l6 pressure drop in reactors
TRANSCRIPT
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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 + − = ÷ ÷ ÷+
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Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr e!t, "ni#ersity of $llinois at "r%ana-Cham!aign
'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= −
( ) ( ) . .< / . . /
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Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr e!t, "ni#ersity of $llinois at "r%ana-Cham!aign
'e#ie() CS2' *!eration . A B -r . :C .
Calculate the CS2' #olume re0uired to get a con#ersion of .
Mole %alance
'ate la(
Stoichiometry 7!ut C . in
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?
.
.
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Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr e!t, "ni#ersity of $llinois at "r%ana-Cham!aign
'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
= →
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Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr e!t, "ni#ersity of $llinois at "r%ana-Cham!aign
'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
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Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr e!t, "ni#ersity of $llinois at "r%ana-Cham!aign
'e#ie() Siing CS2's for /nd *rder '=n
• Mole %alance
• 'ate la(s
• Stoichiometry
• Com%ine
or
Calculate the CS2' #olume re0uired to get a con#ersion of .
. A B -r . :C ./ "i#$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− =
. .
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Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr e!t, "ni#ersity of $llinois at "r%ana-Cham!aign
'e#ie() n CS2's in SeriesC .
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Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr e!t, "ni#ersity of $llinois at "r%ana-Cham!aign
'e#ie() $sothermal CS2's in Parallel
3 .<
3 .
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Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr e!t, "ni#ersity of $llinois at "r%ana-Cham!aign
Li0uid Phase 'eaction in P3'L$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(
Stoichiometry 7!ut C . in
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
( ) ( )
? . .< .
//<
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Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr e!t, "ni#ersity of $llinois at "r%ana-Cham!aign
Li0uid Phase 'eaction in PB'L$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(
Stoichiometry 7!ut C . in
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 . .< .
//<
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Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr e!t, "ni#ersity of $llinois at "r%ana-Cham!aign
$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
−−= → =
+ +
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Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr e!t, "ni#ersity of $llinois at "r%ana-Cham!aign
$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(
Stoichiometry 7!ut C . in
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
( )( )
( )
/ . . .<
.//
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Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr e!t, "ni#ersity of $llinois at "r%ana-Cham!aign
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
− == =
( )
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Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr e!t, "ni#ersity of $llinois at "r%ana-Cham!aign
Pressure ro! in P3's & PB's
.S PF.SE)Considering ideal gas
!hase %eha#ior 7;
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Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr e!t, "ni#ersity of $llinois at "r%ana-Cham!aign
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(
Stoichiometry 7!ut C . in
terms of 8
Com%ine
9e need to relate PTP
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Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr e!t, "ni#ersity of $llinois at "r%ana-Cham!aign
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
= − + ÷ ÷
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Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr e!t, "ni#ersity of $llinois at "r%ana-Cham!aign
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
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Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr e!t, "ni#ersity of $llinois at "r%ana-Cham!aign
.nalytical Solutions to PTP<
Sometimes PTP
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Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr e!t, "ni#ersity of $llinois at "r%ana-Cham!aign
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
− −= = =
− ÷ ÷+
= .< .< .
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Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr e!t, "ni#ersity of $llinois at "r%ana-Cham!aign
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 . .
/<
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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