chemical and biochemical reaction

January 14th, 2016

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The paper contain three similar question with different data. I need to solve question with steps , formula, calculation, and graphs.

08/12/2015
1
University of Huddersfield
Department of Chemistry. School of Applied Sciences
CHAPTER 4:
Design and selection of reactors for one
simple reactions.
Chemical Engineering 3 (SHC4012)
Chemical and Biochemical Reaction Engineering (SIC2023)
SIC2023: Chemical and Biochemical Reaction Engineering
SHC4012: Chemical Engineering 3 CHAPTER 4
• One reactor performing the entire process
• Combinations of reactors performing the entire process
• Recycling reactor
Perfect mix Plug flow
?????? = ????. ?? ???? ?????? = ????. ?? ????
90% of conversion
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SIC2023: Chemical and Biochemical Reaction Engineering
SHC4012: Chemical Engineering 3
4.2.2. Stirred tank reactors working in series.
Although the concentration is uniform in each reactor, there is a change in
concentration as fluid moves from reactor to reactor. If we represent
graphically the conversion obtained for one, three, and ten reactors in series,
using the same total volume, we see the following,
CHAPTER 4
Page 10
SIC2023: Chemical and Biochemical Reaction Engineering
SHC4012: Chemical Engineering 3
4.2.2. Stirred tank reactors working in series.
CHAPTER 4
This suggests that when we increase the number of well mixed
reactors keeping the total volume constant, the behaviour is closer
to _____________________________ PLUG FLOW REACTOR .
Page 10
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SIC2023: Chemical and Biochemical Reaction Engineering
SHC4012: Chemical Engineering 3
4.2.2.1. Series of perfect mix continuous reactors of EQUAL size.
When all the reactors have the same volume, the performance equation for
this system is
??
????
= ??
????
????
= ??
???
-????
???? ???????????????? = ??????
When we work with a series of tanks of equal size, the 3 aims of design are:
• XA at the end of a certain number of reactors of the same volume.
• Number of reactors of fixed volume to achieve a certain conversion.
• Volume of the reactors required when the conversion and the number of
reactors is fixed (less common).
CHAPTER 4
Page 11
SIC2023: Chemical and Biochemical Reaction Engineering
SHC4012: Chemical Engineering 3
Example 4.4. In the autocatalytic reaction of example 4.2, the best
option for 90% of conversion was the plug flow pattern. Compare the
continuous perfectly mixed reactor and the plug flow of example 4.2 at
90% of conversion, with the total volume of two tanks of equal size in
series. What conversion do we obtain after the first tank?
We approach the well mixed tanks to a perfectly mixed contact pattern.
Hence, we need to solve the following equation:
????+??????????,?? = ????????????,?? + ???? ????????,?? =
????,?? – ????,??
?? – ????,?? ????,?? + ??
+
????,?? – ????,??
?? – ????,?? ????,?? + ??
As we have reactors of equal size: ????????????,?? = ???? ????????,??
????,?? – ????,??
?? – ????,?? ????,?? + ??
=
????,?? – ????,??
?? – ????,?? ????,?? + ??
CHAPTER 4
Page 11
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What value of t1
/t2
I need to find in the graph is if both reactors have the same
volume? _____
What value of XA,1 we have?
SIC2023: Chemical and Biochemical Reaction Engineering
SHC4012: Chemical Engineering 3
????,1 = 0.65
????+??????????,?? =
0.65 – 0
1 – 0.65 0.65 + 0.01 +
0.9- 0.65
1 – 0.9 0.9 + 0.01 = 5.57
?????????????? ???? ???? =
??. ????????
????????,??
=
??. ???? × ????
??. ???? × ?????? = ????. ?? ????
CHAPTER 4
??
Two PM of equal size in series
?????????????? ???? ???? = ????. ?? ????
Page 11-12
SIC2023: Chemical and Biochemical Reaction Engineering
SHC4012: Chemical Engineering 3 CHAPTER 4
Comparing the tanks in series
with the other two configurations,
the two tanks in series are
BETTER THAN SINGLE
REACTORS
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SIC2023: Chemical and Biochemical Reaction Engineering
SHC4012: Chemical Engineering 3
4.2.2.2. Series of perfect mix continuous reactors of DIFFERENT size.
When the volumes are different:
??
????
=
??=1
??
????
????
=
??=1
??
???? – ????-1
-????
???? ???????????????? =
??=1
??
????
When we need to design a series of tanks of different sizes we must
consider:
? Conversion for a given reactor system.
? Best reactor system to achieve a given conversion.
CHAPTER 4
… Page 12
SIC2023: Chemical and Biochemical Reaction Engineering
SHC4012: Chemical Engineering 3
Example 4.5. In the same autocatalytic reaction conditions of Example
4.2 and 4.4, if we use two tanks in series of different size, what is the
best configuration to obtain 90% of conversion?
(CA,0 = 200 mol m–3
, CP,0 = 2 mol m–3
, q0 = 30 m3 h
–1
, kA = 0.02 m3 mol–1 h
–1
).
????+??????????,?? ?????? =
????,?? – ????,??
?? – ????,?? ????,?? + ??
+
????,?? – ????,??
?? – ????,?? ????,?? + ??
????+??????????,?? ?????? =
????,??
?? – ????,?? ????,?? + ??. ????
+
??. ?? – ????,??
??. ??????
CHAPTER 4
XA,0 and XA,2 are fixed (0 and 0.90)
We can only optimise the system changing ????,??
Page 13
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SIC2023: Chemical and Biochemical Reaction Engineering
SHC4012: Chemical Engineering 3
????+??????????,?? ?????? =
????,??
?? – ????,?? ????,?? + ??. ????
+
??. ?? – ????,??
??. ??????
CHAPTER 4
What conversion at the
outlet of the first reactor
does it show minimum
volume or space time of
the configuration?
????,?? = ??. ????
Page 13
SIC2023: Chemical and Biochemical Reaction Engineering
SHC4012: Chemical Engineering 3
???????? =
???? ????,?????? – ????,????
????????,?? ?? – ????,?????? ????,?????? + ??
?????????? ?? =
???? × (??. ???? – ??)
??. ???? × ?????? ?? – ??. ???? ??. ???? + ??. ???? = ????. ???? ????
?????????? ?? =
???? × (??. ?? – ??. ????)
??. ???? × ?????? ?? – ??. ?? ??. ?? + ??. ???? = ????. ???? ????
?????????????? ???? ???? = ????. ???? + ????. ???? = ????. ?? ????
Two PM of different size in series
?????????????? ???? ???? = ????. ?? ????
CHAPTER 4
Page 13-14
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SIC2023: Chemical and Biochemical Reaction Engineering
SHC4012: Chemical Engineering 3
Do you think
that we have
an important
improvement
with tanks of
different sizes?
CHAPTER 4
Comparing the four
configurations, the
best option is
2 different size CSTR
NO
Page 14
SIC2023: Chemical and Biochemical Reaction Engineering
SHC4012: Chemical Engineering 3
4.2.3. Reactors of different type working in series.
If reactors of different types are put in series, such as a mixed flow reactor followed by a plug flow
reactor, which in turn is followed by another mixed flow reactor, we may write for the three reactors
??1
????
=
??1 – ??0
-??1

??2
????
=
????
-??
??2
??1
=
????
-??
–
????
-??
??1
??0
??2
??0
??3
????
=
??3 – ??2
-??3

CHAPTER 4
If reactors of different types are put in series, such as a well-mixed
flow reactor followed by a tubular reactor, which in turn is followed by
another well-mixed flow reactor, we may write for the three reactors:
Page 14
??1
????
=
??1 – ??0
-??1
??2
????
=
??1
??2 ????
-??
??3
????
=
??3 – ??2
-??3
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SIC2023: Chemical and Biochemical Reaction Engineering
SHC4012: Chemical Engineering 3 CHAPTER 4
Example 4.6. Following the previous examples of autocatalytic
reaction, find the best combination of one tubular reactor with one
continuous stirred tank reactor to obtain at conversion at 90%.
Approach the reactors to ideal contact patterns. (CA,0 = 200 mol m–3
,
CP,0 = 2 mol m–3
, q0 = 30 m3 h
–1
, kA = 0.02 m3 mol–1 h
–1
).
In this case we have two options:
Page 15
SIC2023: Chemical and Biochemical Reaction Engineering
SHC4012: Chemical Engineering 3
In the option A:
??????+????????????,?? ?????? =
????,?? – ????,??
?? – ????,?? ????,?? + ??
+
??
?? + ??
????
????,?? + ?? ?? – ????,??
????,?? + ?? ?? – ????,??
In the option B:
??????+????????????,?? ?????? =
??
?? + ??
????
????,?? + ??
?? ?? – ????,??
+
????,?? – ????,??
?? – ????,?? ????,?? + ??
CHAPTER 4
??????+???? = ?????? + ??????
??????+???? = ?????? + ??????
Page 15
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SIC2023: Chemical and Biochemical Reaction Engineering
SHC4012: Chemical Engineering 3
Let’s check option A:
What conversion does it show
minimum volume?
??????+????????????,?? ?????? =
????,??
??- ????,?? ????,?? + ??. ????
+ ??. ???? ????
??. ???? ?? – ????,??
??. ?? ????,?? + ??. ????
?????? =
30 × 0.5
0.02 × 200 1 – 0.5 0.5 + 0.01 = 14.7 ??3
?????? =
30 × 0.99
0.02 × 200 ????
0.91 1 – 0.5
0.1 0.5 + 0.01 = 16.2 ??3
?????????????? ???? ????+???? = ?????? + ?????? = ????. ?? + ????. ?? = ????. ?? ????
CHAPTER 4
????,?? = ??. ??
Pages 15-16
SIC2023: Chemical and Biochemical Reaction Engineering
SHC4012: Chemical Engineering 3
Let’s check option B:
What conversion does it show
minimum volume?
??????+????????????,?? ?????? =
????,??
??- ????,?? ????,?? + ??. ????
+ ??. ???? ????
??. ???? ?? – ????,??
??. ?? ????,?? + ??. ????
What does it mean?
It means than there is no
configuration of plug flow +
perfect mix that can improve the
performance of only one plug
flow reactor
CHAPTER 4
????,?? = ??. ??
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SHC4012: Chemical Engineering 3
PM + PF in series
?????????????? ???? ????+???? = ????. ?? ????
PF + PM in series
??????+???? = ?????? = ????. ?? ????
OPTION A OPTION B
CHAPTER 4
1 Tubular 1 CSTR 2 CSTR =Size 2 CSTR ?Size CSTR + Tubular Tubular + CSTR
50.6 74.2 41.8 41.1 30.9 50.6
Page 16
SIC2023: Chemical and Biochemical Reaction Engineering
SHC4012: Chemical Engineering 3
4.3. RECYCLE REACTOR
4.3.1. Performance equation
In certain situations it is advantageous to divide the product stream
from a tubular reactor and return a portion of it to the entrance of the
reactor. With this configuration it is possible that a tubular reactor
acquires characteristics of a well mixed continuous reactor. This
situation is frequently considered in the design of catalytic reactors.
Page 17
CHAPTER 4
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SIC2023: Chemical and Biochemical Reaction Engineering
SHC4012: Chemical Engineering 3 CHAPTER 4
Page 17
This recycle ratio can be made to vary from zero to infinity. This means that
as the recycle ratio is raised the behaviour shifts from plug flow (R = 0) to
perfectly mixed flow (R = 8). Thus, recycling provides an alternative to
obtain various degrees of backmixing in a tubular reactor.
We need to define a new parameter, ????,??
‘
, that will be the feed rate of A if
the stream entering the reactor (fresh feed + recycle) were unconverted.
Imagine that instead of the point Q of Figure 4.6 we had the following
configuration:
Figure 4.7
SIC2023: Chemical and Biochemical Reaction Engineering
SHC4012: Chemical Engineering 3
To obtain the performance equation for our reactor the reaction system Page 18
can be treated as it is shown in Figure 4.8:
And our reference inlet will now be F’A,0, defined as,
????,0
‘ =
?? ??h????h ?????????? ?????????? ???? ????
?????????????????????? ?????????????? ???????????? +
?? ???????????????? ????
????????h ????????
????,0
‘ = ????,0 + ??????,0 = (1 + ??)????,0 (4.3.2)
CHAPTER 4
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SIC2023: Chemical and Biochemical Reaction Engineering
SHC4012: Chemical Engineering 3
As we need to know the performance equation of our plug reactor with
recirculation we need to integrate the general performance equation
between XA,1 and XA,2
According to our scheme of Figure 4.8 it is like to integrate between X’A,1
and X’A,2. Hence,
?? = -????,0
‘
????,1
‘
????,2
‘
??????
????
Page 18
CHAPTER 4
SIC2023: Chemical and Biochemical Reaction Engineering
SHC4012: Chemical Engineering 3
?? = -????,0
‘
????,1
‘
????,2
‘
??????
????
?? = -????,0 ?? + 1 ??
??+1
????,4
????,4 ??????
????
????,0
‘ = ????,0 + ??????,0 = (1 + ??)????,0
????,2
‘ =
????,0
‘ – ????,2
????,0
‘ =
????,0
‘ – ????,4 + ????,3
????,0
‘ =
????,0
‘ – ????,4 + ??????,4
????,0
‘ =
????,0
‘ – ????,4 1 + ??
????,0
‘
If we use the equation 4.3.2 to relate the Figure 4.7 with Figure 4.5:
????,2
‘ =
????,0
‘ – ????,4 1 + ??
????,0
‘ =
(1 + ??)????,0 – ????,4 1 + ??
(1 + ??)????,0
=
????,0 – ????,4
????,0
= ????,4
????,2
‘ = ????,4
????,1
‘ =
????,0
‘ – ????,1
????,0
‘ =
????,0
‘ – ????,0 + ????,3
????,0
‘ =
1 + ?? ????,0 – ????,0 – ??????,4
(1 + ??)????,0
????,1
‘ =
????,0 + ??????,0 – ????,0 – ??????,4
(1 + ??)????,0
=
?? ????,0 – ????,4
(1 + ??)????,0
=
??????,0????,4
(1 + ??)????,0
=
??????,4
1 + ??
????,1
‘ =
??
1 + ??
????,4 (4.3.3)
Page 18 (4.3.4)
CHAPTER 4
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SIC2023: Chemical and Biochemical Reaction Engineering
SHC4012: Chemical Engineering 3
The area of this integral is
??
??+1
????,4
????,4 ??????
????
= ????,4 –
??
?? + 1
????,4
1
-?? ??
In with the value of ?? ?? is the average value of reaction rate in
the range XA,1 and XA,2. Then
??????
????,0
= ?? + 1 ????,4 –
??
?? + 1
????,4
1
-?? ??
= ????,4
1
-?? ??
?????? = ?? + 1 ????,4 –
??
?? + 1
????,4
????,0
-?? ??
= ????,4
????,0
-?? ??
(4.3.5)
(4.3.6)
CHAPTER 4
SIC2023: Chemical and Biochemical Reaction Engineering
SHC4012: Chemical Engineering 3
So the graphical representation of this reactor is
The area in grey is the value of the integral times FA,0 of the equation 4.3.4. The rectangle
is the volume of the recycling reactor.
CHAPTER 4
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SIC2023: Chemical and Biochemical Reaction Engineering
SHC4012: Chemical Engineering 3 CHAPTER 4
SIC2023: Chemical and Biochemical Reaction Engineering
SHC4012: Chemical Engineering 3
4.3.2. Optimal value of R
When we observe graphically how R
influences the volume, it can be inferred
that there will be an optimum recycling
ratio for minimum volume.
• In the case of kinetics in which the
curve FA,0/(-rA
) vs XA
always increases,
the best Ratio is R=0 (Plug flow)
• When the kinetic shows a minimum in
the curve FA,0/(-rA
) vs XA
the recycling
can be optimised.
R will be optimum when:
????,0
-????,1
=
????,0
-?? ??
If we represent graphically
CHAPTER 4

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