Lecture 2
Review of Lecture 1
Definition of Conversion, X
Develop the Design Equations in terms of X
Size CSTRs and PFRs given –rA= f(X)
Conversion for Reactors in Series
Review the Fall of the Tower of CRE
1
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Conversion - Chemical Reaction Engineering - Lecture Slides, Slides of Engineering Chemistry
Chemical Reaction Engineering covers Heat Effects, Isothermal Design, Stoichiometry, Rate Laws, Mole Balance and many other topics. This lecture includes: Conversion , Design Equations, Mole Balances, Cstr, Stoichiometry, Evaluate, Batch, Levenspiel Plots, Numerical Evaluations of Integrals, Reaction Engineering
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2012/2013
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Lecture 2 ^ Review of Lecture 1 ^ Definition of Conversion, X ^ Develop the Design Equations in terms of X ^ Size CSTRs and PFRs given –r
= f(X)A
^ Conversion for Reactors in Series ^ Review the Fall of the Tower of CRE
Reactor
Differential
Algebraic
Integral
The GMBE applied to the four major reactor types(and the general reaction A
B)
V^
FA^0
^ F
A rA
CSTR
Vr dN^ dt
A A^ ^
^0
N^ A AN^ A dNA Vr t
Batch
NA
t
dFA dV^
^ rA
F^ A F^ A
dFA drA V
0
PFR
FA
V
dFA dW^
^ rA
^
F^ A F^ A dFA rA W
0
PBR
FA
W
Reactor Mole Balances Summary
Review Lecture 1
CSTR – Example Problem^ (1) Mole Balance:
^
A
A A
A
A A A A A
C r C
r
C
C
F r F V^
^
0 0 0 0 0 0
A A^
kC
r^
(2) Rate Law: (3) Stoichiometry:
^0
A A A
F F C^
Review Lecture 1
CSTR – Example Problem^ (4) Combine:^ V^
C 0 A^0
C^ A ^
kC^ A
(5) Evaluate:
^
^
^
^
^
^
^
3
0 1
0 0 (^03)
(^1). 0 (^23). 0
(^1). 0 (^110)
(^1). 0 min 23
. 0
(^1). 0
(^1). 0 10 min
dm
C C C dm V
C C
A A A A A
^3 391 900 3.^2
dm
V^
Review Lecture 1
Batch
Vr dX dt N
dN dt
dX N
dN
X N
N
N
reacted
A Moles
initially
A Moles
remaining
A Moles
A
A A
A
A
A
A
A
(^00)
0
0
0
Batch
^
X
A A^
dX Vr N t
0 0 Integrating, The necessary
t^ to achieve conversion X.
X X t t
X t
^
0 0
0
A^
A A
dN
r V
dt^
N
CSTR
dN
Adt^
0
Steady State
Vr
dVr
A
A^
Well Mixed
V^
F
A^0
^
FA
rA
CSTR
CSTR volume necessary to achieve conversion X.
V^
F
A^0
^
FA^
FA
X 0
^
rA
XA rA
F
V^
^
0
X
F
F
F
reacted
A
Moles
entering
A
Moles
leaving
A
Moles
A
A
A^
0
0
^
^
0
dVr
F
F^
A A A
PFR
X X V V
X V
^
0 0 PFR volume necessary to achieve conversion X.
dXr
F
V
X
A A ^ ^ ^0
0
Integrating,
Reactor
Differential
Algebraic
Integral
V^
FA^0 X (^) rA
CSTR
FA^0
dX dV^
r
A^
X ^
dXA rA F V
0
0
PFR
Vr dXdt N^
A A^
0
0 ^ ^0
X
A A^
dX Vr N t
Batch
X
t
FA^0
dX dW^
r
A^
^
X
dXA rA F W
0
0
PBR
X
W
Reactor Mole Balances Summary^ in terms of conversion, X
Levenspiel Plots
FA^0 rA
X
F^0 A^ ^ rA
Area = Volume of CSTR
X^1
1 0
X 1
F r
V
AX
A
CSTR
Levenspiel Plots
Numerical Evaluations of Integrals The integral to calculate the PFR volume can beevaluated using method as Simpson’s One-ThirdRule: (See Appendix A.4)
^ ^
1 )( ) (^2) / (^4) ( 1 )^0 ( 3
0
0
0
Xr
Xr
r xF FdXr V
A
A A A
X A A Other numerical methods are: ^ Trapezoidal Rule (uses twodata points) ^ Simpson’s Three-Eight’sRule (uses four data points) ^ Five-Point QuadratureFormula
1 )(X^2 rA 1 )(X^1 rA 1 )^0 (r A r^ A (^1)
0
X^1
X^2
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