lecture 12 - university of michiganelements/5e/powerpoints/2013lectures/lec... · 2019-08-07 ·...
TRANSCRIPT
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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 12
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Lecture 12 – Tuesday 2/19/2013 � Multiple Reactions
� Selectivity and Yield
� Series Reactions
� Complex Reactions
2
A DkD
A UkU
A B C
A + B C + D
A + C E
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� Series: A → B → C � Parallel: A → D
A → U
� Independent: A → B
C → D
� Complex: A + B →C + D
A + C → E
With multiple reactors, either molar flow or number of moles must be used (no conversion!)
3
4 Types of Multiple Reactions
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Instantaneous Overall
Selectivity
Yield
There are two types of selectivity and yield: Instantaneous and Overall.
U
DDU r
rS =U
DDU F
FS =~
A
DD r
rY−
=AA
DD FF
FY−
=0
~
4
Selectivity and Yield
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ABA
BA
U
DUD C
kk
CCkCCk
rrS
2
1
2
21 ===
To maximize the selectivity of D with respect to U run at high concentration of A and use PFR.
DBA 1k⎯→⎯+ BAD CCkr 21=Example: Desired Product:
UBA 2k⎯→⎯+BAU CCkr 2=Undesired Product:
Selectivity and Yield
5
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Gas Phase Multiple Reactions
6
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Multiple Reactions
7
Flow Batch
BB
AA
rdVdF
rdVdF
=
=
VrdtdN
VrdtdN
BB
AA
=
=
A) Mole Balance of each and every species
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Multiple Reactions
8
B) Rates a) Rate Law for each reaction: b) Net Rates: c) Relative Rates:
ACAA
BAAA
CCkrCCkr
22
11
=−
=−
AAi
iAA rrrr 211
+==∑=
riA−ai
= riB−bi
= riCci
= riDdi
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Multiple Reactions
9
C) Stoichiometry Gas:
Liquid:
⎟⎠
⎞⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛=
TT
PP
FFCCA
ATA
0
000
0υAA FC =
Example: A → B → C
(1) A → B k1
(2) B → C k2
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Batch Series Reactions
10
1) Mole Balances
VrdtdN
VrdtdN
VrdtdN
CC
BB
AA
=
=
=
AC
AB
AA r
dtdC r
dtdC r
dtdC
===
V=V0 (constant batch)
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Batch Series Reactions
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2) Rate Laws
B2B1B
A1A
BB1B1
AA1A1
rrrrr
CkrCkr
+=
=
=−
=−Laws
Net rates
1r
1r
1r
1r
C2B2
B1A1
=−
=−
Relative rates
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Example: Batch Series Reactions
12
A → B → C
(1) A → B
(2) B → C
1) Mole Balances
CC
BB
AA r
dtdC r
dtdC r
dtdC
===
t topt
Ci
A B C
OVV =
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Example: Batch Series Reactions
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2) Rate Laws
1r
1r
1r
1r C2B2B1A1 =
−=
−Relative:
B2B2
A1A1
CkrCkr
−=
−=Laws:
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Example: Batch Series Reactions
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3) Combine Species A: Species B:
A1AA CkrdtdC
=−=−
( )tkexpCC 10AA −=
BB rdtdC
=
B2A1B2B1NET BB CkCkrrrr −=+==
( )tkexpCkCkdtdC
10A1B2B −=+
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Example: Batch Series Reactions
15
Using the integrating factor, ( ) ( )tkdtkFI 22 expexp.. == ∫( )[ ] ( )tkkCk
dttkCd A
B1201
2 expexp−=
at t = 0, CB=0
CB =k1CA0
k2 − k1exp −k1t( )− exp −k2t( )⎡⎣ ⎤⎦
BAAC CCCC −−= 0
( ) ( )[ ]tktkAC ekek
kkCC 21 11 12
12
0 −− −−−−
=
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Example: CSTR Series Reactions
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AàBàC What is the optimal ? τ
00 =+− τAAA rCC
000 0
=+−
=+−
τBB
BB
rCVrCv
00
000
0
=+−
=+−
VrvCvCVrFF
AAA
AAA
1) Mole Balances A:
B:
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Example: CSTR Series Reactions
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AàBàC 2) Rate Laws
B2B2
A1A1
CkrCkr
−=
−=Laws:
1 1
1 2 1 2
0A A A
B A B A B
r r k Cr r r k C k C= + = −
= − + = −
Net:
1r
1r
1r
1r C2B2B1A1 =
−=
−Relative:
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Example: CSTR Series Reactions
18
AàBàC 3) Combine
�
CA 0 −CA − k1CAτ = 0
CA =CA 0
1+ k1τ
−CB + k1CA − k2CB( )τ = 0
CB =k1CAτ1+ k2τ
CB =k1CA 0τ
1+ k2τ( ) 1+ k1τ( )
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Example: CSTR Series Reactions
19
AàBàC
€
dCB
dτ= 0
€
τmax =1k1k2
Find that gives maximum concentration of B
( )( )τττ
12
01
11 kkCkC A
B ++=
τ
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20
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End of Lecture 12
21
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Supplementary Slides
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Blood Coagulation
23
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Notations
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26
Notations
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Mole Balances
27
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Mole Balances
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Mole Balances
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Results
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Many metabolic reactions involve a large number of sequential reactions, such as those that occur in the coagulation of blood.
Cut → Blood → Clotting
Figure A. Normal Clot Coagulation of blood (picture courtesy of: Mebs, Venomous and Poisonous
Animals, Medpharm, Stugart 2002, Page 305) 31
Blood Coagulation
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Schematic of Blood Coagulation
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Cut
A + B C D E F
Clot 33