Youn-Woo Lee School of Chemical and Biological Engineering Seoul National University , 599 Gwanangro, Gwanak-gu, Seoul, Korea

Size: px

Start display at page:

Download "Youn-Woo Lee School of Chemical and Biological Engineering Seoul National University , 599 Gwanangro, Gwanak-gu, Seoul, Korea"

Marion Freeman
5 years ago
Views:

1 hemicl Rector esign Y W L Youn-Woo Lee School of hemicl n iologicl Engineering 55-74, 599 Gwnngro, Gwnk-gu, Seoul, Kore ywlee@snu.c.kr

2 第 3 章 Rte Lws n Stoichiometry 化學反應裝置設計 hemicl Rector esign

3 Ojectives fter completing hpter 3, reer will e le to: Write rte lw n efine rection orer n ctivtion energy. Set up stoichiometric tle for oth tch n flow systems n express concentrtion s function of conversion. lculte the equilirium conversion for oth gs n liqui phse rections. Write the comine mole lnce n rte lw in mesures other thn conversion.

4 esign Equtions Rector Size Levenspiel plot tch t r SR R R r W r r Grphicl metho or r vs., the volume of SR n the volume of R cn e represente s the she res in the Levenspiel plots. R r r f If we know the molr flow rte to the rector n the rection rte s function of conversion, then we cn clculte the rector volume necessry to chieve specific conversion.

5 esign Isotherml Rector esign isotherml rector HER 3 r Rte Lws k -r =f HER 2 j = f iometr ry f f j = f = f stoichi

6 rt t Rte Lws

7 3.. Reltive Rtes of Rections If the rte lw epens on more thn one species, we MUS relte the concentrtions of ifferent species to ech other. stoichiometric tle presents the stoichiometric reltionships etween recting molecules for single rection. + c + 2- In formulting our stoichiometric tle, we shll tke species s our sis of clcultion i.e., limiting rectnt n then ivie through y the stoichiometric coefficient of. In orer to put everything on sis of per mole of. c 2-2 he reltionship cn e expresse irectly from the stoichiometry of the rection. r r r c r 3-

8 3.2 Rection Orer n Rte Lw Let tke s the sis of clcultion species is one of the rectnts tht is isppering s result of the rection. he limiting iti rectnt t is usully chosen s our sis for clcultion. he rte of isppernce of, -r, epens on temperture n concentrtion n it cn e written s the prouct of the rection constnt tk n r, k f,... Rte rw Kinetic expression : the lgeric eqution tht reltes r to the species concentrtion

9 3.2. ower Lw Moels n Elementry Rte Lws he epenence of the rection rte r on the concentrtion of the species is lmost without exception etermine y experimentl oservtion. he orer of rection refers to the powers to which the concentrtions re rise in the kinetic rte lw. r k 3-3 orer with respect to rectnt orer with respect to rectnt n = : the overll orer of the rection

10 Unit of Specific Rection Rte he unit of the specific rection rte, k, vry with the orer of the rection. proucts Zero - orer : mol r k { k} m s irst - orer : r k { k } 3-5 s Secon - orer : 3 2 m r k { k} 3-6 mol s hir - orer m / mol : r k { k} 3-7 s

11 Elementry n on-elementry Rection Kinetic rte rw Elementry rection O + H 3 OH H 3 O + OH on-elementry rection O + l 2 Ol 2 -r O = k O H3OH r O k O 3/ 2 l 2 st orer w.r.t. tomic oxygen st orer w.r.t. methnol overll is 2 n orer rection st orer w.r.t. cron monoxie 3/2 orer w.r.t. chorine overll is 5/2 orer rection In generl, first- n secon-orerorer rections re more commonly oserve.

12 etermintion of Rection Rte Lw It is importnt to rememer tht the rte lws re etermine y experimentl oservtion! hey cnnot e euce from rection stoichiometry. hey re function of the rection chemistry n not the type of rector in which the rections occur. Even though numer of rections follow elementry rte lws, t lest s mny rections o not. One must etermine the rection orer from the experiments or from literture.

13 Literture he ctivtion energy, frequency fctor, n rection orer loppy isks n ROMs y tionl Institute of Stnrs n echnology IS Stnr Reference t 22/32 Githersurg, M 2899 les of hemicl Kinetics: Homogeneous Rection, tionl ureu of Stnrs irculr 5 Sept. 95 Suppl. ov. 4, 956, Suppl. 2 ug. 5, 96, Suppl. 3 Sept. 5, 96 Wshington,.., U.S. Government i rinting Office hemicl Kinetics n hotochemicl t for Use in Strtospheric Moeling, Evlute o., JL uliction 92-2, ug. 5, 992, Jet ropulsion Lortories, sen,, US Interntionl Journl of hemicl Kinetics, Journl of hysicl hemistry Journl of tlysis, Journl of pplie tlysis IhE Journl, hemicl Engineering Science, Koren Journl of hemicl Engineering hemicl Engineering ommunictions Inustril n Engineering hemistry Reserch

14 Exmple of Rte Lw

15 Exmple of Rte Lw

16 Exmple of Rte Lw. irst Orer Rection. Secon Orer Rection

17 3.3 k : he specific rection rte the rte constnt he rection rte constnt k is not truly constnt, ut is merely inepenent of the concentrtions of the species involve in the rection. he quntity k is lso referre to s the specific rection rte constnt. It is lmost lwys strongly epenent on temperture. In gs-phse rections, it epens on the ctlyst n totl pressure. In liqui systems, it epens on the totl pressure, ionic strength n choice of solvent. hese other vriles normlly exhiit much less effect econ the specific rection rte thn temperture oes with the exception of supercriticl solvents, such s supercriticl wter. In this text, it will e ssume tht k epens only on temperture.

18 rrhenius eqution Specific rection rte constnt ctivtion energy, J/mol or cl/mol k frequency fctor or pre-exponentil exponentil fctor e mthemticl numer e= E R 9344 : oel rize in chemistry for ionic theory solute emperture, K Gs constnt 8.34 J/mol K.987 cl/mol K 8.34 k m 3 /mol K

19 ctivtion energy ctivtion energy E : minimum energy tht must e possesse y recting molecules efore the rection will occur. E he frction of the collisions etween R l t th i e molecules tht together hve this minimum energy E the kinetic theory of gses ctivtion energy E is etermine experimentlly y crrying out the rection t severl ifferent temperture. ln k ln E R

20 rt t2 Stoichiometry t

21 esign Equtions Rector Size Levenspiel plot tch t r SR R R r W r r Grphicl metho or r vs., the volume of SR n the volume of R cn e represente s the she res in the Levenspiel plots. R r r f If we know the molr flow rte to the rector n the rection rte s function of conversion, then we cn clculte the rector volume necessry to chieve specific conversion.

22 esign Isotherml Rector esign isotherml rector HER 3 r Rte Lws k -r =f HER 2 j = f j = f = f stoichi iometr ry

23 Exmple 3-5: etermintion of j =h j for Gs hse Rection for Gs-hse Rection Isotherml /

24 Stoichiometric le If the rte lw epens on more thn one species, we MUS relte the concentrtions of ifferent species to ech other. stoichiometric tle presents the stoichiometric reltionships etween recting molecules for single rection. + c + 2- r r r c r 3- In formulting lti our stoichiometric tihi ti tle, tl we shll hlltk tke species s our sis of clcultion i.e., limiting rectnt n then ivie through y the stoichiometric coefficient of c 2-2 In orer to put everything on sis of per mole of.

25 3.5 tch System t = t = t i c i tch rectors re primrily use for the prouction o of specilty chemicls n to otin rection rte t in orer to etermine rection rte lws n rte lw prmeters such s k, the specific rection rte.

26 3.5 tch System t time t=, we will open the rector n plce numer of moles of species,,,, n I,,,, n I, respectively t = i t = t Species is our sis of clcultion. i c is the numer of moles of initilly present in the rector. moles of re consume s result of the chemicl rection. - moles of leve in the system. he numer of moles of remining in the rector fter conversion = - = -

27 etermintion of the numer of moles of o etermine the numer of moles of species remining i t time t ft fter moles of hve recte. or every mole of tht rects, / moles of must recte; c he numer of moles of remining in the system, moles of recte moles of initilly moles of isppere

28 Stoichiometric tle o etermine the numer of moles of ech species remining ii fter moles of hve recte, we form the stoichiometric tle le c his stoichiometric tle presents the following informtion. olumn : the prticulr species olumn 2: the numer of moles of ech species initilly present olumn 3: the chnge the numer of moles rought out y rection olumn 4: the numer of moles remining in the system t time t.

29 Stoichiometric le for tch System Remining hnge Initilly Species mol mol mol c c inert I I I I inert I c otl

30 he totl numer of moles per mole of recte c he totl numer of moles in the system, y, c c hnge in the totl numer of moles c hnge in the totl numer of moles mole of recte

31 esign Isotherml Rector esign isotherml rector HER 3 r Rte Lws k -r =f HER 2 j = f j = f = f stoichi iometr ry

32 3.5.. oncentrtion of ech species r k / =f c / j = f = f / = f

33 3.5.. oncentrtion of ech species y y y i i i i / / c c / / / /

34 3.5.2 olume s function of conversion / / / / We nee to otin =f We nee to otin =f - or liquis, volume chnge with rection is negligile when no phse chnges re tking plce = when no phse chnges re tking plce. - or gs-phse rections, the volumetric flow rte most often chnges uring the course of the rection ue to often chnges uring the course of the rection ue to chnge in the totl numer of moles or in temp. or pressure.

35 3.5.2 onstnt-olume tch Rection Systems onstnt volume system =constnt ensity system: he l om clorimeter rector: the volume within the vessel is fixe n will not chnge. = 2 constnt-volume gs-phse isotherml rection occurs when the numer of moles of proucts equls the numer of moles of rectnts. Ex: wter-gs shift rection, O+H 2 O O 2 +H 2 3 or liqui-phse rections tking plce in solution, the solvent usully omintes the sitution. s result, chnges in the ensity of the solute o not ffect the overll ensity of the solution significntly n therefore it is essentilly constntvolume rection process: Most liqui-phse orgnic rections, except polymeriztion.

36 onstnt olume tch Rector

37 onstnt olume System or Liqui phse rections or isotherml n isoric gs-phse rections with no chnge in the totl numer of moles c -r = f r k Eq r = f Levenspiel plot 2 r k

38 Exmple 3-2: Liqui-hse Rection Sop consists of the soium n potssium slts of vrious ftty cis s oleic8=, steric8, plmitic6, luric2, n myristic4 cis. he sponifiction for the formtion of sop from queous custic so n glyceryl sterte is s follow. 3OH + 7 H 35 OO 3 3 H H 35 OO + 3 H 5 OH 3 Letting represent the conversion of soium hyroxie the mole of soium hyroxie recte per mole of soium hyroxie iiill initilly present, set up stoichiometric ihi i tle expressing the concentrtion of ech species in terms of its initil concentrtion n the conversion of. Steric ci

39 Exmple 3-2: Liqui-hse Rection 7 H 35 OO 3 3 H 5 Glyceryl sterte 7 H 35 OO 3 H 5 OH 3 Glycerine=Glycerol

40 Exmple 3-2: Liqui-hse Rection

41 Exmple 3-2 Stoichiometric le 3OH + 7 H 35 OO 3 3 H H 35 OO + 3 H 5 OH 3 oncentrt ion Remining hnge Initilly Species mol/m mol mol mol oncentrt ion Remining hnge Initilly Species I I I inert I otl

42 3.6 low Systems Entering Leving c I I Molr flow rte efinition of concentrtion for flow system moles/time liters/time moles liter 3-27 volumetric flow rte i v i i i i v y y

43 3.6. Equtions for oncentrtions in low Systems tch System low System c / / c / / c / / / /

44 Stoichiometric le for low System ee rte hnge Effluent rte Species to rector in rector from rector mol/time mol/time mol/time Θ c Θ Θ Θ Iinert I ΘI I Θ Θ Θ I c otl le 3-4 c

45 3.6.2 Liqui-hse oncentrtions Entering Leving c I I 3-29 r k = f = f v=f

In flow systems where this type of rection occurs, the molr flow rte will e chnging s the rection progress.

46 3.6.3 hnge in the otl umer of Moles with Rection in the Gs hse Gs-phse rections tht o not hve n equl numer of prouct n rectnt moles. In flow systems where this type of rection occurs, the molr flow rte will e chnging s the rection progress. he volumetric flow rte will lso chnge ue to molr flow chnge. 2 +3H 2 2H 3 2 he comustion chmer of the internl-comustion engine 3 he expning ggses within the reech n rrel of firerm s it is fire. reech : 포미 砲尾 rrel : 총신 銃身

47 tch Rector with rile olume Iniviul concentrtions cn e etermine y expressing the volume for tch system or volumetric flow rte v for flowsystem s function of conversion using the following eqution of stte. Z R 3-3 = temperture, K = totl pressure, tm k; tm=.3 k Z = compressiility fctor R = gs constnt =.826 m 3 tm/gmol K his eqution is vli t ny point in the system t ny time. t time t=, Z R iviing 3-3 y 3-3 n rerrnging yiels Z 3-3 We nee this! Z 3-32

48 Stoichiometric le for tch System Remining hnge Initilly Species mol mol mol c c I I I inert I I I I inert I c otl

49 olume s function of conversion vrile-volume tch rector he totl numer of moles in the system, 3 33 We ivie through y 3-33 y 3-34 where y is mole frction of initilly present. If ll the species in the generlize rection re in the gs phse, then 3-35 y c Eq 3-32 now ecomes Z Z Z Z 3-37

50 olume s function of conversion vrile-volume tch rector In gs-phse systems tht we shll e stuying, the temperture n pressure re such tht the compressiility fctor will not chnge significntly uring the course of the rection; hence Z ~Z. or tch system the volume of the gs t ny time t is 3-38 Eq 3-38 pplies only to vrile-volume tch rector. If the rector is rigi steel continer of constnt volume, then of course =. or constnt-volume continer, =, n Eq cn e use to clculte the pressure insie the rector s function of temperture n conversion.

51 olume s function of conversion vrile-volume flow system o erive the concentrtion of the species in terms of conversion for vrile-volume volume flow system, we shll use the reltionships for the totl concentrtion. he totl concentrtion t ny point in the rector is ZR 3-39 t the entrnce to the rector Z R 3-4 king Eq 3-4/Eq3-39 n ssuming Z~Z, 3-4

52 oncentrtion s function of conversion vrile-volume flow system vrile-volume flow system We cn express the concentrtion eqution of species j for flow system in terms j j j of conversion: j j j j 3-42 j j n he totl molr flow rte is just the sum of the molr flow rtes of ech of the species in the system n is j j I

53 oncentrtion s function of conversion vrile-volume flow system One of the mjor ojective of this chpter is to lern how to express ny given rte lw r s function of conversion. he schemtic igrm in igure 3-6 helps to summrize our iscussion on this point. it he concentrtion of expresse s function of conversion in oth flow n tch systems, for vrious conitions of temperture, pressure, n volume.

54 Expressing concentrtion s function of conversion c Liqui hse Gs hse low tch low tch o hse hnge onstnt olume y v v o hse hnge or o Semipermele Memrnes c v v R y R isotherml Isotherml + o o pp2

55 olume s function of conversion vrile-volume flow system rom le 3-3, the totl molr flow rte cn e written in terms of 3-43 y

56 olume s function of conversion vrile-volume flow system he concentrtion of species j is v j j j j v j j j j v v j j j 3-46

57 oncentrtion s function of conversion Multiple gs-phse rection n memrne rector Multiple gs-phse rection n memrne rector j j j Sustituting for j n in terms of conversion in Eq yiels v j j v j j j iviing numertor n enomintor y, we hve v j j j /

58 oncentrtion s function of conversion Multiple gs-phse rection n memrne rector Reclling y = / n =y,then j j v j 3-46 where v i is the stoichiometric coefficient, which is negtive for rectnts n positive for proucts. pp4 or exmple, for the rection v = -, v = -/, v = c/, v = /, n j = j /. c

59 oncentrtion s function of conversion il l fl t vrile-volume gs flow system le 3-4 / / / c / / c / c / / / I I I I I pp4

60 Exmple 3-4: Mnipultion of the Eqution j =f j Show uner wht conitions n mnipultion the expression for for Show uner wht conitions n mnipultion the expression for for gs flow system reuces to the following eqution in le 3-5. / pp4

61 Exmple 3-4: Mnipultion of the Eqution j =h j 3-45 / E3-4.4 / pp5

62 Exmple 3-5: etermintion of j =h j for Gs hse Rection for Gs-hse Rection Isotherml /

63 Exmple 3-5: etermintion of j =h j for Gs-hse Rection r k y.28

64 = 2 2 2

66 =

69 oncentrtions s function of conversion Limiting iti rectnt t

70 SO 2 2 O 2 SO 3.25 mol/ m oncent trtion. SO 2 SO 3.5 O onversion,

71 Rection rtes s function of conversion SO 2 2 O 2 SO 3 r k k

72 6 5 4 r SO k k 2 2 O 2 SO Levenspiel lot -/r onversion,

ERT 316: REACTION ENGINEERING CHAPTER 3 RATE LAWS & STOICHIOMETRY

ERT 316: REACTION ENGINEERING CHAPTER 3 RATE LAWS & STOICHIOMETRY ER 316: REIO EGIEERIG HER 3 RE LWS & SOIHIOMERY 1 OULIE R 1: Rte Lws Reltive Rtes of Retion Retion Orer & Rte Lw Retion Rte onstnt, k R 2: Stoihiometry th System Stoihiometri le low System Stoihiometri