Lecture note chemical reaction engineering

Chemical Reaction Engineering 3-Feb-09 3Mai Thanh Phong - HCMUT Chapter 1.. Chemical Reaction Engineering 3-Feb-09 7Mai Thanh Phong - HCMUT Chapter 1... Chemical Reaction Engineering 3-F

FCE – HCMC University of Technology

Chemical Reaction Engineering

(Homogeneous Reactions in Ideal Reactors)

Mai Thanh Phong, Ph.D.

VIETNAM NATIONAL UNIVERSITY – HO CHI MINH CITY UNIVERSITY OF TECHNOLOGY

FACULTY OF CHEMICAL ENGINEERING

Chemical Reaction Engineering

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.

n n x

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P product of

amount produced

=

P

n&

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:

01

=

∑

=

N i

i

iA

ν

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

To calculate changes in the mole number of a component i due to reaction, the

following balance has to be respected:

ν ν

k

i i

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:

H

1

ν

∆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 = P 0 = 1 bar and T = T 0 = 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

P

H H

The pressure dependence is usually very small For ideal gas behaviour, the

reaction enthalpy does not depend on pressure.

N

i

i R

=

=

+ Δ

=

Δ

298 1

The correlation of reaction enthalpy and temperature is related to the isobaric

heat capacities of all species involved in the considered reaction, cPi.

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:

P P

R

R T H T T c c

Δ

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Chapter 1 Introduction

ξ μ

• 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:

i

N

i

i P

T

Rd

or

iμ ν

G

ξ

ξ

Or dGR=0 (or in an integrated form: ∆GR = 0)

Thus, the equilibrium is characterized by:

Fig 1-1: Changing of free Gibbs enthalpy

for a chemical reaction

In Figure 1-1 is shown the course of free

Gibbs enthalpy of reaction as a function

of the extent of reaction.

The equilibrium is reached when the free

Gibbs enthalpy of reaction is minimum.

Thus, for the chemical equilibrium:

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Δ free Gibbs energy of formation

Relation between ∆GR and ∆HR

2

0 0

T

H dT

T G

Chapter 1 Introduction

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

( )2 = ln ( )1 − Δ 0 ⎜⎜ ⎛ 1 − 1 ⎟⎟ ⎞

ln K T K T HR

3.3.2 Equilibrium constant and temperature dependence

Van‘t Hoff equation describing the temperature dependence of the equilibrium

constant:

2

0ln

RT

H dT

K

GR0 = − ln Δ

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R i

= • ci is molar concentration of component i

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

dt

dn W

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

• Composition changes with time

• Composition throughout the reactor is uniform

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• 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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FCE – HCMC University of Technology

Chemical Reaction Engineering

(Homogeneous Reactions in Ideal Reactors)

Mai Thanh Phong, Ph.D.

VIETNAM NATIONAL UNIVERSITY – HO CHI MINH CITY UNIVERSITY OF TECHNOLOGY

FACULTY OF CHEMICAL ENGINEERING

Chemical Reaction Engineering

Chapter 2 Interpretation of Batch Reactor Data

1 Rates of reaction

1.1 Description of reaction rates

Reaction rates depend usually in a complex manner on the concentrations, the

temperature and often on the effect introduced by catalysts:

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Chapter 2 Interpretation of Batch Reactor Data

T

k ( ) 0 exp A • E• koAis the pre-exponential factor (not dependent on is the activation energy of the reaction.

the reaction temperature

Chapter 2 Interpretation of Batch Reactor Data

1.2 Rate laws of simple reactions

In this section, rate equations of simple reactions and the corresponding

temporal change of concentration are analyzed A closed system (isothermic,

batch reactor) and aconstant volume are assumed

1.2.1 Irreversible first-order reactions (Decomposition reactions)

A → Products

i

kC dt

dC

ν 1

C A

A k dt C

dCA

Ao 0

(2.1)(2.2)

(2.3)

kt C

CA

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Chapter 2 Interpretation of Batch Reactor Data

The eq (2.3) leads to the temporal course of concentration cA

kt A

1.2.2 Irreversible bimolecular-type second-order reactions

Consider the reaction (A + B → Products) with corresponding rate equation

Chapter 2 Interpretation of Batch Reactor Data

Noting that the amounts of A and B that have reacted at any time t are equal and given by C A0 X A , eq (2.7) can be written in terms of X A as

(2.9)

(2.10)

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Chapter 2 Interpretation of Batch Reactor Data

After breakdown into partial fractions, integration, and rearrangement, the finalresult in a number of different forms is

Chapter 2 Interpretation of Batch Reactor Data

1.2.3 Empirical rate equations of nth order

When the mechanism of reaction is not known, we often attempt to fit the data

with an nth-order rate equation of the form

(2.14)which on separation and integration yields

(2.15)

1.2.4 Zero-order reactions

Integrating and noting that C A

can never become negative,

we obtain directly:

(2.16)

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Chapter 2 Interpretation of Batch Reactor Data

1.2.5 Irreversible Reactions in Parallel

Consider the simplest case, A decomposing by two competing paths

The rates of change of the three components are given by

(2.17)(2.18)(2.19)

Chapter 2 Interpretation of Batch Reactor Data

The k values are found using all three differential rate equations First of all,

eq (2.17), which is of simple first order, is integrated to give

(2.20)Then dividing eq (2.18) by eq (2.19) we obtain the following

which integrated gives simply

(2.21)

(2.22)

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Chapter 2 Interpretation of Batch Reactor Data

1.2.6 Irreversible Reactions in Series

Consider the reaction

Rate eqautions for the three components are

(2.23)(2.24)

(2.25)

Chapter 2 Interpretation of Batch Reactor Data

Assuming that at t = 0, concentration of A is C A0 , and no R or S present,

integration of eq (2.23) gives

(2.26)

To find the changing concentration of R, substitute the concentration of A from

eq (2.26) into the differential equation governing the rate of change of R, eq

(2.24); thus

Solving the above differential equation gives

(2.27)

(2.28)

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Chapter 2 Interpretation of Batch Reactor Data

Chapter 2 Interpretation of Batch Reactor Data

By differentiating Eq (2.28) and setting dC R ldt = 0, the maximum concentration of

R and the time at which it occours can be found:

(2.32)

(2.33)

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Chapter 2 Interpretation of Batch Reactor Data

Figure 2.1 Typical concentration-time

curves for consecutive first-order reactions

Figure 2.1 shows the general

• and S rises continuously, the

greatest rate of increase of S

Chapter 2 Interpretation of Batch Reactor Data

1.2.7 First-Order Reversible Reactions

The simplest case is the opposed unimolecular-type reaction

(2.34a)

Starting with a concentration ratio M = C R0 /C A0 th e rate equation is

At equilibrium dC A /dt = 0 Hence from Eq (2.34) we find the fractional

conversion of A at equilibrium conditions to be

(2.34b)

(2.35)

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Chapter 2 Interpretation of Batch Reactor Data

and the equilibrium constant to be

Chapter 2 Interpretation of Batch Reactor Data

For the bimolecular-type second-order reactions

1.2.8 Second-Order Reversible Reactions

with the restrictions that C A0 = C B0 , and C R0 = C S0 = 0, the integrated rate

equations for A and B are all identical, as follows

(2.39a)

(2.39b)(2.39c)(2.39d)

(2.40)

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Chapter 2 Interpretation of Batch Reactor Data

kt A

2 Determination of kinetic parameters

For the integral method, the concentration-time-course of one commponent is

the unknown parameters can be calculated

by non-linear regression or using the

linearised form of the integrated rate

equation:

A tipycal measurement is depicted in

Figure 2.2

After this measured data are compared

with theoretical integrated reaction rate

equation, for example:

kt C

Chapter 2 Interpretation of Batch Reactor Data

Figure 2.3 Determination of the reaction rate constant k using the

integrated method in a linearised formulation

2.6 of 2.3The measured data can be inllustrated in a ln(CA/CA0) vs T diagram The slope

of the straight line leads to the reaction rate constant (Figure 2.3)

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Chapter 2 Interpretation of Batch Reactor Data

2.2 Differential method

For the differential method, also measurements of concentration-time courses are necessary

By means numerical and/or graphic differentiation of all measuring data of

concentration C A (t) the derivative dC A /dt can be determined The measured data

can be approximated as a straight line in the reaction rate-concentration-diagram

The procedure is as follows:

1 Plot the C A vs t data, and then by eye carefully draw a smooth curve to

represent the data

2 Determine the slope of this curve at suitably selected concentration values

These slopes dC A /dt = r, are the rates of reaction at these compositions.

3 Search for a rate expression to represent this r A vs C A data, either by

(a) picking and testing a particular rate form, r A = kf (C A ), see Fig 2.4, or

(b) testing an nth-order form r A = kC A n by taking logarithms of the rate equation (see Fig 2.5)

Chapter 2 Interpretation of Batch Reactor Data

Figure 2.4 Test for the particular rate

form rA = kf(C A) by the differential

form

Figure 2.5 Test for an nth-order rate

method by the differential method

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Chapter 2 Interpretation of Batch Reactor Data

Problems

1 Aqueous A at a concentration C A0 = 1 mol/liter is introduced into a batch reactor where it reacts away to form product R according to stoichiometry A Æ R The

concentration of A in the reactor is monitored at various times, as shown below:

a) For C A0 = 500 mol/m3 find the conversion of reactant after 5 hours in the batch reactor

b) Find the rate for the reaction

2 For the elementary reactions in series

find the maximum concentration of R and when it is reached