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Chemical Reaction Engineering

Day I:
Reaction Kinetics


Dr. Asawin Meechai

Department of Chemical Engineering, King
Mongkut’s

of
Technology,
Thonburi

September 11, 09

Contents


Overview of chemical reaction engineering


Chemical reactions


Chemical reactors


Chemical kinetics



Rate of reactions



Rate equations



Effect of temperature on rate of reaction



Conversion/Rate equations in term of conversion



Workshop

Overview

of

Chemical Reaction Engineering (CRE)

A PFD of an Industrial Chemical Plant

Source: en.Wikipedia.org/wikiProcess flow diagram


What’s going on?

Chemical

process

Raw

material

Separation

process

Separation

process

Products

By products



Chemical

reactions



Chemical

reactors



How

to

design

a

reactor

to

achieve

certain

goals?



Chemical

reaction

engineering

(CRE)

What’s CRE?


Chemical reaction engineering is concerned with the
exploitation of chemical reactions on a commercial scale.


It's goal is the successful design and operation of chemical
reactors.


Reactor design uses information, knowledge and experience
from a variety of areas
-

thermodynamics, chemical kinetics,
fluid mechanics, heat and mass transfer, and economics.


CRE for
beginners

Chemical
kinetics

Reactor
design

We design reactors for what?


The design of a chemical reactor deals with multiple aspects
of chemical engineering.


Chemical engineers design reactors to maximize net present
value for the given reaction.


Designers ensure that the reaction proceeds with the highest
efficiency towards the desired output product, producing the
highest yield of product while requiring the least amount of
money to purchase and operate.


What is chemical reaction?



A chemical reaction is a process that always results in the
interconversion

of chemical substance.


The substance or substances initially involved in a chemical
reaction are called reactants.


Chemical reactions are usually characterized by a chemical
change, and they yield one or more products.

C
10
H
8
+ 12 O
2

→ 10 CO
2

+ 4 H
2
O

Reaction types


Isomerisation
, in which a chemical compound undergoes a
structural rearrangement without any change in its net atomic
composition



Direct combination or synthesis, in which 2 or more chemical
elements or compounds unite to form a more complex
product:




N
2

+ 3 H
2

→ 2 NH
3




Chemical decomposition or
analysis
, in which a compound is
decomposed into smaller compounds or elements:




2 H
2
O → 2 H
2

+ O
2

Reaction types (cont’d)


Single displacement or substitution, characterized by an element
being displaced out of a compound by a more reactive element:



2 Na(s) + 2
HCl
(
aq
) → 2
NaCl
(
aq
) + H
2
(g)



Double displacement reaction, in which two compounds exchange
ions or bonds to form different compounds:



NaCl
(
aq

+ AgNO
3
(
aq
) → NaNO
3
(
aq
) +
AgCl
(s)



Combustion, a kind of
redox

reaction in which any combustible
substance combines with an oxidizing element, usually oxygen, to
generate heat and form oxidized products.



C
10
H
8
+ 12 O
2

→ 10 CO
2

+ 4 H
2
O

Chemical Reactors


Chemical reactors are vessels designed to contain chemical
reactions


Common types of reactors


Batch reactor (Batch)


Continuous stirred tank reactor (CSTR) or
Backmix

reactor


Plug flow reactor (PFR)


Packed bed reactor (PBR)



Ideal reactors


Perfectly mixed


No variation in the rate of reaction throughout the reactor volume


Batch

reactor


All reactants are supplied to the reactor
at the outset. The reactor is sealed and
the reaction is performed. No addition of
reactants or removal of products during
the reaction.


Vessel is kept perfectly mixed. This
means that there will be uniform
concentrations
.


The temperature will also be uniform
throughout the reactor
-

however, it may
change with time.

NaOH

CH
3
COOC
2
H
5

Sodium hydroxide + ethyl acetate = sodium acetate + ethanol

C
2
H
5
OH

CH
3
COONa

and

Unreacted NaOH

CH
3
COOC
2
H
5

Example of a liquid phase batch reaction.

http://www.engin.umich.edu/~CRE/01chap/html/reactors/photos.htm#amoco

Typical Commercial Batch Reactor


Usually employed for liquid phase
reactions.



Use for gas phase usually in
laboratory for kinetic studies.

Schematic representation of a CSTR

Continuous Stirred Tank Reactor (CSTR)

Characteristics of CSTR


Perfect mixing: the properties of the reaction mixture are
uniform in all parts of the vessel and identical to the
properties of the reaction mixture in the exit stream
(i.e. C
A, outlet

=

C
A, tank
)


The inlet stream
instantaneously

mixes with the bulk of the
reactor volume.


A CSTR reactor is assumed to reach steady state. Therefore
reaction rate is the same at every point, and time
independent.

Cutaway view of a
Pfaudler CSTR/ Batch
Reactor

http://www.engin.umich.edu/~CRE/01chap/html/reactors/photos.htm#amoco

Spherical reactors

http://www.engin.umich.edu/~CRE/01chap/html/reactors/photos.htm#amoco

Hydrotreating

unit

http://www.engin.umich.edu/~CRE/01chap/html/reactors/photos.htm#amoco

Plug Flow Reactor (PFR), Tubular
reactor


Steady state process


At a given position, for any cross
-
section there is no pressure, temperature
or composition change in the radial direction.


The reactants are continuously consumed as they flow down the length of
the reactor.


No diffusion from one fluid element to another.


All fluid element have same residence time.

Used for either gas phase or liquid phase
reactions.

Two tubular reactors. Furnaces on the back. Heat exchangers on
the front.

http://www.engin.umich.edu/~CRE/01chap/html/reactors/photos.htm#amoco

Packed Bed Reactor (PBR)


Packed bed reactors, also known as fixed bed
reactors, are often use for catalytic processes.


PBRs are heterogeneous reaction systems


When designing a PBR, one must take into
account the active life of the catalyst.


This will affect the length of time a bed of
catalyst may be used and thus how long the
reactor may be run before the catalyst needs
to be regenerated.

Selection of Reactors


Batch


small scale


production of expensive products (e.g. pharmacy)


high
labor

costs per batch


difficult for large
-
scale production


CSTR : most homogeneous liquid
-
phase flow reactors


when intense agitation is required


relatively easy to maintain good temperature control


the conversion of reactant per volume of reactor is the smallest of the
flow reactors
-

very large reactors are necessary to obtain high
conversions


PFR : homogeneous gas
-
phase flow reactors


PBR: heterogeneous flow reactors (gas
-
solid, liquid
-
solid)


relatively easy to maintain


usually produces the highest conversion per reactor volume (weight of
catalyst if it is a packed
-
bed catalyze gas reaction) of any of the flow
reactors


difficult to control temperature within the reactor

Example Reactor Types


Noncatalytic

homogeneous gas
reactor


Homogeneous liquid reactor


Liquid
-
liquid reactor


Gas
-
liquid reactor


Non
-
catalytic gas
-
solid reactor


Fixed bed


Fluidised

bed


Fixed bed catalytic reactor


Fluid bed catalytic reactor


Gas
-
liquid
-
solid reactor



Ethylene
polymerisation



Mass
polymerisation

of styrene


Saponification

of fats


Nitric acid production



Iron production


Chlorination of metals


Ammonia synthesis


Catalytic cracking (petroleum)


Hydrodesulphurisation

of oils

Chemical Kinetics

Chemical kinetics


Study the rate of reactions (
-
r
A
)


How fast of a number of moles of one chemical species are
being consumed to form another chemical species.


The rate of a reaction can be expressed as the rate of
disappearance of a reactant or as the rate of appearance of a
product.


Consider species: A

B


-
r
A

= the rate of a disappearance of species A per unit volume

r
B

= the rate of formation of species B per unit volume


For a catalytic reaction, we refer to
-
r
A
'
, which is the rate of
disappearance of species A on a per mass of catalyst basis.


Relative rates of reaction


For a reaction:





Rate of formation of C = c/a (rate of disappearance of A)

Refer to Stoichiometry

Exercise 1: 10 min





Write the rate of reaction of each component.

a)

b)

c)

d)

e)

Rates of reaction depends basically on


Reactant concentrations



Surface area



Pressure



Activation energy



Temperature



Catalyst


Rate law (Rate equation)



Algebraic equation accurately describes the reaction rate
as a function of concentration and temperature.



Why functions of concentrations and temperature?




How do molecules react? By collision

Where

:



A=

Frequency

factor

(
1
/time)


E=

Activation

energy,

J/mol

or

cal/mol


R=

Gas

constant,

8
.
314

J/mol

K

(or

1
.
987

cal/mol

K)


T=

Absolute

temperature,

K

Arrhenius Equation

It

was

the

Swedish

chemist

Svante

Arrhenius

who

first

suggested

that

the

temperature

dependence

of

the

specific

reaction

rate

constant,

k
,

could

be

correlated

by

an

equation

of

the

type
:


Empirical Observations.

Rate of reaction and temperature

1/
T

ln k

-
E/R

Activation

energy

determined

experimentally

by

carrying

out

the

reaction

at

several

temperatures
.

After

taking

the

natural

logarithm

of

the

Arrhenius

equation

:

How can we determine
A

and
E
?

Example 1
Calculate the activation energy for the first
-
order decomposition
reaction of benzene diazonium chloride to give chlorobenzene and nitrogen:

Arrhenius Equation

ln
k
A

1/T

Arrhenius Equation

Exercise 2: (15
mins
)

1.
From an experiment of hydrolysis of
tert
-
butyl bromide, the rate
constants (
k
) are found to be 1.45x10
-
5

s
-
1

at 25*C, and 22x10
-
5

s
-
1

at 50*C. Determine the activation energy and the frequency
factor.





Back to Rate laws



a

,
b

… = reaction order with respect to C
A
, C
B
.



a

+
b

+ ... = overall order



It can
only

be determined experimentally

Elementary reaction & Elementary rate laws


Elementary reaction is one that evolves a single step
.


The
stoichiometric

coefficients in an elementary reaction are
identical to the powers in the rate law
:




An elementary reaction has an elementary rate law.


Some reaction follows an elementary rate law is not an
elementary reaction.

2NO + O
2



2NO
2

Consider the general reversible reaction:

At equilibrium

r
A
=0

Therefore:

Therefore:

Thermodynamic equilibrium relationship

r
fA

= r
bA

Thermodynamic equilibrium constant

Reversible reaction

K
C

T

K
C

T

Endothermic

Exothermic

Interesting questions to be asked



How can we quantify how far a reaction has
progressed?



How many moles of product C are formed for every
mole reactant A consumed?

t = 0

N
A0

N
B0

N
C0

N
D0

N
I0

t = t

N
A

N
B

N
C

N
D

N
I

Batch reactor

=?

Stoichiometry

Conversion


Definition


The conversion X
A

is the number of moles of A that have
reacted per mole of A fed to the system:

Rate of reaction as a function of
conversion

For batch:

Can you derive it yourself?

t = 0

N
A0

N
B0

N
C0

N
D0

N
I0

t = t

Batch reactor

Species

Initial

mole

Change

mole

Remaining

mole

Concentration*

(volume change or
not)

A

N
A0

B

N
B0

C

N
C0

D

N
D0

I

N
I0

--

Total

N
T0

*
constant volume
here

Rate law in term of conversion


Major objective:


Rate law
-
r
A

as a function of conversion:


e.g.

Example 2
:
Soap consists of the sodium and potassium salts of various
fatty acids such as oleic,
stearic
,
palmitic
,
lauric
, and
myristic

acids.
The
saponification

for the formation of soap from aqueous caustic
soda and
glyceryl

stearate

is



If the initial mixture consists solely of sodium hydroxide at a
concentration of 10 mol/dm
3

(i.e., 10 mol/L or 10
kmol
/m
3
) and of
glyceryl

stearate

at a concentration of 2 mol/dm
3
, what is the
concentration of
glycerine

when the conversion of sodium hydroxide
is (a) 20% and (b) 90% ?

Only the reactants NaOH and (C
17
H
35
COO)
3
C
3
H
5

are initially present:

C
=

D
=0.

X = 20%

X = 90%

liquid phase reaction:

Try to derive equations
expressing the concentration of each species in
terms of its initial concentration and the conversion X by yourself!!!!

How about equation for flow system?

entering

F
A0

F
B0

F
C0

F
D0

F
I0

Leaving

F
A

F
B

F
C

F
D

F
I

Continuous
-
flow reactor

=?

Specie
s

Feeding rate

mole/t

Change

mole/t

Effluent rate

mole/t

A

F
A0

B

F
B0
=
Θ
B
F
A0

C

F
C0
=
Θ
C
F
A0

D

F
D0
=
Θ
D
F
A0

I

F
I0
=
Θ
I
F
A0

--

Total

F
T0

Rate law in term of conversion (for
flow)

Liquid phase
:

Volume change with reaction is negligible when no phase changes
are taking place.

Exercise 3: 10
mins

1. For an elementary reaction,
2NO + O
2



2NO
2
,
taking place in
a batch reactor, write the rate laws and then express them in
term conversion.

Thing gets more complicated for gas
-
phase!


Gas
-
phase:


The reaction volume (V) or volumetric flow rate (
v
) most
often changes during the course of the reaction because
of a change in the total number of moles or in
temperature or pressure


e.g.


4 mol

2 mol


Variable volume


Equation of state

t = 0

from
stoichiometric

table

1


Variable volumetric flow rate


entering

For species j

1

From
stoichiometric

table

Stoichiometric coefficient

Specie
s

Feeding rate

mole/t

Change

mole/t

Effluent rate

mole/t

A

F
A0

B

F
B0
=
Θ
B
F
A0

C

F
C0
=
Θ
C
F
A0

D

F
D0
=
Θ
D
F
A0

I

F
I0
=
Θ
I
F
A0

--

Total

F
T0

Example 3: A mixture of 28% SO
2

and 72% air is charged to a flow reactor in which SO
2

is
oxidized:

First, set up a stoichiometric table using only the symbols (i.e., Θ
i
, F
i
) and then prepare a
second stoichiometric table evaluating numerically as many symbols as possible for the case
when the total pressure is 1485 kPa (14.7 atm) and the temperature is constant at 227

C.

Taking SO
2

as the basis of calculation:



Change concentration!!

If the rate law for this reaction were first order in SO
2

(i.e., A) and in O
2

(i.e.,
B) with k=200 dm
3
/mol
.
s:

Exercise 4: (30 min)

Problem: The reversible gas
-
phase decomposition of nitrogen
tetroxide
, N
2
O
4
, to
nitrogen dioxide, NO
2
, is to be carried out at constant temperature. The feed
consists of pure N
2
O
4

at 340 K and 202.6
kPa

(2 tam). The concentration equilibrium
constant,
K
c
, at 340 K is 0.1 mol/dm
3.

(a) Calculate the equilibrium conversion of N
2
O
4

in a constant
-
volume batch
reactor.

(b) Calculate the equilibrium conversion of N
2
O
4

in a flow reactor.

(c) Assuming the reaction is elementary, express the rate of reaction solely as a
function of conversion for a flow system and for a batch system.

Exercise 4: The reversible gas
-
phase decomposition of nitrogen tetroxide, N
2
O
4
, to
nitrogen dioxide, NO
2
, is to be carried out at constant temperature. The feed
consists of pure N
2
O
4

at 340 K and 202.6 kPa (2 tam). The concentration equilibrium
constant, K
c
, at 340 K is 0.1 mol/dm
3.

concentration equilibrium constant:

at equilibrium !!

(a) Calculate the equilibrium conversion of N
2
O
4

in a
constant
-
volume batch reactor
.

at
equilibrium !!

(b) Calculate the equilibrium conversion of N
2
O
4

in a
flow reactor
.

at equilibrium !!

for batch system


for flow system


(c) Assuming the reaction is elementary, express the rate of reaction solely as a
function of conversion for a flow system and for a batch system.

Elementary reaction:

(d) Determine the CSTR volume necessary to achieve 80% of the equilibrium
conversion.

CSTR design equation

Reference



Elements of Chemical Reaction Engineering, H. Scott Fogler,
Prentice Hall International Series, 4rd Edition, 2006.