4. The material balances for isothermal ideal reactor models

Transcription

1 Summay Geneal mateal balane f eatng system Bath eat Cntnuus-flw eats: CST (Cntnuus Sted Tank eat) P (Plug lw eat) Steady state f CST and P Desgn tasks : utlet (fnal nvesn), gven vlume f eat x vlume f eat, gven utlet nvesn

2 4. The mateal balanes f sthemal deal eat mdels T=nst. Abtay vlume element Inlet nvetve mla flws (ml/s) A 0 k, k... 2 n ( t) ( t) Mla balane f spees 0 n d d k, k k t t Oveall mla balane k, k k, k k k Outlet nvetve mla flws (ml/s) d d... k 2 n t k

3 nst. T=nst. Pefet mxng Q Heat flux Bath eats Mxe Manmete P=f(t) Labaty Phamaeutal ndusty Speal hemals Plymes... A 0 k, k n ( t) ( t) lume f eatn mxtue Mla balane f spees n d t 0 k, k k dn k k, k.

4 eat vlume nstant ( =nst.) dn d n d k,,... k, k 2 eat pessue nstant (P = knst.) n. dn d. d d ln k k, k d k k, k d ln T alulate P( t) ( t) state equatn f(t,p,, m pstn) = 0 s needed

5 Example Cnstant vlume sthemal bath eat, deal gas mxtue P T n k dn dp T T T k, k k, k k k k Cnstant pessue sthemal bath eat, deal gas mxtue T P n d ln( ) T P d T dn T T P P P k, k k, k k k k k, k d T k, k k, k k P k y k, k k, k k k P y T *

6 Example Cnstant vlume bath eat, lqud mxtue nstant pessue Send de evesble eatn d d d d 2 3 k 2 k 2 k k 2 2 A (l) + A 2(l) A 3(l),, d d k k k, t 0,,, 0 ml/l t mle/l mle/l 0 t/mn 2 2 e 2 kt 2 kt 2 3

7 Cntnuus-flw eats Cntnuus Sted Tank eat CST A 0 k, k n ( t) nst lume f eat Mla balane f spees 0 k, k k dn Oveall mla balane k k, k dn We need suplementay nfmatn state behav f eatn mxtue stat-up (shut-dwn) mla flw ates f ndvdual spees

8 d Cnstant pessue sthemal CST, deal gas mxtue It ases fm veall mla balane (vlume f eat, s nstant) n dn k, k k, k k k dn k, k k and mla balane f spees bemes y k, k k, k k k dn P dy ( y y ) ( y ) T k k, k k dy T T = ( y y ) ( ), y k k, k P P k Inlet vlumet flw ate s T P Mean esdene tme f eatn mxtue (based n nlet flw ate) s gven by T n p 0 y P T

9 and mla balane f spees bemes fnally dy T = ( y y ) ( ), y k k, k P k If nly ne eatn takes plae: dy T = ( y y ) ( y ), P.00 Example Stat-up f an sthemal CST O / 2O 2 g 2 g 2 g = kp, k 2.028x0 m le.pa. m n.m y, y y y 0 (= O, 2=O, 3=, 4=H e) t 0, y 0 y y 0, y 0. l =0 m, T =320 C, P 0 kpa O umeal slutn f balane equatns y (-) O (fatnal) nvesn f 2 O* ) =( )/ He 2 O t (s) * ) The equatn s vald nly at steady state

10 Steady state,, k, k k If nly ne eatn takes plae:,, usng fatnal nvesn f key spees ( ) a) T he vlum e f eat f gven utlet nvesn ( ) Smple substtutn b) T he utlet nvesn f gven vlum e f eat ( ) ( ) 0 f Gaphal numeal (teatve) slutn

11 Gaphal assessment f the CST vlume ( ) ( ) Levenspel dagam usually v

12 Gaphal assessment f the utlet nvesn ( )

13 Casade f CST ( n ) ( n ) ( n ) ( n ) Steady state n-th membe f the asade ( n ) ( n ) ( n ) ( n ),, n, C ST ( n ) ( n) ( n ) ( n ) ( ) ( n ) ( n ) ( n ) ( n ) ( n ) ( n ) ( ), n, C ST

14 Gaphal assessment f the utlet nvesn n the asade f CST ( ) () ( 2 ) () Hmewk 6 Pve that In the lmt () ( n ) ( n) n ( k ), ( n ) k n lm e, n ( n ) (2) f fst de nstant-vlume eatn.

15 Plug lw eat P ( ) ( ) v Tubula eats Hgh pdutn apaty Catalyt eats (e.g. ammna synthess)... z z + z S z + Mla balane f spees ( t, z ) ( t, z ) = ( t, z), k, k t S z k

16 Steady state d d k, k, k If nly ne eatn takes plae: d d, usng fatnal nvesn f key spees d ( ) d ( 2 ) d ( ) () y y, m useful elatns: m m 3 m la vlum e (m m le )

17 BATCH, CST, P (PBC), ne eatn, fatnal nvesn f key mpnent BATCH n d ( ) 0 0 t t d ( ) 0 0 t t CST P CST ( ) ( ) PBC Paked Bed Catalyt eat P d d ( ) ( ) 0 0 W d d ( ) 0 M 0 M

18 Mean esdene tme BATCH, P d ( ) 0 CST ( ) vlumet flw ate (m 3 /s) f eatn mxtue at nlet nns

19 Gas Huly Spae elty G H S G as vlum et flw ate(m /h) lum e f eat (m ) 3 3 Lqud Huly Spae elty LH S Lqud vlum et flw ate (m /h) lum e f eat (m ) 3 3

20 Tasks. Calulate the vlume f eat (mass f atalyst) (CST, P, PBC) tme f eatn (BATCH) t btan gven nvesn. 2. Calulate the utlet nvesn f gven vlume f eat. 3. Calulate the eatn ate n labaty eat t btan knet law and estmate the knet paametes.

21 = A 0 = subspt f key mpnent BATCH LOW n n n n.. d. n n n n n... x n n. x x. n k n n n. x. x. x x.. x. n n x n. m m m x x. x. x. m m m x x. x. m - m la vlum e f eatn m xtue 3 (m /m l)

22 Gas phase - Ideal state behav x P P T T T P x x. x. m T P x x. P P T T T. x. P n n T P ( x ) T P n n.. T P T P T P T P x x T P x T P.. T P T P T P T P x x

23 Hmewk 7 Calulate vlume f P t pdue 50 kt ethylen/yea. eatn f the st de C 2 H 6(g) C 2 H 4(g) + H 2(g) takes plae at 00 K and 0,6 Mpa. nal nvesn f ethan s 80 %. eatn ate s gven by = k. A k (000 K) = 0,072 s - E = 343,6 kj/ml Pue ethan s fed nt the eat. Assumptns: Ideal gas, mla weght f ethylen s 28,054 kg/kml. K. J. Ladle and B. W. Wehwsk: Knets and Mehansms f the Themal Dempstn f Ethane. I. The Unnhbted eatn, Peedngs f the yal Sety f Lndn. Sees A, Mathematal and Physal Senes, l. 260,. 300 pp. 9-02

24 Hmewk 4 (due afte Chapte 4) Calulate vlumes f CST a P wkng at 50 C and 300 kpa t pdue t COCl 2 /day wth CO nvesn equal t 95 %. A mxtue f CO and Cl 2 (mla at :) s fed at 300 kpa and 50 C. Data k(423 K) = 0.07 (m 3 ml - ) 3/2.s - M COCl2 = kg/kml. Answe: CST = m 3 P = m 3 CO () Cl 2 (2) I COCl 2 (3) 0 CO (g) + Cl 2(g) COCl 2(g) 2 OUT steady state; - key m pnent

25 deal gas 3 3 C l 2 5 / 2 3 / 2 3 C O C l2 T m T P [m /m l] P P P C O 2 T T 2 T 2 k k m m P 5 / 2 0 / / [m l/m /s] m l/s [m l/m ] C ST 5 / 2 5 / 2 5 / / 2 ( ) P k 0.07 T

26 P / / 2 T 2 5 /2 5 / 2 ( ) 0 0 P k P 0 d d d k T / 2 3 m 3

27 Summay Geneal mateal balane f eatng system Bath eat Cntnuus-flw eats: CST (Cntnuus Sted Tank eat) P (Plug lw eat) Steady state f CST and P Desgn tasks : utlet (fnal nvesn), gven vlume f eat x vlume f eat, gven utlet nvesn