Chapter 1 introduction

VIETNAM NATIONAL UNIVERSITY – HO CHI MINH CITY
UNIVERSITY OF TECHNOLOGY

FACULTY OF CHEMICAL ENGINEERING

Chemical Reaction Engineering

(Homogeneous Reactions in Ideal Reactors)
Mai Thanh Phong, Ph.D.

FCE – HCMC University of Technology

Chemical Reaction Engineering


References
1. Octave Levenspiel, “Chemical Reaction Engineering”, John Wiley&Sons, 2002.
2. H. Scot Foggler, “Elements of Chemical Reaction Engineering”,International
students edition, 1989.
3. E.B.Nauman, “Chemical Reactor Design”, John Wiley & sons, 1987.
4. Stanley M. Walas, “Reaction Kinetics for Chemical Engineers”,Int. Student
Edition, 1990.
5. Coulson & Richardsons, “Chemical Engineering – Vol 6”,Elsevier, 1979.
6. Richard M. Felder, “Elementary Principles of Chemical Processes”, John Wiley &
sons, 2000.

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Chapter 1. Introduction
•

Topic of the lecture „Chemical Reaction Engineering“ is the quantitative
assessment of chemical reactions. The selection of suitable reactor types and
their design will be discussed.

•

Reactor design uses information, knowledge, and experience from a variety of
areas: thermodynamics, chemical kinetics, fluid mechanics, heat transfer, mass
transfer, and economics. Chemical reaction engineering is the synthesis of all
these factors with the aim of properly designing a chemical reactor.

•

Thermodynamics tell us in which direction a reaction system will develop and
how far it is from its equilibrium state.

•

Analyses of kinetics provide information about the rate with which the system will
approach equilibrium.

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Chapter 1. Introduction
I.

Basic Parameter

Description of the amount of a substance i:
Number of moles:

mi
ni 
Mi

Mi = molecular weight

Molar concentration:

ni
ci 
V

V = volume

Mole fraction:

ni
xi 
 nj
j

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Chapter 1. Introduction
Progress of chemical reactions:
Conversion:

ni 0  ni
Xi 
ni 0

If V = const:

ci 0  ci
Xi 
ci 0

Extent of reaction:

ni  ni 0

i

Performance criteria:
Productivity:

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produced amount of product P
n P 
operating time
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Chapter 1. Introduction
II. Stoichiometry of chemical reactions:
Stoichiometry is based on mass conservation and thus quantifies general laws
that must be fulfilled during each chemical reaction.
Starting point of a quantitative analysis is the following formulation of a chemical
reaction:
N

 A 0
i 1

i

i

This equation describes the change of the number of moles of N components
A1, A2, ... AN. The νi are the stoichiometric coefficients of component i. They have
to be chosen in such a way that the moles of all elements involved in the chemical
reaction remain constant.
A convention is that reactants have negative stoichiometric coefficients and products
have positive stoichiometric coefficients.
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Chapter 1. Introduction
As an example the stoichiometric equation for the oxidation of carbon monoxide
is given by:
2CO + O2 → 2CO2
with

νCO = -2, vO2 = -1, vCO2 = 2

To calculate changes in the mole number of a component i due to reaction, the
following balance has to be respected:

ni ni 0  i
From this equation results the important stoichiometric balance:

ni 0  ni ni nk 0  nk nk



i
i
k
k
Using the conversion X of a component k, the above equation becomes:

i
ni ni 0 
nk 0 X k
k

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Chapter 1. Introduction
III. Chemical thermodynamics:

Chemical thermodynamics deal with equilibrium states of reaction system. This
Section will concentrate on the following two essential areas:
a) The calculation of enthalpy changes connected with chemical reactions, and
b) The calculation of equilibrium compositions of reacting systems.
3.1 Enthalpy of reaction
The change of enthalpy caused by a reaction is called reaction enthalpy ∆HR.
This quantity can be calculated according to the following equation:
N

H R  i H Fi
i 1

∆HFi is the enthalpy of formation of component i
∆HR < 0, the reaction is exothermic
∆HR > 0, the reaction is endothermic
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Chapter 1. Introduction
It is simple to calculate the reaction enthalpy at a certain standard state ∆HR0 from
the corresponding standard enthalpies of formation ∆HFi0. The standard enthalpies
of formation are available from databases for P = P0 = 1 bar and T = T0 = 298 K.
For pure elements like C, H2, O2,...: ∆HFi0 = 0.
The reaction enthalpy is a state variable. Thus, a change depends only on the

Initial and the end state of the reaction and does not dependent on the reaction
parthway.
3.2 Temperature and pressure dependence of reaction enthalpy

 H R 
 H R 
d H R  
 dP  
 dT
 P  T
 T  P
The pressure dependence is usually very small. For ideal gas behaviour, the
reaction enthalpy does not depend on pressure.
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Chapter 1. Introduction
The correlation of reaction enthalpy and temperature is related to the isobaric
heat capacities of all species involved in the considered reaction, cPi.
N

T

i 1

Pi
T 298 K

H R T  H R0   i

c T dT

Assuming that the reactants and the products have different but temperature
independent heat capacities, the temperarue dependence of the reaction
enthalpy can be estimated as follows:

H R T  H R0  T  T0 cP ,products  cP ,reactants 

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Chapter 1. Introduction
3.3 Chemical equilibrium
• Chemical reactions approach to an equilibrium, when the product and reactant
concentrations do not change anymore.
• A reacting system is in chemical equilibrium if the reaction rates of the forward
and backward reactions are equal.
• The basic quantity required to indentify the equilibrium state is the Gibbs free

enthalpy of reaction GR.
• The change of this quantity becomes zero when the equilibrium is reached (i.e.
dGR = 0)
For constant pressure and temperature, the change of free Gibbs enthalpy of
reaction can be described as follows:
N

dGR  i i d
i 1

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or

N
 dGR 

  i i
 d  T , P i 1

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Chapter 1. Introduction

The equilibrium is reached when the free

Gibbs enthalpy of reaction is minimum.
Thus, for the chemical equilibrium:

 dGR 

 0
 d  T , P

Free Gibbs enthalpy

In Figure 1-1 is shown the course of free
Gibbs enthalpy of reaction as a function
of the extent of reaction.

 GR 

 0



T ,P

Or dGR=0 (or in an integrated form: ∆GR = 0)
Thus, the equilibrium is characterized by:
N

 
i 1

i

i

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0

 GR 

  0



T ,P

 GR 

  0
   T , P


Fig. 1-1: Changing of free Gibbs enthalpy
for a chemical reaction

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Chapter 1. Introduction
3.3.1 Reation free Gibbs enthalpy, ∆GR
N

G  i GFi0
0
R

GFi0

i 1

free Gibbs energy of formation

Relation between ∆GR and ∆HR





d GR0 T
H R0

dT
T2

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Chapter 1. Introduction
3.3.2 Equilibrium constant and temperature dependence
Relationship between the free Gibss enthalpy and the equilibrium constant:

GR0 T   RT ln K
 GR0 

K exp 
 RT 
Van‘t Hoff equation describing the temperature dependence of the equilibrium
constant:

d ln K 
H R0

dT
RT 2

For a small temperature range, ∆HR is constant, thus:

H R0
ln K T2  ln K T1 
R
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 1 1
  
 T2 T1 

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Chapter 1. Introduction
4. Reaction rate
Based on unit volume of reacting fluid:

1 1 dni
r
 i VR dt

• VR is volume of the reaction mixture
• ni is mole number of component i
• t is reaction time

If VR is constant:

1 dci
r
 i dt

• ci is molar concentration of component i

Based on unit mass of solid in solid-liquid systems:

1 1 dni
r
 i W dt

• W is mass of solid

Based on unit solid surface of solid-liquid or solid-gas systems:

1 1 dni
r
 i S dt
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• S is solid surface area
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Chapter 1. Introduction
5. Standard Reactors
To carry out chemical reactions discontinuously operated reactors or
continuously operated reactors can be used.
• Discontinuously: more frequently applied to produce fine chemicals

• Continuously: more advantageous for the production of larger amounts of bulk
chemicals.
To study the different behavior of these types of reactors another important criterion
serves to distinguish two limiting cases: mixed flow and plug flow behavior
For theoretical studies and to compare the different reactors, four different ideal
reactors can be defined using the above classification:
a) Batch Reactor (BR, perfectly mixed, discontinuous operation):
Features:
• All components are in the reactor before the reaction starts
• Composition changes with time
• Composition throughout the reactor is uniform
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Chapter 1. Introduction
Adv.:
• Simple, flexible, high conversion…
Disadv.:
• Dead times for charging, discharging, cleaning,…
• Difficult to control and automate
•…
BR are applied in particular for:
• Relatively slow reactions
• Slightly exothermic reactions

Areas of application for BR are:
• Reactions in pharmaceutical industry
• Polymerisation reactions
• Dye production
• Speciality chemicals

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Chapter 1. Introduction
b) Semi-batch Reactor (SBR): perfectly mixed, semi continuous operation
Features:
• One reactant is introduced first and then the
second is dosed in a controlled manner.
• Composition changes with time
• Composition throughout the reactor is uniform

Adv.:
• Controlled reaction rate and heat generation
• ...
Disadv.:
• Same as BR
• More complicated than BR
•…

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Chapter 1. Introduction
c) Continuously Stirred Tank Reactor (CSTR): perfectly mixed, continuous operation
A,B

A,B,products

Features:
• Reactants are continuously introduced,
products (+ unconverted reactants) are
continuously withdrawn
• Composition does not change with time
• Composition throughout the reactor is uniform
Adv.:
• Controlled heat generation
• Easy to control and automate
• No dead times
• Constant product quality,...
Disadv.:
• Complicated
• Can become unstable
• Large investmnent cost,...

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Chapter 1. Introduction
d) Plug Flow Tubular Reactor (PFTR): no mixing, continuous operation

A, B

tubular reactor

A, B,
products

Features:
• Composition varies from point to point along a flow path
Adv.:
•High conversion
•Easy to automate
•No dead times
•Better to cool (compare to stirred tanks)
•…
Disadv.:
•Complicated

•Danger of “hot spot”
•…
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