Conversion and Reactor Sizing - Reactor Engineering Course Block 2

CH2: Conversion and Reactor Sizing
RE2
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Chemical Reaction Engineering Methodology

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Content
• Section 1: Conversion and Molar Balances
– Conversion
– Molar Balances in terms of Conversion
– CSTR & PFR vs. PBR (Gaseous phase)
• Section 2: Reactor sizing
– Sizing of a CSTR
– Sizing of a PFR
– CSTR vs. PFR sizing
• Section 3: Reactor in series
– CSTR in series
– PFR in series
– CSTR+PFR in series and its sequence
• Section 4: Space-Time and Spatial-Velocity
– Space-Time
– Spatial-Velocity

Section 1
Conversion and Molar Balances

Introduction to Conversion
• We choose the limiting reactant as a basis of
calculation
• Relate to all other species
• Then we quantify “how far” does the reaction
goes
aA+bB  cC + dD
A+b/a ·B  c/a ·C + d/a ·D

Definition of Conversion
• XA= Moles of A reacted / Moles of A fed
• By logic means… 0 <= XA <= 1
• Note that as X increases, the reaction converts
more reactant of A to (a) given product(s)

Conversion Example
• 284.4 gmol of A is fed to a reactor. After 4 hours,
the outlet stream contains 20.3 gmol of A… What
is the conversion
– a) moles of A reacted b) moles of A fed
– Moles of a reacted = (284.4– 20.3)gmol = 264.4 gmol
– Moles fed (is given in the data) = 284.4 gmol
– XA= 264.4/284.4 = 0.9296 as fraction or 92.96%
XA= Moles of A reacted / Moles of A fed

Why Conversion?
• It help us to establish a “standard”
– e.g. not speak of flows (there are many flows possible)
– conversion is only between 0 and 1
• Its easier to get a 100% of reaction progress
• Example:
– 100 gmol of A are fed and 70 gmol of A are transformed to
products
• 70% conversion is achieved
– 35.4 gmol of A are fed and 12.4 gmol of A are transformed to
products
• 35% conversion is achieved
– We could say that the first reaction is 2 times efficient as the
second one, independent of the flows

Molar Balances of Reactors in terms of Conversion
• We’ve seen before how to change from Flows
to Concentration (by volume or volumetric
flow rate)
• This time we use the definition of conversion
to transform all the design equations to
Equations in terms of Conversion!
• This is very useful
• Specially in one-reaction reactors

Batch Reactor & Conversion
XA= moles of A reacted / moles of A fed
NA= moles of A at the outlet (exit or final)
NA0 = moles of A at the inlet (initial)
Moles of A reacted = NA0-NA
Moles of A fed = NA0
XA= (NA0-NA)/NA0 or express it for NA (moles of A at any moment)
NA = NA0(1-XA)

• Now lets apply these concepts and equations to our existing
Design Equations

Differential From 

Integral Form 

Continuous Flow Reactors & Conversion
XA= moles of A per unit time reacted / moles of A per unit time fed
FA= moles of A at the outlet per unit time (exit or final)
FA0 = moles of A at the inlet per unit time (initial)
Moles of A reacted per unit time = FA0-FA
Moles of A fed per unit time = FA0
XA= (FA0-FA)/FA0 or express it for FA (moles of A per unit time, any moment)
FA = FA0(1-XA)

Continuous Flow Reactors & Conversion
• Now lets apply these concepts and equations to our
existing Design Equations
– CSTR
– PFR
– PBR
• The conversion equation is exactly the same!

CST-Reactor & Conversion
Substitute this into original equation

Plug Flow Reactor & Conversion

Differential Form

Integral Form

• Very similar to PFR…
Packed Bed Reactor & Conversion
Differential Form
of a PBR 

Packed Bed Reactor & Conversion
Integral Form of a PBR

Exercise: Which one is which?
Batch Reactor
CSTR
PFR
PBR

Summary of Reactor in terms of Conversion
Batch Reactor
CSTR
PFR
PBR

Problems
• Go to next Section: Reactor Sizing
• Here we will apply the equations we just got

Reactor Sizing
• It is normal to calculate the size needed for a
certain reaction/process to achieve certain
conversion XA
• The size is an important factor and it implies $
• The bigger the reactor gets, the higher the price

CSTR Sizing
• Sizing implies calculation of Volumes…
• Normally you calculate a volume
– With this volume and the type of reactor you:
• Choose a Diameter
• Choose a Height/Length of the reactor
• In a CSTR, the Volume is represented in a
graph by the “Rectangle”
– The height is Fa0/-rA
– The base is the conversion XA

CSTR Sizing
• It is common that the student thinks the
volume is the “shaded” area under the curve
• This is not the case
• A CSTR is an Algebraic calculation, it will never
be an area under the curve
• A CSTR’s Volume is always the area of the
rectangle
– Height
– Base

CSTR Sizing
• Examples for different rates of reaction “shapes”
• The red-marked area is the “Volume” of that CSTR
tank
• 80% Conversion in this case…

CSTR Sizing
• Note that the data of rate of reaction does not
depends on the reactor!
• It can be used for all types of reactors!
• Even though you use one specific reactor
– It applies to any reactor!

CSTR Sizing
• Example 2-2 Sizing CSTR
CH2: Elements of Chemical Reaction Engineering
H. Scott Fogler (4th Edition)

CSTR Sizing

CSTR Sizing
• B) Shade the Volume in the graph

PFR Sizing
• Sizing a PFR is a little bit more complex than CSTR due to the “Integral”
concept
• This is NOT an algebraic calculation
• It is common that the student thinks the area under the curve is the
volume
– He is RIGHT!
• The area under the curve of the rate of reaction will give you the volume

PFR Sizing
• Many rates of reaction get “under”
• The area is generally lower as a CSTR
• Take care, this is NOT always the case
– When not?
– We will see this case later on…

PFR Sizing

PFR Sizing
• A)

PFR Sizing

PFR SizingFlow = 4 mol/s

PFR Sizing
Flow = 4 mol/s

PFR Sizing
• A)

PFR Sizing
• Volume vs. Different Conversions

PFR Sizing
• Volume vs. Rate of Reactions

Comparing CSTR vs. PFR
• If you’ve done the problems, you will see that when
we use CSTR or PFR the volumes change for the
SAME reaction!
• This is due to the “Volume” calculation in our Design
Equations
– CSTR  Algebraic Concept (b·h)
– PFR  Integral Concept (area under curve)

Comparing CSTR vs. PFR
• But when do we use CSTR and PFR?
• Main concept
– Assume that minimizing the Volume is priority!
– Ignore all costs associated to engineering the
project!
• You WILL need to have the rates of reactions
for every conversion (at least intervals)

CSTR vs. PFR Sizing
• CSTR Volumes (min, NA, max)
• PFR Volumes (min, NA, max)

CSTR vs. PFR Sizing
• Lets analyze these two cases

CSTR vs. PFR Sizing
• Lets analyze these two cases
Green  PFR Volume
Pink  CSTR Volume

CSTR vs. PFR Sizing Exercise

PFR volume for
0%

PFR volume for
20%

PFR volume for
40%

PFR volume for
60%

PFR volume for
80%

CSTR volume for
0%

CSTR volume for
20%

CSTR volume for
40%

CSTR volume for
60%

CSTR volume for
80%

Section 3
Reactor in Series

Reactor in Series
• Now lets suppose we have different existing
reactors in the plant
• We could arrange them to maximize our
production/conversion
• What order are the best orders?
– PFR + PFR
– CSTR + CSTR
– CSTR + PFR
– PFR+ CSTR
• The fun starts here!

Single Pass Conversion vs. Global Conversion
• Single Pass conversion: Conversion of ONE
unit (one reactor)
– XAi= Moles reacted in that reactor / Moles fed to that reactor
• Global Conversion: Conversion so far
– XA= Moles reacted so far / Moles fed to first reactor

CSTR in Series
NOTE X2: Global
Conversion to this point

CSTR in Series

CSTR in Series
• We get these two equations…
Similar:
FA0
Rate of Reactions valued @ Outlet
conversions: 40% and 80%

CSTR in Series
TIP:
a) Calculate Volume for CSTR #1 (easy)
b) Calculate Volume for CSTR #2 (not so easy)

CSTR in Series
Volume of
CSTR #1
Volume of
CSTR #2
Total Volume

CSTR in Series
• Note that
– For 1 CSTR to get 80% Conversion  6.4 m3
– For this new arrangement (2 CSTR @ 40% and
80%) We needed  4.02 m3 which is 30% less
• Is it worth it?
• Reactor Sizing is not the only $$ to decide!

CSTR in Series
• Try 3 and more CST-Reactors in series
• If you want to see examples like this, go to the
web page!
• Check out the Reactor Engineering Course!

Approximation of a PFR with CSTR
• What would happen if we add a lot of CSTR in
our process?
• The volume will approximate that of a PFR
• Similar to trapezoidal rule (rectangles in this
case)

CH2: Elements of Chemical
Reaction Engineering

• Therefore
• If N is the number of CSTR reactors placed in
Series
• And N  infinity
• Then the Volume required for those CSTR in
total is the same as ONE PFR

More Problems for CSTR/PFR sizing?
• Need more Problems? Check out the course!
– www.ChemicalEngineeringGuy.com
• Courses
–Reactor Engineering
»Solved Problems Section
• CH2 – Conversion and Reactor Sizing

PFR in Series
• In the case of PFR, is not that “amazing”
• The distribution is exactly the same!
• Why? Mathematically:
And so on…

1 PFR

2 PFR

3 PFR

PFR in Series Exercise
Tips:
a) Calculate Reactor Volume #1
b) Calculate Reactor Volume #2
c) Calculate Reactor Volume for that of 80% done in only ONE PFR

• Analyze the “X” intervals
• From 0.0 to 0.8

• We could actually continue adding…
0 to 0.1
0.1 to 0.2
0.2 to 0.4
0.4 to 0.6
0.6 to 0.7
0.7 t 0.8 Total Volume
would be = 2.1 m3

2 PFR
Total Volume
would be = 2.1 m3

1 PFR
Total Volume
would be = 2.1 m3

CSTR + PFR Series
• Now, things get interesting
• The combination of these two types of
reactors will help us to minimize the volume
required to carry on a reaction to a certain
conversion

Best vs. Worst Arrangements
Min. Volume Max. Volume

CSTR + PFR Series: Exercises

Flow of 50 mol/s
CSTR PFR CSTR

• Tips
– Calculate Volume of CS-Reactor #1
– Calculate Volume of PFR #2
– Calculate Volume of CST-Reactor #3
– Add all the volumes
– Analyze why would they choose that setting

More Problems for CSTR and PFR in series?
• Courses

Section 4
Space-Time and Spatial-Velocity

Space-Time
• Space time is obtained by dividing the reactor
volume by the volumetric flow rate. Then you
get units of TIME
• This “Time” may be the “residence time”
• Time necessary to process one reactor volume
of fluid based on entrance conditions
– Holding Time
– Residence Time
• NOTES: Measured at the entrance/inlet

Space-Time
• Typical Space-Times
– Batch Reactors  minutes to many hours
– CSTR  minutes to hours
– PFR  seconds to 1 hour

Space-Time: Exercise
• Tank Volume = 0.20 m3
• Volumetric Flow rate = 0.01 m3/s
– Space-Time = Reactor Volume / Vol. Flow
• 0.20/0.01 = 20 seconds

Spatial-Velocity
• Is the inverse of the Space-Time
– SV = 1/Space-Time
– SV = Volumetric Flow Rate / Tank Volume
• LHSV and GHSV
– Liquid Hourly S-V
– Gas Hourly S-V

Space-Time & Spatial Velocity

More Problems for Space-Time and Spatial-Velocity?
• Courses

Summary

Questions and Problems
• There are 12 problems in this section.
• All problems are solved in the next webpage
• Courses

End of Block RE2
• We’ve practiced the Design Equations
– Now we have Equations in terms of Flows,
Concentrations and Conversion
• We’ve see how CSTR vary their volume
according to the rate of reaction
• We’ve seen also the PFR Volume, which is the
area under the “Rate of Reaction Function”

End of Block RE2
• We have experimented when it is more
suitable to use a CSTR or a PFR
• We know how to minimize the Volume of the
whole process
• You are familiar with the Space-Time and
Spatial-Velocity concepts

More Information…
• Get extra information here!
– Directly on the WebPage:
• www.ChemicalEngineeringGuy.com/courses
– FB page:
• www.facebook.com/Chemical.Engineering.Guy
– Contact me by e-mail:
• Chemical.Engineering.Guy@gmail.com

Text Book & Reference
Essentials of Chemical
H. Scott Fogler (1st Edition)
Chemical Reactor
Analysis and Design
Fundamentals
J.B. Rawlings and J.G.
Ekerdt (1st Edition)
Elements of Chemical

Bibliography
Elements of Chemical Reaction Engineering
We’ve seen  CH2

Conversion and Reactor Sizing - Reactor Engineering Course Block 2

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Conversion and Reactor Sizing - Reactor Engineering Course Block 2