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7/23/2019 Topic 4 - Design of Ideal Reactors for Single Reaction
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7/23/2019 Topic 4 - Design of Ideal Reactors for Single Reaction
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Subtopics:Ideal Batch Reactor
Steady state mixed fow reactor(MFR)
Steady state plug fow reactor
Space time and space elocity
!olding time and space time "orfow reactor
Si#e comparison o" single reactors
Re"erence: Fogler and $eenspiel
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Reactors coered in %opic & are:
'Batch Reactor Steady State MFR * Mixed FlowReactor+ Steady State ,FR * ,lug Flow
Reactor
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ApplicationSmall scale production/one-off production
Pharmaceutical and fermentation
Advantages
Easy to cleanHigh conversion per volume
Flexiility of operation-same reactor can
produce one product one time and a different
product the next
!isadvantages"
High operating cost
Product #uality more variale than with
continuous operation
$deal %atch &eactor
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$deal %atch &eactor
Material Balance: In - .ut / ,roduct 01ccumulation
' '
Batch Reactor Design Equation
2 the reactants are initially charged into a container3 are wellmixedand are le"t to react "or certain period
4 Recall the batch reactor design e5uation
Vr dt
dNA
A = ( )X1 N NAoA −=
Vr dt
dX N
AAo −=
( )
∫ −=
tX
0A
Ao
Vr
dX Nt
diferentialorm
integralorm
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$deal %atch &eactor
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6raphical representation o" the per"ormancee5uations "or batch reactors3 isothermal and non*isothermal7 6eneral case
8onstant*density systems
only
$deal %atch &eactor
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Steady State (ixed Flow &eactor )(F&*
1pplication
1 production o" where agitation isre5uired
8ontinuous production
1dantages
9asy to clean
6ood temperature control
$ow operating cost (labour)
isadantages:
$owest conersion per unit
olume
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Steady State (ixed Flow &eactor )(F&*
4 %he contents are well stirred and uni"orm throughout
+ The exit stream from this reactor has the same
composition as the fluid within the reactor
4Recall the 8S%R esign 95uation:
( )X1FFAoA −=
A
AAo
r
FFV
−
−=
( )exit
A
Ao
r
XFV
−
=
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4 esign e5uation A
A Ao
r
F F V
−
−
=
In terms o"conersion A
Ao
r
X F V
−
=
Reactor si#ing3 theolume o" MFR canbe calculated "rom
s A
Ao
r
F
−
X
A
Ao
r
F
−
X
SS-(F&
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4 Reactors in series can also be designed proided there are noside streams by de;ning the oerall conersion at any point
reactor firsttofedAof moles
i pointtoupreactedAof moles=i X
Mole balance at reactor '
Mole balance at reactor
0111
=+− V r F F A A Ao
1
1
1
A
Ao
r
X F V
−
=
02221
=+− V r F F A A A
( )
2
12
2
A
Ao
r
X X F V
−
−=
SS-(F&
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Steady State Plug Flow Reactor
1pplication
For large scale production
,roduction with "ast reactions<high temperature Both homogenous and heterogeneous reaction
8ontinuous production
1dantages
!igh conersion per olume
$ow operating cost
6ood heat trans"er
isadantages:
=ndesired thermal gradients may exist
,oor temperature control
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4esign e5uation A
A
r dV
dF =
In terms o"conersion
A Ao r
dV
dX F −=
∫ −=
X
A
Ao
r
dX F V
0
%he olume o" ,FR can be represented as
shaded area under the cure
* 1rea under the curecan be calculated usingnumerical method such
as Simpson>s Rule
Steady State Plug Flow Reactor
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Space Time and Space elocity
o
V
υ
τ =
Space time3 isobtained by diidingreactor olume by
the olumetric fowrate entering thereactor
τ
%ime ta?en "or fuid
to enter reactorbased on entrancecondition - olumeand olumetric rate
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+ Space velocity, S is defined as
τ
υ 1==
V
SV o
V LHSV
liquid o |υ
=
V GHSV o STP|υ
=
Space Time and Space elocity
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For %atch reactor
∫ =
A
Ao
C
C A
A
r
dC d τ
∫ −
=
Ao
A
C
C A
A
r
dC τ
A A r
dt
dC =
!olding time and Space Time or Reactor
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A
A Ao
r
F F V
−
−
=
For .ST&/(F&,
A
o
A
o
Ao
o r
F F V
−
−
=
υ υ
υ
A
A Ao
r
C C
−
−
=τ
!olding time and Space Time or Reactor
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For PF&
A
A
r
dC d =τ
A
A
r dF dV =
∫ −
=
X
A
Aor
dX F V
0
∫ −=
X
A
Ao
r
dX C
0
τ
!olding time and Space Time or Reactor
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Si"e #omparison o Single Reactors
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Si"e #omparison o Single Reactors
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9xam @ A 1pril ''
%he li5uid phase o" reaction A -» B is an elementary
reaction in a fow reactor with 85% conersion o" 1 %he inlet concentration o" 1 is + mol<liter and theolumetric fowrate isC liter<hr1dditional in"ormation: ?1 0 D hr*'
a) etermine the space time and olume i" this
reaction is carried out in a 8S%R(& mar?s)
b) etermine the space time and olume i" thisreaction is carried out in a ,FR
(& mar?s)c) Repeat part (a) and (b) i" the reaction now obeys
nd order ?inetics(E mar?s)
d) 8hoose the best reactor "or both order o" reactionand usti"y your answer
(C mar?s)
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9G .F %.,I8 &