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Chemical Reaction Engineering (CRE) is the field that studies the rates and mechanisms of chemical reactions and the design of the reactors in which they take place. Lecture 21
Chemical Reaction Engineering (CRE) is the field that studies the rates and mechanisms of
chemical reactions and the design of the reactors in which they take place.
Lecture 21
Web Lecture 21 Class Lecture 17 – Tuesday 3/19/2013 � Gas Phase Reactions � Trends and Optimums
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3
User Friendly Equations relate T, X, or Fi Review Last Lecture
1. Adiabatic CSTR, PFR, Batch, PBR achieve this:
0ˆ =Δ= PS CW!
XEB =Θi∑ CPi
T −T0( )−ΔHRx
X =Θi∑ CPi
T −T0( )−ΔHRx
( )∑Θ
Δ−+=
iPi
Rx
CXHTT 0
4
User Friendly Equations relate T, X, or Fi 2. CSTR with heat exchanger, UA(Ta-T) and a large coolant flow rate:
XEB =
UAFA0
T −T a( )"
#$
%
&'+ Θi
!CPi∑ T −T 0( )
−ΔHRx
T Ta
Cm!
Fi0
X
5
User Friendly Equations relate T, X, or Fi 3. PFR/PBR with heat exchange:
FA0 T0
Coolant Ta
3A. In terms of conversion, X
( ) ( )
( )∑ Δ+Θ
Δʹ′+−=
XCCF
THrTTUa
dWdT
pPiA
RxAaB
i
~0
ρ
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User Friendly Equations relate T, X, or Fi 3B. In terms of molar flow rates, Fi
( ) ( )
∑
Δʹ′+−=
i
ij
Pi
RxAaB
CF
THrTTUa
dWdT ρ
4. For multiple reactions ( )
∑
∑ Δ+−=
i
ij
Pi
RxijaB
CF
HrTTUa
dVdT ρ
5. Co-Current Balance ( )
cPc
aA
CmTTUa
dVdT
!−
=
7
Reversible Reactions
endothermic reaction
exothermic reaction
KP
T
endothermic reaction
exothermic reaction
Xe
T
Heat Exchange
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Example: Elementary liquid phase reaction carried out in a PFR
FA0 FI
Ta cm! Heat Exchange
Fluid
BA⇔
The feed consists of both inerts I and Species A with the ratio of inerts to the species A being 2 to 1.
Heat Exchange
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a) Adiabatic. Plot X, Xe, T and the rate of disappearance as a function of V up to V = 40 dm3.
b) Constant Ta. Plot X, Xe, T, Ta and rate of disappearance of A when there is a heat loss to the coolant and the coolant temperature is constant at 300 K for V = 40 dm3. How do these curves differ from the adiabatic case.
Heat Exchange
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c) Variable Ta Co-Current. Plot X, Xe, T, Ta and rate of disappearance of A when there is a heat loss to the coolant and the coolant temperature varies along the length of the reactor for V = 40 dm3. The coolant enters at 300 K. How do these curves differ from those in the adiabatic case and part (a) and (b)?
d) Variable Ta Countercurrent. Plot X, Xe, T, Ta and rate of disappearance of A when there is a heat loss to the coolant and the coolant temperature varies along the length of the reactor for V = 20 dm3. The coolant enters at 300 K. How do these curves differ from those in the adiabatic case and part (a) and (b)?
Heat Exchange
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Example: PBR A ↔ B
5) Parameters
• For adiabatic:
• Constant Ta:
• Co-current: Equations as is
• Counter-current:
0dWdTa =
T)-T toT-T flip(or )1(dWdT
aa−⋅
0=Ua
Reversible Reactions
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1) Mole Balances
)1( FrdWdX
0AAʹ′−=
0A
A
0A
BA
b
Fr
Fr
dVdX
VW
−=ρʹ′
−=
ρ=
Reversible Reactions
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2) Rate Laws
)2( ⎥⎦
⎤⎢⎣
⎡−−=
C
BAA KCCkr
)3( 11exp1
1 ⎥⎦
⎤⎢⎣
⎡⎟⎟⎠
⎞⎜⎜⎝
⎛−=TTR
Ekk
)4( 11exp2
2 ⎥⎦
⎤⎢⎣
⎡⎟⎟⎠
⎞⎜⎜⎝
⎛−
Δ=
TTRHKK Rx
CC
Reversible Reactions
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3) Stoichiometry
5( ) CA =CA0 1− X( ) p T0 T( )
6( ) CB =CA0Xp T0 T( )
FT = FT 0dpdW
=αpFTFT0
TT0
!
"#
$
%&= −
α2p
TT0
!
"#
$
%&
W = ρV
dpdV
= −αρb2p
TT0
!
"#
$
%&
Note: Nomenclature change for 5th edition p ≡ y
Reversible Reactions
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Parameters
bARx
CA
TCTHKTREkF
ρα , , , , ,)15()7( , , , , , ,
002
2110
Δ
−
3) Stoichiometry: Gas Phase
v = v0 1+εX( ) P0
PTT0
5( ) CA =FA0 1− X( )v0 1+εX( )
PP0
T0
T=CA0 1− X( )
1+εX( )pT0
T
6( ) CB =CA0X1+εX( )
pT0
T
7( ) dpdW
=−α2p
FTFT 0
TT0
=−α2p
1+εX( ) TT0
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Example: PBR A ↔ B
Reversible Reactions Gas Phase Heat Effects
KC =CBe
CAe
=CA0XepT0 T
CA0 1− Xe( ) pT0 T
8( ) Xe =KC
1+KC
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Reversible Reactions Gas Phase Heat Effects Example: PBR A ↔ B
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Exothermic Case: Xe
T
KC
T
KC
T T
Xe ~1
Endothermic Case:
Example: PBR A ↔ B
Reversible Reactions Gas Phase Heat Effects
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€
dTdV
=−rA( ) −ΔHRx( )−Ua T −Ta( )
∑FiCPi
∑FiCPi= FA0 ∑ΘiCPi
+ΔCPX$% &'
Case 1: Adiabatic and ΔCP=0
€
T = T0 +−ΔHRx( )X∑ΘiCPi
(16A)
Additional Parameters (17A) & (17B)
€
T0, ∑ΘiCPi=CPA
+ΘICPI
Reversible Reactions Gas Phase Heat Effects
Heat effects: ( )( ) ( )
( )9 0∑
−−Δ−−=
PiiA
ab
RxA
CF
TTUaHr
dWdT
θρ
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Case 2: Heat Exchange – Constant Ta
Reversible Reactions Gas Phase Heat Effects
( ) )C17( TT 0V , Cm
TTUadVdT
aoaP
aa
cool
==−
=!
Case 3. Variable Ta Co-Current
Case 4. Variable Ta Countercurrent
( ) ? 0 ==−
= aP
aa TVCm
TTUadVdT
cool!
Guess Ta at V = 0 to match Ta0 = Ta0 at exit, i.e., V = Vf
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Reversible Reactions Gas Phase Heat Effects
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Endothermic
PFR
€
A→←B
€
dXdV
=
k 1− 1+1
KC
⎛
⎝ ⎜
⎞
⎠ ⎟ X
⎛
⎝ ⎜
⎞
⎠ ⎟
υ0 , Xe =
KC1+ KC
€
XEB =∑Θ iCPi
T−T0( )−ΔHRx
=CPA
+Θ ICPI T− T0( )−ΔHRx
T0
XXEB
Xe
€
T = T0 +−ΔHRx( )X
CPA+ΘICPI
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Conversion on temperature Exothermic ΔH is negative Adiabatic Equilibrium temperature (Tadia) and conversion (Xeadia)
( )PA
Rx0 C
XHTT Δ−+=
C
Ce K1
KX+
=
X
Xeadia
Tadia T 28
Adiabatic Equilibrium
X2
FA0 FA1 FA2 FA3
T0 X1 X3 T0 T0
Q1 Q2
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X
T
X3
X2
X1
T0
Xe
( )Rx
PiiEB H
TTCX
Δ−
−=∑ 0θ
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T
X
Adiabatic T and Xe
T0
exothermic
T
X
T0
endothermic
PIIPA
Rx
CCXHTT
Θ+
Δ−+= 0
Trends: Adiabatic
Gas Flow Heat Effects
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Effects of Inerts in the Feed
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€
k1+ΘI
⎛
⎝ ⎜
⎞
⎠ ⎟
Endothermic
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As inert flow increases the conversion will increase. However as inerts increase, reactant concentration decreases, slowing down the reaction. Therefore there is an optimal inert flow rate to maximize X.
First Order Irreversible
Adiabatic:
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As T0 decreases the conversion X will increase, however the reaction will progress slower to equilibrium conversion and may not make it in the volume of reactor that you have.
Therefore, for exothermic reactions there is an optimum inlet temperature, where X reaches Xeq right at the end of V. However, for endothermic reactions there is no temperature maximum and the X will continue to increase as T increases.
X
T
Xe
T0
X
T
X
T
Gas Phase Heat Effects
Adiabatic:
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Effect of adding inerts
X
T
V1 V2 X
T T0
∞=ΘI
0I =Θ
Xe
X
€
X =T −T0( )CpA +θ ICpI[ ]
−ΔHRx
Gas Phase Heat Effects
Exothermic Adiabatic
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As θI increase, T decrease and
€
dXdV
=k
υ0 Hθ I( )
k
θI
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KC
V
XeX
V
T
V
Xe
V
k
V
Xe
XFrozen
V
OR
Endothermic
T
V
KC
V
Xe
V
XeX
V
k
V
Exothermic
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Adiabatic
Heat Exchange
T
V
KC
V
Xe
V
XeX
V
Endothermic
T
V
KC
V
Xe
V
XeX
V
Exothermic
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End of Web Lecture 21 End of Class Lecture 17
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