Chapter 5 Ideal Reactors for a Single Reaction 5.2 steady-state mixed flow reactor 5.2 steady-state mixed flow reactor For the mixed flow reactor: =0 Input = output + disappearance.
Download ReportTranscript Chapter 5 Ideal Reactors for a Single Reaction 5.2 steady-state mixed flow reactor 5.2 steady-state mixed flow reactor For the mixed flow reactor: =0 Input = output + disappearance.
Slide 1
Chapter 5
Ideal Reactors for a Single
Reaction
5.2 steady-state
mixed flow reactor
Slide 2
5.2 steady-state mixed flow reactor
For the mixed flow reactor:
=0
Input = output
+
disappearance by reaction
+
accumulation
the composition is uniform throughout
Element of volume
The whole reactor
Slide 3
Molar feed rate
of component A
Slide 4
Introducing these three terms into Eq.(10), we obtain
rearrangement
Slide 5
xAi
If the feed on which
conversion is based
XAi
If the products are contained in the feed:
(12)
Slide 6
The above expressions have the simple relation
between the four terms:
XA, -rA, V, FA0
Knowing any three allows the forth to be found directly
In design of reactor
The size of reactor
needed for a given duty
The extent of conversion
in a reactor of given size
In kinetic studies
The reaction rate may
be easily obtained
without integration
Make its use very
attractive in kinetic studies
Slide 7
Performance Equations
Batch reactor
t N A0
X
0
A
dX
A
( rA )V
Integrating
For general case
Mixed flow reactor
(11)
Algebraic
For general case
Slide 8
For the case of constant-density
Change conversion
to concentration
Slide 9
Graphical representation
General case
Constant-density system only
Slide 10
First-order reaction, constant density system
CA=CA0(1-XA)
(14)
Slide 11
General case, linear expansion
N A N A 0 (1 X A )
VC A V 0 C A 0 (1 X A )
Slide 12
First-order reaction
Slide 13
Second-order reaction
rA kC
2
A
and
A 0
The performance equation becomes
k
C A0 C A
C
or
CA
1
2
A
1 4 kC A 0
2 k
(*)
Slide 14
5.3 steady-state plug flow reactor
The composition of the fluid varies
from point to point along a flow path
The material balance for a differential
element of volume dV
=0
Input = output
+
disappearance by reaction
+
accumulation
Slide 15
For the differential element of volume
– cylinder with the thickness of dl
Slide 16
(16)
Slide 17
(16)
This is a differential equation, for the reactor as a
whole the expression must be integrated.
rA is dependent on the concentration or conversion
of materials. Grouping the terms accordingly, we
obtain
Slide 18
Thus
Batch reactor
t N A0
X
0
A
dX
A
( rA )V
(3)
Slide 19
If the feed on which conversion is based, or,
there are products in the feed
XAi: A conversion in the feed (inlet)
XAf: A conversion in the outlet
Slide 20
For the special case of constant-density system
and
The performance equation can be expressed in
terms of concentration
Slide 21
Eqs. 17 to 19 can be written either in terms of
concentrations or conversions.
For systems of changing density, it is more
convenient to use conversions.
Whatever its form, the performance equations
interrelate:
Rate of reaction
Extent of reaction
Reactor volume
Feed rate
If any one of
these quantities
is unknown it
can be found
from the others
Slide 22
Graphical representation
Slide 23
X
0
A
(1 A ) A (1 X A )
1 X
dX
A
A
(21)
Slide 24
Plug flow reactor
Mixed flow reactor
rA varies with position
rA is constant in reactor
Slide 25
Comparing Plug flow reactor with batch reactor
Plug flow reactor
identical
Batch reactor
t N A0
X
0
A
dX
A
( rA )V
C A0
X
0
A
dX
A
rA
Slide 26
By comparing the performance expressions of
batch reactor with those of plug flow reactor:
(1) For system of constant density
(constant-volume batch or constantdensity plug flow) the performance
equations are identical, for plug
flow is equivalent to t for the batch
reactor, and equation can be used
interchangeably.
Slide 27
(2) For systems of changing density there
is no direct correspondence between
the batch and the plug flow equations
and the correct equation must be used
for each particular situation. In this
case the performance equations cannot
be used interchangeably.
Slide 28
Example 5.3 Mixed flow reactor performance
The elementary liquid-phase reaction
With rate equation
Slide 29
☆
稳态操作，可以用书中推导的方程
☆
混合后进料的浓度应是原有浓度的一半
☆
根据A和B的多少来定
☆
密度恒定，相应公式
Slide 30
SOLUTION
The concentration of components in the
mixed feed stream is
These data show that B is the limiting component,
so for 75% conversion of B and ε=0,
For no density change, the performance
equation of Eq.13 gives
desired
Slide 31
The composition in the reactor and in the exit stream is
Slide 32
EXAMPLE 5.5
The homogeneous gas decomposition of phosphine
proceeds at 649℃ with the first-order rate
What size of plug flow reactor operating at 649 ℃ and
460kPa can produce
80% conversion of a
feed consisting of 40
mol of pure
phosphine per hour?
Slide 33
Let A=PH3, R=P4, S=H2. Then the reaction be comes
Homogenous gas reaction
Changing density
First-order reaction
Slide 34
Slide 35
The distinction between space time and residence time
for flow reactor
Holding time
Slide 36
Slide 37
Slide 38
Slide 39
Slide 40
PROBLEMS 5.1, 5.4, 5.5, 5.13
Chapter 5
Ideal Reactors for a Single
Reaction
5.2 steady-state
mixed flow reactor
Slide 2
5.2 steady-state mixed flow reactor
For the mixed flow reactor:
=0
Input = output
+
disappearance by reaction
+
accumulation
the composition is uniform throughout
Element of volume
The whole reactor
Slide 3
Molar feed rate
of component A
Slide 4
Introducing these three terms into Eq.(10), we obtain
rearrangement
Slide 5
xAi
If the feed on which
conversion is based
XAi
If the products are contained in the feed:
(12)
Slide 6
The above expressions have the simple relation
between the four terms:
XA, -rA, V, FA0
Knowing any three allows the forth to be found directly
In design of reactor
The size of reactor
needed for a given duty
The extent of conversion
in a reactor of given size
In kinetic studies
The reaction rate may
be easily obtained
without integration
Make its use very
attractive in kinetic studies
Slide 7
Performance Equations
Batch reactor
t N A0
X
0
A
dX
A
( rA )V
Integrating
For general case
Mixed flow reactor
(11)
Algebraic
For general case
Slide 8
For the case of constant-density
Change conversion
to concentration
Slide 9
Graphical representation
General case
Constant-density system only
Slide 10
First-order reaction, constant density system
CA=CA0(1-XA)
(14)
Slide 11
General case, linear expansion
N A N A 0 (1 X A )
VC A V 0 C A 0 (1 X A )
Slide 12
First-order reaction
Slide 13
Second-order reaction
rA kC
2
A
and
A 0
The performance equation becomes
k
C A0 C A
C
or
CA
1
2
A
1 4 kC A 0
2 k
(*)
Slide 14
5.3 steady-state plug flow reactor
The composition of the fluid varies
from point to point along a flow path
The material balance for a differential
element of volume dV
=0
Input = output
+
disappearance by reaction
+
accumulation
Slide 15
For the differential element of volume
– cylinder with the thickness of dl
Slide 16
(16)
Slide 17
(16)
This is a differential equation, for the reactor as a
whole the expression must be integrated.
rA is dependent on the concentration or conversion
of materials. Grouping the terms accordingly, we
obtain
Slide 18
Thus
Batch reactor
t N A0
X
0
A
dX
A
( rA )V
(3)
Slide 19
If the feed on which conversion is based, or,
there are products in the feed
XAi: A conversion in the feed (inlet)
XAf: A conversion in the outlet
Slide 20
For the special case of constant-density system
and
The performance equation can be expressed in
terms of concentration
Slide 21
Eqs. 17 to 19 can be written either in terms of
concentrations or conversions.
For systems of changing density, it is more
convenient to use conversions.
Whatever its form, the performance equations
interrelate:
Rate of reaction
Extent of reaction
Reactor volume
Feed rate
If any one of
these quantities
is unknown it
can be found
from the others
Slide 22
Graphical representation
Slide 23
X
0
A
(1 A ) A (1 X A )
1 X
dX
A
A
(21)
Slide 24
Plug flow reactor
Mixed flow reactor
rA varies with position
rA is constant in reactor
Slide 25
Comparing Plug flow reactor with batch reactor
Plug flow reactor
identical
Batch reactor
t N A0
X
0
A
dX
A
( rA )V
C A0
X
0
A
dX
A
rA
Slide 26
By comparing the performance expressions of
batch reactor with those of plug flow reactor:
(1) For system of constant density
(constant-volume batch or constantdensity plug flow) the performance
equations are identical, for plug
flow is equivalent to t for the batch
reactor, and equation can be used
interchangeably.
Slide 27
(2) For systems of changing density there
is no direct correspondence between
the batch and the plug flow equations
and the correct equation must be used
for each particular situation. In this
case the performance equations cannot
be used interchangeably.
Slide 28
Example 5.3 Mixed flow reactor performance
The elementary liquid-phase reaction
With rate equation
Slide 29
☆
稳态操作，可以用书中推导的方程
☆
混合后进料的浓度应是原有浓度的一半
☆
根据A和B的多少来定
☆
密度恒定，相应公式
Slide 30
SOLUTION
The concentration of components in the
mixed feed stream is
These data show that B is the limiting component,
so for 75% conversion of B and ε=0,
For no density change, the performance
equation of Eq.13 gives
desired
Slide 31
The composition in the reactor and in the exit stream is
Slide 32
EXAMPLE 5.5
The homogeneous gas decomposition of phosphine
proceeds at 649℃ with the first-order rate
What size of plug flow reactor operating at 649 ℃ and
460kPa can produce
80% conversion of a
feed consisting of 40
mol of pure
phosphine per hour?
Slide 33
Let A=PH3, R=P4, S=H2. Then the reaction be comes
Homogenous gas reaction
Changing density
First-order reaction
Slide 34
Slide 35
The distinction between space time and residence time
for flow reactor
Holding time
Slide 36
Slide 37
Slide 38
Slide 39
Slide 40
PROBLEMS 5.1, 5.4, 5.5, 5.13