introduction and molar balances - reactor engineering course block 1
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CH1: Introduction & Molar Balances
RE1
Chemical Engineering Guy
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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)
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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.
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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.
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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
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Types of Reactor
• Batch vs. Semi-Batch vs. Continuous
• Catalytic vs. Non-Catalytic
• Homogeneous vs. Heterogeneous
• By category– Batch Reactor
– Semi-continuous Reactor
– Continuous Stirred Tank Reactor (CSTR)
– Plug Flow Reactor (PFR)
– Packed Bed Reactor (PBR)
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Industrial Reactors
CST-Reactor
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Industrial ReactorsCST-Reactor + Jacket System
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Industrial Reactors
PF-Reactor
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Industrial Reactors
PF-Reactor
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Industrial Reactors
PB-Reactor
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Industrial Reactors
PB-Reactor
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Lab Reactors
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Lab Reactors
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Lab Reactors
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Lab Reactors
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Lab Reactors
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Lab Reactors
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Micro-Reactors
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Micro-Reactors
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Thermal Insulation
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Thermal Insulation
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Thermal Insulation
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Thermal Insulation
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Thermal Insulation
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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)
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Section 2
Molar Balances of Reactors
Section 2: Molar Balances of Reactors
• Molar Balance Methodology
• Molar Balance Equation
– Batch Reactor
– Continuous Stirred Tank Reactor (CSTR)
– 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
Rate of Reaction -rA
• 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
Rate of Reaction -rA
• 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)
Rate of Reaction -rA
• 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)
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Rate of Reaction -rA
• 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”
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Rate of Reaction -rA
• 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)
Rate of Reaction -rA
• 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!
Rate of Reaction -rA
• 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”
General Mole Balance Equation
Mass Balance on Species J
Substitute Pj-Cj with Gj
Substitute Inlet, Outlet and Accumulation terms
General Mole Balance Equation
Our master equation for any system, any reactorThis 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
The concept of Generation Gj
• What if our rate of reaction or volume changes through the system?
The concept of Generation Gj
• We would have to calculate each Generation individually and then add them up for the “total” or “overall” generation of the system
The concept of Generation Gj
• Adding each one…
• Substituting Gj= rj·V
The concept of Generation Gj
• Applying the correct limits to n infinity and Volume as a differential Volume in space
The concept of Generation Gj
• By definition of Integral…
• We get an equation of Generation that takes every generation term in the space of the system
The concept of Generation Gj
• Substituting the Generation concept of our master Equation
The concept of Generation Gj
• 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
Batch Reactor GMBE
Let’s develop that integral…
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Batch Reactor GMBE
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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
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Batch Reactor GMBE
A B
Not typical in literature
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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
• Lets apply the General Molar Balance Equation
No variation due to perfect mixing
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CSTR GMBE
• Lets apply the General Molar Balance Equation
Forcing -rj
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CSTR GMBE
• Lets apply the General Molar Balance Equation
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
No accumulation (Continuous Process)
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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 partof 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 derivtiveLets “force” the derivative… get the limit of the ΔV be 0
Plug Flow Reactor
Plug Flow Reactor
We get this cool derivative!
Lets integrate!
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Plug Flow Reactor
And lets force once again -rA
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Plug Flow Reactor
This is our PFR master equation!
Packed Bed Reactor
• Description
– Heterogeneous reactions
– Fluid-Solid phases
– Ideal for Catalyst bed reactions
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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
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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
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Packed Bed Reactor
• Operation
– The fluid interact with the catalyst bed
– There is reactions, the products go to the outlet
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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
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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
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Packed Bed Reactor and –r’A
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Packed Bed Reactor and –r’A
No accumulation continuous process in steady state
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Packed Bed Reactor and –r’A
Lets check out that differential volume/mass disk (pink)
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Packed Bed Reactor and –r’A
As in the PFR… We force that “Derivative” concept
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Packed Bed Reactor and –r’A
Which is very similar to the PBR!
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Packed Bed Reactor and –r’A
NOTE: This equation is only valid if there is NO pressure drops (we will deal with that in further chapters)
Master Equation for PBR
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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
Flow vs. Concentration
• How do we relate them!?
• One uses time
• The other uses volume of solution
Flow vs. Concentration
• 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 ConcentrationBatch
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
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From Flow to ConcentrationCSTR
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
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From Flow to ConcentrationPFR
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
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From Flow to ConcentrationPFR
If you continue to develop the equation
And Integrate to find out the limits
You end up with this Equation for “Volume”
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From Flow to ConcentrationPBR
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The design Equation for a PBR
Substitute Flows in terms of Concentration
If volumetric flow is constant, take it out of the derivative
From Flow to ConcentrationPBR
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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
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a) Reactor volume (do not substitute data, just variables)b) Reactor Volume if the exiting concentration is 10% of the entering
concentrationc) What reactor would you choose?
Do it for CSTR, PFR… PBR (need more data)
Examples of Continuous Reactors
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Examples of Continuous Reactors
• You get this equation…
• The volume for a CSTR
Examples of Continuous Reactors
Examples of Continuous Reactors
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Examples of Continuous Reactors
• You get this equation…
• The volume for a PFR
Examples of Continuous Reactors
Definitively choose PFR due to lower volume requirement
Molar Balances of Reactors Summary
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Concentratrion
Theoretical Summary
Theoretical Summary
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
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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)
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End of Block RE1
• This is just the first step on the course
• We’ve seen the first step for the Reactor Engineering Methodology:
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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.
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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
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Text Book & Reference
Essentials of Chemical Reaction EngineeringH. Scott Fogler (1st Edition)
Chemical Reactor Analysis and Design FundamentalsJ.B. Rawlings and J.G.
Ekerdt (1st Edition)
Elements of Chemical Reaction EngineeringH. Scott Fogler (4th Edition)
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Bibliography
Elements of Chemical Reaction EngineeringH. Scott Fogler (4th Edition)
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We’ve seen CH1
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