Lecture (10) Reactor Sizing and Design
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1 Lectue ( Rect Szng nd esgn. Genel Mle lnce Equtn Mle blnce n speces t ny nstnce n tme t ; lumn system te f flw te f genetn te f flw te f ccumultn f nt system f n systemby xn f ut f system f wthn system F..4. F = Enteng ml flw te f speces (ml/tme F = Extng ml flw te f speces (ml/tme G = Rte(ttl te f genetn(fmtn f speces (ml/tme=. = lume (e.g. m 3 = te f genetn(fmtn f speces (mle/tme.vl = numbe f mles f speces nsde the system lume (mle f ves wth pstn n the system, G F d G G, Let m, G, m, m, hen genel mle blnce:- G d
2 F d F d 4.2 Fm ths genel mle blnce equtn we cn develp the desgn equtns f the vus types f ndustl ects: btch, sem-btch. nd cntnuus-flw ects. REOR SZG ESG R OE tch Rect stheml Opetn Opete unde unstedy stte ethe nflw n utflw f ectnts pducts f the ectn mxtue s pefectly mxed s: nstnt te f ectn thughut the ect vlume mpstn f (stn mpstn =f (tme empetue f (stn empetue f (tme del estctns Mle lnce F, F
3 F d F d d d d..4.4 Let's cnsde the smeztn f speces n btch ect s the ectn pceeds. the numbe f mles f deceses nd the numbe f mles f nceses, s shwn n Fgue belw he tme t necessy t educe the ntl numbe f mles t fnl numbe f mle cn be estmted s : fm equtn 4.4 d 4.4 d ntegtng wth lmts tht t : t = = stt f ectn nd t t = t = ectn tme (end f ectn we btn t d..4.5 mles f mles f mles f ected ected cnsumed ntlly fed mles f fed t t
4 numbe f mle emn un-ected fte tme t, mles f mles f mles f n ecte (emn t ntlly fed t ected cnsumed tme t the ect t t Sub n equtn 4.5 nd 4.4 d t d d.4.6 t t d 4.7 ffeentl fm tch Rect esgn Equtn m ntegl fm Used n the ntepettn f Lb Rte t
5 Spce tme Men Resdence me= s the tme necessy t pcess ne ect mmmmmmmmmmmmmmmmmmm vlume f flud bsed n entnce cnns. t =t+t t cnstnt vlume btch ect.e cnstnt densty ectn mxtue. = * then; equtns 4.4 nd 4.5 becme ( : d t d..4.8.(rectn me Evlutn f Rectn me Gphclly: Fm equtn 4.7 plt t estmte ectn tme vs. nd evlute the e unde the cuve e t t * t e d O Fm equtn 4.7 plt t estmte ectn tme vs. nd evlute the e unde the cuve d t
6 e t e Exmple Evlutn f Rectn me umeclly: eed f ( t sze ects clculte ectn tme F the ectns n whch the te depends nly n the cncenttn f ne speces then Fst de nd evesble :- f (, k t d k k d t k. ln e kt Secnd de nd evesble :-, 2 k d d t 2 k k 2 t k, kt
7 nth de nd evesble :-, n k kt n Exmple mlecul Rectns n n n n k t n when the te lw depends n me thn ne speces, we must elte the cncenttns f the dffeent speces t ec2h the "s functn f cnvesn f ( ". hs eltnshp s mst esly estblshed wth the d f Stchmetc tble. n fmultng u stchnetsc tble, we shll tke speces cmpnent s u bss f clcultn (.e.. lmtng ectnt nd then dvde thugh by the stchmetc ceffcent f, n de t put eveythng n bss f "pet mle f ". Stchnetsc tble pesents the fllwng nfmtn lumn : the ptcul speces lumn 2: the numbe f mles f ech speces ntlly pesent lumn 3: the chnge n the numbe f mles bught but by ectn lumn 4: the numbe f mles emnng n the system t tme t lumn 5: cncenttns s functn f cnvesn f ech speces nsde the genel ectn; Stchmety set up f equtns wth s bss b c d he te lw s : k b c K d
8 nstnt lume (nstnt ensty lqud-phse nd sme f gs phse ectn system fll nt ths ctegy. Stchmetc ble tch System Spece ntl hnge Remnng ncenttn - = ( = -(b/ = [ (b/] b = +(c/ = [ +(c/] c = +(d/ = [ +(d/] d = = = = + Whee = / = / = y /y = (d/ + (c/ (b/ - Expess tble n tems f cncenttns ncenttn (btch: b b
9 Mle blnce equtn nd the te lw e cupled nd then slved Exmple ble lume (ble ensty, but wth nstnt nd ndvdul cncenttn cn be detemned by expessng the vlume f btch system s functn f cnvesn usng the equtn f stte: =ZR..t ny tme n the ectn =ZR t ny tme =;when ectn s ntted hen, Z Z.4.9 hnge n the ttl numbe f mles dung ectn n gs phse ectn system, but wth cnstnt tempetue nd pessue, nd the cmpessblty fct wll nt chnge sgnfcntly dung the cuse f the ectn, Whee = + = (d/ + (c/ (b/ = (chnge n ttl numbe f mle / (mle f ected y d d c c
10 hen y b t cmplete cnvesn.e =, = f ; theefe, f.4. = (chnge n ttl numbe f mle f cmplete cnvesn / (ttl mles fed hen the vlume s functn f cnvesn :.4.2 ncenttn t vble vlume densty Spece - (b/ (c/ ( - (b/ ( (c/ ( - (d/ - (d/ ( ( - (b/ ( ( (c/ - (d/ (
11 ( ( Exmple n-stheml Opetn hemcl ects cn lbete bsb vey lge munts f enegy, nd the hndlng f ths enegy s m cncen n ectn engneeng. t s mptnt t estmte the tempetue ncese decese n n dbtc ect n whch n het s dd emved, nd exthemc ect nd ls the cmpstn f the ectn mxtue t ny tme. Enegy lnce Het Geneted by Rectn Het dn nd + Remvl by wll = Het ccumulted by Rectn H ( Q U( d p, = ectn tempetue K = wll tempetue K R= efeence tempetue K = het tnsfe e m 2 p = specfc het KJ/Kml U = vell het tnsfe KJ/s.m 2.K
12 H =enthlpy chnge n the ectn pe mle f ectng he numbe f mles f speces t ny s = hen enegy blnce s : d U H p, ( (.4.3 Enegy nd mle blnce equtns wth the te lw e cupled nd then slved Mle blnce equtn H s clculted s p R R d H H he te lw s equed s functn f tempetue nd cmpstn ble lume (ble ensty, nd/ "ble n nn-stheml" he vlume f btch system s functn f cnvesn s :- Z Z Z Z f the cmpessblty fct wll nt chnge sgnfcntly dung the cuse f the ectn Z =Z ncenttn t vble vlume (densty, nd/ Spece d p U H p, ( ( d
13 ( ( (b/ - ( (b/ - ( (b/ - (c/ ( (c/ ( (c/ (d/ - ( (d/ - ( (d/ - ( ( Exmple btch ect s usully well mxed, s tht my neglect the specl vtn n tempetue nd speces cncenttn. tch ects peted dbtclly e ften used t detemne the ectn des, ctvtn eneges, nd specfc ectn tes f exthemc ectns by mntng the tempetue-tme tectes f dffeent ntl cnns. n dbtc petn f btch ect Q d H p, (.4.4 Enegy nd mle blnce equtns wth the te lw e cupled nd then slved: dbtc Opetn f tch Rect d p H p, (
14 p H ( H, p, p ;Whee = ntl tempetue Exmple Equlbum nvesn he hghest cnvesn tht cn be cheved n evesble ectns s the equlbum cnvesn E. F enhemc ectns, the equlbum cnvesn nceses wth ncesng tempetue up t mxmum f.. F exthemc ectns, the equlbum cnvesn deceses wth ncesng tempetue Fgue ( shw the vtn f the cncenttn equlbum cnstnt s functn f tempetue f n exthemc ectn the cespndng equlbum cnvesn E s functn f tempetue. Fgue ( shw the vtn f the cncenttn equlbum cnstnt nd equlbum cnvesn s functn f tempetue f n exthemc ectn.
15 detemne the mxmum cnvesn tht cn be cheved n n exthemc ectn ced ut dbtclly, we fnd the ntesectn f the equlbum cnvesn s functn f tempetue,wth tempetue cnvesn eltnshps fm the enegy blnce E p, ( H..4.5 Gphcl slutn f equlbun nd enegy blnce equtns t btn the dbtc tempetue nd the dbtc equlbun cnvesn E. Exmple
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