gve by Abed et al r k 5 P HS P SO k P HO r 5 k 5 y HS y SO P total k y HO P total E R expressed terms of partal pressure ( stadard pressure ut) expressed terms of mole fracto y r ( y,, P ) 5 k P ( ) y HS y SO P Reactor Smulato 5 k P ( ) y HO P furace = total, furace CO, furace HS, furace = 86 = 5 = 5 We have roughly mole from the furace (but oly 5 mole of H S), or roughly 5 m volume hus, a reasoable order-of-magtude catalyst volume s m hus, we ca see that order to shrk reactor sze ad crease partal pressure of H S to speed up coverso, we may eed to reduce ert compoets frst (eg, CO, N, etc), whch costtute the bulk of the of Claus reactor feed V cat m volume of catalyst (also closely related to reactor sze) P = 5 5 Pa claus = 485 d ν r ν r( y,, P) d( t, ) V cat ν r, claus, P Ital reacto rate IC t furace t r, claus, P = t

18 8 HSRemoval-EergyBalacemcd Call a route to solve ODE step steps from t= to t f t rkfxed t,, t f, step, d t t claus submatrx( t,,,, compoet) t Claus Catalytc Step at =48K Ital composto ths tso = 75 mole Composto (moles) 5 Fal composto claus = 74 mole, S Fractoal coverso claus, S = 987 ths tso 5 5 HS SO Elemetal S me (sec) Equlbrum based o values at ed of ru K claus, P = 55, S Equlbrum based o thermophyscal data K claus, = 46 Aother way s to tegrate the extet of reacto (whch s a scalar) rather tha tegrate the umber of moles (whch s a vector) claus ε furace ν ε claus ε dε t, ε V cat r, claus, P IC ε t claus ε Call a route to solve ODE t f tε rkfxed ε t,, t f, step, dε t tε ε tε t Claus Catalytc Step at =48K 6 Composto (moles) 4 5 5

19 me (sec) HS SO Elemetal S Extet of Reacto 9 HSRemoval-EergyBalacemcd For a plug flow reactor (PFR), substtute tme t wth reactor legth z dz u F where u s the velocty of the flow, whch s the volumetrc flow A PFRcrosssecto rate F dvded by the crosssectoal area of the vod space (f PFR s a packed bed) At a superfcal velocty of m/s, each secod a batch reactor traslates to m legth a packed bed reactor (or PFR) hus, operatg at a temperature ( C=48K) that allows 95% of the H S to be coverted leads to a log reacto tme (~ sec) or reactor sze (~m) We re-do the reactor smulato at aother so that reactor tme or sze s more realstc Aga, be forewared that the reacto rate expresso here proposed by Abed et al s cosstet wth thermodyamcs, ad as t, t wll lkely lead to a composto correspodg to the equlbrum composto hus, we may later have to substtute wth a dfferet, more realstc rate expresso claus 6 75 claus = 875 d( t, ) V cat ν r, claus, P Call a route to solve ODE t f t rkfxed t,, t f, step, d t t claus submatrx( t,,,, compoet) t Claus Catalytc Step at =87K Ital composto ths tso = 75 mole Composto (moles) 5 Fal composto claus = 74 mole, S Fractoal coverso claus, S = 99 ths tso Equlbrum based o values at ed of ru HS SO Elemetal S me (sec) K claus, P = 778, S Equlbrum based o thermophyscal data K claus, = 84 he above shows a urealstc approach ast t because the reacto over-shoots the equlbrum values at hgh If we are terested approach equlbrum (say, 95%) at dfferet temperatures, ths ketc model cosstecy becomes a ssue I the ext secto, we do a realty check Cosstecy check o the above Abed model At equlbrum, the forward reacto equals the

20 HSRemoval-EergyBalacemcd reverse reacto Claus Reacto / H S + / SO S + / H O + heat Based o the emprcal reacto rate expresso, we have for equlbrum, r k 5 P HS P SO k P HO emprcal fttg k k P HO P 5 HS P SO k k exp E E R P HO K eq P HS P SO P P k k P SO P P k k exp E E R P SO P P hus, the gve reacto rate becomes at a product-to-reactat rato that does ot correspod to the thermodyamc defto I other words, the gve rate reacto rate expresso wll lead to a o-equlbrum composto as t Based o the thermodyamc defto of equlbrum, we have, P HO K eq P HS P SO P P exp ΔG R exp ΔH ΔS R exp ΔS R exp ΔH R hus, the expoetal term relates the Arheus actvato eerges of the forward ad reverse reactos to ΔH of the reacto, whle the pre-expoetal term relates the pre-arheus costats to ΔS of the reacto A comparso of the expoetal terms shows that there s a ~X dscrepacy the actvato eerges for the forward ad reverse reactos he orgal source of the ketc parameters (Elser et al, Catalyss oday, 79-8, , ) explas away that these umbers are merely emprcal ad may clude mass trasfer effects A examato of the pre-expoetal term also dcates that there s a sgfcat dfferece, lkely due to the /(P SO ) term expoetal term from rate expresso: = E E 66 4 expoetal term from thermodyamcs: ΔH o claus, = ΔH o (, ) = k pre-expoetal term from rate expresso: = 99 k ΔS o claus, pre-expoetal term from thermodyamcs: exp = R We ca force the pre-expoetal factors to match, but t s probably meagless P P P SO 7 4 k P P = k P P SO hermodyamcally cosstet ketc model We make a adjustmet to the reverse reacto, whle keepg the forward reacto uchaged

21 whle keepg the forward reacto uchaged HSRemoval-EergyBalacemcd E E ΔH rx E E ΔH o (, ) E = 5 5 k k exp k ( ) k exp ΔS orx R k E R k exp k ( ) k exp reacto rate expresso for lqud form of S ΔS o (, ) E R R k = y HO K y HS y SO P P r ( y,, P ) 5 k P ( ) y HS y SO P 5 k P ( ) y HO P reacto rate expresso for gaseous form of S y S y HO K y HS y SO P P r ( y,, P ) 5 k P ( ) y HS y SO P 5 5 k P ( ) y yho S P 5

22 HSRemoval-EergyBalacemcd Dyamc Smulato of Isothermal Reactor wth a thermodyamcally cosstet model (low ) claus 75 claus = 485 d( t, ) V cat ν r, claus, P Call a route to solve ODE t f t rkfxed t,, t f, step, d t t claus submatrx( t,,,, compoet) t Claus Catalytc Step at =48K Ital composto ths tso = 75 mole Composto (moles) 5 Fal composto claus = 7 mole, S Fractoal coverso claus, S = 99 ths tso Equlbrum based o values at ed of ru 5 5 HS SO Elemetal S me (sec) K claus, P = 86, S Equlbrum based o thermophyscal data K claus, = 46 Dyamc Smulato of Isothermal Reactor wth a thermodyamcally cosstet model (hgh ) claus 6 75 claus = 875 d( t, ) V cat ν r, claus, P Call a route to solve ODE t f 5 t rkfxed t,, t f, step, d t t claus submatrx( t,,,, compoet) t Claus Catalytc Step at =87K Ital composto ths tso = 75 mole Composto (moles) 5 Fal composto claus = 4 mole, S Fractoal coverso claus, S = 58 ths tso

23 4 5 HS SO Elemetal S me (sec) HSRemoval-EergyBalacemcd Equlbrum based o values at ed of ru K claus, P = 84, S Equlbrum based o thermophyscal data K claus, = 84

24 4 HSRemoval-EergyBalacemcd Dyamc Smulato of Adabatc Reactor Materal balace tal ν ε ake dervatve of the above equato wrt tme t to derve a dyamc materal balace equato d d tal d tal ν dε dε where the rate of chage of the extet of reacto ε s the rate of reacto r d ν r d( t,, ) V cat ν r,, P Ital composto s fxed ad does ot chage wth tme We also apply the defto of reacto rate (whch s chage extet of reacto wrt tme t) Ethalpy balace Adabatc Q= For a adabatc reactor, temperature s ot costat Need a dyamc d/ equato derved from ethalpy balace Q ε ΔH rx98, let std C P (, ) d ake dervatve of the above equato wrt tme t dq dε d std ΔH, let rx98 C P (, ) d dq dε r ΔH rx98 r d, let d std std d std C P (, ) d d C P (, ) C P (, ) d C P (, ) d d C P (, ) d( t,, ) V cat r,, P ΔH rx98 C P (, ) d( t,, ) IC P (, ) Combe the above two ODEs to oe vector fucto (because Mathcad's "rkfxed" wats all ODEs to be tegrated to be specfed oe vector fucto) d d d d( t,, ) stack( d( t,, ), d( t,, ) ) where submatrx(,, compoet,, ) s the frst compoet elemets the combed vector compoet s the ext elemet the combed vector d ( t ) t k dt b t ( t ) ( ) d t, submatrx(,, compoe

25 5 HSRemoval-EergyBalacemcd d( t, ) stack d t, submatrx(,, compoet,, ), compoet, ( ) furace t stack t, ( ) Call a route to solve ODE t f 5 t rkfxed t,, t f, step, d extract depedet varable t, ad depedet varables ad t t claus submatrx( t,,,, compoet) t clausadabatc t compoet Claus Catalytc Step, Adabatc Composto (moles) HS SO Elemetal S me (sec) Claus Catalytc Step, Adabatc emperature (K) Fal temperature: clausadabatclast( = K t) me (sec) Ital temperature: furace = 7654 K he fal temperature s partal agreemet wth the adabatc temperature calculated before Specfcally, cotug oto Reacto drectly over a catalyst bed wll rase the adabatc temperature by 9K for 95% coverso he above smulato rases by oly ~65K because the reactor s ot reachg 95% coverso Moral of the story: we eed to make sure we are usg a vald rate expresso Otherwse, we wll be mssg out o relevat behavors or reach wrog coclusos We mght be playg a garbage-, garbage-out computer game No Mathcad or Chemcad wll pot ths out for us As we perform

26 6 HSRemoval-EergyBalacemcd "by had" calculato, we become aware of what the assumptos are (ad these are what we wll later relax or optmze) ad what we eed to cosder crtcally As demostrate prevously, aother way s to tegrate the extet of reacto (whch s a scalar) rather tha tegrate the umber of moles (whch s a vector) claus ε furace ν dε ε r dε t, ε, V claus ε cat r,, P claus ε d t, ε, dε t, ε, ΔH rx98 ν IC P (, ) claus ε C P (, ) Combe the above two ODEs to oe vector fucto (because Mathcad's "rkfxed" wats all ODEs to be tegrated to be specfed oe vector fucto) ε ε dε( t, ε) dε t, ε, ε IC ε t d t, ε, ε furace Call a route to solve ODE t f 5 tε rkfxed ε t,, t f, step, dε t tε ε tε clausadabatc tε t Claus Catalytc Step, Adabatc 6 Composto (moles) me (sec) HS SO Elemetal S Extet of Reacto Claus Catalytc Step, Adabatc Fal temperature: 76 l d b = K

27 emperature (K) 74 7 HSRemoval-EergyBalacemcd clausadabatclast( K t) me (sec) Ital temperature: furace = 7654 K

28 8 HSRemoval-EergyBalacemcd Lookg forwardwhat s ext? At hgh, reacto s fast, but coverso suffers At low, reacto s slooow, but coverso s hgher A strategy s to react at hgh frst, the swtch to low to squeeze out the last bt of coverso Optmze these dfferet temperatures so that we reach the target coverso (95%) a short tme he path we have followed thus far process desg: Step Uderstad the desg objectves (remove H S) & sythesze geeral processg steps: a) absorber to remove H S, b) regeerate solvet, c) covert H S to a value-added product (va the Claus process) Step Materal balace Setp Eergy balace Step Rate (reacto ketcs, mass & heat trasfer rate) --> rate aalyss leads to process tme & sze he path we shall follow hereafter process desg: Step 4 Optmzato (what-f) --> optmzato lets you decde operatg parameters & coos Step 5 Add bells & whstles to optmze Geeral strategy: start wth rough 'by had" calculato, the refe calculato wth Chemcad