9.nin-ideal_flow (1)

8/9/2019 9.Nin-ideal_flow (1)

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NON-IDEAL FLOW

Residence Time Distribution

A. Sarath Babu

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SCO E!

" Desi#n o$ non-idea% reactors

" Identi$& the 'ossib%e de(iations

" )easurement o$ RTD

*ua%it& o$ mi+in#

" )ode%s $or mi+in#

" Ca%cu%atin# the e+it con(ersion in 'ractica%reactors

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ractica% reactor 'er$ormance de(iates $rom thato$ idea% reactor,s !

" ac ed bed reactor Channe%in#" CSTR / Batch Dead 0ones1 B&'ass" FR de(iation $rom '%u# $%o2 dis'ersion" De(iation in residence times o$ mo%ecu%es" the %on#itudina% mi+in# caused b& (ortices andturbu%ence"Fai%ure o$ im'e%%ers 3mi+in# de(ices

4o2 to desi#n the ractica% reactor 55What desi#n e6uation to use 55A''roach! 789 Desi#n idea% reactor

7:9 Account3correct $or de(iations 3


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De(iations

In an idea% CSTR1 the reactant concentration is uni$orm

throu#hout the (esse%1 2hi%e in a rea% stirred tan 1 thereactant concentration is re%ati(e%&high at the pointwhere the feed enters and low in the stagnant regionsthat de(e%o' in corners and behind ba$$%es.

In an idea% '%u# $%o2 reactor1 a%% reactant and 'roductmo%ecu%es at an& #i(en a+ia% 'osition mo(e at the same ratein the direction o$ the bu% $%uid $%o2. 4o2e(er1 in a rea%'%u# $%o2 reactor1 $%uid (e%ocit& 'ro$i%es1 turbu%ent mi+iand mo%ecu%ar di$$usion causemolecules to move withchanging speeds and in different directions.

The de(iations $rom idea% reactor conditions 'ose se(era%

'rob%ems in the desi#n and ana%&sis o$ reactors. 4


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ossib%e De(iations $rom idea%it&!

Short Circuitin# or B&- ass Reactant $%o2s into the tan throu#h thein%et and then direct%& #oes out throu#h the out%et 2ithout reactin# i$ thein%et and out%et are c%ose b& or i$ there e+ists an eas& route bet2een thet2o.

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8. Dead 0one :. Short Circuitin#

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Three conce'ts are #enera%%& used to describe the

de(iations $rom idea%it&!

" the distribution o$ residence times 7RTD9" the 6ua%it& o$ mi+in#

" the mode% used to describe the s&stem

These conce'ts are re#arded as characteristics o$)i+in#.

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Ana%&sis o$ non-idea% reactors is carried out in

three %e(e%s!

First Le(e%!

" )ode% the reactors as idea% and account or

correct $or the de(iationsSecond Le(e%!

" ;se o$ macro-mi+in# in$ormation 7RTD9

Third Le(e%!" ;se o$ micro-mi+in# in$ormation mode%s $or

$%uid $%o2 beha(ior10


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RTD Function!

" ;se o$ 7RTD9 in the ana%&sis o$ non-idea% reactor

'er$ormance )ac )u%%in / Weber 8" Dan 2erts 78?9 or#ani@ationa% structure

" Le(ens'ie% / Bischo$$1 4imme%b%au / Bischo$$1 Wen / Fan1 Shinner

" In an& reactor there is a distribution o$

residence times

" RTD e$$ects the 'er$ormance o$ the reactor

" RTD is a characteristic o$ the mi+in# 11


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)easurement o$ RTD

RTD is measured e+'erimenta%%& b& in ectin# an inert

matreria% ca%%ed tracer at t ? and measurin# itsconcentration at the e+it as a $unction o$ time.

In ection / Detection 'oints shou%d be (er& c%ose to

the reactor 12


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ASS;) TIONS

8. Constant $%o2rate u7%3min9 and $%uid densit& 7#3%9.:. On%& one $%o2in# 'hase.=. C%osed s&stem in'ut and out'ut b& bu% $%o2 on%& 7i.e.no di$$usion across the s&stem boundaries9.

. F%at (e%ocit& 'ro$i%es at the in%et and out%et.>. Linearit& 2ith res'ect to the tracer ana%&sis1 that is1the ma#nitude o$ the res'onse at the out%et is direct%&'ro'ortiona% to the amount o$ tracer in ected.

. The tracer is com'%ete%& conser(ed 2ithin the s&stemand is identica% to the 'rocess $%uid in its $%o2 andmi+in# beha(ior.

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Desirab%e characteristics o$ the tracer!

" non reacti(e s'ecies

" easi%& detectab%e

" shou%d ha(e 'h&sica% 'ro'erties simi%ar to thato$ the reactin# mi+ture

" com'%ete%& so%ub%e in the mi+ture

" shou%d not adsorb on the 2a%%s

" Its mo%ecu%ar di$$usi(it& shou%d be %o2 andshou%d be conser(ed

" co%ored and radio acti(e materia%s are the

most 2ide%& used tracers 14


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T&'es o$ tracer in'uts!

" u%se in'ut

" Ste' in'ut

" Ram' in'ut

" Sinusoida% in'utu%se / Ste' in'uts are most common

Ram' in'ut

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u%se in'ut o$ tracer

In u%se in'ut N? mo%es o$ tracer is in ected in one

shot and the e$$%uent concentration is measured

The amount o$ materia% that has s'ent an amount o$

time bet2een t and t t in the reactor!

N C7t9 ( t 16


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The $raction o$ materia% that has s'ent an amount o$

time bet2een t and t t in the reactor!

dN C7t9 ( dt

=0

0 )( dt t vC N

For 'u%se in'ut

0

)( N N

t t E =

=

0

)(

)()(

dt t C

t C t E

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C cur(e

1)(0

=

dt t E 18


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10

1

)( t timeresidenceahaving Fractiondt t E

t

= 1

1

)( t timeresidenceahaving Fractiondt t E t

>=

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The a#e o$ an e%ement is de$ined as the time e%a'sed

since it entered the s&stem.

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( )12100

.......(22

)(

+++++= nn C C C C C hdt t C 21


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Disad(anta#es o$ 'u%se in'ut" in ection must be done in a (er& short time

" 2hen the c-cur(e has a %on# tai%1 the ana%&sis can #i(e rise to inaccuracies

" amount o$ tracer used shou%d be no2n

" ho2e(er1 re6uire (er& sma%% amount o$ tracer

com'ared to ste' in'ut

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Ste' in'ut o$ tracer

In ste' in'ut the conc. o$ tracer is e't at this

%e(e% ti%% the out%et conc. e6ua%s the in%et conc.

=t

out dt t E C C 0

0 )(

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stepC

t C

dt

d

t E

= 0)(

)(

For ste' in'ut!

Disad(anta#es o$ Ste' in'ut!

" di$$icu%t to maintain a constant tracer conc.

" RTD $n re6uires di$$erentiation can %ead

to errors" %ar#e amount o$ tracer is re6uired

" need not no2 the amount o$ tracer used24


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Characteristics o$ the RTD!

" E7t9 is ca%%ed the e+it a#e distribution $unction

or RTD $unction" describes the amount o$ time mo%ecu%es ha(e

s'ent in the reactor

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Cumu%ati(e a#e distribution $unction F7t9!

=

t

dt t E t F 0

)()(

=t

dt t E t F )()(1

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Relationship between the E and F cur es

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Cumu%ati(e a#e distribution $unction F7t9!

Washout $unction W7t9 8 - F7t9! 28


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E and F Cur(es 2ith b&'assin#

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E and F Cur(es 2ith Dead s'ace

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=0

32/3

3 )()(1 dt t E t t S m

What is the si#ni$icance o$ these moments 55

)oments o$ RTD!

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I$ the distribution cur(e is on%& no2n at a number o$discrete time (a%ues1 t i1 then the mean residence time is#i(en b&!

This is 2hat &ou use in the %aborator&

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Gariance! re'resents the s6uare o$ the distribution

s'read and has the units o$ 7time9:

the #reater the (a%ue o$ this moment1 the#reater the s'read o$ the RTD

use$u% $or matchin# e+'erimenta% cur(es toone $ami%& o$ theoretica% cur(es

S e2ness! the ma#nitude o$ this moment measures the

e+tent that the distribution is s e2ed inone direction or other in re$erence to the mean

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S'ace time (s. )ean residence time!

=0

)( dt t tE t m0v

V =

The S'ace time and )ean residence time 2ou%d be

e6ua% i$ the $o%%o2in# t2o conditions are satis$ied!

" No densit& chan#e

" No bac mi+in#

In 'ractica% reactors the abo(e t2o ma& not be (a%id

and hence there 2i%% be a di$$erence bet2een them.38


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Norma%i@ed RTD $unction E7 9 !

)()( t E E = /t =

=0

)(1 dt t E

=0

)(1 d E

What is the si#ni$icance o$ E7 9 55

4o2 does E7 9 (s. %oo s %i e $or t2o idea% CSTRso$ di$$erent si@es 55

4o2 does E7t9 (s. t %oo s %i e $or t2o idea%CSTRs o$ di$$erent si@es 55

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;sin# the norma%i@ed RTD $unction1 it is 'ossib%e to

com'are the $%o2 'er$ormance inside di$$erentreactors.

I$ E7 9 is used1 a%% 'er$ect%& mi+ed CSTRs ha(enumerica%%& the same RTD.

I$ E7t9 is used1 its numerica% (a%ues can chan#e $ordi$$erent CSTRs based on their si@es.

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d


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RTD in idea% reactors!

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$ d %


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RTD $or idea% FR!)()( = t t E

00)( = t whent 0)( == t whent

=1)( dt t

= )()()( g dt t t g

===0)()( dt t t dt t tE t

m

===0

222 0)()()()( dt t t t dt t E t t mm

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RTD $ id % CSTR!


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RTD $or idea% CSTR!

===0

/ /)( dt tedt t tE t t m

===0

/2

22 )()()(

dt e

t dt t E t t t

m

)ateria% ba%ance on tracer st to 'u%se in'ut!

in out accumu%ation ? (C GdC3dt C7t9 C? e -t3

/

0

/0

/

0

0

)()()(

t

t

t

edt eC

eC dt t C

t C t E

===

=e E )(

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RTD $or FR-CSTR series!


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RTD $or FR CSTR series!

For a 'u%se tracer in'ut into CSTR the out'ut

2ou%d be ! C7t9 C?e-t3 s

Then the out%et 2ou%d be de%a&ed b& a time ' at the

out%et o$ the FR. RTD $or the s&stem 2ou%d be!

pt t E


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I$ the 'u%se o$ tracer is introduced into the FR1

then the same 'u%se 2i%% a''ear at the entrance o$

the CSTR ' seconds %ater. So the RTD $or FR-CSTR

a%so 2ou%d be simi%ar to CSTR- FR.

Thou#h RTD is same $or both1 'er$ormance is

di$$erent

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R t d %i # 2ith RTD!


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Reactor mode%in# 2ith RTD!

I. 0ero 'arameter mode%s!

7a9Se#re#ation mode%7b9)a+imum mi+edness mode%

II. One 'arameter mode%s!7a9Tan s-in-series mode%

7b9Dis'ersion mode%

III. T2o 'arameter mode%s!

)icro-mi+in#mode%s

)acro-mi+in#mode%s

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S i d % 2 / 02i i 1 8 9


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Se#re#ation mode% 7Dan 2erts / 02ieterin#1 8H9

Characteristics!" F%o2 is (isua%i@ed in the $orm o$ #%obu%es

" Each #%obu%e consists o$ mo%ecu%es be%on#into the same residence time

" Di$$erent #%obu%es ha(e di$$erent Res. Times

" No interaction3mi+in# bet2een di$$erent%obu%es

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)ean con(ersion o$ #%obu%es s'endin# bet2een t and t dt in the reactor

7Con(ersion achie(ed a$ter s'endin# a time t in the reactor9

7Fraction o$ #%obu%es that s'end bet2een t and t dt in the reactor9dt t E t x xd )()(

_ =

=0

_

)()( dt t E t x x

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) ( i i FR i # S # # i d %!


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)ean con(ersion in a FR usin# Se#re#ation mode%!

E+am'%e! A R1 I order1 Constant densit&

Order I for et x kt =1)(

==00

_

)(1)()1( dt t E edt t E e x kt kt

k kt edt t e x

== 1)(10

_

)ean con(ersion 'redicted b& Se#re#ation mode%matches 2ith idea% FR

55

) ( i i CSTR i # S # # ti d %!


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)ean con(ersion in a CSTR usin# Se#re#ation mode%!


==0

/

0

_ /)(1 dt eedt t E e x t kt kt

k

k x

+=

1

_

)ean con(ersion 'redicted b& Se#re#ation mode%matches 2ith idea% CSTR

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) ( i i ' ti % t i #


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)ean con(ersion in a 'ractica% reactor usin#

Se#re#ation mode%!


==00

_

)(1)()( dt t E edt t E t x x kt

" conduct tracer e+'eriment on the 'ractica% reactor" measure C7t9 and e(a%uate E7t9

" '%ot and e(a%uate mean con(ersion

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T i i 7TIS9 ) d %!


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Tan s in series 7TIS9 )ode%!

)ateria% ba%ance on the I reactor $or tracer!

G8 dC83dt -( C 8

C8 C? e+'7-t3

89

)ateria% ba%ance on the II reactor $or tracer!

G: dC: 3dt ( C 8 ( C: dC: 3dt C: 3 : C?e+'7-t3 :9 : 58

/0 ttC ttC /2

0


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2/

2

02

t e

t C C = it

i

et C

C Similarly

/2

03 2

=

it

i

et

dt t C

t C t E

/3

2

03

33

2)(

)()( ==

For n e6ua% si@ed CSTRs!it

ni

n

en

t

t E

/1

)1()(

= 59

Tota% n t3 n t3


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Tota% n i t3 n t3 i

n

nt

n

i

n

i e

n

nne

n

t n E E i

=

==

)1(

)(

)1(

)()(1

/1

As the number becomes %ar#e1the beha(ior o$ the s&stema''roaches that o$ FR

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The Dis'ersion )ode%!


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The Dis ersion )ode%!

" The Dis'ersion )ode% is used to describe non-idea% FR

" A+ia% dis'ersion is ta en into consideration

" Ana%o#ous to Fic ,s %a2 o$ di$$usion su'erim'osed on the

$%o2

Da Di$$usi(it& coe$$icientJ ; su'er$icia% (e%ocit&J

L Characteristic %en#th63

Bac mi+in# or dis'ersion1 is used to re'resent the combined action o$ a%%'h 1 %& % % di$$ i 1 b % i i #1 d


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Idea% %u# $%o2

'henomena1 name%& mo%ecu%ar di$$usion1 turbu%ent mi+in#1 and nuni$orm (e%ocities1 2hich #i(e rise to a distribution o$ residence times inthe reactor.

I$ the reactor is an idea% '%u# $%o21 the tracer 'u%se tra(erses throu#hthe reactor 2ithout distortion and emer#es to #i(e the characteristicidea% '%u# $%o2 res'onse. I$ di$$usion occurs1 the tracer s'reads a2a&$rom the center o$ the ori#ina% 'u%se in both the u'stream anddo2nstream directions.

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C%osed (esse% Dis'ersion )ode%!


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C%osed (esse% Dis ersion )ode%!

Da Dam oh%er number C?n-8

)1(22

22

2r Pe

r r m

e Pe Pet

=

2/22/2

2/

)1()1(4

1 !Pe!Pe Pe

e!e!!e

x +=

Pe "! a /41 +=

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"he #$a#is% labeled &&'acro'i#in()) 'easures the breadth o* the residenceti'e distribution+ ,t is -ero *or piston *low% *airl. broad *or the e#ponentialdistribution o* a stirred tan/% and broader .et *or situations in ol in(b.passin( or sta(nanc.+

"he .$a#is is 'icro'i#in(% which aries *ro' none to co'plete+ icro'i#in(e**ects are uni'portant *or piston *low and ha e 'a#i'u' i'portance *orstirred tan/ reactors+

ell$desi(ned reactors will usuall. *all in the nor'al re(ion bounded b. thethree ape#es% which correspond to piston *low% a per*ectl. 'i#ed "R% and

a co'pletel. se(re(ated "R+69

ithout e en 'easurin( the R" % li'its on the per*or'ance o* 'ost real


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reactors can be deter'ined b. calculatin( the per*or'ance at the threeape#es o* the nor'al re(ion+

"he calculations re uire /nowled(e onl. o* the rate constants and the'ean residence ti'e+

hen the residence ti'e distribution is /nown% the uncertaint. aboutreactor per*or'ance is (reatl. reduced+

real s.ste' 'ust lie so'ewhere alon( a ertical line in or'al Re(ion+

"he upper point on this line corresponds to 'a#i'u' 'i#edness andusuall. pro ides one bound li'it on reactor per*or'ance+

hether it is an upper or lower bound depends on the reaction'echanis'+

"he lower point on the line corresponds to co'plete se(re(ation andpro ides the opposite bound on reactor per*or'ance+

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ANYCLARIFICATIONS ?

Kuhn, Thomas. . . no theory ever solves all the puzzles with which it is confronted at

agiven time; nor are the solutions already achieved often perfect.

9.nin-ideal_flow (1)

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