SAFE OPERATION OF TUBULAR (PFR) ADIABATIC REACTORS. FIGURE 1: Temperature as a function of space time in an adiabatic PFR with exothermic reaction.
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1 he 47 Lctu Fall 5 SFE OPERION OF UBULR (PFR DIBI REORS I a xthmic acti th tmatu will ctiu t is as mvs alg a lug flw act util all f th limitig actat is xhaust. Schmatically th aiabatic tmatu is as a fucti f sac tim, masu fm th act tac, taks th fm shw i Figu. a if FIGURE : matu as a fucti f sac tim i a aiabatic PFR with xthmic acti. h fial aiabatic tmatu a : a ( Δ H + ρ [ + β ] ( is ft xcssiv f highly xthmic systms ( β lag a s t b avi. I such situatis th l ul f thumb suggsts that w shul at i such a way that th iflcti it, i.. th it f maximum tmatu is, is v ach. his imlis that max w at with < wh is th valu f sac tim at which th iflcti it ccus.
2 he 47 Lctu Fall 5 Lt us w vl a cvit a siml fmula f us by acticig gis which wul guaat saf ati. si a -th ivsibl acti: R k R ( x ( t aiabatic citis tmatu a cvsi a lat by th aiabatic li quati ( + β x (3 If w fi, as i th cas f wall cl acts, th imsilss tmatu by γ (4 th cvsi i Eq. (3 ca b xss i tms f imsilss tmatu as: wh with x (5 β γ (6 γ E R (7 h at f acti valuat at aiabatic citis i tms f imsilss tmatu is btai by usig th aiabatic li q (5 t lac cvsi. h sult is: ( ( R ( γ + γ R a wh th at valuat at th f citi is: E R ( R k (8 (9 h gy balac f aiabatic PFR ati is: ( Δ H ( R a ρ ( Witt i tms f imsilss tmatu it bcms:
3 he 47 Lctu Fall 5 R γ ( γ + wh th chaactistic acti tim is: ( R ( R ( h iitial citi is (3 W ca wit Eq. ( i th mst cmact way by fiig th Damkhl umb as th ati f chaactistic css tim a acti tim, i.. Da ( R (4 R Equati ( a iitial citi (3 bcm: ( Da γ ( γ + (5 t Da (6 Nw w wat t hav th act sht ugh (limit th cvsi achivabl s that w ca k th iflcti it ut f th act i.. w t lt it ccu i th act. h citical tmatu at iflcti it, if, is btai by sttig ( Da (7 which sults i a quati f if yilig: [ γ + 4 ( γ + γ ]; γ if (8a, (8b if 3
4 he 47 Lctu Fall 5 h sult f th zth acti, q (8b, ca b btai by alyig th L Hsital ul t q (8a. btt aach is t tic that f quati (5 iicats that ( Da > always, s that th is iflcti it as th at f tmatu is ks isig util all actat is lt. h at x, fm q (5 it fllws that max a thf max a. W ca itgat th ifftial quati (5 by saatig th vaiabls t btai th citical valu f Da a, hc, f Da Da ( Da if γ ( + γ (9 laly f giv valus f aamts γ, β, βγ, a acti, w ca valuat if fm q (8a a th calculat th valu f Da by umically valuatig th itgal i q (9. Usig th th fiitis f Da a w gt th citi f saf ati which ca b xss as: Da < Da k R R ρ ( Δ H E Da ( gt a cvit, asy t mmb valu f Da, th fllwig aximatis a ft ma. Fist, th hius c f th at cstat tmatu is lac by a xtial c, i ffct γ ( + γ ( Substitutig this aximati i q (5 yils via q (7 t a w aximat valu f th tmatu at iflcti it ( if ( a Substitutig q ( a q ( it q (9 yils ( Da a u u u (3 4
5 he 47 Lctu Fall 5 h fial aximati (which is csvativ i atu as it assums th wst ssibl cas f zth acti igs th slww f th tmatu is u t th csumti f th actat, which is th sam as takig i q (3. his yils u u ( Da, u ( [ ] ( f lag ugh a (4 F highly xthmic actis a claly ( Da. a, Substitutig this it q ( givs th csvativ citi f saf ati. It is cstuctiv t t that this sam quati (a with tim t lacig k R R ρ ( Δ H E t < (a is us t tmi th s call tim f tu tim t xlsi i batch systms. his tim t iflcti it t may b vy lg f lw but bcms quit sht if th systm f high activati gy is xs t high. Hc, chmicals that may b saf t st at 5 may b xlsi if xs t 4 5! SFE OPERION OF DIBI SR h mass balac f a ivsibl -th acti is: x ( R (5 h aiabatic quati lats cvsi a tmatu x (6 ( Δ H ρ U substituti f imsilss tmatu w gt fm q (5 lt Da γ ( γ + (7 G ( ( γ + γ (8a 5
6 he 47 Lctu Fall 5 L (8b Da ( W kw fm bf that G is a sigmial cuv i a sts hat gat by acti. L is th hat mval at (i.., hat mv by ssibl hat f th flui that flws thugh th SR. W kw that u t th itsctis a ssibl btw G a L lis. avi th itscti laig t xcssivly high tmatus w must assu that itsctis at lw tmatus a availabl. h last missibl atig citi is th wh li L is als tagt t cuv G as schmatically shw i Figu. G L ( ( 3 3 FIGURE : Schmatic f th G, L vs. laly as Da icass th sl f th L li cass s that ( Da ( Da < ( Da 3 < (9 Whil atig aiabatic tmatus at a a acctabl, 3 sts t lag a tmatu jum. Hc, w must assu that th L li always itscts th G li at its lw tmatu bach. h citical it is ach wh L is als tagt t th G li. F saf aiabatic ati w thf qui 6
7 he 47 Lctu Fall 5 L G (3 L G (3 lyig th abv t qs (8a a (8b, a usig th quality sig i q (3, w gt th quati f th maximum missibl tmatu max m. h citical valu f th sac tim ca b btai fm th citical valu f Da, which i tu sults fm substitutig th xssi f it q (3. gt a siml, asy t mmb xssi, usually w agai lac yils γ ( + γ with. his ( (3 h gativ sig i ft f th squa t s t b tak as w a itst i th lw f th tw tmatus at which th L li cul b tagt t th cuv G. h quati (3 yils: ( Da a (33 csvativ stimat, with, yils a Da (34 F saf ati th k ( Δ H E R R ρ (35 7
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