module6a

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CHEE 321: Chemical Reaction EngineeringCHEE 321: Chemical Reaction Engineering

Module 6: Non-Isothermal Reactors (Chapter ! "ogler#

http://www.queensu.ca/

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Topics to be covered in this ModuleTopics to be covered in this Module

Module 6a ($ections %2! %3! %&! %6%1 ' "ogler! &th

Edition# )e*elop Energy Balance e+uations ,or ,lo reactors%

Enthalp.! Heat Capacit.! and Heat o, Reaction and relationship /eteen them

Heat trans,er rates ,or C$0R and "RR

4lgorithms ,or Non-isothermal C$0R and "R

Module 6/ ($ections %5 and %#

E+uili/rium Con*ersion (Re*ersi/le Reactions# in Reactors

' Con*ersion attaina/le during adia/atic operation o, endothermic ande7othermic reactors

' Increasing Con*ersion /. inter-stage cooling and heating

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8h. )o 8e Need Energ. alance 98h. )o 8e Need Energ. alance 9

E*er. reaction proceeds ith release or a/sorption o,heat%

0he amount o, heat released or absorbed depends on

' the nature o, reacting s.stem

' the amount o, material reacting

' temperature and pressure o, reacting s.stem

and can /e calculated ,rom heat o, reaction (∆HR7n#

Most industrial reactors ill re+uire heat input or heat

remo*al! hence! e need energ. /alance%

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Energ. alance ,or $ingle ReactionEnerg. alance ,or $ingle Reaction

4n e7othermic reaction is carried out

in an adia/atic plug ,lo reactor%

Ho ould .ou calculate the reactor

*olume re+uired to achie*e a certain

amount o, con*ersion! 9

8e need to relate X and T ----; Energ. alance E+uation

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=eneral "orm o, Energ. alance=eneral "orm o, Energ. alance

Rate o,accumulation

o, the energ.

ithin the

s.stem

' > ' ?

dt

E d E F E F W Q out out inin

@=−+−

Rate o, orAdone by the

s.stem on

the

surroundings

sW

Q

Rate o, ,loo, heat to the

s.stem ,rom

the

surrounding

Rate o, energ.added to the

s.stem /.

mass ,lo into

the s.stem

inin E F

Rate o, energ.leaving the

s.stem /.

mass ,lo out

o, the s.stem

out out E F Control Bolume

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=eneral "orm o, Energ. alance(,or multi component s.stem#

dt

E d

E F E F W Q out i

n

i

iini

n

i

i

@

11 =−+− ∑∑ ==

sW

Qnn E F

E F

E F

!

%%%

!

!

22

11

nn E F

E F

E F

!

%%%

!

!

22

11

Ne7t! e ill e*aluate the 8D and ED terms

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sW

Qnn E F

E F

E F

!

%%%

!

!

22

11

nn E F

E F

E F

!

%%%!

!

22

11

Work Flowof RateW W s +=

out i

n

i

iini

n

i

i V P F V P F @@ 8orA "lo-o, Rate

11

∑∑==

+−=

Rate o, ,lo orA is rate o, orA to

get mass into and out o, the s.stem

In a chemically reacting systems, there are usually two types of work that

need to be accounted for – i! "haft Work e#g# work done by impellers in a

$"T% and batch reactor! and ii! &low Work

E*aluation o, the 8orA (8# term

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sW

Qnn E F

E F

E F

!

%%%

!

!

22

11

nn E F

E F

E F

!

%%%!

!

22

11

%%%2

2

+++= z g u

U E i

ii

Energ. E i is the sum o, internal! Ainetic! potential

and an. other t.pe o, energies%

For a maority of reactors! only internal energy is im"ortant

ii U E ≅∴

E*aluation o, the E term

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=eneral "orm o, Energ. alance(,or multi component s.stem#

dt

E d

E F E F W Q out i

n

i

iini

n

i

i

@

11 =−+− ∑∑ ==

sW

Qnn E F

E F

E F

!

%%%

!

!

22

11

nn E F

E F

E F

!

%%%

!

!

22

11

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Energ. alance E+uation in terms o, Enthalp.Energ. alance E+uation in terms o, Enthalp.

dt

E d E F E F W Q

out i

n

i

iini

n

i

i

@

11

=−+− ∑∑==

dt

E d U F U F PV F PV F W Q

out i

n

i

iini

n

i

iout i

n

i

iini

n

i

i s

@

1111

=−+−+− ∑∑∑∑====

dt

E d # F # F W Q

out i

n

i

iini

n

i

i s

@

11

=−+− ∑∑==

PV U # += $ow!

8e no ha*e! Energy Balance E%uation in terms of Ent&al"y

'ubstituting a""ro"riate values of E i and Rate of Work

Ne7t! e ill ,ocus on the ent&al"y terms

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Heres hat ell do ith Enthalp. terms

E7press # i in terms o, Enthalp. o, "ormation ( # io #

and Heat Capacit. (("i#

E7press F i in terms o, con*ersion (,or singlereaction# or rates o, reaction

)e,ine Heat o, Reaction (∆HR7n#

)e,ine ∆ Cp

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Enthalp. Relationships: 'ingle Reaction 'ystem

FF

FF

FF

FF

FF

1

FF

) )

* *

( (

B B

+ +

n

i

ii

F #

F #

F #

F #

F #

F # )n ∑=

=

FF

FF

FF

!

%%%

!

!

) )

B B

+ +

# F

# F

# F

) )

B B

+ +

# F

# F

# F

!

%%%

!

!

) )

* *

( (

B B

+ +

n

i

ii

F #

F #

F #

F #

F #

F # ,ut ∑=

=1

- .-

*ad (

ac B

ab + +→+

FF

F

F

F

F

#(

#(

#(

#(

#1(

) ) + )

* +d

( +(

B + B

+ +

F F F

/ a

d F F

/

a

c F F

/ a

b F F

/ F F

==

+=

+=

−=

−=

θ

θ

θ

θ

F i in terms o, F +. and /

,rom stoichiometr.

I, 4 is the limiting reactant

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/ F - # - # a

b- #

a

c- #

a

d

- # - # - # - # - # - #

- # - # - # - # F

- # F - # F

+ + B( *

) ) ) * * *( ( (

B B B + + +

i

n

i

ii

n

i

i

⋅−−+−

−+−+−+

−+−=

−

∑∑ ==

F

FFFFFF

FFFFF

1

FF

1

F

#G(#(#(#(H

I#G(#(H#G(#(H#G(#(H

#G(#(H#G(#(JH

#(#(

θ θ θ

θ

[ ]GH#G(#(H#(#( FFF1

F

1

FF

1

F R0n +ii

n

i

i +i

n

i

ii

n

i

i # / F - # - # F - # F - # F ∆⋅⋅−

−=− ∑∑∑

===

θ

Enthalp. Relationships: 'ingle Reaction 'ystem

∆HR7n

Ne7t! e ill e*aluate the di,,erent terms o, RH$

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∫ =+=-

- -

"iref

o

ii

ref

d- ( - # - # #(#(

E7pressing Hi(0# in terms o, Hio and Cpi

[ ] ∫ =−F

#(#( FF

-

-

iii d- ("- # - # 0here,ore!

[ ]GH#G(#(H#(#( FFF1

F

1

FF

1

F R0n +ii

n

i

i +i

n

i

ii

n

i

i # / F - # - # F - # F - # F ∆⋅⋅−

−=−

∑∑∑ ===θ

ref ref oi - at i1 1 s"eciesof formationof #eat - # =#(

# i is available from

(&emical Engg &andbook

For no "&ase c&ange

Enthalp. at an. gi*en temperature is related to enthalp. at a re,erence

temperature and heat capacit.

[ ] ∫ ∑ ⋅=−⋅=F

1FF

-

-

ii

n

iiii d- ("- # - # θ θ !!4nd!

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Heat o, Reaction (∆HR7n#

#G(#(#(#(H#( - # - # a

b- #

a

c- #

a

d - # + B( * R0n −−+=∆

d- ("- # - # -

- - ref

o

R0n R0nref

∫ = ∆+∆=∆ #(#(∴

+ B( * ("("a

b("

a

c("

a

d (" −−+=∆here!

[ ]GH#G(#(H#(#( FFF1

F

1

FF

1

F R0n +ii

n

i

i +i

n

i

ii

n

i

i # / F - # - # F - # F - # F ∆⋅⋅−

−=− ∑∑∑===

θ

Heat o, reaction is de,ined as:

∫ =

+=-

- -

"iref

o

ii

ref

d- ( - # - # #(#(

Enthalp. at an. gi*en temperature is:

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=eneral "orm o, Energ. alance

dt

E d E F E F W Qout i

n

i

iini

n

i

i

@

11

=−+− ∑∑==

sW

Qnn E F

E F

E F

!

%%%

!

!

22

11

nn E F

E F

E F

!

%%%

!

!

22

11

dt

E d # F # F W Q out i

n

i

iini

n

i

i s

@

11=−+− ∑∑ ==

Energy Balance E%uation in terms of Ent&al"y

[ ]dt

E d - # / F d- (" F W Q R0n +

-

-

ii

n

i

+ s

@#(G F

1

F

F

=∆⋅⋅−

−−

∫ ∑=θ

Energy Balance E%uation in terms of (onversion

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Heat 0rans,er (K# to,rom

Reactors

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Heat 0rans,er (K# to a C$0R Heat 0rans,er (K# to a C$0R

4ssuming C$0R temperature!T ! is spatiall. uni,orm

"or high coolant ,lo rates (0a1 ≅ 0a2?0a#:

Heat trans,erred /eteen coolant and reactor

(,rom energ. /alance on the coolant#

#( 21 aacc - - ("mQ −= #G(#(#(

21

21

aa

aa

- - - - ln2

- - U+

−−−=

−−=

!e'p!

cc

acc("m

U+- - ("mQ

11

#( - - U+Q a −=

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Heat 0rans,er (K# to a "R Heat 0rans,er (K# to a "R

0otal heat trans,erred to the reactor

Heat trans,er rate at a gi*en location in a "R

Remem/er! in "RR the concentration and reaction rates *ar.

along the reactor length% K ill liAel. *ar. too%

∫ ∫ −=−= V

a

+

a dV - - aU d+- - U Q #(#(

#( - - UadV

Qd a −=

Qd

0

0a

a ? heat e7change area*olume

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Non-Isothermal Reactors

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Non-isothermal "lo Reactor Non-isothermal "lo Reactor

[ ]

−=⋅⋅−∆+∆−− ∑

=

#(L

#(@#( F1

FF - - "( F / F - - "( - # W Q i

n

i

i + +ref ref R0n s θ

(pplication)* "pecial $ase+ (diabatic %eactor with o "haft Work

[ ]!-!

!.

ref ref R0n

i

n

i

i

EB- - "( - #

- - "(

/ −∆+∆

−

−=∑

=F

1

θ

-

/ EB

F

F

=

=

W

Q

I , C p

t e r m M M

∆ H R

7 n

4ppl.ing K ? F and 8s?F in the a/o*e e+uation! e get

i h l lN i h l "l R

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(pplication)/+ $"T% with 0eat 1'change2 no shaft work

[ ]

−=⋅⋅−∆+∆−− ∑

=

#(L

#(@#( F1

FF - - "( F / F - - "( - # W Q i

n

i

i + +ref ref R0n s θ

[ ] #(L#(@#(#( F1F

- - "( / - - "( - #

F

- - U+i

n

i

iref ref R0n

+

a −=⋅−∆+∆−− ∑

=

θ

et us see i, e can appl. these concepts to sol*e a C$0R pro/lem%

4ppl.ing 8s?F in the a/o*e e+uation! e get

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Class ro/lem O6

0he ,olloing li+uid-phase reaction is carried out in a C$0R ith heat

e7change:

0he ,eed stream contains 4 and in e+uimolar ratio% 0he total molar

,lo rate is 2F mols% 0he inlet temperature is 325 P! the inlet

concentration o, 4 is 1%5 molar! and the am/ient temperature in theheat e7changer is 3FF P%

Calculate the reactor *olume necessar. to achie*e FQ con*ersion%

4dditional in,ormation

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(pplication)3+ 4&% with 0eat 1'change

)i,,erentiating the Energ. alance e+uation ith respect to B! e get

dV

Qd

B B>∆B

T "4F

0F

"4e

0e

∑∑==

=−−+−n

i

ii

n

i

ii s

dV

d# F #

dV

dF

dV

W d

dV

Qd

11

FF

F1

F

1

F =−+− ∑∑ == in

i

ii

n

i

i s # F # F W Q

N i h l "l RN i th l "l R t

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dV

Qd

B B>∆B

T a

T

a ? speci,ic sur,ace area ,or heat trans,er ? area*olume

< ? o*erall heat trans,er coe,,icient

0a ? 0emperature o, heat trans,er ,luid (outside o, the reactor#

#( - - UadV

Qd a −=

-&e first term on 3#' can be written as

(pplication)3+ 4&% with 0eat 1'change cont#!

∑∑==

=−−+−n

i

ii

n

i

ii s

dV

d# F #

dV

dF

dV

W d

dV

Qd

11

FF

et us e*aluate the di,,erential terms o, the E e+uation

N i h l "l RN i th l "l R t

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#( ii r

dV

dF =

d

r

c

r

b

r

a

r *( B +

+=

+=

−=

−

#(#(#(#(

#( +i r −=ν


∑∑==

=−−+−n

i

ii

n

i

ii s

dV

d# F #

dV

dF

dV

W d

dV

Qd

11

FF


-&e derivative in t&e t&ird term on 3#' can be written as

Recall! t&at for a reaction4 a+ 5 bB 6 c( 5 d*! t&e reaction rates

are related by t&e stoic&iometric coefficients

N i th l "l R tN i th l "l R t

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dV

d- ("

dV

d# i

i =

+= ∫

=

-

- -

"iref

o

ii

ref

d- ( - # - # #(#(


∑∑==

=−−+−n

i

ii

n

i

ii s

dV

d# F #

dV

dF

dV

W d

dV

Qd

11

FF


-&e derivative in t&e fift& term on 3#' can be written as

∑ ∑= =

=

n

i

n

i

iii

idV

d- (" F

dV

d# F

1 1

-&e fift& term on 3#' can be written as


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∑∑==

=−−−+−−n

i

ii

n

i

i +iadV

d- (" F # r - - Ua

11

F#(FF#( ν

#(

#(#(#(

1

1

- (" F

- # r - - aU

dV

d- n

i

ii

n

ii +ia

∑∑

=

=

⋅

⋅−⋅−−⋅⋅=ν

Rearranging t&e above e%uation in terms of d-7dV! we get

'ubstituting! t&e derivative terms into t&e Energy Balance E%uationwe get



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#(

#(#(#(

1

1

- (" F

- # r - - aU

dV

d- n

iii

n

i

i +ia

∑

∑

=

=

⋅

⋅−⋅−−⋅⋅

=

ν

Ho do e sol*e non-isothermal "R pro/lems9

#( +ii r

dV

dF −=ν #(F + + r

dV

d/ F =−or #!( - / f =

#!( - / g =

8e M

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Tther ,orms o, E e+uation ,or "Rs

#(

#(#(#(

1

1

- (" F

- # r - - aU

dV d-

n

i

ii

n

i

i +ia

∑

∑

=

=

⋅

⋅−⋅−−⋅⋅

=

ν

8ou may note

t&at for

e0ot&ermic

reaction! t&is

term will

result in an

increase in - G#(H

#G(H#(#(

1

F (" / - (" F

- # r - - aU

dV

d- n

i

ii +

R0n +a

∆⋅+⋅⋅

∆−⋅−+−⋅⋅=

∑=

θ

For single reaction systems in term of conversion

#(

#G(H#(#(

1

- (" F

- # r - - aU

dV

d- n

i

ii

R0n +a

∑=

⋅

∆−⋅−+−⋅⋅=

For single reaction systems

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Class ro/lem O

It is proposed to design pilot plant ,or the production o, +llyl

(&loride% 0he ,eed stream comprises & moles prop.lenemolechlorine% 0he reactor ill /e *ertical tu/e o, 2 inc& I)% 0he

com/ined ,eed molar ,lo rate is F%6 g-molh% 0he inlet pressure is

2 atmospheres% 0he ,eed stream temperature is 25 C% Calculate

4ll.l Chloride production as a ,unction o, tu/e length ,or the

,olloing 2 cases:

Case-1: "R UacAeted ith heat e7change ,luid circulated at 25 C

Case-2: 4dia/atic operation o, "R

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Class ro/lem O (cont%#

0 is in Pel*in and " is in atm

< ? 2 8m2-P

)∆HR7n1(2S#?11F!FFF mol

)∆HR7n2(2S#?11!5FF mol

M(I %1($TI5: Cl2 > C3H6 V CH2?CH-CH2Cl > HCl

"I61 %1($TI5: Cl2 > C3H6 V CH2Cl-CHCl-CH3

236

1 molesminGWG6331Fe7p1F3%3#(

6322atm&r " "

R- r # ( (l (l ⋅⋅⋅⋅−×=−

23

2 molesminWGHG15SF

e7pH1#(6322

atm&r " " R-

r # ( (l (l ⋅⋅⋅⋅−

=−

9l:

9 mol : c

9 mol : c

9 mol : c

9 mol : c

#(l P

ide +llyl(&lor P

# ( P

(l P

⋅=

⋅=

⋅=

⋅=

12#(

3F#(

11#(

1F#(

36#(

63

2

module6a

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