Introduction and Molar Balances - Reactor Engineering Course Block 1

CH1: Introduction & Molar Balances
RE1
Chemical Engineering Guy
www. Chemical Engineering Guy .com

Content
• Section 1: Introduction to Reactors
– Types of Reactors
– Reactor Kinetics
– Uses of Reactors
– Rate of Reaction and the Molar Balance Equation
• Section 2: Molar Balances of Reactors
– Batch Reactor
– Continuous Stirred Tank Reactor (CSTR)
– Plug-Flow Reactor (PFR or Tubular Reactor)
– Packed-Bed Reactor (PBR)

Section 1
Introduction to Reactors

What is a Reactor?
• Equipment used to carry on a
chemical reaction
• Chemical engineers design
reactors to maximize net present
value for the given reaction.

What is a Reactor?
• Designers ensure that the reaction proceeds
– highest efficiency towards the desired output
product
– producing the highest yield of product
– require the least amount of money to purchase
and operate.

Why do we need reactors?
• To convert materials to other useful
materials!
• Control reactions in a safe manner
• Have a specific unit for that “operation”
• Easier to maximize efficiency

Types of Reactor
• Batch vs. Semi-Batch vs. Continuous
• Catalytic vs. Non-Catalytic
• Homogeneous vs. Heterogeneous
• By category
– Batch Reactor
– Semi-continuous Reactor
– Plug Flow Reactor (PFR)
– Packed Bed Reactor (PBR)

Industrial Reactors
CST-Reactor

Industrial Reactors
CST-Reactor + Jacket System

Industrial Reactors
PF-Reactor

Industrial Reactors
PB-Reactor

Lab Reactors

Micro-Reactors

Thermal Insulation

CH1 - Break
• We’ve seen so far…
– Section 1: Introduction to Reactors
– Types of Reactors
– Reactor Kinetics
– Uses of Reactors
– Rate of Reaction and the Molar Balance Equation
• What’s left…
– Section 2: Molar Balances of Reactors
• Batch Reactor
• Continuous Stirred Tank Reactor (CSTR)
• Plug-Flow Reactor (PFR or Tubular Reactor)
• Packed-Bed Reactor (PBR)

Section 2
Molar Balances of Reactors

Section 2: Molar Balances of Reactors
• Molar Balance Methodology
• Molar Balance Equation
– Batch Reactor
– Plug-Flow Reactor (PFR or Tubular Reactor)
– Packed-Bed Reactor (PBR)
• Flows vs. Concentrations
• Summary

Chemical Reaction Engineering Methodology

Chemical Reaction Engineering Methodology
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Chemical Reaction
• A chemical reaction takes place when a
detectable number of molecules of one
or more species have lost their
“identity” and assumed to form new
structure or configuration of atoms
• Mass is not created nor destroyed
– Molecules change in structure

Rate of Reaction -rA
• Tells us how fast a number of one chemical
species are being consumed to form another
chemical species
• Chemical species  any chemical component
or even an element
• We can call this phenomena also as
“disappearance” of species
– This is actually a transformation

• Applied example:
–The rate of reaction of A (disappearance f a
species “A”)
• Is the number of A molecules that lose their chemical
identity per unit time per unit volume
• This is done through the breaking and subsequent re-
forming of chemical bonds
• This is done while the chemical reaction takes place

• Units of Rate of Reaction of A
–Moles of A per unit volume per unit time
• Mol A / (m3·s)
• Mol A / (L·s)
• gmol A / (dm3·min)

• A + 2B  C + D
• -rA= 1 gmol of A/ (dm3·s)
• rA= -1 gmol of A/ (dm3·s)
• -rB= 2 gmol of B/ (dm3·s)
• rC=1 gmol of C/ (dm3·s)
• -rD= -1 gmol of D/ (dm3·s)

• A + 2B  C + D
• -rA= 1 gmol of A/ (dm3·s)
• rA= -1 gmol of A/ (dm3·s)
• -rB= 2 gmol of B/ (dm3·s)
• rC=1 gmol of C/ (dm3·s)
• -rD= -1 gmol of D/ (dm3·s)
1 gmol of A “disappears”
1 gmol of A “appears”
2 gmol of B “disappear”
1 gmol of C “appears”
1 gmol of D “appears”

• Rate of Reaction of A  –rA
• Rate of Production of A  rA
– Rate of Reaction of A = -Rate of Production of A
– So you’ll get
• -rA = -(rA)
• -rA = -rA

Rate of Reaction –r’A
• We will be using a speciall rate of reaction for
packed bed reactors
• This is just an introduction, we will analyze it
further on the PBR section
• -r’A is essentially the same…
– instead of basing our “Volume” of the reactor, we
base it to the “mass” of our catalyst (bed)
• -r’A [=] gmol A / (kg cat · s)

Rate of Reaction –r’A
• -rA [=] gmol A / (dm3 · s)
Vs
• -r’A [=] gmol A / (kg cat · s)

• Important NOTE!
• The rate of Reaction does NOT depends of the
reactor!
• Makes sense… one reaction will be carried, no
matter if the reactor is nice, big, small, long,
continuous, batch operated, etc.
• Do not confuse the Molar Balances with the
Rates of Reactions!

• The Rate of Reaction depends
–Solely in the material being reacted
–Reaction conditions (T, P, etc.)
–Type of catalyst
–Species Concentration
• AT that specific point of space

General Mole Balance Equation
• To perform a mole balance
– Specify the boundary of the system
– Specify a “species” in this case we use “j”

Mass Balance on Species J
Substitute Pj-Cj with Gj
Substitute Inlet, Outlet and Accumulation terms

Our master equation for any system, any reactor
This is the “General Mole Balance Equation”

The concept of Generation Gj
• Units [=] gmol of j being generated / time
– Generated
+ if produced or
– if being reacted
• NOTE
–If all the system is spacially uniform
throughtout the system
• Then Gj = rj·V
• rj = rate of reaction of j

• What if our rate of reaction or volume changes
through the system?

• We would have to calculate each Generation
individually and then add them up for the
“total” or “overall” generation of the system

• Adding each one…
• Substituting Gj= rj·V

• Applying the correct limits to n  infinity and
Volume as a differential Volume in space

• By definition of Integral…
• We get an equation of Generation that takes
every generation term in the space of the system

• Substituting the Generation concept of our
master Equation

• Now we can apply this equation to many reactors!
Actual Master Equation for Molar Balances in Reactors

Application of the General Molar
Balance Equations to Reactors
• We have our “master” equation
• Let’s apply this equation to our reactors
– Batch Reactor
– Continuous Stirred Tank Reactor
– Plug Flow Reactor
– Packed Bed Reactor

Batch Reactor
• Description
– Typical for small-scale operations such as labs
– Useful for testing new processes or conditions
– Manufacture of expensive products
– If Continuous Process is not possible
– Higher conversions
– High cost labor
– Variation of products form batch to batch
– Difficult to scale-up

Batch Reactor
• Operation
– The reactor gets charged
– The reactor starts operating (reacting)
– The reactor gets discharged at certain point of
time
– The reactor is cleaned
– Another cycle starts
– Transient state!  Accumulation term

Batch Reactor GMBE
• General Mole Balance Equation on a Batch
Reactor

Batch Reactor GMBE
Let’s develop that integral…

Batch Reactor GMBE

Batch Reactor GMBE
Batch Reactor Design Equation
*Charging and Discharging the Reactor is not analyzed!

Batch Reactor Example
• Lets suppose we have
A  B
• Calculate the time needed to achieve certain
amount of NA

Batch Reactor GMBE
A  B
Apply for Species “A”

Batch Reactor GMBE
A  B
Separate and Integrate

Batch Reactor GMBE
A  B
Not typical in literature

Batch Reactor GMBE
A  B
Lets force -rA

Batch Reactor GMBE
A  B
Integral Form of a Batch Reactor Design Equation

Moles of A vs. Moles of B in time

Continuous Flow Reactors MBE
• Continuous Stirred Tank Reactor CSTR
• Plug Flow Reactor PFR
• Packed Bed Reactor PBR
• Many others may be also included
• Typical operation is Steady State!

CSTR
• Description
– There is at least one inlet of reactive material
– There is at least one outlet of product material
– No accumulation in the tank (will not spill)
– Steady State, no integrals!
– Continuously and Perfectly stirred
– Liquid phase reaction
– Temperature and concentrations are the same in
all the vessel (idealistic)

CSTR
• In theory, concentration in the top is the same
as the outlet

CSTR
• Operation
–Designed for long time continuous
operation
–It needs lot of time to achieve
concentration, conversion, temperature,
pressure, levels and other variables due to
the size

CSTR
• Operation
–Start-up is the process in which this type of
tanks are started up… This process is a
transient state
–Operation is in steady state
–Change of conditions is transient state
–Shutting-down is also a transient state

CSTR GMBE
• Lets apply the General Molar Balance Equation
Steady State  no Accumulation

CSTR GMBE
No variation due to perfect mixing

CSTR GMBE
Forcing -rj

CSTR GMBE
Our CSTR Design Equation

Plug Flow Reactor
• Description
– Also known as Tubular Reactors
– Cylindrical pipe reactors
– Operated in steady state
– Often gas-phase reactions
– Reactants are consumed as they pass through
pipe
– Simplest form of reactor
– Concentration varies across the pipe length!

Plug Flow Reactor
• Operation
– Plug Flow is forced
– No radial variation throughout the pipe
– Pipe incrustation might happen, there is a
maintenance program to follow
– Easy/Cheap to buy, operate
– No high conversions

Plug Flow Reactor
Revisiting “Plug Flow” vs. “Laminar Flow”

Plug Flow Reactor
• Lets analyse one tube… and one section of it

Plug Flow Reactor
No accumulation (Continuous Process)

Plug Flow Reactor
There are two problems
• Fj0 and Fj
• rj varies with “length”

Plug Flow Reactor
Lets analyze this “disk”

Plug Flow Reactor
The value of V at the initial part
of the disk
The value of V+ΔV at the final
part of the disk
Fj valued in “V”, the initial part of
the disk
Fj valued in “V+ΔV”, the final part
of the disk

Plug Flow Reactor
Re-evaluate Inlets, Outlets, and rj·Volume

Plug Flow Reactor
If you are good at math… this has a familiar expresion of a derivtive
Lets “force” the derivative… get the limit of the ΔV be 0

Plug Flow Reactor
We get this cool derivative! 
Lets integrate!

Plug Flow Reactor
And lets force once again -rA

Plug Flow Reactor
This is our PFR master equation!

Packed Bed Reactor
• Description
– Heterogeneous reactions
– Fluid-Solid phases
– Ideal for Catalyst bed reactions

Packed Bed Reactor
• Description
– We base our study in the reactor’s catalyst mass
rather than the reactor’s volume
– Steady State Operation, no accumulation
– If gases; there is pressure drop
– Concentration of product(s) changes with length

Packed Bed Reactor
• Operation
–Typically a clean catalyst is placed
–The catalyst bed is fixed so it does not moves
as fluid passes by
–The inlet is open… Fluid starts entering the
reactor

Packed Bed Reactor
• Operation
–The fluid interact with the catalyst bed
–There is reactions, the products go to the
outlet

Packed Bed Reactor
• Operation
–The catalyst is sometime saturated; it must be
changed
–The catalyst may be “poisoned” so it must be
changed as well

Packed Bed Reactor and –r’A
• We are talking about “Mass of Catalyst”
• Now we analyze –r’A
• Consider –rA [=] moles of A / Vol·time
• Consider –r’A [=] moles of A / mass cat·time
-rA x Volume of Reactor = moles of A per unit time
-r’A x Mass of Catalyst = moles of A per unit time

No accumulation  continuous process in steady state

Lets check out that differential
volume/mass disk (pink)

As in the PFR… We force
that “Derivative” concept

Which is very similar to the PBR!

NOTE: This equation is only valid if there is NO pressure
drops (we will deal with that in further chapters)
Master Equation for PBR

Flow vs. Concentration
• We’ve done our balances using flow rates
– Flow Rate [=] gmol of A / time
• In Reactor Engineering, specially at lab scale,
we use a lot Concentration terms
– Concentration [=] gmol of A / volume of solution

• How do we relate them!?
• One uses time
• The other uses volume of
solution

• The relationship between them is of course
volume/time
• We know it in chemical engineering as
volumetric flow rate
– Volumetric Flow [=] volume / time

From Moles to Concentration
Batch
Design Equation of a Batch Reactor
Substituting this formula!
You get this equation… 
You get a First-Order Differential Equation 
If Volumetric Flow is constant, take it out 

From Flow to Concentration
CSTR
Design Equation of a CSTR 
Substitute all Flows with Concentration·Volumetric Flows 
If inlet and outlet volumetric flow rates are the same… 
You end up with Concentration terms 

PFR
Design Equation of a PFR
Substitute all Flows with
Concentration·Volumetric Flows 
If inlet and outlet volumetric flow rates are
the same the it is a constant… 
You end up with Concentration terms 

PFR
If you continue to develop the equation 
And Integrate to find out the limits 
You end up with this Equation for
“Volume”

PBR
The design Equation for a PBR
Substitute Flows in terms of
Concentration 
If volumetric flow is constant, take
it out of the derivative 

PBR
If you continue to develop it…
Integrating limits
Our final equation (forcing –rA)

Examples of Continuous Reactors
• Given the next reaction
– Reaction A  B
– Volumetric flow = 10 dm3/min
– Volumetric flow at inlet is the same at outlet
– Rate of reaction –rA = kCA k = 0.23 min-1
a) Reactor volume (do not substitute data, just variables)
b) Reactor Volume if the exiting concentration is 10% of the entering
concentration
c) What reactor would you choose?
Do it for CSTR, PFR… PBR (need more data)

• You get this equation…
• The volume for a CSTR

• You get this equation…
• The volume for a PFR

Definitively choose PFR due to lower volume requirement

Molar Balances of Reactors Summary
Concentratrion

Questions and Problems
• There are 22 problems in this section.
• All problems are solved in the next webpage
– www.ChemicalEngineeringGuy.com
• Courses
–Reactor Engineering
»Solved Problems Section
• CH1 – Introduction and Molar Balances

End of Block RE1
• We’re done with this chapter!
• It is short, but SUPER important
• You learned how to do General Molar
Balances on the most typical Reactors
• You have now design equations for different
types of reactor (you can calculate, flows,
volumes and even rate of reactions)

End of Block RE1
• This is just the first step on the course
• We’ve seen the first step for the Reactor
Engineering Methodology:

End of Block RE1
• You don’t need to remember how to get each
equation
– Even though it helps a lot
• Only be sure where does it comes from
– The General Molar Balance Equation
• And know when you can and can’t use it
– Idealities, types of process, etc.

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
Reaction Engineering
H. Scott Fogler (1st Edition)
Chemical Reactor
Analysis and Design
Fundamentals
J.B. Rawlings and J.G.
Ekerdt (1st Edition)
Elements of Chemical
Reaction Engineering
H. Scott Fogler (4th Edition)

Bibliography
Elements of Chemical Reaction Engineering
H. Scott Fogler (4th Edition)
We’ve seen  CH1

Introduction and Molar Balances - Reactor Engineering Course Block 1

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