ERT 316: REACTION ENGINEERING

CHAPTER 1MOLE BALANCES

Lecturer: Miss Anis Atikah Ahmad

Email: anisatikah@unimap.edu.my

Tel: +604-976 3245

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OUTLINE

Introduction Chemical Species Chemical Reaction Rate of Reaction General Mole Balance Equation Batch Reactor Continuous-Flow Reactors Industrial Reactors

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INTRODUCTION

Application of Chemical Reaction Engineering

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1. CHEMICAL SPECIES

What are chemical species? Any chemical component or element with a

given identity. Identity of a chemical species is determined

by the kind, number, and configuration of that species’ atoms.

Kind of species- methane, butene, butane

Number of atoms- eg: CH4: 1 C, 4 H Configuration of atoms- arrangement of

the atoms4

Can they be considered as different Can they be considered as different SPECIES?SPECIES?

Kind: Same (Butene)Kind: Same (Butene)Number of atoms: Same (CNumber of atoms: Same (C44HH88))Configuration: Different arrangementConfiguration: Different arrangement

ANSWER: Yes. We consider them as two different species because they have different configurations.

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2. CHEMICAL REACTION

Chemical reaction is any reaction when one or more species lost their identity and produce a new form by a change in the kind or number of atoms in the compound, and/or by a change in structure or configuration of these atoms.

HOW????

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2. CHEMICAL REACTION

Species may lose its chemical identity by: 1) Decomposition (by breaking down the

molecule into smaller molecule) Eg: C ⇌ A + B 2) Combination (reverse of decomposition) 3) Isomerization ( neither add other

molecule nor breaks into smaller molecule)

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It tells how fast a number of moles of one chemical species to form

another chemical chemical species.species.

3. RATE OF REACTION, Ar

,the rate of reaction: is the number of moles of A reacting (disappearing) per unit time per unit volume ( ).

, is the rate of formation (generation) of species A.

, is a heterogeneous reaction rate: the no of moles of A reacting per unit time per unit mass of catalyst ( catalyst)

Ar

sdmmol 3/

Ar

Ar

gsmol /

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4. THE GENERAL MOLE BALANCE EQUATION A mole balance of species j at any instant

time:

Rate of flow of j into the system

(moles/time)

Rate of flow of j out of the

system (moles/tim

e)

Rate of generation of j

by chemical reaction within

the system (moles/time)

Rate of accumulation of j within the system

(moles/time)

In - Out + Generation = Accumulation

dt

dN j

Fj0 - Fj + =dt

dN jV

jdVr0

Fj0 - Fj + Gj =

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4. THE GENERAL MOLE BALANCE EQUATION

GjFj0 Fj

General mole balance:

Fj0 - Fj + Gj = dNj/dt

In - Out + Generation = Accumulation

Consider a system volume :System volume

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THE GENERAL MOLE BALANCE EQUATION

Condition 1: If all the the system variables (eg: T, C) are

spatially uniform throughout a system volume:

Gj = rj.V volume

volumetime

moles

time

moles

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Condition 2: If the rate of formation, rj of a species j for

the reaction varies with position in the system volume:

The rate of generation ∆Gj1:

∆Gj1=rj1∆V1

THE GENERAL MOLE BALANCE EQUATION

Fj0 Fj

rj1

rj2

∆V1∆V2

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The total rate of generation within the system volume is the sum of all rates of generation in each of the subvolumes.

Taking the limit M∞, and ∆V0 and integrating,

4. THE GENERAL MOLE BALANCE EQUATION

M

iiji

M

ijij VrGG

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V

jdVrG0

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TYPE OF REACTORS

REACTORS

Batch

ContinuousFlow

in

out

5. BATCH REACTORS

The reactants are first placed inside the reactor and then allowed to react over time.

Closed system: no material enters or leaves the reactor during the time the reaction takes place.

Operate under unsteady state condition.

Advantage: high conversion

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the conditions inside the reactor

(eg: concentration, temperature)

changes over time

5. BATCH REACTORS: DERIVATION Batch reactor has neither inflow nor

outflow of reactants or products while the reaction is carried out:

FA0 = FA = 0

General Mole Balance on System Volume V

FA0 - FA + =dt

dN AV

AdVr0

V

AA dVr

dt

dN

0 16

Assumption: Well mixed so that no variation in the rate of reaction throughout the reactor volume:

Rearranging;

Integrating with limit at t=0, NA=NA0

& at t=t1, NA=NA1,

5. BATCH REACTORS: DERIVATION

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Vrdt

dNA

A

Vr

dNdt

A

A

0

1

1

0

1

A

A

A

A

N

N A

AN

N A

A

Vr

dN

Vr

dNt

6. CONTINUOUS-FLOW REACTORS: STEADY STATE

1. Continuous-Stirred Tank Reactor (Backmix/ vat)

open system: material is free to enter or exit the reactor

reactants are fed continuously into the reactor.products are removed continuously.

operate under steady state condition perfectly mixed: have identical properties (T, C) everywhere within the

vessel. used for liquid phase reaction

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6.1 CONTINUOUS-STIRRED TANK REACTOR

DERIVATION General Mole Balance:

Assumption: 1.steady state:

2. well mixed:

Mole balance: FA - FA + = 019

FA0 - FA + =dt

dN AV

AdVr0

0dt

dN A

VrdVr A

V

A 0

VrA

A

AA

A

AA

r

FF

r

FFV

00 design equationfor CSTR

6. CONTINUOUS-FLOW REACTORS: STEADY STATE

2. Plug Flow/Tubular Reactor Consist of cylindrical hollow pipe. Reactants are continuously consumed as they flow down the length of the reactor. Operate under steady state cond. No radial variation in velocity, conc, temp, reaction rate. Usually used for gas phase reaction

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6.2 PLUG FLOW REACTOR

DERIVATION General Mole Balance:

Assumption: 1.steady state:

Differentiate with respect to V:21

FA0 - FA + =dt

dN AV

AdVr0

0dt

dN A

,0 AA r

dV

dF

FA0 - FA + = 0V

AdVr0

AA r

dV

dF

6.2 PLUG FLOW REACTOR

DERIVATION

Rearranging and integrating between   V = 0, FA = FA0

   V = V1, FA = FA1

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AA r

dV

dF

A

A

r

dFdV

1

0

1

0

A

A

F

F A

AV

r

dFV

0

1

1

0

1

A

A

A

A

F

F A

AF

F A

A

r

dF

r

dFV

6. CONTINUOUS-FLOW REACTORS: STEADY STATE

3. Packed-Bed Reactor (fixed bed reactor) Often used for catalytic process Heterogeneous reaction system (fluid-solid) Reaction takes place on the surface of the catalyst. No radial variation in velocity, conc, temp, reaction rate

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6.3 PACKED BED REACTOR

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DERIVATION General Mole Balance:

Assumption: 1.steady state:

Differentiate with respect to W:

FA0 - FA + =dt

dN A dWrA'

0dt

dN A

FA0 - FA + = 0 dWrA'

'A

A rdW

dF

the reaction rate is based on mass of solid catalyst, W, rather than reactor volume

6.2 PACKED BED REACTOR

DERIVATION

Rearranging and integrating between   W = 0, FA = FA0

   W = W1, FA = FA1

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'A

A

r

dFdW

1

0

1

'0

A

A

F

F A

AV

r

dFW

0

1

1

0

''1

A

A

A

A

F

F A

AF

F A

A

r

dF

r

dFW

'A

A rdW

dF

SUMMARY OF REACTOR MOLE BALANCE

ReactorDifferential

FormAlgebraic

FormIntegral Form  Comment

Batch  

No spatial variations, unsteady

state

CSTR -   -No spatial variations,

steady state

PFR  Steady state

PBR   Steady state

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Vrdt

dNA

A

A

AA

r

FFV

0

0

1

1

A

A

F

F A

A

r

dFV

AA r

dV

dF

'A

A rdW

dF

0

1

'1

A

A

F

F A

A

r

dFW

0

1

1

A

A

N

N A

A

Vr

dNt

INDUSTRIAL REACTORS

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Packed-Bed Reactor at Sasol Limited Chemical

INDUSTRIAL REACTORS

28Fixed-Bed Reactor at British Petroleum (BP): using a colbalt-molybednum catalyst to convert

SO2 to H2S

INDUSTRIAL REACTORS

29Fluidized Catalytic Cracker at British Petroleum (BP): using H2SO4 as a catalyst to bond butanes and

iso-butanes to make high octane gas