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REACTION ENGINEERING

CKB 20104

CHAPTER 1

MOLE BALANCE

CHAPTER 1

MOLE BALANCE

1.1 Definition of reaction rate

1.2 The general mole balance

1.3 Types of reactor in industry

Objectives

Upon the completion of this chapter, students are able to:

• Define the rate of chemical reaction

• Apply mole balance equation in reactors systems

• Identify the commercial / industries reactor system

Introduction

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Introduction

Reaction?

Occurs when a chemical species

lost its chemical identity and a

new compound forms

Chemical

Identity

Kind

Number

Configuration

Introduction

Reaction?

3 ways

decomposition

combination

isomerization

reactant →→→→ product + by-product

reactant + reactant →→→→ product

Reaction Rate

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1.1 DEFINITION OF REACTION RATE

The reaction rate is the rate at which a

species loses its chemical identity per

unit volume

Can be expressed either as

1. The rate of disappearance of a

reactant

or

2. The rate of appearance of a product

1.1 DEFINITION OF REACTION RATE

Consider species A:

• The rate of reaction, -rA is the number

of moles of A reacting (disappearing)

per unit time per unit volume [e.g.

mol/dm3.s]

• It is a function of concentration,

temperature, pressure and types of

catalyst (if any)

A B

1.1 DEFINITION OF REACTION RATE

Consider species A:

• Independent of the reaction system

(batch, CSTR, plug flow, etc.)

• Used to relate the rate of reaction, - rA,

to the concentration of reacting species

and to the temperature at which the

reaction occurs [e.g. -rA = k(T)CA].

A B

1.1 DEFINITION OF REACTION RATE

EXAMPLE 1

Given reaction as A B

REACTANT PRODUCT

Therefore

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

-rB = The rate of disappearance of species

B per unit volume

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1.1 DEFINITION OF REACTION RATE

• For reactants, the rate of disappearance is

a positive (+) number.

• For products, the rate of disappearance is

a negative (-) number because they are being

formed and not disappearing.

REACTAN

T

PRODUC

T

A B

1.1 DEFINITION OF REACTION RATE

• For reactants, the rate of formation is a

negative (-) number because they are

disappearing and not being formed.

• For products, the rate of formation is a

positive (+) number.

REACTAN

T

PRODUC

T

A B

1.1 DEFINITION OF REACTION RATE

Consider the reaction

in which the rate of disappearance of A is 5 moles

of A per dm3 per second at the start of the

reaction. At the start of the reaction:

1. What is -rA?

2. What is the rate of formation of B?

3. What is the rate of formation of C?

4. What is the rate of disappearance of C?

5. What is the rate of formation of A, rA?

6. What is -rB?

1.1 DEFINITION OF REACTION RATE

• The rate law is an equation which links

the reaction rate with concentrations or

pressures of reactants and constant

parameters

• Determined from the experiments

observations and gives the rate of

reaction as a function of reacting species

concentration and temperature;

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1.1 DEFINITION OF REACTION RATE

• For example given the reaction of

• Based on Power Law Model, the reaction rate, -rA is given as

where

k = specific reaction rate constant

)Ck(C r- BAA

βα=

A + B → C + D

1.1 DEFINITION OF REACTION RATE

• CA and CB is function of concentrations of

component A and B (mol/L)

• The exponent of α and β are called the

reaction orders

• The order of reaction with respect to a

certain reactant is defined, as the power to

which its concentration term in the rate

equation is raised

)Ck(C r- BAA

βα=

1.1 DEFINITION OF REACTION RATE

A reaction follows an ELEMENTARY RATE LAW if the REACTION ORDER of EACH REACTANT is IDENTICAL with the STOCHIOMETRIC COEFFICIENT of THE REACTANT for the reaction as written.

Example:

• For reaction of

The rate law would be -rA = k CA CB

• For reaction of 2NO + O2 2NO2

The rate law would be -rNO = k CNO2 CO

A + B C + D

1.1 DEFINITION OF REACTION RATE

EXAMPLE:

Given the reaction as A + 2B → C

CASE 1

1. If stated the reaction follows ELEMENTARY

RATE LAW, then the rate law and order of

reaction can be obtained from the

stoichiometric coefficient.

2. Therefore the rate equation is -rA = kCA1CB

2.

3. The reaction order with respect to A would be

1 and with respect to B would be 2, the total

reaction order would be 2+1=3

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1.1 DEFINITION OF REACTION RATE

EXAMPLE:

Given the reaction as A + 2B → C

CASE 2

1. If stated the reaction obeys a NON-

ELEMENTARY RATE LAW, therefore the

rate equation cannot be determined by

looking at the stoichiometric coefficient.

2. Additional information are needed from

experimental works or literature to deduce the

rate law and the order of reaction

Moles Balances

1.2 THE GENERAL MOLE BALANCE

Entering molar

flow rate of A

(mol/time)

Volume (e.g. m3)

Exiting molar

flow rate of A

(mol/time)

Rate of generation

of A (mol/time)

Number of moles of A

inside the system volume

Rate of

generation of A

(mole/time.vol)

Rate of flow

of A into the

system

(moles/time)

Rate of generation

of A by chemical

reaction within system

(moles/time)

Rate of flow

of A out of

the system

(moles/time)

+ - =

Rate of

accumulation

of A within system

(moles/time)

=

Rate of flow

of A into the

system

(moles/time)

Rate of generation

of A by chemical

reaction within system

(moles/time)

Rate of flow

of A out of

the system

(moles/time)

+ - =

Rate of

accumulation

of A within system

(moles/time)

In + Generation - Out = Accumulation

FAO + GA - FA = dNA/dt

1.2 THE GENERAL MOLE BALANCE

dt

dN.dVrFF A

V

AAoA =+− ∫Basic Equation for Chemical Reaction Engineering

∫=V

AA .dVrG

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Types of Reactor in

Industry

Reactor

Batch

Continuous

Industrial

Continuous stirred tank

reactor (CSTR)

Tubular reactor

Simple batch

CSTR

Tubular reactor

Fixed/

Packed bed

Fluidized

bed

1.3 TYPES OF REACTOR IN

INDUSTRY

Key Characteristics

• unsteady-state operation (by definition)

• no spatial variation of concentration or temperature (well-

mixed)

• mainly used for small scale operation

• suitable for slow reactions

• mainly (not exclusively) used for liquid-phase reaction

• has neither inflow nor outflow of reactants or products while

reaction is carried out, FAO = FA = 0

1.3 TYPES OF REACTOR IN INDUSTRY

BATCH REACTORS

1.3 TYPES OF REACTOR IN INDUSTRY

BATCH REACTORS

Batch volume equation

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Models Development:

Batch System

FAo + GA = dNA/dt + FA

0 0

Thus,

Knowing that : GA = rAV

form) (integral Vr

dNt

form) ial(different dt

dNVr

A

Ao

N

N A

A

AA

∫=

=

Key Characteristics

• steady state operation

• used in series

• no spatial variation of concentration or temperature (well-mixed)

• mainly used for liquid phase reaction

• suitable for viscous liquid

• Reactants are continuously introduced into the reactor while products are continuously removed.

CSTRs are also known as

back-mix reactors

1.3 TYPES OF REACTOR IN INDUSTRY

CONTINUOUS STIRRED TANK

REACTOR

1.3 TYPES OF REACTOR IN INDUSTRY

CONTINUOUS STIRRED TANK

REACTOR

CSTR Volume Equation

Models Development:

CSTR System

FAo + GA = dNA/dt + FA

0

Thus,

FAo + rAV = FA

FAo

FA

form) (algebraic )(r

FFV

A

AAo −

−=

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Key Characteristics

• steady-state operation

• consists of a cylindrical pipe which the reactants and

products can flow through

• spatial variation in axial direction but not in radial direction

• suitable for fast reaction mainly used for gas phase reaction

• temperature control may be difficult

• there are no moving parts

1.3 TYPES OF REACTOR IN INDUSTRY

PLUG FLOW REACTOR

1.3 TYPES OF REACTOR IN INDUSTRY

PLUG FLOW REACTOR

PFR Volume Equation

Models Development:

PFR System

FAo + GA = dNA/dt + FA

FA|V + rA ∆V = FA|V+∆V

(FA|V+∆V - FA|V ) / ∆V = rA

Taking the limit as ∆V→0,

FAo FAGj

V V + ∆V

0

form) (algebraic )(r

dFV

form) ial(different rdV

dF

A

Ao

F

F A

A

AA

∫=

=

Summary

Differential

Equation

Algebraic

Equation

Integral

Equation

Remarks

Batch Conc. changes with

time but is uniform

within the reactor.

Reaction rate

varies with time.

CSTR Conc. inside

reactor is uniform.

(rA) is constant.

Exit conc = conc

inside reactor.

PFR Concentration and

hence reaction

rates vary spatially.

)V(rdt

dNA

A = ∫=A

A0

N

N A

A

)V(r

dNt

)(r

FFV

A

AA0

−

−=

AA r

dV

dF= ∫=

A

A0

F

F A

A

)(r

dFV

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Thank you