Fundamentals of Chemical

Kinetics

Introduction
Definitions
General Mole Balance Equation
• Batch (BR)
• Continuously Stirred Tank
Reactor (CSTR)
• Plug Flow Reactor (PFR)
• Packed Bed Reactor (PBR)

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Chemical Reaction Engineering

• Chemical Reaction Engineering (CRE) is the field that studies the rates and mechanisms
of chemical reactions and the design of the reactors in which they take place.

• Chemical reaction engineering is at the heart of virtually every chemical process.

It separates the chemical engineer from other engineers.

Industries that Draw Heavily on Chemical Reaction Engineering (CRE) are:

CPI (Chemical Process Industries)
Examples like Dow, DuPont, Amoco, Chevron

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Materials on the Web

http://www.umich.edu/~elements/5e/

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Chemical Identity

• A chemical species is said to have reacted when it has lost its chemical
identity.
• The identity of a chemical species is determined by the kind, number, and
configuration of that species’ atoms.
• A chemical species is said to have reacted when it has lost its chemical
identity.

• There are three ways for a species to loose its identity:

1. Decomposition CH3CH3  H2 + H2C=CH2
2. Combination N2 + O2  2 NO
3. Isomerization C2H5CH=CH2  CH2=C(CH3)2

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Reaction Rate

• The reaction rate is the rate at which a species looses its chemical
identity per unit volume.

• The rate of a reaction (mol/dm3/s) can be expressed as either:

• The rate of Disappearance of reactant: -rA
or as
• The rate of Formation (Generation) of product: rP

Consider the isomerization

AB
rA = the rate of formation of species A per unit volume
-rA = the rate of a disappearance of species A per unit volume
rB = the rate of formation of species B per unit volume
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Reaction Rate

EXAMPLE: AB
If Species B is being formed at a rate of
0.2 moles per decimeter cubed per second, i.e.,
rB = 0.2 mole/dm3/s

Then A is disappearing at the same rate:

-rA= 0.2 mole/dm3/s
The rate of formation (generation of A) is:
rA= -0.2 mole/dm3/s

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Reaction Rate

• For a catalytic reaction we refer to –rA’ , which is the rate of disappearance

of species A on a per mass of catalyst basis. (mol/gcat/s)

NOTE: dCA/dt is not the rate of reaction

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Reaction Rate

Consider species j:
1. rj is the rate of formation of species j per unit volume [e.g. mol/dm3s]
2. rj is a function of concentration, temperature, pressure, and the type of
catalyst (if any)
3. rj is independent of the type of reaction system (batch, plug flow, etc.)
4. rj is an algebraic equation, not a differential equation
(e.g. -rA = kCA or -rA = kCA2)

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Building Block 1: General Mole Balances

System
Volume, V

Fj0 Gj Fj

Molar Flow Molar Flow  Molar Rate  Molar Rate 

 Rate of    Rate of   Generation    Accumulation
       
Species j in  Species j out  of Species j  of Species j 
dN j
Fj 0  Fj  Gj 
dt
 mole   mole   mole   mole 
          
 time   time   time   time  10
Building Block 1: General Mole Balances

If spatially uniform:

G j  r jV
If NOT spatially uniform:

V1
 V2
rj1
rj 2
G j1  rj1V1
G j 2  rj 2 V2

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Building Block 1: General Mole Balances

n
G j   rji Vi
i 1

Take limit
n

Gj   rji Vi   r dV
j
i1 lim V  0 n  

 12
Building Block 1: General Mole Balances

General Mole Balance on System Volume V System

Volume, V

FA0 GA FA

In  Out  Generation  Accumulation

dN A
FA 0  FA   rA dV 
dt

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Batch Reactor - Mole Balances

Batch

dN A
FA0  FA   rA dV 
dt
FA0  FA  0

Well-Mixed r A dV  r AV
dN A
 rAV
dt
14 14
Batch Reactor - Mole Balances

dN A
Integrating dt 
rAV
t  0 N A  N A0
when
t  t NA  NA

NA
dN A
t 
N A0
 rAV

Time necessary to reduce the number of moles of A from NA0 to NA.

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Batch Reactor - Mole Balances

NA
dN A
t 
N A0
 rAV

NA

t 16
CSTR - Mole Balances

CSTR

dN A
FA 0  FA   rA dV 
dt

Steady State dN A
0
 dt
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CSTR - Mole Balances

Well Mixed  r dV  r V
A A

FA 0  FA  rAV  0

FA 0  FA
V
 rA
CSTR volume necessary to reduce the molar flow rate
from FA0 to FA.
 18
Plug Flow Reactor - Mole Balances

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Plug Flow Reactor - Mole Balances

V

FA FA


V V  V
 

 In  Out  Generation 
at V   at V  V   in V 0
     
FA V  FA V  V  rA V 0
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Plug Flow Reactor - Mole Balances

Rearrange and take limit as ΔV0

FA V  V  FA V
lim  rA
V  0 V

dFA
 rA
dV

This is the volume necessary to reduce the entering molar

flow rate (mol/s) from FA0 to the exit molar flow rate of FA.

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Plug Flow Reactor - Mole Balances

PFR

dN A
FA0  FA   rA dV 
dt
dN A
Steady State 0
dt

FA0  FA   rA dV  0

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Plug Flow Reactor - Mole Balances: Alternative Derivation

Differientiate with respect to V

0
dFA
  rA
dFA
dV
 rA
dV
FA
dF A
The integral form is: V   rA
 FA 0

This is the volume necessary to reduce the entering molar flow

rate (mol/s) from FA0 to the exit molar flow rate of FA.

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Packed Bed Reactor - Mole Balances
W
PBR
FA FA

W W  W
  dN A
FA W   FA W  W   rA W 

dt
Steady State dN A
0
dt
F A W  W  F A W
lim  rA
W  0 W 24
Packed Bed Reactor - Mole Balances

Rearrange:
dFA
 rA
dW
The integral form to find the catalyst weight is:
FA
 dFA
W 
FA 0
rA

PBR catalyst weight necessary to reduce the entering molar

flow rate FA0 to molar flow rate FA.

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Reactor Mole Balances Summary

The GMBE applied to the four major reactor types

(and the general reaction AB)
Reactor Differential Algebraic Integral
NA NA
dN A dN A
Batch  rAV t 
dt rV
N A0 A
t
CSTR FA 0  FA
V
rA FA
FA
dFA dFA
PFR  rA V 
dV FA 0
drA
V

FA
dFA FA
PBR dFA
 dW
 rA W 
FA 0
rA
W 26
Reactors with Heat Effects

• Propylene glycol is produced by the hydrolysis of propylene oxide:

 EXAMPLE: Production of Propylene Glycol in an Adiabatic CSTR

H SO
CH 2  CH  CH 3  H 2O 
2

4
CH 2  CH  CH 3
O OH OH


  

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 v0

Propylene
Glycol

What are the exit conversion X and exit temperature T?

Solution: Let the reaction be represented by
A+BC
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1. Mole Balance and design equation:

The design equation in terms of X is

2. Rate Law:

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3. Stoichiometry (liquid phase, ν = ν0):

4. Combining yields

Solving for X as a function of T and recalling that τ = V/ν0 gives

This equation relates temperature and conversion through the mole balance.

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b. Stoichiometry (CA0, Θi, τ): The total liquid volumetric flow rate entering the
reactor is
c. Evaluate mole balance terms: The conversion calculated from the mole
balance, XMB:

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5. The energy balance for this adiabatic reaction in which there is negligible
energy input provided by the stirrer is

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d. Evaluate energy balance terms:

Substituting all the known quantities into the energy balance gives us

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7. Solving

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Analysis

We have applied our CRE algorithm to calculate the Conversion (X=0.84) and
Temperature (T=614 °R) in a 300 gallon CSTR operated adiabatically.

T=535 °R

X=0.84
A+BC
T=614 °R
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Separations

Filtration Distillation Adsorption

These topics do not build upon one another.

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Reaction Engineering

Mole Balance Rate Laws Stoichiometry

These topics build upon one another.

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 Heat Effects
Isothermal Design

Stoichiometry
Rate Laws
Mole Balance

CRE Algorithm

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 Mole Balance Rate Laws

Be careful not to cut corners on any of the

CRE building blocks while learning this material!

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 Heat Effects
Isothermal Design

Stoichiometry
Rate Laws

Mole Balance

Otherwise your Algorithm becomes unstable.

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Supplemental Slides: Additional Applications of CRE

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Supplemental Slides: Additional Applications of CRE

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Supplemental Slides: Additional Applications of CRE

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Supplemental Slides: Additional Applications of CRE

Hippo Digestion (Ch. 2)

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Supplemental Slides: Additional Applications of CRE

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Supplemental Slides: Additional Applications of CRE

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Supplemental Slides: Additional Applications of CRE

Smog (Ch. 1)

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Supplemental Slides: Additional Applications of CRE

Chemical Plant for Ethylene Glycol (Ch. 5) 50

Supplemental Slides: Additional Applications of CRE

Wetlands (Ch. 7 DVD-ROM) Oil Recovery (Ch. 7)

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Supplemental Slides: Additional Applications of CRE

Cobra Bites
(Ch. 8 DVD-ROM)

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Supplemental Slides: Additional Applications of CRE

Lubricant Design (Ch. 9)

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Supplemental Slides: Additional Applications of CRE

Plant Safety
(Ch. 11,12,13)

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