gas–liquid and gas-liquid-solid reactions
TRANSCRIPT
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Gas – Liquidand
Gas- Liquid –Solid Reactions
A. Gas –Liquid Systems
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Proper Approach to Gas-LiquidProper Approach to Gas-LiquidReactionsReactions
References• Mass Transfer theories• Gas-liquid reaction regimes• Multiphase reactors and selection criterion• Film model: Governing equations, problemcomplexities• xamples and !llustrative Results
• "olution #lgorithm $computational concepts%
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Transport E ects in Gas-LiquidTransport E ects in Gas-Liquid
ReactionsReactions
Two- lm theory &' ('G' (hitman, )hem' * Met' ng', + & . $& +/%' +' (' 0' 1e2is * (' G' (hitman, !nd' ng' )hem', &3, +&4$& + %'
Penetration theory 5' 6' 7anc82erts, Trans' Farada9 "oc', 3 / $& 4 %' 5' 6' 7anc82erts, Trans' Farada9 "oc', . / $& 4&%' 5' 6' 7anc82erts, Gas-1iquid Reactions, McGra2-;ill,
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Two- lm Theory AssumptionsTwo- lm Theory Assumptions
!" A sta nant layer e#ists in $oth the as andthe liquid phases"
%" The sta nant layers or lms ha&e ne li i$lecapacitance and hence a local steady-statee#ists"
'" (oncentration radients in the lm are one-dimensional"
)" Local equili$rium e#ists $etween the the asand liquid phases as the as-liquid interface
*" Local concentration radients $eyond thelms are a$sent due to tur$ulence"
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Two-Film Theory ConceptTwo-Film Theory Concept W.G. Whitman, Chem. & Met. Eng., 29 14 !192"#.W.G. Whitman, Chem. & Met. Eng., 29 14 !192"#.
Bulk LiquidBulk Gas
p A p Ai
CAi
•
•
CAb
x = 0
xx + x
L
Liquid FilmGas Film
x = Lx = G
p Ai = H A CAi
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Two-Film TheoryTwo-Film Theory- $ingle %eaction in the i'(i) Film -- $ingle %eaction in the i'(i) Film -
A (g) + b B (liq) P (liq)
RA kg-moles A
m 3liquid - s = - k mn C A
m C Bn
Closed form solutions only possible for linear kinetics or when linear appro imations are introduced
! " # are non$olatile
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Film Theory Mo)el *or a $ingle +on olatileFilm Theory Mo)el *or a $ingle +on olatileGa - i'(i) %eactionGa - i'(i) %eaction
2*
2
2
2
( ) ( ) ( )
0
0 0
A L
B L
A g bB l P l
d A D r at x A A at x A A
dx
d B dB D br at x at x B Bdx dx
δ
δ
+ →
= = = = =
= = = = =
% &iffusion - reaction equations for a sin'le reaction in the liquid film
are(
% )n dimensionless form* the equations become dependent on twodimensionless parameters* the +atta number +a and q , (
( )1/ 2
1* **
21
m nmn
m n D L B A mn L
R A
For r k A B
t B D Ha D k A B q
t m bA D
−
=
= =+>=
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% &iffusion - reaction equations for a
sin'le reaction in the liquid film are(
A A A A R xC Dt C +∂∂
=∂∂
2
2
B B
B B R
xC D
t C +∂∂=∂∂ 2
2
Penetration Theory +odelPenetration Theory +odel
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Compari on etween TheorieCompari on etween Theorie
• Film theory :– kL∝ D, δ - film thickness
• /enetration theory :
– kL∝ D1/2Higbie model t * - life of surface li uid
element
Danck!erts model s - a"erage rate of surface
rene!al
'
* A
L R D
k C C δ
=−>
'
* *2 A
L
R Dk
C C t π =−
>
'
* A
L
Rk Ds
C C =−
>
=
=
=
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Ga - i'(i) %eaction %egimeGa - i'(i) %eaction %egime
Very l!"
#apid pseud!$s% !r m%& !rder
' s%a %a e!us Fas% (m )
Ge eral (m ) !r ' %ermedia%e l!" *i usi! al
' s%a %a e!us , ur a-e
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%eaction-0i**( ion %egime 0e*ine)%eaction-0i**( ion %egime 0e*ine)y Characteri tic Timey Characteri tic Time
% Slow reaction re'ime %* //% # kL=k L0
– Slow reaction-diffusion re'ime ( %* //% # //% .
– Slow reaction kinetic re'ime ( %* //% . //% #
% ast reaction re'ime ( %* %# kL=1 A k L0 k L0
– )nstantaneous reaction re'ime( kL
= 1A
kL
0
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Gas Abs!rp%i! A--!mpa ied by #ea-%i! i %&e Liquid
Assume 3 - nd order rate
Ha%%a 4umber 3
1i 4umber3
1 &a -eme % Fa-%!r3
H k k K g L L
111 +=
2$
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1ig&% (A 6 H) regimes -a be dis%i guis&ed3
A7 ' s%a %a e!us rea-%i! !--urs i %&e liquid ilm
B7 ' s%a %a e!us rea-%i! !--urs a% gas8liquid i %er a-e
% Hig& gas8liquid i %er a-ial area desired% 4! 8is!%&ermal e e-%s likely
29
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C7 #apid se-! d !rder rea-%i! i %&e ilm7 4! u rea-%ed A pe e%ra%es i %!bulk liquid
*7 Pseud! irs% !rder rea-%i! i ilm: same Ha umber ra ge as C7
Abs!rp%i! ra%e pr!p!r%i! al %! gas8liquid area7 4! 8is!%&ermal e e-%s s%illp!ssible7
2;
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.aximum %empera%ure di ere -e a-r!ss ilm de el!ps a% -!mple%e mass%ra s er limi%a%i! s
>empera%ure di ere -e !r liquid ilm "i%& rea-%i!
>rial a d err!r required7 4! is!%&ermali%y se ere !r as% rea-%i! s7
e7g7 C&l!ri a%i! ! %!lue e
2?
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- $(mmary -- $(mmary -imiting %eaction-0i**( ion %egimeimiting %eaction-0i**( ion %egime
"lo2 reaction 8inetic regime• Rate proportional to liquid holdup and reaction rate and in?uenced b9
the overall concentration driving force• Rate independent of 8 la @and overall concentration driving force
"lo2 reaction-diAusion regime• Rate proportional to 8 la @and overall concentration driving force• Rate independent of liquid holdup and often of reaction rate
Fast reaction regime• Rate proportional to a @,square root of reaction rate and driving force to
the po2er $nB&%C+ $nth order reaction%• Rate independent of 8 l and liquid holdup
!nstantaneous reaction regime• Rate proportional to 8 1 and a @• Rate independent of liquid holdup, reaction rate and is a 2ee8 function
of the solubilit9 of the gas reactant
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Gas- liquid – solid systems
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9;
G Li id S lid C l / d R i A0'12!0l13#0l1
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Gas Limi%i g #ea-%a % (C!mple%ely e%%ed Ca%alys%)
( )( )
( ) ( )( )
( )( )
( )( )
( )
( ) pv B p s Bl
A
g
H
g Bvo A
sl p
a
g B
s B pv
Av
k ak a K
H A A
k R
sreact mmol
A Aa
A H
Aa
sreact mmol
sreact mmol Ak
scat mmol Ak
A
η ε
ε η
ε η
−++=−=
−
−
−
Ω=
1111
1
:.RATE(APPARENT)OVERALL
k :solid-Liquid-
:liquid-!"s-
lu#$%$"& o% ou i $%
.RATETRAN+PORT
lu#$%$"& o% ou i $%
.1 :,ATAL +TNRATE
olu#$&" "l s u i $%
.:RATENET ,
0
s
11
0
0
0
5$
Gas – Liquid Solid Cataly/ed Reaction A0'12!0l13#0l1
*epe de e ! Appare % #a%e C! s%a % ( k ) !
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*epe de -e ! Appare % #a%e C! s%a % ( k app ) !>ra sp!r% ( k ls , p ) a d i e%i- Parame%ers ( k v )
( ) ( ) ( )
( )
( )( )
( ) ( ) sreact mmol a B Bk
sreact mmol Bk
scat mmol Bk
l P l B g A
p sl ls
B s pv
v
.:lu#$)%$"& o% ou i( $%
%" $T%" s o%
.1:lu#$)%$"& o% ou i( $%
&" "l siR" $
.:olu#$)&" "l s u i( $%
%" $i $ i&&" "l s$ $d&o# l$ $lo ,"s$-l$)( o ol" i%$"& "li#i i 3Liquid
:R$"& io
0
0
0
−
−
=+
ε η
( )( )
( ) Bv p pls
L Lapp Bv p
k ak
B Bk Bk
sreact mmol
ε η
ε η
−+
=−−
111
1
.%"'$(" "%$ ')O $%"ll
1
Liquid limiting reactant (nonvolatile) 4 Case of completely wetted catalyst
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Clearly is determined by transport limitations and byreactor type and flow re'ime.
)mpro$in' only impro$es if we are not already transport
4ur task in catalytic reactor selection* scale-up and desi'n is toeither ma imi/e $olumetric producti$ity* selecti$ity or product
concentration or an ob5ecti$e function of all of the abo$e. 6he keyto our success is the catalyst. or each reactor type consideredwe can plot feasible operatin' points on a plot of $olumetricproducti$ity $ersus catalyst concentration.
vm
aS vm
#"5vm
#"5 x x #"5 x#"5vm
aS
io&o &$ %"&" "l s
"& i is $&i i&
0 =
=
reactor mcat kg
x
cat kg P kg
S a
2?
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ey M(ltipha e %eactorey M(ltipha e %eactor
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( le Col(mn in )i**erent mo)e( le Col(mn in )i**erent mo)e
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ey M(ltipha e %eactor /arameterey M(ltipha e %eactor /arameter
Tram$ou,e P" et al" .(hemical Reactors / 0rom1esi n to 2peration3 Technip pu$lications 4%55)6
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2@
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58$0908$00
$08$00$08;090008$0 9
$;08?00
90
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9$
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.ul%ip&ase #ea-%!r >ypes !r C&emi-alpe-ial%y a d Pe%r!leum Pr!-esses
95
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3. Basic Design Equations forMultiphase Reactors
5'#' Ramachandran, 5' 1' Mills and M' 5'7udu8ovic
rama>2ustl'edu D dudu>2ustl'edu
(hemical Reaction En ineerin
Multiphase Reaction Engineering:Multiphase Reaction Engineering:
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>ypes ! .ul%ip&ase #ea-%i! s
Gas8liquid "i%&!u% -a%alys%
Gas8liquid "i%& s!luble -a%alys%
Gas8liquid "i%& s!lid -a%alys% Gas8liquid8liquid "i%& s!luble
or s!lid -a%alys%
Gas8liquid8liquid "i%& s!luble
or s!lid -a%alys% 0two liquid phases1
%raig&% !r"ard
C!mplex
#ea-%i! >ype *egree ! *i i-ul%y
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Hierar-&y ! .ul%ip&ase #ea-%!r .!dels
1mpiri-al
'deal Fl!" Pa%%er s
P&e !me !l!gi-al
V!lume8A eragedC! ser a%i! La"s
P!i %8"ise C! ser a%i!La"s
%raig&% !r"ard
'mpleme %a%i! ' sig&%
Very li%%le
Very *i i-ul%!r 'mp!ssible
ig i i-a %
.!del >ype
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!asic Reactor 6ypes for Systems 7ith SolidCatalyst 0 three or four phase systems1
%Systems with mo$in' catalysts- stirred tank slurry systems- slurry bubble columns- loop slurry reactors- three phase fluidi/ed beds 0ebulated beds1
%Systems with sta'nant catalysts-packed beds with two phase flow( down flow*up flow* counter-current flow- monoliths and structured packin'
- rotatin' packed beds
P& ! A %i l # %! P !
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P&e !me a A e-%i g lurry #ea-%!r Per !rma -e
Fl!" dy ami-s ! %&e mul%i8p&ase dispersi!8 Fluid &!ldups , &!ldup dis%ribu%i!8 Fluid a d par%i-le spe-i i- i %er a-ial areas8 Bubble siDe , -a%alys% siDe dis%ribu%i! s
Fluid ma-r!8mixi g8 P*FEs ! #>*s !r %&e ari!us p&ases
Fluid mi-r!8mixi g8 Bubble -!ales-e -e , breakage8 Ca%alys% par%i-le aggl!mera%i! , a%%ri%i!
Hea% %ra s er p&e !me a8 Liquid e ap!ra%i! , -! de sa%i!8 Fluid8%!8"all luid8%!8i %er al -!ils e%-7
1 ergy dissipa%i!8 P!"er i pu% r!m ari!us s!ur-es
(e.g 7 s%irrers luid8 luid i %era-%i! s )
#ea-%!r .!del
P&e !me a A e-%i g Fixed8Bed #ea-%!r Per !rma -e
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Fluid dy ami-s ! %&e mul%i8p&ase l!"s
8 Fl!" regimes , pressure dr!p8 Fluid &!ldups , &!ldup dis%ribu%i!8 Fluid8 luid , luid8par%i-le spe-i i- i %er a-ial areas8 Fluid dis%ribu%i!
Fluid ma-r!8mixi g8 P*FEs ! #>*s !r %&e ari!us p&ases
Hea% %ra s er p&e !me a8 Liquid e ap!ra%i! , -! de sa%i!
8 Fluid8%!8"all luid8%!8i %er al -!ils e%-7
1 ergy dissipa%i!8 Pressure dr!p
(e.g 7 s%irrers luid8 luid i %era-%i! s )
#ea-%!r .!del
P&e !me a A e-%i g Fixed8Bed #ea-%!r Per !rma -e
8l t f th R t 9 d l
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8lements of the Reactor 9odel
.i-r! !r L!-al A alysis .a-r! !r Gl!bal A alysis
Gas 8 liquid mass %ra s er
Liquid 8 s!lid mass %ra s er
' %erpar%i-le a d i %er8p&ase mass %ra s er
' %rapar%i-le a d i %ra8p&ase di usi!
' %rapar%i-le a d i %ra8p&ase &ea% %ra s er
Ca%alys% par%i-le "e%%i g
Fl!" pa%%er s !r %&e gas liquid a d s!lids
*y ami-s ! gas liquida d s!lids l!"s
.a-r! dis%ribu%i! s !%&e gas liquid a d
s!lids Hea% ex-&a ge
%&er %ypes ! %ra sp!r%
p&e !me a
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#ea-%!r *esig Variables
#ea-%!r Pr!-ess #ea-%i! Fl!" =
Per !rma -e Variables #a%es Pa%%er s
C! ersi! Fl!" ra%es i e%i-s .a-r!
ele-%i i%y ' le% C , > >ra sp!r% .i-r!
A-%i i%y Hea% ex-&a ge
Feed #ea-%!r i
> iC i
Pr!du-%!u%
> !u%C !u%
d l d d l l
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'dealiDed .ixi g .!dels !r .ul%i8p&ase ( >&ree P&ase) #ea-%!rs
.!del Gas8P&ase Liquid P&ase !lid8P&ase #ea-%!r >ype
$ Plug8 l!" Plug8 l!" Fixed >ri-kle8Bed
Fl!!ded8Bed
5 Ba-k mixed Ba-k mixed Ba-k mixed .e-&a i-ally agi%a%ed
2 Plug8Fl!" Ba-k mixed Ba-k mixed Bubble -!lum 1bulla%ed 8 bed Gas8Li % , L!!p
'deal Fl!" Pa%%er s i ul%ip&ase #ea %!rs
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deal Fl! Pa%%er s i .ul%ip&ase #ea-%!rs1xample3 .e-&a i-ally Agi%a%ed #ea-%!rs
t
XG(t)
0
δ (t)
t
XL(t)
0
δ (t)
t
EG(t)
0
δ (t- g )
τ g
t
EL(t)
- t / Leτ L
0
H
QL
QG
QL
QG
τ ε ε
L
r ! L
L
"
#= − −( )1τ ε ! r !
!
"
#=
V R = v G + V L + V C 1 = ε G + ε L + ε C
or
i t Ab l t 9 t f th
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irst Absolute 9oment of the6racer Response for 9ulti-phase Systems
For a single mobile phase in contact with p stagnant phases:
µ1 =V1 + K 1j V j
j = 2
p
∑Q 1
For p mobile phases in contact with p - 1 mobile phases:
µ1 =V1 + K 1j V j
j = 2
p
∑Q1 + K 1j Q j
j = 2
p
∑
K1j =C jC1
equil.is %&e par%i%i! -!e i-ie % ! %&e %ra-er
be%"ee p&ase $ a d I
R l ti ' th #& f th 6 ) l
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Relatin' the #& of the 6racer )mpulseResponse to Reactor #erformance
JF!r a y sys%em "&ere %&e -! aria -e ! s!I!ur %imes is Der!(i.e., "&e %&e %ra-er lea es a d re8e %ers %&e l!"i g s%ream a%%&e same spa%ial p!si%i! ) %&e P*F ! s!I!ur %imes i %&e rea-%i!e ir! me % -a be !b%ai ed r!m %&e exi%8age P*F !r a
! 8ads!rbi g %ra-er %&a% remai s -! i ed %! %&e l!"i g p&ase
ex%er al %! !%&er p&ases prese % i %&e sys%em7K
F!r a irs%8!rder pr!-ess3
∫ ∞
0
H-A
p
e = X - dt1t08: e tt10kc
∫ ∞
0
(-e = dt1t08 e tt1;
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)llustrations of )deal-9i in' 9odelsfor 9ultiphase Reactors
D
G L Plug8 l!" ! gas Ba-kmixed liquid , -a%alys%
Ba%-& -a%alys% Ca%alys% is ully "e%%ed
D
G L Plug8 l!" ! gas Plug8 l!" ! liquid
Fixed8bed ! -a%alys% Ca%alys% is ully "e%%ed
%irred %a k
Bubble C!lum>ri-kle 8 Bed
Fl!!ded 8 Bed
Li iti ' f ) t i i R ti R t
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Limitin' orms of )ntrinsic Reaction Rates
Reaction SchemeD A 4 6 &8 4l6 (4l6
G Li i%i # % % d Pl 8Fl!" ! Li id
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D
G L
Gas Limi%i g #ea-%a % a d Plug8Fl!" ! Liquid
$7 Gase!us rea-%a % is limi%i g
57 Firs%8!rder rea-%i! "r% diss!l ed gas
27 C! s%a % gas8p&ase -! -e %ra%i!
97 Plug8 l!" ! liquid
;7 's!%&ermal !pera%i!
>l A B
C C 1/ >>l L L A A B B
C DC D ν
Gas Reactant Limitin' and #lu' low of Liquid
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Gas Reactant Limitin and #lu low of Liquid
)onstant gas phaseconcentration valid for pure
gas at high ?o2 rate
) o
n c e n
t r a
t i o n o r #
x i a l ; e
i g h t
Relative distance from catal9st particle
( ) ( ) 0d$% A A Aad$' k A A Aak A# A#r sl p sr l
(
Bl d$ $ l l $ l l −−+−
+
$
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Concept of Reactor 8fficiency
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Concept of Reactor 8fficiency=
Rη Rate of r#n in the Entire Reactor with Transport E ects
+a#imum Possi$le Rate
)onversion of Reactant @
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) @$in terms of Reactor cienc9%
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Gas #ea-%a % Limi%i g a d Ba-kmixed Liquid
D
G L
$7 Gase!us rea-%a % is limi%i g
57 Firs%8!rder rea-%i! "r% diss!l ed gas
27 C! s%a % gas8p&ase -! -e %ra%i!
97 Liquid a d -a%alys% are ba-kmixed
;7 's!%&ermal !pera%i!
a k
Bubble C!lum
Key Assumptions
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Gas Reactant Limitin and 8ac;mi#ed
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LiquidA at the catalyst surfaceDA at the catalyst surfaceD
0or Reactant 8D0or Reactant 8D$
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LiquidSol&in the +odel Equations
Fl!" Pa%%er C! -ep%s
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Fl! Pa%%er C! ep%s!r Vari!us .ul%ip&ase ys%ems
A BA 8 i gle plug l!" p&ase l!" !gas !r liquid "i%& ex-&a ge be%"ee%&e m!bile p&ase a d s%ag a % p&ase7
Fixed beds, rickle-beds, packed
bubble columnsB 8 i gle p&ase l!" ! gas !r
liquid "i%& ex-&a ge be%"ee apar%ially ba-kmixed s%ag a % p&ase7
!emi-batch slurries, "luidi#ed-beds,ebullated beds
Fl!" Pa%%er C! -ep%s
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p!r Vari!us .ul%ip&ase ys%ems
C * 1C * 8 C! -urre % !r-!u %er-urre % %"!8p&asel!" (plug l!" !r dispersedl!") "i%& ex-&a ge
be%"ee %&e p&ases a ds%ag a % p&ase7
rickle-beds, packed orempty bubble columns
1 8 1x-&a ge be%"ee %"!l!"i g p&ases ! e !
"&i-& &as s%r! g i %er alre-ir-ula%i! 7$mpty bubble columns and"luidi#ed beds
Strate ies for +ultiphase Reactor
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Selection
• Strate y le&el JD (atalyst desi n strate y
gas-solid s9stems: catal9st particle siEe, shape, porousstructure, distribution of active materialgas-liquid s9stems: choice of gas-dispersed or liquid-disperseds9stems, ratio bet2een liquid-phase bul8 volume and liquid-phase diAusion la9er volume
• Strate y le&el JJD JnKection and dispersion strate ies$a% reactant and energ9 inHection: batch, continuous, pulsed,staged, ?o2 reversal$b% state of mixedness of concentrations and temperature:2ell-mixed or plug ?o2$c% separation of product or energ9 in situ$d% contacting ?o2 pattern: co-, counter-, cross-current
• Strate y le&el JJJD (hoice of hydrodynamic owre ime
e'g', pac8ed bed, bubbl9 ?o2, churn-turbulent regime, dense-phase or dilute-phase riser transport
Strate ies for +ultiphase Reactor
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Selection
R' 0rishna and "'T' "ie, ) ", , p' + $& %
Two-0ilm TheoryD +ass and eatTwo-0ilm TheoryD +ass and eat
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) J ( T ), j ( C g g
i 11
Gas 0ilm Liquid 8ul;
) J ( T ), j ( C g g i ) J ( T ), j ( C L L
i
) J ( T ), j ( C L L
i 11
Gas 8ul;
∑=
∆−= )R
* R
+ *
+
H Rdx
, d
12
2
)(κ
∑=
−= )R
*
+ * *-
+ -
- RdxC d
D1
2
2υ
Liquid 0ilm
(ell B th0 X
f
) j ( ,i N
1 X
f
) j ( ,i N
1 X f
) j ( ,i q0)(6 = .
+ *-q
mδ δ
yyTransferTransfer
eat0ilm
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-Transfer
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∑=
∆−=
)R
* * *r
+
L R H d/ , d
162
2
))((λ
8"("!
8"("%
( )01
600
)()(====
−∆−+−=−∑ /
+ -
-
)S
- - s
+
$
g
o0t g /
+
L d/
dC D H , ,
d/
d, λ
( )m
+ /
L
L
/
+
Lm
, ,
d/
d,
δ δ λ λ δ
δ −−−=− =
=
)(
Gas-Liquid lm
Transfer
8u$$le (olumn +i#in (ell +odel8u$$le (olumn +i#in (ell +odel
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8u$$le (olumn +i#in (ell +odel8u$$le (olumn i#in (ell odel
- )ells arranged in diAerent modes to simulate the averaged ?o2
patterns-
(ells in seriesDG and L mi#ed ow
(ells inseries-parallel
com$ination
E#chan e$etweenMpward anddownwardmo&in liquid
Liquid Gas Liquid Gas
(ell !
(ell 9
(ell K
(ells in seriesDG plu ow L mi#ed ow
Prototype cell
+i#in (ell +odel for as-liquid+i#in (ell +odel for as-liquid
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systemssystems9o&el features
•
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9on-1imensionali,ed parameters
7aria$les
Reaction $ased
re+ -
+
- + - g re+ -
g
- g - C C cand C C c 66==
re+ - g
re+ -re+ - H C C 666 /=%
L%$
L&$ll3L
Au
k "V=α %$ %$ 6ii ,,=ω
re+ *
re+ L
m Lcell * R
C #
a" M
)( δ ε −=re+
a* *
R,
E =γ
re+ L p L L DC Le ρ λ =
%$ L
L
%$ 76% 7 T,
,89
ρ∆
−=%$ %$
2#
%$ 72
7 ,:
R 8"
δ=
-
g re+ -m- M D
k H B- 66
δ =
+ass transfer $ased
re+ L
re+ re+ *r
*,
C D H
λ β
)( 6∆−=
L
m g H B- λ
δ =
re+ L
re+ ---S -S ,
C D H
λ β 666
)( ∆−=
re+ - g re+
L
re+ +- H 0
0
6=γ
%$
iis =
g pm g
Lcell gl g
C m
" aS
6δ λ
=m L p L
Lcell gl L
C m
" aS
δ λ
6
=
eat transfer $ased
odel
m
/ δ ξ = g re+ g
g
## + =
re+
L
L
, , =θ
re+
g
g
, , =θ
+eat of reactionparameter
!ulk reaction number +atta number Arrheniusnumber +eat of reactionparameter
&amkohler number !iot number
!iot number +eat of solutionparameter
Liquid heattransfer number
Gas heattransfer number
Lewis number
&iffusi$itiesratio
8ffecti$e G
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- 6as @hat R'7', van "2aaiH ('5'M', 0uipers, J'#'M', 6ersteeg,G'F', KMasstransfer 2ith complex chemical reaction in gas-liquid L, )hem' ng' "ci',
4 , &+&-&/3, $& %
- 6as @hat R'7', van "2aaiH ('5'M', 0uipers, J'#'M', 6ersteeg,G'F', KMasstransfer 2ith complex chemical reaction in gas-liquid L, )hem' ng' "ci',4 , &/.-& ., $& %
- #l- baidi @';' and "elim M';' $& +%, K Role of 1iquid Reactant 6olatilit9in Gas #bsorption 2ith an xothermic ReactionL, #!)h J', /N, /3/-/.4,$& +%
- @hattachar9a, #', Gholap, R'6', )haudhari, R'6', KGas absorption 2ithexothermic bimolecular $&,& order% reactionL, #!)h J', //$ %, &4 .-&4&/,$& N.%
- Pan ar;ar 7"G" Sharma +"+ ', K)onsecutive reactions: Role of Mass Transfer factorsL, + , 43&-43 , $& . %
- Pan ar;ar 7"G" Sharma +"+ ', K"imultaneous absorption and reactionof t2o gasesL, + , ++ .-+/ 3, $& . %
Reactions
Types of eat GenerationTypes of eat Generation
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Types of eat GenerationTypes of eat Generation
!" %eat of solution 4N s 6 which is enerated at the as-
liquid interface due to the physical process of asdissolution
% %eat of &apori'ation 4N &6 of &olatile reactants due toe&aporati&e coolin in o#idation reaction
'" %eat of reaction 4N r 6 which is enerated in the lmnear the as-liquid interface 4for fast reactions6 or inthe $ul; liquid 4for slow reactions6"O Mncontrolled heat eneration can lead toD
!" Mndesired production of $y-products%" Thermally-induced product decomposition'" Jncreased rate of catalyst deacti&ation)" Local hot spots and e#cess &apor eneration*" Reactor runaway and unsafe operation
O +odelin of simultaneous mass and heat transporte ects in the lm is necessary for accurate predictions
w+ass Transfer Rates in Gas Liquid+ass Transfer Rates in Gas Liquid
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+ass Transfer Rates in Gas-Liquid+ass Transfer Rates in Gas-LiquidReactionsReactions
!" Physical transport and thermodynamicproperties of the reaction medium e#hi$it
&arious de rees of temperature dependence
%" >inetic parameters e#hi$it e#ponentialdependence on the local temperature
'" Jnsta$ilities at the as-liquid reactioninterface that are dri&en $y surface tension
e ects 4+aran oni e ect6 and density e ects
Typical $y tem with +ota le 3eat E**ectTypical $y tem with +ota le 3eat E**ect
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Typical $y tem with +ota le 3eat E ectTypical $y tem with +ota le 3eat E ect
#hah $ %hattachar&ee, in'(ecent)d"ances +, 1 .
/ropertie an) nter*acial Temperat(re/ropertie an) nter*acial Temperat(re
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/ropertie an) nter acial Temperat(rep ) p (%i e *or $ome /ractical $y tem%i e *or $ome /ractical $y tem
#hah $ %hattachar&ee, in '(ecent )d"ances in the 0ngineering )nal sisof ulti3hase (eacting # stems,+ 4ile 0astern, 1 .
t % t *t % t *
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a oratory %eactor *ora oratory %eactor *orGa - i'(i) %eaction ineticGa - i'(i) %eaction inetic
(ase !D Sin le non-isothermal reaction(ase !D Sin le non-isothermal reaction
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G1 second order reaction
B Ak dx Ad
D A 222
=
A D
Bk Ha 02
22 δ =
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! "# $ %
& ' '$ ( % % 4Bi! F!"*6 ' % 4Bi! F56
Temp'
)onc'
Reaction "cheme:# B v@ );a O & , q O ' 4, γ O ++,γ s O -.'4, γ vap O +,βsO ' &, βvap O - ' 4,@i;g O &
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m g Hg B-
δ κ
=
Bi Hg ↑ → Temp ↓
A
b B m ref
D
C k Ha
22 δ
=
Ha ↑ → Rxn ↑ → Temp. ↑
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Axial *ispersi! .!del ( i gle P&ase)
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p ( g )@asis: 5lug ?o2 2ith
superimposed KdiAusionalL orKedd9L transport in the
direction of ?o2 R
d$ C
0 $
C D
t C
ax +∂−
∂∂=
∂∂
2
2
> E O $ C
D0C C 0 ax ∂∂
−=00> E O 1
0=∂∂ $ C
1et L $
2 =ax
ax D0L
Pe =0 L
3 =
R3 2d C
2C
Pet C
3 ax
+∂−∂∂=
∂∂
2
21
> η O 2
C
PeC C
ax ∂
∂−=
10 > η O & 0=
∂
∂
2
C
Axial *ispersi! .!del
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R3
2d
C
2
C
Pet
C 3
ax
+∂−∂∂=
∂∂
2
21
> η O 2C
PeC C
ax ∂∂
−=1
0 > η O & 0=∂∂
2C
Axial *ispersi! .!del !r %&e Liquid "i%&C! s%a % Gas8P&ase C! e %ra%i! 8 $
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C! s%a % Gas8P&ase C! -e %ra%i! 8 $+ass 8alance of A in the liquid phase
$
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C! s%a % Gas8P&ase C! -e %ra%i! 8 5
Axial *ispersi! .!del !r %&e Liquid "i%&C! s%a % Gas8P&ase C! -e %ra%i! 8 2
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C! s%a % Gas8P&ase C! -e %ra%i! 8 2
A*. .!del3 B!u dary C! di%i! s
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Comments re'ardin' a ial dispersion model
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Comments re ardin a ial dispersion model0A&91
% 6he model is $ery popular because it has only a sin'leparameter* a ial dispersion coefficient* & a * the $alue ofwhich allows one to represent R6&s between that of astirred tank and of a plu' flow. 6he reactor model is usually
written in dimensionless form where the #eclet number fora ial dispersion is defined as(
'i#$&o $&'ios'i&&;"%"&'$%i
'i#$dis $%sio"5i"ls'i&&;"%"&'$%i
/
//
2
===5 L
D L D L5 Pe axaxax
#e a => plu' flow
#e a =? complete back mi in'
A&9 comments continued-:
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% @se of A&9 was populari/ed by the work of&anckwerts* Le$enspiel* !ischoff* 5. Smith andmany others in the : B?s throu'h : ?s.
% Since & a encompasses the effects of thecon$ecti$e flow pattern* eddy as well asmolecular diffusion* prediction of the A ial #ecletDumber with scale –up is e tremely difficult as atheoretical basis e ists only for laminar andturbulent sin'le phase flows in pipes.
% 9oreo$er use of A&9 as a model for the reactoris only ad$isable for systems of #eclet lar'erthan E 0preferably :?1.
A&9 comments continued
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A&9 comments continued -
% +owe$er* A&9 leads to the boundary $alueproblem for calculation of reactor performancewith inlet boundary conditions which are neededto preser$e the mass balance but unrealistic for
actual systems. Since at lar'e #eclet numbersfor a ial dispersion the R6& is narrow* reactorperformance can be calculated more effecti$elyby a tanks in series model or se're'ated flowmodel.
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i l C
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inal Comments% 6o impro$e predictability of multiphase reactor
models and reduce the risk of scale-up* theyshould be increasin'ly de$eloped based onproper physical description of hydrodynamics in
these systems.% )mpro$ed reactor scale descriptions coupled withad$ances on molecular and sin'le eddy 0sin'leparticle1 scale will facilitate the implementation of
no$el en$ironmentally beni'n technolo'ies byreducin' the risk of such implementations.
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#ea-%i! ys%em
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y
9<
*isad a %ages ! emi8Ba%-& lurry #ea-%!r
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g y
% Ba%-& a%ure 6 ariable pr!du-%
% L!" !lume%ri- pr!du-%i i%y (due %! l!" -a%alys% l!adi ga d limi%ed pressure)
% Pressure limi%a%i! (s&a % seal)
% Hig& p!"er -! sump%i!% P!!r sele-%i i%y (due %! &ig& liquid %! -a%alys% !lume
ra%i! a d u desirable &!m!ge e!us rea-%i! s)
% Ca%alys% il%ra%i! %ime -! sumi g
% Ca%alys% make8up required
% xyge mass %ra s er limi%a%i! s
9
P!%e %ial Ad a %ages ! Fixed Bed ys%em
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g y
9?
lurry s Fixed Bed% i%& ! d i ! % l % %i l k d8b d
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% i%& pr!per desig ! -a%alys% par%i-les a pa-ked8bedrea-%!r "i%& -!8-urre % d!" 8 l!" ! gas a d liquid b!%&i par%ial "e%%i g regime a d i i du-ed pulsi g regime-a ar surpass %&e !lume%ri- pr!du-%i i%y a dsele-%i i%y ! %&e slurry sys%em ye% require a !rder !mag i%ude less ! %&e a-%i e -a%alys% -!mp! e %7
% M desirable &!m!ge !us rea-%i! s are suppressed i%&e ixed bed rea-%!r due %! mu-& &ig&er -a%alys% %!liquid !lume ra%i!
% Fa%&er ad a %age is a--!mplis&ed i ixed beds by!pera%i! a% &ig&er pressure ( ! m! i g s&a %s %! seal)7
% Fixed bed !pera%i! requires l! g %erm -a%alys% s%abili%y!r ease ! i si%u rege era%i! 7
9@
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#e ere -es
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:. &uduko$ic* 9.#.* Larachi* .* 9ills* #.L.* K9ultiphaseReactors – Re$isited * Chem. 8n'. Science* EM:* : E-: E 0: 1.
. &uduko$ic* 9.#.* Larachi* .* 9ills* #.L.* K9ultiphaseCatalytic Reactors( A #erspecti$e on Current Nnowled'eand uture 6rends * Catalysis Re$iews* MM0::1* : F- MB
0 ?? 1.F. Le$enspiel* 4cta$e* Chemical Reaction 8n'ineerin'* F rd
8dition* 7iley* : .
M. 6rambou/e* #.* 8u/en* H.#.* KChemical Reactors – rom
&esi'n to 4peration * ) # #ublications* 8ditions 68C+D)#*#aris* rance 0 ?? 1.
9;
or any process chemistry in$ol$in' morethan one phase one should (
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than one phase one should (
% Select the best reactor flow pattern based on thekinetic scheme and mass and heat transferrequirements of the system*
% Assess the ma'nitude of heat and mass transfereffects on the kinetic rate
% Assess whether desi'n requirements can be metbased on ideal flow assumptions% &e$elop scale-up and scale-down relations% ;uantify flow field chan'es with scale if needed
for proper assessment of reactor performance% Couple physically based flow and phasecontactin' model with kinetics