L6 Pressure Drop in Reactors

8/20/2019 L6 Pressure Drop in Reactors

1/21

L6-1

Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr e!t, "ni#ersity of $llinois at "r%ana-Cham!aign

'e#ie() Logic of $sothermal 'eactor esign$n *ut- +eneration .ccumulation1 Set u! mole %alance for

s!ecific reactor

/ eri#e design e0 in

terms of . for each

reactor

Batch CS2' P3'

4 Put C 5 is in terms of

.

and !lug into r .

Plug r . into design e0 and sol#e for the

time 7%atch8 or #olume 7flo(8 re0uired

for a s!ecific .

79e (ill al(ays loo:

conditions (here ;

∫

XAA

A0A0

dXt =N

-r V ∫

XA dX

AV =FA0 -rA0

? 5 5< 5 5 d@3 3 r d?

dt− + =∫

A0 A

A

F XV=

-r

5< 5 .< . < < 5

. <

C C 2 ;PC

1 P 2 ;

ν

ε

+ = ÷ ÷ ÷+ n

. 5r :C− =

n 5< 5 .< . < < .

. <

C C 2 ;Pr :

1 P 2 ;

ν

ε + − = ÷ ÷ ÷+


2/21

L6-/


'e#ie() Batch 'eactor *!eration

Batch ?olume is constant, ??<

Mole %alance

'ate la(

Stoichiometry 7!ut C . in

terms of 8

Com%ine

. A B -r . :C ./ 2nd order reaction rate

Calculate the time re0uired for a con#ersion of . in a constant ? %atch reactor

$ntegrate this e0uation in

order to sol#e for time, t B e a b l e t o d o t h e s e 4 s

t e p s , a n d

t h e n i n t e

g r a t e t o s o l v e

f o r t i m e

f o r

A N Y R E A C T I

N

. . .<

d@ ?

dtr −=

./

.r :C− =

. .< .C C 71 8= −

( ) ( ) . .< / . . /


3/21

L6-4


'e#ie() CS2' *!eration . A B -r . :C .

Calculate the CS2' #olume re0uired to get a con#ersion of .

Mole %alance

'ate la(


terms of 8

Com%ine

!st order reaction rate

Put 3 .

. .r :C− =

. .< .C C 71 8= −

( )

.<

.< .

3 ?

:C 1

=

−

( ) .< < .

.< .

C ?

:C 1

υ → =

−

r

3?

.

.


4/21

L6-


'e#ie() Scaling CS2's

S!ace time τ 7residence time8 re0uired toachie#e . for 1

st order irre#ersi%le r=n

$f one :no(s the #olume of the !ilot-scale reactor re0uired to achie#e .,

ho( is this information used to achie#e . in a larger reactor

: in the small reactor is the same as : in the %igger reactor

9ant . in the small reactor to %e the same as . in the %igger reactor

υ

E0 is for a 1st order r=n only>

( ) .<

.

:

?1 υ = −

( ) ( )< . < .

small %igger . .

:no(n) ? (ant) ?

: 1 : 1

υ υ = =

− −

( )= −

.

< .

?: 1 υ

= →


5/21

L6-D


'e#ie() am:hler @um%er, a

Estimates the degree of con#ersion that can %e o%tained in a flo( reactor

3irst order irre#ersi%le reaction)

1st order

irre#ersi%lereaction

Second order irre#ersi%le reaction)

/nd order

irre#ersi%lereaction

Fo( is . related to a in a first order irre#ersi%le reaction in a flo( reactor

$f a G


6/21

L6-6


'e#ie() Siing CS2's for /nd *rder '=n

• Mole %alance

• 'ate la(s

• Stoichiometry

• Com%ine

or

Calculate the CS2' #olume re0uired to get a con#ersion of .

. A B -r . :C ./ "i#$id%phase 2nd order reaction rate

$n terms of con#ersion

$n terms of s!ace time

$n terms of . as a

function of a

E0 is for a /nd order

li0uid irre#ersi%le r=n

Be a%le to do these ste!s>

( ) .< .<

.<

1 / :C 1 6 :C

/ :C

τ τ

τ

+ − +=

.

.< < .<

.r r

3 C ?

υ = =

− −

./

.r :C− =

. .


7/21

L6-J


'e#ie() n CS2's in SeriesC .


8/21

L6-


'e#ie() $sothermal CS2's in Parallel

3 .<

3 .


9/21

L6-I


Li0uid Phase 'eaction in P3'L$O"$ PF.SE) Ci f7P8 → no !ressure dro!

Calculate vol$me re0uired to get a con#ersion of . in a &'R

/. A B -r . :C

.

/ 2nd order reaction rate

Mole %alance

'ate la(


terms of 8

Com%ine

Li0uid-!hase /

nd

order reaction in P3'

B e a b l e t o d o t h e s e 4 s t e p s ,

i n t e g r a t e ( s o l v e f o r )

f o r A N Y

R * E R R + N

See .!!endi= . for integrals

fre0uently used in reactor design

−= . .

.<

d r

d? 3

− = /

. .r :C

−= . .< .C C 71 8

( ) ( )=

− .< .

.<

/

.

/C 1 d

? 3

:

d

( ) ( )

? . .< .

//<


10/21

L6-1<


Li0uid Phase 'eaction in PB'L$O"$ PF.SE) Ci f7P8 → no !ressure dro!

Calculate catal,st -eight re0uired to get a con#ersion of . in a &BR/. A B -rQ . :C .

/

2

nd

order reaction rate

Mole %alance

'ate la(


terms of 8

Com%ine

Li0uid-!hase /nd order reaction in PB' B e a b l e t o d o

t h e s e 4 s t e p s

, i n t e g r a t e

( s o l v e f o r )

f o r A N Y R *

E R R + N −

= . . .<

r Rd

d9 3

=− ./

.r R :C

−= . .< .C C 71 8

( ) ( )=

− .< .

.<

/

.

/C 1 d

9 3

:

d

( ) ( )→ =∫ ∫

−

9 . .< .

//<


11/21

L6-11


$so%aric, $sothermal, $deal '=ns in

2u%ular 'eactors

.S PF.SE)

1 1 1

as-!hase reactions are usually carried out in tu%ular reactors 7P3's & PB's8 Plug flo() no radial #ariations in concentration, tem!erature, & ∴ -r .

@o stirring element, so flo( must %e tur%ulent

3 .< 3 .

Stoichiometry for %asis s!ecies .)

5< 5 .< . < < 5

. <

C C 2 ;PC

1 P 2 ;

ν

ε

+ = ÷ ÷ ÷+

5< 5 .< . 5

.

C C C

1

ν

ε

+→ =

+

( ) .< . .< .< . . .

. .

C 1 C C C C

1 1 ε ε

−−= → =

+ +


12/21

L6-1/


$so%aric, $sothermal, $deal '=n in P3'.S PF.SE) Ci f7ε8 → no ∆P, ∆2, or ∆;

Calculate P3' #olume re0uired to get a con#ersion of .

/. A B -r . :C ./ 2nd order reaction rate

Mole %alance

'ate la(


terms of 8

Com%ine

as-!hase /nd

order r=n in P3'

no ∆P, ∆2, or ∆;

$ntegral .-J in a!!endi=

−= . .

.<

d r

d? 3

./

.r :C− =

( ) ( )

( )

// .< . .

</

. .

C 1

1

:d

? 3d

−=

+ ε

( )( )

( )

/ . . .<

.//


13/21

L6-14


Effect of ε on υ and .

ε) e=!ansion factor, the fraction of change in ? !er mol . reactedυ υ0 (ith increasing . Shorter residence time than (hen υ = υ0 Lo(er con#ersion !er #olume of reactor 7(eight of catalyst8 than if υ = υ<

2f 2< .

2<

@ @ Change in total moles at 1

@ total moles fedε

− == =

( )


14/21

L6-1


Pressure ro! in P3's & PB's

.S PF.SE)Considering ideal gas

!hase %eha#ior 7;


15/21

L6-1D


Pressure ro! in PB's.S PF.SE) . A B -rQ . :C .

/

Calculate d .Td9 for an isothermal ideal gas !hase reaction (ith ∆P

2nd order reaction rate

Mole %alance

'ate la(


terms of 8

Com%ine

9e need to relate PTP


16/21

L6-16


Ergun E0uation relates P to 9

ifferential form of Ergun e0uation

for !ressure dro! in PB')

.C) cross-sectional area ρC) !article densityβ) constant for each reactor, calculated using a com!le=

e0uation that de!ends on !ro!erties of %ed 7gas density,

!article sie, gas #iscosity, #oid #olume in %ed, etc8

α) constant de!endant on the !ac:ing in the %ed

2his e0uation can %e sim!lified to)

( ) .<

dy 21

d9 /y 2

α ε

= − + ÷

( )<

c c <

/

. 1 P

β

α ρ φ = −<

P

y P=2f 2<

.<2<

@ @

y@ε δ

−= =

( )#olume of solid

1 ) fraction of solid in %ed total %ed #olume

φ −

( )

( )< .< <

PdP 21

d9 / 2 P P

α ε

= − + ÷ ÷

L6 1J


17/21

L6-1J


as Phase 'eaction in PB' (ith UP.S PF.SE) . A B -rQ . :C .

/

Calculate d .Td9 for an isothermal ideal gas !hase reaction (ith ∆P

2nd order reaction rate

Mole %alance

Com%ine (ith rate la(

and stoichiometry

'elate PTP


18/21

L6-1


.nalytical Solutions to PTP<

Sometimes PTP


19/21

L6-1I


Pressure ro! E=am!le.S PF.SE) . A B 2nd order reaction rate

2his gas !hase reaction is carried out isothermally in a PB' 'elate thecatalyst (eight to .

1<

ε < and isothermal, so)Plug

into C .

Plug into PB'

design e0)

-rQ . :C ./

Sim!lify, integrate, and sol#e for . in terms of 9 or 9 in terms of .)

2f 2<

2<

@ @ 1 1<

@ 1ε

− −= = =

− ÷ ÷+

= .< .< .


20/21

L6-/<


Pressure ro! E=am!le . A B -rQ . :C .

/ 2nd order gas phase r.n non%elementar, rate

2his gas !hase reaction is carried out isothermally in a PB' 'elate the

catalyst (eight to .

Sol#e for .

'earrange

e0 for 9)

( )( )→ = −∫ ∫

−

9 . .

/<


21/21

L6-/1

Slides courtesy of Prof M L Kraft Chemical & Biomolecular Engr e!t "ni#ersity of $llinois at "r%ana Cham!aign

@e=t 2ime

Startu! of a CS2' under isothermal conditionsSemi-%atch reactor

L6 Pressure Drop in Reactors

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